Tire simulation method, tire simulation device, and program
The tire simulation method addresses convergence issues by correcting friction forces in tire models, improving simulation accuracy and completeness.
Patent Information
- Authority / Receiving Office
- JP · JP
- Patent Type
- Applications
- Current Assignee / Owner
- TOYO TIRE CORP
- Filing Date
- 2024-11-08
- Publication Date
- 2026-05-20
AI Technical Summary
Convergence issues during tire performance simulation calculations, particularly in rolling analysis, lead to incomplete analysis results due to deviations from actual behavior, especially in complex calculations.
A tire simulation method that includes creating a tire model with finite elements, calculating sliding velocity and ground pressure, determining friction coefficients, and applying correction coefficients to improve friction force calculations, ensuring convergence through correction and inverse correction processes.
Enhances convergence of simulation calculations while maintaining analytical accuracy by correcting friction forces, particularly in low slip ratio regions, leading to more precise tire performance predictions.
Smart Images
Figure 2026084008000001_ABST
Abstract
Description
Technical Field
[0001] The present disclosure relates to a tire simulation method, a tire simulation device, and a program, and particularly to the simulation of rolling analysis of a tire.
Background Art
[0002] In recent years, in order to improve the development and design efficiency of pneumatic tires, prediction of tire performance such as frictional force has been performed by numerical analysis using a computer. For example, Patent Document 1 discloses a tire simulation method for setting the value of the friction coefficient between a tire and a road surface by using rubber viscoelastic characteristics in the simulation of a tire.
Prior Art Documents
Patent Documents
[0003]
Patent Document 1
Summary of the Invention
Problems to be Solved by the Invention
[0004] In the simulation for predicting tire performance, the convergence of the convergence calculation during analysis is an important factor for obtaining the simulation result. In the convergence calculation, there are cases where it does not converge when it greatly deviates from the actual behavior. For example, when a certain value during the convergence calculation exceeds the threshold value, the analysis calculation is stopped. Particularly, in the rolling analysis where the calculation is complex, the above problem appears remarkably.
[0005] <00000३३>[Means for solving the problem]
[0006] The tire simulation method according to the present invention includes a tire model creation step of creating a tire model modeled with a finite number of elements having nodes; a rolling analysis calculation step of calculating the sliding velocity and ground pressure of the nodes by performing a rolling analysis using the tire model; a friction coefficient calculation step of determining the friction coefficient of the nodes based on the sliding velocity and the ground pressure; and a friction force calculation step of calculating the friction force of the nodes based on the ground pressure and the friction coefficient, wherein the method further includes a friction force correction step of determining a correction coefficient to correct the friction force of the nodes based on the sliding velocity of the nodes and calculating the corrected friction force of the nodes by multiplying the friction force by the correction coefficient; and a tire force calculation step of calculating the tire force, which is a force acting on the tire model, based on the friction force and the overall corrected friction force. [Effects of the Invention]
[0007] According to the tire simulation method, tire simulation apparatus, and program of the present invention, it is possible to improve the convergence of convergence calculations during simulation while maintaining the accuracy of analytical calculations. [Brief explanation of the drawing]
[0008] [Figure 1] This is a flowchart illustrating the tire simulation method according to this embodiment. [Figure 2] This is a flowchart illustrating another example of the tire simulation method according to this embodiment. [Figure 3] This is a block diagram showing a tire simulation device according to this embodiment. [Figure 4] This figure illustrates correction factor data showing the correction factor for sliding speed. [Figure 5] This figure shows the relationship between the slip ratio and the ratio of braking force to longitudinal load in the embodiment. [Figure 6]This figure shows the relationship between the measured values and the examples and comparative examples.
[0009] Hereinafter, with reference to the drawings, an example of an embodiment of the tire simulation method, tire simulation apparatus, and program according to the present invention will be described in detail. The embodiments described below are merely examples, and the present invention is not limited to these embodiments. Furthermore, forms obtained by selectively combining the multiple embodiments and modifications described below are included in the present invention.
[0010] The simulation method for predicting tire performance according to this embodiment will be described in detail using Figures 1 and 2. Figure 1 is a flowchart of the tire simulation method according to this embodiment. Figure 2 is a flowchart showing another example of the tire simulation method according to this embodiment.
[0011] The tire simulation method according to this embodiment calculates the tire force acting on the tire model using rolling analysis. The tire simulation method may be performed, for example, using the tire simulation device 1 described later.
[0012] In the tire model creation process, a tire model is created using a finite number of elements, each having multiple nodes (Step S1). Specifically, the dimensional specifications of the tire, such as its external shape and internal structure, as well as the shape, arrangement, and material properties of each tire component, such as the tread rubber, are input. In addition, the road surface model may be created simultaneously with the tire model creation process.
[0013] In the rolling condition setting step, rolling conditions are set as conditions for performing rolling analysis using the tire model created in the tire model creation step (step S2). Rolling conditions include conditions on the tire model side, such as rim size and air pressure. In addition, a road surface model on which the tire model will roll is created, and conditions for the road surface model, such as the coefficient of friction, are set. As will be described in more detail later, in this embodiment, the slip ratio and the like are set as rolling conditions for each cycle of rolling analysis.
[0014] In the slip ratio setting process, the slip ratio is set as the rolling condition (step S3). In the slip ratio setting process, steps S4 to S9, described later, constitute one cycle, and the slip ratio is changed in each cycle. In the slip ratio setting process, for example, the slip ratio is increased in each cycle.
[0015] In the rolling motion analysis calculation step, the sliding speed and contact pressure at each node are calculated at the slip ratio set in the slip ratio setting step (step S4). Specifically, in the rolling motion analysis calculation step, the sliding speed and contact pressure at each node are calculated by performing a rolling motion analysis using the tire model and road surface model described above. Next, in the friction coefficient calculation step, the friction coefficient at each node is calculated at the slip ratio set in the slip ratio setting step based on the sliding speed and contact pressure obtained in the rolling motion analysis calculation step (step S5).
[0016] In the friction force calculation step, the friction force at each node is calculated based on the ground pressure and friction coefficient at each node, according to the slip ratio set in the slip ratio setting step (step S6). The calculated friction forces may be linked to each node and stored in memory 12.
[0017] In the frictional force correction process, a correction coefficient for correcting the frictional force calculated in the frictional force calculation process is obtained for each node of the tire model, and the frictional force for each node is multiplied by the correction coefficient to calculate the corrected frictional force for each node at the slip ratio set in the slip ratio setting process (step S7). Note that the correction coefficient takes a value greater than 0 and less than or equal to 1, and preferably approaches 1 as the slipping speed increases. Thereby, since correction for reducing the frictional force can be performed in the low slip ratio region where convergence calculation is difficult, the convergence of the convergence calculation is improved.
[0018] In the frictional force correction process, in addition to the correction coefficient, an overall correction coefficient that takes a value greater than 0 and less than or equal to 1 and is applied with the same value to all nodes may be set, and the corrected frictional force for each node may be calculated by multiplying the frictional force for each node by the correction coefficient and the overall correction coefficient. Thereby, since correction for reducing the frictional force of all nodes can be performed, the convergence of the convergence calculation is improved.
[0019] In the convergence determination process, a convergence calculation is performed based on the corrected frictional force at each slip ratio, and it is determined whether to continue or interrupt the rolling analysis (step S8). That is, in the convergence determination process, the corrected frictional force at at least two slip ratios is required. In the convergence determination process, if there is only data on the corrected frictional force at one slip ratio, it is determined in the convergence determination process to continue the rolling analysis (YES in step S8).
[0020] In the convergence determination process, if the convergence calculation does not converge (NO in step S8), it is regarded as non-convergent, the rolling analysis is stopped, and the analysis is terminated halfway. In this case, since the analysis is interrupted in an incomplete state, a solution cannot be obtained. If the convergence calculation converges (YES in step S8), proceed to the next step.
[0021] Next, it is determined whether the slip ratio set in the slip ratio setting step has reached a predetermined value (step S9). If the slip ratio has not reached the predetermined value (NO in step S9), the process returns to the slip ratio setting step, increases the slip ratio, and performs the calculations in steps S9 to S14 again. If the slip ratio has reached the predetermined value (YES in step S9), the rolling analysis is terminated, and the process proceeds to the next step.
[0022] The tire force calculation step calculates the tire force acting on the tire model based on the friction force at each node calculated in the friction force calculation step (step S10). The tire force is, for example, the longitudinal force acting along the circumferential direction of the tire model and the lateral force Fy acting along the axial direction of the tire model. The longitudinal force includes the driving force acting in the forward direction of the tire and the braking force Fx acting in the opposite direction to the forward direction of the tire. The braking force Fx is, for example, the sum of the friction forces generated along the direction of travel of the tire model at all nodes. In addition, the longitudinal load Fz acting in the vertical direction may be calculated in the tire force calculation step from rolling analysis conditions, etc.
[0023] Figure 2 will be used to describe in detail another example of the tire simulation method according to this embodiment. Figure 2 is a flowchart illustrating another example of the tire simulation method according to this embodiment, and the same steps as in the flowchart in Figure 1 are given the same step numbers. Note that the explanation of the same steps will be omitted. The flowchart in Figure 2 differs from the flowchart in Figure 1 in that the friction force calculation step and the corrected friction force calculation step are performed simultaneously, and that it includes an inverse correction step.
[0024] In the corrected friction force calculation step of the tire simulation method shown in Figure 2, the corrected friction force is calculated based on the ground pressure, friction coefficient, and correction coefficient (step S20). That is, the corrected friction force is calculated directly without first calculating the friction force to be corrected. In detail, the corrected friction force is calculated based on the ground pressure at each node, the friction coefficient at each node, and the correction coefficient at each node.
[0025] The tire simulation method shown in Figure 2 includes an inverse correction step. The inverse correction step performs an inverse correction on the corrected friction force after the completion of the rolling analysis, i.e., after the completion of the convergence calculation (step S21). In detail, the inverse correction step calculates an inverse correction coefficient, which is the reciprocal of the correction coefficient calculated in the friction force correction step, and multiplies it by the corrected friction force at each node to calculate an inverse corrected friction force that eliminates the influence of the correction coefficient. In other words, the inverse corrected friction force is substantially the same value as the friction force calculated in the friction force calculation step.
[0026] In the tire force calculation step of the tire simulation method shown in Figure 2, the tire force is calculated using the inversely corrected friction force calculated in the inverse correction step. This makes it possible to calculate the tire force without the influence of the correction coefficient, thus maintaining the accuracy of the simulation.
[0027] Furthermore, the tire simulation method described above can be implemented by having a computer execute each step of the tire simulation method as a procedure using a program that executes the tire simulation method.
[0028] The tire simulation apparatus 1 according to this embodiment will be described in detail with reference to Figure 3. Figure 3 is a block diagram showing the tire simulation apparatus 1 that performs tire performance prediction according to this embodiment. The tire simulation apparatus 1 according to this embodiment has a configuration capable of executing the above tire simulation method.
[0029] The tire simulation device 1 according to this embodiment is composed of a computer equipped with a control device 10 including a processor 11 and memory 12, and performs predictive simulations of tire performance. The tire simulation device 1 may consist of one computer or multiple computers. Furthermore, some of the functions of the tire simulation device 1 may reside on a server or the like connected via a communication network.
[0030] The tire simulation device 1 comprises an input unit 13 and an output unit 14. The input unit 13 is an input interface for inputting information necessary for running the simulation, and examples include a keyboard and a mouse. The information input by the input unit 13 includes, for example, analysis conditions and tire model creation conditions. The output unit 14 is a liquid crystal display, organic EL display, etc., on which the input screen, simulation results, and other output screens are displayed.
[0031] The tire simulation device 1 has a tire model creation unit 15 that creates a numerically analyzable tire model modeled with a finite number of elements having multiple nodes. The tire model creation unit 15 sets, for example, the shape of the model and the number of mesh divisions. The tire model creation unit 15 creates a tire model based on the information necessary to create a numerically analyzable tire model acquired by the input unit 13, etc. Specifically, it creates a tire model based on various dimensional specifications such as the external shape and internal structure of the tire, material properties such as Young's modulus, Poisson's ratio and specific gravity for each component that makes up the tire, such as the tread, belt and carcass, and various evaluation conditions such as internal pressure and load. This information may be input via a keyboard, a recording medium such as a CD-ROM, or a network.
[0032] In detail, the tire model creation unit 15 uses the tire shape in a natural equilibrium state as the reference shape, models this reference shape using FEM, and creates a three-dimensional tire model that is modeled with a finite number of elements, each having multiple nodes. The finite elements are identified using three-dimensional coordinates (for example, XYZ coordinates where the longitudinal direction of the tire is the X axis, the tire width direction is the Y axis, and the vertical direction is the Z axis). The method of creating such a tire model is publicly known, and it can be modeled using known methods. Alternatively, a previously created tire model may be input from the input unit 13, in which case the tire model creation unit 15 sets the input tire model as the analysis target. As will be described in more detail later, the tire model divided into a finite number of elements has a finite number of nodes located on the boundaries of the finite number of elements and connecting each element. In rolling analysis, the sliding velocity and ground pressure are calculated for each of these nodes.
[0033] The tire simulation device 1 has a rolling condition setting unit 16 that sets rolling conditions as conditions for performing rolling analysis of the tire model created by the tire model creation unit 15. Rolling conditions include conditions on the tire model side, such as rim size and air pressure. In addition, a road surface model on which the tire model rolls is created, and conditions for the road surface model, such as the coefficient of friction, are set. As will be described in more detail later, in this embodiment, the slip ratio is set as a rolling condition.
[0034] The tire simulation device 1 has a rolling analysis unit 17 that performs rolling analysis based on the tire model and rolling conditions obtained above. The rolling analysis unit 17 has a slip ratio setting unit 18 that sets the slip ratio in the braking analysis. The slip ratio setting unit 18 changes the slip ratio gradually with each calculation cycle as a rolling condition, for example. The slip ratio setting unit 18 sets the road surface speed (vehicle speed V) relative to the tire. V ) and tire rotation speed V T In order to change the slip ratio S determined by the road surface speed (vehicle speed V), V ) and tire rotation speed V T The slip ratio S is given by the following equation (1).
[0035]
number
[0036] In the braking analysis of this embodiment, the process starts with a slip ratio of 0%, and the slip ratio setting unit 18 gradually increases the slip ratio at a predetermined rate at each calculation step of the rolling analysis. The rate at which the slip ratio is increased may be constant for each calculation cycle, but it may also be possible to set a larger rate in the initial stages of the rolling analysis and then decrease the rate thereafter to reach the slip ratio at which the target physical quantity is obtained more quickly. In this embodiment, it is preferable that the rate at which the slip ratio is increased is constant in order to improve accuracy in the low slip ratio region. For example, the slip ratio setting unit 18 increases the slip ratio by 1% each cycle.
[0037] The rolling analysis unit 17 includes a rolling analysis calculation unit 19 that performs rolling analysis calculations using the rolling conditions set in the rolling condition setting unit 16 and the slip ratios set in the slip ratio setting unit 18. The rolling analysis calculation unit 19 performs rolling analysis using a tire model and calculates the sliding speed and contact pressure at each node for each slip ratio. After the slip ratio is increased in the slip ratio setting unit 18, the rolling analysis calculation unit 19 calculates the deformation state of the tire model by rolling analysis at that slip ratio. The rolling analysis calculation unit 19 may, for example, associate the calculation results such as the sliding speed and contact pressure at each node with the node number and store them in the memory 12.
[0038] The rolling analysis unit 17 includes a friction coefficient calculation unit 20 that calculates the friction coefficient for each node based on the sliding speed and ground pressure obtained by the rolling analysis calculation unit 19. The friction coefficient calculation unit 20 may, for example, pre-set a table showing the relationship between ground pressure, sliding speed, and friction coefficient. This table can be determined in advance based on analytical calculations and experiments.
[0039] The friction coefficient calculation unit 20 may pre-set a function (specifically, a quadratic function, a higher-order function, an exponential function, a logarithmic function, etc.) in which the ground pressure and sliding speed are independent variables and the friction coefficient is the dependent variable. The friction coefficient calculation unit 20 calculates the friction coefficient from the ground pressure and sliding speed based on this function. This function can be determined in advance based on analytical calculations and experiments, etc.
[0040] The rolling analysis unit 17 has a friction force calculation unit 21 that calculates the friction force for each node at each slip ratio based on the ground pressure for each node obtained by the rolling analysis calculation unit 19 and the friction coefficient for each node obtained by the friction coefficient calculation unit 20. Specifically, the friction force calculation unit 21 obtains the friction force for each node by multiplying the vertical force, which is obtained by dividing the ground pressure by the contact area where the node contacts the road surface, by the friction coefficient. The friction force calculation unit 21 may, for example, associate the node number with the friction force of the node with that node number and record it in the memory 12.
[0041] The rolling analysis unit 17 has a friction force correction unit 22 that calculates a correction coefficient for each node based on the sliding velocity for each node obtained by the rolling analysis calculation unit 19, and calculates a corrected friction force for each node by multiplying the friction force by the correction coefficient. Specifically, the friction force correction unit 22 calculates a correction coefficient for each node from correction coefficient data that shows the correction coefficient for the sliding velocity. The friction force correction unit 22 may, for example, associate the node number with the corrected friction force of the node having that node number and record it in the memory 12. The friction force correction unit 22 may also function simultaneously with the friction force calculation unit 21. That is, the friction force calculation unit 21 may calculate the corrected friction force for each node from the vertical force, friction coefficient, and correction coefficient.
[0042] The correction coefficient data is as illustrated in Figure 4. The correction coefficient data illustrated in Figure 4 is a graph showing the correspondence between slip speed and the correction coefficient. The correction coefficient in the correction coefficient data takes values between 0 and 1. As illustrated in Figure 4, the correction coefficient data is a graph in which the correction coefficient approaches 1 as the slip speed increases. In detail, in the correction coefficient data of Figure 4, the correction coefficient becomes 1 above a certain slip speed. Also, in the slip speed range up to the point where the correction coefficient becomes 1, the correction coefficient increases logarithmically. According to the above correction coefficient, it is possible to correct the frictional force at each node, especially the frictional force in the low slip ratio region, thereby improving the convergence of the convergence calculation.
[0043] The friction force correction unit 22 may also set an overall correction coefficient in addition to the above correction coefficient, which is applied to all nodes of the tire model. The overall correction coefficient takes a value greater than 0 and less than 1, and the same value is applied to all nodes. For example, the value of the overall correction coefficient is 0.8. In this case, it is calculated by multiplying the friction force calculated in the corrected friction force calculation by the correction coefficient and the overall correction coefficient. By setting an overall correction coefficient, a correction can be made to reduce the friction force, thereby improving the convergence of the convergence calculation.
[0044] The rolling analysis unit 17 has a convergence determination unit 23 that performs a convergence calculation based on the corrected friction force at each slip ratio calculated by the friction force correction unit 22 and determines whether to continue or interrupt the rolling analysis. The convergence determination unit 23 may, for example, perform the convergence determination based on the sum of the corrected friction forces at all nodes at each slip ratio.
[0045] The convergence determination unit 23 may, for example, determine that convergence is possible and continue the rolling analysis if the difference in corrected friction force at each slip ratio is below a predetermined threshold. Alternatively, the convergence determination unit 23 may be configured to determine that convergence is impossible and interrupt the rolling calculation when the difference in corrected friction force at each slip ratio exceeds a predetermined threshold. The convergence calculation and convergence determination method in the convergence determination unit 23 are not particularly limited.
[0046] In this embodiment, the rolling analysis unit 17 performs the analysis while increasing the slip ratio from 0 until the slip ratio reaches a predetermined value. That is, the rolling analysis may be terminated when the slip ratio reaches a predetermined value. The predetermined value is, for example, a slip ratio of 100%. In the low slip ratio region, where the slip ratio is low, the contact surface between the tire model and the road surface model has both areas where the contact surface slips and areas where it does not slip (adhered areas), which complicates the convergence calculation and increases the likelihood of the convergence calculation stopping. Therefore, the friction force correction unit 22 can be used to correct the friction force used in the convergence calculation, thereby improving the convergence of the convergence calculation.
[0047] The tire simulation apparatus according to this embodiment may have an inverse correction unit 24 that calculates an inverse correction coefficient, which is the reciprocal of the correction coefficient, for each node, and after convergence determination, multiplies the corrected friction force by the inverse correction coefficient to calculate an inverse corrected friction force that eliminates the influence of the correction coefficient. As will be described in detail later, when calculating the tire force from the corrected friction force, a smaller value is calculated compared to when calculating the tire force from the friction force before correction. That is, the accuracy of the tire force calculated using the corrected friction force is degraded. However, by performing inverse correction after convergence determination, it is possible to calculate an inverse corrected friction force that eliminates the influence of the correction coefficient, thereby preventing a deterioration in calculation accuracy while improving the convergence of the convergence calculation.
[0048] If the friction force correction unit 22 sets an overall correction coefficient in addition to the correction coefficient, the inverse correction unit 24 may set an inverse overall correction coefficient, which is the reciprocal of the inverse correction coefficient and the overall correction coefficient, and multiply it by the corrected friction force to calculate an inverse corrected friction force that eliminates the influence of the correction coefficient and the overall correction coefficient.
[0049] The tire simulation apparatus according to this embodiment may include a tire force calculation unit 25 that calculates the tire force acting on the entire tire model based on the results of the rolling analysis unit 17. Specifically, the tire force calculation unit 25 calculates the tire force acting on the tire model using the uncorrected friction force calculated by the friction force calculation unit 21. By using the uncorrected friction force, it is possible to calculate a tire force that is not affected by the correction coefficient. As a result, the accuracy of the analysis can be maintained even if the friction force is corrected.
[0050] Tire forces include, for example, longitudinal forces acting along the circumferential direction of the tire model, lateral forces Fy acting along the axial direction of the tire model, longitudinal loads Fz acting in the vertical direction, and the resultant force of these forces. The longitudinal forces include the driving force acting in the forward direction of the tire and the braking force Fx acting in the opposite direction to the forward direction of the tire. The braking force Fx is, for example, the sum of the frictional forces generated along the direction of travel of the tire model at all nodes. The longitudinal load Fz can be obtained from rolling analysis conditions, etc.
[0051] The tire force calculation unit 25 may calculate the tire force (longitudinal force, lateral force) acting on the tire model based on the friction force calculated for each node by the friction force calculation unit 21 of the rolling analysis unit 17, if the friction force is stored in the memory 12. By calculating the tire force using the friction force before correction, it is possible to calculate a tire force that is not affected by the correction coefficient.
[0052] Furthermore, the tire force calculation unit 25 may calculate the tire force based on the inversely corrected friction force, which eliminates the influence of the correction coefficient calculated by the inverse correction. More specifically, the tire force calculation unit 25 may use the inversely corrected friction force to calculate the braking force Fx in the tire model. For example, the tire force calculation unit 25 calculates the braking force Fx by summing the friction forces generated along the direction of travel of the tire model at all nodes. By calculating the tire force using the inversely corrected friction force, it is possible to calculate the tire force that eliminates the influence of the correction coefficient. [Examples]
[0053] The present invention will be further described below with reference to examples, but the present invention is not limited to these examples.
[0054] <Examples> [Creating a tire model] In this example, a numerically analyzable tire model consisting of a finite number of elements with multiple nodes was created based on a tire with a tire size of 215 / 50R17.
[0055] [Rolling Condition Setting] For the rolling motion analysis, a load of 4822N was applied to the axle of the tire model, and the internal pressure was set to 250kPa. In addition, a road surface model was created, and the speed on the road surface (i.e., the vehicle's speed) was set to 60km / h.
[0056] [Rolling analysis] A rolling motion analysis was performed using the finite element method with the above tire model and rolling motion analysis conditions. In this rolling motion analysis, the friction coefficient was calculated from the contact pressure and sliding velocity at each node for each slip ratio, and the frictional force at each node was calculated from the contact pressure and friction coefficient. Furthermore, a correction coefficient was determined according to the sliding velocity at each node, and a corrected frictional force was calculated by multiplying this by the frictional force. The convergence of the rolling motion analysis was then determined based on this corrected frictional force. The slip ratio was increased by 1% increments from 0% to 25% during the rolling motion analysis.
[0057] [Tire force calculation] After determining the convergence of the rolling motion analysis, the braking force acting on the tire model was calculated based on the uncorrected friction force obtained from the rolling motion analysis. Here, the braking force Fx was calculated by summing the friction forces acting in the opposite direction to the tire's direction of travel at all nodes. In addition, the longitudinal load Fz acting vertically downward on the axle of the tire model was calculated from the rolling motion analysis conditions.
[0058] <Comparative Example> The simulation was performed in the same manner as in the example, except that the braking force of the tire model was calculated based on the corrected friction force.
[0059] [Evaluation of the ratio of braking force Fx to longitudinal load Fz (Fx / Fy)] The analysis results for the examples and comparative examples are shown in Figures 5 and 6. In this example, the braking force coefficient μ, obtained by dividing the braking force Fx by the longitudinal load Fz, is used to compare the examples and comparative examples. Figure 5 shows the braking force coefficient μ of the examples, comparative examples, and measured values in the region from a slip ratio of 0% to a slip ratio of 25%. Figure 6 shows the relationship between the measured values of the examples and comparative examples in the region from a slip ratio of 1% to a slip ratio of 5%. In Figure 5, the values of the examples and comparative examples are shown with the value of the example set to 100. The measured values of the braking force Fx and longitudinal load Fz were obtained experimentally. In the experiment, the braking force Fx and longitudinal load Fz were measured under the same conditions as in the above analysis calculation.
[0060] As shown in Figure 5, it can be confirmed that the embodiment approaches the measured value in the low slip ratio region compared to the comparative example. In particular, in the slip ratio region of 0% to 10%, the embodiment approaches the measured value compared to the comparative example. The low slip ratio region is called the steady-state driving region and is an important region related to the braking distance of the tire, etc. The steady-state driving region is, for example, the slip ratio region of 0% to 10%.
[0061] As shown in Figure 6, when comparing the comparative example and the example for slip ratios of 1% to 5%, it can be confirmed that the results of the example are closer to the measured values. In other words, in the low slip ratio region, it can be confirmed that the simulation method of the example yields more accurate calculation results than the simulation method of the comparative example. [Explanation of symbols]
[0062] 1 Simulation device, 10 Control device, 11 Processor, 12 Memory, 13 Input unit, 14 Output unit, 15 Tire model creation unit, 16 Rolling condition setting unit, 17 Rolling analysis unit, 18 Slip ratio setting unit, 19 Rolling analysis calculation unit, 20 Friction coefficient calculation unit, 21 Friction force calculation unit, 22 Friction force calculation unit, 23 Convergence determination unit, 24 Inverse correction unit, 25 Tire force calculation unit
Claims
1. A tire model creation process involves creating a tire model that is modeled using a finite number of elements with nodes, A rolling analysis calculation process is performed using the aforementioned tire model to calculate the sliding velocity and contact pressure at the nodes. A friction coefficient calculation step in which the friction coefficient of a node is determined based on the sliding speed and the ground pressure, A friction force calculation step that calculates the friction force at a node based on the ground pressure and the coefficient of friction, A tire simulation method including, A friction force correction step involves determining a correction coefficient to correct the friction force at a node based on the sliding velocity of the node, and calculating the corrected friction force at the node by multiplying the friction force by the correction coefficient. A tire force calculation step that calculates the tire force, which is the force acting on the tire model, based on the friction force or the corrected friction force, A tire simulation method, including the following.
2. The tire simulation method according to claim 1, wherein the tire force is at least one of a longitudinal force acting along the circumferential direction of the tire model and a lateral force acting along the axial direction of the tire model.
3. The process includes a convergence determination step in which a convergence calculation is performed based on the corrected friction force, and a determination is made as to whether to continue or interrupt the rolling analysis. The tire simulation method according to claim 1, wherein the tire force calculation step calculates the tire force after a convergence determination based on the friction force calculated in the friction force calculation step.
4. The tire simulation method according to claim 1, wherein the friction force calculation step and the friction force correction step are performed simultaneously.
5. The process includes a reverse correction step in which an inverse correction coefficient, which is the reciprocal of the correction coefficient, is determined, and the inverse correction coefficient is multiplied by the corrected friction force to calculate a reverse corrected friction force that eliminates the influence of the correction coefficient. The tire simulation method according to claim 4, wherein the tire force calculation step calculates the tire force based on the inversely corrected friction force.
6. The tire simulation method according to claim 1, wherein in the friction force correction step, in addition to the correction coefficient, an overall correction coefficient is set which takes a value greater than 0 and less than or equal to 1 and is applied to all nodes with the same value, and the corrected friction force is calculated by multiplying the friction force by the correction coefficient and the overall correction coefficient.
7. The process includes a reverse correction step in which an inverse correction coefficient, which is the reciprocal of the correction coefficient, and an inverse overall correction coefficient, which is the reciprocal of the overall correction coefficient, are determined, and the inverse correction coefficient and the inverse overall correction coefficient are multiplied by the corrected friction force to calculate a reverse corrected friction force that eliminates the influence of the correction coefficient and the overall correction coefficient. The tire simulation method according to claim 6, wherein the tire force calculation step calculates the tire force based on the inversely corrected friction force.
8. The tire simulation method according to claim 1, wherein the correction coefficient takes a value between 0 and 1, and becomes closer to 1 as the slip speed increases.
9. A program for causing a computer to execute the tire simulation method described in any one of claims 1 to 8.
10. A tire model creation unit that creates a tire model modeled with a finite number of elements having nodes, A rolling analysis calculation unit calculates the sliding velocity and contact pressure of the nodes by performing a rolling analysis using the aforementioned tire model. A friction coefficient calculation unit that determines the friction coefficient of a node based on the sliding speed and the ground pressure, A friction force calculation unit calculates the friction force at a node based on the ground pressure and the coefficient of friction, A tire simulation device including, A friction force correction unit calculates a correction coefficient for correcting the friction force at a node based on the sliding velocity of the node, and calculates the corrected friction force at the node by multiplying the friction force by the correction coefficient. A tire force calculation unit calculates the tire force, which is the force acting on the tire model, based on the friction force or the corrected friction force. A simulation device having the following features.