JP6746509B2 - Dynamic vibration absorber and its design method - Google Patents

Description

The present invention relates to a dynamic vibration reducer that suppresses a resonance phenomenon in an object and a design method thereof.

There is known a dynamic vibration reducer that adds a spring and a mass body to an object to tune the natural frequency and suppress a resonance phenomenon around the natural frequency of the object. Among such dynamic vibration reducers, one using a leaf spring has a structure in which one end of the leaf spring is fixed to an object by a spring fixing metal fitting, and a weight is attached to the vicinity of the other end of the leaf spring in a positionally adjustable manner. Further, in such a leaf spring type dynamic vibration reducer, there is one in which a viscoelastic body is added as a damper (see Patent Document 1).

JP, 7-317372, A

By the way, the rigidity (Young's modulus) and the damping characteristic of the viscoelastic body greatly change depending on the ambient temperature. Therefore, in the dynamic vibration absorber using the viscoelastic body, the characteristics of the entire dynamic vibration absorber change depending on the ambient temperature. Therefore, even if the dynamic vibration absorber satisfies the target natural frequency and the target damping ratio at the reference temperature, the natural frequency or the damping ratio may deviate from the target value due to a change in ambient temperature. The natural frequency can be easily adjusted by changing the position of the weight or the shape of the leaf spring, but the damping ratio cannot be easily adjusted. Therefore, it is required to suppress the change of the damping ratio due to the change of the ambient temperature as much as possible.

The present invention has been made in view of such circumstances, and a main object of the present invention is to provide a dynamic vibration reducer capable of suppressing a change in damping ratio due to a change in ambient temperature, and a design method thereof.

In order to solve the above-mentioned problems, a dynamic vibration reducer according to one aspect of the present invention is a dynamic vibration reducer in which a damping ratio changes according to a temperature change, and a column fixed to an object and a longitudinal center. A first leaf spring fixed to the column, and a second leaf spring fixed to the column at the center in the longitudinal direction and arranged parallel to the first leaf spring and having a rigidity higher than that of the first leaf spring. A mass body attached to the first leaf spring and a viscoelastic body that connects the first and second leaf springs and that decreases in rigidity as the temperature rises, and the object vibrates. In this case, the deformation amount of each of the first and second leaf springs and the viscoelastic body changes according to the temperature change, and the damping ratio changes so as to show a peak with respect to the temperature change. And the damping ratio, the rigidity of the first and second leaf springs and the viscoelastic body is set so that the peak of the damping ratio is located within the operating temperature range.

In this aspect, in the dynamic vibration reducer, the rigidity of the first and second leaf springs and the viscoelastic body are set so that the peaks coincide with the reference temperature within the operating temperature range in the relationship between the temperature and the damping ratio. It may have been done.

Further, in the above aspect, in the dynamic vibration reducer, the damping ratio at the reference temperature is equal to or higher than a target damping ratio in the relationship between the temperature and the damping ratio, and the damping ratio at the upper limit or the lower limit of the operating temperature range is the target. The rigidity of the first and second leaf springs and the viscoelastic body may be set so as to be less than or equal to the damping ratio.

Further, in the above aspect, in the dynamic vibration reducer, in the relationship between temperature and natural frequency, the first and second leaf springs and the viscoelastic body are arranged so that the natural frequency at the reference temperature matches the target natural frequency. The rigidity may be set.

Further, in the above aspect, the dynamic vibration reducer supports the first and second leaf springs so that their positions can be adjusted in the longitudinal direction, and adjusts the support positions of the first and second leaf springs to adjust the position. You may further provide the 1st and 2nd support member which adjusts the rigidity of a 1st and 2nd leaf spring.

Further, in the above aspect, the dynamic vibration reducer further includes a support body disposed between the first and second leaf springs, and each of the first and second support members is the support body. The position may be adjustable in the longitudinal direction.

Further, in the above aspect, each of the first and second support members is formed so as to become thinner toward each of the first and second leaf springs, and the first and second leaf springs are provided at the tip thereof. A top portion that abuts and a bottom portion that abuts the support body on the opposite side of the top portion, and a distance between the top portion and the bottom portion of the first support member is the first support member on the support body. Is set to be larger than the distance between the first leaf spring and the contact surface of the support body to the bottom portion of the first support member in a state in which is not arranged, and the top portion of the second support member The distance between the bottom portion and the second leaf spring in a state where the second support member is not arranged on the support body and the contact surface of the support body to the bottom portion of the second support member. It may be set larger than the distance between them.

In addition, another method of designing a dynamic vibration absorber according to the present invention is a column fixed to an object, a first leaf spring fixed to the column at the center in the longitudinal direction, and a column spring fixed to the column at the center in the longitudinal direction. A second leaf spring having a rigidity higher than that of the first leaf spring and arranged in parallel with the first leaf spring; a mass body attached to the first leaf spring; and the first and second leaf springs. A method for designing a dynamic vibration reducer comprising a viscoelastic body connecting a spring, wherein a step of setting a characteristic of a damping ratio of the dynamic vibration reducer that changes with temperature, and a characteristic of the damping ratio at a working temperature A step of determining whether or not the peak of the damping ratio is located within the range, and in the case where the peak of the damping ratio is not located within the operating temperature range, the position of the peak with respect to the temperature is adjusted so as to change the position of the peak. Resetting the characteristic.

In this aspect, in the step of setting the characteristic of the damping ratio, the damping ratio for each stiffness when the rigidity of the viscoelastic body is changed when the loss coefficient of the viscoelastic body is set to a constant representative loss coefficient is set. On the other hand, the loss coefficient of the viscoelastic body is calculated by multiplying the ratio of the loss coefficient of the viscoelastic body and the representative loss coefficient in each stiffness when the rigidity of the viscoelastic body is changed for each stiffness. In the step of determining the characteristic of the damping ratio, which is the relationship between the rigidity and the damping ratio in the case where the loss coefficient is changed according to, and resetting the characteristic of the damping ratio, the loss coefficient of the viscoelastic body is set to With respect to the damping ratio for each rigidity when the rigidity of the viscoelastic body is changed in the case of a constant representative loss coefficient, the ratio of the loss coefficient of the viscoelastic body and the representative loss coefficient in each rigidity, The characteristic of the damping ratio may be redetermined by changing the rigidity and multiplying when the characteristic of the damping ratio is determined.

Further, in the above aspect, in the determining step, it may be determined whether or not the peak matches the reference temperature in the operating temperature range in the characteristic of the damping ratio.

Further, in the above aspect, in the characteristic of the damping ratio, the design method of the dynamic vibration absorber has a step of determining whether or not a damping ratio at the peak is within a predetermined range based on a target damping ratio, and at the peak. Resetting the characteristic of the damping ratio by adjusting a parameter defining the relationship between the rigidity of the first leaf spring and the rigidity of the second leaf spring when the damping ratio is not within the predetermined range. You may further have and.

Further, in the above aspect, the design method of the dynamic vibration absorber is characterized in that, in the characteristic of the damping ratio, a step of determining whether or not the damping ratio at the peak is within a predetermined range based on the target damping ratio, The method may further include the step of resetting the characteristic of the damping ratio by adjusting the plate thickness of the second plate spring when the damping ratio is not within the predetermined range.

Further, in the above aspect, the design method of the dynamic vibration absorber, after setting the characteristics of the damping ratio, so that the natural frequency of the dynamic vibration absorber at the peak of the damping ratio matches the target natural frequency, The method may further include the step of adjusting the characteristics of the natural frequency that changes with respect to temperature by determining the rigidity of each of the first and second leaf springs and the viscoelastic body.

Further, in the above aspect, the dynamic vibration reducer supports the first and second leaf springs so that their positions can be adjusted in the longitudinal direction, and adjusts the support positions of the first and second leaf springs to adjust the position. The dynamic vibration absorber designing method further includes first and second support portions for adjusting the rigidity of the first and second leaf springs, and the rigidity of each of the first and second leaf springs is determined. The method may further include the step of adjusting the support positions of the first and second support portions so as to match the rigidity of the first and second leaf springs.

Further, in the above aspect, in the method for designing the dynamic vibration reducer, the first and second leaf springs are modeled as shell elements, and the viscoelastic body is modeled as a solid element, and Young's modulus or shear is used as a rigidity characteristic of the solid element. The method may further include the step of giving a coefficient and giving a loss coefficient as a damping characteristic of the solid element to determine initial characteristics of the damping ratio and the natural frequency by a finite element method.

Further, in the above aspect, in the step of setting the characteristic of the damping ratio, the Young's modulus or the shear coefficient is changed to change the rigidity of the viscoelastic body, and the damping ratio at each rigidity is obtained to obtain the damping ratio. The characteristics of may be set.

According to the dynamic vibration reducer and the design method thereof according to the present invention, it is possible to suppress the change in the damping ratio due to the change in the ambient temperature.

FIG. 3 is a schematic diagram showing the configuration of the dynamic vibration reducer according to the first embodiment. FIG. 3 is a diagram showing an element model equivalent to the dynamic vibration reducer according to the first embodiment. The schematic diagram which shows the state when a dynamic vibration absorber deform|transforms. The graph which shows the shear elastic modulus of a viscoelastic body, and the relationship with temperature. The graph which shows the relationship between the loss coefficient of a viscoelastic body, and temperature. The graph which shows an example of the temperature characteristic of each damping ratio and natural frequency of a dynamic vibration absorber. FIG. 3 is a block diagram showing the configuration of the design support device according to the first embodiment. 3 is a flowchart showing a procedure of a method for designing a dynamic vibration reducer according to the first embodiment. The flowchart which shows the procedure of an initial condition setting process. The graph which shows the relationship between the standard rigidity ratio of a viscoelastic body, and a loss coefficient. Flow chart showing the procedure of the damping ratio design process The figure which shows an example of a 1st graph. The figure for demonstrating the determination process of a 2nd graph. The figure which shows an example of a 2nd graph. The figure for demonstrating adjustment of the peak value of a damping ratio. The figure for demonstrating adjustment of reference rigidity ratio in the peak of damping ratio. The flowchart which shows the procedure of a natural frequency design process. The figure for demonstrating adjustment of a natural frequency. 6 is a flowchart showing the procedure of a method for designing a dynamic vibration reducer according to the second embodiment. The flowchart which shows the procedure of an initial condition setting process. The figure which shows an example of a FEM model. The flowchart which shows the procedure of a damping ratio design process. FIG. 7 is a schematic diagram showing a configuration of a dynamic vibration reducer according to the third embodiment. The perspective view which shows the structure of a support part. The perspective view which shows the structure of a 1st support member.

Hereinafter, preferred embodiments of the present invention will be described with reference to the drawings. Each embodiment described below exemplifies a method and an apparatus for embodying the technical idea of the present invention, and the technical idea of the present invention is not limited to the following. Absent. The technical idea of the present invention can be variously modified within the technical scope described in the claims.

(Embodiment 1)
<Structure of dynamic vibration absorber>
In the present embodiment, a dynamic vibration reducer having two leaf springs and a viscoelastic body and a design method thereof will be described. FIG. 1 is a schematic diagram showing the configuration of the dynamic vibration reducer according to the present embodiment. The dynamic vibration reducer 100 includes a first leaf spring 101, a second leaf spring 102, a mass body 103, and a viscoelastic body 104.

The first leaf spring 101 and the second leaf spring 102 are arranged parallel to each other and horizontally, and are fixed to the support column 105, which is a rigid body, at the center in the longitudinal direction. The column 105 is fixed to the object 200 at the lower end. A mass body 103 is attached to each of both ends of the first leaf spring 101. A columnar viscoelastic body 104 is arranged between the first leaf spring 101 and the second leaf spring 102 at both ends of the first leaf spring 101 and the second leaf spring 102, respectively. The first leaf spring 101 and the second leaf spring 102 are connected by. The shape of the viscoelastic body 104 is not limited to a column, and may be a column having a cross section other than a circle, such as a prism.

The 1st leaf spring 101 and the 2nd leaf spring 102 are comprised by the cold rolling steel strip for springs, the stainless steel strip for springs, etc. Further, as the viscoelastic body 104, for example, an acrylic rubber-based material is used.

FIG. 2 is a diagram showing an element model equivalent to the dynamic vibration reducer 100. The element model shown in FIG. 2 is equivalent to half of the dynamic vibration reducer 100 (the portion surrounded by the broken line in FIG. 1). As shown in FIG. 2, each of the first leaf spring 101 and the second leaf spring 102 functions as an elastic element. Further, the viscoelastic body 104 functions as an elastic element and a damping element connected in parallel. The thickness of the second plate spring 102 is larger than the thickness of the first plate spring 101, from which the rigidity (spring constant) _{k 2} of the second plate spring 102 of the first plate spring 101 stiffness (spring constant) _{k 1} Is also big. The rigidity (spring constant) k of the viscoelastic body 104 is sufficiently smaller than the rigidity k ₁ and k ₂ .

FIG. 3 is a schematic diagram showing a state when the dynamic vibration reducer 100 is deformed. When the object 200 vibrates, the support column 105 that is a rigid body also vibrates, and both the first leaf spring 101 and the second leaf spring 102 bend. At this time, since the rigidity k ₁ is smaller than the rigidity k ₂ , the first leaf spring 101 is deformed more than the second leaf spring 102. The viscoelastic body 104 is deformed according to the difference between the deformation amounts of the both. The natural frequency of the dynamic vibration reducer 100 is set near the natural frequency of the object 200. Thereby, the vibration of the object 200 is absorbed.

FIG. 4 is a graph showing the relationship between the shear elastic modulus of the viscoelastic body 104 and temperature, and FIG. 5 is a graph showing the relationship between the loss coefficient of the viscoelastic body 104 and temperature. In FIG. 4, the horizontal axis represents temperature and the vertical axis represents shear elastic modulus. In addition, in FIG. 5, the horizontal axis represents temperature and the vertical axis represents loss coefficient. The shear modulus of elasticity is also called the rigidity modulus and is an index showing the high rigidity of the material. As shown in FIG. 4, the shear elastic modulus of the viscoelastic body 104 decreases monotonically with temperature. That is, the rigidity of the viscoelastic body 104 increases as the temperature decreases. The loss coefficient is an index showing the damping characteristic of the material. As shown in FIG. 5, the loss coefficient of the viscoelastic body 104 also changes with temperature. Therefore, such a temperature characteristic of the viscoelastic body 104 affects the characteristic of the damping ratio of the dynamic vibration reducer 100.

As described above, the rigidity of the viscoelastic body 104 increases as the temperature decreases. Therefore, when the ambient temperature is low, the amount of deformation of the viscoelastic body 104 is small, and accordingly, the amount of deformation of the second plate spring 102 is large. Therefore, the curve showing the relationship between the temperature and the damping ratio of the dynamic vibration absorber 100 has a peak.

FIG. 6 is a graph showing an example of the temperature characteristics of the damping ratio and the natural frequency of the dynamic vibration reducer 100. In FIG. 6, the vertical axis represents the damping ratio and the magnitude of the natural frequency, and the horizontal axis represents the ratio of rigidity to the reference rigidity of the viscoelastic body 104 (hereinafter referred to as “reference rigidity ratio”). Here, the use temperature trend and the reference temperature at which the use of the dynamic vibration reducer 100 is assumed are set for the dynamic vibration reducer 100. The reference temperature is set within the usage temperature range, and in this embodiment, the reference temperature is 20° C. and the usage temperature range is 10° C. or higher and 30° C. or lower. As described above, the reference temperature is preferably the median value of the usage temperature trend, but is not limited to the median value as long as it is set within the usage temperature trend. The reference rigidity is the rigidity of the dynamic vibration reducer 100 at the reference temperature. The rigidity of the viscoelastic body 104 decreases monotonously with temperature. Therefore, the reference rigidity ratio also monotonically decreases according to the temperature. Therefore, the horizontal axis in FIG. 6 corresponds to the temperature.

As shown in FIG. 6, the curve showing the temperature characteristic of the damping ratio of the dynamic vibration reducer 100 according to the present embodiment (shown by the broken line in the figure) has a peak at the reference temperature. The damping ratio at the reference temperature (20° C.) is 15%, the damping ratio at the upper limit (30° C.) of the usage temperature range is about 12%, and the damping ratio at the lower limit (10° C.) is about 11%. The target damping ratio of the dynamic vibration reducer 100 is 15%, and the damping ratio at the reference temperature matches the target damping ratio. Further, the damping ratios at the upper and lower limits of the usage temperature range are smaller than the target temperature range. The damping ratio of the dynamic vibration reducer 100 at the reference temperature does not have to be the same as the target damping ratio, as long as it is equal to or higher than the target damping ratio. Further, the damping ratio at the upper and lower limits of the usage temperature range may be equal to or less than the target damping ratio. For example, if the damping ratio at the reference temperature is set to 17.5%, the damping ratio at the usage temperature is around 12.5%. By doing so, the difference between the damping ratio and the target damping ratio in the usage temperature range can be reduced. As described above, according to the dynamic vibration reducer 100 of the present embodiment, since the peak of the damping ratio is located in the operating temperature range, particularly at the reference temperature, the change of the damping ratio due to the change of the ambient temperature in the operating temperature range. Can be suppressed.

On the other hand, the natural frequency of the dynamic vibration reducer 100 decreases monotonously with temperature. The natural frequency at the reference temperature is 20 Hz, which matches the target natural frequency. The natural frequency at the upper limit of the usage temperature range is about 17 Hz, and the natural frequency at the lower limit is about 25 Hz. In this way, by setting the natural frequency at the reference temperature to be near the target natural frequency, it is possible to reduce the difference between the natural frequency and the target natural frequency within the usage temperature range.

<Dynamic vibration absorber design method>
Next, a method of designing the dynamic vibration reducer according to the present embodiment will be described. In the dynamic vibration absorber design method according to the present embodiment, the temperature characteristics of the damping ratio and the natural frequency of the dynamic vibration absorber are determined based on theoretical formulas.

ここで、ｔ_１は第１板バネ１０１の厚さを、ｔ_２は第２板バネ１０２の厚さを、ｂは第１板バネ１０１及び第２板バネ１０２の幅を、Ｌは支柱１０５から質量体Ｍの重心位置までの距離（図１参照）を、Ｅは第１板バネ１０１及び第２板バネ１０２のヤング率を、それぞれ示している。 First, a theoretical formula used for designing a dynamic vibration absorber will be described. The stiffnesses k ₁ and k ₂ of the first leaf spring 101 and the second leaf spring 102 are given by equation (1).

Here, t ₁ is the thickness of the first leaf spring 101, t ₂ is the thickness of the second leaf spring 102, b is the width of the first leaf spring 101 and the second leaf spring 102, and L is the strut 105. To the center of gravity of the mass M (see FIG. 1), and E indicates the Young's modulus of the first leaf spring 101 and the second leaf spring 102, respectively.

ここで、Ａは粘弾性体１０４の断面積を、ｄはその厚さを、Ｅ_ｄはその貯蔵弾性率を、ηはその損失係数を、ｋはそのばね定数、つまり剛性をそれぞれ示している。 The complex rigidity k ^* =k(1+ηj) of the viscoelastic body 104 is expressed by the following equation (2).

Here, A is a cross-sectional area of the viscoelastic body 104, d is its thickness, E _d is its storage elastic modulus, η is its loss coefficient, and k is its spring constant, that is, rigidity. ..

At this time, the overall rigidity K _all and the overall loss coefficient η _{all of the} element model shown in FIG. 2 are expressed as follows.

但し、Ｍは質量体１０３の質量を示す。 Further, the natural frequency f and the damping ratio ζ of the dynamic vibration reducer 100 are respectively expressed as follows.

However, M represents the mass of the mass body 103.

Here, the relationship between the stiffness k ₁ stiffness k ₂ and the first leaf spring 101 of the second plate spring 102 can be expressed by the following equation by using the coefficient alpha (7).

If the loss coefficient of the viscoelastic body 104 is assumed to be constant irrespective of temperature, the stiffness k _peak of the viscoelastic body 104 at which the damping ratio becomes maximum has a slope of 0 when the damping ratio ζ is differentiated by the stiffness k. It is k when. Therefore, the equation (9) is obtained from the equation (8).

By substituting the rigidity k _peak given by the equation (9) into the equations (6) and (4), the peak value ζ _{peak of the} damping ratio is obtained by the following equation (10).

Next, the configuration of the design support device that supports the design of the dynamic vibration reducer using the above theoretical formula will be described. FIG. 7 is a block diagram showing the configuration of the design support system according to the present embodiment. The design support device 300 is realized by the computer 400. As shown in FIG. 7, the computer 400 includes a main body 500, an input unit 600, and a display unit 700. The main body 500 includes a CPU 501, a ROM 502, a RAM 503, a reading device 504, a hard disk 505, an input/output interface 506, and an image output interface 507. The CPU 501, the ROM 502, the RAM 503, the reading device 504, the hard disk 505, the input/output interface 506, The image output interface 507 and the image output interface 507 are connected by a bus.

The CPU 501 executes the computer program loaded in the RAM 503. Then, the CPU 501 executes the design support program 510, which is a computer program for design support, so that the computer 400 functions as the design support apparatus 300.

The ROM 502 is configured by a mask ROM, PROM, EPROM, EEPROM or the like, and stores a computer program executed by the CPU 501, data used for the computer program, and the like.

The RAM 503 is configured by SRAM, DRAM, or the like. The RAM 503 is used to read the design support program 510 recorded in the hard disk 505. Further, the RAM 503 is used as a work area of the CPU 501 when the CPU 501 executes a computer program.

The hard disk 505 is installed with various computer programs to be executed by the CPU 501, such as an operating system and application programs, and data used for executing the computer programs. The design support program 510 is also installed on this hard disk 505.

Further, the hard disk 505 is provided with a viscoelastic body physical property database (viscoelastic body physical property DB) 520 that stores physical property data of the material of the viscoelastic body. The viscoelastic material property DB 520 stores Young's modulus, loss coefficient, and reference rigidity ratio data at each temperature for each frequency.

The input/output interface 506 is, for example, a serial interface such as USB, IEEE1394, or RS-232C, a parallel interface such as SCSI, IDE, or IEEE1284, and an analog interface such as a D/A converter or an A/D converter. It is configured. An input unit 600 including a keyboard and a mouse is connected to the input/output interface 506, and a user can input data to the computer 400 by using the input unit 600.

The image output interface 507 is connected to the display unit 700 composed of an LCD, a CRT or the like, and outputs a video signal according to the image data given from the CPU 501 to the display unit 700. The display unit 700 displays an image (screen) according to the input video signal.

Next, the operation of the design support device will be described. FIG. 8 is a flowchart showing the procedure of the method for designing the dynamic vibration reducer 100 according to the present embodiment. The design method of the dynamic vibration damper 100 according to the present embodiment includes an initial condition setting step S110, a damping ratio design step S130, and a natural frequency design step S150.

ここで、ｆ_０は制振対象物の固有振動数を示し、μは対象物２００と動吸振器１００との質量比を示している。 FIG. 9 is a flowchart showing the procedure of the initial condition setting step S110. In the initial condition setting step S110, the CPU 501 first determines the target natural frequency f _opt and the target damping ratio ζ _opt of the dynamic vibration reducer 100 according to the following equations (step S111).

Here, f ₀ represents the natural frequency of the vibration suppression target, and μ represents the mass ratio between the target 200 and the dynamic vibration reducer 100.

Next, the CPU 501 identifies the relationship between the reference stiffness ratio and the loss coefficient at the target natural frequency of the viscoelastic body 104 (step S112). FIG. 10 is a graph showing the relationship between the reference rigidity ratio and the loss coefficient. In FIG. 10, the horizontal axis represents the reference rigidity ratio, and the vertical axis represents the loss coefficient. As described above, the reference rigidity ratio and the loss coefficient of the viscoelastic body 104 each change depending on the temperature. Therefore, if the reference rigidity ratio changes, the loss coefficient changes accordingly. In the example shown in FIG. 10, a reference stiffness ratio-loss coefficient curve at a frequency of 0.5 Hz (shown by a broken line in the figure) and a reference stiffness ratio-loss coefficient curve at a frequency of 20 Hz (shown by a solid line in the figure) are shown. ing. In step S112, the COU 501 extracts the reference rigidity ratio and the loss coefficient corresponding to the target natural frequency from the viscoelastic body property DB 520, and stores these relationships in the hard disk 505. Here, the curve may be functionalized by a known curve fitting method such as the least square method. In step S112, the CPU 501 may display the specified relationship between the reference rigidity ratio and the loss coefficient on the display unit 700 as a graph.

Referring back to FIG. Next, the CPU 501 sets the representative loss coefficient η _α of the viscoelastic body 104 (step S113). The representative loss coefficient η _α can be an average value of the loss coefficients of the viscoelastic body 104 at the usage temperature. It should be noted that the representative loss coefficient η _α does not have to be the above average value and can be set to any value. However, while the actual loss coefficient changes with temperature, the representative loss coefficient η _α is approximated in the following processing, so the difference between the representative loss coefficient η _α and the loss coefficient at the actual operating temperature is If it is large, the approximation error due to calculation will be large. Therefore, it is preferable that the representative loss coefficient η _{α be} an average loss coefficient within the usage temperature range. Further, in step S113, the user may input a loss coefficient to be the representative loss coefficient η _α from the input unit 600, and the CPU 501 may set this as the representative loss coefficient η _α .

Next, the CPU 501 sets initial values of the parameters k ₁ , α, and k (step S114). In this process, the CPU 501 calculates k ₁ , α, k by using the expressions (3) to (10). When the process of step S114 ends, the initial condition setting step S110 ends.

FIG. 11 is a flowchart showing the procedure of the damping ratio designing step S130. In the damping ratio designing step S130, first, the CPU 501 changes the rigidity k of the viscoelastic body 104 to 1/10 to 10 times, and calculates the natural frequency and the damping ratio for each rigidity (step S131). In this processing, the CPU 501 uses equations (3) to (6) and uses the representative loss coefficient η _α .

Next, the CPU 501 generates a first graph showing the characteristic of the natural frequency and the characteristic of the damping ratio for the reference rigidity ratio calculated in step S131, and stores the first graph in the hard disk 505 (step S132). FIG. 12 is a diagram showing an example of the first graph. In FIG. 12, the horizontal axis represents the reference rigidity ratio, and the vertical axis represents the natural frequency and the damping ratio. In the example shown in FIG. 12, the peak of the damping ratio is located at the reference rigidity ratio “2”, and the peak value is about 11%. Further, the natural frequency at the reference rigidity ratio “1” is about 18 Hz. However, the calculation result shown in FIG. 12 is obtained by approximating the loss coefficient by a constant representative loss coefficient η _α and includes an error. Note that in the process of step S132, the CPU 505 may cause the display unit 700 to display the graph of generation 1.

Referring back to FIG. Next, the CPU 501 determines the second graph showing the relationship between the rigidity and the damping ratio when the loss coefficient of the viscoelastic body is a loss coefficient that changes according to temperature (step S133). This processing will be described in detail. FIG. 13 is a diagram for explaining the determination process of the second graph. The CPU 501 reads the relationship between the reference stiffness ratio and the loss coefficient at the target natural frequency from the hard disk 505, divides each loss coefficient by the representative loss coefficient, and calculates the ratio between the loss coefficient and the representative loss coefficient (hereinafter, “representative coefficient”). Calculated as η/η _α . Hereinafter, a graph showing the relationship between the rigidity ratio and the representative loss coefficient ratio will be referred to as a "representative loss coefficient ratio graph". The CPU 501 aligns the horizontal axis of the representative loss coefficient graph with the horizontal axis of the first graph at a predetermined position, and multiplies each damping ratio of the first graph by each representative loss coefficient ratio of the representative loss coefficient graph. .. As a result, the CPU 501 determines the second graph.

ここで、粘弾性体１０４の剛性ｋは、第２板バネ１０２の剛性ｋ_２に対して十分に小さいため、式（１３）の分母の第１項及び第２項に含まれるｋ／ｋ_２は０に近い値となり、当該第１項及び第２項を実質的に無視できる。したがって、式（１３）における分母の第１項及び第２項に含まれるηの影響は軽減され、η_ａｌｌは粘弾性体１０４の損失係数に概ね比例する。 The loss coefficient η _all of the designed dynamic vibration absorber 100 can be expressed by the following equation from the equation (4).

Here, since the rigidity k of the viscoelastic body 104 is sufficiently smaller than the rigidity k ₂ of the second leaf spring 102, k/k ₂ included in the first and second terms of the denominator of Expression (13). Becomes a value close to 0, and the first term and the second term can be substantially ignored. Therefore, the influence of η contained in the first and second terms of the denominator in Expression (13) is reduced, and η _all is approximately proportional to the loss coefficient of the viscoelastic body 104.

Therefore, by multiplying the typical loss coefficient ratio η/η _α by the damping ratio ζ calculated using the typical loss coefficient η _α , the damping ratio ζ′ in which the influence of the typical loss coefficient is removed can be calculated (equation ( 14)). That is, the attenuation ratio shown in the second graph takes into consideration the loss coefficient η that changes with temperature.

Referring back to FIG. The CPU 501 determines whether or not the reference rigidity ratio at the peak of the second graph and the reference rigidity ratio at the reference temperature match (step S134). FIG. 14 is a diagram showing an example of the second graph. In the example shown in FIG. 14, the reference rigidity ratio at the peak is about 3.4. In step S134, it is determined whether the temperature at this peak matches the reference temperature. Specifically, if the temperature at the peak is within the allowable range around the reference temperature, it is determined that the temperature matches the reference temperature, and if it is outside the allowable range, it is determined that the temperature does not match the reference temperature.

上式（１５）のβを調整することが、代表損失係数グラフの横軸をずらすことに相当する。 The processes of steps S133 and S134 will be described more specifically. Here, the reference spring rigidity of the viscoelastic body at the reference temperature and the reference rigidity is k _base , the rigidity ratio regarding the shape change is γ _f , and the rigidity ratio regarding the temperature change is γ _t . The first graph shows the change in the rigidity ratio with respect to the change in shape, which is defined as ζ ₀ (γ _f ). On the other hand, the representative loss coefficient graph shows changes in the reference rigidity ratio with respect to changes in temperature (see FIG. 13). Since γ _f and γ _t can be changed independently of each other, they can be expressed by the following equation.

Adjusting β in the above equation (15) corresponds to shifting the horizontal axis of the representative loss coefficient graph.

このとき、式（１５）から次式（１７）が導かれる。

The loss coefficient at the rigidity ratio for each temperature is η(γ _t ), and the curve of the typical loss coefficient ratio graph is defined by the following expression (16).

At this time, the following equation (17) is derived from the equation (15).

ここで、次式（１９）が成立するγ_ｆの値をγ_{ｆｐｅａｋ}とする。

このγ_{ｆｐｅａｋ}が次式を満たせば、基準温度の際に修正減衰比ζ_ｎがピークであることを示す。なお、実際のステップＳ１３４の処理では、厳密にγ_{ｆｐｅａｋ}がβに一致することを求めておらず、βを中心とした許容範囲内であればβに一致したものとして取り扱う。 The curve (corrected damping ratio) ζ _n (γ _f ) of the second graph is expressed by the following equation (18).

Here, the value of γ _f for which the following equation (19) is satisfied is γ _fpeak .

If this γ _fpeak satisfies the following equation, it indicates that the modified damping ratio ζ _n has a peak at the reference temperature. In the actual process of step S134, it is not strictly required that γ _fpeak is coincident with β, and it is treated as coincident with β if it is within the allowable range around β.

In step S134, if the reference rigidity ratio at the peak of the second graph does not match the reference temperature, that is, if γ _fpeak does not match β (NO in step S134), the CPU 501 _proceeds to step S133. After returning, the positions of the horizontal axis of the first graph and the horizontal axis of the representative loss coefficient ratio graph are different from those of the previous time, the first graph and the representative loss coefficient ratio graph are multiplied, and the second graph is determined again. For example, in determining the second graph for the first time, the respective horizontal axes are aligned so that the reference rigidity ratio “1” of the first graph and the reference rigidity ratio “1” of the representative loss coefficient ratio match. In the second determination of the second graph, the reference rigidity ratio “1” of the first graph and the reference rigidity ratio “1.1” of the representative loss coefficient ratio are matched so that the horizontal axis of each horizontal axis matches. Alignment is done. Since the rigidity k of the viscoelastic body 104 can be easily changed by changing the shape of the viscoelastic body 104, the reference rigidity can be set arbitrarily. Therefore, the position of the horizontal axis can be shifted as described above.

Referring back to FIG. When the reference rigidity ratio at the peak of the second graph and the reference temperature match, that is, when γ _fpeak matches β (YES in step S134), the CPU 501 sets the peak damping ratio to the target damping ratio. It is determined whether or not it is within the base reference range (step S135). The reference range can be a range centered on the target damping ratio or a range in which the target damping ratio is the lower limit and a value larger than the target damping ratio by a predetermined position is the upper limit.

この式（２０）は次式（２１）のようにα_ｏｐｔの式として変形できる。

これにより、ＣＰＵ５０１は係数α_ｏｐｔを算出し、これを新たな係数αとする。次のステップＳ１３１の処理では、新たな係数αを用いて計算が行われる。しかし、損失係数ηが一定の代表損失係数η_αとするという近似が含まれているため、新たな係数αを使用したとしても必ずしも減衰比のピーク値ζ_ｐｅａｋが目標減衰比ζ_ｏｐｔに一致するとは限らない。このため、ステップＳ１３１〜Ｓ１３６を繰り返し実行することで、最適な係数αが求まり、ζ_ｐｅａｋがζ_ｏｐｔに近づく。 When the damping ratio at the peak is out of the reference range (NO in step S135), CPU 501 adjusts coefficient α based on the difference between the target damping ratio and the damping ratio at the peak (step S136), and returns the process to step S131. Here, the process of step S136 will be described in detail. The coefficient α and the peak value ζ _peak of the damping ratio are simply expressed by Expression (10) when the loss coefficient η of the viscoelastic body 104 is set to a constant representative loss coefficient η _α . The CPU 501 calculates a coefficient α _opt that satisfies the target damping ratio ζ _opt based on this equation. Assuming that the coefficient α used in the previous calculation is α ₀ and the damping ratio ζ at that time is ζ ₀ , it can be arranged by the following equation.

This equation (20) can be transformed into an equation of α _opt as in the following equation (21).

Thereby, the CPU 501 calculates the coefficient α _opt and sets it as a new coefficient α. In the process of the next step S131, the calculation is performed using the new coefficient α. However, since the approximation that the loss coefficient η is the constant loss coefficient η _α is included, even if the new coefficient α is used, the peak value ζ _{peak of the} damping ratio does not always match the target damping ratio ζ _opt. Not necessarily. Therefore, by repeatedly executing steps S131 to S136, the optimum coefficient α is obtained, and ζ _peak approaches ζ _opt .

The adjustment formula for α is not limited to the above formula (21). By using the following equations (22) and (23), which are simpler than the equation (21), it is possible to bring ζ _peak closer to ζ _opt by repeatedly executing steps S131 to S136. In particular, using Expression (23), it is possible to relatively quickly converge ζ _peak to ζ _opt .

FIG. 15 is a diagram for explaining the adjustment of the peak value ζ _peak of the damping ratio. In this figure, the target damping ratio ζ _opt is set to 15%. In the graph on the upper side of the figure, ζ _peak is about 13, which is _outside the reference range based on the target damping ratio ζ _opt . Processing of steps S131~S136 by repeating, zeta _peak is adjusted, as in the bottom graph in FIG, zeta _peak is adjusted to about 15%.

Referring back to FIG. If the damping ratio at the peak is within the reference range (YES in step S135), the CPU 501 multiplies the reference stiffness k of the viscoelastic body 104 by the value of the reference synthesis ratio at the peak of the damping ratio, and the peak of the damping ratio becomes the reference. The rigidity ratio is adjusted so that it is located at "1" (step S137). This processing will be described in detail. FIG. 16 is a diagram for explaining the adjustment of the reference rigidity ratio at the peak of the damping ratio. In the upper graph in the figure, the reference rigidity ratio at the peak of the damping ratio is 5. In this case, the CPU 501 multiplies the reference rigidity k of the viscoelastic body by 5. As a result, the curve of the damping ratio shifts to the left so that the reference rigidity ratio becomes 1 at the peak of the damping ratio, as shown in the lower graph in the figure. The reference rigidity can be easily adjusted by changing the shape of the viscoelastic body 104. For example, when the reference rigidity is multiplied by 5, the thickness d of the viscoelastic body 104 in Expression (2) may be multiplied by 1/5 or the cross-sectional area A may be multiplied by 5. When the processing of step S137 as described above is finished, the damping ratio designing step S130 is finished.

FIG. 17 is a flowchart showing the procedure of the natural frequency designing step S150. In the natural frequency design step S150, first, the CPU 501 adjusts the natural frequency at the reference rigidity ratio "1" so as to match the target natural frequency (step S151). This processing will be described in detail. FIG. 18 is a diagram for explaining the adjustment of the natural frequency. Here, the target natural frequency is 20 Hz. In the graph on the upper side of the figure, the natural frequency at the reference rigidity ratio "1" is 25 Hz. The CPU 501 multiplies all the rigidity k ₁ , k ₂ , k of the element model by (20/25) ² (=0.64) in order to adjust the natural frequency 25 Hz to the target natural frequency 20 Hz. If all the rigidity is multiplied by 0.64, it will be 0.64 ³ times for all terms in Eq. (4). As a result, the denominator and the numerator will be 0.64 ³ times, respectively, and thus the loss will be reduced. The coefficient η _all does not change. Therefore, the natural frequency can be changed without changing the damping ratio by multiplying all the rigidity by the same value. As a result of this adjustment, as shown in the lower graph in the figure, the natural frequency at the reference rigidity ratio "1" matches the target natural frequency.

Referring back to FIG. Next, the CPU 501 determines the parameters t ₁ , t ₂ , b, L, A and d so as to satisfy the stiffnesses k ₁ , k ₂ and k determined as described above (step S152). With the above, the natural frequency designing step S150 is completed, and all the steps of the method of designing the dynamic vibration reducer 100 are completed.

(Embodiment 2)
A method of designing the dynamic vibration reducer according to the present embodiment will be described. In the dynamic vibration absorber design method according to the present embodiment, the temperature characteristics of the damping ratio and the natural frequency of the dynamic vibration absorber are determined using the finite element method structural analysis. Since the configurations of the dynamic vibration reducer and the design support device according to the present embodiment are the same as the configurations of the dynamic vibration absorber 100 and the design support device 300 described in the first embodiment, the same components are the same. The reference numerals are given and the description thereof is omitted.

FIG. 19 is a flowchart showing the procedure of the method of designing the dynamic vibration reducer 100 according to the present embodiment. The design method of the dynamic vibration reducer 100 according to the present embodiment includes an initial condition setting step S210, a damping ratio designing step S230, and a natural frequency designing step S250.

FIG. 20 is a flowchart showing the procedure of the initial condition setting step S210. The processing of steps S211 to S214 is the same as the processing of steps S111 to S114 described in the first embodiment, and thus the description thereof is omitted.

After step S214, the CPU 501 executes the FEM modeling step S220. In the FEM modeling step S220, the CPU 501 first determines the parameters L, b, t ₁ and t ₂ from the rigidity k ₁ and the coefficient α (step S221). For example, if the values of the parameters L and b are determined in advance, t ₁ and t ₂ may be determined using the equation (1).

Next, the CPU 501 determines the cross-sectional area A and the thickness d of the viscoelastic body 104 based on the rigidity k (step S222). Subsequently, the CPU 501 creates an FEM analysis model using the first leaf spring 101 and the second leaf spring 102 as shell elements and the viscoelastic body 104 as a solid element (step S223). In the process of step S223, the physical properties of the material (Young's modulus, Poisson's ratio, density, etc.), the length L, the width b, and the thicknesses t ₁ and t ₂ of the leaf spring are given to the shell element. In addition, a Young's modulus or a shear elastic coefficient is given to the solid element as a rigidity characteristic of the viscoelastic body 104, and a loss coefficient is given as a damping characteristic of the viscoelastic body 104. FIG. 21 is a diagram showing an example of the created FEM model. In FIG. 21, reference numeral 800 indicates a FEM model, 801 indicates a shell element of the first leaf spring 101, 802 indicates a shell element of the second leaf spring 102, and 804 indicates a solid element. Regarding the connection between the shell elements 801, 802 and the solid element 804, it is preferable to offset by half the plate thickness of the shell elements 801, 802 so that they will be connected at the opposing surfaces of the shell elements 801, 802, but without offsetting. Joining the solid elements at the nodal point at the center of the thickness of the shell elements 801, 802 results in less error. The thickness d of the viscoelastic body is the height of the solid element 804, that is, the distance between the nodes of the shell elements 801 and 802. Further, the solid element 804 is divided into at least two in the thickness direction (in FIG. 21, it is divided into five).

Thus, the FEM modeling step S220 ends, and the initial condition setting step S210 ends.

FIG. 22 is a flowchart showing the procedure of the damping ratio designing step S230. In the damping ratio designing step S230, first, the CPU 501 changes the Young's modulus or the shear elastic coefficient given as the rigidity characteristic of the viscoelastic body 104 to 1/10 to 10 times, and the Young's modulus or the shear elastic coefficient is calculated by the FEM model. Then, the natural frequency and the damping ratio are calculated by the complex eigenvalue analysis using the FEM model (step S231). In this processing, the CPU 501 uses the representative loss coefficient η _α in the FEM structural analysis.

The processes of steps S232 to S236 are the same as the processes of steps S132 to S136 described in the first embodiment, and thus the description thereof will be omitted.

After adjusting the coefficient α in step S236, the CPU 501 updates the thickness t ₂ of the shell element 802 according to α (step S237). When the process of step S237 ends, the CPU 501 returns the process to step S231. By repeatedly executing the processing of steps S231 to S237, ζ _peak approaches ζ _opt .

Further, since the process of step S238 is similar to the process of step S137 described in the first embodiment, the description thereof will be omitted. With the above, the damping ratio designing step S230 is completed.

Since the natural frequency designing step S250 is the same as the natural frequency designing step S150 described in the first embodiment, the description thereof will be omitted.

As described above, the dynamic vibration reducer 100 is designed using the FEM structural analysis. In the calculation by the theoretical formula, the error may become large due to the influence of the structure of the dynamic vibration absorber, boundary conditions, shear deformation of the viscoelastic body, and the like. By using the FEM structural analysis as described above, it is possible to design with higher accuracy.

(Embodiment 3)
In the present embodiment, a dynamic vibration reducer whose spring rigidity can be adjusted by adjusting a supporting position and a design method thereof will be described. FIG. 23 is a schematic diagram showing the configuration of the dynamic vibration reducer according to the present embodiment. In the dynamic vibration reducer 300, a support portion 301 is provided on the first leaf spring 101 and the second leaf spring 102.

The support part 301 includes a support 311 arranged between the first plate spring 101 and the second plate spring 102 in parallel with the first plate spring 101 and the second plate spring 102, and first and second support members 315a and 315b attached to the support 311. And have. 24 is a perspective view showing the configuration of the support portion 301, and FIG. 25 is a perspective view showing the configuration of the first support member 315a. As shown in FIG. 24, the support body 311 has two flanges 313 vertically arranged in parallel to each other and one horizontally arranged web 312 connecting the two flanges 313, and the cross-sectional shape thereof is H. I am in a shape. A plurality of screw holes 314 are provided in the longitudinal direction on both the portion of each flange 313 closer to the first leaf spring 101 and the portion closer to the second leaf spring 102 than the web 312. In the two flanges 313, these screw holes 314 are provided so as to face each other. Further, on both upper and lower sides of the support 311, there are formed recesses which are surrounded by the two flanges 313 and the web 312 and are long in one direction. The first support member 315a is arranged in the upper recess, and the second support member 315b is arranged in the lower recess. The first and second support members 315a and 315b have the same shape, and each have a rectangular parallelepiped base 316 and a protrusion 317 protruding in a triangular shape from one surface of the base 316 (see FIG. 25). Each of the first and second support members 315a and 315b is inserted into the above-mentioned recess with the base 316 facing the web 312 (see FIG. 24). When the first support member 315a is arranged in the upper recess, the protrusion 317 projects from the upper end of the support 311. Further, from the lower end of the support body 311, the protruding portion 317 of the second support member 315b arranged in the lower concave portion projects from the lower end of the support body 311. As shown in FIG. 25, the protrusion 317 has a triangular prism shape that is long in the width direction of the support 311. The tip of the protrusion 317 is one apex 318 of a triangular prism, and has a taper shape that becomes thinner toward the tip. The first leaf spring 101 contacts the top 318 of the protrusion 317 of the first support member 315a, and the second leaf spring 102 contacts the top 318 of the protrusion 317 of the second support member 315b (see FIG. 23). ). Since the protruding portion 317 has a triangular prism shape, the first and second leaf springs 101 and 102 and the protruding portion 317 are in contact with each other at a linear portion extending in the width direction.

Further, even if the first plate spring 101 vibrates, the apex 318 of the first support member 315a is formed so that the first plate spring 101 and the apex 318 of the first support member 315a do not separate from each other. It is pressed against 101. Specifically, one surface of the base portion 316 of each of the first and second support members 315a and 315b on the support body 311 side (that is, one surface on the opposite side of the top portion 318) is a bottom portion 319 that is in contact with the support body 311. ing. The distance between the top 318 and the bottom 319 of the first support member 315a is slightly larger than the distance between the first leaf spring 101 and the web 312 when the first support member 315a is not arranged on the support 311. The dimensions are adjusted so that As a result, the top 318 of the first support member 315a is pressed against the first plate spring 101, and the first plate spring 101 is prevented from separating from the first support member 315a even if vibration occurs. The same applies to the positional relationship between the second leaf spring 102 and the second support member 315b.

The user screws the bolt 320 into the screw hole 314 provided in the flange 313, and brings the tip of the bolt 320 into contact with the base portions 316 of the first and second support members 315a and 315b. Each of the support members 315a and 315b is fixed to the support 311. As a result, the first and second plate springs 101 and 102 are supported by the first and second support members 315a and 315b fixed to the support 311.

The support 311 is a rigid body made of metal such as iron, and the first and second support members 315a and 315b are also rigid bodies made of metal. For this reason, the first leaf spring 101 is supported by the first support members 315a on both sides of the column 105 to form a pin support structure at these support positions. Similarly, the second leaf spring 102 also has a pin support structure by the second support members 315b on both sides of the column 105.

但し、ｉ＝１，２を、ｘ_１は第１板バネ１０１の支柱１０５から第１支持部材３１５ａによる支持位置までの距離を、ｙ_１は第１板バネ１０１の第１支持部材３１５ａによる支持位置から質量体Ｍの重心位置までの距離を、ｘ_２は第２板バネ１０２の支柱１０５から第２支持部材３１５ｂによる支持位置までの距離を、ｙ_２は第２板バネ１０２の第２支持部材３１５ｂによる支持位置から質量体Ｍの重心位置までの距離を、それぞれ示している。 The positions of the first and second support members 315a and 315b can be freely changed in the recess surrounded by the flange 313 and the web 312, respectively. Further, by mounting the bolt 320 in the screw hole 314 at the position where the first and second support members 315a and 315b are arranged, each of the first and second support members 315a and 315b can be fixed at that position. In this way, the spring rigidity of the first and second leaf springs 101 and 102 can be adjusted by changing the support positions of the first and second support members 315a and 315b. The stiffnesses k ₁ and k ₂ of the first and second plate springs 101 and 102 in the dynamic vibration reducer 300 according to the present embodiment are given by the following equation (24).

However, i=1, 2, x ₁ is the distance from the column 105 of the first leaf spring 101 to the support position by the first support member 315a, and y ₁ is the support by the first support member 315a of the first leaf spring 101. The distance from the position to the center of gravity of the mass body M, x ₂ is the distance from the column 105 of the second leaf spring 102 to the support position by the second support member 315b, and y ₂ is the second support of the second leaf spring 102 The distance from the support position of the member 315b to the center of gravity of the mass body M is shown.

The configuration of the dynamic vibration absorber design support apparatus and the dynamic vibration absorber design method according to the present embodiment are the same as the configuration of the dynamic vibration absorber design support apparatus and the dynamic vibration absorber design method according to the first or second embodiment. Therefore, the description thereof will be omitted. In the present embodiment, similar to the method of designing the dynamic vibration reducer according to the first or second embodiment, the optimum stiffnesses k ₁ and k ₂ are determined so that they match the obtained stiffnesses k ₁ and k _2. First, the support positions of the first and second plate springs 101 and 102 by the first and second support members 315a and 315b are determined. Accordingly, when it is desired to finely adjust the rigidity of the first and second leaf springs 101 and 102 that have already been subjected to the thickness adjustment processing, the first and second support members 315a and 315b are slid in the recesses to change the support positions. Only by adjusting, the rigidity of the first and second leaf springs 101, 102 can be easily adjusted to the optimum value without replacing the first or second leaf spring 101, 102 of the dynamic vibration absorber. Therefore, when fine adjustment of the rigidity of the first and second leaf springs 101 and 102 is required, there is no need to remanufacture the first and second leaf springs 101 and 102, and the first and second support members The rigidity can be easily finely adjusted only by adjusting the support positions of 315a and 315b.

(Other embodiments)
In the first to third embodiments described above, in the relationship between the temperature and the damping ratio of the dynamic vibration reducer 100, the rigidity k ₁ , k ₂ , k is set so that the peak of the damping ratio matches the reference temperature. However, it is not limited to this. The rigidity k ₁ , k ₂ , k may be set so that the peak is located at a temperature other than the reference temperature as long as it is within the operating temperature range.

Further, in the above-described first to third embodiments, the configuration in which all the processes of the design support program 510 are executed by the single computer 400 has been described, but the present invention is not limited to this, and design support is possible. It is also possible to provide a distributed system in which the same processing as the program 510 is distributed and executed by a plurality of devices (computers).

Further, in the above-described third embodiment, one support body 311 is arranged between the first and second leaf springs 101 and 102, and the first and second support members 315a arranged on both upper and lower sides of this support body 311. , 315b have been described to support each of the first and second leaf springs 101 and 102, but the present invention is not limited to this. A support is provided separately for each of the first and second leaf springs 101 and 102, and the first support member 315a is attached to one of the supports to support the first leaf spring 101, and the other support has the first support member 315a. The second support member 315b may be attached to support the second plate spring 102. However, the configuration of the third embodiment is preferable because the number of parts can be reduced, and the configuration is simple and space-saving.

Further, in the third embodiment described above, the configuration (pin support structure) in which the first and second support members 315a and 315b are pressed against the first and second leaf springs 101 and 102 to support is described, but the present invention is not limited to this. It is not something that is done. The first and second plate springs 101 and 102 may be supported by a cantilever structure by fixing some parts of the first and second plate springs 101 and 102 to a support by bolts or the like. It is possible. However, in order to fix the first and second leaf springs 101 and 102, it is necessary to sandwich each of the first and second leaf springs 101 and 102 from above and below with bolts and nuts, etc. The configuration of form 3 is preferable because it can reduce the number of parts, is simple and saves space.

INDUSTRIAL APPLICABILITY The dynamic vibration reducer and the design method thereof according to the present invention are useful as a dynamic vibration reducer that suppresses resonance phenomenon in an object and a design method thereof.

100 Dynamic Vibration Absorber 101 First Leaf Spring 102 Second Leaf Spring 103 Mass Body 104 Viscoelastic Body 200 Object 300 Design Support Device 400 Computer 501 CPU
505 hard disk 510 design support program 600 input section 700 display section 801 and 802 shell element 804 solid element

Claims (16)

A dynamic vibration absorber whose damping ratio changes according to temperature changes,
A pillar fixed to the object,
A first leaf spring fixed to the column at the center in the longitudinal direction,
A second leaf spring fixed to the column at the center in the longitudinal direction and arranged in parallel with the first leaf spring and having a rigidity higher than that of the first leaf spring;
A mass body attached to the first leaf spring;
A viscoelastic body that connects the first and second leaf springs and decreases in rigidity as the temperature rises,
The amount of deformation of each of the first and second leaf springs and the viscoelastic body when vibration occurs in the object changes according to the temperature change, and the damping ratio changes with a peak with respect to the temperature change. Is configured as
In the relationship between the temperature and the damping ratio, the rigidity of the first and second leaf springs and the viscoelastic body are set so that the peak of the damping ratio is located within the operating temperature range.
Dynamic vibration absorber. In the relationship between the temperature and the damping ratio, the rigidity of the first and second leaf springs and the viscoelastic body are set so that the peaks coincide with the reference temperature within the operating temperature range.
The dynamic vibration reducer according to claim 1. In the relationship between the temperature and the damping ratio, the damping ratio at the reference temperature is equal to or higher than the target damping ratio, and the damping ratio at the upper limit or the lower limit of the operating temperature range is equal to or lower than the target damping ratio. 2 The stiffness of leaf spring and viscoelastic body is set,
The dynamic vibration reducer according to claim 2. In the relationship between temperature and natural frequency, the rigidity of the first and second leaf springs and the viscoelastic body is set so that the natural frequency at the reference temperature matches the target natural frequency.
The dynamic vibration reducer according to any one of claims 1 to 3. The first and second leaf springs are supported so that their positions can be adjusted in the longitudinal direction, and the rigidity of the first and second leaf springs is adjusted by adjusting the support positions of the first and second leaf springs. Further comprising first and second support members,
The dynamic vibration reducer according to any one of claims 1 to 4. Further comprising a support disposed between the first and second leaf springs,
Each of the first and second support members is arranged in the support body so as to be positionally adjustable in the longitudinal direction,
The dynamic vibration reducer according to claim 5. Each of the first and second support members is formed so as to become thinner toward each of the first and second leaf springs, and has a top portion at the tip end that abuts against the first and second leaf springs, It has a bottom portion that abuts the support on the opposite side of the top portion,
The distance between the top portion and the bottom portion of the first support member is equal to that of the first leaf spring and the first support member of the support body in a state where the first support member is not arranged on the support body. It is set larger than the distance between the bottom surface and the contact surface,
The distance between the top portion and the bottom portion of the second support member is equal to that of the second leaf spring of the support and the second support member of the support in a state where the second support member is not arranged on the support. It is set to be larger than the distance between the contact surface and the bottom.
The dynamic vibration reducer according to claim 6. A pillar fixed to the object, a first leaf spring fixed to the pillar at the center in the longitudinal direction, and a first leaf spring fixed to the pillar at the center in the longitudinal direction and arranged in parallel with the first leaf spring. A method for designing a dynamic vibration absorber, comprising: a second leaf spring having higher rigidity than a leaf spring; a mass body attached to the first leaf spring; and a viscoelastic body connecting the first and second leaf springs. There
Setting a characteristic of the damping ratio of the dynamic vibration absorber that changes with temperature,
In the characteristic of the damping ratio, a step of determining whether or not the peak of the damping ratio is located within the operating temperature range,
Resetting the characteristic of the damping ratio so as to change the position of the peak with respect to temperature when the peak of the damping ratio is not located within the operating temperature range.
Dynamic vibration absorber design method. In the step of setting the characteristic of the damping ratio, with respect to the damping ratio for each rigidity when the rigidity of the viscoelastic body is changed in the case where the loss coefficient of the viscoelastic body is a constant representative loss coefficient, The loss coefficient of the viscoelastic body is changed according to temperature by multiplying the ratio of the loss coefficient of the viscoelastic body and the representative loss coefficient in each stiffness when the rigidity of the viscoelastic body is changed for each stiffness. Determining the characteristic of the damping ratio, which is the relationship between the rigidity and the damping ratio when the loss coefficient is
In the step of resetting the characteristic of the damping ratio, with respect to the damping ratio for each stiffness when the rigidity of the viscoelastic body is changed when the loss coefficient of the viscoelastic body is set to a constant representative loss coefficient, The ratio of the loss coefficient of the viscoelastic body in each stiffness and the representative loss factor is multiplied by changing the stiffness when determining the characteristic of the damping ratio, thereby redetermining the characteristic of the damping ratio,
The method for designing a dynamic vibration reducer according to claim 8. In the determining step, in the characteristic of the damping ratio, it is determined whether or not the peak matches a reference temperature in the operating temperature range,
A method for designing a dynamic vibration reducer according to claim 8. In the characteristic of the damping ratio, a step of determining whether the damping ratio at the peak is within a predetermined range based on the target damping ratio,
When the damping ratio at the peak is not within the predetermined range, the characteristic of the damping ratio is re-adjusted by adjusting the parameter that defines the relationship between the rigidity of the first leaf spring and the rigidity of the second leaf spring. Further comprising a step of setting,
A method for designing a dynamic vibration reducer according to claim 8. In the characteristic of the damping ratio, a step of determining whether the damping ratio at the peak is within a predetermined range based on the target damping ratio,
Further adjusting the thickness of the second leaf spring when the damping ratio at the peak is not within the predetermined range, thereby resetting the characteristic of the damping ratio.
A method for designing a dynamic vibration reducer according to claim 8. After setting the characteristics of the damping ratio, each of the first and second leaf springs and the viscoelastic body so that the natural frequency of the dynamic vibration absorber at the peak of the damping ratio matches the target natural frequency. Further comprising adjusting the characteristic of the natural frequency that varies with temperature by determining the stiffness of
A method for designing a dynamic vibration reducer according to claim 8. The dynamic vibration reducer supports each of the first and second plate springs so as to be positionally adjustable in the longitudinal direction, and adjusts the support positions of the first and second plate springs to adjust the first and second plate springs. Further comprising first and second support parts for adjusting the rigidity of the spring,
The method further includes the step of adjusting the support positions of the first and second support parts so that the rigidity of each of the first and second leaf springs matches the determined rigidity of each of the first and second leaf springs. Have,
The method for designing a dynamic vibration reducer according to claim 13. The first and second leaf springs are modeled as shell elements, and the viscoelastic body is modeled as a solid element. Young's modulus or shear coefficient is given as the rigidity characteristic of the solid element, and loss coefficient is given as the damping characteristic of the solid element. And further determining the initial characteristics of the damping ratio and the natural frequency by the finite element method,
A method for designing a dynamic vibration reducer according to any one of claims 8 to 14. In the step of setting the characteristics of the damping ratio, the Young's modulus or the shear coefficient is changed to change the rigidity of the viscoelastic body, and the damping ratio at each rigidity is obtained, thereby setting the characteristics of the damping ratio.
The method for designing a dynamic vibration reducer according to claim 15.

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