JP7764751B2 - Heat transfer calculation method between mold and green tire - Google Patents

Description

This disclosure relates to a method for calculating heat transfer between a mold and a green tire.

Patent Document 1 listed below describes a method for calculating heat transfer between a mold and a green tire. In this method, a computer is used to calculate heat transfer at the contact surface between a green tire model and a mold model. This green tire model includes a second portion that fills the grooves, and the thermal conductivity of the elements of this second portion is defined to be greater than the thermal conductivity of the corresponding region of the green tire.

Patent No. 6871528

In the above method, to set the thermal conductivity of the second portion, simulations are repeatedly performed using a raw tire model that includes the second portion and a second tire model that does not include the second portion. For this reason, the method of Patent Document 1 required a long calculation time.

This disclosure was devised in light of the above-mentioned circumstances, and its primary objective is to provide a method that can quickly calculate heat transfer between a mold and a green tire.

The present disclosure relates to a method for using a computer to perform heat transfer calculations between a mold having protrusions for forming groove-like portions consisting of grooves or sipes, and a raw tire having tread rubber that is in contact with the mold and in which the groove-like portions are formed by the protrusions, the method comprising the steps of: defining, on the computer, a mold model in which the mold is discretized into multiple elements; discretizing the raw tire into multiple elements and defining, on the computer, a raw tire model that includes at least a tread rubber model; and assigning predetermined thermal conductivities to the elements of the tread rubber model. a step of defining a contact surface between the tread rubber model and the mold model based on the thermal conductivity; and a step of calculating heat transfer at the contact surface between the tread rubber model and the mold model based on the thermal conductivity, wherein the mold model includes a first omitted portion in which at least a portion of the protrusion is omitted, and the tread rubber model includes a second omitted portion in which a groove-shaped portion corresponding to the first omitted portion is made a non-groove-shaped portion, and the step of defining the thermal conductivity includes a step of specifying the thermal conductivity of the tread rubber model based on the thermal conductivity of the protrusion and the thermal conductivity of the tread rubber.

By adopting the above steps, the disclosed method for calculating heat transfer between a mold and a raw tire makes it possible to calculate heat transfer between the mold and the raw tire in a short amount of time.

FIG. 1 is a perspective view showing a computer for executing the method for calculating heat transfer between a mold and a green tire according to the present embodiment. FIG. 1 is a cross-sectional view showing a tire to be evaluated. FIG. 2 is a partial cross-sectional view of a mold, a bladder, and a green tire during the vulcanization process. 4 is a cross-sectional view of the mold and green tire of FIG. 3 taken along line AA. 1 is a flowchart showing the processing steps of a method for calculating heat transfer between a mold and a raw tire according to the present embodiment. 1A and 1B are diagrams illustrating a mold model, a raw tire model, and a bladder model used in the heat transfer calculation method of the present embodiment. FIG. 7 is a cross-sectional view of the mold model and the raw tire model (tread rubber model) taken along the line B-B in FIG. 6. 10 is a flowchart illustrating an example of a processing procedure of a thermal conductivity defining step. 3 is a flowchart showing a processing procedure of a method for vulcanizing a raw tire according to the present embodiment. 1A is a graph showing the relationship between the temperature of the tread rubber and the vulcanization time for the examples and experimental examples, and FIG. 1B is a graph showing the relationship between the temperature at the outer end position of the outer belt and the vulcanization time for the examples and experimental examples. (a) is a graph showing the relationship between the temperature of the tread rubber and the vulcanization time for the comparative example and the experimental example, and (b) is a graph showing the relationship between the temperature at the outer end position of the outer belt and the vulcanization time for the comparative example and the experimental example.

Embodiments of the present disclosure will be described below with reference to the drawings. It should be understood that the drawings may contain exaggerated representations and representations that differ from the dimensional proportions of the actual structure in order to facilitate understanding of the contents of the disclosure. Furthermore, identical or common elements are designated by the same reference numerals throughout each embodiment, and redundant explanations will be omitted. Furthermore, the specific configurations shown in the embodiments and drawings are intended to aid in understanding the contents of the present disclosure, and the present disclosure is not limited to the specific configurations shown.

In the method for calculating heat transfer between a mold and a raw tire of this embodiment (hereinafter sometimes simply referred to as the "heat transfer calculation method"), heat transfer calculations between the mold and the raw tire are performed using a computer.

[computer]
1 is a perspective view showing a computer for executing the method for calculating heat transfer between a mold and a green tire according to this embodiment. The computer 1 according to this embodiment includes, for example, a main body 1a, a keyboard 1b, a mouse 1c, and a display device 1d. The main body 1a is provided with, for example, a central processing unit (CPU), ROM, work memory, a storage device such as a magnetic disk, and disk drive devices 1a1 and 1a2. The storage device also stores in advance software and the like for executing the heat transfer calculation method according to this embodiment.

[tire]
2 is a cross-sectional view showing a tire 2 to be evaluated. The tire 2 of this embodiment is configured as, for example, a pneumatic tire for a passenger car. However, the tire 2 is not limited to this form and may be configured as, for example, a pneumatic tire for heavy loads or a tire for a motorcycle. The tire 2 of this embodiment is configured to include a rubber member 3 and a fibrous member 4.

The rubber members 3 in this embodiment include, for example, tread rubber 3a, sidewall rubber 3b, clinch rubber 3c, bead apex rubber 3d, and inner liner rubber 3e. The tread rubber 3a is arranged radially outward of the outer belt 4c in the tread portion 2a. The sidewall rubber 3b is arranged axially outward of the carcass 4a in the sidewall portion 2b. The clinch rubber 3c is fixed radially inward of the sidewall rubber 3b. The bead apex rubber 3d extends radially outward from the bead core 5. The inner liner rubber 3e is arranged on the inner surface of the carcass 4a.

In this embodiment, the fibrous member 4 includes, for example, a carcass 4a, an inner belt 4b, and an outer belt 4c. The carcass 4a extends from the tread portion 2a through the sidewall portion 2b to the bead core 5 of the bead portion 2c. The inner belt 4b and the outer belt 4c are disposed radially outward of the carcass 4a and inside the tread rubber 3a.

In this embodiment, groove portions 6 are formed on the outer surface 2o of the tread rubber 3a (tread portion 2a). The groove portions 6 are configured as grooves 7 or sipes 8.

The grooves 7 in this embodiment include at least one circumferential groove 7A that extends continuously around the tire circumference in the tread portion 2a. As a result, the tread portion 2a in this embodiment is formed with multiple land portions 9 separated by the circumferential grooves 7A. Each land portion 9 in this embodiment is provided with at least one sipe 8, and in this embodiment, multiple sipes 8. Note that each land portion 9 may also be provided with multiple lateral grooves (not shown) that extend in a direction that intersects with the circumferential groove 7A.

[Vulcanization molding]
The tire (vulcanized tire) 2 of this embodiment is manufactured, according to convention, by vulcanizing and molding an unvulcanized tire (shown in FIG. 3) including an unvulcanized rubber member 3. Here, "unvulcanized" includes all states that have not yet reached complete vulcanization, and the so-called semi-vulcanized state is included in this "unvulcanized" state. FIG. 3 is a partial cross-sectional view of the mold 11, bladder 12, and green tire 2L during the vulcanization process. FIG. 4 is a cross-sectional view taken along the line A-A of the mold 11 and green tire 2L of FIG. 3.

The vulcanization process of this embodiment uses, for example, a mold 11 for shaping the outer surface 2o of the tire 2 (raw tire 2L) and a bladder 12 that expands within the cavity of the raw tire 2L set in the mold 11.

The mold 11 of this embodiment is configured to include, for example, a pair of sidewall molding dies 13, 13 having sidewall molding surfaces 13s, and a tread molding die 14 having a tread molding surface 14s. The tread molding die 14 is divided in the tire circumferential direction. By fitting these sidewall molding dies 13 and tread molding die 14 together, a molding surface 11s capable of molding the outer surface 2o of the tire 2 is formed. A heating means (not shown), such as an electric heater, is arranged in the mold 11.

The mold of this embodiment has protrusions 18. The protrusions 18 are used to form groove-like portions 6 consisting of grooves 7 or sipes 8 in the tread rubber 3a of the raw tire 2L. The protrusions 18 of this embodiment include first protrusions 18A for forming circumferential grooves 7A (grooves 7) and second protrusions 18B (blades in this example) for forming sipes 8.

In this embodiment, the bladder 12 is made of, for example, an expandable rubber-like elastic material. A high-pressure fluid (not shown) is supplied to the internal space 12s of the bladder 12 from, for example, a supply means (not shown). The high-pressure fluid may be, for example, a mixture of water vapor and at least one inert gas, such as nitrogen, or multiple inert gases. The temperature of the high-pressure fluid is set, for example, to approximately 140 to 220°C.

During the vulcanization process, the green tire 2L is heated and pressurized between the mold 11 and the bladder 12 to produce a vulcanized tire 2 (shown in Figure 2). The outer surface 2o of the tread rubber 3a of the green tire 2L comes into contact with the mold 11, and protrusions 18 on the mold 11 form groove-like portions 6 (in this example, circumferential grooves 7A and sipes 8).

During the vulcanization process, the protrusions 18 of the mold 11 penetrate into the portions of the raw tire 2L where the grooves 6 are formed, and as a result, heat from the mold 11 is more easily transferred to these portions than to portions where the grooves 6 are not formed, making the temperature more likely to rise. Therefore, when calculating heat transfer between the mold 11 and the raw tire 2L using a computer 1 (shown in Figure 1), it is important to consider the ease of heat transfer through the protrusions 18 of the mold 11 and the grooves 6 of the raw tire 2L.

[Method for calculating heat transfer between a mold and a raw tire (first embodiment)]
Next, the heat transfer calculation method of this embodiment will be described. Fig. 5 is a flowchart showing the processing steps of the heat transfer calculation method between the mold and the raw tire of this embodiment.

In the heat transfer calculation method of this embodiment, first, a mold model in which the mold 11 (shown in Figure 3) is discretized into multiple elements is defined in the computer 1 (shown in Figure 1) (step S1). Figure 6 is a diagram showing the mold model 21, raw tire model 32, and bladder model 22 used in the heat transfer calculation method of this embodiment. In Figure 6, the raw tire model 32 is colored to make it easy to distinguish from the mold model 21 and bladder model 22.

In step S1 of this embodiment, as shown in FIG. 6, based on the design data (e.g., CAD data) of the mold 11 (shown in FIG. 3), the mold 11 is discretized (modeled) into a plurality (a finite number) of elements F(i) (i = 1, 2, ...) that can be handled by numerical analysis. This results in a mold model 21. The mold model 21 has an internal space 21i formed therein for placing the raw tire model 32. The mold model 21 of this embodiment is set as a three-dimensional model. However, the mold model 21 may also be set as a two-dimensional model.

Numerical analysis methods that can be used include, for example, the finite element method, finite volume method, finite difference method, and boundary element method. In this embodiment, the finite element method is used. Each element F(i) can be, for example, a tetrahedral solid element. In the case of a two-dimensional model, quadrilateral elements can be used.

Each element F(i) has multiple nodes 34. Numerical data such as the element number, node number, node coordinate values, and material properties (rigidity, Young's modulus, thermal conductivity, density, specific heat, thermal expansion coefficient, etc.) of the mold 11 (shown in Figure 3) are defined for each element F(i). Such a mold model 21 can be easily set (modeled) using, for example, commercially available meshing software.

The mold model 21 of this embodiment includes a pair of first mold models 23, 23 that model a pair of sidewall molds 13, 13 (shown in FIG. 3), and a second mold model 24 that model a tread mold 14 (shown in FIG. 3). The first mold model 23 and the second mold model 24 are combined together to form a molding surface 21s for molding the outer surface 32o of the raw tire model 32.

In this embodiment, the mold model 21 defines a protrusion portion 28 that models the protrusion 18 (shown in Figure 3). The protrusion portion 28 models the first protrusion 18A that forms the circumferential groove 7A of the raw tire 2L shown in Figure 3. This protrusion portion 28 is defined on the molding surface 21s of the second molding mold model 24.

Figure 7 is a cross-sectional view taken along the line B-B of the mold model 21 and raw tire model 32 (tread rubber model 33) in Figure 6. In Figure 7, the mold model 21 and raw tire model 32 are shown exploded, and the elements F(i) and G(i) shown in Figure 6 are omitted.

The mold model 21 of this embodiment is defined to include a first omitted portion 31 in which at least a portion of the protrusion 18 (shown in FIG. 3) is omitted. The first omitted portion 31 of this embodiment is obtained by removing the second protrusion 18B for forming the sipe 8 of the raw tire 2L shown in FIG. 3. This first omitted portion 31 is defined on the molding surface 21s of the second molding mold model 24 (in this example, it is set to be a surface continuous with the molding surface 21s).

In this way, in step S1 of this embodiment, the mold model 21 can be defined in a simplified manner by using the first omitted portion 31, which is obtained by removing a portion of the protrusion 18 shown in Figure 3 (in this embodiment, the second protrusion 18B, which has a more complex shape than the first protrusion 18A). Therefore, in this embodiment, the mold model 21 can be defined in a short amount of time. The mold model 21 is stored in the computer 1 (shown in Figure 1).

[Define raw tire model (tread rubber model)]
Next, in the heat transfer calculation method of this embodiment, as shown in Fig. 6 , a raw tire model 32 (tread rubber model 33) in which the raw tire 2L (shown in Fig. 3) is discretized into a plurality of elements is defined in the computer 1 (shown in Fig. 1) (step S2). As long as the raw tire model 32 of this embodiment includes at least the tread rubber model 33, other models (for example, a sidewall rubber model 39, etc.) may be omitted. The raw tire model 32 of this embodiment includes not only the tread rubber model 33 but also other models.

In this embodiment, for example, based on design data (e.g., CAD data) for the mold 11 (shown in FIG. 3), the raw tire 2L (shown in FIG. 3) is discretized (modeled) into a plurality (a finite number) of elements G(i) (i = 1, 2, ...) that can be handled by numerical analysis. This sets up a raw tire model 32 that includes a tread rubber model 33.

In this embodiment, the raw tire model 32 is set as a three-dimensional model. Note that if the mold model 21 is defined as a two-dimensional model, the raw tire model 32 may also be set as a two-dimensional model.

Element G(i) is the same as element F(i) of the mold model 21. Each element G(i) is composed of multiple nodes 37. Numerical data such as the element number, node number, node coordinate values, and material properties (rigidity, Young's modulus, thermal conductivity, density, specific heat, thermal expansion coefficient, etc.) of the raw tire 2L (shown in Figure 3) are defined for each element F(i).

The raw tire model 32 of this embodiment includes a tread rubber model 33 that models the tread rubber 3a (shown in FIG. 3) of the raw tire 2L. The tread rubber model 33 of this embodiment defines a groove portion 35 that models the groove portion 6 (shown in FIG. 3) of the raw tire 2L. The groove portion 35 of this embodiment models the circumferential groove 7A (shown in FIG. 3).

As shown in FIG. 7 , the tread rubber model 33 of this embodiment includes a second omitted portion 36 in which the groove portion 6 corresponding to the first omitted portion 31 is replaced with a non-groove portion. The second omitted portion 36 of this embodiment is a filled-in sipe 8 (shown in FIGS. 3 and 4 ) corresponding to the second protrusion 18B of the mold 11 (a non-groove portion). The second omitted portion 36 of this embodiment is defined on the outer surface 32o of the tread rubber model 33 (in this example, it is set to be a surface continuous with the outer surface 32o). Such a second omitted portion 36 allows the raw tire model 32 to be defined in a simplified manner, enabling the raw tire model 32 to be defined in a short amount of time.

As shown in Figure 6, in this embodiment, the contour of the outer surface 32o of the raw tire model 32 matches the contour of the molding surface 21s of the mold model 21. Between the outer surface 32o of the raw tire model 32 and the molding surface 21s of the mold model 21, the element G(i) of the raw tire model 32 and the element F(i) of the mold model 21 do not share nodes 34, 37. This allows any boundary condition to be set between the outer surface 32o of the raw tire model 32 and the molding surface 21s of the mold model 21. The raw tire model 32 is stored in the computer 1 (shown in Figure 1).

[Enter bladder model]
Next, in the heat transfer calculation method of this embodiment, a bladder model 22 is defined in the computer 1 (shown in FIG. 1) (step S3). In this embodiment, for example, based on design data (e.g., CAD data) of the mold 11 and the bladder 12 shown in FIG. 3, the bladder 12 is modeled (discretized) with a plurality (a finite number) of elements H(i) (i = 1, 2, ...) that can be handled by a numerical analysis method. In this way, the bladder model 22 is set. The bladder model 22 of this embodiment is set as a three-dimensional model. Note that, when the mold model 21 and the raw tire model 32 are defined as two-dimensional models, the bladder model 22 may be set as a two-dimensional model.

Element H(i) is similar to element F(i) of mold model 21 and element G(i) of raw tire model 32. Each element H(i) is composed of multiple nodes 38. Numerical data such as element number, node number, node coordinate values, and material properties (rigidity, Young's modulus, thermal conductivity, density, specific heat, thermal expansion coefficient, etc.) of bladder 12 (shown in Figure 3) are defined for each element H(i). Bladder model 22 is stored in computer 1 (shown in Figure 1).

[Arrangement of Unvulcanized Tire Model and Bladder Model]
Next, in the heat transfer calculation method of this embodiment, the computer 1 (shown in FIG. 1) places the raw tire model 32 and the bladder model 22 in the internal space 21i of the mold model 21 (step S4). In step S4 of this embodiment, the raw tire model 32 and the bladder model 22 can be placed in the internal space 21i of the mold model 21 based on, for example, a procedure similar to the placement step of Patent Document 1.

[Define thermal conductivity of tread rubber model]
Next, in the heat transfer calculation method of this embodiment, a predetermined thermal conductivity is defined for the element G(i) of the tread rubber model 33 (thermal conductivity definition step S5). The thermal conductivity of this embodiment is used to calculate heat transfer at the contact surface between the tread rubber model 33 and the mold model 21 in the heat transfer calculation step S7 described below. Figure 8 is a flowchart showing an example of the processing procedure of the thermal conductivity definition step S5.

[Determining the thermal conductivity of the tread rubber model]
In the thermal conductivity definition step S5 of this embodiment, first, the thermal conductivity of the tread rubber model 33 shown in FIGS. 6 and 7 is specified (step S51).

The heat transfer calculations of this embodiment use a mold model 21 including a first omitted portion 31 in which the protrusions 18 (second protrusions 18B) shown in FIG. 7 are omitted, and a tread rubber model 33 including a second omitted portion 36 in which the groove portions 6 (sipes 8) corresponding to the first omitted portion 31 are non-groove portions. For this reason, for example, when calculating heat transfer between the mold model 21 and the tread rubber model 33 based on the thermal conductivity of the tread rubber 3a shown in FIG. 3, it is difficult to take into account the ease of heat transfer through the protrusions 18 of the mold 11 and the groove portions 6 of the raw tire 2L.

In step S51 of this embodiment, the thermal conductivity of the tread rubber model 33 (shown in FIGS. 6 and 7) is determined based on the thermal conductivity of the protrusions 18 (shown in FIG. 3) and the thermal conductivity of the tread rubber 3a (shown in FIG. 3). This makes it possible to take into account the ease of heat transfer through the protrusions 18 and groove portions 6 in the heat transfer calculations described below in step S51 of this embodiment. The thermal conductivity of the protrusions 18 and tread rubber 3a, etc., can be obtained as appropriate, for example, based on conventional procedures.

The thermal conductivity of the tread rubber model 33 is not particularly limited, as long as it is determined based on the thermal conductivity of the protrusions 18 (shown in Figure 3) and the thermal conductivity of the tread rubber 3a (shown in Figure 3). In this embodiment, a calculation formula is used that can determine the thermal conductivity of the tread rubber model 33. The process for deriving the calculation formula is explained below.

Generally, the thermal resistance of an object can be calculated by dividing the thickness of the object by the thermal conductivity of the object, and the thermal resistance R _new of the tread rubber 3 a can be determined by the following formula (3). Note that in this embodiment, the thermal resistance R _new is exemplified as the thermal resistance per predetermined pitch. One pitch is not particularly limited, and can be determined, for example, based on a plurality of pattern constituent units that make up the tread pattern (for example, any pattern constituent unit is defined as one pitch).

where:
λ _new : Thermal conductivity of the tread rubber 3a p: Length per pitch in the circumferential direction of the tire B: Depth of the tread rubber 3a in the radial direction of the tire

In the above formula (3), the thermal conductivity λ _new is multiplied by the circumferential length p of the tire per pitch (shown in FIG. 4) to obtain the thermal conductivity λ _new p per pitch. Then, the depth B of the tread rubber 3a is divided by the thermal conductivity λ _new p per pitch to calculate the thermal resistance R _new of the tread rubber 3a per pitch (shown in FIG. 4).

When the groove portions 6 (sipes 8) are formed by the protrusions 18 (second protrusions 18B) of the mold 11 shown in Fig. 4 as in this embodiment, the thermal conductivity λ _new of the tread rubber 3a in the above formula (3) needs to take into account the thermal conductivity of the protrusions 18 and the thermal conductivity of the tread rubber 3a. In step S51 of this embodiment, this thermal conductivity λ _new is determined.

Here, the tread rubber 3a can be divided into a first region 51 from the outer surface (tread surface) 2o of the tread rubber 3a to the inner ends 6i of the groove portions 6 in the tire radial direction, and a second region 52 from the inner ends 6i of the groove portions 6 to the inner end 20 of the tread rubber 3a. Therefore, the thermal resistance R _new of the tread rubber 3a can be calculated by adding together the thermal resistance Rd of the first region 51 and the thermal resistance Rd _~B of the second region 52, as shown in the following formula (4). Note that in this embodiment, the thermal resistances Rd and Rd _~B are, for example, a predetermined thermal resistance per pitch, similar to the thermal resistance R _new .

The thermal resistance Rd of the first region 51 can be expressed by the following equation (5):

where:
λ _R : Thermal conductivity of tread rubber 3 a λ _M : Thermal conductivity of protrusions 18 p : Length per pitch in the tire circumferential direction N : Total number of protrusions 18 per pitch t : Thickness of protrusions 18 in the tire circumferential direction d : Depth of protrusions 18 in the tire radial direction

In the above formula (5), the total thickness (length) Nt of the protrusions 18 per pitch is calculated by multiplying the thickness (length) t of the protrusions 18 (in this example, the second protrusions 18B) in the tire circumferential direction by the total number N of the protrusions 18 per pitch. This total Nt is multiplied by the thermal conductivity λ _M of the protrusions 18 to calculate the thermal conductivity of the protrusions 18 per pitch (i.e., λ _M Nt).

In the above formula (4), the total value p-Nt of the circumferential length of the tread rubber 3a per pitch is calculated by subtracting the total value Nt of the thicknesses (lengths) of the protrusions 18 per pitch from the circumferential length _{p of the tread rubber 3a per pitch. The total value (1-Nt) is multiplied by the thermal conductivity λR} of the tread rubber 3a to calculate the thermal conductivity of the tread rubber 3a per pitch (i.e., _λR (1-Nt)).

These thermal conductivities λ _M Nt and λ _R (1-Nt) are added together to determine the thermal conductivity per pitch of the first region 51. The thermal resistance Rd per pitch of the first region 51 is determined by dividing the radial depth d of the groove portion 6 (radial depth of the protrusion 18) by this thermal conductivity.

Next, the thermal resistance R _d~B of the second region 52 can be expressed, for example, by the following equation (6).

where:
λ _R : Thermal conductivity of the tread rubber 3 a p : Length per pitch in the circumferential direction of the tire d : Depth of the protrusion 18 in the radial direction of the tire B : Depth of the tread rubber 3 a in the radial direction of the tire

In the above formula (6), the depth B of the tread rubber 3a in the tire radial direction is subtracted by the depth d of the protrusion 18 (in this example, the second protrusion 18B) in the tire radial direction to obtain the depth B-d of the second region 52 (from the inner end 6i of the groove portion 6 to the inner end 20 of the tread rubber 3a). The thermal conductivity λ _R of the tread rubber 3a is multiplied by the length p in the tire circumferential direction per pitch to obtain the thermal conductivity λ _R p of the tread rubber 3a per pitch of the second region 52. The thermal resistance R _d~B per pitch of the second region 52 is calculated by dividing the depth B-d by this thermal conductivity λ _R p.

Then, the thermal resistance R _new of the tread rubber model 33 in the above formula (3), the thermal resistance R d of the first region 51 in the above formula (5), and the thermal resistance R _d~B of the second region 52 in the above formula (6) are substituted into the above formula (4). Then, by solving for the thermal conductivity λ _new , the following formula (1) is obtained.

λ _new : Thermal conductivity of tread rubber model 33 λ _R : Thermal conductivity of tread rubber 3a λ _M : Thermal conductivity of protrusions 18 p: Length per pitch in the tire circumferential direction N: Total number of protrusions 18 per pitch t: Thickness of protrusions 18 in the tire circumferential direction d: Depth of protrusions 18 in the tire radial direction B: Depth of tread rubber 3a in the tire radial direction

The above formula (1) uses the ratio λ _R /λ _M of the thermal conductivity λ _R of the tread rubber 3a to the thermal conductivity λ _M of the protrusions 18, the ratio Nt/p of the protrusions 18 per pitch in the tire circumferential direction, and the ratio (1-Nt/p) of the tread rubber 3a per pitch in the tire circumferential direction. Furthermore, the formula uses the ratio d/B of the depth d of the first region 51 (depth of the protrusions 18) to the depth B of the tread rubber 3a, and the ratio (1-d/B) of the depth B-d of the second region 52 to the depth B of the tread rubber 3a.

In the above formula (1), by substituting the above parameters including the thermal conductivity λ _M of the protrusions 18 and the thermal conductivity λ _R of the tread rubber 3a, it is possible to easily specify the thermal conductivity λ _new of the tread rubber model 33 that can take into account the ease of heat transfer through the protrusions 18 and the groove portions 6. The thermal conductivity λ _new of the tread rubber model 33 is stored in the computer 1 (shown in FIG. 1 ).

[Define thermal conductivity of tread rubber model]
Next, in the thermal conductivity definition step S5 of this embodiment, the thermal conductivity λ _new of the specified tread rubber model 33 is defined for each element G(i) of the tread rubber model 33 shown in Fig. 6 (step S52). In step S52, the thermal conductivities set for all elements G(i) of the tread rubber model 33 are updated to the thermal conductivity λ _new of the tread rubber model 33 specified in step S51. The updated thermal conductivity λ _new is stored in the computer 1 (shown in Fig. 1).

[Boundary condition definition]
Next, in the heat transfer calculation method of this embodiment, boundary conditions for calculating heat transfer between the raw tire model 32, the mold model 21, and the bladder model 22 are defined in the computer 1 (shown in FIG. 1) (step S6). The boundary conditions of this embodiment include, for example, the initial temperatures of the mold model 21, the raw tire model 32, and the bladder model 22, as well as the temperature conditions of the mold model 21 and the bladder model 22 during the vulcanization process. The temperature conditions of this embodiment include the time-series temperatures of the mold 11 and the bladder 12 shown in FIG. 3 during the heating process and the cooling process. These boundary conditions can be defined, for example, based on a procedure similar to the boundary condition definition process of Patent Document 1. These boundary conditions are input into the computer 1 (shown in FIG. 1).

[Calculate heat transfer]
Next, in the heat transfer calculation method of this embodiment, the computer 1 (shown in FIG. 1) calculates heat transfer at the contact surface 40 between the tread rubber model 33 and the mold model 21 (step S7). In step S7 of this embodiment, the mold model 21 with an increased temperature is calculated based on the initial temperature and temperature conditions of the mold model 21. As a result, in step S7, heat transfer at the contact surface 40 between the raw tire model 32 (tread rubber model 33) and the mold model 21 is calculated.

Furthermore, in step S7 of this embodiment, the bladder model 22 with an increased temperature is calculated based on the initial temperature and temperature conditions of the bladder model 22. As a result, in step S7, heat transfer at the contact surface 42 between the raw tire model 32 and the bladder model 22 is calculated.

In this way, in step S7 of this embodiment, the temperature of the raw tire model 32 can be calculated based on the temperatures of the mold model 21 and the bladder model 22. As a result, in step S7 of this embodiment, the temperature of the rubber member 3 (tread rubber model 33) that changes from moment to moment during vulcanization molding (in this example, the heating process and cooling process) can be calculated, similar to the actual vulcanization process shown in Figure 3.

In step S7 of this embodiment, similar to Patent Document 1, thermal analysis (heat transfer calculation) is performed for each unit step of the simulation until a predetermined heat transfer calculation time has elapsed. Thermal analysis can be performed using commercially available finite element analysis application software such as Abaqus from Dassault Systèmes, LS-DYNA from LSTC, or NASTRAN from MSC.

In this embodiment, as shown in FIG. 7, a mold model 21 including a first omitted portion 31 and a tread rubber model 33 including a second omitted portion 36 are used. Therefore, compared to when, for example, a mold model (not shown) that does not include the first omitted portion 31 and a tread rubber model (not shown) that does not include the second omitted portion 36 are used, heat transfer calculations at the contact surface 40 between the mold model 21 and the tread rubber model 33 can be simplified. Therefore, in this embodiment, calculation time can be shortened.

Furthermore, the thermal conductivity of the tread rubber model 33 in this embodiment is defined based on the thermal conductivity of the protrusions 18 (shown in FIG. 3) and the thermal conductivity of the tread rubber 3a (shown in FIG. 3). Therefore, in this embodiment, heat transfer calculations can be performed that take into account the ease of heat transfer through the protrusions 18 and the groove portions 6. As a result, in this embodiment, as in Patent Document 1, for example, it is not necessary to repeatedly perform simulations using a raw tire model that includes the second omitted portion 36 and a second tire model (not shown) that does not include the second omitted portion 36 in order to set the thermal conductivity of the second omitted portion 36. Therefore, in this embodiment, it is possible to calculate heat transfer between the mold 11 and the raw tire 2L in a short amount of time.

Furthermore, in this embodiment, the thermal conductivity of the tread rubber model 33 is defined based on the above formula (1), which uses parameters including the dimensions of the protrusions 18 and grooves 6. Therefore, in this embodiment, it is possible to easily and accurately perform heat transfer calculations that take into account the ease of heat transfer through the protrusions 18 and grooves 6.

It is believed that heat from the mold 11 (shown in Figure 3) is transferred from the outside to the inside in the thickness direction of the tread rubber 3a (shown in Figure 3). For this reason, in step S7, only heat transfer in the thickness direction of the tread rubber model 33 may be calculated. This eliminates heat transfer calculations in directions other than the thickness direction, thereby shortening the calculation time. Note that the thickness direction is specified as the direction perpendicular to the outer surface 32o of the tread rubber model 33 at any position on that outer surface 32o (the tire radial direction).

In step S7 of this embodiment, it is desirable to calculate physical quantities related to the vulcanization state of the raw tire 2L (shown in Figure 3). Such physical quantities are used to evaluate the vulcanization state of the raw tire 2L. There are no particular limitations on the physical quantities, as long as they relate to the vulcanization state of the raw tire 2L. In this embodiment, the physical quantities include at least one of the temperature of the raw tire 2L, the equivalent vulcanization amount, and the degree of vulcanization.

The temperature of the raw tire is calculated for each unit step of the simulation at node 37 of element G(i) that constitutes the tread rubber model 33 (raw tire model 32). As a result, in step S7 of this embodiment, time-series temperature data of the tread rubber model 33 (raw tire model 32) is obtained.

The equivalent vulcanization amount ECU can be calculated, for example, based on the temperature (time-series temperature data) of the raw tire model 32 and equation (2) of Patent Document 1. The degree of vulcanization indicates the rate at which vulcanization has progressed from an unvulcanized state, and can be calculated, for example, using equation (3) of Patent Document 1. These physical quantities are stored in computer 1 (shown in Figure 1).

[Output physical quantity]
Next, in the heat transfer calculation method of this embodiment, the computer 1 (shown in FIG. 1) outputs physical quantities related to the vulcanization state of the raw tire 2L (shown in FIG. 3) (step S8). The output format of the physical quantities is not particularly limited. The physical quantities of this embodiment are output to an output device such as a display device 1d of the computer 1 or a printer. In this embodiment, the temperature, equivalent vulcanization amount, and degree of vulcanization of the raw tire 2L are output, but any one of them may be output.

[Evaluating physical quantities]
Next, in the heat transfer calculation method of this embodiment, the vulcanization state of the raw tire 2L (shown in FIG. 3) is evaluated based on physical quantities related to the vulcanization state of the raw tire 2L (step S9). The evaluation in this embodiment is performed by the computer 1 (shown in FIG. 1), but may also be performed by an operator.

The vulcanization state can be evaluated as appropriate based on physical quantities related to the vulcanization state of the raw tire 2L (shown in Figure 3). In this embodiment, the quality of the vulcanization state is evaluated based on predetermined thresholds set for the temperature, equivalent vulcanization amount, and degree of vulcanization of the raw tire 2L.

If it is determined in step S9 that the vulcanization state of the raw tire 2L (shown in Figure 3) is good ("Yes" in step S9), then tire 2 (shown in Figure 2) is manufactured (step S10), for example, based on the vulcanization conditions and design factors of the raw tire 2L.

On the other hand, if it is determined in step S9 that the vulcanization state of the raw tire 2L (shown in Figure 3) is not good ("No" in step S9), the vulcanization conditions and design factors of the raw tire 2L are changed (step S11), and steps S1 to S9 are performed again.

In this way, the heat transfer calculation method of this embodiment makes it possible to confirm physical quantities related to the vulcanization state of a raw tire 2L (shown in FIG. 3) through simulations using a computer 1 (shown in FIG. 1). Furthermore, the heat transfer calculation method of this embodiment makes it possible to evaluate the vulcanization state of the raw tire 2L based on the output physical quantities. Furthermore, if the heat transfer calculation method of this embodiment determines that the vulcanization state is not good, it makes it possible to change the vulcanization conditions, design factors, etc. of the raw tire 2L based on the output physical quantities. As a result, the heat transfer calculation method of this embodiment makes it possible to design and manufacture a tire 2 in which the raw tire 2L is vulcanized in a good state.

[Method for calculating heat transfer between a mold and a green tire (second embodiment)]
[Determining the thermal conductivity of the tread rubber model]
In the embodiments described above, the thermal conductivity specified by the above formula (1) was defined for the element G(i) of the tread rubber model 33 shown in Fig. 6 , but the present invention is not limited to this. For example, as shown in Fig. 4 , when the volume of the tread rubber 3a is larger than the volume of the protrusions 18, a formula that is a simplification of the above formula (1) may be used. In this embodiment, the thermal conductivity is specified based on the following formula (2).

where:
λ _new : Thermal conductivity λ _R : Thermal conductivity of tread rubber d: Depth of protrusion 18 in the tire radial direction B: Depth of tread rubber 3a in the tire radial direction

The above formula (2) is a simplification of the above formula (1) by assuming that the ratio λ _R /λ _M of the thermal conductivity λ _R of the tread rubber 3a to the thermal conductivity λ _M of the protrusions in the above formula (1) is approximately zero. Such formula (2) makes it possible to easily define the thermal conductivity of the tread rubber model 33.

Note that when the volume of the protrusions 18 is large, the influence of the thermal conductivity λ _M of the protrusions 18 becomes greater, making it difficult to accurately calculate the heat transfer between the mold 11 and the raw tire 2L when using the above formula (2). Therefore, in the thermal conductivity definition step S5, it is preferable to specify the thermal conductivity of the tread rubber model 33 based on the above formula (2) when the volume of the tread rubber 3a is 70% or more of the volume of the protrusions 18. This makes it possible to easily define the thermal conductivity of the tread rubber model 33 while maintaining the calculation accuracy of the heat transfer between the mold 11 and the raw tire 2L.

[Method for calculating heat transfer between a mold and a raw tire (third embodiment)]
In the embodiments described above, as shown in Fig. 7 , the mold model 21 including the first omitted portion 31 where the second protrusions 18B of the mold 11 have been removed, and the raw tire model 32 including the second omitted portion 36 where the sipes 8 have been filled have been defined. However, the present invention is not limited to this. For example, a mold model (not shown) including the first omitted portion where both the first protrusions 18A and the second protrusions 18B of the mold 11 shown in Fig. 3 have been removed, or a raw tire model (not shown) including the second omitted portion where both the circumferential grooves 7A and the sipes 8 have been filled may be defined. In this case, in the thermal conductivity definition step S5, the thermal conductivity of the tread rubber model 33 is specified based on the thermal conductivity of the first protrusions 18A and the second protrusions 28B and the thermal conductivity of the tread rubber 3a.

In this embodiment, the mold model 21 and raw tire model 32 shown in Figures 6 and 7 can be further simplified, allowing the mold model 21 and raw tire model 32 to be defined in a short amount of time. Furthermore, in this embodiment, the heat transfer calculation at the contact surface 40 (shown in Figure 6) between the mold model 21 and raw tire model 32 can be further simplified, thereby reducing the calculation time.

[Method of vulcanizing raw tires]
The physical quantities related to the vulcanization state of a raw tire calculated based on the heat transfer calculation methods of the above-described embodiments may be used in a method for vulcanizing a raw tire (hereinafter, simply referred to as a "vulcanization method"). The vulcanization method of this embodiment uses a computer 1 (shown in FIG. 1).

In the vulcanization method of this embodiment, the physical quantities related to the vulcanization state of the raw tire 2L (shown in Figure 3) obtained by the heat transfer calculation methods of the previous embodiments are used as the objective function, and the vulcanization conditions of the raw tire 2L are used as design factors to find an optimal solution for the design factors that optimizes the objective function. The raw tire 2L is then vulcanized based on this optimal solution. The vulcanization conditions include, for example, the set temperature of the mold 11 (shown in Figure 3) and the vulcanization time for each set temperature.

The optimal solution for the design factors is found based on an optimization algorithm using computer 1 (shown in Figure 1). The optimization algorithm is used to determine the optimal design factors (e.g., the parameters mentioned above) that satisfy an arbitrary objective function under certain constraints. Examples of optimization algorithms include genetic algorithms (GA) and particle swarm optimization (PSO). Such optimization algorithms are suitable for searching for a global optimal solution while avoiding falling into a local solution. The calculation method of this embodiment uses particle swarm optimization (PSO), which has a relatively short calculation time, but genetic algorithms (GA) and other algorithms may also be used.

In particle swarm optimization (PSO), multiple initial conditions (first generation) are created, the objective function for each condition is calculated, and optimization is performed by updating each condition (generational change) to approach the most desirable objective function. Random numbers are used to update each condition, allowing a wide search for optimal conditions. Details of particle swarm optimization (PSO) can be found in various publications, such as "Particle Swarm Optimization and Nonlinear Systems," IEICE Fundamentals Review (Institute of Electronics, Information and Communication Engineers), Vol. 5, No. 2, August 2011.

[Enter constraints]
9 is a flowchart showing the processing steps of the raw tire vulcanization method of this embodiment. In the vulcanization method of this embodiment, first, predetermined constraints are input to the computer 1 (shown in FIG. 1) (step S21). The constraints are conditions (design criteria) that must be met when vulcanizing the raw tire 2L (shown in FIG. 3). The constraints of this embodiment include the range of set temperatures for the mold 11 (shown in FIG. 3) and the range of vulcanization time for each set temperature. Such constraints are set appropriately depending on, for example, the specifications and structure of the raw tire 2L. The constraints are stored in the computer 1 (shown in FIG. 1).

[Enter raw tire vulcanization conditions]
Next, in the vulcanization method of this embodiment, predetermined vulcanization conditions (initial values of the vulcanization conditions) of the raw tire 2L (shown in FIG. 3) are input to the computer 1 (shown in FIG. 1) (step S22). The initial values of the vulcanization conditions are input as first-generation design parameters.

In this embodiment, the initial values of the vulcanization conditions are the set temperature of the mold 11 (shown in Figure 3) and the vulcanization time for each set temperature. These set temperatures and vulcanization times are determined within the ranges of their respective constraints.

In this embodiment, multiple vulcanization conditions are set, including the set temperature of the mold 11 (shown in Figure 3) and the vulcanization time for each set temperature. These vulcanization conditions differ from each other in at least some of the set temperature and vulcanization time. The initial values of the vulcanization conditions are stored in the computer 1 (shown in Figure 1).

[Obtaining physical quantities related to the vulcanization state of raw tires]
Next, in the design method of this embodiment, the computer 1 (shown in FIG. 1) calculates physical quantities related to the vulcanization state of the raw tire 2L (shown in FIG. 3) based on the vulcanization conditions (step S23). The physical quantities of this embodiment are obtained based on the processing procedures of the heat transfer calculation methods of the previous embodiments.

In step S23 of this embodiment, first, heat transfer at the contact surface between the tread rubber model 33 and the mold model 21 shown in Figures 6 and 7 is calculated for each initial value of the vulcanization conditions. The thermal conductivity of the tread rubber model 33 used in the heat transfer calculation is determined based on the thermal conductivity of the protrusions 18 shown in Figure 3 and the thermal conductivity of the tread rubber 3a.

Next, in step S23 of this embodiment, physical quantities related to the vulcanization state of the raw tire are calculated based on heat transfer calculations at the contact surface between the tread rubber model 33 and the mold model 21 shown in Figure 6. The physical quantities are not particularly limited as long as they relate to the vulcanization state of the raw tire 2L (shown in Figure 3). The physical quantities of this embodiment include at least one of the temperature, equivalent vulcanization amount, and degree of vulcanization of the raw tire 2L. These physical quantities can be obtained using the procedure described above.

In step S23 of this embodiment, physical quantities related to the vulcanization state of raw tire 2L (shown in Figure 3) (temperature of raw tire 2L, equivalent vulcanization amount, and degree of vulcanization) are calculated for each of multiple vulcanization conditions. These physical quantities are stored in computer 1 (shown in Figure 1).

[Determine the objective function]
Next, in the vulcanization method of the present embodiment, the computer 1 (shown in FIG. 1) determines whether or not the objective function is satisfied (step S24). In the objective function of the present embodiment, physical quantities related to the vulcanization state of the raw tire 2L (shown in FIG. 3) are set.

In step S24 of this embodiment, first, from among the multiple vulcanization conditions, the vulcanization conditions that provide the best physical quantities related to the vulcanization state of the raw tire 2L (shown in Figure 3) are selected. Then, for the selected vulcanization conditions, if the physical quantities related to the vulcanization state of the raw tire 2L satisfy a predetermined threshold, it is determined that the objective function is satisfied. The threshold is set appropriately based on, for example, the degree of adverse effect on physical properties associated with over-vulcanization.

If it is determined that the objective function is satisfied ("Yes" in step S24), the selected vulcanization conditions are determined as the optimal solution for the design variables (step S25). Then, based on the vulcanization conditions determined as the optimal solution, raw tire 2L (shown in Figure 3) is vulcanized (step S26).

On the other hand, if it is determined that the objective function is not satisfied ("No" in step S24), the design factors (vulcanization conditions) are updated based on the optimization algorithm (step S27), and steps S23 and S24 are performed again.

[Update design factors]
In step S27 of updating the design factors of this embodiment, the computer 1 (shown in FIG. 1) updates the design factors (vulcanization conditions) based on an optimization algorithm. In step S27 of this embodiment, for example, among the multiple vulcanization conditions, the vulcanization condition selected in step S24 (i.e., the vulcanization condition with the best objective function) is excluded, and the other vulcanization conditions are updated (generational change). Such design factor updating (generational change) can be appropriately performed based on particle swarm optimization (PSO) with reference to the above-mentioned paper, etc. The updated design factors are stored in the computer 1.

After the design factors have been updated, steps S23 and S24 are performed again based on the vulcanization conditions that produce the best objective function and other vulcanization conditions. Therefore, with the vulcanization method of this embodiment, raw tire 2L (shown in Figure 3) can be vulcanized based on the optimal solution of the design factors (in this example, the vulcanization conditions) that satisfies the objective function.

In the design method of this embodiment, the heat transfer calculation method of the previous embodiments is used to calculate physical quantities related to the vulcanization state of raw tire 2L (shown in Figure 3), so the physical quantities for each vulcanization condition can be calculated in a short time. Therefore, the design method of this embodiment makes it possible to quickly find the optimal solution for the design factors that satisfies the objective function.

The above describes in detail a particularly preferred embodiment of the present disclosure, but the present disclosure is not limited to the illustrated embodiment and can be modified and implemented in various ways.

Heat transfer calculations were performed between the mold and raw tire shown in Figures 2 and 3 (Example, Comparative Example, and Conventional Example). In the Example, Comparative Example, and Conventional Example, a mold model, a raw tire model, and a bladder model were defined. The mold model was defined to include a first omitted portion in which the protrusions (second protrusions) are omitted. The tread rubber model was defined to include a second omitted portion in which the groove-like portions (sipes) corresponding to the first omitted portion are non-groove-like portions.

Next, in the examples, comparative examples, and conventional examples, a raw tire model and a bladder model were placed in the internal space of the mold model, and heat transfer at the contact surface between the tread rubber model and the mold model was calculated. Then, the temperature of the tread rubber and the temperature at the outer end position of the outer belt in the tire axial direction were calculated as physical quantities related to the vulcanization state of the raw tire.

In the example, the thermal conductivity of the tread rubber model was determined based on the thermal conductivity of the protrusions and the thermal conductivity of the tread rubber, following the processing procedure shown in Figure 8. The above equation (1) was used to determine the thermal conductivity. The determined thermal conductivity was defined for the elements of the tread rubber model.

In the comparative example, the thermal conductivity of the tread rubber was defined as an element of the tread rubber model. In the conventional example, based on the procedure of Patent Document 1, simulations were repeatedly performed using a raw tire model including the second omitted portion and a second tire model not including the second omitted portion to determine the thermal conductivity of the tread rubber model.

A vulcanization process was carried out using the mold and raw tire shown in Figures 2 and 3 (experimental example). The temperature of the tread rubber and the temperature of the outer belt at the outer end position in the tire axial direction were calculated. The common specifications are as follows:
Tire size: 205/75R17.5
Protrusion depth d: 2.0 mm
Tread rubber depth B: 10.5 mm

Figure 10(a) is a graph showing the relationship between the temperature of the tread rubber and the vulcanization time for the Examples and Experimental Examples. Figure 10(b) is a graph showing the relationship between the temperature at the outer end position of the outer belt and the vulcanization time for the Examples and Experimental Examples. Figure 11(a) is a graph showing the relationship between the temperature of the tread rubber and the vulcanization time for the Comparative Examples and Experimental Examples. Figure 11(b) is a graph showing the relationship between the temperature at the outer end position of the outer belt and the vulcanization time for the Comparative Examples and Experimental Examples.

The test results showed that the Example and Conventional Example were able to calculate temperatures closer to those of the experimental example than the Comparative Example. Furthermore, unlike the Conventional Example, the Example did not require repeated simulations using a raw tire model including the second omitted portion and a second tire model not including the second omitted portion, thereby reducing calculation time by 50% compared to the Conventional Example. Therefore, the Example was able to calculate heat transfer between the mold and the raw tire in a short time and with high accuracy.

[Note]
The present disclosure includes the following aspects.

[Disclosure 1]
A method for using a computer to calculate heat transfer between a mold having protrusions for forming groove-like portions consisting of grooves or sipes and a green tire having tread rubber that is in contact with the mold and in which the groove-like portions are formed by the protrusions, comprising:
a step of defining a mold model in the computer by discretizing the mold into a plurality of elements;
a step of discretizing the raw tire into a plurality of elements and defining a raw tire model including at least a tread rubber model in the computer;
Defining a predetermined thermal conductivity for the element of the tread rubber model;
a step in which the computer calculates heat transfer at a contact surface between the tread rubber model and the mold model based on the thermal conductivity,
the mold model includes a first omission portion in which at least a part of the protrusion is omitted,
the tread rubber model includes a second omitted portion in which a groove portion corresponding to the first omitted portion is made a non-groove portion,
the step of defining the thermal conductivity includes a step of specifying the thermal conductivity of the tread rubber model based on the thermal conductivity of the protrusions and the thermal conductivity of the tread rubber.
A method for calculating heat transfer between the mold and the green tire.
[Disclosure 2]
The method for calculating heat transfer between a mold and a green tire according to Disclosure 1, wherein the step of specifying the thermal conductivity specifies the thermal conductivity based on the following formula (1):
where:
λ _new : Thermal conductivity of tread rubber model λ _R : Thermal conductivity of tread rubber λ _M : Thermal conductivity of protrusions p : Length per pitch in the tire circumferential direction N : Total number of protrusions per pitch t : Thickness of protrusions in the tire circumferential direction d : Depth of protrusions in the tire radial direction B : Depth of tread rubber in the tire radial direction [Disclosure 3]
The method for calculating heat transfer between a mold and a green tire described in Disclosure 1, wherein the step of specifying the thermal conductivity specifies the thermal conductivity based on the following formula (2) when the volume of the tread rubber is 70% or more of the volume of the protrusions:
where:
λ _new : Thermal conductivity λ _R : Thermal conductivity of tread rubber d: Depth of protrusion in the tire radial direction B: Depth of tread rubber in the tire radial direction [Disclosure 4]
The method for calculating heat transfer between a mold and a green tire according to any one of Disclosures 1 to 3, wherein the step of calculating heat transfer calculates only heat transfer in the thickness direction of the green tire.
[Disclosure 5]
the step of calculating heat transfer calculates a physical quantity related to the vulcanization state of the raw tire,
The method for calculating heat transfer between a mold and a green tire according to any one of Disclosures 1 to 4, further comprising, after the step of calculating the heat transfer, a step in which the computer outputs the physical quantity.
[Disclosure 6]
The method for calculating heat transfer between a mold and a raw tire described in the present disclosure 5, wherein the physical quantity includes at least one of the temperature of the raw tire, an equivalent vulcanization amount, and a degree of vulcanization.
[Disclosure 7]
A method for vulcanizing a green tire, comprising:
a step of inputting predetermined vulcanization conditions of the raw tire into a computer; and a step of calculating physical quantities related to the vulcanization state of the raw tire by the computer based on the vulcanization conditions and a heat transfer calculation method described in any one of Disclosures 1 to 6.
a step in which the computer determines an optimal solution of the design factors by using the vulcanization conditions as design factors and the physical quantities as objective functions, based on an optimization algorithm under predetermined constraint conditions, to optimize the objective function;
and vulcanizing the green tire based on the optimal solution.
A method for vulcanizing raw tires.

S1: Step of defining a mold model; S2: Step of defining a raw tire model; S5: Step of defining thermal conductivity for elements of a tread rubber model

Claims (6)

A method for using a computer to calculate heat transfer between a mold having protrusions for forming groove-like portions consisting of grooves or sipes and a green tire having tread rubber that is in contact with the mold and in which the groove-like portions are formed by the protrusions, comprising:
a step of defining a mold model in the computer by discretizing the mold into a plurality of elements;
a step of discretizing the raw tire into a plurality of elements and defining a raw tire model including at least a tread rubber model in the computer;
Defining a predetermined thermal conductivity for the element of the tread rubber model;
a step in which the computer calculates heat transfer at a contact surface between the tread rubber model and the mold model based on the thermal conductivity,
the mold model includes a first omission portion in which at least a part of the protrusion is omitted,
the tread rubber model includes a second omitted portion in which a groove portion corresponding to the first omitted portion is made a non-groove portion,
The step of defining the thermal conductivity includes a step of specifying the thermal conductivity of the tread rubber model based on the following formula (1) :
A method for calculating heat transfer between the mold and the green tire.
where:
λ _new : Thermal conductivity of the tread rubber model
λ _R : Thermal conductivity of tread rubber
λ _M : Thermal conductivity of the protrusion
p: circumferential length of one pitch
N: Total number of protrusions per pitch
t: Thickness of the protrusion in the tire circumferential direction
d: Depth of the protrusion in the radial direction of the tire
B: Depth of tread rubber in the radial direction of the tire A method for using a computer to calculate heat transfer between a mold having protrusions for forming groove-like portions consisting of grooves or sipes and a green tire having tread rubber that is in contact with the mold and in which the groove-like portions are formed by the protrusions, comprising:
a step of defining a mold model in the computer by discretizing the mold into a plurality of elements;
a step of discretizing the raw tire into a plurality of elements and defining a raw tire model including at least a tread rubber model in the computer;
Defining a predetermined thermal conductivity for the element of the tread rubber model;
a step in which the computer calculates heat transfer at a contact surface between the tread rubber model and the mold model based on the thermal conductivity,
the mold model includes a first omission portion in which at least a part of the protrusion is omitted,
the tread rubber model includes a second omitted portion in which a groove portion corresponding to the first omitted portion is made a non-groove portion,
The step of defining the thermal conductivity includes a step of specifying the thermal conductivity of the tread rubber model based on the following formula (2) when the volume of the tread rubber is 70% or more of the volume of the protrusions:
A method for calculating heat transfer between the mold and the green tire.
where:
λ _new : Thermal conductivity of the tread rubber model
λ _R : Thermal conductivity of tread rubber
d: Depth of the protrusion in the radial direction of the tire
B: Depth of tread rubber in the radial direction of the tire A method for using a computer to calculate heat transfer between a mold having protrusions for forming groove-like portions consisting of grooves or sipes and a green tire having tread rubber that is in contact with the mold and in which the groove-like portions are formed by the protrusions, comprising:
a step of defining a mold model in the computer by discretizing the mold into a plurality of elements;
a step of discretizing the raw tire into a plurality of elements and defining a raw tire model including at least a tread rubber model in the computer;
Defining a predetermined thermal conductivity for the element of the tread rubber model;
a step in which the computer calculates heat transfer at a contact surface between the tread rubber model and the mold model based on the thermal conductivity,
the mold model includes a first omission portion in which at least a part of the protrusion is omitted,
the tread rubber model includes a second omitted portion in which a groove portion corresponding to the first omitted portion is made a non-groove portion,
the step of defining the thermal conductivity includes a step of specifying the thermal conductivity of the tread rubber model based on the thermal conductivity of the protrusions and the thermal conductivity of the tread rubber,
the step of calculating heat transfer calculates heat transfer only in the thickness direction of the raw tire.
A method for calculating heat transfer between the mold and the green tire. the step of calculating heat transfer calculates a physical quantity related to the vulcanization state of the raw tire,
4. The method for calculating heat transfer between a mold and a green tire according to claim 1, further comprising the step of outputting the physical quantity by the computer after the step of calculating heat transfer . 5. The method for calculating heat transfer between a mold and a green tire according to claim 4, wherein the physical quantity includes at least one of a temperature of the green tire, an equivalent vulcanization amount, and a degree of vulcanization . A method for vulcanizing a green tire, comprising:
inputting predetermined vulcanization conditions for the raw tire into a computer;
a step of calculating, by the computer, a physical quantity related to a vulcanization state of the raw tire based on the vulcanization conditions and the heat transfer calculation method according to any one of claims 1 to 5;
a step in which the computer determines an optimal solution of the design factors by using the vulcanization conditions as design factors and the physical quantities as objective functions based on an optimization algorithm under predetermined constraint conditions, thereby optimizing the objective function;
and vulcanizing the green tire based on the optimal solution.
A method for vulcanizing raw tires .