JP7609459B2 - Spring elements for vertical seismic isolation bearings - Google Patents

Description

The present invention relates to a spring element used in a vertical seismic isolation bearing, which is applicable to important social infrastructure such as bridges on important logistics roads and nuclear power plants, and which has a bearing capacity exceeding 10 MN, safety against excessive vertical earthquake motion that exceeds expectations, a service life exceeding 50 years, and adaptability to the installation environment.

In the Niigata Chuetsu earthquake (2004) and the Kumamoto earthquake (2016), large earthquake accelerations caused great damage to social infrastructure. Vertical accelerations exceeding the gravitational acceleration were observed in these earthquakes. It has also been pointed out that during earthquakes, longitudinal waves traveling from deep underground to the ground surface can cause impulsive vertical forces on structures, potentially resulting in serious damage to the structures (see Non-Patent Document 1). In order to support the early recovery of societies affected by earthquakes, it is desirable for important social infrastructure such as bridges on important logistics roads and nuclear power plants to maintain a minimum level of functionality even against such excessive vertical earthquake motions. In preparation for the construction and renewal of important social infrastructure, it is considered necessary to develop earthquake motion countermeasure technologies that can also handle excessive vertical earthquake motions.

Three-dimensional seismic isolation, which combines horizontal and vertical seismic isolation bearings, can dramatically improve the safety of important social infrastructure during earthquakes. Horizontal seismic isolation bearings such as laminated rubber bearings are widely used, but vertical seismic isolation bearings for use in important social infrastructure are still under development. For example, in the field of nuclear power generation, a vertical seismic isolation bearing with a dead load reaction force of 10 MN using 72 disc springs is being researched (see Non-Patent Document 2). In this bearing, six disc springs are stacked in series and three in parallel to accommodate the load, deformation, and natural frequency, and four sets of stacked disc springs are arranged in a plane to form the spring element of the vertical seismic isolation bearing. The spring element of this vertical seismic isolation bearing has many parts, many of which are exposed, so it can be installed in an indoor environment, but is considered unsuitable for installation in an outdoor environment from the perspective of maintenance and management related to corrosion prevention, etc.

Although it is difficult to say that it can withstand forces of 10 MN or more, there is technology such as a suspension device that utilizes the elasticity of an elastic body such as rubber (Patent Document 1).

Patent No. 3296909

2017 and 2018 Kansai Branch Research Committee of the Japan Society of Civil Engineers: Research Committee on Vertical Seismic Isolation Structures for Urban Direct Earthquakes - Results Report -, Kansai Branch of the Japan Society of Civil Engineers (Public Interest Incorporated Foundation), March 2019 Takayuki Miyagawa and 5 others: Research and Development of 3D Seismic Isolation Devices, Part 2: Specifications of 3D Seismic Isolation Devices, Abstracts of Academic Lectures at the Architectural Institute of Japan Annual Meeting (Tohoku), September 2018.

The spring elements of vertical seismic isolation bearings applied to important social infrastructure, etc., are required to have spring performance that ensures that the spring elements remain sound even when subjected to rare earthquake motions and extremely rare earthquake motions accompanied by large accelerations over a service life of more than 50 years, and that no serious damage is caused to the spring elements even when subjected to excessive earthquake motions that exceed expectations. Indicators of spring performance include maximum bearing capacity, maximum deformation, spring constant, and service life. Adaptability to the installation environment, such as the ability to install in an outdoor environment, and the difficulty of maintenance are also important. Because the spring elements constantly support the superstructure, it is necessary to recognize that replacement or repair of parts related to spring performance is difficult.

If the weight and vertical natural frequency of the superstructure supported by the spring element of the vertical seismic isolation bearing are 10MN and 3Hz, respectively, the required spring constant is 363kN/mm. For extremely rare vertical earthquake motion, the maximum bearing capacity is generally set to 1.65 times the weight, but considering excessive vertical earthquake motion that exceeds the assumption, the maximum bearing capacity is set to twice the weight, and the maximum bearing capacity and maximum deformation amount are 20MN and 55mm, respectively. The service life is set to 50 years. If there is a spring element that can achieve such spring performance, can be installed in an outdoor environment, and has a simple structure, fewer parts, and is easy to inspect and maintain compared to existing technologies such as those shown in Non-Patent Document 2, it can be used as a vertical seismic isolation bearing applied to important social infrastructure, etc. If the spring element has the necessary damping performance, it can be used as a vertical seismic isolation bearing. If the damping performance is insufficient, it is necessary to use a combination of the spring element and a damping device.

The present invention provides a spring element for a vertical seismic isolation bearing that has a mechanism for generating restoring force and deformation that differs from that of conventional spring elements such as disc springs, and that satisfies the required spring performance, can be installed in outdoor environments, has a simple structure, has a small number of parts, and is easy to inspect and maintain.

In the first aspect of the present invention, we have shown the minimum number of components required to generate a restoring force and deformation amount, the characteristics that each component should have, and the characteristics of the deformation amount.

First, the vertical seismic isolation bearing spring element of the present invention supports the upper structure from below, is located above the lower structure on which seismic motion acts, and the amount of vertical compressive deformation caused by the weight of the upper structure increases or decreases according to the seismic motion. It comprises at least an inner member, an outer member that is placed on the outside of the inner member, and a compression member that is stored without gaps in the storage space formed between the inner member and the outer member.

Secondly, the inner member includes an annular inner seating surface, the center of each of the following circular shapes being on the central axis of the inner member, which is positioned to support the upper structure from below or is positioned to be supported from below by the lower structure, a cylindrical large diameter guide surface extending from the outer circumference of the inner seating surface in the direction of the inward normal vector of the inner seating surface, an annular inner support surface forming a corner with the large diameter guide surface and extending to the back side of the inner seating surface, and a cylindrical small diameter pressure surface forming a corner with the inner circumference of the inner support surface and extending in the direction of the inward normal vector of the inner seating surface. The inner member has a mechanical property in which the radius of the small diameter pressure surface decreases due to the surface pressure acting on the small diameter pressure surface, and the radius of the small diameter pressure surface returns to its original value when the surface pressure acting on the small diameter pressure surface is eliminated.

Thirdly, the outer member includes an annular outer seating surface, the center of each of the following circular shapes being on the central axis of the outer member, which is positioned to be supported from below by the lower structure or to support the upper structure from below, a small diameter guide surface in the form of a circular hole surface that extends from the inner circumference of the outer seating surface in the direction of the inward normal vector of the outer seating surface and slides into engagement with the small diameter pressure surface, an annular outer support surface that forms a corner with the small diameter guide surface and extends to the back side of the outer seating surface, and a large diameter pressure surface in the form of a circular hole surface that forms a corner with the outer circumference of the outer support surface, extends in the direction of the inward normal vector of the outer seating surface, and slides into engagement with the large diameter guide surface. The outer member has a mechanical property in which the radius of the large diameter pressure surface increases due to the surface pressure acting on the large diameter pressure surface, and the radius of the large diameter pressure surface returns to its original value when the surface pressure acting on the large diameter pressure surface is eliminated.

Fourth, the storage space is surrounded by the inner support surface, the small diameter pressure surface, the outer support surface, and the large diameter pressure surface by assembling the inner member and the outer member in a state in which the inner support surface and the outer support surface face each other, the large diameter guide surface and the large diameter pressure surface slide in engagement, and the small diameter pressure surface and the small diameter guide surface slide in engagement.

Fifth, the compression member is formed primarily from a material having a smaller elastic modulus than the materials forming the inner support surface, the small diameter pressure surface, the outer support surface, and the large diameter pressure surface, and is stored in the storage space while in sliding contact with the inner support surface, the small diameter pressure surface, the outer support surface, and the large diameter pressure surface.

Sixthly, the amount of compressive deformation occurring in the vertical seismic isolation bearing spring element of the present invention is characterized in that it includes a main amount of compressive deformation occurring due to slippage between the small diameter pressure surface and the compression member, slippage between the large diameter pressure surface and the compression member, a decrease in the radius of the small diameter pressure surface, and an increase in the radius of the large diameter pressure surface, or includes a secondary amount of compressive deformation occurring due to a decrease in the volume of the compression member in addition to the main amount of compressive deformation.

First, for example, the inner member and the outer member are a containment vessel that contains the compression member without any gaps, and the compression member is contained in the containment vessel without any gaps. The inner member, the outer member and the compression member support the weight of the upper structure, causing a compressive deformation, and the compressive deformation increases or decreases in response to seismic motion, making them the minimum components that provide vertical seismic isolation function.

From the second point of view, for example, the inner member is a steel cylinder whose outer diameter changes in two stages. The surface with the larger outer diameter is the large diameter guide surface, and the surface with the smaller outer diameter is the small diameter pressure surface, and the boundary between them is the inner support surface. The inner seating surface is the end surface on the side with the larger outer diameter. The inner seating surface preferably indirectly supports the upper structure from below via another member, but may also directly support the upper structure from below without using another member. Alternatively, the inner seating surface is preferably indirectly supported from below by the lower structure via another member, but may also directly support the lower structure from below without using another member. The inner seating surface is positioned in a position relative to the upper structure or lower structure that allows it to support them. There are no restrictions on the shape and structure of the inner radial inside of the inner member.

Here, surface pressure is the force per unit area that occurs between two surfaces that are in contact with each other and press against each other, pushing each surface at a right angle. The inward normal vector is a vector that is perpendicular to the surface, has its origin on the surface, and its end point on the side of the material that forms the surface.

From the third point of view, for example, the outer member is a steel cylinder whose inner diameter changes in two stages. The surface with the smaller inner diameter is the small diameter guide surface, and the surface with the larger inner diameter is the large diameter pressure surface, and the boundary between them is the outer support surface. The outer seating surface is the end surface on the side with the smaller inner diameter. The outer seating surface is preferably indirectly supported from below by the lower structure via another member, but may also be directly supported from below by the lower structure without using another member. Alternatively, the outer seating surface is preferably indirectly supported from below by the upper structure via another member, but may also be directly supported from below by the upper structure without using another member. The outer seating surface is positioned in a position relative to the lower structure or upper structure that allows support for these. There are no restrictions on the shape and structure of the outer radial outer side of the outer member.

Fourthly, to explain the shape of the storage space in an easy-to-understand way, the inner support surface and the outer support surface are both annular, the small diameter pressure surface is a cylindrical surface, and the large diameter pressure surface is a circular hole-shaped surface, so the shape of the storage space surrounded by the inner support surface, the small diameter pressure surface, the outer support surface, and the large diameter pressure surface is cylindrical.

Fifth, for example, the compression member is molded into the same shape as the storage space, using rubber as the main material. The shape of the compression member is cylindrical. By simultaneously assembling the inner member, compression member, and outer member, the compression member is stored without gaps within the storage space, in sliding contact with the four surfaces that form the storage space. The elastic modulus of the material will be described later.

Sixth, the weight of the superstructure causes slippage between the compression member and the small and large diameter pressure surfaces, reducing the radius of the small diameter pressure surface and increasing the radius of the large diameter pressure surface, resulting in the occurrence of the primary compression deformation. Furthermore, if the volume of the compression member decreases, this reduction in volume causes the occurrence of a secondary compression deformation, and the compression deformation amount includes the secondary compression deformation amount in addition to the primary compression deformation amount.

In this first viewpoint, firstly, when there is nothing in the storage space, when the weight of the upper structure is applied to the inner seating surface or the outer seating surface, the inner member and the outer member continue to slide against each other in the vertical direction, and the gap between the inner support surface and the outer support surface continues to decrease, and the gap does not return to its original size even if the weight is removed. Furthermore, when surface pressure acts on the small diameter pressure surface and the large diameter pressure surface, the radius of the small diameter pressure surface decreases and the radius of the large diameter pressure surface increases, increasing the spatial cross-sectional area in the horizontal plane of the storage space, and when the action of the surface pressure is removed, the spatial cross-sectional area returns to its original size, resulting in a feature in which the spatial cross-sectional area does not change even if the gap between the inner support surface and the outer support surface changes.

Secondly, when the compression member is in the storage space, the weight of the upper structure is transferred in the following order: inner or outer bearing surface, which is positioned to support the upper structure from below, inner or outer support surface, compression member, outer or inner support surface, and outer or inner bearing surface, which is positioned to be supported from below by the lower structure. Surface pressure is generated on the inner support surface, outer support surface, small diameter pressure surface, large diameter pressure surface, and compression member surface. Until the resultant force of the surface pressure generated on the inner support surface and the outer support surface is balanced with the weight, respectively, the storage space and the compression member are equally deformed, and slippage occurs at the portions where the surface of the compression member contacts the small diameter pressure surface and the large diameter pressure surface, respectively. The action of the surface pressure increases the spatial cross-sectional area and the cross-sectional area of the compression member in the horizontal plane, and the volume of the compression member decreases. The increase in the spatial cross-sectional area and the decrease in the volume of the compression member reduce the distance between the inner support surface and the outer support surface, resulting in the characteristic of the amount of compressive deformation being expressed.

For example, the inner member and the outer member are a containment vessel that contains the compression member without gaps, a passive compression vessel that compresses the compression member into a triaxial compression state by the weight of the upper structure, and a pressure vessel that confines the compression member within the containment space. The compression member is a liquid-like elastic member that converts the weight of the upper structure into an internal force, applies the internal force to the surface of the containment space, and deforms in response to the deformation of the containment space. The reason for this liquid-like behavior is that the compression member is formed primarily from a material with a smaller elastic modulus than the materials that form the inner support surface, small diameter pressure surface, outer support surface, and large diameter pressure surface.

Thirdly, when earthquake motion is applied, the vertical inertial force of the superstructure affects the increase in the spatial cross-sectional area and the decrease in the volume, which in turn changes the amount of decrease in the space between the inner and outer support surfaces, resulting in an increase or decrease in the amount of compressive deformation.

Fourth, when the main material forming the compression member is an incompressible material, the volume of the compression member does not decrease, and the amount of compression deformation is characterized by an increase in the spatial cross-sectional area.

The aforementioned amount of main compressive deformation is manifested by the decrease in radius of the small-diameter pressure surface and the increase in radius of the large-diameter pressure surface, so the compression member needs to have the property of efficiently converting the weight of the superstructure into surface pressure acting on these stress surfaces, and the deformation property of following the radial deformation of the small-diameter pressure surface and the large-diameter pressure surface. Therefore, a material with a small elastic modulus and a Poisson's ratio close to 0.5 or 0.5 (incompressible) is suitable as the main material for the compression member. In addition, since these characteristics may be generated by plastic deformation, an elastic-plastic material with a small elastic modulus, a Poisson's ratio close to 0.5, and which undergoes plastic flow under small stress is also suitable as the main material.

The aforementioned secondary compression deformation amount is expressed by the volumetric reduction amount of the compression member, and the volumetric reduction amount is inversely proportional to the bulk modulus, so from the viewpoint of increasing the secondary compression deformation amount, a material with a small bulk modulus is suitable as the main material of the compression member. The bulk modulus of an elastic material is a coefficient with the elastic modulus in the numerator and (1-2 x Poisson's ratio) in the denominator, so as the elastic modulus decreases, the bulk modulus decreases, but conversely, as the Poisson's ratio approaches 0.5, the bulk modulus increases. Therefore, taking into account the viewpoints of expressing the primary compression deformation amount and increasing the secondary compression deformation amount, a material with a small elastic modulus is suitable as the main material of the compression member. Therefore, it is preferable that the main material of the compression member has a smaller elastic modulus than the materials forming the four sides of the storage space.

The elastic modulus, Poisson's ratio and bulk modulus of steel are approximately 2.0×10⁵N/mm², about 0.3 and about 1.7 x 10⁵N/mm²The hardness of chloroprene rubber with a hardness of 65° is about 4.0. N/mm², about 0.4998 and about 3.4×10³N/mm²and those of pure lead are about 1.5 × 10⁴N/mm², about 0.45 and about 5.0×10⁴N/mm²The elastic modulus of laminated rubber bearings for bridges is 1.8 to 4.2. N/mm²The rubber material used is:

For example, in the first aspect, it is possible to configure the four sides of the storage space to be made of steel, and the main material forming the compression member to be rubber or pure lead. The elastic modulus of steel is approximately 50,000 to 100,000 times that of rubber, so rubber can easily deform in response to deformations in the storage space. The elastic modulus of steel is approximately 13 times that of pure lead, but pure lead has an elastic modulus of 4 N/mm²The compressive stress of the compression member assumed in this invention is 40 to 80. N/mm²Within this range, pure lead easily becomes plastically fluid and can deform in accordance with the deformations of the storage space.

In the second aspect of the present invention, a method for preventing the expansion of the main material of a compression member under triaxial compression stress at the sliding engagement between the large-diameter guide surface and the large-diameter pressure surface and at the sliding engagement between the small-diameter guide surface and the small-diameter pressure surface in the first aspect is shown. Specifically, the compression member is provided with a short hollow cylindrical outer sliding member that is arranged in the storage space, slides against the inner support surface and the large-diameter pressure surface, closes the outer gap that occurs at the sliding engagement between the large-diameter pressure surface and the large-diameter guide surface, abuts against the main material of the compression member, and does not contact the small-diameter pressure surface, preventing the expansion of the main material from the outer gap, and a short hollow cylindrical inner sliding member that is arranged in the storage space, slides against the outer support surface and the small-diameter pressure surface, closes the inner gap that occurs at the sliding engagement between the small-diameter pressure surface and the small-diameter guide surface, abuts against the main material, and does not contact the large-diameter pressure surface, preventing the expansion of the main material from the inner gap. The outer sliding member and the inner sliding member are formed into a short hollow cylinder by stacking sliding materials with irregular cross-sectional shapes and an overall shape of a ring or discontinuous ring in a direction perpendicular to the radius of the ring.

For example, the second viewpoint shows a configuration in which the main material of the compression member is pure lead or rubber, and the sliding material is formed from a copper alloy deformed wire rod with a rectangular cross section. The sliding material is preferably formed from a material that is softer in hardness than the material forming the large diameter pressure surface or small diameter pressure surface, harder than the main material, and has self-lubricating properties. Note that a deformed cross section refers to a cross section that is not circular. Wire rod refers to one with a circular cross section, and deformed wire rod refers to one with a non-circular cross section.

In the third aspect of the present invention, since the function of pressing the outer sliding member against the large diameter pressure surface and the function of pressing the inner sliding member against the small diameter pressure surface in the configuration of the outer sliding member and the inner sliding member in the second aspect depend on the material properties of the main material of the compression member, a method of expressing the pressing function by using a material with properties different from that of the main material is shown. Specifically, the compression member further includes an annular outer pressing member that is arranged in the storage space on the corner side formed by the small diameter pressure surface and the inner support surface, slides against the small diameter pressure surface, the inner support surface, and the outer sliding member, abuts against the main material, and presses the outer sliding member against the large diameter pressure surface, and an annular inner pressing member that is arranged in the storage space on the corner side formed by the large diameter pressure surface and the outer support surface, slides against the large diameter pressure surface, the outer support surface, and the inner sliding member, abuts against the main material, and presses the inner sliding member against the small diameter pressure surface. The outer pressure member and the inner pressure member are formed from a material that has a smaller elastic modulus and a larger Poisson's ratio than the materials that form the inner support surface, the small diameter pressure surface, the outer support surface, and the large diameter pressure surface, respectively.

For example, the third viewpoint shows a configuration in which the main material of the compression member is rubber, and the material of the outer pressing member and the inner pressing member is pure lead. As mentioned above, pure lead has a bulk modulus about seven times larger than that of rubber, and becomes plastic at a stress of about 4 N/ ^mm2 . This improves the swelling prevention effect compared to the second viewpoint.

In the fourth aspect of the present invention, a method for improving the second and third aspects is presented, in which when the overall shape of the sliding material is annular, the pressing function may be suppressed due to the generation of internal forces in the circumferential direction of the sliding material, and when the overall shape has discontinuous parts, the main material may bulge from the discontinuous parts of the sliding material. Specifically, the outer sliding member and the inner sliding member are replaced with a spiral annular sliding member in which a deformed wire is wound in a spiral shape. By replacing a sliding member whose overall shape is annular or discontinuous annular with a continuous spiral annular sliding member without discontinuous parts, the effect of preventing bulging can be improved.

In the fifth aspect of the present invention, since it is necessary to maintain a sliding state between the compression member and the inner support surface, the small diameter pressure surface, the outer support surface, and the large diameter pressure surface over the 50-year service life, a method is presented in which the inner support surface, the small diameter pressure surface, the outer support surface, and the large diameter pressure surface can maintain their surface properties over 50 years. Specifically, the inner member has a large diameter guide surface, inner support surface, and small diameter pressure surface formed of corrosion-resistant steel, and the outer member has a small diameter guide surface, outer support surface, and large diameter pressure surface formed of corrosion-resistant steel.

For example, the corrosion-resistant steel material is an austenitic stainless steel material or an austenitic stainless steel material that is a combination material of clad steel.

In the sixth aspect of the present invention, we have shown a shape and structure of the radial center side suitable for the inner member. Specifically, the inner member has a concentric layer structure extending from the small diameter pressure surface toward the radial inside.

For example, if the strength of the inner member satisfies safety requirements, the number of layers may be one, or to improve safety, the number of layers may be two or more, and a filler material may be placed on the radial center side. If the number of layers exceeds two, it is advisable to introduce an initial tensile stress on the small diameter pressure surface in order to integrate the inner member and to reduce the circumferential compressive stress generated on the small diameter pressure surface. The outer and inner layers may be made of different materials, for example, a corrosion-resistant steel material may be used for the outer layer on the small diameter pressure surface side and a high yield point steel material may be used for the inner layer.

In the seventh aspect of the present invention, a shape and structure suitable for the outer radial portion of the outer member are shown. Specifically, the outer member has a concentric layer structure extending from the large diameter pressure surface toward the outer radial portion.

For example, if the strength of the outer member satisfies safety requirements, the number of layers may be one, or to improve safety, the number of layers may be two or more. If the number of layers exceeds two, it is advisable to introduce an initial compressive tensile stress into the large-diameter pressure surface in order to integrate the outer member and to reduce the circumferential tensile stress that occurs on the large-diameter pressure surface.

In the eighth aspect of the present invention, the shape and structure of the outer radius that is most suitable for the outer member is shown. Specifically, the outer member is provided with a deformed wire or wire wound and stacked in the circumferential direction and the central axis direction of the outer member on the radially outer side of the concentric layer structure of the outer member, and an initial compressive stress in the circumferential direction is introduced to the large diameter pressure surface.

For example, the outer member is subjected to a circumferential tensile stress that gradually decreases from the large-diameter pressure surface toward the radially outer side. When a constant tension is applied to a deformed wire rod with a rectangular cross section made of high yield point steel material and the deformed wire rod is wound and stacked in the radial and circumferential axial directions on the radially outer side of the concentric layer structure of the outer member, the wire rod is compressed on the large-diameter pressure surface and tensile on the outermost radial side, and an initial normal stress in the circumferential direction that gradually changes between the two is introduced. In the eighth aspect, the circumferential tensile stress generated on the large-diameter pressure surface is reduced, and the tensile stress generated in the deformed wire rod at the radially outermost side is made smaller than the yield strength of the deformed wire rod, thereby improving the strength and safety of the outer member. Compared to wire rods with a circular cross section, deformed wire rods with a rectangular cross section have fewer gaps between them when wound and stacked, and initial normal stress can be introduced efficiently. The cross-sectional shape of the deformed wire rod is not limited to a rectangular cross section.

In the ninth aspect of the present invention, a method of connecting the spring element of the present invention to an upper structure and a lower structure is shown. Specifically, the vertical seismic isolation spring element further comprises at least one of an upper hollow laminated rubber that supports the upper structure and is supported on the inner seating surface or the outer seating surface, and a lower hollow laminated rubber that is supported on the lower structure and supports the outer seating surface or the inner seating surface.

In addition to relative vertical displacement, horizontal relative displacement and relative angular displacement occur between the upper and lower structures both at normal times and during earthquakes. Therefore, these structures and the spring elements are connected with laminated hollow rubber bearings, and the impact of the horizontal relative displacement and relative angular displacement on the spring elements is mitigated by the deformation of the laminated hollow rubber bearing, while the weight of the upper structure can be transmitted to the lower structure via the laminated hollow rubber bearing and the spring elements. In addition, radial deformation of the inner or outer seating surface is elastically restrained by the shear deformation of the laminated hollow rubber bearing.

According to the invention of the present application, the inner member and the outer member are a containment vessel in which the height and volume of the containment space change by easily sliding relative to each other in the vertical direction, the compression vessel uses the weight of the upper structure to compress the compression member in the containment vessel into a triaxial compression state, and the pressure vessel confines the compression member in the triaxial compression state in the containment space. When surface pressure acts on the small diameter pressure surface and the large diameter pressure surface, the spatial cross-sectional area in the horizontal plane of the containment space increases. The compression member is formed mainly from a material with a smaller elastic modulus than the material forming the large diameter pressure surface and the small diameter pressure surface, so that it is a member with elasticity like a liquid that is in the containment space, converts the weight of the upper structure into an internal force in a triaxial compression state, and applies the internal force as surface pressure to the large diameter pressure surface and the small diameter pressure surface of the containment space, and deforms in accordance with the deformation of the containment space while sliding against the large diameter pressure surface and the small diameter pressure surface.

The storage space and the compression member deform equally until the resultant force of the surface pressure acting on the inner support surface and the outer support surface balances the weight, and the spring element experiences a compressive deformation amount according to the weight. Since the volume of the compression member and the volume of the storage space are always equal, when the spatial cross-sectional area of the storage space increases or the volume of the compression member decreases according to the weight, the height of the compression member and the storage space decrease equally. The amount of decrease in height caused by an increase in the spatial cross-sectional area of the storage space is the main compressive deformation amount, and the amount of decrease in height caused by a decrease in the volume of the compression member is the secondary compressive deformation amount. If the compressible member is incompressible, the secondary compressive deformation amount does not occur, so the compressive deformation amount of the spring element includes the main compressive deformation amount. If the compression member is compressible, the compressive deformation amount includes the secondary compressive deformation amount in addition to the main compressive deformation amount. These two deformation amounts account for the majority of the compressive deformation amount.

The spring element of the present invention has a minimum number of components: an inner member, an outer member, and a compression member. The number of parts in Non-Patent Document 2 is estimated at 72 at the very least, so the number of parts in the spring element of the present invention is extremely small.

The compression members are inside the containment space and do not come into contact with the outside air. The inner surface and end faces of the inner member require anti-corrosion measures such as painting, but they are inside a space that can be inspected and maintained and closed. The outer surface and end faces of the outer member are exposed to the outside air and require anti-corrosion measures such as painting, but the surfaces of the outer member that require anti-corrosion measures have a simple shape, so inspection and maintenance are not difficult.

According to the inventor's calculations, in order to accommodate the weight of a superstructure of 10 MN, it is expected that a spring element with a vertical natural frequency of approximately 3 Hz can be realized by setting the radii of the small and large pressure surfaces to approximately 95 cm and 100 cm, respectively, making the height of the compression member approximately 100 cm, and using vulcanized natural rubber as the main material of the compression member. This is equivalent to approximately 10 times the dimensions of the spring element in Example 1 described below.

The inner and outer components, with a radius of about 100 cm, can be manufactured using standard manufacturing techniques for pressure vessels and penstocks. The vulcanized natural rubber component, with inner radius x outer radius x height of 95 cm x 100 cm x 100 cm, can be manufactured using tire manufacturing techniques for large mining trucks.

The vertical seismic isolation bearing spring element of the present invention therefore provides a vertical seismic isolation bearing spring element that meets the spring performance required to withstand a superstructure weight of 10 MN, can be installed in outdoor environments, has a simple structure, has a small number of parts, and is easy to inspect and maintain.

1 is a three-dimensional diagram showing an outline of the basic configuration of an example of a cylindrical spring 1 in a vertical seismic isolation bearing spring element according to an embodiment of the present invention. 1 is a central cross-section showing an outline of the basic configuration of an example of a cylindrical spring 1 in a vertical seismic isolation bearing spring element according to an embodiment of the present invention. FIG. 3 is a three-dimensional view showing the shape of the inner member 2 of FIGS. 1 and 2 . FIG. 3 is a three-dimensional view showing the shape of the outer member 4 of FIGS. 1 and 2 . 5 is an assembly diagram (central cross-sectional view) of the inner member 2 of FIG. 3 and the outer member 4 of FIG. 4. FIG. 3 is a three-dimensional view showing the shape of the compression member 3 in FIGS. 1 and 2 . FIG. 3 is a diagram defining basic dimensions of the cylindrical spring 1 of FIG. 1 and FIG. 2 . FIG. 7 is a diagram defining the surface pressure acting on the cylinder of FIG. 6 and the amount of radial deformation of the cylinder inner surface and the cylinder outer surface. 7 is a schematic diagram illustrating the shape change of the cylinder in FIG. 6 before and after deformation. FIG. 1 is a graph showing the relationship between axial strain, volumetric strain, and cross-sectional strain of a cylinder in equation (13a). Photographs showing the appearance of the test specimen and each part. 1 is a photograph showing the appearance of a compression test device and a test specimen. 1 is a graph showing the compression force-deformation curves for the first and fourth cycles with a maximum deformation of 5 mm. 13 is a graph showing the compression force-deformation curve of the fourth cycle in which the origin has been shifted. 13 is a graph showing a comparison of the restoring force of a test specimen with that of the theoretical formula. 1 is a graph showing an estimated effect of the bulk modulus on the initial tangent stiffness and deformation amount of a test specimen. FIG. 13 is a diagram showing measured values of circumferential strain. FIG. 2 is a diagram showing an outer sliding member, an outer pressing member, an inner sliding member, and an inner pressing member. FIG. FIG. 2 is a diagram showing the layer structure of the inner member. FIG. 2 is a diagram showing the layer structure of the outer member. FIG. 2 is a diagram showing the arrangement of an inner hollow laminated rubber and an outer hollow laminated rubber.

Below, an embodiment of the present invention will be described with reference to the drawings. Note that the present invention is not limited to this embodiment.

1. Overview of the invention Natural rubber (NR), chloroprene rubber (CR) and high damping rubber (HDR) are widely used as materials for laminated rubber bearings. Despite these, rubber has a nearly incompressible property due to its Poisson's ratio being close to 0.5, and it is known that the bulk modulus of elasticity under triaxial compression is dramatically larger than the elastic modulus. For example, a triaxial compression test of a styrene-butadiene rubber cylinder housed in a steel hole has yielded a bulk modulus of elasticity of 2.2 to 2.3 GPa. Based on this compression test, it is believed that a compression spring utilizing the bulk modulus of rubber can be realized if there is a means to confine the rubber in the containment space inside the containment vessel without any gaps, apply a compressive force to the containment vessel, and make the stress of the rubber in the triaxial compression state balance the compressive force.

Starting from this idea and referring to the drawings, the inventors of the present application propose, as a spring element for use in a vertical seismic isolation bearing, a cylindrical spring 1 consisting of an inner member 2, an outer member 4 located on the outside of the inner member 2, and a compression member 3 that is tightly enclosed in a cylindrical storage space 1C formed between the inner member 2 and the outer member 4. A pair of compression forces act on the inner member 2 and the outer member 4. The inner member 2 and the outer member 4 correspond to the aforementioned storage vessel, the storage space 1C corresponds to the aforementioned storage space, and the compression member 3 corresponds to the aforementioned rubber.

The inner member 2 and the outer member 4 have support surfaces and pressure surfaces that form a corner. By assembling the inner member 2 and the outer member 4 so that the two support surfaces face the direction of the compressive force (hereafter abbreviated as the axial direction) and the two stress surfaces face the direction perpendicular to the compressive force (hereafter abbreviated as the axial direction), the storage space 1C is formed by these four surfaces. The compression member 3 is made primarily of a material with a smaller elastic modulus than the material that forms the four surfaces of the storage space 1C, and is molded into the same shape as the storage space 1C, and is enclosed within the storage space 1C without any gaps, with the surface of the compression member 3 in sliding contact with the four surfaces.

The storage space 1C has a volume reduction characteristic in which the axial height and volume of the storage space 1C decrease in conjunction with the decrease in the axial assembled height of the inner member 2 and the outer member 4, and a volume increase characteristic in which the spatial cross-sectional area and volume of the storage space 1C in the plane perpendicular to the axis increase in conjunction with the surface pressure acting on the two pressure surfaces. When a pair of compressive forces act on the cylindrical spring 1, the surface of the compression member 3 and the two stress surfaces slide, and the two characteristics of the storage space 1C become effective, generating surface pressure on the surface of the compression member 3, the two pressure surfaces, and the two support surfaces, decreasing the height and volume of the storage space 1C based on the volume reduction characteristic, increasing the spatial cross-sectional area and volume of the storage space 1C based on the volume increase characteristic, and decreasing the volume of the compression member 3 based on the bulk modulus of elasticity.

The volume of the storage space 1C and the volume of the compression member 3 must always be equal, and the internal force of the cylindrical spring 1 must be balanced with the compressive force. Until the amount of change in the volume of the storage space 1C before and after deformation and the amount of change in the volume of the compression member 3 based on the bulk modulus are equal, and until the resultant force of the surface pressure acting on the support surface is balanced with the compressive force, it is considered that the shapes of the storage space 1C and the compression member 3 will deform equally while the surface of the compression member 3 and the two pressure surfaces of the storage space 1C slide. The amount of reduction in the height of the storage space 1C caused by an increase in the spatial cross-sectional area of the storage space 1C is called the main compressive deformation amount, and the amount of reduction in the height of the storage space 1C caused by a decrease in the volume of the compression member 3 is called the secondary compressive deformation amount. The compressive deformation amount of a cylindrical spring includes the above-mentioned main compressive deformation amount and secondary compressive deformation amount, and these two deformation amounts are considered to account for the majority of the compressive deformation amount.

The aforementioned amount of main compressive deformation is manifested by an increase in the spatial cross-sectional area of the storage space 1C, i.e., a decrease in the radius of the small-diameter pressure surface and an increase in the radius of the large-diameter pressure surface, so the compression member needs to have the property of efficiently converting the weight of the superstructure into surface pressure acting on these stress surfaces, and the deformation property of following the radial deformation of the small-diameter pressure surface and the large-diameter pressure surface. Therefore, from the viewpoint of manifesting the amount of main compressive deformation, a material with a small elastic modulus and a Poisson's ratio close to 0.5 or 0.5 (incompressible) is suitable as the main material of the compression member. In addition, since these characteristics may be generated by plastic deformation, an elastic-plastic material with a small elastic modulus, a Poisson's ratio close to 0.5, and which undergoes plastic flow under small stress is also suitable as the main material.

The aforementioned secondary compression deformation amount is expressed by the volumetric reduction amount of the compression member, and the volumetric reduction amount is inversely proportional to the bulk modulus of the material, so from the viewpoint of increasing the secondary compression deformation amount, a material with a small bulk modulus is suitable as the main material of the compression member. The bulk modulus of an elastic material is a coefficient with the elastic modulus in the numerator and (1-2 x Poisson's ratio) in the denominator, so as the elastic modulus decreases, the bulk modulus decreases, but conversely, as the Poisson's ratio approaches 0.5, the bulk modulus increases. Therefore, taking into account the viewpoints of expressing the primary compression deformation amount and increasing the secondary compression deformation amount, a material with a small elastic modulus is suitable as the main material of the compression member. Therefore, it is preferable that the main material of the compression member has a smaller elastic modulus than the materials forming the four sides of the storage space.

First, the basic structure of the cylindrical spring 1, the characteristics of the inner member 2 and outer member 4, and the volumetric decrease and increase properties of the storage space 1C will be explained below. Second, the relationship between the restoring force and the amount of deformation will be derived from the equivalence of the volumes of the storage space 1C and the compression member 3, and the balance between the external force and the internal force of the cylindrical spring 1. Finally, the restoring force characteristics and strain characteristics of the spring obtained through compression testing using a 1/10-scale spring specimen will be described.

2. Basic structure of the cylindrical spring 1 (1) Overview of the basic structure Figures 1 and 2 show the basic structure of the cylindrical spring 1. The numbers in the figures are the reference numbers of each component of the cylindrical spring 1. In the text, the corresponding reference numbers are shown immediately after the component names. Figure 1 is an isometric three-dimensional drawing, and in the drawing, the parts sandwiched between the 90° intersection angle and the total angle of 360° around the central axis 8 (hereinafter abbreviated as axis) are cut and removed. Figure 2 is a central cross-sectional view. Since the cylindrical spring 1 has an axisymmetric shape, only the part to the right of the axis is drawn in the drawing. The components are divided into three types of patterns on the cut surface: oblique lines, dots, and black paint. The direction of the arrow of the axis 8 is called the positive direction of the axis, and the direction opposite to the positive direction is called the negative direction. The upper structure and lower structure are not shown in the figures. If the upper structure is on the positive side of the axis 8, the lower structure is considered to be on the negative side, and if the lower structure is on the positive side, the upper structure is considered to be on the negative side.

1 and 2, the cylindrical spring 1 has an inner member 2 with an annular inner bearing surface 2A, an outer member 4 with an annular outer bearing surface 4A surrounding the inner member 2 from the outside in the direction perpendicular to the axis, and a compression member 3 between the inner member 2 and the outer member 4. The inner bearing surface 2A and the outer bearing surface 4A have an axis 8 as the center of the circumference. It is assumed that a uniformly distributed compressive force q that is symmetrical and parallel to the axis acts on the inner bearing surface 2A and the outer bearing surface 4A, and the spring generates a deformation in the axial direction. The height of the spring when the uniformly distributed compressive force is not acting is defined as h _total , and the height 1Z of the spring when the uniformly distributed compressive force acts is defined as h _total -w. Here, w is the amount of deformation of the spring in the axial direction, and the positive and negative signs of the deformation are positive when the height of the spring decreases. The resultant force of q is defined by equation (1).

Here, Q is the resultant compressive force of q, and a is the area on which q acts. The cylindrical spring 1 resists a compressive force of Q>0, but does not resist a tensile force of Q<0.

(2) Assembly and geometric characteristics of each component a) Inner component 2
3 is a three-dimensional diagram showing the shape of the inner member 2. In addition to the inner bearing surface 2A, the inner member 2 has a cylindrical large diameter guide surface 2C that forms a corner with the inner circumference of the outer edge of the inner bearing surface 2A and extends in the negative direction of the axis, an annular inner support surface 2D that forms a corner with the large diameter guide surface 2C and extends to the back side of the inner bearing surface 2A, and a cylindrical small diameter pressure surface 2B that forms a corner with the inner circumference of the inner support surface 2D and extends in the negative direction of the axis. The large diameter guide surface 2C, the inner support surface 2D, and the small diameter pressure surface 2B have the axis 8 as the center of the circumference. It should be particularly noted that the small diameter pressure surface 2B and the large diameter guide surface 2C are parallel to the axis 8. The inner support surface 2D may be inclined in the direction perpendicular to the axis. In the figure, the radius of the inner surface 2E of the inner member 2 is drawn as being constant in the axial direction, but the radius may be changed in the axial direction, the inner surface side may have a concentric single-layer structure or a multi-layer structure, another member may be attached to the inner surface side, or the inner surface side may be filled with a material different from the material forming the small diameter pressure surface 2B.

b) Outer member 4
4 is a three-dimensional diagram showing the shape of the outer member 4. In addition to the outer bearing surface 4A, the outer member 4 has a small diameter guide surface 4C in the form of a circular hole surface, which forms a corner with the inner circumference of the outer bearing surface 4A, extends in the positive direction of the axis, and slides with the small diameter pressure surface 2B, an annular outer support surface 4D which forms a corner with the small diameter guide surface 4C and extends to the back side of the outer bearing surface 4A, and a large diameter pressure surface 4B in the form of a circular hole surface, which forms a corner with the outer circumference of the outer support surface 4D, extends in the positive direction of the axis, and slides with the large diameter guide surface 2C. The small diameter guide surface 4C, the outer support surface 4D, and the large diameter pressure surface 4B have the axis 8 as the center of the circumference. It should be particularly noted that the small diameter guide surface 4C and the large diameter pressure surface 4B are parallel to the axis. The outer support surface 4D may be inclined in the direction perpendicular to the axis. In the figure, the radius of the outer surface 4E of the outer member 4 is drawn as being constant, but the radius may be changed in the axial direction, and another member may be attached to the outer surface side to give the outer surface side a single-layer structure or a multi-layer structure, or a deformed wire or the like may be wound around the outermost side.

c) Formation of storage space 1C and volume reduction characteristics of storage space 1C Figure 5 is an assembly diagram (central cross-sectional view) of the inner member 2 and the outer member 4. The inner support surface 2D and the outer support surface 4D are opposed to each other in the axial direction, the large diameter guide surface 2C and the large diameter pressure surface 4B are slidably fitted to each other with an outer gap 1A therebetween, and the small diameter guide surface 4C and the small diameter pressure surface 2B are slidably fitted to each other with an inner gap 1B therebetween. It is preferable that the size of the outer gap 1A and the inner gap 1B in the axial direction be as small as possible. The small diameter pressure surface 2B and the large diameter pressure surface 4B are opposed to each other in the axial direction, the inner support surface 2D and the outer support surface 4D are opposed to each other in the axial direction, and these four surfaces form a cylindrical storage space 1C. These four surfaces are called the inner surfaces of the storage space 1C. However, there are roughly annular outer gaps 1A and inner gaps 1B on the inner support surface 2D side and the outer support surface 4D side of this storage space 1C, respectively. The axial distance between the inner support surface 2D and the outer support surface 4D is called the height 1Y of the storage space 1C. The axial distance between the inner seating surface 2A and the outer seating surface 4A is called the assembly height 1Z of the inner member 2 and the outer member 4.

When the assembly height 1Z decreases due to the action of the compressive force, the height 1Y of the storage space 1C also decreases equally. Under conditions where the spatial cross-sectional area of the storage space 1C in the axially orthogonal plane does not change regardless of the reduction in the height of the storage space 1C, the volume of the storage space 1C decreases by an amount equivalent to the product of the reduction in height and the spatial cross-sectional area, and the storage space 1C exerts a volumetric compression effect on the object in the storage space 1C. Under conditions where an object is inside the storage space 1C and the surface of the object is in sliding contact with the inner surface of the storage space 1C, the volumetric compression effect generates compressive stress in the object, and surface pressure is generated between the surface of the object and the inner surface of the storage space 1C. Furthermore, if the object has a volumetric reduction property, the volume of the object decreases based on the bulk elasticity coefficient. The amount of volume reduction of the object and the amount of volume reduction of the storage space 1C are equal. These properties are called the volume reduction characteristics of the storage space 1C.

d) Compression member 3
FIG. 6 is a three-dimensional diagram showing the shape of the compression member 3 (5+6+7). The compression member 3 has a cylindrical shape equivalent to the storage space 1C shown in FIG. 5 as a standard shape. The shape of the compression member 3 is preferably such that the compression member 3, the inner member 2, and the outer member 4 can be assembled together, and the surface of the compression member 3 is in sliding contact with the inner surface of the storage space 1C, so that the compression member 3 is enclosed in the storage space 1C without any gaps. The compression member 3 may also be assembled while being pressed between the inner member 2 and the outer member 4. The compression member 3 has an outer sealing ring 5, a cylinder 6, and an inner sealing ring 7. These are stacked in the axial direction as shown in the figure. The height 3Z of the compression member 3 is h _m , and the height 6Z of the cylinder 6 is h. From the viewpoint of ensuring the effective deformation amount of the cylindrical spring 1 in the axial direction, the ratio h/h _m is suitable to be 0.8 or more and close to 1. The outer sealing ring 5, the cylinder 6, and the inner sealing ring 7 may be integrated.

5 and 6, the compression member 3 is enclosed in the storage space 1C without any gaps, with its own surface in sliding contact with the inner surface of the storage space 1C. Specifically, the cylinder inner surface 3C (5C+6C+7C) and the cylinder outer surface 3D (5D+6D+7D) of the compression member 3 are in sliding contact with the small diameter pressure surface 2B and the large diameter pressure surface 4B, respectively, with lubricating liquid or/and lubricant. The first end surface 3A of the compression member 3 (the first end surface 5A of the outer sealing ring 5) is in sliding contact with the inner support surface 2D with lubricating liquid or/and lubricant and closes the outer gap 1A. The second end surface 3B (the second end surface 7B of the inner sealing ring) is in sliding contact with the outer support surface 4D with lubricating liquid or/and lubricant and closes the inner gap 1B. Please note that the surface of the compression member 3 is not connected to the small diameter pressure surface 2B, the inner support surface 2D, the large diameter pressure surface 4B, and the outer support surface 4D. The compression member 3 may be formed by filling the storage space 1C with the material that forms the compression member 3.

(3) Mechanical properties of each component a) Inner component 2
3 and 6, the small diameter pressure surface 2B of the inner member 2 is in sliding contact with the cylinder inner surface 3C of the compression member 3 with lubricating liquid or/and lubricant, so that surface pressure and frictional stress act on the small diameter pressure surface 2B. When surface pressure acts on the small diameter pressure surface 2B of the inner member 2, the small diameter pressure surface 2B is deformed, and when the surface pressure is removed, the small diameter pressure surface 2B returns to its original shape. The relationship between the surface pressure acting on the small diameter pressure surface 2B and the amount of radial deformation of the small diameter pressure surface 2B is elastic, but the relationship between the surface pressure and the amount of deformation may include a history difference due to internal friction of the material forming the inner member 2, etc. It is preferable that the small diameter pressure surface 2B has a surface property suitable for sliding with the cylinder inner surface, such as a small friction coefficient with the cylinder inner surface and little wear of the cylinder inner surface. It is preferable that the surface roughness of the small diameter pressure surface 2B is smaller than the surface roughness of the cylinder inner surface. It is preferable that the small diameter pressure surface 2B is applied with lubricating liquid or/and lubricant. From the viewpoint of increasing the amount of possible deformation of the small diameter pressure surface 2B, it is preferable to introduce an initial tensile stress in the circumferential direction to the small diameter pressure surface and its vicinity by shrink fitting or filling with an expansion material. It is preferable to attach, embed or attach a sliding material to the large diameter guide surface 2C in preparation for sliding with the large diameter pressure surface 4B. It is also preferable to provide a seal to the large diameter guide surface 2C in sliding contact with the large diameter pressure surface 4B to prevent leakage of lubricating liquid and intrusion of liquid, dust, etc. from the outside.

b) Outer member 4
4 and 6, the large-diameter pressure surface 4B of the outer member 4 is in sliding contact with the cylinder outer surface 3D of the compression member 3 with lubricating liquid or/and lubricant, so that the large-diameter pressure surface 4B is subjected to surface pressure and frictional stress. When surface pressure acts on the large-diameter pressure surface 4B of the outer member 4, the large-diameter pressure surface 4B is deformed, and when the surface pressure is removed, the large-diameter pressure surface 4B returns to its original shape. The relationship between the surface pressure acting on the large-diameter pressure surface 4B and the amount of radial deformation of the large-diameter pressure surface 4B is elastic, but the relationship between the surface pressure and the amount of deformation may include a history difference due to internal friction of the material forming the outer member 4. It is preferable that the large-diameter pressure surface 4B has a surface property suitable for sliding with the cylinder outer surface, such as a small friction coefficient with the cylinder outer surface and little wear of the cylinder outer surface. It is preferable that the surface roughness of the large-diameter pressure surface 4B is smaller than the surface roughness of the cylinder outer surface. It is preferable that the large-diameter pressure surface 4B is applied with lubricating liquid or/and lubricant. From the viewpoint of increasing the amount of possible deformation, it is preferable to introduce an initial compressive stress in the circumferential direction to the large diameter pressure surface 4B and its vicinity by shrink fitting, welding fitting, wire wrapping, etc. It is preferable to attach, embed, or attach a sliding material to the small diameter guide surface 4C in preparation for sliding with the small diameter pressure surface 2B. It is also preferable to provide a seal to the small diameter guide surface 4C in sliding contact with the small diameter pressure surface 2B to prevent leakage of lubricating liquid and intrusion of liquid, dust, etc. from the outside.

c) Volume increase characteristics of the storage space 1C When surface pressure acts on the small diameter pressure surface 2B and the large diameter pressure surface 4B, the radius of the small diameter pressure surface 2B decreases, the radius of the large diameter pressure surface 4B increases, and the spatial cross-sectional area of the storage space 1C increases. Under conditions where the height of the storage space 1C does not change, the volume of the storage space 1C increases due to the action of surface pressure by an amount equivalent to the product of the increase in the spatial cross-sectional area due to the action of surface pressure and the height of the storage space 1C. When the action of surface pressure is eliminated, the two radii return to their original values, so the spatial cross-sectional area and volume return to their original values. Under conditions where an object is confined in the storage space 1C with no gaps and the surface of the object is in sliding contact with the inner surface of the storage space 1C, when compressive stress occurs in the object, surface pressure is generated on the small diameter pressure surface 2B, the large diameter pressure surface 4B, and the surface of the object in sliding contact with them, and the spatial cross-sectional area of the storage space 1C and the cross-sectional area in the plane perpendicular to the axis of the object increase according to the surface pressure. These properties are called the volume increase characteristics of the storage space 1C.

d) Cylinder 6
3, 4, 6 and 8 (details will be described later), the cylinder inner surface 6C and the cylinder outer surface 6D of the cylinder 6 are in sliding contact with the small diameter pressure surface 2B and the large diameter pressure surface 4B, respectively, accompanied by lubricating liquid or/and lubricant, so that surface pressure and frictional stress act on the cylinder inner surface 6C and the cylinder outer surface 6D. The first end surface 6A and the second end surface 6B of the cylinder 6 are in sliding contact with the outer sealing ring 5 and the inner sealing ring 7, respectively, so that surface pressure and frictional stress act on the first end surface 6A and the second end surface 6B, respectively. As the material of the cylinder 6, a material that has a smaller bulk modulus or elastic modulus than the small diameter pressure surface 2B and the large diameter pressure surface 4B and has a deformation performance and compressive strength that can follow the deformation of the storage space 1C is suitable. For example, viscoelastic materials such as natural rubber, chloroprene rubber, high damping rubber, and polyurethane rubber that can be cast are suitable as the material of the cylinder 6. Elastic materials with similar properties are also suitable. An elastoplastic material such as pure lead, which has a low yield point and is prone to plastic flow, is also suitable as the material for the cylinder 6 in terms of deformation performance. When it is necessary to reduce the spring constant, it is preferable to use a material with a smaller elastic modulus, a smaller bulk modulus, and high deformation performance and compressive strength as the material for the cylinder. The cylinder 6 may be formed of different materials for each part. The ratio of the total volume or total mass of the materials suitable for the cylinder 6 to the volume or mass of the cylinder 6 should be 0.8 or more, and a ratio close to 1 is suitable. The cylinder inner surface 6C and the cylinder outer surface 6D of the cylinder 6 should have surface properties suitable for sliding between the small diameter pressure surface 2B and the large diameter pressure surface 4B, respectively. For example, the cylinder inner surface 6C and the cylinder outer surface 6D should have fine recesses that can hold a lubricating liquid such as silicone oil and/or a lubricant such as fluororesin fine powder. The cylinder inner surface 6C and the cylinder outer surface 6D may be covered with a woven fabric such as fluororesin fiber, and the woven fabric may be impregnated with a lubricating liquid such as silicone oil.

e) Outer sealing ring 5 and inner sealing ring 7
5, 6 and 8 (details will be described later), the outer sealing ring 5 is in sliding contact with the inner support surface 2D, the large-diameter pressure surface 4B and the first end surface 6A of the cylinder 6 (see FIG. 8), respectively, and transmits a compressive force to the inner support surface 2D and the first end surface 6A of the cylinder 6, enabling the outer member 4 and the inner member 2 to move relative to each other in the axial direction, and preventing the cylinder from expanding into the outer gap. From the viewpoint of sliding with the large-diameter pressure surface and preventing the cylinder from expanding into the outer gap, it is preferable that the outer sealing ring 5 has a sliding material on the inner support surface side 2D and the large-diameter pressure surface 4B side that is softer in hardness than the large-diameter pressure surface 4B, harder than the cylinder 6, and has self-lubrication. It is preferable to introduce an initial surface pressure to the portion where the cylinder outer surface 5D of the outer sealing ring 5 is in sliding contact with the large-diameter pressure surface 4B of the outer member 4. The inner sealing ring 7 is in sliding contact with the outer support surface 4D, the small diameter pressure surface 4B, and the second end surface 6B of the cylinder 6, respectively, and transmits a compressive force to the outer support surface 4D and the second end surface 6B of the cylinder 6, allowing the outer member 4 and the inner member 2 to move relative to each other in the axial direction, and preventing the cylinder from expanding into the inner gap. From the viewpoint of sliding with the small diameter pressure surface 2B and preventing the cylinder from expanding into the inner gap, it is preferable that the inner sealing ring 7 has a sliding material on the outer support surface 4D side and the small diameter pressure surface 2B side that is softer than the small diameter pressure surface 2B, harder than the cylinder 6, and has self-lubrication. It is preferable to introduce an initial surface pressure to the portion where the cylindrical inner surface 7C of the inner sealing ring 7 is in sliding contact with the small diameter pressure surface 2B of the inner member 2.

(4) Principle of transmission and deformation of uniformly distributed compressive force First, the transmission path of the uniformly distributed compressive force will be explained, and then the principle of deformation of the cylindrical spring 1 will be explained based on the volume reduction characteristic, volume increase characteristic, and bulk modulus of the material forming the compression member 3 (cylinder 6) of the storage space 1C. Since the surface of the compression member 3 is in sliding contact with the inner surface of the storage space 1C accompanied by lubricating liquid or/and lubricant, and the small diameter pressure surface 2B and the large diameter pressure surface 4B are parallel to the axis, it is considered that the majority of the uniformly distributed compressive force is transmitted by the surface pressure generated on the inner seat surface 2A, the inner support surface 2D, the first end surface and the second end surface of the compression member 3, the outer support surface, and the outer seat surface 4A of the compression member 3, as well as the stress of the members interposed between each surface generated due to the surface pressure, and the remaining part of the uniformly distributed compressive force is transmitted by the friction stress generated on the inner stress surface, the outer inner pressure, the inner surface and the outer surface of the cylinder, and the stress of the inner member 2, the outer member 4, and the compression member 3 generated due to the friction stress.

When a uniformly distributed compressive force acts on the cylindrical spring 1, the inner and outer cylindrical surfaces of the compression member 3 slide against the small diameter pressure surface 2B and large diameter pressure surface 4B, respectively, and the volume reduction characteristic of the storage space 1C becomes effective, the height and volume of the storage space 1C decrease, compressive stress is generated in the compression member 3, and surface pressure is generated on the surface of the compression member 3 and the inner surface of the storage space 1C. At the same time, the volume increase characteristic becomes effective, and the spatial cross-sectional area and volume of the storage space 1C increase. Furthermore, if the cylinder of the compression member 3 has volume reduction properties, the volume of the compression member 3 (cylinder) decreases based on the bulk elasticity coefficient. If the cylinder 6 does not have volume reduction properties, the volume of the compression member 3 (cylinder) does not decrease.

The volume of the storage space 1C and the volume of the compression member 3 must always be equal, and the uniformly distributed compression force and the internal force of the cylindrical spring 1 must be balanced. Therefore, when the compression member 3 (cylinder) has a volume reduction property, the shapes of the storage space 1C and the compression member 3 are equally deformed, and at the same time, the inner surface of the storage space 1C and the surface of the compression member 3 are considered to slide against each other until the sum of the volume reduction amount of the storage space 1C based on the volume reduction characteristic and the volume increase amount of the storage space 1C based on the volume increase characteristic becomes equal to the volume reduction amount of the compression member 3 (cylinder) based on the bulk elasticity coefficient, and the sum of the resultant force of the axial component of the surface pressure acting on the inner support surface 2D and the resultant force of the axial component of the friction stress acting on the small diameter pressure surface is balanced with the resultant force (compression force) of the uniformly distributed compression force, and the sum of the resultant force of the axial component of the surface pressure acting on the outer support surface and the resultant force of the axial component of the friction stress acting on the large diameter pressure surface is balanced with the resultant force (compression force) of the uniformly distributed compression force.

If the cylinder 6 does not have a volume reduction property, the amount of volume reduction of the storage space 1C based on the volume reduction property is equal to the amount of volume increase of the storage space 1C based on the volume increase property.

If the effects of frictional stress are not taken into consideration, it is reasonable to assume that the height of the storage space 1C and the height of the compression member 3 decrease due to the decrease in the volume of the compression member 3 (cylinder) based on the bulk modulus of elasticity and the increase in the spatial cross-sectional area of the storage space 1C. Assuming that the axial deformation of the inner member 2 and the outer member 4 is smaller than the decrease in the height of the compression member 3, it is believed that the axial deformation of the spring is expressed by the decrease in the height of the compression member 3. In addition, the compression member 3 needs to have the deformation performance and strength to follow the deformation of the storage space 1C.

It is believed that the deformation associated with the increase in the cross-sectional area of the compression member 3 may occur not only due to elastic deformation but also due to elastoplastic deformation. However, if elastoplastic deformation occurs, attention must be paid to residual deformation.

Assuming that the amount of axial deformation of each of the outer sealing ring 5 and the inner sealing ring 7 is small, the reduction in the height of the cylinder 6 can be considered the amount of axial deformation of the spring. When the uniformly distributed compressive force is no longer acting, the amount of deformation of the spring is thought to return to its original state due to the volume decrease and increase characteristics of the storage space 1C and the elasticity of the cylinder 6. However, residual deformation may occur due to frictional stress in the sliding parts, internal friction or plastic deformation of the cylinder, etc.

If the deformation of the cylinder 6 is limited to the elastic range, the bulk modulus or elastic modulus of the material forming the cylinder 6, the finished shape of the cylinder 6, the radius of the small diameter pressure surface 2B and the large diameter pressure surface 4B, the deformation characteristics of the small diameter pressure surface 2B against the surface pressure, the deformation characteristics of the large diameter pressure surface 4B against the surface pressure, the friction coefficient between the small diameter pressure surface 2B and the inner cylinder surface, and the friction coefficient between the outer cylinder surface and the large diameter pressure surface 4B are thought to be related to the compression force and deformation amount of the spring. The smaller the bulk modulus of elasticity is and the greater the increase in the spatial cross-sectional area of the storage space 1C due to the surface pressure, the smaller the spring constant of the cylindrical spring 1 is thought to be. If the decrease in the volume of the cylinder 6 is not taken into consideration, the elastic modulus may be used as an indicator instead of the bulk modulus of elasticity to select the material. Note that as the deformation amount of the compression spring increases, the outer gap and the inner gap each expand, so care must be taken to prevent the cylinder from bulging.

3. Relationship between compression force and deformation (1) Basic dimensions and material constants In Figure 7, the basic dimensions of the cylindrical spring 1 are defined. The radius of the inner surface of the inner member 2, the radius of the small diameter pressure surface and the inner surface of the cylinder, the radius of the outer surface of the cylinder and the large diameter pressure surface, and the radius of the outer surface of the outer member 4 are respectively r ₀ , r ₁ , r ₂ , and r ₃ . The height of the inner member 2 and the height of the large diameter guide surface are respectively h _in and h _in,g , and the height of the outer member 4 and the height of the small diameter guide surface are respectively h _out and h _out,g . The height w _cr in the figure is defined as the geometric limit deformation. The values in parentheses () are the dimensions of the test specimen described later. The inner member 2 and the outer member 4 are elastic bodies, and their elastic coefficients and Poisson's ratios are respectively E _s and ν _s . The outer sealing ring and the inner sealing ring are elastic bodies, and their deformation and volume change are small, so their influence on the axial deformation is not considered. In addition, the influence of friction stress on the balance of forces and deformation is not considered. The material constants of the cylinder will be described later.

(2) Principle of Cylindrical Spring 1 It is assumed that the cylinder is in a state of equal compression on three axes, and that the approximation equation (2) holds true for the cylinder.

Here, p, B, V, and ΔV are the surface pressure acting on each surface of the cylinder, the bulk modulus of elasticity, the volume before deformation, and the volume loss after deformation. If the elastic modulus and Poisson's ratio of the cylinder are E and ν, respectively, then B, E, and ν are related by equation (3).

In Figure 8, the surface pressure acting on the cylinder and the amount of radial deformation of the inner and outer surfaces are defined. Surface pressure p acts uniformly on the inner and outer surfaces of the cylinder, the first end face (6A), and the second end face (6B). Although the figure shows the surface pressure acting on only a portion, the surface pressure acts uniformly on each surface. The amounts of radial deformation of the inner and outer surfaces of the cylinder when p acts are _u1 and _u2 , respectively. The positive and negative signs of the deformation are positive in the direction in which the radius increases.

Figure 9 is a schematic diagram of the shape change of a cylinder before and after deformation. In the figure, the shape of the cylinder before deformation is shown by a thin dashed line, and the shape after deformation is shown by a thick solid line. The heights of the cylinder before and after deformation are h and h-w, respectively, and w is the amount of deformation in the axial direction of the cylinder. The amounts of radial deformation of the inner and outer surfaces of the cylinder are _u1 and _u2 , respectively, so the radii of the inner and outer surfaces after deformation are _r1 + _u1 and _r2 + _u2 , respectively. It is assumed that these radii do not change in the height direction. Since it is assumed that the cylinder is in a state of uniform compression on three axes, a normal stress σ _θ, which is equal in magnitude to p, is generated in the circumferential direction of the cylinder, as shown in Figure 9(b).

The cross-sectional area of the cylinder before deformation is A. Cross-sectional area A is the area of the part shown by the diagonal line slanting upwards to the left in Figure 9(b). The volume V before deformation is the sum of the volume _V1 corresponding to the part with the diagonal line slanting upwards to the right in Figure 9(a) and the volume _V2 corresponding to the part with the diagonal line slanting upwards to the left in Figure 9(a). Here, _V1 is the amount of volume reduction of the cylinder based on the volume reduction characteristics of the containment space 1C. A, V, _V1 , and _V2 can be expressed by equations (4) to (7).

The cross-sectional area increase and the volume increase of the cylinder based on the volume increase characteristics of the storage space 1C are ΔA and _V3 , respectively. The area increase ΔA is the area of the two arc-shaped elongated parts shown by the diagonal lines slanting upward to the right in FIG. 9(b). The volume increase _V3 is the volume corresponding to the two elongated parts shown by the diagonal lines slanting upward to the right in FIG. 9(a). The volume of the cylinder after deformation is _V2 + _V3 . ΔA and _V3 can be expressed by equations (8) to (9), respectively. Using the volume reduction ΔV of the cylinder after deformation, the equation for the balance of the volume before and after deformation is equation (10). From equations (6), (9), and (10), the volume reduction ΔV is expressed by equation (11). From equations (2), (5), and (11), equation (12) is obtained. By changing equation (12) to an equal equation and transforming the equation, equation (13a) is obtained. Here, ΔA/A| _p indicates the cross-sectional strain ΔA/A when the surface pressure is p. Since w/h and p/B in equation (13a) are the axial strain and volumetric strain of the cylinder, respectively, it can be considered from equation (13a) that the axial strain of the cylinder at surface pressure p is determined by the volumetric strain and cross-sectional strain, and the amount of deformation in the axial direction of the cylinder is determined by the amount of volume reduction and the amount of cross-sectional area increase. The amount of cross-sectional area increase can be easily calculated if the relationship between the amounts of deformation _u1 , _u2 , and p is known.

Figure 10 shows the relationship between the axial strain, volumetric strain, and cross-sectional strain of a cylinder in formula (13a). The change in axial strain is shown for the range of cross-sectional strain from 0% to 5%, limited to three cases of volumetric strain: 0%, 2%, and 4%. It should be noted that the volumetric strain and cross-sectional strain in the figure are both generated at the same surface pressure. Since the area strain is ΔA/A≦0.05<<1, the axial strain can be approximately considered to be the sum of the volumetric strain and the cross-sectional strain according to formula (13a). From the figure, it can be confirmed that for each of the three cases of volumetric strain, the axial strain increases roughly in proportion to the increase in the cross-sectional strain, and that the axial strain can be roughly considered to be the sum of the volumetric strain and the cross-sectional strain. From this, it is thought that the axial strain of a cylinder can be increased by increasing the volumetric strain and the cross-sectional strain.

Possible methods for increasing volumetric strain include decreasing the bulk modulus of elasticity and increasing the surface pressure. The greater the triaxial compressive strength of the material forming the cylinder, and the greater the strength of the small diameter pressure surface and the large diameter pressure surface, the greater the surface pressure can be. Possible methods for increasing cross-sectional area strain include increasing the amount of increase in cross-sectional area and decreasing the cross-sectional area. The cylindrical spring 1 exhibits an increase in cross-sectional area by decreasing the radius of the small diameter pressure surface and increasing the radius of the large diameter pressure surface.

The amount of deformation of the cylindrical spring 1 is determined by the axial strain and height of the cylinder, so if the longitudinal strain is fixed, the amount of deformation can be increased by increasing the height, and if the amount of deformation is fixed, the height can be decreased by increasing the longitudinal strain, and it is believed that the required axial strain is determined when the height and amount of deformation are fixed. Equation (13a) shows the principle of axial deformation of the cylindrical spring 1.

(3) Surface pressure and deformation amount Substituting equation (8) into equation (13a) and transforming the equation, we obtain equation (13b). The radial deformation amount of the cylinder inner surface and the small diameter pressure surface must be equal, and the radial deformation amount of the cylinder outer surface and the large diameter pressure surface must be equal. The radial deformation coefficient of the small diameter pressure surface with respect to the surface pressure is n _in and that of the large diameter pressure surface are n _out , respectively, and the relationship between the surface pressure and the radial deformation amount is expressed by equations (14a) and (14b). The radius of the small diameter pressure surface decreases due to the action of the surface pressure, so u ₁ <0. Substituting equations (14a) and (14b) into equation (13b) and further transforming the equation, we obtain equations (15a) and (15b). Here, Ψ(x) is called the axial elastic function with the surface pressure x as a variable. Ignoring the effect of frictional stress occurring on the small diameter pressure surface and the large diameter pressure surface, the surface pressure p acting on the first end surface and the second end surface is expressed by equation (16) using the cross-sectional area A of the cylinder before deformation and the compressive force _Qr with the effect of frictional stress omitted. Here, _Qr corresponds to the restoring force of the cylindrical spring 1. Substituting equation (16) into equation (15a), equation (17) is obtained. Here, (A/h)Ψ(x= _Qr /A) on the right side of equation (17) is considered to represent the tangent stiffness of the _Qr -w curve. From equation (17), the amount of deformation in the axial direction of the cylinder is a nonlinear function of the restoring force _Qr . If the initial tangent stiffness at the origin of the _Qr -w curve is _K0 , _K0 is given by equation (18). In addition, in equations (15b) and (18), if the bulk modulus is set to B = ∞ and the terms related to B in these equations are eliminated, the elastic function and initial tangent stiffness for a cylinder that does not have volume reduction properties can be obtained.

(4) Deformation coefficients of small diameter pressure surface and large diameter pressure surface Considering the inner member 2 as a thick-walled cylinder with surface pressure p acting on the small diameter pressure surface (cylinder outer surface) and the outer member 4 as a thick-walled cylinder with surface pressure p acting on the large diameter pressure surface (cylinder inner surface), the deformation coefficients n _in and n _out are derived from Lame's theory of thick cylinder. According to the theory of thick cylinder, the radial deformation amount of the small diameter pressure surface is expressed by formulas (19a) to (19d). Similarly, the radial deformation amount of the large diameter pressure surface is expressed by formulas (20a) to (20d). Since the inner member 2 and the outer member 4 have parts that do not contact the cylinder, it is considered that the radial deformation amount and surface pressure are not uniform in the axial direction. It is considered that the actual radial deformation amount becomes smaller than the deformation amount in formula (19a) as the height h of the cylinder is smaller than the height h _in of the inner member 2. The same applies to the outer member 4. Using the height ratio h/h _in of the cylinder to the inner member 2, the coefficient e _in /E _s in equation (19a) is reduced and corrected as in equation (21), and the deformation coefficient n _in is defined by equation (21). Similarly, using the height ratio h/h _out of the cylinder to the outer member 4, b _out /E _s in equation (20a) is reduced and corrected as in equation (22), and the deformation coefficient n _out is defined by equation (22). n _in and n _out may be determined by other methods depending on the actual surface pressure and deformation amount of the inner member 2 and the outer member 4, respectively, without relying on equations (21) and (22).

(5) Evaluation of stress and strain of the inner member 2 and the outer member 4 Because the actual radial deformation of the small diameter pressure surface and the large diameter pressure surface is considered to change in the axial direction, it is considered that deformations larger than _u1 and _u2 obtained using equations (14a) and (14b) will occur in some places. _u1 and _u2 obtained using equations (14a) and (14b) are called the medium deformations, and the large deformations expected to occur in some places are called the high deformations. Here, we will describe a method for estimating the high deformations from the medium deformations and approximately obtaining the stress and strain of the inner member 2 and the outer member 4 from the high deformations.

A polar coordinate system (θ, r, z) is set up to define the stress generated inside the thick cylindrical wall of the inner member 2 and the outer member 4. Here, θ, r and z are the angle, radius and axial coordinates, respectively. The positive sign of the coordinate z is downward. The normal stresses in the θ, r and z directions are represented as σ _θ , σ _r and σ _z, respectively, and the positive and negative signs of these normal stresses are positive in the case of compression. It is assumed that the magnitude of _{σ θ} and σ _r does not change in the axial direction, and that the magnitude of σ _z is constant regardless of the coordinate.

If the strain in the circumferential direction (θ direction) and the deformation in the radial direction (r direction) are ε _θ and u, respectively, the relationship between these and each normal stress is given by equation (23). Here, the positive and negative signs of σ _θ , σ _r and σ _z indicate compression. Furthermore, equation (24) holds true at any point on the thick-walled cross section. Here, C is a constant.

The medium normal stresses in the circumferential and radial directions on the small diameter pressure surface of the inner member 2 are respectively σ _in,θ,1 and σ _in,r,1 . The normal stress in the axial direction is assumed to be small and is omitted. Since the boundary condition in the radial direction gives σ _in,r,1 =p, applying these normal stresses and u ₁ obtained from equation (14a) to equation (23) gives equation (25). The medium normal stresses in the circumferential and radial directions on the inner surface of the inner member 2 are respectively σ _in,θ,0 and σ _in,r,0 . The normal stress in the axial direction is assumed to be small and is omitted. In addition, since no surface pressure acts on the inner surface, σ _in,r,0 =0. Using the relationship in equation (24), equation (26) is obtained.

The medium normal stresses in the circumferential and radial directions on the large diameter pressure surface of the outer member 4 are respectively σ _out,θ,2 and σ _out,r,2 . The normal stress in the axial direction is assumed to be small and is omitted. Furthermore, from the boundary conditions, σ _out,r,2 =p, so by applying these normal stresses and u ₂ obtained from equation (14b) to equation (23), equation (27) is obtained. The medium normal stresses in the circumferential and radial directions on the outer surface of the outer member 4 are respectively σ _out,θ,3 and σ _out,r,3 . The normal stress in the axial direction is assumed to be small and is omitted. Furthermore, since no surface pressure acts on the inner surface, σ _out,r,3 =0. Using the relationship in equation (24), equation (28) is obtained. The intermediate normal stresses obtained by equations (25), (26), (27) and (28) are multiplied by the reciprocals of the coefficients h/h _in and h/h _out used in equations (21) and (22) to estimate the high normal stresses by equations (29) and (30), where σ _h,in,θ,j , j=0,1 and σ _h,out,θ,j , j=2,3 are the high normal stresses in the circumferential direction of the inner member 2 and the outer member 4, respectively.

In the compression test of the cylindrical spring 1 described later, the circumferential strains of the inner surface of the inner cylinder and the outer surface of the outer cylinder are measured. The medium and high levels of these strains are calculated by dividing the normal stresses shown in equations (26), (28), (29), and (30) by the elastic modulus. The calculation formulas are shown in equations (31a), (31b), (32a), and (32b). Here, ε _in,θ,0 and ε _h,in,θ,0 are the medium and high circumferential strains of the inner surface of the inner member 2. ε _out,θ,3 and ε _h,out,θ,3 are the medium and high circumferential strains of the outer surface of the outer member 4.

4. Cylindrical spring 1 specimen and compression test (1) Specifications of the specimen In order to confirm the mechanical validity of cylindrical spring 1, a 1/10 scale spring specimen is manufactured and a compression test is carried out to examine the relationship between the compressive force and the deformation amount of the specimen, as well as the strain of the specimen. The basic dimensions of the specimen are shown in Figure 7. Table 1 shows the specifications of the specimen excluding the basic dimensions.

The material of the inner member 2 and the outer member 4 is a steel pipe equivalent to carbon steel material for mechanical structures (S45C). The material of the cylinder is chloroprene rubber, hardness 65 degrees (CR-A65). The outer sealing ring and the inner sealing ring will be described later. The photograph shown in Figure 11 shows the appearance of the test specimen and each member. Figure 11 (a) shows the appearance of the inner member 2. The inner seating surface 2A, the small diameter pressure surface 2B, the large diameter guide surface 2C, the inner support surface 2D, and the inner surface 2E can be seen. The inner seating surface 2A has a groove for passing the lead wire of the strain gauge. The number of grooves is 8. The height of the inner member 2 excluding the groove depth of 15 mm is set to h _in = 121 mm. The arithmetic mean roughness of the small diameter pressure surface is 0.2 to 0.4 μm.

Figure 11(b) shows the external appearance of the outer member 4. The large diameter pressure surface 4B, small diameter guide surface 4C, outer support surface 4D, and outer surface 4E are visible. The outer seat surface 4A is not visible. The arithmetic mean roughness of the large diameter pressure surface is 0.7 to 1.0 μm. The radial dimensions of the storage space 1C (1C in Figure 6) formed by assembling the inner member 2 and the outer member 4 are r ₁ = 104 mm and r ₂ = 109 mm.

Figure 11(c) shows the external appearance of the cylinder. The dimensions of the cylinder are _r1 = 104 mm, _r2 = 109.5 mm, and h = 80 mm. The cylinder was manufactured by cutting a commercially available block of material. The arithmetic mean roughness of the cylinder outer surface 6D and cylinder inner surface 6C is approximately 1 μm. The inner radii of the cylinder and the space are equal, but the outer radius of the cylinder is larger than the outer radius of the space, so the cylinder is confined by being pushed into the storage space 1C.

Figure 11(d) shows the external appearance of the outer and inner sealing rings. The material is polyacetal (flexural modulus 2200N/ ^mm2 , Rockwell hardness M78, Poisson's ratio 0.35). The standard dimensions are inner diameter 208mm x outer diameter 218mm x thickness 5mm. The inner and outer diameters of these sealing members were finely adjusted to fit the finished shapes of the large and small diameter pressure surfaces.

Figure 11(e) shows the appearance of the test specimen. The inner member 2, compression member 3, and outer member 4 were each submerged in a silicone oil tank (dynamic viscosity 10,000 mm ² /s, specific gravity 0.975, 25°C), and the air on the surface of the members was removed in a vacuum vessel, and these members were assembled. The geometric limit deformation and total height of the test specimen were w _cr =25 mm and h _total =146 mm, respectively. From the finished dimension of the geometric limit deformation after confining the cylinder, w _cr =25 mm, the height of the cylinder after confinement was estimated to be h=90 mm. The basic dimensions in Figure 7 are based on the height of this cylinder after confinement. Four strain gauges were attached to the outer surface 4E of the outer member 4 to measure the circumferential strain. Although not visible in the photograph in the figure, four strain gauges were also attached to the inner surface 2E of the inner member 2.

Referring to Table 1, the elastic modulus and Poisson's ratio of the steel pipe are set to 2.0×10 ⁵ N/mm ² and 0.3, respectively. The Poisson's ratio of 0.4998 and the elastic modulus of 4.05 N/mm ² of chloroprene rubber were assumed based on literature research. The Poisson's ratio was taken from "Fujimoto Kunihiko, Tezuka Satoru: Bulk Modulus and Poisson's Ratio of Rubber, Journal of the Japan Rubber Association, Vol. 59, No. 7, pp. 385-398, 1986" for similar rubber. The bulk modulus calculated from the elastic modulus and Poisson's ratio is 3375 N/mm ^2. Since the Poisson's ratio is close to 0.5, the elastic modulus was set to three times the static shear modulus. The static shear modulus was estimated from the hardness of 65 degrees using the empirical formula (33) that determines the relationship between hardness _Hs and static shear modulus G for natural rubber (NR). The estimated static shear modulus is 1.35 N/ ^mm2 .

From equation (16), the surface pressure at a compressive force of 117.3 kN is 35.1 N/ ^mm2 , and from equation (17), the axial deformation is calculated to be 4.24 mm. The compressive force of 117.3 kN is the restoring force of the test specimen measured in the compression test described below. From equation (18), the initial tangential stiffness is calculated to be 26.6 kN/mm2. The middle circumferential compressive stress of the cylinder is calculated to be 35.1 N/ ^mm2 . The middle and high circumferential compressive stresses on the inner surface 2E of the inner member 2 are calculated to be 206 N/ ^mm2 and 278 N/ ^mm2 . The middle and high circumferential tensile stresses on the large diameter pressure surface 4B of the outer member 4 are calculated to be 189 N/ ^mm2 and 254 N/ ^mm2 . The medium and high circumferential compressive strains at the inner surface 2E of the inner member 2 are calculated to be 1030× ^10-6 and 1390× ^10-6 . The medium and high circumferential tensile strains at the outer surface 4E of the outer member 4 are calculated to be 770× ^10-6 and 1030× ^10-6 . These strains are compared with the strains measured in the compression experiment of the test specimen described later.

(2) Compression test procedure The photograph in Figure 12 shows the appearance of the compression test device and the test specimen. The capacity of the device is 250kN. In the photograph in Figure 12, the loading tool, loading plate, test specimen, support plate, beam, displacement gauge (two on the left and right), and strain gauge lead wires can be seen. The loading tool is an accessory of the device. The loading plate transmits the compression force from the loading tool to the inner seat 2A of the inner member 2. The support plate transmits the compression force from the beam of the device to the outer seat 4A of the outer member 4. A mirror-finished stainless steel plate (thickness 1mm) and a fluororesin sheet (thickness 0.05mm) coated with silicone oil (dynamic viscosity ^10,000mm2 /s, specific gravity 0.975, 25℃) were sandwiched between the loading plate and the inner seat 2A to reduce the radial friction between the loading plate and the inner seat 2A. The same treatment was performed between the outer seat 4A and the support plate. Six-cycle compression tests were carried out with maximum deformations of 1.5 mm, 3 mm, and 5 mm, respectively, at a loading rate of 0.885 mm per minute.

(3) Deformation-Compression Curve Figure 13 is a graph showing the compression force-deformation curves for the first and fourth cycles with a maximum deformation of 5 mm. The dashed line in the figure is the curve for the first cycle, and the solid line is the curve for the fourth cycle. The curves for the second to sixth cycles are close to each other and the difference between them cannot be seen in the figure, so the two curves for the first and fourth cycles are shown. In addition, the curves for the maximum deformation of 1.5 mm and 3 mm are also close to the curve for the maximum deformation of 5 mm, so the difference between them cannot be seen, so they are not shown. It can be seen from the figure that the compression force in the fourth cycle is slightly reduced compared to the first cycle. The maximum deformation in the fourth cycle is w _max =4.95 mm, and the height of the cylinder after assembly is h=90 mm, so the maximum axial strain of the cylinder is w _max /h=0.055. The maximum compression force is Q _max =135 kN.

In the curve for the fourth cycle, it can be seen that the amount of deformation increases as the compressive force increases, and that the amount of deformation returns to normal when the compressive force is decreased. A tendency for the rate of increase in compressive force to increase as the amount of deformation increases is confirmed. There is a difference in compressive force for the same amount of deformation when loading and unloading, and a tendency for the difference in compressive force to increase as the amount of deformation increases. The restoring force and friction force are calculated assuming that the difference in compressive force when loading and unloading is due to friction in the sliding parts between the cylinder and the large diameter pressure surface and between the cylinder and the small diameter pressure surface.

(4) Restoring force and frictional force Figure 14 is a graph showing the compressive force-deformation curve of the fourth cycle with the origin shifted. When the curves of the loading process and the unloading process are best approximated by a cubic function in the deformation range of 0.5 mm to 4.5 mm, the two functions shown in equations (34a) and (34b) are obtained. Here, Q ₊ (w) and Q _- (w) are approximate functions of the compressive force in the loading process and the unloading process, respectively, and the units of force and deformation are kN and mm, respectively. When the restoring force included in the compressive force is set to 1/2 the sum of the compressive forces in the loading process and the unloading process, and the frictional force is set to 1/2 the difference between the compressive forces in the loading process and the unloading process, and equations (34a) and (34b) are applied, the approximate functions of the restoring force and the frictional force shown in equations (35a) and (35b) are obtained. Here, Q _r (w) and Q _f (w) are approximate functions of the restoring force and the frictional force, respectively.

FIG. 14 illustrates the restoring force of Equation (35a) and the frictional force of Equation (35b). _Qr (w) is shown by a solid line, and _Qf (w) is shown by a dashed line. From the restoring force-deformation curve in the figure, it can be seen that the restoring force increases monotonically as the deformation increases, and that the rate of increase in the restoring force increases as the deformation increases. From the frictional force-deformation curve in the figure, it can be seen that the initial frictional force is 4.1 kN, and that the frictional force increases slightly as the deformation increases. The restoring force and frictional force at a deformation of 4.5 mm are 117.3 kN and 7.7 kN, respectively. The magnitude of the frictional force is about 6.5% of the magnitude of the restoring force.

15 is a diagram for comparing the restoring force of the test specimen, the restoring force of equation (17) under the condition of B = 3375 N/ ^mm2 where a volume reduction occurs (see Table 1), and the condition of B = ∞ where no volume reduction occurs. Comparing the restoring forces at around a deformation of 4.5 mm, it is confirmed that the restoring force of the test specimen is approximately 5% smaller than the restoring force of equation (17) under the condition where a volume reduction occurs, and approximately 36% smaller than the restoring force of equation (17) under the condition where no volume reduction occurs.

(5) Bulk modulus, initial tangent stiffness, and deformation Figure 16 shows the relationship between the initial tangent stiffness and bulk modulus of the test specimen calculated using formula (18), and the relationship between the bulk modulus and deformation of the test specimen calculated using formula (17) with the restoring force fixed at 117.3kN. The basic dimensions shown in Figure 7 and the specifications of the test specimen in Table 1 were used for the calculation. The initial tangent stiffness (●: TEST) obtained in the compression test and the deformation at a restoring force of 117.3kN (◯: TEST) are shown together. However, the bulk modulus was set to 3375N/ ^mm2 as shown in Table 1.

From the figure, it can be confirmed that as the bulk modulus becomes smaller, the initial tangent stiffness becomes monotonically smaller, and conversely, the deformation amount becomes monotonically larger, and the ratio of decrease and increase becomes larger as the bulk modulus becomes smaller. Since a decrease in the initial tangent stiffness and an increase in the deformation amount result in a decrease in the spring constant, it is considered that the spring constant of the cylindrical spring 1 can be reduced by reducing the bulk modulus. For example, the elastic modulus of the chloroprene rubber used in the test specimen is about 4N/ ^mm2 , and natural rubber (NR) for seismic isolation with an elastic modulus of about 1.8N/ ^mm2 is standardized. Assuming that the Poisson's ratio of natural rubber for seismic isolation is about 0.4998, the bulk modulus is estimated to be about 1500N/ ^mm2 . If such a material is used in the test specimen, it is considered that the initial tangent stiffness will decrease by about 5kN/mm (about 20%) and the deformation amount will increase by about 1mm (about 20%).

(6) Circumferential strain of the inner member 2 and the outer member 4 Figure 17 shows the average measured strain in the circumferential direction measured on the inner surface of the inner member 2 and the outer surface of the outer member 4 at the restoring force of 117.3 kN and the axial deformation of 4.5 mm in Figure 14. The average measured strain is the strain obtained by multiplying the sum of the measured strains in the loading and unloading processes by 1/2. The medium and high calculated strains in the circumferential direction shown in Table 1 are also shown. On the inner surface of the inner member 2, compressive strains of 670 x 10 ^-6 , 1210 x 10 ^-6 , and 1140 x 10 ^-6 occurred near the first end face, the center, and the second end face of the cylinder, respectively. It can be confirmed that the strain is maximum near the center of the cylinder, and the closer to the inner bearing surface 2A, the smaller the strain becomes. It can be confirmed that the measured strain near the second end face and the center of the cylinder is between the medium and high calculated strains. The high-order calculated strain is about 1.15 times the maximum measured strain.

On the outer surface of the outer member 4, tensile strains of 880× ^10-6 , 1000× ^10-6 , and 670× ^10-6 occurred near the first end face, the center, and the second end face of the cylinder, respectively. It can be confirmed that the strain is maximum near the center of the cylinder, and decreases the closer to the outer bearing surface 4A. It can be confirmed that the measured strains near the first end face and the center of the cylinder are between the medium and high calculated strains. The high calculated strain was comparable to the measured strain. Since the maximum measured strains of both the inner member 2 and the outer member 4 are between the medium and high calculated strains, the process of deriving the relationship between the restoring force and the deformation amount in equation (17) is generally considered to be mechanically appropriate.

Because the circumferential strain changes in the axial direction in both the inner member 2 and the outer member 4, it is believed that axial bending stress and radial and axial shear stresses occur in the inner member 2 and the outer member 4. When assessing the safety of the inner member 2 and the outer member 4, it is necessary to take these stresses into account in addition to the circumferential normal stress.

(7) Estimation of cross-sectional strain and volumetric strain The two curves ε ₀ (z) and ε ₃ (z) shown in Figure 17 are cubic functions passing through the average measured strain and measurement position on the inner surface of the inner member 2 and the outer surface of the outer member 4, respectively. These cubic functions are expressed by equations (36a) and (36b). Here, z is the coordinate representing the measurement position. The units of strain and measurement position z in equations (36a) and (36b) are 10 ^-6 and mm. The range of z where the inner member 2 and the outer member 4 contact the cylinder is shown by equation (36c). The height of the cylinder after deformation is 85.5 mm. The area enclosed by ε ₀ (z) is calculated by integrating equation (36a) within the range of equation (36c), and the obtained area is divided by the height of the cylinder in equation (36c) to estimate the medium circumferential strain ε _in,θ,0 on the inner surface of the inner member 2. From ε _in,θq,0, we return to equation (25) via equations (31a) and (26), and estimate the amount of radial deformation u ₁ at the small diameter pressure surface of the inner member 2. Similarly, from equation (36b), we estimate the medium circumferential strain ε _out,θ,3 at the outer surface of the outer member 4, and return to equation (27) via equations (32a) and (28), and estimate the amount of radial deformation u ₂ at the large diameter pressure surface of the outer member 4.

Once the deformation amounts _u1 and _u2 are determined, the cross-sectional area increase amount ΔA of the cylinder based on the volume increase characteristics can be determined from equation (8), and the volume increase amount _V3 of the cylinder based on the volume increase characteristics can be determined by substituting ΔA and the axial deformation amount w into equation (9). The volume decrease amount _V1 of the cylinder based on the volume decrease characteristics can be determined from equation (6). The volume decrease amount ΔV of the cylinder can be determined by substituting _V1 and _V3 into equation (11). Furthermore, the cross-sectional area strain and volume strain can be estimated from ΔA and ΔV.

Table 2 compares the volumetric strain, cross-sectional strain, and axial strain of the cylinder between the theoretical calculations and the estimated values based on compression tests.

It is confirmed that there is no difference between the calculated and estimated volumetric strains, and that the calculated cross-sectional strains and axial strains are both slightly smaller than the estimated values. In addition, since the axial strain is close to the sum of the volumetric strain and the cross-sectional strain, it is considered that formula (13a) holds for the test specimen. The ratio of volumetric strain to cross-sectional strain is approximately 1:4, and the amount of deformation in the axial direction of the test specimen is mainly caused by the cross-sectional strain, but the amount caused by the volumetric strain is also considered to be an effective amount for the extension of the deformation.

5. Summary As a spring element for use in vertical seismic isolation bearings, we proposed a cylindrical spring 1 consisting of an inner member 2, an outer member 4 located outside the inner member 2, and a compression member 3 that is tightly enclosed within a containment space 1C formed between the inner member 2 and the outer member 4. First, we explained the basic structure of the cylindrical spring 1, the characteristics of the inner member 2 and the outer member 4, and the volume decrease and increase characteristics of the containment space 1C. Secondly, we derived the relationship between the restoring force and the amount of deformation from the equivalence of the volumes of the containment space 1C and the compression member 3, and the balance between the external force and the internal force of the cylindrical spring 1. Finally, we described the restoring force characteristics and strain characteristics of the spring obtained from a compression test using a 1/10-scale spring specimen.

The findings are summarized below. 1) When a compressive force is applied to the cylindrical spring 1, a deformation occurs in the axial direction, and when the compressive force is removed, the deformation returns to the original amount. 2) When comparing the same deformation amount, the force during the unloading process is smaller than the force during the loading process, and the difference in force increases as the deformation amount increases. 3) The restoring force increases monotonically as the deformation amount increases, and the rate of increase in the restoring force tends to increase as the deformation amount increases. 4) The inner member 2 and the outer member 4 generate circumferential strain whose magnitude changes in the axial direction. In the safety evaluation of these members, it is necessary to consider the change in circumferential strain. 5) The deformation amount is expressed by the decrease in the radius of the small diameter pressure surface of the inner member 2, the increase in the radius of the large diameter pressure surface of the outer member 4, and the decrease in the volume of the compression member 3 (cylinder) based on the bulk elasticity coefficient. 6) The relationship between the restoring force and the deformation amount can be expressed by a formula due to the equality of the volumes of the storage space 1C and the compression member 3 (cylinder) and the balance between the external force and the internal force of the cylindrical spring 1.

This conclusion is based on knowledge gained from compression tests under limited conditions using a 1/10-scale test specimen and numerical calculations assuming material constants, but from the relationship between the restoring force and deformation of the obtained cylindrical spring 1, it is believed that the proposed cylindrical spring 1 may be usable as a spring element for vertical seismic isolation bearings. By accurately determining the bulk modulus of elasticity during compression of the viscoelastic material that makes up the cylinder, and the radial deformation of the small diameter pressure surface and large diameter pressure surface, the equation for the relationship between the restoring force and deformation is believed to be useful for the basic design of cylindrical spring 1, etc.

A second embodiment is described below, which is an improved method of preventing the bulging of a cylinder using a sealing ring according to the first embodiment. With reference to Figs. 2, 5, 6, and 8, when the compressive force increases, the radius of the small diameter pressure surface 2B decreases and the radius of the large diameter pressure surface 4B increases based on the volume increase characteristics. An increase in the radius of the large diameter pressure surface 4B leads to a decrease in the surface pressure of the cylinder outer surface 5D of the outer sealing ring 5 that is in sliding contact with the large diameter pressure surface 4B of the outer member 4, and the bulging prevention function of the outer sealing ring 5 against the first end surface 6A of the cylinder 6 may be reduced. In addition, a decrease in the radius of the small diameter pressure surface 2B leads to a decrease in the surface pressure of the cylinder inner surface 7C of the inner sealing ring 7 that is in sliding contact with the small diameter pressure surface 2B of the inner member 2, and the bulging prevention function of the inner sealing ring 7 against the second end surface 6B of the cylinder 6 may be reduced.

Figure 18 shows the configuration of the outer sealing ring 5 and inner sealing ring 7, which have improved anti-bulging function for the cylinder. First, the configuration of the outer sealing ring will be explained, and then the configuration of the inner sealing ring will be explained.

The outer sealing ring 5 (5E+5F) has an outer pressing member 5E and an outer sliding member 5F, both of which are short cylindrical in shape. The outer sliding member 5F is located in the storage space 1C on the outer gap 1A side, and is in sliding contact with the large diameter pressure surface 4B and the inner support surface 2D, and abuts against the first end surface 6A of the cylinder 6, blocking the outer gap 1A and preventing the cylinder 6 from expanding from the outer gap 1A. The outer pressing member 5E is located in the storage space 1C on the corner side formed by the inner support surface 2D and the small diameter pressure surface 2B, and is in sliding contact with the small diameter pressure surface 2B and the inner support surface 2D, and abuts against the first end surface 6A of the cylinder and the outer sliding member 5F, helping to prevent the outer sliding member 5F from expanding relative to the cylinder 6.

The outer pressing member 5E is subjected to a compressive force transmitted from the inner support surface 2D and the first end surface 6A of the cylinder 6 as surface pressure, which generates compressive longitudinal strain in the axial direction and expansive lateral strain in the direction perpendicular to the axis. The expansive lateral strain generated in the outer pressing member 5E generates a compressive stress (surface pressure) at the contact portion 5G between the outer pressing member 5E and the outer sliding member 5F. This compressive stress increases the radius of the outer sliding member 5F in accordance with the increase in the radius of the large diameter pressure surface 4B, and the surface pressure between the outer cylinder surface 5D and the large diameter pressure surface 4B of the outer sliding member 5F is maintained. Since the compressive force increases, the compressive stress increases, so that the outer pressing member 5E reduces or eliminates the decrease in surface pressure between the outer cylinder surface 5D and the large diameter pressure surface 4B of the outer sliding member 5F caused by the deformation of the small diameter pressure surface 2B and the large diameter pressure surface 4B. The sliding contact between the outer pressing member 5E and the inner support surface 2D increases the radial expansive strain that occurs in the outer pressing member compared to when the outer pressing member 5E is connected to the inner support surface 2D. Therefore, the outer pressing member 5E that slides against the inner support surface 2D is an important member that enhances the effect of the outer sliding member 5F in preventing the cylinder 6 from expanding.

The outer sliding member 5F is pressed against the large-diameter pressure surface 4B and slides against it to prevent the main material of the cylinder 6 from entering the sliding contact portion and prevent the cylinder 6 from expanding from the outer gap 1A. Since the cylindrical spring 1 is intended to have a service life of more than 50 years, in order to maintain the expansion prevention function for the cylinder 6 over a long period of time, it is preferable that the outer sliding member 5F has a multiple structure in which the sliding material 5H, which is a deformed wire material with a rectangular cross section or the like formed into a circular ring, is stacked in the axial direction to multiply the expansion prevention function. The cross-sectional shape of the deformed wire material is not limited to a rectangular cross section, and may be an L-shape or a shape in which an L-shape and an inverted L-shape are connected. Even if the sliding material 5H on the cylinder side 6 expands, the expansion is prevented by the adjacent sliding material on the inner support surface side 2D, so that the sliding material overlaps in the axial direction to multiply the expansion prevention function. The sliding material 5H of the outer sliding member 5F increases in radius due to the pressing stress, so tensile stress is generated in the circumferential direction. This tensile stress in the circumferential direction acts to prevent an increase in the radius of the sliding material 5H. If an increase in the radius of the sliding material is prioritized, the sliding material should be in a circular shape with discontinuous parts such as bias cuts, so that the tensile stress in the circumferential direction is small. However, it is preferable to overlap the sliding materials 5H so that the discontinuous parts do not communicate with each other in the axial direction and become a bulging path for the cylinder 6, that is, so that the discontinuous parts do not overlap in the axial direction.

The inner sealing ring 7 (7E+7F) has an inner pressing member 7E and an inner sliding member 7F, both of which are short cylindrical in shape. The inner sliding member 7F is located in the storage space 1C on the inner gap side 1B, and is in sliding contact with the small diameter pressure surface 2B and the outer support surface 4D, and is in contact with the inner pressing member 7E and the second end surface 6B of the cylinder, blocking the inner gap 1B and preventing the cylinder 6 from expanding from the inner gap 1B. The inner pressing member 7E is located in the storage space 1C on the corner side formed by the outer support surface 4D and the large diameter pressure surface 4B, and is in sliding contact with the large diameter pressure surface 4B and the outer support surface 4D, and is in contact with the second end surface 6B of the cylinder and the inner sliding member 7F, helping to prevent the inner sliding member 7F from expanding relative to the cylinder 6.

The inner pressing member 7E is transmitted as a surface pressure from the outer support surface 4D and the second end surface 6B of the cylinder 6, generating compressive longitudinal strain in the axial direction and expansive lateral strain in the direction perpendicular to the axis. The expansive lateral strain generated in the inner pressing member 7E generates a pressing stress (surface pressure) at the contact portion 7G between the inner pressing member 7E and the inner sliding member 7F. This pressing stress reduces the radius of the inner sliding member 7F in accordance with the reduction in the radius of the small diameter pressure surface 2B, and the surface pressure between the inner cylinder surface 7C of the inner sliding member 7F and the small diameter pressure surface 2B is maintained. Since the pressing stress increases as the compressive force increases, the inner pressing member reduces or eliminates the reduction in the surface pressure between the outer cylinder surface 7C and the small diameter pressure surface 2B of the inner sliding member 7F caused by the deformation of the small diameter pressure surface 2B and the large diameter pressure surface 4B. The sliding contact between the inner pressing member 7E and the outer support surface 4D increases the radial expansive strain that occurs in the inner pressing member 7E compared to when the inner pressing member 7E is connected to the outer support surface 4D. Therefore, the inner pressing member 7E that slides against the outer support surface 4D is an important member that enhances the effect of the inner sliding member 7F in preventing the cylinder 6 from expanding.

The inner sliding member 7F prevents the main material of the cylinder 6 from entering the inner gap 1B by sliding against the small diameter pressure surface 2B while being pressed against the small diameter pressure surface 2B, and prevents the cylinder 6 from expanding from the inner gap 1B. For the same reason as the outer sliding member 5F, the inner sliding member 7F is preferably made of a multi-layer structure in which sliding materials 7H, which are made by molding irregular wire material with a rectangular cross section or the like into a circular ring shape, are stacked in the axial direction to provide multiple expansion prevention functions. The sliding material 7H of the inner sliding member 7F is reduced in radius by pressure stress, so compressive stress is generated in the circumferential direction. This compressive stress in the circumferential direction has the effect of preventing the reduction of the radius of the sliding material. If the reduction of the radius of the sliding material is prioritized, the sliding material 7H should be in the form of a circular ring having discontinuous parts, similar to the sliding material 5H of the outer sliding member 5F, and the sliding materials 7H should be stacked so that the discontinuous parts do not overlap in the axial direction.

The inner pressing member 7E and the outer pressing member 5E generate a pressing stress by utilizing expansive lateral strain perpendicular to the axis, so the material for the outer pressing member and the inner pressing member should have a smaller elastic coefficient, a larger Poisson's ratio, and less volume loss due to compression than the inner support surface, the outer support surface, the large diameter pressure surface, and the small diameter pressure surface. Materials suitable for the cylinder 6 are also suitable. Pure lead, fiber-reinforced rubber, or hard rubber are suitable materials for the outer pressing member and the inner pressing member. The outer pressing member and the inner pressing member may each be integral with the cylinder.

The sliding materials 5H and 7H must have the ability to deform to follow the radial deformation of the large diameter pressure surface 4B or the small diameter pressure surface 2B, resistance to bending stress caused by the expansion of the outer gap 1A or the inner gap 2B, and good sliding performance with the inner support surface, outer support surface, small diameter pressure surface, and large diameter pressure surface. The material of the sliding materials 5H and 7H is suitable to be softer in hardness than the material forming the inner support surface, outer support surface, small diameter pressure surface, and large diameter pressure surface, harder than the material forming the cylinder, and to be self-lubricating. High tensile steel or alloy steel is suitable for the material of these support surfaces and pressure surfaces, so copper alloy or fiber-reinforced synthetic resin is suitable for the material of the sliding materials 5H and 7H.

In the case of the annular sliding members 5H and 7H having discontinuous portions, even if the sliding members 5H and 7H are stacked in the axial direction so that the discontinuous portions do not overlap, there is a possibility that the cylinder 2 may bulge from the discontinuous portions. The reason for providing the discontinuous portions is to reduce the generation of normal stress in the circumferential direction and to increase the pressing effect of the outer pressing member 5E and the inner pressing member 7E.

Figure 19 shows an inner spiral sliding member 5FS and an outer spiral sliding member 7FS that eliminate discontinuous parts and reduce the occurrence of circumferential normal stress. The outer sliding member 5F and the inner sliding member 7F in Figure 18 are replaced with the outer spiral sliding member 5FS and the inner spiral sliding member 7FS in Figure 19. The two spiral sliding members are made of a material suitable for the sliding members 5H and 7H, and are formed by winding a continuous deformed wire 9 around an axis in a spiral shape without discontinuous surfaces and stacking it in the axial direction. The cross-sectional width 9B is larger than the maximum gap between the inner gap and the outer gap, and is preferably three times or more the maximum gap. The cross-sectional thickness 9A is preferably larger than the maximum gap. The outer spiral sliding member is preferably made larger in outer radius 9D than the radius of the large diameter pressure surface 4B to introduce initial surface pressure. The inner spiral sliding member is preferably made smaller in inner radius 9C than the radius of the small diameter pressure surface 2B to introduce initial surface pressure.

In the case of an outer spiral sliding member, the end faces 9E and 9F are preferably shaped to contact the inner support surface 2D and the first end face 6A of the cylinder, respectively. In the case of an inner spiral sliding member, the end faces 9E and 9F are preferably shaped to contact the second end face 6B of the cylinder and the outer support surface 4D, respectively.

The cylindrical spring is intended to have a service life of more than 50 years, so the small diameter pressure surface 2B of the inner member 2 and the large diameter pressure surface 4B of the outer member 4 must maintain a sliding contact state with the compression member 3 for a period of more than 50 years. When the compression member 3 is formed from a combination of a viscoelastic material such as rubber, a low yield point elastic-plastic material such as pure lead, and a copper alloy, it is preferable to form the small diameter pressure surface 2B and the large diameter pressure surface 4B from a corrosion-resistant steel material such as a stainless steel plate. A compressive stress occurs in the circumferential direction on the small diameter pressure surface 2B, and a tensile stress occurs in the circumferential direction on the large diameter pressure surface 4B. When the cylindrical spring is large to accommodate the weight of the superstructure, the inner member 2 and the outer member 4 must be formed from a high yield point steel material with high strength and a wide elastic range to ensure safety in terms of strength and the amount of radial deformation.

Corrosion-resistant steel materials such as austenitic hot-rolled stainless steel plate (JIS G4304), stainless clad steel (JIS G 3601) made of this material, or stainless steel forgings for pressure vessels (JIS G 3214) can be formed into a cylindrical or circular hole pressure surface by combining bending and welding or forging and grinding. However, the yield strength of SUS304, a representative austenitic stainless steel plate (205 N/ ^mm2 , JIS G4304), is lower than the yield strength of chromium-molybdenum steel forgings (360-755 N/ ^mm2 , JIS G 3221), the yield strength of high yield point steel plates for bridges (500-700 N/ ^mm2 , JIS G 3140), or the yield strength of high yield point steel plates for welded structures (665-685 N/ ^mm2 , JIS G 3128).

Therefore, it is preferable to form the small diameter pressure surface 2B side and the large diameter pressure surface 4B side with corrosion-resistant steel, and the opposite side of the pressure surface with high yield point steel having higher strength than the corrosion-resistant steel, and the inner member 2 or the outer member 4 has a layered structure in which the corrosion-resistant steel and the high yield point steel are stacked concentrically. Furthermore, in the process of forming the layered structure by shrink fitting or the like, it is preferable to introduce an initial tensile stress in the circumferential direction on the small diameter pressure surface 2B side and an initial compressive stress in the circumferential direction on the large diameter pressure surface 4B side to increase the available elastic range in the circumferential direction on the stress surface side. However, with the introduction of these initial stresses, an initial compressive stress in the circumferential direction is introduced on the inner surface 2E of the inner member 2, and an initial tensile stress in the circumferential direction is introduced on the outer surface 4E of the outer member 4, so attention must be paid to safety in terms of strength. Even if it is not necessary to use corrosion-resistant steel depending on the usage environment, the inner member and the outer member may have a layered structure from the viewpoint of ensuring safety in terms of strength and the amount of deformation in the radial direction. The number of layers may exceed two.

In addition, since compressive stress occurs in the circumferential direction in the inner member 2, from the viewpoint of buckling strength, it may be possible to use a thick-walled single-layer structure using corrosion-resistant steel such as stainless steel forgings for pressure vessels (JIS G 3214).

Figure 20 shows an example of an inner member 2 having a concentric two-layer structure. From the shaft 8 side, the inner member is provided with an inner surface side body portion 2G forming the inner surface 2E, a small diameter pressure surface side body portion 2F forming the small diameter pressure surface 2B, and a large diameter guide surface side body portion 2H forming the large diameter guide surface 2C and the inner support surface 2D. The inner seat surface 2A is formed by the end faces of the inner surface side body portion 2G, the small diameter pressure surface side body portion 2F, and the large diameter guide surface side body portion 2H on the positive side of the shaft 8.

The large diameter guide surface side body 2H, the small diameter pressure surface side body 2F and the inner surface side body 2G are preferably manufactured by bending, welding and grinding using austenitic stainless steel plate, stainless clad steel made of austenitic stainless steel plate and rolled steel for welded structure, and high yield point steel plate for welded structure. The small diameter pressure surface side body 2F and the inner surface side body 2G are integrated by shrink fitting so that the rolled steel for welded structure and the high yield point steel for welded structure abut against each other. The large diameter guide surface side body 2H and the small diameter pressure surface side body 2F are integrated by welding or shrink fitting.

In the inner member 2 of FIG. 20, the inner support surface 2D and the small diameter pressure surface 2B are formed of austenitic stainless steel plate, so that the sliding contact state with the compression member can be maintained for a long period of time. The inner side 2E is formed of high yield point steel material, so safety can be ensured against circumferential compressive stress within a range that does not exceed the yield strength or buckling strength of the high yield point steel material. By performing appropriate corrosion prevention treatment of the inner seat surface 2A, the inner surface 2E, and the end surface 2I on the negative side of the shaft 8, galvanic corrosion can be prevented.

Figure 21 shows an example of an outer member 4 having a concentric two-layer structure. From the shaft side 8, the inner member 4 has a large diameter guide surface side body 4H that forms the small diameter guide surface 4C and the outer support surface 4D, a large diameter pressure surface side body 4F that forms the large diameter pressure surface 4B, and an outer surface side body 4G that forms the outer surface 4E. The outer seat surface 4A is formed by the end faces of the small diameter guide surface side body 4H, the large diameter pressure surface side body 4F, and the outer surface side body 4G on the negative side of the shaft 8.

The small diameter guide surface side body 4H, the large diameter pressure surface side body 4F and the outer surface side body 4G are preferably manufactured by bending, welding and grinding using austenitic stainless steel plate, stainless clad steel plate made of austenitic stainless steel plate and rolled steel for welded structure, and high yield point steel plate for welded structure. The large diameter pressure surface side body 4F and the outer surface side body 4G are integrated by shrink fitting so that the rolled steel for welded structure and the high yield point steel for welded structure abut against each other. The small diameter guide surface side body 4H and the large diameter pressure surface side body 4F are integrated by welding or shrink fitting.

In the outer member 4 in FIG. 21, the outer support surface 4D and the large diameter pressure surface 4B are formed from austenitic stainless steel plate, so they can maintain a sliding contact state with the compression member for a long period of time. The outer surface side 4E is formed from high yield point steel material, so safety can be ensured against circumferential tensile stress within a range that does not exceed the yield strength of the high yield point steel material. By appropriately performing anticorrosion treatment on the outer seat surface 4A, the outer surface 4E, and the end surface 4I on the positive side of the shaft 8, galvanic corrosion can be prevented.

The outer surface side barrel portion 4G may be formed by winding an irregular wire rod having a higher yield point than the material forming the large diameter pressure side barrel portion 4F around the outer circumference of the large diameter pressure side barrel portion 4F and stacking it in the axial and radial directions. The cross-sectional shape of the irregular wire rod is preferably rectangular, but other cross-sectional shapes are also acceptable. The irregular wire rod is preferably wound with an initial tension to generate an initial compressive stress in the circumferential direction on the large diameter pressure side 4B. In this method, the large diameter pressure side 4B is compressive and the outer surface 4E is tensile in terms of the normal stress in the circumferential direction, and an initial stress that gradually changes in a step shape can be introduced between the large diameter pressure side 4B and the outer surface 4E. This method ensures the strength safety of the outer member 4 and the amount of deformation in the radial direction.

When the radial deformation of the inner seating surface 2A and the outer seating surface 4A are restrained, the deformation coefficients of the small diameter pressure surface 2B and the large diameter pressure surface 4B decrease, and the initial tangential stiffness of the cylindrical spring 1 increases. This means that the vertical natural frequency of the vibration system consisting of the cylindrical spring 1 and the superstructure increases. Since the cylindrical spring 1 aims to have a vertical natural frequency of 3 Hz or less to obtain a seismic isolation effect, when connecting the cylindrical spring 1 to the superstructure and the substructure, the smaller the radial deformation restraint placed on the inner seating surface 2A and the outer seating surface 4B by both structures, the better.

The superstructure expands, contracts, and bends due to temperature changes, the substructure sinks and tilts due to changes in the groundwater level, and the superstructure and substructure are subject to complex deformations due to seismic motion. Therefore, the cylindrical spring 1 must be connected to the superstructure and substructure via a means that can reliably transmit the compressive force without damaging the cylindrical spring 1 due to these deformations.

Figure 22 shows a method of connecting a cylindrical spring 1 using a hollow laminated rubber to an upper structure and a lower structure. The figure shows a central cross section. The upper structure and lower structure are not shown in the figure. If the upper structure is on the positive side of the shaft 8, the lower structure is on the negative side, and if the lower structure is on the positive side, the upper structure is on the negative side.

The inner member 2 comprises an inner hollow laminated rubber 2J and an inner connecting plate 2K located between the inner seat surface 2A and the upper structure or lower structure. The inner hollow laminated rubber 2J is a laminated rubber with a hollow short cylinder shape on the axial side 8, in which rubber and steel plates are alternately laminated in the axial direction 8, and the rubber is connected to the adjacent steel plate. The inner first connecting surface 2M of the inner connecting plate 2K is connected to the upper structure or lower structure. The inner hollow laminated rubber 2J is connected to the inner seat surface 2A, and is connected to or in sliding contact with the inner second connecting surface 2L of the inner connecting plate 2K. When connecting the inner hollow laminated rubber 2J to the inner seat surface 2A, it is preferable to connect the rubber to the inner seat surface 2A by vulcanization adhesion or the like, but it is also possible to connect a steel plate to which the rubber is connected to the inner seat surface 2A. When the inner hollow laminated rubber 2J is brought into sliding contact with the inner second connection surface 2L, it is preferable to bring the steel plate to which the rubber is connected into sliding contact with the inner second connection surface 2L via a low-friction sliding material and a sliding fluid. The number of rubber layers is one or more. The inner second connection surface 2L may be a part of the surface of a horizontal seismic isolation bearing that is separately installed and connected to the upper structure or lower structure.

The outer member 4 comprises an outer hollow laminated rubber 4J and an outer connection board 4K located between the outer seat surface 4A and the lower structure or upper structure. The outer hollow laminated rubber 4J is a laminated rubber with a hollow short cylinder shape on the axial side 8, and rubber and steel plates are alternately laminated in the axial direction 8, with the rubber connected to the adjacent steel plate. The outer second connection surface 4M of the outer connection board 4K is connected to the lower structure or upper structure. The outer hollow laminated rubber 4J is connected to the outer seat surface 4A, and is connected or in sliding contact with the outer first connection surface 4L of the outer connection board 4K. When connecting the outer hollow laminated rubber 4J to the outer seat surface 4A, it is preferable to connect the rubber to the outer seat surface 4A by vulcanization adhesion or the like, but it is also possible to connect the steel plate to which the rubber is connected to the outer seat surface 4A. When the outer hollow laminated rubber is brought into sliding contact with the outer second connection surface 2L, it is preferable to bring the steel plate to which the rubber is connected into sliding contact with the outer first connection surface 4L via a low-friction sliding material and a sliding fluid. The number of rubber layers is one or more. The outer second connection surface 4L may be a part of the surface of a horizontal seismic isolation bearing connected to the lower structure or upper structure.

The radial deformation of the inner seat 2A and the outer seat 4A is elastically restrained by the shear stiffness of the rubber connected to the inner seat 2A and the outer seat 4A, but since the maximum radial deformation of these seats does not exceed 0.5% of the radius, the effect of the elastic restraint by the rubber on the vertical natural frequency can be ignored. The force acting on the cylindrical spring 1 by the horizontal relative displacement and relative angular displacement of the upper structure and lower structure is mitigated by the shear deformation, bending deformation, and torsional deformation of the inner hollow laminated rubber 2J and/or the outer hollow laminated rubber 4J.

By appropriately determining the specifications of the inner hollow laminated rubber 2J and/or the outer hollow laminated rubber 4J, the horizontal natural frequency of the vibration system consisting of the cylindrical spring 1 and the superstructure can be set to approximately 0.25 Hz. This adds a horizontal seismic isolation function in addition to the vertical seismic isolation function.

When the inner second connection surface 2L and the inner hollow rubber bearing 2J are in sliding contact and/or the outer first connection surface 4L and the outer hollow rubber bearing 4J are in sliding contact, these hollow rubber bearings correspond to elastic sliding bearings in horizontal seismic isolation, and when horizontal inertial force during an earthquake that exceeds the frictional force of the sliding contact occurs in the superstructure, slippage occurs at the sliding contact, and the horizontal seismic isolation effect is improved by mitigating the effect of horizontal earthquake motion on the superstructure. It is advisable to provide the inner support plate 2K with an inner protrusion 2N that protrudes toward the inner hollow rubber bearing 2J, or the outer support plate 4K with an outer protrusion 4N that protrudes toward the outer hollow rubber bearing 4J, to limit the relative horizontal displacement that occurs at each sliding contact point. The inner protrusion 2N and outer protrusion 4N may be installed on the outside, respectively.

In addition, by providing an inner opening 2O in the inner connection board 2K or an outer opening 4O in the outer connection board 4K, and providing an inspection passageway in the upper structure or lower structure that connects to these openings, it becomes possible to inspect the inside of the cylindrical spring 1. This makes it possible to inspect and maintain the outside and inside of the cylindrical spring, enabling it to have a useful life of more than 50 years.

Hollow rubber bearings are horizontal seismic isolation bearings that were put into practical use in the 1990s, but by combining the cylindrical springs of this invention with hollow rubber bearings, it is possible to realize a three-dimensional seismic isolation bearing that integrates vertical and horizontal seismic isolation bearings, something that has not been realized until now.

The inner hollow laminated rubber 2J and the outer hollow laminated rubber 4J that are connected to or in sliding contact with the upper structure are sometimes collectively referred to as the upper hollow laminated rubber, and the inner hollow laminated rubber 2J and the outer hollow laminated rubber 4J that are connected to or in sliding contact with the lower structure are sometimes collectively referred to as the lower hollow laminated rubber. In other words, the upper hollow laminated rubber that is connected to the inner seating surface 2A is the inner hollow laminated rubber 2J, and the upper hollow laminated rubber that is connected to the outer seating surface 4A is the outer hollow laminated rubber 4J. Also, the lower hollow laminated rubber that is connected to the outer seating surface 2A is the outer hollow laminated rubber 4J, and the lower hollow laminated rubber that is connected to the inner seating surface 2A is the inner hollow laminated rubber 4J.

1: cylindrical spring, 1A: outer gap, 1B: inner gap, 1C: storage space, 1Y: height, 1Z: assembly height, 2: inner member, 2A: inner seat, 2B: small diameter pressure surface, 2C: large diameter guide surface, 2D: inner support surface, 2E: inner surface, 2F: small diameter pressure surface side body part, 2G: inner surface side body part, 2H: large diameter guide surface side body part, 2I: negative direction side end face, 2J: inner hollow laminated rubber, 2K: inner contact Continuation panel, 2L...Inner second connection surface, 2M...Inner first connection surface, 2N...Inner protrusion, 2O...Inner opening, 3...Compression member, 3A...First end surface, 3B...Second end surface, 3C...Cylinder inner surface, 3D...Cylinder outer surface , 3Z...height, 4...outer member, 4A...outer seat surface, 4B...large diameter pressure surface, 4C...small diameter guide surface, 4D...outer support surface, 4E...outer surface, 4F...large diameter pressure surface side body, 4G...outer surface side body, 4H. ...Large diameter guide surface side trunk, 4I...End face on the forward side, 4J...Outer hollow laminated rubber, 4K...Outer connection board, 4L...Outer first connection surface, 4M...Outer second connection surface, 4N...Outer protrusion, 4O...Outer opening, 5... Outer sealing ring, 5A... First end surface, 5E... Outer pressing member, 5F... Outer sliding member, 5G... Contact portion, 5H... Sliding material, 5FS... Inner spiral sliding member, 6... Cylinder, 6A... First end surface , 6B... Second end surface, 6C... Cylinder inner surface, 6D... Cylinder outer surface, 6Z... Height, 7... Inner sealing ring, 7B... Second end surface, 7C... Cylinder inner surface, 7E... Inner pressing member, 7F... Inner sliding member, 7G...・Abutment part, 7H...Sliding material, 7FS...Outer spiral sliding member, 8...Central shaft, 9...Deformed wire material, 9A...Thickness, 9B...Width, 9C...Inner radius, 9D...Outer radius, 9E...End face, 9F...End face

Claims (7)

The upper structure is supported from below, and is located on the lower structure on which the seismic motion acts. The amount of vertical compressive deformation caused by the weight of the upper structure increases or decreases according to the seismic motion.
At least an inner member;
an outer member disposed outwardly relative to the inner member;
A vertical seismic isolation bearing spring element comprising a compression member stored without gaps in a storage space formed between the inner member and the outer member,
The inner member includes :
An annular inner bearing surface disposed at a position supporting the upper structure from below or at a position supported by the lower structure from below;
a cylindrical large-diameter guide surface that forms an angle at an outer periphery of the inner seat surface and extends parallel to a central axis of the inner member ;
an annular inner support surface that forms an angle with the large diameter guide surface and extends to a rear side of the inner seat surface;
a cylindrical small-diameter pressure surface that forms a corner portion at an inner peripheral edge of the inner support surface and extends parallel to a central axis of the inner member ;
a radius of the small diameter pressure surface is reduced by a surface pressure acting on the small diameter pressure surface, and when the surface pressure acting on the small diameter pressure surface is eliminated, the radius of the small diameter pressure surface is restored to its original value;
The outer member includes :
An annular outer bearing surface disposed at a position supported from below by the lower structure or at a position supporting the upper structure from below;
a small diameter guide surface having a circular hole shape, the small diameter guide surface forming a corner on an inner edge circumference of the outer seat surface, extending parallel to a central axis of the outer member , and slidingly fitted to the small diameter pressure surface;
an annular outer support surface that forms an angle with the small diameter guide surface and extends to a rear side of the outer seat surface;
a large-diameter pressure surface having a circular hole shape, the large-diameter pressure surface forming a corner portion at an outer peripheral circumference of the outer support surface, extending parallel to a central axis of the outer member, and slidingly fitted into the large-diameter guide surface;
a radius of the large-diameter pressure surface increases due to a surface pressure acting on the large-diameter pressure surface, and when the surface pressure acting on the large-diameter pressure surface is eliminated, the radius of the large-diameter pressure surface returns to its original value;
The storage space includes:
the inner member and the outer member are assembled in a state in which the inner support surface and the outer support surface face each other, the large diameter guide surface and the large diameter pressure surface are slidably fitted together, and the small diameter pressure surface and the small diameter guide surface are slidably fitted together, thereby being surrounded by the inner support surface, the small diameter pressure surface, the outer support surface, and the large diameter pressure surface,
The compression member is
the small diameter pressure surface and the large diameter pressure surface are formed mainly using a material having a smaller elastic modulus than a material forming the small diameter pressure surface and the large diameter pressure surface, and the small diameter pressure surface is stored in the storage space without any gaps while being in sliding contact with the inner support surface, the small diameter pressure surface, the outer support surface, and the large diameter pressure surface,
A spring element for vertical seismic isolation support, characterized in that the compressive deformation amount includes a main compressive deformation amount generated by slippage between the small diameter pressure surface and the compression member, slippage between the large diameter pressure surface and the compression member, a decrease in the radius of the small diameter pressure surface, and an increase in the radius of the large diameter pressure surface, or includes a secondary compressive deformation amount generated by a decrease in the volume of the compression member in addition to the main compressive deformation amount. The spring element for vertical seismic isolation bearing described in claim 1, characterized in that the compression member has portions formed from different materials, and at least one of the portions is formed using a material with a low elastic modulus as the main material. The spring element for vertical seismic isolation bearing according to claim 1 or 2, characterized in that the material having a small elastic modulus has viscoelasticity or low yield point elastic-plasticity. The compression member is
an outer sliding member having a short hollow cylindrical shape that is disposed within the storage space, is in sliding contact with the inner support surface and the large diameter pressure surface, and closes an outer gap that occurs at a sliding engagement portion between the large diameter pressure surface and the large diameter guide surface;
3. The spring element for vertical seismic isolation bearing as described in claim 1 or claim 2, comprising: a short hollow cylindrical inner sliding member that is arranged in the storage space, is in sliding contact with the outer support surface and the small diameter pressure surface , and closes an inner gap that occurs at the sliding engagement portion between the small diameter pressure surface and the small diameter guide surface. The compression member is
an annular outer pressing member that is disposed in the storage space on a side of a corner portion formed by the small diameter pressure surface and the inner support surface, and is in sliding contact with the small diameter pressure surface, the inner support surface, and the outer sliding member, and presses the outer sliding member against the large diameter pressure surface;
an annular inner pressing member that is disposed in the storage space on a side of a corner portion formed by the large diameter pressure surface and the outer support surface, and is in sliding contact with the large diameter pressure surface, the outer support surface, and the inner sliding member, and presses the inner sliding member against the small diameter pressure surface;
The spring element for vertical seismic isolation bearing described in claim 4, wherein the outer pressure member and the inner pressure member are formed of a material having a smaller elastic coefficient and a larger Poisson's ratio than the materials forming the inner support surface, the small diameter pressure surface, the outer support surface, and the large diameter pressure surface, respectively . The spring element for vertical seismic isolation bearing according to claim 4, wherein the outer sliding member and the inner sliding member are sliding materials having an irregular cross-sectional shape and an overall shape of a ring or a discontinuous ring, stacked in a direction perpendicular to a radius of the ring shape. 5. The spring element for vertical seismic isolation bearing according to claim 4 , wherein the outer sliding member and the inner sliding member are replaced with a spiral annular sliding member formed by winding a deformed wire in a spiral shape.