JP6938976B2 - Calculation method of rubber strip winding conditions and tire manufacturing method - Google Patents

Description

The present invention is a method for calculating winding conditions for forming an annular rubber member by spirally winding a strip-shaped rubber strip on a wound body, and manufacturing a tire. Regarding the method.

The following Patent Document 1 describes an annular shape forming a rubber product such as a pneumatic tire by spirally winding a strip-shaped rubber strip on the outer peripheral surface of a wound body such as a cylindrical former or a rigid core. We are proposing a so-called strip wind method for forming rubber members.

Japanese Patent No. 4160245

In order to form the annular rubber member into a pre-designed target cross-sectional shape, it is important to appropriately set the winding conditions including, for example, the winding pitch and the number of windings of the rubber strip. However, since the winding conditions are set based on trial and error by the operator and empirical rules so far, the finish of the annular rubber member tends to vary depending on the skill level of the operator, and has a target cross-sectional shape. There is a problem that it is difficult to stably form an annular rubber member.

The present invention has been devised in view of the above circumstances, and an object of the present invention is to provide a method for calculating winding conditions of a rubber strip capable of stably forming an annular rubber member in a target cross-sectional shape. There is.

In the present invention, a computer is used to calculate winding conditions for spirally winding a strip-shaped rubber strip around an object to be wound to form an annular rubber member having a predetermined target cross-sectional shape. This is a method for inputting a constraint condition for winding the rubber strip into the computer, and a first method for identifying the error of the rubber member from the target cross-sectional shape in the computer. The step of inputting the objective function and the step of the computer finding at least one optimum solution of the winding condition satisfying at least the first objective function under the constraint condition based on the optimization algorithm. It is characterized by including.

In the method for calculating the winding condition of the rubber strip according to the present invention, the winding condition is the winding pitch of the rubber strip and the circumference of the wound body on which the winding start end of the rubber strip is arranged. It may include at least one of the directional positions.

In the method for calculating the winding condition of the rubber strip according to the present invention, the constraint conditions are the number of times the rubber strip is wound, the axial position of the wound body on which the winding start end of the rubber strip is arranged, and so on. It may include at least one of the initial winding pitch of the rubber strip, the folding back position of the winding of the rubber strip, and the cross-sectional shape of the rubber strip.

In the method of calculating the winding condition of the rubber strip according to the present invention, the first objective function may include an acceptable error from the target cross-sectional shape.

In the method for calculating the winding condition of the rubber strip according to the present invention, the permissible error includes a first permissible error and a second permissible error larger than the first permissible error, and the second permissible error. May be set in a portion of the cross-sectional shape of the rubber member where the required accuracy is relatively low.

In the method for calculating the winding condition of the rubber strip according to the present invention, the step of further including the step of inputting at least one of the initial winding conditions to the computer and obtaining the optimum solution is the winding condition. Based on the above, a step of calculating the cross-sectional shape of the rubber member and a step of updating the winding condition based on the optimization algorithm so that the cross-sectional shape of the rubber member approaches the target cross-sectional shape. It may be included.

In the method for calculating the winding condition of the rubber strip according to the present invention, the computer further includes a step of inputting a second objective function for specifying a variation in the cross-sectional shape of the rubber member in the circumferential direction, and the optimum In the step of finding the solution, at least one of the optimum solutions of the winding conditions satisfying at least both the first objective function and the second objective function may be obtained.

The method for calculating the winding condition of the rubber strip according to the present invention further includes a step of inputting a third objective function for specifying the fluctuation amount of the winding pitch of the rubber strip into the computer, and the optimum solution. In the step of obtaining the optimum solution, at least one of the winding conditions satisfying at least both the first objective function and the third objective function may be obtained.

The present invention is a method for manufacturing a tire, which comprises a step of forming the rubber member under the winding conditions obtained by the calculation method according to any one of claims 1 to 8.

In the method of calculating the winding condition of the rubber strip of the present invention, the step of inputting the constraint condition for winding the rubber strip and the first objective function for specifying the error from the target cross-sectional shape are input to the computer. The process includes the process of finding at least one optimal solution of the winding condition that satisfies at least the first objective function under the constraint condition by the computer based on the optimization algorithm. According to the calculation method of the rubber strip of the present invention, it is possible to calculate the winding condition of the rubber strip capable of stably forming the annular rubber member in the target cross-sectional shape without being influenced by the skill level of the operator. can.

It is a perspective view which shows an example of the computer which executes the calculation method of the winding condition of a rubber strip. It is sectional drawing which shows an example of a raw tire. It is a side view explaining an example of the process of forming an annular rubber member. It is a top view explaining an example of the process of forming an annular rubber member. (A) and (b) are cross-sectional views explaining an example of the process of forming an annular rubber member. It is a flowchart which shows an example of the processing procedure of the calculation method of the winding condition of a rubber strip. It is a graph which shows an example of the cross-sectional shape of an annular rubber member calculated based on a target cross-sectional shape and a winding condition. It is a partially enlarged view of FIG. It is a flowchart which shows an example of the processing procedure of the optimum solution calculation process. It is a flowchart explaining the calculation method of the winding condition of the rubber strip of another embodiment of this invention. It is a side sectional view of an annular rubber member. It is a flowchart which shows an example of the processing procedure of the optimum solution calculation process of another Embodiment of this invention. It is a flowchart explaining the calculation method of the winding condition of the rubber strip of still another embodiment of this invention. It is a flowchart which shows an example of the processing procedure of the optimum solution calculation process of another Embodiment of this invention.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
In the calculation method of the winding condition of the rubber strip of the present embodiment (hereinafter, may be simply referred to as “calculation method”), the strip-shaped rubber strip is spirally wound around the wound body to form an annular rubber member. It is a method for calculating the winding condition for forming by using a computer. In the present embodiment, the annular rubber member is exemplified as a tire component used for forming an unvulcanized raw tire, but is not limited to such an embodiment. Here, the unvulcanized term includes all aspects that have not been completely vulcanized, and the so-called semi-vulcanized state is included in this "unvulcanized".

FIG. 1 is a perspective view showing an example of a computer 1 that executes a calculation method. The computer 1 includes a main body 1a, a keyboard 1b, a mouse 1c, and a display device 1d. The main body 1a is provided with a processing unit (CPU), a ROM, a working memory, a storage device such as a magnetic disk, and disk drive devices 1a1, 1a2 and the like. The storage device stores in advance a processing procedure (program) for executing the calculation method of the present embodiment.

FIG. 2 is a cross-sectional view showing an example of a raw tire. The raw tire 2T is formed by laminating an annular rubber member (tire constituent member) 3. The annular rubber member 3 includes a tread rubber 3a, a sidewall rubber 3b, a clinch rubber 3c, a bead apex rubber 3d, an inner liner rubber 3e, and a cushion rubber 3f. In the present embodiment, the annular rubber member 3 for which the winding condition of the rubber strip is calculated is exemplified by the tread rubber 3a, but another annular rubber member 3 may be used.

FIG. 3 is a side view illustrating an example of a process of forming the annular rubber member 3. FIG. 4 is a plan view illustrating an example of a process of forming the annular rubber member 3. 5 (a) and 5 (b) are cross-sectional views illustrating an example of a process of forming the annular rubber member 3. As shown in FIGS. 3, 4 and 5 (a), in the step of forming the annular rubber member 3, first, as in the conventional strip wind method, the winding start end (circumferential end) of the rubber strip 4 is formed. Part) 4s is fixed to the outer peripheral surface 5o of the wound body 5. Next, in the step of forming the annular rubber member 3, as shown in FIG. 4, the rubber strip 4 is moved in the axial direction of the wound body 5 at a constant winding pitch P, and the wound body is moved. It is wound on the outer peripheral surface 5o of 5. As a result, as shown in FIG. 5B, the annular rubber member 3 is formed. The initial winding pitch (not shown) in which the rubber strip 4 is rotated once from the winding start end 4s is different from the subsequent winding pitch P. In the present embodiment, the initial winding pitch of the rubber strip 4 is smaller than the subsequent winding pitch. As a result, the rubber strip 4 on the winding start end 4s side is wound around the rubber strip 4 that makes one round from the winding start end 4s, so that the rubber strip 4 can be prevented from coming off from the wound body 5.

The rubber strip 4 is made of unvulcanized rubber. The cross-sectional shape of the rubber strip 4 of the present embodiment is formed to have a width larger than the thickness. The width and thickness of the rubber strip 4 are not particularly limited. As an example of the rubber strip 4, the width is about 1.0 to 5.0 mm and the thickness is about 0.5 to 1.5 mm. The rubber strip 4 is supplied by an applicator 7 formed in a conveyor shape.

As shown by the virtual line in FIG. 5A, the annular rubber member 3 has a pre-designed target cross-sectional shape Vs set. The target cross-sectional shape Vs is defined by, for example, CAD data. In order to form the annular rubber member 3 having such a target cross-sectional shape Vs, it is important to appropriately set the winding conditions of the rubber strip 4.

As an example of the winding condition (that is, the design variable) of the rubber strip 4, for example, the winding pitch P of the rubber strip 4 (shown in FIG. 4) and the winding start end 4s of the rubber strip 4 (shown in FIG. 3). ) Is arranged at least one of the positions in the circumferential direction of the wound body 5 (hereinafter, may be simply referred to as “the position in the circumferential direction of the winding start end”). As the winding conditions of the present embodiment, the winding pitch P of the rubber strip 4 (shown in FIG. 4) and the position in the circumferential direction of the winding start end 4s are adopted. As shown in FIG. 3, the position in the circumferential direction of the winding start end 4s is defined by the central angle α1 of the wound body 5 determined with reference to the predetermined reference position Bp of the wound body 5. .. In addition, the winding condition of the rubber strip 4 includes not only the position in the circumferential direction of the winding start end 4s but also the axial position of the winding start end 4s in the wound body 5 (the position in the width direction of the tread rubber 3a). ) May be included.

Conventionally, the winding conditions of the rubber strip 4 have been set based on trial and error by an operator and empirical rules so far. Therefore, the finish of the annular rubber member 3 (shown in FIG. 5B) tends to vary depending on the skill level of the operator, and the annular rubber member having the target cross-sectional shape Vs (shown in FIG. 5A). It is difficult to form 3 stably.

In the calculation method of the present embodiment, at least one optimum solution of the winding condition of the rubber strip 4 is obtained based on the optimization algorithm using the computer 1 without depending on the skill level of the operator.

The optimization algorithm is for determining the optimum condition (in this embodiment, the winding condition of the rubber strip 4 (shown in FIG. 4)) that satisfies an arbitrary objective function under certain constraints. Is. Examples of the optimization algorithm include a genetic algorithm (GA (Genetic Algorithm)), a particle swarm optimization (PSO), and the like. Such an optimization algorithm is suitable for finding a wide-area optimum solution while preventing it from falling into a local solution. In the calculation method of the present embodiment, particle swarm optimization (PSO) having a relatively short calculation time is adopted, but a genetic algorithm (GA) or the like may be adopted.

In particle swarm optimization (PSO), multiple initial conditions (first generation) are created, the objective function of each condition is obtained, and each condition is updated (alternation of generations) so as to approach the most preferable objective function. Optimization is done at. By using random numbers to update each condition, the optimum condition is searched for in a wide area. Details of particle swarm optimization (PSO) are described in various documents such as IEICE Fundamentals Review (Institute of Electronics, Information and Communication Engineers) Vol.5 No.2, August 2011 "Particle Swarm Optimization and Nonlinear Systems". Has been done.

In the calculation method of the present embodiment, the winding conditions (design variables) for obtaining the optimum solution include the winding pitch P of the rubber strip 4 (shown in FIG. 4) and the position in the circumferential direction of the winding start end 4s (FIG. 4). It contains at least one of) (shown in 3). In the present embodiment, the winding pitch P of the rubber strip 4 and a group of positions in the circumferential direction of the winding start end 4s are set as one winding condition, and the winding conditions (the winding pitch P of the rubber strip 4 and the winding pitch P). The optimum solution (position in the circumferential direction of the winding start end 4s) is calculated. FIG. 6 is a flowchart showing an example of the processing procedure of the calculation method.

In the calculation method of the present embodiment, first, the constraint condition for winding the rubber strip 4 (shown in FIG. 4) is input to the computer 1 (step S1). The constraint condition is a condition (that is, a design standard) that must be satisfied in the formation of the annular rubber member 3. In the optimum solution calculation step S4 described later, the optimum solution of the winding condition is calculated based on the constraint condition.

The constraint conditions of the present embodiment include, for example, the number of windings of the rubber strip 4 (shown in FIG. 5A), the axial position of the wound body 5 on which the winding start end 4s of the rubber strip 4 is arranged, and the like. It includes at least one of the initial winding pitch of the rubber strip 4, the folding position of the winding of the rubber strip 4, and the cross-sectional shape of the rubber strip 4. The constraint conditions of the present embodiment are the number of windings of the rubber strip 4, the axial position of the wound body 5 on which the winding start end 4s of the rubber strip 4 is arranged, the initial winding pitch of the rubber strip 4, and the initial winding pitch of the rubber strip 4. The folding position of the winding of the rubber strip 4 is set. These constraints are based on, for example, the design information of the annular rubber member 3 (target cross-sectional shape Vs) and the structural drawing of the rubber product (raw tire 2T in the present embodiment) in which the annular rubber member 3 is used. Is set. These constraints are input to the computer 1.

Next, in the method of creating the present embodiment, at least one of the initial winding conditions (first-generation winding conditions) is input to the computer 1 (step S2). The initial winding condition is used in the calculation of the cross-sectional shape 10 (shown in FIG. 7) of the annular rubber member 3 in the optimum solution calculation step S4 described later. In the present embodiment, a plurality of winding conditions (a winding pitch P (shown in FIG. 4) and a group of positions in the circumferential direction of the winding start end 4s (shown in FIG. 3)) are set.

Each winding condition can be appropriately determined. Each winding condition may be directly input by the operator or may be randomly determined using a random number of the computer 1. When the random number of the computer 1 is used for random determination, it is desirable that the ring-shaped rubber member 3 is randomly determined within a range feasible in the manufacturing process. As a result, in the optimum solution calculation step S4 described later, it is possible to prevent the optimum solution from being calculated based on the winding conditions that cannot be realized in the manufacturing process. Further, the number of winding conditions can be set as appropriate. In this embodiment, 100 to 1000 initial winding conditions are set. The initial winding conditions are stored in the computer 1.

Next, in the calculation method of the present embodiment, the first method for specifying to the computer 1 the error of the annular rubber member 3 (shown in FIG. 7) from the target cross-sectional shape Vs (shown in FIG. 5 (a)). The objective function is input (step S3). The first objective function of the present embodiment includes an allowable error (margin of error) from the target cross-sectional shape Vs. The first objective function Fa is defined by the following equation (1).

ここで、
Ｆａ：第１目的関数
Ｅ_n：ゲージ誤差
δＰ_n：許容誤差
Ｔ_n：目標断面形状の半径方向の高さ
Ｒ_n：巻回条件で計算された環状のゴム部材の断面形状の半径方向の高さ
n：断面形状の幅方向位置を特定するための添字（１〜ｍ）
m：幅方向位置の個数

here,
Fa: first objective function E _n: the gauge error [delta] P _n: Tolerance T _n: the height in the radial direction of the target cross section R _n: the radial cross-sectional shape of the computed annular rubber member in the winding condition high difference
n: Subscript (1 to m) for specifying the position of the cross-sectional shape in the width direction
m: Number of positions in the width direction

FIG. 7 is a graph showing an example of the target cross-sectional shape Vs and the cross-sectional shape 10 of the annular rubber member 3 calculated based on the winding conditions. FIG. 8 is a partially enlarged view of FIG. 7. In the graphs of FIGS. 7 and 8, the height of the outer peripheral surface 5o (shown in FIG. 3) of the wound body 5 in the radial direction is set to zero on the radial coordinate axis y. Further, in the graphs of FIGS. 7 and 8, the tire equator C of the cross-sectional shape 10 of the rubber member 3 shown in FIG. 5B is set to zero on the coordinate axis x in the width direction.

In the above formula (1), the gauge error E _n, and, for the ratio E _n / [delta] P _n of the gauge error E _n tolerances and [delta] P _n, as shown in FIG. 8, the cross-sectional shape of the annular rubber member 3 It is calculated at each width direction position 8 spaced apart from each other in the width direction of 10. The first objective function Fa of the formula (1), for the ratio E _n / [delta] P _n of each widthwise position 8 shows the total value of all the widthwise position 8. Therefore, the smaller the value calculated by the first objective function Fa, the closer the cross-sectional shape 10 of the annular rubber member 3 is to the target cross-sectional shape Vs.

The interval between the positions 8 in the width direction can be appropriately set. The interval of this embodiment is set to, for example, 0.5 to 2.0 mm. Further, in the present embodiment, the permissible error δP _n is set to the same value at all the width direction positions 8. The value of this margin of error δP _n can be appropriately set based on the accuracy required for the annular rubber member 3.

The first objective function Fa is not limited to the above equation (1), and for example, the margin of error δP _n may be omitted. Further, the first objective function Fa may be the difference (area error) between the area of the target cross-sectional shape Vs and the area of the cross-sectional shape of the annular rubber member 3. The first objective function Fa is stored in the computer 1.

Next, in the calculation method of the present embodiment, the computer 1 obtains at least one optimum solution of the winding conditions (optimal solution calculation step S4). In the optimum solution calculation step S4 of the present embodiment, at least one optimum solution of the winding condition satisfying at least the first objective function Fa is obtained under the constraint condition based on the optimization algorithm. In the present embodiment, "satisfying the first objective function Fa" means that the value of the first objective function Fa satisfies a predetermined reference value (that is, the error is smaller than the reference value). Means. The reference value is appropriately set according to the accuracy required for the annular rubber member 3. FIG. 9 is a flowchart showing an example of the processing procedure of the optimum solution calculation step S4.

In the optimum solution calculation step S4 of the present embodiment, first, the cross-sectional shape 10 (shown in FIG. 7) of the annular rubber member 3 is calculated based on the input winding conditions (initial winding conditions) (shown in FIG. 7). Step S41). The cross-sectional shape 10 of the annular rubber member 3 is a constraint condition (that is, the number of turns of the rubber strip 4, the axial position of the wound body 5 on which the winding start end 4s of the rubber strip 4 is arranged, and the rubber strip 4. Based on the initial winding pitch and the folding position of the winding of the rubber strip 4, the winding conditions (that is, the winding pitch P of the rubber strip 4 (shown in FIG. 4), the circumferential direction of the winding start end 4s). Is calculated for each position (shown in FIG. 3).

The calculation method of the cross-sectional shape 10 (shown in FIG. 7) of the annular rubber member 3 is not particularly limited, but is, for example, based on the cross-sectional shape of the rubber strip 4 (shown in FIG. 5A). The shape of the stacked layers may be calculated, or may be calculated by simulation using the finite element method or the like. It is desirable that the cross-sectional shape 10 (shown in FIG. 7) of the annular rubber member 3 is calculated in consideration of the deformation of the cross-sectional shape of the rubber strip 4 in the lower layer. In the calculation of the cross-sectional shape 10 of the annular rubber member 3, the winding pitch P (shown in FIG. 4) under the winding condition is when the winding of the rubber strip 4 is folded back at the end portion of the cross-sectional shape 10 in the width direction. In addition, it is allowed to fluctuate. The calculated cross-sectional shape 10 of the annular rubber member 3 is stored in the computer 1.

Next, in the optimum solution calculation step S4 of the present embodiment, the first objective function Fa is calculated for each of the cross-sectional shapes 10 (shown in FIG. 7) of the annular rubber member 3 calculated for each winding condition (shown in FIG. 7). Step S42). The first objective function Fa is calculated using the above equation (1). The first objective function Fa of each winding condition is stored in the computer 1.

Next, in the optimum solution calculation step S4 of the present embodiment, the winding condition is updated (generational change) based on the optimization algorithm so that the first objective function Fa approaches the best winding condition (generational change). Step S43). In step S43, first, the first objective function Fa is the best (that is, the value of the first objective function Fa is the closest to the reference value, or the value of the first objective function Fa satisfies the reference value most). The winding condition is selected. Then, in step S43, the other winding conditions are updated so as to approach the best winding conditions.

The update of the winding condition (alternation of generations) of the present embodiment can be appropriately carried out based on the particle swarm optimization (PSO) with reference to the above-mentioned papers and the like. In step S43 of the present embodiment, the winding pitch P and the positions of the winding start end 4s in the circumferential direction are updated for each winding condition (design variable). Each updated winding condition is stored in the computer 1.

Next, in the optimum solution calculation step S4 of the present embodiment, it is determined whether or not the predetermined update end condition is satisfied (step S44). The update end condition can be set as appropriate. As the update end condition of the present embodiment, an upper limit value (for example, 40 to 200) of the update number (number of generations) of the winding condition specified by the operator is set. As a result, in the calculation method of the present embodiment, it is possible to prevent the winding condition from being updated more than necessary in the step S43, so that it is possible to prevent an increase in the calculation time.

Further, the update end condition is a condition for determining that the local solution has fallen (for example, in step S44, when the rate of change of the first objective function Fa is lower than a predetermined upper limit value, "Y". Conditions, etc.) may be set. With such an update end condition, the optimum solution of the winding condition can be efficiently obtained. The upper limit of the rate of change of the first objective function Fa is appropriately set. The update end condition is stored in the computer 1.

When it is determined in step S44 that the update end condition is satisfied (“Y” in step S44), a series of processes in the optimum solution calculation step S4 is completed, and the next step S5 is carried out. On the other hand, if it is determined in step S44 that the update end condition is not satisfied (“N” in step S44), steps S41 to S44 are performed again. As a result, in the optimum solution calculation step S4 of the present embodiment, each winding condition can be updated (generational change) toward the optimum solution of the winding condition until the update end condition is satisfied.

Next, in the calculation method of the present embodiment, it is determined whether or not the first objective function Fa is satisfied (that is, whether the value of the first objective function Fa satisfies a predetermined reference value). (Step S5). In step S5 of the present embodiment, first, among the winding conditions of the final generation, the winding condition having the best first objective function Fa is selected. Then, it is determined whether or not the first objective function Fa of the selected winding condition satisfies the reference value (that is, whether the error is smaller than the reference value).

When it is determined in step S5 that the value of the first objective function Fa satisfies the reference value (“Y” in step S5), the selected winding condition is determined as the optimum solution of the winding condition. (Step S6). On the other hand, when it is determined that the value of the first objective function Fa does not satisfy the reference value (“N” in step S5), the initial winding condition is newly input (step S2), steps S3 to step S3 to step. S5 is carried out again. As a result, in the calculation method of the present embodiment, the optimum solution of the winding condition satisfying the first objective function Fa can be reliably calculated.

As described above, according to the calculation method of the rubber strip of the present embodiment, the annular rubber member 3 shown in FIG. 5B is formed based on the optimization algorithm without being influenced by the skill level of the operator. It is possible to calculate the winding conditions of the rubber strip that can be stably formed in the target cross-sectional shape Vs (shown in FIG. 5A).

Then, in the tire manufacturing method of the present invention (hereinafter, may be simply referred to as "manufacturing method"), as shown in FIGS. 3 and 4, based on the winding conditions obtained by the above calculation method. It includes a step of forming an annular rubber member 3 (shown in FIG. 5B) by spirally winding the band-shaped rubber strip 4 around the wound body 5. Thereby, in the manufacturing method of the present invention, the annular rubber member 3 having the target cross-sectional shape Vs can be surely formed.

In the calculation method of the present embodiment, as shown in FIG. 8, the same margin of error δP _n is set at each width direction position 8 of the cross-sectional shape 10 of the annular rubber member 3, but in such an embodiment. Not limited. In the cross-sectional shape 10 of the annular rubber member 3, the portion 11 that does not touch the road surface (including the portion where the groove of the tread portion is formed) 11 has lower required accuracy than the portion 12 that touches the road surface. Therefore, the permissible error δP _n may be set to a different value depending on the required accuracy at each position 8 in the width direction.

The margin of error δP _n of the present embodiment includes a first margin of error and a second margin of error larger than the first margin of error. The value of the first tolerance and the value of the second margin of error can be appropriately set according to the accuracy required for the annular rubber member 3. The first tolerance is set to the same value as the margin of error δP _{n set in the previous embodiment.}

The first margin of error is set at the portion that touches the road surface (that is, the portion where the required accuracy is relatively high) 12. On the other hand, the second margin of error is set at the portion 11 that does not touch the road surface (that is, the portion where the required accuracy is relatively low) 11. Thus, in this embodiment, it is possible to increase the tolerance [delta] P _n of the portion 11 which does not contact with the road surface, can be given a sharp tolerances [delta] P _n in each position in the width direction 8. Therefore, in this calculation method, the optimum solution of the winding condition can be obtained in a short time.

In the previous embodiments, the optimum solution of the winding condition satisfying the first objective function Fa has been obtained, but the present invention is not limited to such an embodiment. For example, even if the optimum solution of the winding condition that satisfies the first objective function Fa and further satisfies the second objective function for specifying the variation in the cross-sectional shape 10 of the annular rubber member 3 in the circumferential direction is obtained. good. As a result, in the calculation method of this embodiment, the annular rubber member 3 having the target cross-sectional shape Vs (shown in FIG. 5A) is formed, and the annular rubber member 3 having a good FV (force variation) is formed. The winding conditions that can be formed can be obtained. In this embodiment, the same configurations as those in the previous embodiment are designated by the same reference numerals, and the description thereof may be omitted.

FIG. 10 is a flowchart illustrating a calculation method according to another embodiment of the present invention. FIG. 11 is a side sectional view of the annular rubber member 3. FIG. 11 shows a state in which the annular rubber member 3 is cut in the circumferential direction at the position 8 in the width direction shown in FIG. Further, as shown in FIG. 11, in this embodiment, at each width direction position 8 (shown in FIG. 8) of the cross-sectional shape 10 of the annular rubber member 3, a plurality of circumferential positions spaced apart from each other in the circumferential direction. 15 is defined. The interval between the circumferential positions 15 can be appropriately set, for example, according to the accuracy of calculating the variation in the cross-sectional shape 10 of the annular rubber member 3 in the circumferential direction.

The calculation method of this embodiment further includes a step S9 of inputting to the computer 1 a second objective function for specifying the variation in the cross-sectional shape 10 (shown in FIG. 8) of the annular rubber member 3 in the circumferential direction. .. The second objective function Fb is defined by the following equation (2).

ここで、
Ｆｂ：第２目的関数
Ｗ１_n：周方向位置の最大厚さ
Ｗ２_n：周方向位置の最小厚さ
n：断面形状の幅方向位置を特定するための添字（１〜ｍ）
m：幅方向位置の個数

here,
Fb: Second objective function W1 _n : Maximum thickness of the _{circumferential position W2 n} : Minimum thickness of the circumferential position
n: Subscript (1 to m) for specifying the position of the cross-sectional shape in the width direction
m: Number of positions in the width direction

In the above equation (2), the maximum thickness W1 _n of the circumferential position is the annular rubber member 3 calculated at the plurality of circumferential positions 15 shown in FIG. 11 at each width direction position 8 shown in FIG. It shows the largest thickness among the thicknesses of. The minimum thickness W2 _{n at} the circumferential position indicates the smallest thickness among the thicknesses of the annular rubber member 3 calculated at the plurality of circumferential positions 15 shown in FIG. Therefore, in the above equation (2), W1 _{n −} W2 _n indicates a variation in the circumferential direction of the cross-sectional shape 10 of the annular rubber member 3 at each width direction position 8 shown in FIG. Then, the second objective function Fb is obtained by calculating the total value of all the width direction positions 8 for _{the variation (W1 n −} W2 _n ) of each width direction position 8. Therefore, the smaller the value calculated by the second objective function Fb, the smaller the variation in the cross-sectional shape 10 of the annular rubber member 3 in the circumferential direction.

FIG. 12 is a flowchart showing an example of the processing procedure of the optimum solution calculation step S4 according to another embodiment of the present invention. In the optimum solution calculation step S4 of this embodiment, based on the optimization algorithm, at least one optimum of the winding condition satisfying at least both the first objective function Fa and the second objective function Fb under the constraint condition. A solution is required. In the present embodiment, "satisfying the second objective function Fb" means that the value of the second objective function Fb satisfies a predetermined reference value (that is, the variation is smaller than the reference value). Means. The reference value is appropriately set according to the accuracy required for the annular rubber member 3.

In the optimum solution calculation step S4 of this embodiment, the second objective function Fb (shown in the above equation (2)) is calculated for each of the cross-sectional shapes 10 of the annular rubber member 3 calculated for each winding condition S45. Is further included. The second objective function Fb is input to the computer 1.

In step S43 of this embodiment, the winding conditions are updated (generational change) based on the optimization algorithm so that the first objective function Fa and the second objective function Fb approach the best winding conditions.

As shown in FIG. 10, in step S5 of this embodiment, whether the value of the first objective function Fa and the second objective function Fb are satisfied (that is, the value of the first objective function Fa satisfies the reference value. And, it is determined whether or not the second objective function Fb satisfies the reference value).

In step S5 of this embodiment, first, among the winding conditions of the final generation, the winding condition in which the first objective function Fa and the second objective function Fb are the best is selected. Then, whether the first objective function Fa of the selected winding condition satisfies the reference value (that is, whether the error is smaller than the reference value) and whether the second objective function Fb satisfies the reference value. (That is, whether the variation is smaller than the reference value) is determined. Thereby, in the calculation method of this embodiment, the optimum solution of the winding condition satisfying the first objective function Fa and the second objective function Fb can be reliably calculated.

In the previous embodiment, the optimum solution of the winding condition that satisfies both the first objective function Fa and the second objective function Fb has been obtained, but the present invention is not limited to such an embodiment. For example, the optimum solution of the winding condition that satisfies the first objective function Fa and further satisfies the third objective function for specifying the fluctuation amount of the winding pitch P (shown in FIG. 4) of the rubber strip 4 is obtained. May be done. The amount of fluctuation of the winding pitch P is the winding pitch (not shown) when the winding pitch P cannot be wound when the rubber strip 4 is folded back, and the winding pitch P. It means a difference. The smaller the fluctuation amount of the winding pitch P, the smaller the load on the applicator 7 that supplies the rubber strip 4.

As a result, in the calculation method of this embodiment, the load on the applicator 7 that supplies the rubber strip 4 is small while forming the annular rubber member 3 having the target cross-sectional shape Vs (shown in FIG. 5A). The winding condition can be obtained. FIG. 13 is a flowchart illustrating a calculation method according to still another embodiment of the present invention. In this embodiment, the same configurations as those in the previous embodiment are designated by the same reference numerals, and the description thereof may be omitted.

The calculation method of this embodiment further includes a step S10 of inputting to the computer 1 a third objective function for specifying the fluctuation amount of the winding pitch P (shown in FIG. 4) of the rubber strip 4. The third objective function Fc is defined by the following equation (3).

ここで、
Ｆｃ：第３目的関数
Ｐｓ_i：巻付けピッチの変動量
i：変動量を特定するための添字

here,
Fc: Third objective function Ps _i : Fluctuation amount of winding pitch
i: Subscript to identify the amount of fluctuation

In the above formula (3), the fluctuation amount Ps _i of the winding pitch is the fluctuation amount when the winding pitch P (shown in FIG. 4) fluctuates in the step S41 for calculating the cross-sectional shape of the annular rubber member 3. Shown. Then, the third objective function Fc is obtained by specifying the largest of all the variable quantities Ps _i. Therefore, the smaller the value calculated by the third objective function Fc, the smaller the load on the applicator 7.

FIG. 14 is a flowchart showing an example of the processing procedure of the optimum solution calculation step S4 according to another embodiment of the present invention. In the optimum solution calculation step S4 of this embodiment, based on the optimization algorithm, at least one optimum of the winding condition satisfying at least both the first objective function Fa and the third objective function Fc under the constraint condition. A solution is required. In the present embodiment, "satisfying the third objective function Fc" means that the value of the third objective function Fc satisfies a predetermined reference value (that is, the fluctuation amount Ps _i of the winding pitch is the reference. It means that it is smaller than the value). The reference value is appropriately set according to the durability of the applicator 7, for example.

In the optimum solution calculation step S4 of this embodiment, the third objective function Fc (shown in the above equation (3)) is calculated for each of the cross-sectional shapes 10 of the annular rubber member 3 calculated for each winding condition S46. Is further included. The third objective function Fc is input to the computer 1.

In step S43 of this embodiment, the winding conditions are updated (generational change) based on the optimization algorithm so that the first objective function Fa and the third objective function Fc approach the best winding conditions.

As shown in FIG. 13, in step S5 of this embodiment, is the value of the first objective function Fa and the third objective function Fc satisfied (that is, the value of the first objective function Fa and the third objective function Fc)? However, it is determined whether or not the predetermined reference value is satisfied.

In step S5 of this embodiment, first, among the winding conditions of the final generation, the winding condition in which the first objective function Fa and the third objective function Fc are the best is selected. Then, whether the first objective function Fa of the selected winding condition satisfies the reference value (that is, whether the error is smaller than the reference value) and whether the third objective function Fc satisfies the reference value. (That is, _{whether or not the fluctuation amount Ps i} of the winding pitch is smaller than the reference value) is determined. Thereby, in the calculation method of this embodiment, the optimum solution of the winding condition (design variable) satisfying the first objective function Fa and the third objective function Fc can be reliably calculated.

In the previous embodiment, the optimum solution of the winding condition satisfying both the first objective function Fa and the third objective function Fc has been obtained, but the present invention is not limited to such an embodiment. For example, the optimum solution of the winding condition satisfying the first objective function Fa, the second objective function Fb, and the third objective function Fc may be obtained.

In the previous embodiments, the optimum solution of the winding condition has been obtained based only on the particle swarm optimization (PSO) or the genetic algorithm (GA), but the present invention is not limited to such an embodiment. For example, in the optimum solution calculation step S4, the optimum solution of the winding condition may be obtained by switching to another optimization method such as a linear programming method on the way. As a result, a better optimum solution for winding conditions can be obtained in a short time.

Further, in the conventional embodiments, the number of turns of the rubber strip 4 is included as a constraint condition, but the present invention is not limited to such an embodiment. The number of turns of the rubber strip 4 may be set as a winding condition (that is, a design variable) instead of a constraint condition. As a result, for example, when the rubber strip 4 is wound by a pair of applicators (not shown) arranged apart from each other in the axial direction of the wound body 5, the number of times the rubber strip 4 of each applicator is wound is increased. The optimal solution for can be found. Further, the constraint condition may further include the cross-sectional shape of the rubber strip 4 (shown in FIG. 5A).

Although the particularly preferable embodiments of the present invention have been described in detail above, the present invention is not limited to the illustrated embodiments and can be modified into various embodiments.

According to the processing procedure shown in FIGS. 6 and 9, the winding conditions for spirally winding the strip-shaped rubber strip on the wound body to form an annular rubber member having a target cross-sectional shape set the computer. Calculated using (Example). In the embodiment, the constraint conditions for winding the rubber strips and the first objective function Fa shown in the above equation (1) were input to the computer. Then, in the embodiment, the optimum solution of the winding condition satisfying at least the first objective function Fa was calculated by the computer based on the optimization algorithm under the constraint condition.

In addition, for comparison, winding conditions were set based on trial and error by the operator and empirical rules so far (comparative example).

Then, the cross-sectional shape of the rubber member was calculated using a computer based on the winding conditions calculated in the examples and the winding conditions set in the comparative examples. Then, the cross-sectional shape of the rubber member of the example and the cross-sectional shape of the rubber member of the comparative example were evaluated for their errors from the target cross-sectional shape. The details of the constraint conditions and the winding conditions are as described in the above specification.

As a result of the test, the cross-sectional shape of the rubber member of the example was closer to the target cross-sectional shape than the cross-sectional shape of the rubber member of the comparative example. Therefore, in the method of producing the examples, the annular rubber member could be stably formed in the target cross-sectional shape.

S1 Step of inputting the constraint condition S3 Step of inputting the first objective function S4 Finding the optimum solution of the winding condition satisfying the first objective function

Claims (9)

A method for calculating winding conditions using a computer for spirally winding a strip-shaped rubber strip around an object to be wound to form an annular rubber member having a predetermined target cross-sectional shape. There,
The process of inputting the constraint conditions for winding the rubber strip into the computer, and
A step of inputting a first objective function for specifying an error of the rubber member from the target cross-sectional shape into the computer, and
A step of inputting a second objective function for specifying a variation in the cross-sectional shape of the rubber member in the circumferential direction into the computer, and
The computer is based on the optimization algorithm under the constraint condition satisfies a reference value the value of the first objective function is predetermined, and the reference value of the second objective function is predetermined A method for calculating a winding condition of a rubber strip, which comprises a step of obtaining at least one optimum solution of the winding condition satisfying a value.
A method for calculating winding conditions using a computer for spirally winding a strip-shaped rubber strip around an object to be wound to form an annular rubber member having a predetermined target cross-sectional shape. There,
The process of inputting the constraint conditions for winding the rubber strip into the computer, and
A step of inputting a first objective function for specifying an error of the rubber member from the target cross-sectional shape into the computer, and
A step of inputting a third objective function for specifying the fluctuation amount of the winding pitch of the rubber strip into the computer, and
Based on the optimization algorithm, the computer satisfies the predetermined reference value of the value of the first objective function under the constraint condition, and the value of the third objective function is a predetermined reference value. A method for calculating a winding condition of a rubber strip, which comprises a step of obtaining at least one optimum solution of the winding condition satisfying a value.
The constraint conditions are the number of times the rubber strip is wound, the axial position of the wound body on which the winding start end of the rubber strip is arranged, the initial winding pitch of the rubber strip, and the winding of the rubber strip. The method for calculating the winding condition of the rubber strip according to claim 1 or 2, which includes the folding position of the rubber strip and at least one of the cross-sectional shapes of the rubber strip. The method for calculating a rubber strip winding condition according to any one of claims 1 to 3, wherein the first objective function includes an acceptable error from the target cross-sectional shape. The permissible error includes a first permissible error and a second permissible error larger than the first permissible error.
The method for calculating a rubber strip winding condition according to claim 4, wherein the second margin of error is set in a portion of the cross-sectional shape of the rubber member where the required accuracy is relatively low. The first margin of error is set at the portion that comes into contact with the road surface.
The method for calculating a winding condition of a rubber strip according to claim 5, wherein the second margin of error is set in a portion that does not touch the road surface.
Any of claims 1 to 6, wherein the winding condition includes at least one of the winding pitch of the rubber strip and the circumferential position of the wound body on which the winding start end of the rubber strip is arranged. How to calculate the winding conditions of the rubber strip described in.
The computer further comprises the step of inputting at least one of the initial winding conditions.
The steps for obtaining the optimum solution include a step of calculating the cross-sectional shape of the rubber member based on the winding conditions and a step of calculating the cross-sectional shape of the rubber member.
The winding of the rubber strip according to any one of claims 1 to 7, which includes a step of updating the winding condition based on the optimization algorithm so that the cross-sectional shape of the rubber member approaches the target cross-sectional shape. How to calculate the times condition. It ’s a tire manufacturing method.
A method for manufacturing a tire, which comprises a step of forming the rubber member under the winding conditions obtained by the calculation method according to any one of claims 1 to 8.

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