Method for creating a calculation model, and method for calculating the time-series temperature change of a pneumatic tire.

Abstract

To provide a method for creating a calculation model capable of reducing a calculation burden of a time-series temperature change.SOLUTION: A method is used to create a calculation model 12 for calculating a time-series temperature change in a pneumatic tire rolling on a road surface. The method includes the steps of: inputting a road surface model 13; inputting a tread rubber model 14 in which a first heat radiation relationship is defined between the road surface model 13 and itself; inputting an inner liner rubber model 15 in which a second heat radiation relationship is defined between the tread rubber model 14 and itself; and inputting a tire internal air model 16 in which a third heat radiation relationship is defined between the inner liner rubber model 15 and itself. Each of the road surface model 13, the tread rubber model 14, the inner liner rubber model 15, and the tire internal air model 16 is defined so as to have a spatially uniform temperature distribution.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] The present invention relates to a method for creating a computational model and a method for calculating the time-series temperature change of a pneumatic tire. [Background technology]

[0002] Patent Document 1, listed below, describes a method for simulating tire temperature. This method uses a tire model that models the tire with a finite number of elements. [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2017-9482 [Overview of the project] [Problems that the invention aims to solve]

[0004] In the method described above, the heat balance between heat generation and heat dissipation is calculated for each element of the tire model. Therefore, this method has the problem of being unsuitable for real-time vehicle simulations due to the high computational load on tire temperature.

[0005] This invention was devised in view of the above-described circumstances, and its main objective is to provide a method for creating a computational model that can reduce the computational load of time-series temperature changes. [Means for solving the problem]

[0006] The present invention relates to a method for creating a computational model for calculating the time-series temperature change of a pneumatic tire rolling on a road surface, comprising the steps of: inputting a road surface model into a computer; inputting a tread rubber model with a first heat dissipation relationship defined between it and the road surface model into the computer; inputting an inner liner rubber model with a second heat dissipation relationship defined between it and the tread rubber model into the computer; and inputting a tire internal air model with a third heat dissipation relationship defined between it and the inner liner rubber model into the computer, wherein the road surface model, the tread rubber model, the inner liner rubber model, and the tire internal air model are each defined to have a spatially uniform temperature distribution. [Effects of the Invention]

[0007] The present invention's method for creating a computational model of a pneumatic tire, by employing the above-described steps, can create a computational model that can reduce the computational load of time-series temperature changes. [Brief explanation of the drawing]

[0008] [Figure 1] This is a perspective view showing the method for creating the calculation model of this embodiment and a computer for executing the calculation method. [Figure 2] This is a cross-sectional view showing an example of a pneumatic tire. [Figure 3] This flowchart shows the processing steps for creating the calculation model of this embodiment. [Figure 4] This is a conceptual diagram of the calculation model of this embodiment. [Figure 5] This flowchart shows the processing procedure for calculating the time-series temperature change of a pneumatic tire according to this embodiment. [Figure 6] These are graphs showing the relationship between slip angle and time under different driving conditions; (a) is the graph for the first driving condition, and (b) is the graph for the second driving condition. [Figure 7]The graphs show the time-series temperature changes under the first driving conditions; (a) shows the time-series temperature changes of the tread contact surface, and (b) shows the time-series temperature changes of the tire cavity surface and the air inside the tire. [Figure 8] The graphs show the relationship between tire temperature and time (time-series temperature change) under the second driving conditions. (a) shows the time-series temperature change of the tread contact surface, and (b) shows the time-series temperature change of the inner surface of the tire and the air inside the tire. [Modes for carrying out the invention]

[0009] Embodiments of the present invention will be described below with reference to the drawings. It should be understood that the drawings contain exaggerations and representations that differ from the actual dimensional ratios of the structures in order to aid in understanding the content of the invention. Furthermore, the same or common elements are denoted by the same reference numerals throughout each embodiment, and redundant explanations are omitted. Moreover, the specific configurations shown in the embodiments and drawings are for the purpose of understanding the content of the present invention, and the present invention is not limited to the specific configurations shown in the drawings.

[0010] In the method for creating the calculation model of this embodiment (hereinafter sometimes simply referred to as the "creation method"), a calculation model for a pneumatic tire is created. This calculation model is used to calculate the time-series temperature change of a pneumatic tire rolling on a road surface. This time-series temperature calculation is performed based on the procedure of the method for calculating the time-series temperature change of a tire (hereinafter sometimes simply referred to as the "calculation method") described later. A computer is used in the creation method and calculation method of this embodiment.

[0011] [computer] Figure 1 is a perspective view showing a computer for executing the calculation model creation method and calculation method of this embodiment. The computer 1 of this embodiment consists of a main unit 1a, a keyboard 1b, a mouse 1c, and a display device 1d. The main unit 1a is provided with, for example, a processing unit (CPU), ROM, working memory, a storage device such as a magnetic disk, and disk drive devices 1a1 and 1a2. Software for executing the creation method and calculation method of this embodiment is pre-stored in the storage device.

[0012] [tire] Figure 2 is a cross-sectional view showing an example of a pneumatic tire 2. In this embodiment, the pneumatic tire (hereinafter sometimes simply referred to as "tire") 2 is exemplified as a pneumatic tire for a passenger car, but is not particularly limited. Tire 2 may also be a tire of another category, such as a heavy-duty tire for trucks and buses.

[0013] The tire 2 of this embodiment is composed of a tread rubber 3, an inner liner rubber 4, a carcass 5, and a belt layer 6.

[0014] The tread rubber 3 is positioned radially outward of the belt layer 6. In this embodiment, the tread rubber 3 is provided with a tread contact surface 2o that contacts the road surface 7.

[0015] The inner liner rubber 4 is positioned inside the carcass 5 and constitutes the inner surface 2i of the tire. This inner liner rubber 4 is made of air-impermeable rubber.

[0016] The carcass 5 is composed of at least one carcass ply 5A, in this embodiment one carcass ply 5A. The carcass ply 5A in this embodiment is arranged across the tread portion 2a and a pair of sidewall portions 2b, 2b, and across a pair of bead portions 2c, 2c. The carcass ply 5A has carcass cords (not shown) arranged at an angle of, for example, 75 to 90 degrees with respect to the tire equator C.

[0017] The belt layer 6 is located on the radially outer side of the carcass 5 and inside the tread portion 2a. The belt layer 6 in this embodiment consists of two belt plies 6A and 6B in which belt cords (not shown) are arranged at an angle of, for example, 10 to 35 degrees with respect to the circumferential direction of the tire. These belt plies 6A and 6B are overlapped in a direction in which the belt cords intersect each other.

[0018] A pair of bead portions 2c, 2c are mounted on the rim 8r of the wheel 8. The tire cavity 9, which is the space enclosed by the rim 8r and the tire cavity surface 2i, holds (fills) the tire's internal air 10.

[0019] Incidentally, when the tire 2 rolls on the road surface 7, it generates heat due to friction between the tread rubber 3 (tread contact surface 2o) and the road surface 7, and deformation of the tire 2, for example. On the other hand, heat is dissipated (heat is transferred) between the road surface 7 and the tread rubber 3, between the tread rubber 3 and the inner liner rubber 4 (including the carcass 5 and belt layer 6 in this example), and between the inner liner rubber 4 and the air inside the tire 10. Furthermore, heat is dissipated (heat is transferred) between the air inside the tire 10 and the wheel 8, between the wheel 8 and the outside air 11, and between the outside air 11 and the tread rubber 3. Due to the heat balance between these heat generation and heat dissipation, the temperature of the tire 2 rolling on the road surface 7 changes over time. Therefore, when creating a calculation model to calculate the time-series temperature change of the tire 2, it is preferable to consider the heat balance of these heat generation and heat dissipation.

[0020] [How to create a computational model] Next, the method for creating the calculation model of this embodiment will be described. Figure 3 is a flowchart showing the processing steps for creating the calculation model of this embodiment. Figure 4 is a conceptual diagram of the calculation model 12 of this embodiment.

[0021] The calculation model 12 created by the method of creation of this embodiment includes a road surface model 13, a tread rubber model 14, an inner liner rubber model 15, and a tire internal air model 16.

[0022] The road surface model 13 models the road surface 7 (shown in Figure 2) on which the tire 2 rolls. The tread rubber model 14 models the tread rubber 3 (shown in Figure 2). The inner liner rubber model 15 models the inner liner rubber 4 (shown in Figure 2). The tire internal air model 16 models the internal air 10 (shown in Figure 2) of the tire.

[0023] The calculation model 12 of this embodiment includes a wheel model 17 and an ambient air model 18. The wheel model 17 is a model of the wheel 8 (shown in Figure 2). The ambient air model 18 is a model of the ambient air 11 (shown in Figure 2). However, the calculation model 12 is not limited to this configuration, and depending on the calculation accuracy required for the calculation model 12, for example, the wheel model 17 and the ambient air model 18 may be omitted.

[0024] The computational model 12 in this embodiment is created as a mathematical model. Therefore, in the creation method of this embodiment, it is not necessary to model the tire 2 (shown in Figure 2) with a finite number of elements, as in Patent Document 1, thus simplifying the computational model 12 and enabling modeling in a short time.

[0025] [Enter road surface model] In the creation method of this embodiment, first, the road surface model 13 is input into the computer 1 (shown in Figure 1) (step S1). The road surface model 13 of this embodiment is defined to have a spatially uniform temperature distribution.

[0026] "Having a spatially uniform temperature distribution" means that the temperature is uniform in all areas of the space that constitutes the road surface model 13. Therefore, in this embodiment, in each unit time (for example, 1 second) in which the temperature is calculated using the calculation method described later, the entire road surface model 13 has a single temperature T rIt is defined as having a uniform temperature distribution. By defining the road surface model 13 to have a spatially uniform temperature distribution in this way, the road surface model 13 can be simplified. As a result, the road surface model 13 can be modeled in a short time in process S1.

[0027] Road surface model 13 temperature T r This is set appropriately according to the road surface 7 on which the tire 2 being analyzed, as shown in Figure 2, rolls. In this embodiment, assuming that the temperature of the road surface 7 does not change (remains constant) during the rolling of the tire 2, the temperature T of the road surface model 13 is set. r This is defined as a constant (for example, 0 to 80°C). This eliminates the need to calculate the temperature change of the road surface model 13 in the calculation method described later, thus shortening the calculation time. Depending on the required calculation accuracy, the road surface model 13 is defined as having a temperature T that changes per unit time. r It may be set.

[0028] In step S1 of this embodiment, the road surface model 13 is defined as temperature T r This is defined. Road surface model 13 (temperature T r ) is input to computer 1 (shown in Figure 1).

[0029] [Enter tread rubber model] Next, in the creation method of this embodiment, the tread rubber model 14 is input into the computer 1 (shown in Figure 1) (step S2). The tread rubber model 14 of this embodiment is defined to have a spatially uniform temperature distribution.

[0030] "Having a spatially uniform temperature distribution" means that the temperature is uniform in all regions of the space that constitutes the tread rubber model 14. Therefore, in this embodiment, at each unit time (for example, 1 second) in which the temperature is calculated using the calculation method described later, the entire tread rubber model 14 is at a single temperature T out(That is, a uniform temperature distribution) is defined as such. Thus, by defining the tread rubber model 14 to have a spatially uniform temperature distribution, the tread rubber model 14 can be simplified. Thereby, in step S2, the tread rubber model 14 can be modeled in a short time.

[0031] Temperature T out is set as the temperature of the tread contact surface 14o in the tread rubber model 14. Thereby, the temperature measured at the tread contact surface 2o of the tire 2 shown in FIG. 2 and the temperature T of the tread contact surface 14o of the calculation model 12 shown in FIG. 4 out can be easily compared.

[0032] A first heat dissipation relationship is defined between the tread rubber model 14 and the road surface model 13 in the present embodiment. The first heat dissipation relationship in the present embodiment is a parameter indicating the ease of heat dissipation between the tread rubber 3 and the road surface 7 shown in FIG. 2. Due to such a first heat dissipation relationship, considering the actual heat dissipation between the tread rubber 3 and the road surface 7, the temperature T of the tread contact surface 14o of the calculation model 12 shown in FIG. 4 out can be calculated.

[0033] The first heat dissipation relationship in the present embodiment includes a heat dissipation coefficient κ1 from the tread contact surface 14o of the tread rubber model 14 to the road surface model 13. The heat dissipation coefficient κ1 in the present embodiment indicates the ease of heat transfer from the tread contact surface 2o shown in FIG. 2 to the road surface 7. This heat dissipation coefficient κ1 is a proportional constant based on Newton's law of cooling and depends on the heat capacity, surface area, thermal conductivity, etc. of the tread rubber 3 and the road surface 7. Such a heat dissipation coefficient κ1 can be easily identified (fitted) based on measured values such as the temperature of the tread rubber 3 (tread contact surface 2o) of the tire 2 rolling on the road surface 7 in step S7 described later.

[0034] As shown in Figure 4, it is preferable that a second heat dissipation relationship is defined between the tread rubber model 14 and the inner liner rubber model 15 in this embodiment. The second heat dissipation relationship in this embodiment is a parameter that indicates the ease of heat dissipation between the tread rubber 3 and the inner liner rubber 4 shown in Figure 2. Considering the actual heat dissipation between the tread rubber 3 and the inner liner rubber 4 based on this second heat dissipation relationship, the temperature T of the tread contact surface 14o in the calculation model 12 shown in Figure 4 is calculated. out This can be calculated.

[0035] The second heat dissipation relationship of this embodiment includes a heat dissipation coefficient κ2 from the tread contact surface 14o of the tread rubber model 14 to the inner cavity surface 15i of the inner liner rubber model 15. The heat dissipation coefficient κ2 of this embodiment indicates how easily heat is transferred from the tread contact surface 2o of the tread rubber 3 to the inner cavity surface 2i of the inner liner rubber 4, as shown in Figure 2. This heat dissipation coefficient κ2 is a proportionality constant based on Newton's law of cooling and depends on the heat capacity, surface area, and thermal conductivity of the tread rubber 3 and inner liner rubber 4 (in this example, including the carcass 5 and belt layer 6 arranged inside them). Such a heat dissipation coefficient κ2 can be easily identified (fitted) in step S7 described later, based on measured values ​​such as the temperature of the tread rubber 3 (tread contact surface 2o) of the tire 2 rolling on the road surface 7 and the temperature of the inner cavity surface 2i of the inner liner rubber 4.

[0036] As shown in Figure 4, it is preferable that a fourth heat dissipation relationship is defined between the tread rubber model 14 and the ambient air model 18 in this embodiment. The fourth heat dissipation relationship in this embodiment is a parameter that indicates the ease of heat dissipation between the tread rubber 3 and the ambient air 11, as shown in Figure 2. Considering the actual heat dissipation between the tread rubber 3 and the ambient air 11 based on this fourth heat dissipation relationship, the temperature T of the tread contact surface 14o of the calculation model 12 shown in Figure 4 is calculated. out This can be calculated.

[0037] The fourth heat dissipation relationship of this embodiment includes a heat dissipation coefficient κ3 from the tread contact surface 14o of the tread rubber model 14 to the ambient air model 18. The heat dissipation coefficient κ3 of this embodiment indicates how easily heat is transferred from the tread rubber 3 (the portion of the tread contact surface 2o that is not in contact with the road surface 7) to the ambient air 11, as shown in Figure 2. This heat dissipation coefficient κ3 is a proportionality constant based on Newton's law of cooling and depends on the heat capacity, surface area, and thermal conductivity of the tread rubber 3 and the ambient air 11. Such a heat dissipation coefficient κ3 can be easily identified (fitted) in step S7 described later, based on measured values ​​such as the temperature of the tread rubber 3 (tread contact surface 2o) of the tire 2 rolling on the road surface 7 and the temperature of the ambient air 11.

[0038] In step S2 of this embodiment, a first heat conduction equation is defined based on the following equation (1), which shows the time-series temperature change of the tread contact surface 14o of the tread rubber model 14 shown in Figure 4.

[0039]

number

[0040] Equation (1) above is a differential equation based on Newton's law of cooling. dT out / dt is the temperature T of the tread contact surface 14° of the tread rubber model 14. out This shows the rate of change over time.

[0041] In equation (1) above, Q / W on the right-hand side represents the temperature T of the tread contact surface 14o (tread rubber model 14) per unit time (1 second in this example). out This shows the increase in temperature. This temperature increase can be determined by dividing the amount of heat Q generated per unit time at the tread contact surface 2o of the tire 2 shown in Figure 2 by the heat capacity W of the tread rubber 3.

[0042] The amount of heat generated Q at the tread contact surface 2o can be appropriately determined based on conventional methods. In this embodiment, the amount of heat generated Q is calculated based on the tire force measured at the tread contact surface 2o of the tire 2 shown in Figure 2 and the slip speed. The tire force includes axial forces in the longitudinal and lateral directions.

[0043] The heat capacity W of the tread rubber 3 can be appropriately determined based on conventional methods. In this embodiment, the heat capacity W can be easily identified (fitted) in step S7 described later, based on measured values ​​such as the temperature of the tread rubber 3 (tread contact surface 2o) of the tire 2 rolling on the road surface 7 shown in Figure 2, and the temperature of the inner liner rubber 4's inner cavity surface 2i.

[0044] In the right-hand side of equation (1) above, the terms excluding Q / W represent the temperature T of the tread contact surface 14o (tread rubber model 14) per unit time (1 second in this example). out This shows the decrease.

[0045] The above equation (1) κ1(T out -T r ) represents the amount of heat dissipated (decrease) from the tread contact surface 14o of the tread rubber model 14 to the road surface model 13 per unit time (1 second in this example). This amount of heat dissipation is calculated using the heat dissipation coefficient κ1 and the temperature difference (T) between the tread contact surface 14o and the road surface model 13. out -T r It increases in proportion to ).

[0046] The above equation (1) κ2(T out -T in ) represents the amount of heat dissipation (decrease) from the tread contact surface 14o of the tread rubber model 14 to the inner cavity surface 15i of the inner liner rubber model 15 per unit time (1 second in this example). This amount of heat dissipation is calculated using the heat dissipation coefficient κ2 and the temperature difference (T) between the tread contact surface 14o and the inner cavity surface 15i. out -T in It increases in proportion to ).

[0047] The above equation (1) κ3(T out -T e ) represents the amount of heat dissipated (decrease) from the tread contact surface 14o of the tread rubber model 14 to the ambient air model 18 per unit time (1 second in this example). This amount of heat dissipation is calculated using the heat dissipation coefficient κ3 and the temperature difference (T) between the tread contact surface 14o and the ambient air model 18. out -T e It increases in proportion to ).

[0048] Thus, in the first heat conduction equation of equation (1) above, the temperature T of the tread contact surface 14o (tread rubber model 14) is calculated per unit time (1 second in this example). out The heat balance between the increase and decrease in temperature can be calculated. This first heat conduction equation defines a tread rubber model 14 that can calculate the time-series temperature change of the tread contact surface 14o. The tread rubber model 14 is input into computer 1 (shown in Figure 1).

[0049] [Enter inner liner rubber model] Next, in the creation method of this embodiment, the inner liner rubber model 15 is input into the computer 1 (shown in Figure 1) (step S3). The inner liner rubber model 15 of this embodiment is defined to have a spatially uniform temperature distribution.

[0050] "Having a spatially uniform temperature distribution" means that the temperature is uniform in all regions of the space constituting the inner liner rubber model 15. Therefore, in this embodiment, at each unit time (for example, 1 second) in which the temperature is calculated using the calculation method described later, the entire inner liner rubber model 15 maintains a single temperature T in It is defined as having a (uniform temperature distribution). By defining the inner liner rubber model 15 to have a spatially uniform temperature distribution in this way, the inner liner rubber model 15 can be simplified. As a result, the inner liner rubber model 15 can be modeled in a short time in process S3.

[0051] temperature T in This is set as the temperature of the inner liner rubber model 15i of the tire. As a result, the temperature measured at the inner liner surface 2i of tire 2 shown in Figure 2 and the temperature T of the inner liner surface 15i of the tire in the calculated model 12 shown in Figure 4 are compared. in This makes comparisons easier.

[0052] In this embodiment, the inner liner rubber model 15 has the above-described second heat dissipation relationship defined between it and the tread rubber model 14. Considering the actual heat dissipation between the inner liner rubber 4 and the tread rubber 3 shown in Figure 2, the temperature T of the tire inner surface 15i in the calculation model 12 shown in Figure 4 is determined based on this second heat dissipation relationship. in This can be calculated.

[0053] The second heat dissipation relationship of this embodiment includes a heat dissipation coefficient κ4 from the inner liner rubber model 15's inner surface 15i to the tread contact surface 14o of the tread rubber model 14. The heat dissipation coefficient κ4 of this embodiment indicates how easily heat is transferred from the inner liner rubber 4's inner surface 2i to the tread contact surface 2o of the tread rubber 3, as shown in Figure 2. This heat dissipation coefficient κ4 is a proportionality constant based on Newton's law of cooling and depends on the heat capacity, surface area, and thermal conductivity of the tread rubber 3 and inner liner rubber 4 (including the carcass 5 and belt layer 6 arranged inside them in this example). Such a heat dissipation coefficient κ4 can be easily identified (fitted) in step S7 described later, based on measured values ​​such as the temperature of the inner liner rubber 4's inner surface 2i and the temperature of the tread rubber 3 (tread contact surface 2o) of the tire rolling on the road surface 7.

[0054] In this embodiment, it is preferable that a third heat dissipation relationship is defined between the inner liner rubber model 15 and the tire internal air model 16. The third heat dissipation relationship in this embodiment is a parameter that indicates the ease of heat dissipation between the inner liner rubber 4 and the tire internal air 10, as shown in Figure 2. Considering the actual heat dissipation between the inner liner rubber 4 and the tire internal air 10 based on this third heat dissipation relationship, the temperature T of the tire internal surface 15i in the calculation model 12 shown in Figure 4 is calculated. in This can be calculated.

[0055] The third heat dissipation relationship of this embodiment includes a heat dissipation coefficient κ5 from the inner liner rubber model 15's inner surface 15i to the tire internal air model 16. The heat dissipation coefficient κ5 in this embodiment indicates how easily heat is transferred from the inner liner rubber 4's inner surface 2i to the tire internal air 10, as shown in Figure 2. This heat dissipation coefficient κ5 is a proportionality constant based on Newton's law of cooling and depends on the heat capacity, surface area, and thermal conductivity of the inner liner rubber 4 and the tire internal air 10. Such a heat dissipation coefficient κ5 can be easily identified (fitted) in step S7 described later, based on measured values ​​such as the temperature of the inner liner rubber 4 (tire inner surface 2i) and the temperature of the tire internal air 10 of the tire rolling on the road surface 7.

[0056] In step S3 of this embodiment, a second heat conduction equation is defined based on the following equation (2), which shows the time-series temperature change of the inner liner rubber model 15 tire inner surface 15i shown in Figure 4.

[0057]

number

[0058] Equation (2) above is a differential equation based on Newton's law of cooling. dT in / dt is the temperature T of the inner liner rubber model 15 tire inner lumen surface 15i in This shows the rate of change over time.

[0059] Q on the right side of equation (2) above in / W in This is the temperature T of the inner surface 15i (inner liner rubber model 15) of the tire cavity per unit time (1 second in this example). in This shows the increase in temperature. This temperature increase can be determined by dividing the amount of heat generated due to the deformation of tire 2 during driving (deformation inside the tire), as shown in Figure 2, by the heat capacity of the inner liner rubber 4.

[0060] Heat generation Q due to deformation of tire 2in This can be appropriately determined based on conventional methods. The heat output Q of this embodiment in This is calculated based on the rolling resistance of tire 2.

[0061] Heat capacity of inner liner rubber 4 W in This can be appropriately determined based on conventional methods. Heat capacity W of this embodiment in In step S7 described later, the tire can be easily identified (fitted) based on measured values ​​such as the temperature of the tread rubber 3 (tread contact surface 2o) of the tire 2 rolling on the road surface 7, and the temperature of the inner liner rubber 4 on the inner surface 2i of the tire.

[0062] Of the right-hand side of equation (2) above, Q in / W in The terms excluding this one represent the temperature T of the inner surface 15i (inner liner rubber model 15) of the tire cavity 15i per unit time (1 second in this example). in This shows the decrease.

[0063] The above equation (2) κ4(T in -T out ) represents the amount of heat dissipated (decrease) per unit time (1 second in this example) from the inner liner rubber model 15's inner cavity surface 15i to the tread contact surface 14o of the tread rubber model 14. This amount of heat dissipation is calculated using the heat dissipation coefficient κ4 and the temperature difference (T) between the inner cavity surface 15i and the tread contact surface 14o. in -T out It increases in proportion to ).

[0064] The above equation (2) κ5(T in -T a ) represents the amount of heat dissipation (decrease) from the inner liner rubber model 15's inner lumen surface 15i to the tire internal air model 16 per unit time (1 second in this example). This amount of heat dissipation is calculated using the heat dissipation coefficient κ5 and the temperature difference (T) between the inner lumen surface 15i and the tire internal air model 16. in -T a It increases in proportion to ).

[0065] Thus, in the second heat conduction equation of equation (2) above, the temperature T of the inner surface 15i of the tire (inner liner rubber model 15) is calculated per unit time (1 second in this example). in The heat balance between the increase and decrease in temperature can be calculated. This second heat conduction equation defines an inner liner rubber model 15 that can calculate the time-series temperature change of the inner surface 15i of the tire. The inner liner rubber model 15 is input into computer 1 (shown in Figure 1).

[0066] [Enter tire internal air model] Next, in the creation method of this embodiment, the tire internal air model 16 is input into the computer 1 (shown in Figure 1) (step S4). The tire internal air model 16 of this embodiment is defined to have a spatially uniform temperature distribution.

[0067] "Having a spatially uniform temperature distribution" means that the temperature is uniform in all regions of the space that constitutes the tire internal air model 16. Therefore, in this embodiment, at each unit time (for example, 1 second) in which the temperature is calculated using the calculation method described later, the entire tire internal air model 16 is at a single temperature T a It is defined as having a uniform temperature distribution. By defining the tire internal air model 16 to have a spatially uniform temperature distribution in this way, the tire internal air model 16 can be simplified. As a result, in process S4, the tire internal air model 16 can be modeled in a short amount of time.

[0068] In this embodiment, the tire internal air model 16 has the above-described third heat dissipation relationship defined between it and the inner liner rubber model 15. Considering the actual heat dissipation between the tire internal air 10 and the inner liner rubber 4 shown in Figure 2, the temperature T of the tire internal air model 16 shown in Figure 4 is determined by this third heat dissipation relationship. a This can be calculated.

[0069] The third heat dissipation relationship includes a heat dissipation coefficient κ6 from the tire internal air model 16 to the inner lumen surface 15i of the inner liner rubber model 15. The heat dissipation coefficient κ6 in this embodiment indicates how easily heat is transferred from the tire internal air 10 shown in Figure 2 to the inner lumen surface 2i of the inner liner rubber 4. This heat dissipation coefficient κ6 is a proportionality constant based on Newton's law of cooling and depends on the heat capacity, surface area, and thermal conductivity of the tire internal air 10 and the inner liner rubber 4. Such a heat dissipation coefficient κ6 can be easily identified (fitted) in step S7 described later, based on measured values ​​such as the temperature of the tire internal air 10 and the temperature of the inner liner rubber 4 (tire lumen surface 2i) of the tire 2 rolling on the road surface 7.

[0070] In this embodiment, it is preferable that a fifth heat dissipation relationship is defined between the tire internal air model 16 and the wheel model 17. The fifth heat dissipation relationship in this embodiment is a parameter that indicates the ease of heat dissipation between the tire internal air 10 and the wheel 8, as shown in Figure 2. Considering the actual heat dissipation between the tire internal air 10 and the wheel 8 based on such a fifth heat dissipation relationship, the temperature T of the tire internal air model 16 shown in Figure 4 is determined. a This can be calculated.

[0071] The fifth heat dissipation relationship of this embodiment includes a heat dissipation coefficient κ7 from the tire internal air model 16 to the wheel model 17. The heat dissipation coefficient κ7 of this embodiment represents the ease with which heat is transferred from the tire internal air 10 to the wheel 8, as shown in Figure 2. This heat dissipation coefficient κ7 is a proportionality constant based on Newton's law of cooling and depends on the heat capacity, surface area, and thermal conductivity of the tire internal air 10 and the wheel 8. Such a heat dissipation coefficient κ7 can be easily identified (fitted) in step S7 described later, based on measured values ​​such as the temperature of the tire internal air 10 and the temperature of the wheel 8 of the tire 2 rolling on the road surface 7.

[0072] In step S4 of this embodiment, a third heat conduction equation is defined based on the following equation (3), which shows the time-series temperature change of the tire internal air model 16 shown in Figure 4.

[0073]

number

[0074] Equation (3) above is a differential equation based on Newton's law of cooling. dT a / dt is the temperature T of the tire's internal air model 16. a This shows the rate of change over time.

[0075] Equation (3) above gives the temperature T of the tire's internal air model 16 per unit time (1 second in this example). a This shows the decrease. Note that the tire internal air 10 shown in Figure 2 can be treated as not generating heat due to the tire 2 running, unlike the tread contact surface 2o, etc. Therefore, unlike equations (1) and (2) above, equation (3) does not include a term that shows the temperature increase of the tire internal air model 16.

[0076] The above equation (3) κ6(T a -T in ) represents the amount of heat dissipated (decrease) from the tire internal air model 16 to the inner liner rubber model 15 of the tire cavity surface 15i per unit time (1 second in this example). This amount of heat dissipation is calculated using the heat dissipation coefficient κ6 and the temperature difference (T) between the tire internal air model 16 and the tire cavity surface 15i. a -T in It increases in proportion to ).

[0077] The above equation (3) κ7(T a -T w) represents the amount of heat dissipated (decrease) from the tire internal air model 16 to the wheel model 17 per unit time (1 second in this example). This amount of heat dissipation is calculated using the heat dissipation coefficient κ7 and the temperature difference (T) between the tire internal air model 16 and the wheel model 17. a -T w It increases in proportion to ).

[0078] Thus, in the third heat conduction equation of equation (3) above, the temperature T of the inner surface 15i of the tire is calculated per unit time (1 second in this example). in Based on these factors, the heat balance of the tire internal air model 16 can be calculated. This third heat conduction equation defines a tire internal air model 16 capable of calculating time-series temperature changes. The tire internal air model 16 is input into computer 1 (shown in Figure 1).

[0079] [Enter outdoor air model] Next, in the creation method of this embodiment, the outside air model 18 is input into the computer 1 (shown in Figure 1) (step S5). The outside air model 18 of this embodiment is defined to have a spatially uniform temperature distribution.

[0080] "Having a spatially uniform temperature distribution" means that the temperature is uniform in all regions of the space that constitutes the outside air model 18. Therefore, in this embodiment, at each unit time (e.g., 1 second) in which the temperature is calculated using the calculation method described later, the entire outside air model 18 has a single temperature T e It is defined as having a (uniform temperature distribution). By defining the ambient air model 18 to have a spatially uniform temperature distribution in this way, the ambient air model 18 can be simplified. As a result, in process S5, the ambient air model 18 can be modeled in a short amount of time.

[0081] Outdoor temperature T for Model 18 e This is set appropriately according to the driving environment (outside air 11) of the tire 2 being analyzed, as shown in Figure 2. In this embodiment, assuming that the temperature of the outside air 11 does not change (remains constant) during the rolling of the tire 2, the temperature T of the outside air model 18 is set. eis set as a constant (for example, 0 to 40 °C). As a result, in the calculation method described later, since it is not necessary to calculate the temperature change of the outside air model 18, the calculation time can be shortened. Note that depending on the required calculation accuracy, the outside air model 18 may be set with a temperature T that changes every unit time e is set.

[0082] In the outside air model 18 of the present embodiment, the above-described fourth heat dissipation relationship (heat dissipation coefficient κ3) is defined between the tread rubber model 14. Due to such a fourth heat dissipation relationship, considering the actual heat dissipation between the outside air 11 and the tread rubber 3 shown in FIG. 2, the temperature T of the tread rubber model 14 of the calculation model 12 shown in FIG. 4 a is calculated based on the temperature T of the outside air model 18 e can be calculated.

[0083] In the outside air model 18 of the present embodiment, a sixth heat dissipation relationship (heat dissipation coefficient κ9 described later) is defined between the wheel model 17. The sixth heat dissipation relationship of the present embodiment is a parameter indicating the ease of heat dissipation between the outside air 11 and the wheel 8 shown in FIG. 2. Due to such a sixth heat dissipation relationship, considering the actual heat dissipation between the outside air 11 and the wheel 8, the temperature T of the wheel model 17 of the calculation model 12 shown in FIG. 4 w is calculated based on the temperature T of the outside air model 18 e can be calculated.

[0084] In step S5 of the present embodiment, as the outside air model 18, a temperature T e is defined. The outside air model 18 (temperature T e ) is input to the computer 1 (shown in FIG. 1).

[0085] [Input wheel model] Next, in the creation method of the present embodiment, the wheel model 17 is input to the computer 1 (shown in FIG. 1) (step S6). The wheel model 17 of the present embodiment is defined to have a spatially uniform temperature distribution.

[0086] "Having a spatially uniform temperature distribution" means that the temperature is uniform in all regions of the space that constitutes the wheel model 17. Therefore, in this embodiment, at each unit time (for example, 1 second) in which the temperature is calculated using the calculation method described later, the entire wheel model 17 is at a single temperature T w It is defined as having a (uniform temperature distribution). By defining the wheel model 17 to have a spatially uniform temperature distribution in this way, the wheel model 17 can be simplified. As a result, the wheel model 17 can be modeled in a short time in process S6.

[0087] In this embodiment, the wheel model 17 is defined in relation to the tire internal air model 16, as described above. Considering the actual heat dissipation between the wheel 8 and the tire internal air 10 shown in Figure 2, the temperature T of the wheel model 17 shown in Figure 4 is determined by this fifth heat dissipation relationship. w This can be calculated.

[0088] The fifth heat dissipation relationship of this embodiment includes a heat dissipation coefficient κ8 from the wheel model 17 to the tire internal air model 16. The heat dissipation coefficient κ8 of this embodiment indicates how easily heat is transferred from the wheel 8 to the tire internal air 10, as shown in Figure 2. This heat dissipation coefficient κ8 is a proportionality constant based on Newton's law of cooling and depends on the heat capacity, surface area, and thermal conductivity of the wheel 8 and the tire internal air 10. Such a heat dissipation coefficient κ8 can be easily identified (fitted) in step S7 described later, based on measured values ​​such as the temperature of the wheel 8 and the temperature of the tire internal air 10 of the tire 2 rolling on the road surface 7.

[0089] In this embodiment, it is preferable that the wheel model 17 has the above-described sixth heat dissipation relationship defined between it and the ambient air model 18. Considering the actual heat dissipation between the wheel 8 and the ambient air 11 shown in Figure 2, the temperature T of the wheel model 17 shown in Figure 4 is determined by this sixth heat dissipation relationship. w This can be calculated.

[0090] The sixth heat dissipation relationship of this embodiment includes the heat dissipation coefficient κ9 from the wheel model 17 to the outside air model 18. The heat dissipation coefficient κ9 of this embodiment indicates the ease of heat transfer from the wheel 8 shown in FIG. 2 to the outside air 11. This heat dissipation coefficient κ9 is a proportionality constant based on Newton's law of cooling and depends on the heat capacity, surface area, thermal conductivity, etc. of the wheel 8 and the outside air 11. Such a heat dissipation coefficient κ9 can be easily identified (fitted) based on measured values such as the temperature of the wheel 8 of the tire 2 rolling on the road surface 7 and the temperature of the outside air 11 in step S7 described later.

[0091] In step S6 of this embodiment, based on the following formula (4), a fourth heat conduction equation indicating the time-series temperature change of the wheel model 17 shown in FIG. 4 is defined.

[0092]

Equation

[0093] The above formula (4) is a differential equation based on Newton's law of cooling. dT w / dt indicates the rate of change of the temperature T w of the wheel model 17 with respect to time.

[0094] The above formula (4) represents the temperature T wThis shows the decrease. Note that the wheel 8 shown in Figure 2 does not deform as much as the tire 2, and therefore can be treated as not generating heat due to the tire 2's movement. For this reason, unlike equations (1) and (2) above, equation (4) does not include a term showing the temperature increase of the wheel model 17.

[0095] The above equation (4) κ8(T w -T a ) represents the amount of heat dissipated (decrease) from the wheel model 17 to the tire internal air model 16 per unit time (1 second in this example). This amount of heat dissipation is calculated using the heat dissipation coefficient κ8 and the temperature difference (T) between the wheel model 17 and the tire internal air model 16. w -T a It increases in proportion to ).

[0096] The above equation (4) κ9(T w -T e ) represents the amount of heat dissipated (decrease) from the wheel model 17 to the ambient air model 18 per unit time (1 second in this example). This amount of heat dissipation is calculated using the heat dissipation coefficient κ9 and the temperature difference (T) between the wheel model 17 and the ambient air model 18. w -T e It increases in proportion to ).

[0097] Thus, in the fourth heat conduction equation of equation (4) above, the temperature T of the tire internal air model 16 is calculated for each unit time (1 second in this example). a Based on these factors, the heat balance of the wheel model 17 can be calculated. The definition of this fourth heat conduction equation defines a wheel model 17 that can calculate the time-series temperature change. The wheel model 17 is input into computer 1 (shown in Figure 1).

[0098] [Identify heat dissipation relationships] Next, in the manufacturing method of this embodiment, the computer 1 (shown in Figure 1) identifies the first heat dissipation relationship, the second heat dissipation relationship, and the third heat dissipation relationship (step S7). In step S7 of this embodiment, the first to third heat dissipation relationships (heat dissipation coefficients κ1 to κ2 and κ4 to κ6) are identified based on the measured temperatures of the tread rubber 3, inner liner rubber 4, road surface 7, and internal tire air 10 of the tire 2 rolling on the road surface 7 shown in Figure 2.

[0099] In step S7 of this embodiment, the fourth heat dissipation relationship (heat dissipation coefficient κ3), the fifth heat dissipation relationship (heat dissipation coefficient κ7, heat dissipation coefficient κ8), and the sixth heat dissipation relationship (heat dissipation coefficient κ9) are identified. Furthermore, in step S7 of this embodiment, the heat capacity W of the tread rubber 3 and the heat capacity W of the inner liner rubber 4 of the tire 2 are identified. in These are identified. These are the fourth to sixth heat dissipation relationships, heat capacity W and W in It is identified based on measured temperatures of the tread rubber 3, inner liner rubber 4, road surface 7, wheel 8, tire internal air 10, and outside air 11.

[0100] In step S7 of this embodiment, the tire 2 to be analyzed is first rolled on the road surface 7. The rolling conditions can be set appropriately according to, for example, the usage conditions of the tire 2 to be analyzed.

[0101] Next, in step S7 of this embodiment, the temperatures of the tread rubber 3, inner liner rubber 4, road surface 7, wheel 8, internal tire air 10, and outside air 11 of the rolling tire 2 are measured. Furthermore, in step S7, the tire force (i.e., axial force in the longitudinal and lateral directions), slip speed, and rolling resistance are measured. Each temperature, tire force, slip speed, and rolling resistance can be measured as appropriate using, for example, known sensors.

[0102] The temperatures of the road surface 7, wheel 8, tire internal air 10, and outside air 11 can be measured at any location. On the other hand, the temperature of the tread rubber 3 is measured at the tread contact surface 2o. The temperature of the inner liner rubber 4 is measured at the inner cavity surface 2i of the tire. These temperatures of the tread contact surface 2o and the inner cavity surface 2i can be measured more easily than, for example, the temperature inside the tread rubber 3 and the temperature inside the inner liner rubber 4.

[0103] The temperature of the tread rubber 3 can be measured at any position on the tread contact surface 2o. Depending on the purpose of the analysis, the temperature of the tread rubber 3 may be measured, for example, at the center of the tire axial direction (i.e., the tire equator) and at the point of contact in the circumferential direction of the tire. The temperature of the tread rubber 3 may also be measured as the average temperature in the tire axial direction, or as the average temperature of the point of contact and the point of contact in the circumferential direction of the tire. On the other hand, the temperature of the inner liner rubber 4 can be measured at any position on the inner surface 2i of the tire. Depending on the purpose of the analysis, the temperature of the inner liner rubber 4 may also be measured, for example, at the center of the tire axial direction (i.e., the tire equator) and at the point of contact. The temperature of the inner liner rubber 4 may also be measured as the average temperature in the tire axial direction, or as the average temperature of the point of contact and the point of contact in the circumferential direction of the tire.

[0104] The timing for measuring the temperature of the tread rubber 3, rolling resistance, etc., can be set as appropriate. In this embodiment, in order to accurately identify each heat dissipation relationship (including the first to sixth heat dissipation relationships in this example), the temperature of the tread rubber 3, etc., is measured at multiple measurement times (at each unit time).

[0105] Next, in step S7 of this embodiment, the first to sixth heat dissipation relationships are identified based on the measured values ​​of the tread rubber 3, etc. In this embodiment, first, the first to fourth heat conduction equations (equations (1) to (4) above) are integrated, similar to the conventional method using Newton's law of cooling.

[0106] Next, in this embodiment, the temperature T of the tread contact surface 14o, which is determined by the integrated first to fourth heat conduction equations, is compared with the measured temperature of the tread contact surface 2o. out The first to sixth heat dissipation relationships (heat dissipation coefficients κ1 to κ9) are identified so that they approximate the given values. Such identification (fitting) can be performed based on known optimization calculations, for example, using commercially available computer software (e.g., MATLAB (MATLAB is a registered trademark) from MathWorks, Inc., or Excel (Excel is a registered trademark) from Microsoft Corporation). The identified first to sixth heat dissipation relationships (heat dissipation coefficients κ1 to κ9 in this example) are stored in computer 1 (shown in Figure 1).

[0107] In the manufacturing method of this embodiment, by performing steps S1 to S7 shown in Figure 3, a calculation model 12 (shown in Figure 4) capable of calculating the time-series temperature change of a tire 2 rolling on the road surface 7 shown in Figure 2 can be created. The calculation model 12 is stored in a computer (shown in Figure 1).

[0108] The calculation model 12 of this embodiment can calculate the heat conduction from the road surface model 13 shown in Figure 2 through the tread contact surface 2o and the inner surface 2i of the tire to the internal air model 16 of the tire, based on the first to third heat dissipation relationships. Therefore, the calculation model 12 of this embodiment (shown in Figure 4) can accurately calculate the time-series temperature change of the tire 2 (shown in Figure 2).

[0109] As shown in Figure 4, the calculation model 12 of this embodiment is defined such that the road surface model 13, tread rubber model 14, inner liner rubber model 15, and tire internal air model 16 each have a spatially uniform temperature distribution. As a result, the calculation model 12 of this embodiment does not need to calculate the heat balance for each finite element of each model, as in Patent Document 1, for example. Therefore, the calculation model 12 of this embodiment can reduce the computational load and can be applied, for example, to real-time vehicle simulations.

[0110] The calculation model 12 of this embodiment can calculate heat conduction including the wheel 8 and ambient air 11 shown in Figure 2, based on the fourth to sixth heat dissipation relationships, thus enabling more accurate calculation of the time-series temperature change of the tire 2. As shown in Figure 4, the wheel model 17 and ambient air model 18 are defined to have a spatially uniform temperature distribution, thus reducing the computational load.

[0111] The first to sixth heat dissipation relationships (heat dissipation coefficients κ1 to κ9 in this example) are identified based on measured temperatures of the tread rubber 3 of the tire 2. These measured temperatures tend to differ depending on the structure of the tire 2 (for example, the thickness of the tread rubber 3 and inner liner rubber 4). By identifying the first to sixth heat dissipation relationships (heat dissipation coefficients κ1 to κ9 in this example) based on these measured temperatures, a calculation model 12 capable of calculating the time-series temperature change for tires 2 having various structures can be created.

[0112] [Method for calculating the time-series temperature change of pneumatic tires] Next, the calculation method will be explained. In the calculation method of this embodiment, the time-series temperature change of the tire 2 rolling on the road surface 7 shown in Figure 2 is calculated using the calculation model 12 shown in Figure 4.

[0113] In this embodiment, prior to implementing the calculation method, a calculation model 12 of the tire 2 to be analyzed (i.e., a calculation model in which the first to sixth heat dissipation relationships (in this example, heat dissipation coefficients κ1 to κ9) are identified) is created based on the procedure shown in Figure 2. Figure 5 is a flowchart showing the processing procedure of the calculation method for the time-series temperature change of a pneumatic tire in this embodiment.

[0114] [Create a computational model] In the calculation method of this embodiment, first, computer 1 (shown in Figure 1) creates the calculation model 12 shown in Figure 4 (step S11). In step S11 of this embodiment, the calculation model 12 of the tire 2 to be analyzed (shown in Figure 2) is created based on the processing procedure shown in Figure 2. The calculation model 12 is stored in computer 1.

[0115] [Enter the amount of heat generated] Next, in the calculation method of this embodiment, the amount of heat generated by the rolling tire 2 is input to the computer 1 (shown in Figure 1) (step S12). Step S12 of this embodiment first rolls the tire 2 shown in Figure 2 on the road surface 7 based on predetermined rolling conditions. The rolling conditions are set appropriately according to the tire 2 to be analyzed. The rolling conditions may be rolling on a highway or general road, or the slip angle may be given randomly or at regular intervals.

[0116] Next, the amount of heat generated by the rolling tire 2 is calculated. The amount of heat generated is not particularly limited, as long as it is possible to calculate the time-series temperature change of the tire 2 using the calculation model 12 (shown in Figure 4). In this embodiment, the amount of heat generated includes a first heat generation amount and a second heat generation amount.

[0117] The first heat generation is the amount of heat generated at the tread contact surface 2o of the tire 2 (i.e., the heat generation Q in the first heat conduction equation of equation (1) above). Such a first heat generation can be calculated based on the measured results of the tire force acting on the tire 2 during rolling (i.e., axial force in the longitudinal and lateral directions) and the slip speed.

[0118] The second heat generation is the amount of heat generated due to the deformation of tire 2 (i.e., the heat generation Q in the second heat conduction equation of equation (2) above). in This second heat generation can be calculated based on the rolling resistance acting on tire 2 during rolling.

[0119] In step S12 of this embodiment, tire force (i.e., axial force in the longitudinal and lateral directions), slip speed, and rolling resistance are measured at predetermined unit time intervals (e.g., 1 second). Based on these measurement results, the first heat generation amount and the second heat generation amount are calculated at each unit time interval. The heat generation amounts (first heat generation amount and second heat generation amount) are stored in computer 1 (shown in Figure 1).

[0120] [Calculate the temperature of the computational model] Next, in the calculation method of this embodiment, the computer 1 (shown in Figure 1) calculates the temperature of the calculation model 12 (shown in Figure 4) based on the amount of heat generated by the tire 2 (step S13).

[0121] In step S13 of this embodiment, first, the temperature T of the road surface model 13 of the first heat conduction equation is determined. r A constant is set. This constant is set based on the temperature of the road surface 7 shown in Figure 2. Furthermore, the temperature T of the ambient air model 18 in the first and fourth heat conduction equations is also set. e A constant is set. This constant is set based on the temperature of the ambient air 11 shown in Figure 2.

[0122] Next, in step S13 of this embodiment, the heat conduction equation (differential equation) is integrated into equations (1) to (4) above.

[0123] Next, in step S13 of this embodiment, the first heat generation amount for each unit time is substituted into the heat generation amount Q of the first heat conduction equation (1) that has been integrated above. As a result, the first heat generation amount (heat generation amount Q) is divided by the heat capacity W of the tread rubber 3, and the temperature T of the tread contact surface 14o (tread rubber model 14) is obtained. out The increase is calculated for each unit of time (for example, 1 second).

[0124] Next, in step S13 of this embodiment, the heat generation Q of the second heat conduction equation of the integrated equation (2) above is obtained. in The second heat generation amount for each unit time is substituted into this. As a result, the second heat generation amount (heat generation amount Q) is obtained. in ) However, the heat capacity of the inner liner rubber 4 is W inBy being divided by this, the temperature T of the inner surface 15i of the tire (inner liner rubber model 15) in The increase is calculated for each unit of time (for example, 1 second).

[0125] Next, in step S13 of this embodiment, the temperature T of the tread contact surface 14o out and the temperature T of the inner surface 14i of the tire in Each increase in Q / W and Q in / W in Then, the heat balance is calculated based on the temperature decrease of the calculation model 12, which is determined by each heat dissipation relationship (1st to 6th heat dissipation relationship). Such a heat balance is calculated for each unit time (e.g., 1 second).

[0126] In step S13 of this embodiment, based on the first heat generation, the temperature T of the tread contact surface 14o of the tread rubber model 14 is determined. out The temperature T of the inner liner rubber model 15i of the tire cavity surface 15i is calculated based on the second heat generation. in The following is calculated. Furthermore, these temperatures T out , T in Based on the heat dissipation relationships (heat dissipation coefficients κ1 to κ9), etc., the temperature T of the tire internal air model 16 is determined. a Yes, the temperature of wheel model 17 T w The following calculations are performed. Based on these calculation results, the calculation method of this embodiment makes it possible to calculate the time-series temperature changes of each component (in this example, the tread contact surface 2o, the inner surface of the tire 2i, the wheel 8, and the air inside the tire 10) for a tire 2 rolling on the road surface 7 shown in Figure 2.

[0127] In the calculation method of this embodiment, the heat conduction between the road surface model 13 and the ambient air model 18 can be calculated based on the heat generated by the tire 2 (in this example, the first heat generated and the second heat generated) and the heat dissipation relationships (in this example, the first to sixth heat dissipation relationships). As a result, the calculation method of this embodiment can accurately calculate the time-series temperature change of the tire 2.

[0128] In this embodiment, each model constituting the calculation model 12 (in this example, the road surface model 13 to the ambient air model 18) is defined to have a spatially uniform temperature distribution, thereby reducing the computational load. Therefore, the calculation method of this embodiment can be applied, for example, to real-time vehicle simulation (i.e., simultaneously measuring the heat generated by the tire 2 and calculating the time-series temperature change of the tire 2).

[0129] In this embodiment, since the first to sixth heat dissipation relationships (heat dissipation coefficients κ1 to κ9 in this example) are predetermined based on temperature measurements of the tread rubber 3 of the tire 2, a calculation model 12 that models a tire 2 having any structure can be used. As a result, the calculation method of this embodiment can accurately calculate the time-series temperature change of the tire 2, regardless of the structure of the tire 2.

[0130] [Evaluating time-series temperature changes] Next, in the calculation method of this embodiment, it is evaluated whether the time-series temperature change of tire 2 meets a predetermined standard (step S14). The evaluation may be performed by computer 1 (shown in Figure 1) or by an operator. The standard can be set appropriately according to the performance required of tire 2, etc.

[0131] In this embodiment, if the time-series temperature change of tire 2 is determined to meet the criteria (Yes in step S14), it is determined that tire 2 has the desired performance. In this case, tire 2 is manufactured (commercialized) based on the structure of tire 2 (step S15).

[0132] On the other hand, if it is determined that the time-series temperature change of tire 2 does not meet the criteria ("No" in process S14), the structure of tire 2 is changed (process S16), and processes S11 to S14 are repeated.

[0133] Thus, in the calculation method of this embodiment, the structure of the tire 2 is modified until the time-series temperature change of the tire 2 meets the criteria. This makes it possible to efficiently manufacture (commercialize) a tire 2 with the desired performance.

[0134] Although particularly preferred embodiments of the present invention have been described in detail above, the present invention is not limited to the illustrated embodiments and can be implemented in various modified forms. [Examples]

[0135] Based on the processing procedure shown in Figure 2, a calculation model for calculating the time-series temperature change of a tire was created (Example). In the example, as shown in Figure 4, the calculation model defined a tread rubber model, an inner liner rubber model, a tire internal air model, a wheel model, and an external air model. The first to sixth heat dissipation relationships (heat dissipation coefficients κ1 to κ9) were defined for these models.

[0136] In the embodiment, based on measurements of the tread rubber, inner liner rubber, internal air of the tire rolling on the road surface, and the temperature of the road surface, the heat dissipation relationships 1 to 6 (heat dissipation coefficients κ1 to κ7) and heat capacities W, W were determined. in The following parameters were identified. In the examples, the heat dissipation coefficients κ8 and κ9 were omitted, assuming that the air inside the tire, the wheel, and the outside air were at the same temperature. The identified parameters are as follows: κ1:0.0919675[1 / s] κ2:0.0303917[1 / s] κ3:0.000001[1 / s] κ4:0.0045[1 / s] κ5:0.0000001[1 / s] κ6:0.0032213[1 / s] κ7:0.0071793[1 / s] W: 0.0000001 [Nm / ℃] W in :0.0032213[Nm / ℃]

[0137] Next, in the embodiment, the time-series temperature change of a tire rolling on the road surface was calculated based on the processing procedure shown in Figure 5. The tire driving conditions include a first driving condition in which the slip angle is input randomly, and a second driving condition in which the slip angle is input at regular intervals. Figure 6 is a graph of the driving conditions showing the relationship between the slip angle and time. Figure 6(a) is the graph for the first driving condition, and Figure 6(b) is the graph for the second driving condition.

[0138] Next, in the embodiment, under each driving condition, the heat generated by the pneumatic tire Q, Q in The following parameters were determined for each model, and the temperature of the tread contact surface of the tread rubber model and the temperature of the inner cavity of the tire of the inner liner rubber model were calculated. Then, the heat balance of each model was calculated, and the time-series temperature change of the tire was calculated. The calculated time-series temperature change was compared with the time-series temperature change measured under each driving condition.

[0139] Figure 7 is a graph showing the relationship between tire temperature and time (time-series temperature change) under the first driving conditions. Figure 7(a) is a graph showing the time-series temperature change of the tread contact surface. Figure 7(b) is a graph showing the time-series temperature change of the inner surface of the tire and the air inside the tire. Figures 7(a) and (b) show the time-series temperature change calculated in the example and the time-series temperature change measured in reality.

[0140] Figure 8 is a graph showing the relationship between tire temperature and time (time-series temperature change) under the second driving condition. Figure 8(a) is a graph showing the time-series temperature change of the tread contact surface. Figure 8(b) is a graph showing the time-series temperature change of the inner surface of the tire and the air inside the tire. Figures 8(a) and (b) show the time-series temperature change calculated in the example and the time-series temperature change measured in reality.

[0141] The test results showed that the time-series temperature change calculated in the example was similar to the measured time-series temperature change. Therefore, the example was able to accurately calculate the time-series temperature change of the tire.

[0142] Furthermore, in this embodiment, the road surface model, tread rubber model, inner liner rubber model, and tire internal air model are each defined to have a spatially uniform temperature distribution. Therefore, it is not necessary to calculate the heat balance for each element of each model, as in Patent Document 1. Consequently, this embodiment can reduce the computational load and can be applied, for example, to real-time vehicle simulations.

[0143] [Note] The present invention includes the following embodiments.

[0144] [Invention 1] A method for creating a computational model for calculating the time-series temperature change of a pneumatic tire rolling on a road surface, The process of inputting the road surface model into a computer, The process of inputting a tread rubber model, in which a first heat dissipation relationship is defined with respect to the aforementioned road surface model, into the computer, The process of inputting an inner liner rubber model, in which a second heat dissipation relationship is defined with respect to the tread rubber model, into the computer, The process includes inputting into the computer a tire internal air model in which a third heat dissipation relationship is defined with respect to the inner liner rubber model, The road surface model, the tread rubber model, the inner liner rubber model, and the tire internal air model are each defined to have a spatially uniform temperature distribution. How to create a computational model. [2nd Invention] The process further includes inputting into the computer an outside air model in which a fourth heat dissipation relationship is defined with respect to the tread rubber model, The method for creating a computational model according to the present invention 1, wherein the aforementioned outside air model is defined to have a spatially uniform temperature distribution. [Invention 3] The process further includes inputting a wheel model, in which a fifth heat dissipation relationship is defined with respect to the tire internal air model, into the computer. A method for creating a computational model according to the present invention 1 or 2, wherein the wheel model is defined to have a spatially uniform temperature distribution. [4th Invention] The process includes inputting an outside air model, in which a sixth heat dissipation relationship is defined with respect to the wheel model, into the computer. The method for creating a computational model according to the present invention, wherein the aforementioned outside air model is defined to have a spatially uniform temperature distribution. [5th ​​Invention] A method for creating a calculation model according to any one of inventions 1 to 4, comprising the step of the computer identifying the first heat dissipation relationship, the second heat dissipation relationship, and the third heat dissipation relationship based on measured values ​​of the tread rubber, inner liner rubber, internal air of the pneumatic tire rolling on the road surface, and the temperature of the road surface. [Invention 6] The first heat dissipation relationship includes a heat dissipation coefficient κ1 from the tread contact surface of the tread rubber model to the road surface model, The second heat dissipation relationship includes a heat dissipation coefficient κ2 from the tread contact surface to the inner liner rubber model's inner cavity surface of the tire, The fourth heat dissipation relationship includes a heat dissipation coefficient κ3 from the tread contact surface to the ambient air model, The method for creating a calculation model according to the present invention 2, wherein the step of inputting the tread rubber model includes the step of defining a first heat conduction equation that shows the time-series temperature change of the tread contact surface based on the following equation (1).

number

number

number

number

[0145] 12 Computational Models 13 Road Surface Models 14 Tread Rubber Models 15 Inner liner rubber model 16 Tire internal air model

Claims

1. A method for creating a computational model for calculating the time-series temperature change of a pneumatic tire rolling on a road surface, The process of inputting the road surface model into a computer, The process of inputting a tread rubber model, in which a first heat dissipation relationship is defined with respect to the aforementioned road surface model, into the computer, The process of inputting an inner liner rubber model, in which a second heat dissipation relationship is defined with respect to the tread rubber model, into the computer, The process includes inputting into the computer a tire internal air model in which a third heat dissipation relationship is defined with respect to the inner liner rubber model, The road surface model, the tread rubber model, the inner liner rubber model, and the tire internal air model are each defined to have a spatially uniform temperature distribution. How to create a computational model.

2. The process further includes inputting into the computer an outside air model in which a fourth heat dissipation relationship is defined with respect to the tread rubber model, The method for creating the calculation model according to claim 1, wherein the outside air model is defined to have a spatially uniform temperature distribution.

3. The process further includes inputting a wheel model, in which a fifth heat dissipation relationship is defined with respect to the tire internal air model, into the computer. A method for creating a computational model according to claim 1 or 2, wherein the wheel model is defined to have a spatially uniform temperature distribution.

4. The process includes inputting an outside air model, in which a sixth heat dissipation relationship is defined with respect to the wheel model, into the computer. The method for creating the calculation model according to claim 3, wherein the outside air model is defined to have a spatially uniform temperature distribution.

5. A method for creating a calculation model according to claim 1 or 2, comprising the step of the computer identifying the first heat dissipation relationship, the second heat dissipation relationship, and the third heat dissipation relationship based on measured values ​​of the tread rubber, inner liner rubber, internal air of the pneumatic tire rolling on the road surface, and the temperature of the road surface.

6. The first heat dissipation relationship is the heat dissipation coefficient κ from the tread contact surface of the tread rubber model to the road surface model. 1 Includes, The second heat dissipation relationship is the heat dissipation coefficient κ from the tread contact surface to the inner cavity surface of the inner liner rubber model of the tire. 2 Includes, The fourth heat dissipation relationship is the heat dissipation coefficient κ from the tread contact surface to the ambient air model. 3 Includes, The method for creating a calculation model according to claim 2, wherein the step of inputting the tread rubber model includes the step of defining a first heat conduction equation that shows the time-series temperature change of the tread contact surface based on the following equation (1). [Math 1] Here, T out : Tread contact surface temperature [°C] T r : Road surface model temperature [°C] T in : Temperature of the inner surface of the tire [°C] T e : Outdoor air model temperature [°C] κ 1 : Heat dissipation coefficient from tread contact patch to road surface model [1 / s] κ 2 : Heat dissipation coefficient [1 / s] from the tread contact surface to the inner cavity surface of the tire κ 3 : Heat dissipation coefficient from tread contact surface to ambient air model [1 / s] Q: Heat generation [1 / s] at the tread contact surface of a pneumatic tire W: Heat capacity of the tread rubber of a pneumatic tire [Nm / °C] t: time [s]

7. The second heat dissipation relationship is the heat dissipation coefficient κ from the inner liner rubber model's inner cavity surface to the tread contact surface of the tread rubber model. 4 Includes, The third heat dissipation relationship is the heat dissipation coefficient κ from the inner surface of the tire to the internal air model of the tire. 5 Includes, The method for creating a calculation model according to claim 1 or 2, wherein the step of inputting the inner liner rubber model includes the step of defining a second heat conduction equation that shows the time-series temperature change of the inner surface of the tire based on the following equation (2). [Math 2] Here, T in : Temperature of the inner surface of the tire [°C] T out : Tread contact surface temperature [°C] T a : Tire internal air temperature [°C] κ 4 : Heat dissipation coefficient from the inner surface of the tire to the tread contact surface [1 / s] κ 5 : Heat dissipation coefficient from the inner surface of the tire to the internal air model of the tire [1 / s] Q in : Amount of heat generated due to deformation of pneumatic tires during driving [1 / s] W in Heat capacity of the inner liner rubber of a pneumatic tire [Nm / °C] t: time [s]

8. The third heat dissipation relationship is the heat dissipation coefficient κ from the tire internal air model to the inner surface of the inner liner rubber model. 6 Includes, The fifth heat dissipation relationship is the heat dissipation coefficient κ from the tire internal air model to the wheel model. 7 Includes, The method for creating a calculation model according to claim 3, wherein the step of inputting the tire internal air model includes the step of defining a third heat conduction equation that shows the time-series temperature change of the tire internal air model based on the following equation (3). [Math 3] Here, T a : Tire internal air temperature [°C] T in : Temperature of the inner surface of the tire [°C] T w Wheel model temperature [°C] κ 6 : Heat dissipation coefficient from the tire's internal air model to the tire's inner surface [1 / s] κ 7 : Heat dissipation coefficient from the tire internal air model to the wheel model [1 / s] t: time [s]

9. The fifth heat dissipation relationship is the heat dissipation coefficient κ from the wheel model to the tire internal air model. 8 Includes, The sixth heat dissipation relationship is the heat dissipation coefficient κ from the wheel model to the outside air model. 9 Includes, The method for creating a calculation model according to claim 4, wherein the step of inputting the wheel model includes the step of defining a fourth heat conduction equation that shows the time-series temperature change of the wheel model based on the following equation (4). [Math 4] Here, T w Wheel model temperature [°C] T a : Tire internal air temperature [°C] T e : Outdoor air model temperature [°C] κ 8 : Heat dissipation coefficient from wheel model to tire internal air model [1 / s] κ 9 : Heat dissipation coefficient from wheel model to outside air model [1 / s] t: time [s]

10. A method for calculating the time-series temperature change of a pneumatic tire rolling on a road surface using the calculation model prepared by the method described in claim 1 or 2, The process of inputting the amount of heat generated by the pneumatic tire while it is rolling to the computer, The computer includes the step of calculating the temperature of the calculation model based on the amount of heat generated, How to calculate the time-series temperature change of a pneumatic tire.

11. The heat generation amount includes a first heat generation amount which is the heat generated at the tread contact surface of the pneumatic tire. The method for calculating the time-series temperature change of a pneumatic tire according to claim 10, wherein the calculation step includes a step of calculating the temperature of the tread contact surface of the tread rubber model based on the first heat generation amount.

12. The aforementioned heat generation amount includes a second heat generation amount which is the heat generation amount caused by the deformation of the pneumatic tire. The method for calculating the time-series temperature change of a pneumatic tire according to claim 10, wherein the calculation step includes a step of calculating the temperature of the inner surface of the inner liner rubber model of the tire based on the second heat generation amount.

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