JP5128853B2 - Pneumatic tire design method - Google Patents

Description

  The present invention relates to a method for designing a pneumatic tire, and more particularly, a pneumatic tire such as a pneumatic tire used in an automobile can be efficiently and easily designed using an analysis method such as a finite element method. The present invention relates to a tire design method.

  In general, as a tire design method considering physical properties, a plurality of rubber members with known physical properties are set in advance, the physical properties are changed for each rubber member, a tire with the changed physical properties is prototyped and tested, rolling resistance and The conventional method has been to design and develop by repeating trial manufacture and testing until the target performance is obtained for the spring constant and the like.

  In recent years, with the advancement of computers, design optimization has been performed using a large-scale three-dimensional finite element method analysis model (hereinafter referred to as a finite element model). This is done by dividing the three-dimensional shape of the object into a finite number of elements, creating a finite element model that approximates each element by adding physical properties such as rigidity and mass, and using this model, The objective performance of an object is analyzed under constraint conditions including the shape, structure, or physical quantity of the object, and the optimum structure of the object is obtained.

For example, in the case of tire design, a three-dimensional tire model is created and the tire tread shape and rubber to achieve the target performance such as ride comfort and steering stability under predetermined boundary conditions or constraint conditions. An optimization calculation method has been proposed in which a design factor such as a tire shape, structure, physical quantity, and the like, and a combination thereof are calculated (for example, see Patent Documents 1 and 2).
JP-A-7-164815 JP 2002-222216 A

  Using the above-mentioned technology, create a finite element model (three-dimensional tire model) of the object, give conditions such as external force to the finite element model by the finite element method, and then deform the object at that time. Optimal tire structure and rubber physical properties can be obtained only by simulation.

  However, in the analysis using the three-dimensional tire model, although the calculation can be advanced in consideration of the tire shape at the initial design and the physical properties of the rubber parts, the physical properties that vary during the manufacturing process cannot be considered. That is, the effect of tire vulcanization conditions in the actual production of tires has not been considered. For this reason, in order to determine the best shape, structure, and physical properties in consideration of the final rubber physical properties determined by vulcanization, trial and error of tire prototyping and testing had to be repeated. As described above, there are many cases where tire development is repeated trial and error in trial production and testing, resulting in a very inefficient and high cost.

  The present invention provides a pneumatic tire design method capable of improving target performance in consideration of the effects of tire vulcanization, increasing the efficiency of tire design and development, and providing tires at low cost. The purpose is to provide.

  The present invention seeks design factors and vulcanization conditions that satisfy the target performance by predicting the effect of tire vulcanization on rubber elastic modulus.

  Specifically, the pneumatic tire designing method of the present invention includes (a) a tire basic model representing a tire cross-sectional shape including an internal structure, an objective function representing a physical quantity for tire performance evaluation, and each rubber member of the tire. At least one of a vulcanization condition variable for determining a vulcanization condition for determining physical properties, a design variable for determining physical properties of the rubber member and the reinforcing material, a physical property for evaluating the rubber member and the reinforcing material, a physical quantity for performance evaluation, and a tire size. A step of determining a constraint condition to be constrained; (b) obtaining thermal energy applied to each rubber member of the tire according to a vulcanization condition based on a vulcanization condition variable and determining a physical property value of the rubber member based on the obtained thermal energy (C) a step of obtaining a value of a vulcanization condition variable and a design variable that give an optimum value of an objective function using the obtained physical property value while considering the constraint condition; Includes the step of designing the tire based on the vulcanization conditions variables and design variables gives the optimum value of the number.

In addition , after performing step (a) and before performing step (b), the strain of each rubber member under actual use conditions from the finite element method (this strain includes static strain due to internal pressure and In addition, the step (e) for obtaining the dynamic strain under actual use conditions (for example, when the vehicle is running) and the temperature are performed, and the step (c) is obtained in the step (b). Using the physical property value of the rubber member and the strain and temperature of each rubber member obtained in step (e), the physical property value of the rubber member was updated from the known correspondence between the strain and temperature of each rubber member and the physical property value. Later, using the updated physical property values, the values of the vulcanization condition variables and the design variables that give the optimum values of the objective function are obtained while considering the constraint conditions .

  In the step (b), in order to obtain the heat energy, heat transfer prediction is performed in consideration of the thermal conductivity of the rubber compound, the specific heat, the temperature dependence of the density, and the influence of the heat of vulcanization reaction generated during vulcanization. The physical property value of the rubber member can be obtained based on the heat energy by using the amount of heat and the maximum temperature achieved by each tire member as heat energy.

  In step (c), the sensitivity of the objective function that is the ratio of the change amount of the objective function to the unit change amount of the vulcanization condition variable and the constraint that is the ratio of the change amount of the constraint condition to the unit change amount of the vulcanization condition Based on the sensitivity of the condition and the sensitivity of the objective function, which is the ratio of the change amount of the objective function to the unit change amount of the design variable, and the sensitivity of the constraint condition, which is the ratio of the change amount of the constraint condition to the unit change amount of the design variable , Predicting the amount of change of the vulcanization condition variable and the design variable that gives the optimum value of the objective function while taking into account the constraint conditions, and the objective function when the vulcanization condition variable is changed by an amount corresponding to the predicted amount The value of the constraint condition when the value of the design variable and the design variable are changed by the amount corresponding to the prediction amount, and the value of the objective function and the design variable when the design variable is changed by the amount corresponding to the prediction amount correspond to the prediction amount Amount changed The value of the vulcanization condition variable and the design variable value that give the optimum value of the objective function based on the predicted value and the calculated value and giving the optimum value of the objective function can be obtained based on the predicted value and the calculated value. it can.

  The vulcanization condition variable can represent at least one of a tire mold side temperature, a bladder side temperature, and a vulcanization time.

  The design variable may represent at least one of a Young's modulus, Poisson's ratio of rubber, and a Young's modulus or Poisson's ratio in each direction of the anisotropic reinforcing material.

  According to the present invention, in step (a), a tire basic model representing a tire cross-sectional shape including an internal structure, an objective function representing a physical quantity for tire performance evaluation, and a vulcanization condition for determining physical properties of each rubber member of the tire are determined. A vulcanization condition variable to be determined, a design variable to determine the physical properties of the rubber member and the reinforcing material, and a constraint condition that restricts at least one of the physical properties of the rubber member and the reinforcing material, the physical quantity for performance evaluation, and the tire size. Determine. The tire basic model is preferably divided into a plurality of elements. As an objective function representing a physical quantity for tire performance evaluation, a physical quantity that governs superiority or inferiority of the tire such as rolling resistance and lateral spring constant can be used. As a design variable that determines the physical properties of the rubber member of the tire, elastic modulus such as Young's modulus and Poisson's ratio and loss characteristics for each rubber member can be used. Constraints that restrict the placement of rubber members and rubber members of tires include the restriction of the Young's modulus and Poisson's ratio of the rubber member, the restriction of the longitudinal spring constant of the tire, the restriction of the upper and lower primary natural frequencies, and the restriction of the case rigidity. And belt elastic modulus. The vulcanization condition variable that determines the vulcanization condition that determines the physical properties of each rubber member of the tire includes physical energy that determines the vulcanization condition determined by the mold side temperature, the bladder side temperature, and the vulcanization time.

  The objective function, the vulcanization condition variable, the design variable, and the constraint condition are not limited to the above example, and various things can be determined according to the tire design purpose.

  In the next step (b), the thermal energy applied to each rubber member of the tire under the vulcanization condition based on the vulcanization condition variable is obtained, and the physical property value of the rubber member is obtained based on the obtained thermal energy. When determining the physical properties of the rubber member, in step (b), in order to determine the thermal energy, the thermal conductivity of the rubber compound, the specific heat, the temperature dependence of the density, and the vulcanization reaction that occurs during vulcanization. It is effective to perform heat transfer prediction in consideration of the influence of the heat quantity, and to determine the physical property value of the rubber member based on the heat quantity obtained or the maximum temperature and heat quantity of each tire member as heat energy.

  In the next step (c), the value of the vulcanization condition variable and the value of the design variable that give the optimum value of the objective function are obtained using the obtained physical property values while considering the constraint conditions. Obtaining the value of this design variable includes obtaining the value of the design variable that gives the optimum value of the objective function while satisfying the constraint conditions. In this case, the sensitivity of the objective function, which is the ratio of the change amount of the objective function to the unit change amount of the vulcanization condition variable, and the sensitivity of the constraint condition, which is the ratio of the change amount of the constraint condition to the unit change amount of the vulcanization condition, Based on the sensitivity of the objective function, which is the ratio of the change amount of the objective function to the unit change amount of the design variable, and the sensitivity of the constraint condition, which is the ratio of the change amount of the constraint condition to the unit change amount of the design variable, Predict the amount of change in the vulcanization condition variable and design variable that give the optimum value of the objective function while taking into account the value and design of the objective function when the vulcanization condition variable is changed by an amount corresponding to the predicted amount The value of the constraint condition when the variable was changed by the amount corresponding to the predicted amount, the value of the objective function when the design variable was changed by the amount corresponding to the predicted amount, and the design variable were changed by the amount corresponding to the predicted amount. When constraints If, calculated, and based on the predicted value and the calculated value, it is effective to determine the values of and design variables vulcanization condition variable which gives the optimum value of the objective function while considering the constraint condition. As a result, the value of the vulcanization condition variable and the value of the design variable when the value of the objective function is optimized in consideration of the constraints are obtained.

In step (d), the tire is designed by changing the tire basic model and the like based on the vulcanization condition variable and the design variable that give the optimum value of the objective function. In addition, after performing step (a) and before performing step (b), step (e) for determining strain and temperature of each rubber member under actual use conditions from the finite element method is performed, and step (c) ), Using the physical property value of the rubber member obtained in step (b) and the strain and temperature of each rubber member obtained in step (e), from the known correspondence between the strain and temperature of each rubber member and the physical property value. After updating the physical property value of the rubber member, the updated physical property value is used to obtain the value of the vulcanization condition variable and the design variable value that give the optimum value of the objective function while considering the constraint conditions.

  When designing and developing based on the design method of the present invention, unlike the conventional design and development based on trial and error, designing from the best mode design based on computer calculation and taking into account the vulcanization conditions during production It is possible to evaluate the performance of the tires to a certain extent, achieve remarkable efficiency, and reduce development costs.

  As described above, according to the present invention, the vulcanization condition variable and the design variable that give the optimum value of the objective function in consideration of the constraint condition are obtained, and the optimum rubber member and reinforcing material are obtained from these vulcanization condition variable and design variable. Since the tire having the physical properties is designed, there is an effect that the design / development is highly efficient and the tire having the best structure can be designed at a low cost.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. Hereinafter, prior to the description of the embodiment of the present invention, a comparative example of the present invention will be described first.

[ Comparative Example ]
FIG. 1 shows an outline of a personal computer for carrying out the pneumatic tire designing method according to this comparative example . This personal computer has a keyboard 10 for inputting data and the like, a computer main body that calculates vulcanization condition variables and design variables that satisfy constraint conditions and optimize an objective function, for example, maximum or minimum, according to a program stored in advance 12 and a CRT 14 for displaying a calculation result of the computer main body 12 and the like.

  First, an example of obtaining an elastic modulus (Young's modulus) that is a physical property of each rubber member that reduces rolling resistance while predicting tire vulcanization will be described.

  In determining the Young's modulus, in order to reduce rolling resistance, the Young's modulus, which is a physical property of each rubber member, which makes the distortion energy loss (hysteresis loss) of the tire the minimum value that is the optimum value may be determined. .

  FIG. 2 shows a processing routine of the program according to the present embodiment. In step 100, a tire cross-sectional shape in a natural equilibrium state is set as a reference shape, and this reference shape is modeled by a method capable of numerically and analytically determining a rolling resistance value during load rolling, such as a finite element method. And a tire basic model that represents a tire cross-sectional shape including an internal structure and is divided into a plurality of elements by mesh division. The reference shape is not limited to the tire cross-sectional shape in a natural equilibrium state, and may be any shape. Here, modeling means that the tire shape, structure, material, and pattern are digitized into an input data format to a computer program created based on a numerical / analytical method.

  FIG. 3 shows this tire basic model, and shows a pneumatic tire 20 having a carcass 22 divided into a plurality of rubber members. The carcass 22 is folded back by a bead 26. The inner side of the carcass 22 is an inner liner 24, and a bead rubber 36 is disposed on the inner liner 24 so as to extend. A substantially triangular area formed by the folded carcass 22 is a bead filler 28. A belt 30 is disposed above the carcass 22, a tread rubber 32 having a groove is disposed on the outer side in the radial direction of the belt 30, and a side rubber 34 is disposed on the outer side in the axial direction of the carcass 22. Yes. In addition, although the example which divided | segmented the tire basic model into multiple for every rubber member was given, you may divide | segment into arbitrary shapes, such as a triangle, according to the design objective.

  In the next step 102, an objective function that represents a physical quantity for tire performance evaluation, a constraint condition that restricts physical properties of the rubber member, a vulcanization condition variable that determines a vulcanization condition that determines the physical property of each rubber member of the tire, and a rubber member Determine design variables that determine physical properties. In the present embodiment, in order to design the vulcanization conditions and the elastic modulus (Young's modulus) that reduce the rolling resistance of the tire, the objective function OBJ, the constraint condition G, and the vulcanization condition V are determined as follows.

Objective function OBJ: Rolling resistance value Constraint G: Case stiffness is the same as the current case (case stiffness for existing tires)
Vulcanization condition V: Current equivalent (for example, a condition determined by at least one of mold side temperature, bladder side temperature, and vulcanization time).

The design variable that determines the physical properties of the rubber member is a coefficient that determines the Young's modulus expressed by the following equation (1) so that a predetermined range can be changed from the Young's modulus of the rubber member in the tire basic model. Corresponding. The coefficients that determine the Young's modulus are coefficients r ₁ , r ₂ , r ₃ ,... (Hereinafter, represented by the general formula r _i , where i = 1, 2,..., A predetermined natural number). Young's modulus is set to vary increased or decreased by at a predetermined predetermined increment amount, the coefficient r _i when multiplied by a coefficient Young's modulus of the rubber member in the tire basic model to obtain a Young's modulus of the rubber member Set as a design variable.

e _i = r _i · eo --- (1)
However, e _i: Young's modulus r _i: coefficient eo: Young's modulus of the rubber member in the tire basic model,
It is.

In addition, the vulcanization condition variable that determines the vulcanization condition corresponds to the coefficient that determines the vulcanization condition expressed by the following equation (2) so that the predetermined energy range that can be given at the time of tire manufacture can be changed. Is done. Coefficients that determine the vulcanization conditions are coefficients q ₁ , q ₂ , q ₃ ,... (Hereinafter, expressed as general formula q _j , where j = 1, 2,..., A predetermined natural number) The vulcanization conditions are set so that the vulcanization conditions fluctuate by increasing or decreasing in order by a predetermined increment in order, and the coefficient q _j when multiplying the condition value defining the vulcanization conditions for the rubber member by the coefficient is the vulcanization condition variable Set as.

V _j = q _j · vo --- (2)
Where V _j : vulcanization condition q _j : coefficient (vulcanization condition variable)
vo: Vulcanization conditions for current tires.

Thus objective function OBJ, after determining constraints G, the vulcanizing condition variable q _j and design variables r _i, in step 104 of FIG. 2, to calculate the initial value of the objective function and constraints. That is, the current tire structure (the shape that is the basic tire model of the target tire), the current rubber composition (element composition of the rubber member of the target tire), and the current vulcanization conditions (when manufacturing the target tire) Under the current vulcanization conditions, the initial value of the objective function (for example, tire rolling resistance) and the initial value of the constraint conditions (for example, case rigidity and belt elastic modulus) are calculated.

  The calculation of the initial value is carried out by calculating the heat conduction when the energy is applied under the current vulcanization condition for the tire basic model of the current tire structure having the rubber member with the current rubber composition by the finite element method. Perform physical property calculations. Using the obtained physical property value (for example, Young's modulus), the value of the objective function and the value of the constraint condition are obtained.

  The heat conduction calculation may be performed by heat transfer prediction described below, or may be executed by storing an experimentally obtained value as an initial value and reading this value.

In the next step 106, each varied by a unit amount [Delta] q _j vulcanized condition variable q _j the rubber member of the tire to vary the physical properties of the tire basic model by vulcanization conditions, performing heat transfer calculations. Thereby, the calorie | heat amount (thermal energy) of each part of a tire given by vulcanization conditions can be calculated | required.

  In the heat conduction calculation in step 106, it is preferable that the thermal conductivity and reaction heat of the rubber member are experimentally obtained in advance for each material, stored in a database, and stored. In the present embodiment, in order to perform heat transfer prediction under vulcanization conditions (for example, mold side temperature, bladder side temperature, vulcanization time, etc.), prediction parameters are obtained in advance and stored in a database.

  The prediction parameter is used when calculating heat transfer to each tire member based on vulcanization conditions. Specifically, it corresponds to the thermal conductivity, specific heat, density, reaction heat during vulcanization, and temperature dependence thereof, but these are preferably measured and databased. It is also possible to estimate from the rubber compounding content.

  Therefore, the heat transferability of each rubber member can be obtained by performing unsteady heat conduction calculation based on a prediction parameter utilizing the finite element method under an arbitrary vulcanization condition. Energy) can be calculated (predicted).

  In step 108, the physical property value (Young's modulus) of the rubber member is predicted from the calorific value calculation result of each part of the tire obtained in step 106. In the physical property prediction calculation of the rubber member in this step 108, it is preferable that the relationship between the physical property value of the rubber member and the amount of heat is experimentally obtained in advance for each material, stored in a database, and stored. In the present embodiment, in order to predict the physical property values of the rubber member, the correlation between each of the vulcanization temperature and vulcanization time and the physical properties of the rubber is obtained in advance and stored in a database.

  That is, for each of a plurality of rubber members made of various rubbers, the physical property values of the rubber member when the vulcanization temperature and the vulcanization time are changed are measured in advance in a test environment such as a laboratory. From this result, the properties of the physical properties (rubber elastic modulus such as Young's modulus and loss properties) of the rubber member with respect to the maximum vulcanization temperature and the total heat quantity are obtained as a master curve, and are made into a database. FIG. 4 shows rubber loss characteristics as an example of physical properties of the rubber member. This example of the rubber loss characteristic shows a characteristic that the rubber loss characteristic value is once decreased and then increased as the thermal energy amount is increased. FIG. 5 shows the belt rubber elastic modulus characteristics. This example of the belt rubber elastic modulus shows a characteristic in which the rubber elastic modulus generally gradually increases as the amount of thermal energy increases.

  Therefore, in step 108, first, the maximum vulcanization temperature and the total heat quantity in each tire member (or element) are obtained from the calorific value calculation result of each tire part obtained in step 106. Next, the physical property value (Young's modulus) of the rubber member is obtained by obtaining the physical property value of the rubber member corresponding to the maximum vulcanization temperature and the total heat quantity of each tire member (or element) using the master curve created in the database. Predict.

In the next step 110, each varying by [Delta] r _i design variables r _i a predetermined rubber member in order to change the physical properties of the tire basic model. In the next step 112, the value OBJ _i of the objective function and the value G _{i of the} constraint condition after changing the design variable Δr _i are calculated, and the design is performed according to the following equations (3) and (4) from the results. The sensitivity dOBJ / dr _i of the objective function, which is the ratio of the change amount of the objective function to the unit change amount of the variable, and the sensitivity dG / dr _i of the constraint condition, which is the ratio of the change amount of the constraint condition to the unit change amount of the design variable Are calculated for each design variable.

Further, in order to consider the vulcanization conditions, in Steps 110 and 112, as in the calculation of the initial value, the physical property calculation of the rubber member is performed by the heat conduction calculation when energy is applied under the changed vulcanization conditions, Using the obtained physical property value (for example, Young's modulus), the value of the objective function and the value of the constraint condition are obtained. Then, the value OBJ _j of the objective function and the value G _{j of the} constraint condition after changing the vulcanization condition variable by Δq _j are calculated, and the vulcanization condition is calculated from the results according to the following equations (5) and (6). The sensitivity dOBJ / dq _j of the objective function, which is the ratio of the change amount of the objective function to the unit change amount of the variable, and the sensitivity dG / dq of the constraint condition, which is the ratio of the change amount of the constraint condition to the unit change amount of the vulcanization condition variable _j is calculated for each vulcanization condition variable.

These sensitivity, when the vulcanization condition variable is a unit amount [Delta] q _j changes, may each forecast whether the value of the objective function is how to change the time obtained by the unit amount [Delta] r _i change the design variable.

  In the next step 114, it is determined whether or not the calculation has been completed for all the rubber members. If the calculation has not been completed for all the rubber members, steps 106 to 112 are repeatedly executed.

  In the next step 116, the initial value OBJo of the objective function, the initial value Go of the constraint condition, the initial value qo of the vulcanization condition variable, the initial value ro and the sensitivity of the design variable are used to satisfy the constraint condition by mathematical programming. Predict the amount of design variable change that minimizes the objective function. Using the predicted values of the vulcanization condition variable and the design variable, a Young's modulus correction model in which the Young's modulus of each rubber member is corrected is determined in step 118 without changing the structure of the rubber member constituting the tire. At the same time, the objective function value is calculated.

  In the next step 120, the value of the objective function is determined by comparing the difference between the objective function value OBJ calculated in step 118 and the initial value OBJo of the objective function calculated in step 104 with a threshold value input in advance. It is determined whether or not it has converged, and if the value of the objective function has not converged, the predicted values of the vulcanization condition variable and the design variable obtained in step 116 are used as initial values, and steps 104 to 118 are repeatedly executed. To do. When it is determined that the value of the objective function has converged, the value of the design variable at this time is used as the value of the vulcanization condition variable and the design variable that minimizes the objective function while satisfying the constraint conditions. The value of the vulcanization condition variable and the value of the design variable are used to determine the Young's modulus and vulcanization conditions of each rubber member constituting the tire.

[Implementation Embodiment
It will now be described implementation form of the present invention. Since this implementation mode is the same configuration as Comparative Example, not described configuration for each portion are denoted by the same reference numerals, with reference to FIG. 6 below, the processing routine according to the present implementation mode Only parts different from the processing routine (FIG. 2) described in the comparative example will be described.

In the comparative example described above, the physical property values (Young's modulus) and vulcanization conditions of each rubber member are set so as to satisfy the constraints such as “case rigidity is equivalent to the current” and to minimize the rolling resistance value as an objective function. Although the mode to be determined has been described, under the actual use conditions of the tire, first, an internal pressure is applied to cause strain (static strain) in each rubber member of the tire, and each rubber member by rolling the tire The strain of the rubber member further changes (dynamic strain is added to the static strain), and the temperature of each rubber member also changes as the tire rolls. When the strain and temperature of each rubber member change, physical property values such as Young's modulus of each rubber member change. In the comparative example , there is room for improvement because the effects of distortion and temperature of each rubber member under actual use conditions are not considered.

In the processing routine according to the present implementation embodiment based on the above-mentioned (FIG. 6), after calculating the initial value of the objective function and constraints at step 104. In the next step 105, the operation target of the rubber member constituting the tire The specific rubber member is processed to calculate strain and temperature under actual use conditions. Calculation of the strain and temperature of the rubber member under actual use conditions can be performed, for example, as follows.

  That is, a road surface model that models a road surface is first created, and a road surface state is set for the created road surface model to simulate an actual road surface state. The road surface model is created by dividing the road surface shape into elements, and the road surface state is set by selectively setting the friction coefficient μ of the road surface. The friction coefficient μ of the road surface differs depending on the road surface condition such as dry (DRY), wetness (WET), on ice, on snow, non-paved, etc., so by selecting and setting an appropriate value as the friction coefficient μ of the road surface, The road surface condition can be reproduced. A fluid model may be provided between the road surface and the tire model. The fluid model is a model obtained by dividing a fluid region including a part (or all) of a tire, a ground contact surface, and a region where the tire moves and deforms into elements.

  Next, the boundary condition is set. The boundary conditions are necessary for analysis of the tire model, that is, for simulating the behavior of the tire, and are various conditions given to the tire model. In setting the boundary conditions, first, an internal pressure is applied to the tire model, and at least one of rotational displacement and linear displacement (displacement may be force or speed) and a predetermined load are applied. When considering friction with the road surface, only one of rotational displacement (or force, speed) and straight displacement (or force, speed) is sufficient.

  Subsequently, based on the tire model and the boundary conditions given above, deformation calculation of the tire model under the actual use condition (the state where the tire is rolling at a predetermined speed) is performed by the finite element method. In the tire model deformation calculation, the deformation calculation is repeated in order to obtain the tire rolling state (transient state) (for example, the calculation within 1 msec is repeated), and the boundary condition is updated each time. Also good. In addition, as a calculation time in the deformation calculation of the tire model, a predetermined time can be adopted assuming that the tire deformation is in a steady state. By the above deformation calculation, stress and strain (including static strain due to internal pressure and dynamic strain at the time of tire rolling) generated under actual usage conditions are calculated for each element constituting the tire model. .

  Next, after calculating the heat generation under the actual use conditions for the tire model, the heat transfer inside the tire is calculated. The heat generation calculation is performed by setting a use temperature (environment temperature) and the like as a part of the actual use conditions, and then specifying a heat generation phenomenon that occurs under the actual use conditions for each part of the tire and using the thermal energy. In this case, the heat generated in each part of the tire can be calculated based on strain energy loss and the like. In this heat generation calculation, the heat generation energy of the tread portion generated by the friction generated by the contact with the road surface due to the use of the tire can be used. Also in this case, the heat generated in each part can be calculated based on strain energy loss and the like. The heat generation calculation includes the temperature prediction of each part of the tire. The temperature prediction is to calculate by calculation the level of temperature for all parts of the tire at a preset use temperature. This calculation can be predicted by thermal analysis such as FEM based on the stress and strain of each part of the tire calculated by the deformation calculation described above.

  The heat transfer calculation calculates the energy transfer when the thermal energy applied from inside the tire is transferred inside the tire, and calculates the energy transfer when the heat energy generated inside the tire is transferred to the surroundings. To do. This calculation can be performed by thermal analysis using FEM or the like based on the stress and strain of each part of the tire calculated by the deformation calculation described above. These heat generation calculation and heat transfer calculation are repeatedly performed until the calculation result converges, for example, until a predetermined time elapses or a temperature equilibrium state is reached.

  By the above-described operations (deformation calculation, heat generation calculation, heat transfer calculation), for each element constituting the tire model, the strain under actual use conditions (static distortion due to internal pressure and dynamic during rolling of the tire) For example, an average value of the calculated strain and temperature is calculated for each of a plurality of elements corresponding to the specific rubber member to be calculated. Thereby, the strain and temperature under actual use conditions can be calculated for the specific rubber member to be calculated.

Further, the processing routine according to the present implementation mode (Fig. 6), the prediction calculation of heat conduction calculation described in Comparative Example (step 106) and physical properties of the particular rubber member operand (Young's modulus) to (step 108) After performing, in the next step 109, the physical property value (Young's modulus) of the specific rubber member calculated in step 108 is calculated based on the strain and temperature under the actual use condition of the specific rubber member calculated in the previous step 105. Update. The physical property value (Young's modulus) of the rubber member changes as shown in FIG. 7 as an example with respect to the strain and temperature change of the rubber member. In a storage unit of a personal computer according to the present implementation embodiment, correspondence between the strain and temperature and physical properties of the rubber member shown in FIG. 7 is the map, or is stored in the form of a table or the like, in step 109 Reading out the map or table showing the above correspondence from the storage unit and deriving from the map or table the physical property value corresponding to the strain and temperature under the actual use condition of the specific rubber member calculated in step 105 Thus, the physical property value (Young's modulus) of the specific rubber member predicted and calculated in step 108 is updated.

As a result, the physical property value of the specific rubber member to be calculated is updated to a value that takes into account the effects of strain and temperature under actual use conditions (a value closer to the value under actual use conditions). Further, the processing routine according to the present implementation mode (Fig. 6), similarly to the comparative example, by each [Delta] r _i design variables r _i operand of a particular rubber member is changed (step 110), the sensitivity of the objective function and After calculating the sensitivity of the constraint condition for each design variable (step 112), when it is determined that the calculation has not been completed for all rubber members (when the determination of step 114 is negative), the process returns to step 105. Steps 105 to 114 are repeated until the determination in step 114 is affirmed. Therefore, the strain and temperature under actual use conditions are calculated for all the rubber members constituting the tire, respectively. Each physical property value considering the influence of temperature is set.

Further, the processing routine according to the present implementation mode (Fig. 6), similarly to the comparative example, the flow returns to step 104 if the value of the objective function is determined not to converge in step 120, calculated in step 116 Steps 104 to 120 are repeated using the predicted values of the vulcanization condition variable and the design variable as initial values until the determination in step 120 is affirmed. At this time, in step 105, the rubber members to be performed for each individual rubber member are repeated. The calculation of strain and temperature is performed in the previous step 109 instead of the value set as a premise of the stationary tire used when the calculation is first performed as the physical property value (Young's modulus) of the rubber member. The updated value is used based on the strain and temperature of the rubber member under the usage conditions.

As a result, by repeating Step 104 to Step 120, the accuracy of the calculation result of the strain and temperature of the rubber member in Step 105 is improved (with the actual strain and temperature of the rubber member under actual use conditions). Accordingly, the physical property value (Young's modulus) of the rubber member updated in step 109 is closer to the value under actual use conditions, and the value of the objective function converges accordingly. Thus, at the stage where the determination in step 120 is affirmed, in step 122, the constraint condition such as “the case rigidity is equal to the current value” is satisfied, and the rolling resistance value as the objective function is minimized under the actual use conditions. The physical property value (Young's modulus) and vulcanization conditions of each rubber member can be determined as design variables. Therefore, the according to the implementation mode, in addition to the effects of the tire vulcanizing the tire design and development of the effects of strain and temperature of the rubber member also improved the target performance in consideration of the actual use conditions high efficiency The tire can be provided at low cost.

In processing routine according to the present implementation mode (Fig. 6), had done a calculation of the strain and temperature of the rubber member in the step 105 for each individual rubber members, it is not limited thereto, for example, the aforementioned By performing the deformation calculation, heat generation calculation, and heat transfer calculation, the strain and temperature are calculated for each element that makes up the tire model, so the strain of all rubber members that make up the tire is calculated based on the calculation results. The temperature may be calculated at a time. In this case, after calculating the strain and temperature of all the rubber members in Step 105, Step 106 to Step 114 may be repeated for each rubber member until the determination in Step 114 is affirmed.

  In the above description, the Young's modulus is described as an example of the physical property value of the rubber member to be updated based on the strain and temperature of the rubber member. However, the present invention is not limited to this, and other physical property values of the rubber member may be applied. Is also possible.

  Next, examples of the present invention will be described. In the present embodiment, it is possible to design a tire with further improved rolling resistance.

  First, a tire with low rolling resistance can be obtained by using a tread rubber blend with a low loss. However, as a tire, input to the tire such as tread portion rigidity and case portion rigidity must be taken into consideration. When the case stiffness changes, the tire performance changes because the input to the tread rubber changes. Further, since the amount of heat to the case member and the tread member changes by vulcanizing the tire, the balance of the tire rubber physical properties is determined.

  From these, it is preferable not only to improve tire performance by blending low-loss tread rubber, but also to take into account the rigidity of the case part, the input to the tread part, and the rigidity by vulcanization. Thus, a tire with improved rolling resistance can be designed.

  Therefore, in this example, vulcanization conditions for improving rolling resistance are calculated using the current rubber composition and the current structure.

  A finite element model is created using a tire having a TBR 11R22.5 Rib pattern as a target tire (step 100 in FIG. 2). The objective function is “minimize tire rolling resistance”, the constraint condition is “case rigidity is currently equivalent”, and the vulcanization condition is “current condition” (step 102 in FIG. 2).

  Next, the initial values of the objective function (tire rolling resistance) and constraint conditions (case rigidity or belt elastic modulus) are calculated under the current tire structure, current rubber composition, and current vulcanization conditions (step 104 in FIG. 2).

  Next, heat conduction calculation is performed by slightly changing the vulcanization conditions (step 106 in FIG. 2). A master curve is prepared in advance from the experimental results in advance, and the rubber physical properties are predicted from the heat conduction calculation results (maximum vulcanization temperature, total vulcanization degree) of each part of the rubber member (step 108 in FIG. 2). . The design variables (elastic modulus and loss characteristics of each member) are slightly changed to calculate the objective function (tire rolling resistance) and constraint conditions (case stiffness: belt elastic modulus) and change for each vulcanization condition. The width (sensitivity) is calculated (steps 110 to 112 in FIG. 2).

  These are calculated for all rubber members (step 114 in FIG. 2), and the above sensitivity is used to minimize the objective function (tire rolling resistance) while satisfying the constraints (case rigidity and belt elastic modulus). A change in sulfur condition is predicted (step 116 in FIG. 2). From the prediction results, recalculation is performed until the objective function (tire rolling resistance) converges using a model with a corrected vulcanizing condition, and tire vulcanizing conditions that minimize the objective function (tire rolling resistance) are determined ( Steps 118-122 in FIG.

  As a result, the following results were obtained. While the current condition is Index 100, the optimum vulcanization condition obtained by the optimization according to the above embodiment is Index 110 (good direction).

Further, the results are when determining the tire vulcanization conditions for minimizing the objective function in accordance with the processing routine according to the comparative example (FIG. 2), under the same conditions, the processing routine according to the implementation embodiments (FIG. 6) In consideration of the strain and temperature of the rubber member under actual use conditions, the physical property values (Young's modulus) of each rubber member as design variables so that the rolling resistance value as the objective function is minimized under the actual use conditions ) And vulcanization conditions were determined, the result was Index 115 (good direction). This confirms that tires can be designed and developed to further improve performance under actual use conditions by taking into account the effects of rubber member distortion and temperature under actual use conditions in addition to vulcanization conditions. It was done.

It is the schematic of the personal computer used for the comparative example of this invention. It is a flowchart which shows the processing routine of the comparative example of this invention. It is a diagram which shows a tire basic model. It is a diagram which shows a tread rubber loss characteristic. It is a diagram which shows a belt rubber elastic modulus characteristic. Is a flow chart showing a processing routine according to the implementation embodiments. It is a diagram which shows an example of the correspondence of the distortion of a rubber member, temperature, and a physical-property value.

Explanation of symbols

10 Keyboard 12 Computer body 14 CRT

Claims (5)

(A) a tire basic model representing a tire cross-sectional shape including an internal structure, an objective function representing a physical quantity for tire performance evaluation, a vulcanization condition variable for determining a vulcanization condition for determining physical properties of each rubber member of the tire, and rubber Determining a design variable that determines physical properties of the member and the reinforcing material, and a constraint condition that restricts at least one of the physical properties of the rubber member and the reinforcing material, the physical quantity for performance evaluation, and the tire size.
(B) obtaining physical properties of the rubber member based on the obtained thermal energy while obtaining the thermal energy applied to each rubber member of the tire under the vulcanizing condition based on the vulcanization condition variable.
(C) A step of obtaining the value of the vulcanization condition variable and the value of the design variable that give the optimum value of the objective function while considering the constraint condition using the obtained physical property value.
(D) Designing the tire based on the vulcanization condition variable and the design variable that give the optimum value of the objective function.
A pneumatic tire design method including the above steps,
After performing the step (a) and before performing the step (b), performing a step (e) of obtaining strain and temperature of each rubber member under actual use conditions from a finite element method,
In the step (c), using the physical property value of the rubber member obtained in the step (b) and the strain and temperature of each rubber member obtained in the step (e), the strain, temperature and physical property value of each rubber member are After updating the physical property value of the rubber member from the known correspondence relationship, the value of the vulcanization condition variable and the design variable value that gives the optimum value of the objective function while considering the constraint condition using the updated physical property value. Desired pneumatic tire design method. In the step (b), in order to obtain the heat energy, heat transfer prediction is performed in consideration of the thermal conductivity of the rubber compound, the specific heat, the temperature dependence of the density, and the influence of the heat of vulcanization reaction generated during vulcanization. 2. The method for designing a pneumatic tire according to claim 1, wherein the physical property value of the rubber member is obtained based on the heat energy obtained from the amount of heat and the maximum attainable temperature of each tire member. In step (c), the sensitivity of the objective function, which is the ratio of the change amount of the objective function to the unit change amount of the vulcanization condition variable, and the constraint condition, which is the ratio of the change amount of the constraint condition to the unit change amount of the vulcanization condition. Based on the sensitivity and the sensitivity of the objective function, which is the ratio of the change amount of the objective function to the unit change amount of the design variable, and the sensitivity of the constraint condition, which is the ratio of the change amount of the constraint condition to the unit change amount of the design variable,
While predicting the amount of change in the vulcanization condition variable and design variable that give the optimum value of the objective function while taking into account the constraints,
The value of the objective function when the vulcanization condition variable is changed by the amount corresponding to the predicted amount, the value of the constraint condition when the design variable is changed by the amount corresponding to the predicted amount, and the amount corresponding to the predicted amount of the design variable The value of the objective function when it is changed and the value of the constraint condition when the design variable is changed by an amount corresponding to the predicted amount are calculated,
The method for designing a pneumatic tire according to claim 1, wherein the value of the vulcanization condition variable and the value of the design variable that give the optimum value of the objective function are obtained based on the predicted value and the calculated value while considering the constraint conditions. The method for designing a pneumatic tire according to claim 1, wherein the vulcanization condition variable represents at least one of a tire mold side temperature, a bladder side temperature, and a vulcanization time. 2. The pneumatic tire design method according to claim 1, wherein the design variable represents at least one of a Young's modulus of rubber, a Poisson's ratio, and a Young's modulus or Poisson's ratio in each direction of the anisotropic reinforcing material.

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