JP5493439B2 - Tire rolling resistance evaluation method, tire evaluation system using the same, and tire rolling resistance evaluation program - Google Patents

Description

  The present invention relates to a tire rolling resistance evaluation method for evaluating the rolling resistance of a tire during rolling, a tire evaluation system using the same, and a computer-executable program for executing the tire rolling resistance evaluation method.

Conventionally, a tire is reproduced using a finite element (FE: Finite Element) model obtained by dividing a tire, that is, a pneumatic tire, into a plurality of finite elements, and a physical property is calculated by calculating a characteristic physical quantity at this time. Various evaluation methods have been proposed.
In addition, to reduce the rolling resistance of tires in order to reduce vehicle fuel consumption, there is a strong demand for tire development. As described above, energy loss is achieved by simulation using the Finite Element Method (FEM). And a method for evaluating the rolling resistance of tires have been proposed.

For example, in Patent Document 1 related to the application of the present applicant, using a static finite element analysis method having a short calculation time and a practical method, the heat generation energy of a rotating body such as a high-fidelity tire and the rotating body rolling resistance are measured. A method for investigating and analyzing characteristics is disclosed.
The method disclosed in the cited document 1 is a method capable of obtaining the rolling resistance of a tire with relatively high accuracy even though it is a practical static finite element analysis method with a comparatively low calculation cost. .

In the method disclosed in the cited document 1, as shown in FIG. 12, an internal pressure is applied to the tire 70 made of a viscoelastic body such as rubber to be deformed by applying a load, and the stress and strain under the load and the pneumatic conditions are changed. Thus, a hysteresis loop (Lissajous waveform) is obtained in consideration of the phase difference between the two, and the rolling resistance of the tire can be estimated. That is, when a periodically changing stress is applied to the tire, a phase difference is generated between the generated strain and a Lissajous waveform defined by the change of the strain with the stress is calculated. Since the area of the Lissajous waveform corresponds to the heat generated by the deformation of the tire (viscoelastic body), that is, the energy lost by the deformation, the method disclosed in the cited document 1 considers the effect of the viscoelasticity in the area of the Lissajous waveform. Thus, it is possible to estimate the heat generation energy of the tire and the rolling resistance of the tire with high fidelity.
Here, since the estimation method of the rolling resistance of the tire disclosed in the cited document 1 reproduces the deformation of the tire in the stopped state, as shown in FIG. 12, in the tire 70 in the tire contact area 71a, the load However, in the non-contact area 71b, since the centrifugal force generated by the rotation is not taken into consideration, it is hardly deformed as in the thin dotted line PT, and in this stopped state. The rolling resistance of the tire is estimated based on the deformation of the tire.

Japanese Patent Laid-Open No. 11-237332

Incidentally, since the rolling resistance of a tire is a loss that occurs during its rotation (energy loss due to heat generation), in an actual tire, it is known that there is actually a dynamic amplification factor that increases the rolling resistance. It has been.
However, since the static finite element analysis method disclosed in the cited document 1 does not actually perform the analysis by rotating the tire, although the calculation cost is low, a dynamic amplification factor is added to the evaluation of the rolling resistance. There was a problem that not.
On the other hand, there is a dynamic finite element analysis method performed by actually rotating a tire. In this method, since the simulation is performed by rotating the tire in the same way as the actual usage conditions, the dynamic amplification factor can be reproduced and the estimation accuracy is naturally high, but the calculation takes several days to several weeks. Since the calculation cost is very high, there is a problem that it is not practical.

Note that the dynamic amplification factor of the rolling resistance includes a change in tire deformation due to a difference in speed, and it is known that the rolling resistance has speed dependency.
Furthermore, according to the study by the present inventors, it has been found that in an actual tire, the speed dependency varies depending on the structure, for example, the presence or absence of a belt cover.
For example, FIG. 13 is based on the measurement by the present inventors, and the rolling resistance is set to a speed of 20 km / h to 80 km for a tire of structure F with a belt cover material and a light weight structure G tire without a belt cover material. It is the graph which measured in the range of / h, and plotted the measured value taking speed [km / h] on the horizontal axis and rolling resistance value RR [index] on the vertical axis. In FIG. 13, for easy comparison, the rolling resistance is represented as an index value normalized with a rolling resistance value RR of 100 when the tire speed of the structure F is 20 km / h.

As shown in FIG. 13, the difference in the rolling resistance RR between the tires of the structure F and the tire of the structure G is 24 points as an index value as an effect of reducing the rolling resistance by reducing the weight at a speed of 20 km / h. When the speed is 80 km / h, the index value is 20 points, and the reduction effect due to weight reduction is reduced. The speed dependency of the rolling resistance differs depending on the structure of the tire.
However, in the estimation of the rolling resistance of the tire by the static finite element analysis method disclosed in the cited document 1, the tire deformation due to the difference in speed, particularly the deformation in the non-contact area, that is, the soaring of the tire due to the so-called centrifugal force (see FIG. 3), the tires of the structure F and the tire of the structure G show the same speed dependency, and there is a problem that the estimation accuracy of the rolling resistance value RR is inferior.

  Accordingly, an object of the present invention is to solve the above-mentioned problems of the prior art and use a practical static finite element analysis method with a short calculation time without using a dynamic finite element analysis method. The heat generation energy of the tire including the material, and as a result, the tire rolling resistance can be accurately estimated, and the speed dependency of the tire rolling resistance can be accurately estimated easily and evaluated. A rolling resistance evaluation method, a tire evaluation system using the same, and a tire rolling resistance evaluation program are provided.

In order to achieve the above object, the tire rolling resistance evaluation method according to the first aspect of the present invention uses at least a two-dimensional tire model represented by a plurality of finite elements that reproduces a tire including a viscoelastic material. Static finite element analysis including a tire internal pressure filling processing step for filling the two-dimensional tire model with a predetermined internal pressure and a load loading step for applying a predetermined load to the three-dimensional tire model obtained by connecting the two-dimensional tire model once. A rolling resistance evaluation method for a tire that estimates the rolling resistance of a rolling tire from the stress and strain obtained in the method and a loss factor in the element thereof, in addition to the tire internal pressure filling step and the load loading step, It performs a centrifugal force calculation step of applying to the two-dimensional tire model to calculate the centrifugal force generated when obtained by rolling the tire Ri, performs the centrifugal force calculating step before the load application step, obtained in the centrifugal force computing step displacement, loading a predetermined load to the physical quantity as an initial condition in the three-dimensional tire model including stress and strain A load loading step is performed.

Moreover, it is preferable that the estimation step of the rolling resistance of the tire includes an operation of converting stress and strain of each finite element of the tire into stress and strain referring to a local coordinate system.
Further, in the step of estimating the rolling resistance of the tire, the area of the Lissajous waveform of the stress and strain hysteresis of each finite element is calculated using the stress and strain in each finite element of the tire and the loss factor of the finite element. It is preferable to estimate the rolling resistance of the tire from the sum of the total areas of the Lissajous waveforms of all elements.

Moreover, it is preferable to perform the tire internal pressure filling step before the centrifugal force calculating step.
Further, the estimation step for estimating the rolling resistance of the tire includes the heat generation energy of the entire tire from the stress and strain of the tire calculated by performing the tire internal pressure filling step, the centrifugal force calculation step, and the load loading step. And calculating a travel distance when the tire makes one rotation by performing the tire internal pressure filling step, the centrifugal force calculating step, and the load loading step, and the calculated heating energy of the entire tire and the tire It is preferable to calculate the rolling resistance of the tire based on the travel distance at one rotation.

In order to achieve the above object, a tire evaluation system according to a second aspect of the present invention uses the tire rolling resistance evaluation method according to the first aspect.
In order to achieve the above object, a tire evaluation system according to a second aspect of the present invention is a two-dimensional tire model represented by a plurality of finite elements that reproduces a tire including a viscoelastic material, or the two-dimensional tire model. A tire model generation unit that generates a three-dimensional tire model in which the tires are connected to each other, an internal pressure filling processing unit that fills the generated two-dimensional tire model with a predetermined internal pressure, and a centrifugal force generated when the tire is rolled A stress and strain calculation unit including a centrifugal force calculation unit for calculating a force and applying the force to the two-dimensional tire model; and a load load processing unit for applying a predetermined load to the three-dimensional tire model; and the stress and strain calculation A tire heating energy calculation unit for calculating the heating energy of the entire tire from the stress and strain calculated in the section and a loss coefficient in the tire constituent material; A tire travel distance calculation unit for calculating a travel distance when the tire makes one rotation from a calculation result of the stress and strain calculation unit, and a heat generation energy and a tire travel distance of the entire tire calculated by the tire heat generation energy calculation unit A tire rolling resistance calculation unit that calculates a rolling resistance of the tire based on a travel distance when the tire makes one rotation calculated by the unit, and the load load processing unit has a predetermined three-dimensional tire model. The centrifugal force generated when the tire is rolled by the centrifugal force calculation unit before applying the load of the tire is calculated and applied to the two-dimensional tire model, and the displacement and stress obtained by the centrifugal force calculation unit are calculated. and a physical quantity comprising a strain as an initial condition, to load a predetermined load to the 3-dimensional tire model by the load application processing unit It is characterized in.

  The tire heat generation energy calculating unit converts a stress and strain of each finite element of the tire into stress and strain referring to a local coordinate system, and calculates a stress and strain component at one point in the cross section. And the stress and strain at points adjacent to each other in the circumferential direction using the stress and strain components calculated by the local conversion unit to obtain the stress and strain for one circumference of the tire, thereby changing the stress and strain. Using the stress / strain calculation unit for one round of the tire for calculating the characteristic curve, the stress and strain in each finite element for one round of the tire, and the loss factor of the finite element, the stress and strain of each finite element are calculated. A Lissajous waveform area calculation unit for calculating the area of the hysteresis Lissajous waveform; a heat generation energy density calculation unit for calculating a heat generation energy density from the calculated Lissajous waveform area of each finite element; And a tire volume calculation unit for calculating the volume of the tire in a predetermined region from the calculation result in the strain calculation unit, and a tire heat generation energy for calculating the heat generation energy of the tire using the heat generation energy density and the tire volume in the predetermined region. It is preferable to provide a calculation unit.

  The tire mileage calculation unit is configured to calculate an outer radius of an unloaded tire that is not loaded from a calculation result of the tire model generation unit or the internal pressure filling processing unit of the stress and strain calculation unit. Tire outer radius calculation unit, centrifugal force is applied from the calculation results of the centrifugal force calculation unit and the load load processing unit of the stress and strain calculation unit, and the outer radius of the applied centrifugal force and load loaded tire is loaded The travel distance when the tire makes one revolution using the centrifugal force application / load load tire outer radius calculation unit, the outer radius of the unloaded tire and the outer radius of the centrifugal force application / load load tire is calculated. It is preferable to provide a tire travel distance calculation unit to calculate.

  A tire rolling resistance evaluation program according to a third aspect of the present invention provides a computer-executable program that executes the tire rolling resistance evaluation method according to the first aspect.

  According to the tire rolling resistance evaluation method, the tire evaluation system using the tire, and the tire rolling resistance evaluation program according to the present invention, the calculation time is short and the practical static finite without using the dynamic finite element analysis method. Using the element analysis method, it is possible to accurately estimate the heat generation energy of a tire including a viscoelastic material, and as a result, the rolling resistance of the tire with high accuracy. In addition, the speed dependency of the rolling resistance of the tire is accurate and simple. Can be estimated and evaluated.

1 is a block diagram showing an embodiment of a tire evaluation system of the present invention that implements a tire rolling resistance evaluation method of the present invention. It is a block diagram which shows the detailed structure of one Embodiment of the data calculation part of the tire evaluation system shown in FIG. It is sectional drawing which shows typically an example of the cross-sectional shape of an example of the tire for motor vehicles used as the object of the tire evaluation system shown in FIG. 1, and its deformation | transformation state. FIG. 4 is a partial enlarged cross-sectional view showing an enlarged part of the tire shown in FIG. 3. FIG. 5 is an explanatory schematic diagram illustrating an example of a tire model obtained by modeling a part of the tire illustrated in FIG. 4 with a finite element model. (A) And (b) is a graph which shows the characteristic curve of the stress and distortion of a viscoelastic body with respect to a position, and the characteristic curve of the Lissajous waveform of stress and distortion. It is explanatory drawing explaining the local direction of the local coordinate system of each element of the tire model shown in FIG. 5, (a) is an element of a crown part, (b) is an element of FRR, (c) is an element of a side member. It is explanatory drawing which shows a local coordinate system. It is a flowchart which shows an example of the flow of a process of the rolling resistance evaluation method of the tire of this invention. It is explanatory drawing which shows typically the flow of a process of the rolling resistance evaluation method of the tire shown in FIG. 8, (a), (b), (c) and (d) are respectively calculation of internal pressure and centrifugal force, 3D FE. It is explanatory drawing which shows typically each process of model preparation, load calculation, and heat-generation energy calculation. It is a flowchart which shows an example of the flow of a process of the tire heat_generation | fever energy calculation process of the rolling resistance evaluation method of the tire shown in FIG. It is a graph which shows the result of the Example of this invention, a reference example, and a comparative example. It is sectional drawing which shows typically the cross-sectional shape of the tire for motor vehicles used as the object of the conventional rolling resistance evaluation method of a tire, and its deformation | transformation state. It is a graph which shows the speed dependence of the rolling resistance of the tire from which a structure differs.

  Hereinafter, a tire rolling resistance evaluation method according to the present invention, a tire evaluation system using the tire rolling resistance evaluation method, and a tire rolling resistance evaluation program will be described in detail based on preferred embodiments shown in the accompanying drawings.

FIG. 1 is a block diagram showing an embodiment of a tire evaluation system of the present invention that implements the tire rolling resistance evaluation method of the present invention. FIG. 2 is a block diagram showing a detailed configuration of the tire evaluation system shown in FIG. 1, in particular, a detailed configuration of an embodiment of the data calculation unit thereof.
A tire evaluation system 10 shown in FIG. 1 implements a tire resistance evaluation method that calculates a rolling resistance value of a rolling tire using a static finite element analysis method that takes into account a dynamic amplification factor of the rolling resistance. A tire evaluation system 10 and a tire rolling resistance evaluation method implemented in the system 10 are set with initial data such as tire material data and running conditions, and a plurality of finite elements reproducing the tire. Generates the expressed tire model, applies internal pressure filling processing (also called inflation processing) to the tire model, and loads the ground load set on the tire model when the tire contacts the road surface (contact processing) And the centrifugal force generated in the ungrounded part of the tire when the tire rolls at a predetermined speed. To obtain the heat and energy of the tire from the obtained stress and strain of each element and the loss factor of each element, and from the obtained heat energy The rolling resistance is estimated.

  As shown in the figure, a tire evaluation system 10 constitutes a main part of the tire evaluation system 10 and implements the above-described tire resistance evaluation method of the present invention to calculate and estimate tire rolling resistance. A rolling resistance calculation device 12; an input operation system such as a mouse or keyboard for inputting initial data and operation instructions; and an input device 14 such as a reading device for a storage medium storing initial data and operation instructions. The calculation result such as the rolling resistance value of the tire of the rolling resistance calculation device 12 is output as a soft copy, that is, a display such as an LCD for displaying, a printer that outputs a hard copy on which a monitor or calculation result is recorded, a calculation result, etc. And an output device 16 such as a writing device. The storage medium reading device and the writing device may be configured as a storage medium driver having both reading and writing functions.

Here, the rolling resistance calculation device 12 includes a CPU 18, a memory 20, an input / output interface (I / OIF) 22, an initial data setting unit 24, a tire model generation unit 26, a data calculation unit 28, and a rolling resistance calculation unit. 30 and a data bus 32 connecting them to each other.
The rolling resistance calculation device 12 may be configured by a computer. In this case, the initial data setting unit 24, the tire model generation unit 26, the data calculation unit 28, and the rolling resistance calculation unit. 30, by reading a program stored in the memory 20 or by reading a program stored in a storage medium by the input device 14, an initial data setting module, a model generation module, a data calculation module 22, and It may be formed as each program module group of the rolling resistance calculation module.

The CPU 18 controls and manages the operations of each part of the rolling resistance calculation device 12, particularly the initial data setting unit 24, the tire model generation unit 26, the data calculation unit 28, and the rolling resistance calculation unit 30, and the entire rolling resistance calculation device 12. Control management. Note that the CPU 18 may be a part that substantially performs arithmetic processing on the processing contents of the initial data setting unit 24, the tire model generation unit 26, the data calculation unit 28, and the rolling resistance calculation unit 30.
The memory 20 includes initial data and operation instructions such as tire material data and driving conditions input or read by the input device 14, an initial data setting unit 24, a tire model generation unit 26, and a data calculation unit. 28 and various programs executed by the rolling resistance calculation unit 30, or the results of these units, in particular, the calculation results by the data calculation unit 28 and the rolling resistance calculation unit 30 are stored. It is something to keep.
The input / output interface (I / OIF) 22 includes the input device 14 and the output device 16, and each unit of the rolling resistance calculation device 12, for example, the CPU 18, the memory 20, the initial data setting unit 24, the tire model generation unit 26, and the data calculation unit. 28 and a part that performs data conversion for data transmission / reception between the rolling resistance calculation unit 30 and the rolling resistance calculation unit 30.

  The initial data setting unit 24 receives initial data such as shape data, material data, boundary data, load data, and travel speed (tire rotation speed) data input from the input device 14 when calculating and evaluating tire rolling resistance. The initial data is read from the memory 20 via the I / OIF 22 and the data bus 32 or set via the data bus 32.

The tire model generation unit 26 is a part that creates a tire model to be described later based on initial data such as the shape, material, boundary, load, and rotation speed of the tire set by the initial data setting unit 24.
In the present invention, a tire that is a target of a tire model created by the tire model generation unit 26 will be described.
FIG. 3 is a cross-sectional view schematically showing a configuration of a cross-sectional shape of an example of an automobile tire that is a target of the tire evaluation system and the tire rolling resistance evaluation method shown in FIG. FIG. 4 is a partially enlarged cross-sectional view showing a part of the tire shown in FIG. FIG. 5 is an explanatory schematic diagram illustrating an example of a tire model obtained by modeling a part (upper half) of the tire illustrated in FIG. 4 with a finite element model.

  A tire 70 shown in FIGS. 3 and 4 mainly includes a carcass member 72 as a tire aggregate in which a cord material such as a steel cord is covered with a rubber material of a viscoelastic material, and the expansion of the carcass member 72 in the radial direction. For example, a belt member 74 made of synthetic resin fiber such as nylon or polyester or steel, and an organic fiber cord provided on the upper side of the belt member 74 to cover and protect the belt member 74 From a rubber material of a viscoelastic material provided on the outer side in the radial direction of the belt cover member 75 and the belt member 74 covered with the belt cover member 75 and having a tread pattern that contacts the road surface 84 modeled as a rigid body. The tread member 76 and the end of the carcass member 72 are wound up to fix the carcass member 72 and to be modeled as a rigid body. Having a bead member 78 to allow attachment to 82, and a side member 80 which covers the surface of the side surface.

An example in which the tire shown in FIG. 4 is modeled by a finite element model is shown in FIG.
In the tire model generation unit 26, the tire 70 shown in FIG. 4 is first modeled with a two-dimensional finite element (2DFE) using shape data, material data, and boundary data, and a half part thereof is shown in FIG. A tire model 90 which is a two-dimensional cross-sectional model is created (see FIG. 9A described later). Since the tire 70 is a thing in which the same cross section as shown in FIG. 4 is connected one turn, the tire model (hereinafter also referred to as 2DFE model) 90 shown in FIG. 5 is represented as a two-dimensional cross section model. Such a 2DFE model can be modeled by a three-dimensional finite element (3DFE) in which one round is connected. That is, the tire model generation unit 26 can also create a three-dimensional tire model (hereinafter also referred to as a 3DFE model) 92 in which the tire 70 is three-dimensionally modeled using shape data, material data, and boundary data (see FIG. 3). 9 (b)).

A tire model 90 shown in FIG. 5 includes a tire 70 in which at least the constituent members of the carcass member 72, the belt member 74, the belt cover member 75, the tread member 76, the bead member 78, and the side member 80 are divided into finite elements. The elements of the tire model 90 are constituted by solid elements such as triangles and quadrilaterals, membrane elements, or shell elements.
The tire model 90 is created by setting the geometric shape information of each element (each finite element) and the node position information of each element, and further, the material constant of each element is also set and can be calculated. It becomes a finite element model. Note that the finite element model used in the present invention is not limited to the example shown in FIG. 5, and any model can be used as long as it can evaluate the rolling resistance of the tire.
The tire model 90 shown in FIG. 5 represents a cross-sectional shape (tire shape) when the tire 10 is cut along the radial direction including the tire rotation axis. When the rolling resistance of the tire is calculated using the tire shape, the calculation is performed as an axially symmetric model in which the tire shape as shown in the upper half of FIG. 4 is formed on the tire circumference.

In the present invention, as indicated by a solid line in FIG. 3, the tire 70 is attached to the rim 82, filled with air inside the tire to form a pneumatic tire, and is grounded to the road surface 84. When a load as an automobile is applied to the pneumatic tire 70, the tire 70 is slightly crushed by the load, and the outer shape TP of the ground side portion 71a is deformed flat as shown by a thick broken line PL in FIG. In particular, when the side member 80 is deformed and the tire 70 rotates (rolls) at a predetermined speed, the outer shape TP of the non-grounded portion 71b of the tire 70 is indicated by a dotted line PU in FIG. It is deformed outward (in the radial direction) by centrifugal force according to the rotational speed.
In the prior art, since the deformation due to the centrifugal force depending on the speed as shown by the dotted line PU in FIG. 3 is not taken into consideration, the accurate evaluation of the rolling resistance of the tire cannot be performed with high accuracy as described above. Street.

Next, the data calculation unit 28 will be described. The data calculation unit 28 is a part that uses the tire model 90 generated by the tire model generation unit 26 to calculate tire heat generation energy for calculating the exact rolling resistance of the tire by a tire rolling resistance calculation unit 30 described later. is there.
As shown in FIG. 2, the data calculation unit 28 includes a tire stress / strain calculation unit 34, a tire heat generation energy calculation unit 36, and a tire travel distance calculation unit 38.
In addition, the tire stress / strain calculation unit 34 uses the tire model 90 to apply a centrifugal force to the pneumatic tire 70 filled with an internal pressure representing a state in which air has been filled, and to apply a load, to perform local coordinate conversion, It is a part for calculating the stress and strain of one tire of the tire 70 in a state where it is in contact with the rolling, and an internal pressure filling processing unit 40, a centrifugal force calculation unit 42, a load load processing unit 44, A local coordinate conversion unit 46, a stress and strain calculation unit 48 for one round of the tire, and a local coordinate conversion unit 46 are included.

The internal pressure filling processing unit 40 applies pressure uniformly from the inner peripheral surface side of the tire model 90 in a state where a part of the tire 70 attached to the rim 82, for example, a part around the bead member 78 is partially restrained. This is the part that performs the internal pressure filling process (inflation process). The pressure applied in the internal pressure filling process is preferably an internal pressure as a use condition of the tire 70, but may be a pressure set in advance according to the modeling of the tire model 90.
The centrifugal force calculation unit 42 is a characteristic feature of the present invention. The centrifugal force calculation unit 42 calculates a centrifugal force corresponding to the traveling speed, that is, the rotational speed of the tire 70, to the tire model 90 that has been subjected to the internal pressure filling process. This is a part for calculating the deformation (refer to the dotted line PU shown in FIG. 3) occurring in the non-ground portion of the tire 70 according to the force, that is, calculating the stress due to the centrifugal force applied to the tire model 90 and the distortion due to the deformation. The centrifugal force applied to the tire model 90 is preferably a centrifugal force obtained as a use condition of the tire 70, but may be a centrifugal force measured as a use condition of the tire 70, or may be a tire model. According to the 90 modeling, a centrifugal force set in advance may be used.

As the centrifugal force applied in the centrifugal force calculator 42, a centrifugal force corresponding to an arbitrary traveling speed or rotational speed is input in advance as initial data from the input device 14 or the like for each element of the tire model 90.
For example, when a centrifugal force corresponding to the velocity V (mm / sec) is applied, the distance L in the outer diameter direction from the center point of the arbitrary element and the origin (for example, on CAD when creating a tire model) is obtained, and the angular velocity is obtained. ω (rad / sec) = V (mm / sec) ÷ L (mm) can be calculated, and the square of ω can be set for each arbitrary element. At that time, it is also necessary to previously input the mass density ρ of each element as initial data.
The centrifugal force can be calculated by ω ² (the square of ω) × ρ using the angular velocity ω and the mass density ρ of each element input as initial data. For analysis, it may be specified by ω ² (the square of ω) × ρ.
Here, the centrifugal force calculation is not particularly limited as long as it follows a centrifugal force analysis method provided as a function of a general general-purpose FE (finite element) solver. The unit system of speed, distance, and mass density is arbitrary, and the speed may be km / h and the distance may be km as long as it can be matched.

  In the present invention, the internal pressure filling processing by the internal pressure filling processing unit 40 and the centrifugal force calculation by the centrifugal force calculation unit 42 may be performed directly by the 3DFE model. First, as shown in FIG. As shown in FIG. 9 (b), the 2DFE model 90 created using the data, material data, and boundary data is used. As shown in FIG. 9B, the calculation result (stress, strain, It is preferable that the nodal displacement data and the like be mapped on the 3DFE model 92 obtained by connecting the 2DFE model 90 one turn to converge the internal pressure and centrifugal force calculation on the 3DFE model 92. This is because the calculation time is shorter in the 2DFE model calculation because the number of elements is smaller than in the 3DFE model calculation. In addition, in the case of a tire having the same cross section connected one turn as in the present invention, a force is applied as a centrifugal force in a radial direction such as a condition in which the inner surface is uniformly pressurized as in the internal pressure filling process or a centrifugal force imparting process. Since the stress and strain state for one lap of the tire is considered to be the same everywhere on the rim, the 2DFE model 90 is used for the calculation first, and the calculation result is used as the 3DFE model 92. By mapping to, the calculation time in the 3DFE model 92 can be greatly shortened. As described above, the analysis method for mapping the calculation result of the 2DFE model 90 to the 3DFE model 92 and reducing the calculation time of the 3DFE model 92 is not essential to the present invention, but as a function of a general general-purpose FE solver. What is provided can be used and is easy to apply. Therefore, it is preferable to use from the viewpoint of shortening the calculation time.

In the present invention, after the calculation of the internal pressure and the centrifugal force in the 3DFE model 92 is completed by the internal pressure filling processing unit 40 and the centrifugal force calculation unit 42 in this way, as shown in FIG. A load calculation process is performed on the 3DFE model 92 to calculate the load in the 3DFE model 92.
In the illustrated example, the internal pressure filling processing unit 40 and the centrifugal force calculation unit 42 are provided, and the internal pressure calculation (internal pressure filling processing) and the centrifugal force calculation are respectively performed. However, both are used as the internal pressure and centrifugal force calculation unit. You may configure and perform both calculations together.

In the example shown in FIG. 9C, the load load processing unit 44 loads a load on the tire model (3DFE model) 92 subjected to the internal pressure filling process and the centrifugal force application, more specifically, This is a part that performs a grounding process for applying a load and grounding the road surface 84, and calculates a deformation (see the thick broken line PL shown in FIG. 3) that occurs in the grounded part of the tire 70 in accordance with the loaded load. This is a part for calculating the stress due to the load applied to the model 92 and the strain due to deformation. The load applied to the tire model 92 is preferably a load obtained as a use condition of the tire 70, but may be a load measured as a use condition of the tire 70, or may be a model of the tire model 92. Depending on the conversion, a preset load may be used.
In the present invention, the calculation of the centrifugal force and the deformation caused by the centrifugal force calculation unit 42 is after the internal pressure filling process performed by the internal pressure filling processing unit 40, and the load loading process performed by the load load processing unit 44 and the deformation calculated thereby. However, the present invention is not particularly limited, and the centrifugal force and the deformation (stress and strain) may be calculated after the load treatment.

The local coordinate conversion unit 46 performs an operation to convert the stress and strain of each element of the tire model 92 calculated by the load load processing unit 44 into stress and strain with reference to the local coordinate system, and each element in the tire cross section It is a part which calculates | requires the stress and distortion in.
What is necessary is just to select the local direction of the local coordinate of each element in a tire cross section suitably according to each element. For example, the tire 70 shown in a perspective view in FIG. 7 and modeled by the tire model 90 is centered on the coordinate center, the horizontal tire radial direction 1, the tire width direction is the coordinate axis 2 and the vertical tire radial direction 3. As shown in the perspective view of FIG. 7 (a), which is an enlarged view of the local coordinate system of the elements of the tread member 76 (crown portion) of the tire 70, Like the 3D Cartesian coordinate system, it is composed of a tire circumference (element length) direction 1, an element width direction 2 and an element thickness direction 3, and a belt cover material 75 (Fiber Reinforced Rubber (FRR)). As shown in FIG. 7B, which is an enlarged view, the local coordinate system of the element is not coincident with the three-dimensional orthogonal coordinate system of the tire, but the FRR code orientation direction (element length direction) 1 and element width Direction 2 and element thickness As shown in FIG. 7C which is an enlarged view, the local coordinate system of the elements of the side member 80 constituted by the direction 3 is reversed in the width direction and the thickness direction from the three-dimensional orthogonal coordinate system of the tire. However, it is preferable to configure the tire circumferential (element length) direction 1, the element width direction 2 and the element thickness direction 3.
In the illustrated example, after the load calculation by the load load processing unit 44, the local coordinate conversion by the local coordinate conversion unit 46 is performed. However, after the local coordinate conversion by the local coordinate conversion unit 46, the load by the load load processing unit 44 is performed. The calculation may be performed in the local coordinate system (in the local coordinate system rst shown in FIG. 9C, r is the tire circumferential (element length) direction 1, s is the element width direction 2, and t is the element thickness direction 3. Represents).

  The stress and strain calculation unit 48 for one tire circumference obtains one-component stress and strain at the center of each element in the tire cross section converted into local coordinates by the local coordinate conversion unit 46, and sequentially adjoins in the circumferential direction. This is a part where the stress and strain of the points are obtained, the stress f (θ) and the strain g (θ) for one turn of the tire are obtained, and the change characteristic curve for one turn of the tire is derived.

By the way, in the present invention, as a deformation component used when obtaining the strain g in one element, for example, in the case of the element shown in FIG. 7, it is perpendicular to the element length direction 1 such as the tire circumferential direction and the FRR code orientation direction. 11 direction deformation component 11 caused by stress (perpendicular stress, compression stress) acting perpendicularly to the plane, 22 direction deformation component 22 caused by stress perpendicular to the element width direction 2, and element thickness direction 3 Due to a deformation component 33 in 33 directions generated by stress (tensile stress, compressive stress) acting perpendicularly to the surface perpendicular to the surface and shear stress (shear stress) acting on the surface formed by the element length direction 1 and the element width direction 2 The resulting deformation component 12 in the shear direction 12 and the deformation component in the shear direction 13 generated by the shear stress acting on the surface formed by the element length direction 1 and the element thickness direction 3. 3, it is preferable to consider the six deformation components of the deformation component 23 of shear direction 23 caused by shear stress (shear stress) acting on the plane formed by the elements the width direction 2 and element thickness direction 3.
In the tire stress / strain calculation unit 34, the internal pressure filling processing unit 40, the centrifugal force calculation unit 42, the load load processing unit 44, the local coordinate conversion unit 46, and the stress and strain calculation unit 48 for one round of the tire are being calculated. The results and calculation results, particularly stress and strain values, are preferably stored in the memory 20.

  By the way, in this embodiment, the calculation of the centrifugal force by the centrifugal force calculation unit 42 is after the internal pressure filling process by the internal pressure filling processing unit 40 using the 2DFE model 90 in the tire stress / strain calculation unit 34, and the 3DFE model. However, the present invention is not limited to this, and the Lissajous waveform area calculation unit 50 of the tire heat generation energy calculation unit 36 to be described later is configured. As long as it is before the Lissajous waveform area calculation, the stress and strain of each element in the tire cross section in the local coordinate conversion unit 46 may be calculated. As described above, the centrifugal force calculation unit 42 may calculate the centrifugal force and the deformation caused by the centrifugal force calculation unit 42 in the 3DFE model 92. However, the calculation amount increases and the calculation cost increases. Preferred is as described above.

  The tire heat generation energy calculation unit 36 uses the stress and strain in each element of the tire model 92 from the change characteristic curve of the stress and strain for one turn of the tire model 92 calculated by the tire stress / strain calculation unit 34, Calculate the area of the hysteresis Lissajous waveform (hysteresis loop) of each element by giving a phase delay corresponding to the loss factor of the viscoelastic material for the strain value, and calculate the tire from the area of the Lissajous waveform (graphic) of all the elements for one lap of the tire This is a part for obtaining heat generation energy when 70 rotates once. The tire heat generation energy calculation unit 36 includes a Lissajous waveform area calculation unit 50, a heat generation energy density calculation unit 52, a tire volume calculation unit 54, and a heat generation energy calculation unit 56.

First, the Lissajous waveform area calculation unit 50, as shown in FIG. 9 (d), the stress for one tire of the tire stress / strain calculation unit 34 and the stress f for one tire produced by the strain calculation unit 48. Each of (θ) and strain g (θ) (characteristic curve) is developed into a finite-order Fourier series, and the stress and strain amplitude _An and the stress and strain phase B _n are obtained for each order. In this case, the order for performing Fourier series expansion is preferably 10 to 100, and more preferably 20th to 50th. Here, if it is less than the 10th order, an accurate result cannot be obtained, and if it is more than 100th, the calculation time increases although the accuracy of the result does not change, which is not preferable. Note that the expansion of stress and strain into the Fourier series and the calculation of the amplitude and phase of stress and strain for each order are performed by the Lissajous waveform area calculation unit 50, instead of the tire 1 of the tire stress / strain calculation unit 34 described above. The circumference stress and strain calculation unit 48 may perform the calculation.

Next, the Lissajous waveform area calculation unit 50 calculates the loss coefficient of the viscoelastic material with respect to the stress g (θ) of each element obtained by the stress and the strain calculation unit 48 of the tire circumference of the tire stress / strain calculation unit 34. Given the corresponding phase lag (δ), for each Fourier order, calculate the area (S _n ) of the hysteresis Lissajous waveform (hysteresis loop) of stress f (θ) and strain g (θ). The sum (S _c ) of the product of the Fourier order (n) and the area (S _n ) is _expressed according to the following relational expressions (1-1) and (1-2), that is, these relational expressions (1-1) and (1 -2) is a part determined according to the following formula (1).

ここで、Ｓ_c は成分ｃについての各有限要素の全次数のリサージュ波形の面積の総和、Ｓ_n は次数ｎのリサージュ波形の面積、ｎは次数、ｐはフーリエ級数展開の総次数、Ａ_n ^f は応力の振幅、Ａ_n ^g は歪の振幅、Ｂ_n ^f は応力の位相、Ｂ_n ^g は歪の位相、δは位相遅れである。

Here, the sum of the areas of all the orders of the Lissajous waveform of each finite element for S _c component c, total degree of S _n is the area of the Lissajous waveform of order n, n is the order, p is the Fourier series expansion, A _n ^f is the amplitude of the stress, a _n ^g is the amplitude of the distortion, B _n ^f is the stress phase, B _n ^g is distortion of the phase, [delta] is a phase delay.

In the present invention, the loss coefficient (tan δ) of each member constituting the tire 70 can be measured, for example, under predetermined measurement conditions, and the value can be used as initial input data as a physical property value.
As measurement conditions, for example, using a viscoelastic spectrometer, conditions of a temperature of 60 ° C., a frequency of 20 Hz, an initial strain of 10%, and a dynamic strain of 2% can be exemplified.
In calculating the area of the Lissajous waveform in the Lissajous waveform area calculation unit 50, the numerical value of the loss factor (tan δ) of each member is not used, but the phase difference δ of tan δ is used, the phase difference δ, A Lissajous waveform is obtained from stress and local strain.
By the way, in the present invention, a value corresponding to at least one of temperature dependency, frequency dependency, and strain amplitude dependency is set as the phase lag value (phase difference δ) corresponding to the loss coefficient of the viscoelastic material. Can be used.

Here, the principle of calculation of the heat generation energy of the tire including the viscoelastic material in the present invention will be described based on FIGS. 6 (a) and 6 (b).
6 (a) and 6 (b) show stress and strain characteristic curves of a viscoelastic body with the position as abscissa coordinates and a Lissajous waveform of stress and strain with the strain as abscissa coordinates and the stress as a ordinate coordinate (hysteresis loop). ) Is a graph showing a characteristic curve.
As shown in FIG. 6A, in a viscoelastic body such as a tire, the strain phase is delayed by δ with respect to the stress. Here, 0 <δ <π / 2. As a result, as shown in FIG. 6B, the Lissajous waveform of the viscoelastic body becomes an ellipse, and the area S of the ellipse is energy lost during one cycle of deformation, and this lost energy is expressed as S = π · It is expressed by f · g · sin δ and corresponds to heat generation energy. Here, f is the stress amplitude (A _n ^f described above), and g is the strain amplitude (A _n ^g described above).
Therefore, in the tire stress / strain calculation unit 34 described above, the stress amplitude f, the strain amplitude g, and the phase difference δ are obtained by obtaining the stress and strain of the tire by static finite element analysis using the tire model 90. The heat generation energy can be calculated.

The heat generation energy density calculation unit 52 repeats the above-described calculation process in the Lissajous waveform area calculation unit 50 for all the stress and strain components of each element of the tire model 90, and the total sum S _c of each component for each element. Is a part for obtaining the heat energy density.
The tire volume calculation unit 54 is applied with a centrifugal force from the results of the centrifugal force calculation unit 42 and the load load processing unit 44 of the tire stress / strain calculation unit 34, and the tire model 90 is subjected to strain (deformation (deformation (FIG. 3)). This is a part for determining the volume V of each element from (see))).

The heat generation energy calculation unit 56 calculates the heat generation energy density of each element calculated by the heat generation energy density calculation unit 52 (total ΣS _c for the total number of components q of the total S _c for each component) and the tire volume calculation unit 54. The product (E _di ) with the volume V of each element obtained is determined according to the following formula (2), this product (E _di ) is defined as the heat generation energy at the position of the element, and then the product (E _di) ) And the sum of products (E _di ) obtained for the entire tire is calculated according to the following formula (3), and the heat generation energy E _d of the entire tire (all elements), that is, the heat generated when the tire makes one revolution This is the part that seeks energy.

ここで、Ｅ_diは各有限要素の位置における発熱エネルギ、Ｖは各要素の体積、ｃは変形成分、ｑは全成分数（本発明では、上述したように、６変形成分）、Ｓ_cは各成分毎の各有限要素の面積であり、Ｅ_dはタイヤ全体の発熱エネルギ、ｉは要素数、ｒは２次元断面モデルであるタイヤモデル９０（２ＤＦＥモデル）全要素数である。
こうして、タイヤ発熱エネルギ計算ユニット３６は、タイヤモデル９０が１回転したときの発熱エネルギＥ_dを求めることができる。
なお、タイヤ発熱エネルギ計算ユニット３６におけるリサージュ波形面積算出部５０、発熱エネルギ密度算出部５２、タイヤ体積算出部５４及び発熱エネルギ算出部５６による計算途中の結果や計算結果は、メモリ２０に記憶しておくのが好ましい。

Here, E _di is the heat generation energy at the position of each finite element, V is the volume of each element, c is the deformation component, q is the total number of components (in the present invention, as described above, 6 deformation components), and S _c is The area of each finite element for each component, E _d is the heat generation energy of the entire tire, i is the number of elements, and r is the total number of elements of the tire model 90 (2DFE model) which is a two-dimensional cross-sectional model.
Thus, a tire heating energy computation unit 36 may determine the heating energy E _d of the tire model 90 is rotated 1.
The Lissajous waveform area calculation unit 50, the heat generation energy density calculation unit 52, the tire volume calculation unit 54, and the heat generation energy calculation unit 56 in the tire heat generation energy calculation unit 36 store the results and calculation results during the calculation in the memory 20. It is preferable to leave.

The tire mileage calculation unit 38 is a part that calculates a mileage L when the tire makes one rotation, and includes an outer radius calculation unit 58 for a load-unloaded tire and an outer radius calculation unit for a centrifugal force application / load-loaded tire. 60 and a tire travel distance calculation unit 62.
The loadless unloaded tire outer radius calculation unit 58 is a part for obtaining a tire outer radius (R ₀ ) by a finite element method when no centrifugal force is applied in the tire model 90 and no load is applied, In the illustrated example, the tire outer radius (R ₀ ) can be obtained using the result of the inner pressure filling processing unit 40 of the tire stress / strain calculation unit 34. Note that the tire radius of the tire model 90 itself before the internal pressure filling processing by the internal pressure filling processing unit 40 may be the unloaded tire outer radius (R ₀ ). That is, the outer radius calculation unit 58 can set the tire radius of the tire model 90 itself generated from the tire model generation unit 26 as an unloaded tire outer radius (R ₀ ).

Centrifugal force application / load load tire outer radius calculation unit 60 is a part that applies a centrifugal force in tire model 90 and obtains the tire outer radius (R ₁ ) when a load is applied by a finite element method. Then, the tire outer radius (R ₁ ) can be obtained using the results of the centrifugal force calculator 42 and the load load processor 44 of the tire stress / strain calculator 34. Here, when a centrifugal force is applied in the tire model 90 and a load is applied, as shown in FIG. 3, in the tire 70, the contact-side portion 71a contracts (crushes), and the contact-side tire radius is zero. The load tire outer radius (R ₀ ) is smaller, the non-contacting-side portion 71b expands (swells) outward due to centrifugal force, and the non-grounding-side tire radius is larger than the unloaded tire outer radius (R ₀ ). since the average value of the two may be the outer tire radius (R _1).
When the centrifugal force calculation unit 42 calculates the centrifugal force first, the tire outer radius (R ₁ ) may be obtained using the result of the load load processing unit 44, and the centrifugal force by the centrifugal force calculation unit 42 may be obtained. In the case where the load load processing by the load load processing unit 44 is performed first from the above calculation, the tire outer radius (R ₁ ) may be obtained by using the centrifugal force calculation result by the centrifugal force calculation unit 42. Further, when the centrifugal force calculation by the centrifugal force calculation unit 42 is performed after the local coordinate conversion by the local coordinate conversion unit 46 of the tire heat generation energy calculation unit 36, the calculation result of the centrifugal force by the centrifugal force calculation unit 42 is used. it may be obtained a tire outer radius _{(R 1).}

Tire running distance calculation unit 62, the value of the tire outer radius (R ₁₎ by external radius calculation unit 60 of the centrifugal force applied, load bearing tires, tire outer radius (R ₀ by external radius calculation part 58 of the load unloaded tire ) And the tire travel distance L when the tire makes one revolution according to the following formula (4).
L = 2π {K (R ₁ −R ₀ ) + R ₀ } (4)
Here, R ₀ is an outer radius of the tire when no load is applied, R ₁ is an outer radius of the tire when a centrifugal force is applied and a load is applied, and K is a coefficient in a range of 0 to 1. is there. The coefficient K is a coefficient for obtaining the rolling radius of the tire model 90, and can be appropriately selected within the range of 0 to 1 so as to coincide with the experimental data.
The tire travel distance calculation unit 38 can thus obtain the tire travel distance L when the tire makes one revolution.
The calculation results by the outer radius calculation unit 58 of the unloaded tire, the outer radius calculation unit 60 and the tire travel distance calculation unit 62 of the centrifugal force application / load load tire, particularly the tire outer radius (R ₀ ), (R ₁ ) And the tire travel distance L are preferably stored in the memory 20.
The data calculation unit 28 is basically configured as described above, and can determine the heat generation energy _Ed and the tire travel distance L when the tire model 90 makes one revolution.

The tire rolling resistance calculation unit 30 generates heat generation energy (E _d ) data for one rotation of the tire from the tire heat generation energy calculation unit 36 of the data calculation unit 28, and one rotation of the tire from the tire travel distance calculation unit 38. This is a part for obtaining the rolling resistance RR of the tire when the tire makes one revolution according to the following formula (5) based on the travel distance (L).
RR = E _d / L (5)
Here, E _d is the heat generation energy during one rotation of the tire, and L is the travel distance when the tire makes one rotation.
The calculation result by the tire rolling resistance calculation unit 30, in particular, the tire rolling resistance RR is preferably stored in the memory 20.
The tire evaluation system 10 of the present invention is basically configured as described above.

Next, the effect | action of the tire evaluation system of this invention and the rolling resistance evaluation method of the tire of this invention are demonstrated.
FIG. 8 is a flowchart showing an example of a processing flow of the tire rolling resistance evaluation method of the present invention. FIG. 9 is an explanatory diagram schematically showing a processing flow of the tire rolling resistance evaluation method shown in FIG. 8, wherein (a), (b), (c) and (d) are respectively the internal pressure and centrifugal force. It is explanatory drawing which shows typically each process of calculation, 3DFE model creation, load calculation, and heat-generation energy calculation. FIG. 10 is a flowchart illustrating an example of a processing flow of a tire heat generation energy calculation process of the tire rolling resistance evaluation method illustrated in FIG. 8.

In the tire rolling resistance evaluation method of the present invention, first, in step S100, initial data such as shape data, material data, boundary data, load data, and travel speed (tire rotation speed) data are set. In the tire evaluation system 10 shown in FIG. 1, the initial data setting is performed by the initial data setting unit 24.
Next, in step S102, a 2DFE model, which is a two-dimensional cross-section tire model, is generated based on the set initial data, in particular, using shape data, material data, boundary data, and the like. For example, the tire model (2DFE model) 90 shown in FIG. 5 is generated by the tire model generation unit 26 shown in FIG. 1 (2DFE model creation step: see FIG. 9A).

Subsequently, in step S104, the generated tire model is subjected to an internal pressure filling process, and the stress and strain of each element are calculated. This internal pressure filling process is performed, for example, on the tire model 90 shown in FIG. 5 by the internal pressure filling processing unit 40 of the tire stress / strain calculation unit 34 shown in FIG. 2 (see FIG. 9A).
Next, in step S106, the centrifugal force applied to the tire model 90 filled with the internal pressure according to the running speed (rotational speed) is calculated, and the stress and strain of each element due to the deformation generated in the non-contact portion of the tire are calculated. Is done. This centrifugal force calculation process is performed by the centrifugal force calculator 42 shown in FIG. 2 (see FIG. 9A).
The internal pressure filling processing step 104 and the centrifugal force calculation processing in step S106 may be performed simultaneously (internal pressure / centrifugal force calculation step: see FIG. 9A).

Next, in step S107, the calculation results (stress, strain, nodal displacement data, etc. when filling with internal pressure and applying centrifugal force) are mapped onto the 3DFE model 92 obtained by connecting the 2DFE model 90 once. The internal pressure and centrifugal force calculations are converged on the 3DFE model 92. As a result, the stress and strain of each element in the 3DFE model 92 are calculated, and the 3DFE model 92 is generated (3DFE model creation step: see FIG. 9B).
Next, in step S108, a load loading process is performed in which a load is applied to the tire model (3DFE model) 92 to which an internal pressure and a centrifugal force are applied, and the stress and strain of each element due to the deformation generated in the contact portion of the tire are reduced. Calculated. This load processing is performed by the load processing unit 44 shown in FIG. 2 (load calculation step: see FIG. 9C).

Next, in step S110, the stress and strain of the tire model to which the centrifugal force is applied and the load is applied, calculated in step S108 described above, are converted into stress and strain by referring to the local coordinates by the local coordinate conversion unit 46. Thus, stress and strain in each element in the tire cross section are obtained.
Next, in step S112, the stress and strain for one round of the tire are calculated by the stress and strain calculation unit 48 for one round of the tire in each element in the tire cross section (tire model 90).

Thus, for example, in the tire stress / strain calculation unit 34 shown in FIG. 2, the stress and strain of each element of the tire model 92 are calculated, and the stress and strain for one round of the tire in each element of the tire model 90 are calculated. The
As in the illustrated example, the centrifugal force calculation process of step S106 is preferably performed before the load load process of step S108, but may be performed after the load load process or the heat generation energy of step S114 to be described later. If it is before the Lissajous waveform area calculation in step S126 of the calculation process, it may be after the local coordinate conversion in step S110, but the calculation results of stress and strain in the two-dimensional tire cross-section model (2DFE model 90) in step S107. Is preferably performed before generating a 3DFE model that develops a 3D tire model (2DFE model 92).

  Next, in step S114, the local coordinate transformation is performed in step S110, and the stress and strain for one tire circumference of each element of the tire model 92 obtained in step S112 are used to convert the strain value into the loss coefficient of the viscoelastic material. The area of the Lissajous waveform (hysteresis loop) of the hysteresis of each element is calculated by giving a corresponding phase delay, and the heat generation energy when the tire makes one revolution is obtained from the area of the Lissajous waveform of all elements of the tire model (2DFE model) 90. . The calculation of the heat generation energy when the tire makes one revolution is performed by, for example, the tire heat generation energy calculation unit 36 shown in FIG.

FIG. 10 shows a detailed processing flow of the heat generation energy calculation process performed in step S114.
As shown in FIG. 10, before entering the heat generation energy calculation process of step S114, the stress and strain of the tire model to which the centrifugal force is applied and the load is applied are calculated in step S108 described above, and in step S110. The local coordinate conversion unit 46 converts these stresses and strains into stresses and strains referring to the local coordinates to obtain the stresses and strains in each element in the tire cross section. Next, in step S112, the tires The stress and strain calculation unit 48 for one round calculates data of stress and strain for one round of the tire in each element in the tire cross section.

Thereafter, in the heat generation energy calculation process of step S114, the stress for one turn of the tire in each element in the tire cross section (2DFE model 90) calculated by the stress and strain calculation unit 48 for one turn of the tire in step S123. In step S124, the acquired stress and strain are developed into Fourier series, and the amplitude and phase of the stress and strain are calculated for each order.
Subsequently, in step S126, the Lissajous waveform area calculation unit 50 gives a phase lag (δ) corresponding to the loss coefficient of the viscoelastic material for the strain value of each element, and for each Fourier order, the relational expression (1 -1), the area (S _n ) of the stress and strain Lissajous waveform (hysteresis loop) is calculated.
Next, in step S128, the order (n) of the Fourier series is counted and it is determined whether or not the predetermined order (p) has been reached, that is, whether or not the area (S _n ) has been calculated (predetermined order (p)). If it is less than the predetermined order (p), the process returns to step S126, and the calculation of the area (S _n ) is repeated to reach the predetermined order (p). If so, the process proceeds to the next step S130. In step S128, when the order is less than the predetermined order (p), the calculation time becomes long, but for accuracy, it may be returned to step 123 instead of returning to step S126.

In step S130, the heat energy density calculator 52 calculates the sum (S _c ) of the product of the Fourier order (n) and the determined area (S _n ) according to the relational expression (1-2).
Next, in step S132, the number of stress and strain components (c) is counted, and whether or not the total number of components (q: six components as described above in the present invention) has been reached, that is, the total sum (S _c ) is all. It is determined whether or not the number of components has been calculated (determination of completion of all component calculation is performed). If the total number of components is less than (q = 6), the process returns to step S126, and the area (S _n ) and its sum ( If the calculation of S _c ) is repeated and the total number of components (q = 6) has been reached, the heat energy density, which is the sum of all the components of the sum (S _c ), is calculated in step S 130, and the next step S 134. Proceed to In step S132, when the total number of components is less than (q = 6), the calculation time becomes longer, but instead of returning to step S126, it may be returned to step 123 for accuracy.
In step S134, the tire volume calculation unit 54 calculates the volume V of each element of the tire model 92 to which a centrifugal force is applied and a load is applied.

Next, in step S136, the heat energy calculation unit 56 calculates the product of the (total ΣS _c ) of the heat energy density obtained in step S130 and the volume V obtained in step S134 according to the above equation (2). Then, the heat generation energy (E _di ) at the position of each element is calculated.
Next, in step S138, the number of elements (i) is counted, and whether or not the total number of elements (r) of the 2DFE model 90 has been reached, that is, the heat generation energy (E _di ) at the position of each element is the entire tire (2DFE model). 90, the number of all elements r) is determined (completion of the calculation of the entire tire is determined). If the entire tire has not been reached, the process returns to step S123, and steps S123 to S136 are performed. If the calculation of the heat energy (E _di ) is repeated and the entire tire model 90 (2DFE model) is reached, the process proceeds to the next step S140.

Finally, in step S140, the heat generation energy (E _di ) at the position of each element of the entire tire model 90 is obtained by summing up all the elements of the tire model 90, and the heat generation when the entire tire model 90, that is, the tire rotates once. The energy (E _d ) is calculated.
Thus, the process of calculating the heat generation energy in step S114 is completed, and the heat generation energy (E _d ) when the tire makes one revolution is calculated.

On the other hand, as shown in FIG. 8, in step S116, in response to the result of the internal pressure filling process in step S104, or using the finite element method in the tire model 90, the tire unloading tire of the tire mileage calculation unit 38 The outer radius calculation unit 58 calculates the tire outer radius (R ₀ ) when no centrifugal force is applied and no load is applied. The tire radius of the tire model 90 itself generated in step S102 may be the unloaded tire outer radius (R ₀ ).
In addition, in step S118, the outer radius of the application of the centrifugal force is applied in response to the result of the load application process in step S108 or the result of the centrifugal force calculation process in step S106, or in the tire model 90 using the finite element method. The calculation unit 60 applies a centrifugal force and calculates a tire outer radius (R ₁ ) when a load is applied.

Subsequently, in step S120, the tire travel distance calculation unit 62 uses the value of the tire outer radius (R ₁ ) calculated in step S118 and the value of the tire radius (R ₀ ) calculated in step S116. Then, the tire travel distance L when the tire makes one revolution is calculated according to the above equation (4).
Finally, in step S122, the tire rolling resistance calculation unit 30 causes the heat energy (E _d ) when the tire calculated in step S114 (step S140) makes one revolution and the tire calculated in step S120 make one revolution. Using the tire travel distance L at the time, the tire rolling resistance RR when the tire makes one revolution is calculated according to the above equation (5).
Thus, the tire rolling resistance RR when the tire makes one revolution can be obtained by the tire rolling resistance evaluation method of the present invention.

  The tire rolling resistance evaluation method of the present invention is characterized by including the above-mentioned tire internal pressure filling processing step, centrifugal force calculating step, and load loading step. (1) The tire internal pressure filling Calculating the stress and strain of the tire by performing the step of calculating the centrifugal force and the load loading step, and (2) calculating the stress and strain calculated in this way to stress and strain with reference to a local coordinate system. And calculate the stress and strain components at one point in the cross section. (3) Using the stress and strain components thus calculated, the stress and strain at points adjacent to each other in the circumferential direction are sequentially calculated to obtain one round. Calculate stress and strain change characteristic curves by obtaining stress and strain, and (4) calculate a finite order Fourier series expansion of stress and strain for one round, and change the curve for each Fourier order. (5) Based on the calculation of the area of the Lissajous waveform of the hysteresis for each Fourier series with the phase lag corresponding to the loss factor of the material of each finite element applied to the strain value, the Lissajous of the Fourier order and hysteresis Calculate the sum of the product of the area of the waveform, and repeatedly execute the above-mentioned series of calculation processes (1) to (5) for all the stress and strain components to calculate the sum for each component. Calculating the heat energy density at the position, and (7) calculating the product of the volume of the area including the position and the heat energy density, where the heat energy density characteristic is approximated by the heat energy density at the position, The heat generation energy in the tire is calculated, and the calculation and calculation steps of (8) and above (1) to (7) are repeatedly executed for the entire tire to calculate the heat generation energy of the entire tire. (9) When the outer radius of a tire that is not loaded and the load radius when a load is applied by applying centrifugal force is calculated by the finite element method, and the tire is rotated once using the result (10) The rolling resistance of the tire is calculated on the basis of the heat generation energy at the time of one rotation of the tire calculated in this way and the driving distance at the time of one rotation of the tire.

Here, it is preferable that a value corresponding to at least one of temperature dependency, frequency dependency, and strain amplitude dependency is used as the phase lag value corresponding to the loss coefficient of the viscoelastic material.
Moreover, it is preferable that the calculation of the sum of the areas of the Fourier order and the hysteresis Lissajous waveform is performed according to the relational expression (1).
The order of the Fourier series expansion is preferably selected from 10 to 100.
Further, the calculation of the product E _di of the area S total of _c and the volume V of each component is preferably carried out in accordance with the above equation (2).
The calculation of the travel distance L when the tire makes one revolution is preferably performed according to the relational expression (4).
Moreover, it is preferable that the rolling resistance RR of the tire when the tire makes one rotation is performed according to the relational expression (5).
The tire rolling resistance evaluation method of the present invention is basically configured as described above.

The tire rolling resistance evaluation method described above can be processed on a computer by executing a program.
For example, the tire rolling resistance evaluation program of the present invention has a procedure for causing a computer, specifically a CPU thereof, to perform each step of the above-described tire rolling resistance evaluation method. The program composed of these procedures may be configured as one or a plurality of program modules.
The tire rolling resistance evaluation program comprising the procedures executed by these computers may be stored in a memory (storage device) of the computer or server, or may be stored in a recording medium. The program is read and executed from a memory or a recording medium by the computer (CPU) or another computer at the time of execution. Therefore, the present invention may be a computer-readable memory or recording medium storing a tire rolling resistance evaluation program for causing a computer to execute the tire rolling resistance evaluation method of the first aspect.

  Further, as one mode for performing each of the above calculations, it is possible to perform calculations using a computer. In that case, for example, the following configuration can be used. An apparatus for determining the rolling resistance of a tire including a viscoelastic material by a computer according to the present invention includes an input unit for inputting shape data, material data, boundary data, load data, and travel speed data, shape data, material data, boundary data, and load. Stress and strain for calculating the stress and strain of tires including viscoelastic materials by acquiring data from the input data storage unit for storing data and traveling speed data, and taking into account internal pressure, centrifugal force and load A calculation unit, a stress storage unit for storing the stress, a strain storage unit for storing the strain, a stress from the stress storage unit, a strain from the strain storage unit, and coordinate conversion into stress and strain with reference to a local coordinate system A local coordinate stress and local coordinate strain calculation unit, a local coordinate stress storage unit that stores the local coordinate stress, a local coordinate strain storage unit that stores the local coordinate strain, and a local coordinate stress storage unit One round of local coordinate stress data for one round of tire, local coordinate strain data for one round of the tire is acquired from the local coordinate strain storage unit, and local coordinate stress data and local coordinate strain data for one round of the tire are stored. The local coordinate stress data and the local coordinate strain data are acquired from the minute data storage unit and the one-round data storage unit, and the Fourier series expansion of the finite order of the local coordinate stress and the local coordinate strain for one round is calculated. Lissajous waveform area data calculation unit, which calculates the amplitude and phase of the curve for each order and gives the phase delay according to the loss factor of the material to the strain value to calculate the area of the Lissajous waveform (hysteresis loop) for each Fourier order Lissajous waveform area data storage unit for storing waveform area data, and Lissajous waveform area data for each Fourier order is acquired from the Lissajous waveform area data storage unit A tire heating energy density data calculation unit for calculating the tire heating energy density from the Fourier order and the Lissajous waveform area data, a tire heating energy density data storage unit for storing the tire heating energy density data, and the tire heating energy density data storage A volume data calculation unit for calculating a volume of a region including the position, in which a heat generation energy density characteristic is approximated by the tire heat generation energy density data acquired from a unit, a volume data storage unit for storing the volume data, and the tire heat generation A heat generation energy calculation unit that obtains the tire heat generation energy density data from the energy density data storage unit, acquires the volume data from the volume data storage unit, and calculates heat generation energy, and an output unit that outputs the calculation result.

In the method, system, and program according to the present invention, it is possible to perform a simulation with high fidelity of tire heat generation and tire rolling resistance in consideration of not only internal pressure and load but also centrifugal force due to traveling speed and the like. Further, the loss factor of the material can be changed for each component of stress and strain, and the anisotropy of the loss factor of a fiber reinforced material such as a belt or a carcass can be handled. Further, since the area of the Lissajous waveform is calculated for each deformation frequency of the tire, it is possible to consider a different deformation frequency for each part of the tire. In addition, when calculating the area of the Lissajous waveform, calculation is performed for each deformation frequency of the tire from the amplitude of stress and strain, and it is possible to consider the frequency dependence and strain amplitude dependence of the loss factor of the material. At that time, by appropriately determining the temperature corresponding to the tire part, it is possible to perform an analysis in consideration of the temperature, frequency, and strain amplitude dependence of the material loss coefficient.
According to the method, system, and program of the present invention, it is possible to appropriately evaluate the characteristics of the heat generation energy of the tire including the viscoelastic material, the characteristics of the rolling resistance of the tire, and the like.

  The tire rolling resistance evaluation method, the tire evaluation system using the tire, and the tire rolling resistance evaluation program using the tire rolling resistance evaluation method according to the present invention have been described in detail above, but the present invention is not limited to the above embodiment and departs from the gist of the present invention. Of course, various improvements and changes may be made within the range not to be performed.

The present invention will be specifically described below based on examples.
As an example of the present invention, the tire rolling resistance evaluation method shown in FIGS. 8 and 10 was performed using the tire evaluation system 10 shown in FIGS. 1 and 2.
As initial conditions, the size of the tire used (the rim size in parentheses) was 185 / 65R15 (15 × 5 1 / 2JJ), the internal pressure (air pressure) was 200 kPa, the load was 4 kN, and the traveling speed was 80 km / h.
In this example, the loss coefficient (tan δ) of each member constituting the tire was measured under the following measurement conditions, and the value was used as initial input data as a physical property value. As measurement conditions, a viscoelastic spectrometer was used, and measurement was performed under conditions of a temperature of 60 ° C., a frequency of 20 Hz, an initial strain of 10%, and a dynamic strain of 2%.
Regarding the five types of radial tires for passenger cars of the above sizes, measurement of rolling resistance as a reference example, estimation of rolling resistance by the rolling resistance evaluation method of a tire of the present invention as an example, and JP-A-11- The rolling resistance was estimated by the conventional method disclosed in No. 233332.

  The five types of tires are tires having a structure A, a structure B, a structure C, a structure D, and a structure E as shown in FIG. Here, the tire of the structure A is used as a standard tire (control), and is a radial tire for automobile (covered with a belt cover member 75 such as an organic fiber cord on the belt member 74 having the structure shown in FIG. For example, JEF: jointless full cover & jointless edge cover) 70. The tire of structure B is obtained by reducing the weight of the tread portion of the tire of structure A. The tire of structure C is obtained by reducing the weight of the side portion of the tire of structure A. The tire of the structure D is a tire having a structure different from that of the tire of the structure A (for example, S1: no belt cover material), and the tread portion is lightened. The tire of the structure E is a tire of the structure D, and the side portion is further reduced in weight. Therefore, both the tread portion and the side portion are reduced in weight.

In the reference example, as a rolling resistance test method, a drum tester having a smooth drum surface and made of steel and having a diameter of 1707 mm was used, the ambient temperature was controlled to 21 ± 2 ° C., and the speed was 80 km / h. It was made to drive | work and the rolling resistance in that case was measured.
In the example and the comparative example, the coefficient K for obtaining the rolling radius of the two-dimensional tire model (2DFE model) 90 is 1 (K = 1). In addition, the tire model 90 is configured using four-node elements or three-node elements, and the number of elements r is about 1080 (= 54000/50), and the number of nodes is about 1180 (= 59000/50). . Here, about 5400 is the total number of elements of the three-dimensional tire model (3DFE model) 92, and 50 is the total number of divisions of the 3DFE model 92 in the tire circumferential direction. The total order p in the Fourier series expansion was 30th, and the total number of components q was 6.

  For the five types of tires of each structure, the measurement results of the rolling resistance (RR) of the reference example and the estimation results of the two types of rolling resistance (RR) of the examples and comparative examples of the present invention were obtained. The results are shown in FIG. In FIG. 11, the actual measurement result of the reference example and the two estimation results of the example of the present invention and the comparative example are obtained for each of the reference example, the example, and the comparative example with the result of the structure A as a control. The structure results were normalized with the structure A results. Therefore, the vertical axis of FIG. 11 shows the value of rolling resistance (RR) indexed with the result of structure A as 100.

As is clear from the results of FIG. 11, in the structure B, the tread portion is lighter than the structure A. Therefore, the value of the rolling resistance (RR) is 82 points in the actually measured value of the reference example. Although it is about 20 points lower than A, it is lower at 79 points in the comparative example, whereas it is 81 points in the example of the present invention, which is an improvement of 2 points compared to the comparative example. It was.
In Structure C, since the side portion is lighter than Structure A, the value of rolling resistance (RR) is 91 points in the measured value of the reference example, which is about 10 points lower than Structure A. However, in the comparative example, it is a little lower at 89 points, but in the example of the present invention, it is 90 points, which is an improvement of 1 point compared to the comparative example.

On the other hand, the structure D is a different structure with no belt cover material compared to the structure A, but the tread portion is lighter, so the rolling resistance (RR) value is 88 points in the measured value of the reference example. Although it is about 10 points lower than the structure A, it is much lower at 77 points in the comparative example, but in the example of the present invention, it is 86 points, which is 9 points compared with the comparative example. There was a significant improvement.
On the other hand, in the structure E, since the tread portion is further reduced in weight with respect to the structure D, the value of the rolling resistance (RR) is 84 points in the actually measured value of the reference example, which is about Although it decreased by 4 points and decreased by about 15 points with respect to the structure A, it is much lower at 69 points in the comparative example, but in the example of the present invention, it is 81 points, compared with the comparative example. A significant improvement of 12 points was observed.

From the above results, the structures B and C, which have a reduced rolling resistance (RR) value due to weight reduction with respect to the structure A, have the belt cover material as in the structure A. It is considered that the deformation of the non-contact portion is small, and the error in the example and the comparative example is small with respect to the reference example, and a substantially close value can be obtained. Is small.
However, in the structures D and E having different structures with no belt cover material with respect to the structure A, there is of course a decrease in the rolling resistance (RR) value due to weight reduction, but there is no belt cover material with respect to the structure A. Therefore, it is considered that the deformation of the non-contact portion of the tire due to the centrifugal force is large, and in the examples, a value substantially similar to the reference example can be obtained, and the estimation accuracy of the rolling resistance (RR) is high, whereas in the comparative example Since the deformation of the non-contact portion of the tire due to the centrifugal force is not taken into consideration, it is significantly lower than the reference example, and the estimation accuracy of the rolling resistance (RR) is low and the estimation is insufficient.
From the above, the effect of the present invention is clear.

DESCRIPTION OF SYMBOLS 10 Tire evaluation system 12 Tire rolling resistance calculation apparatus 14 Input device 16 Output device 18 CPU
20 Memory 22 Input / output interface (I / OIF)
24 initial data setting unit 26 tire model generation unit 28 data calculation unit 30 rolling resistance calculation unit 32 data bus 34 tire stress / strain calculation unit 36 tire heat generation energy calculation unit 38 tire mileage calculation unit 40 internal pressure filling processing unit 42 centrifugal force calculation Unit 44 Load load processing unit 46 Local coordinate conversion unit 48 Stress and strain calculation unit for one tire circumference 50 Lissajous waveform area calculation unit 52 Heat generation energy density calculation unit 54 Tire volume calculation unit 56 Heat generation energy calculation unit 58 Outer radius calculation unit 60 Centrifugal force application / load load tire outer radius calculation unit 62 Tire mileage calculation unit 90 Tire model (2DFE model)
92 Tire model (3DFE model)

Claims (8)

Using a two-dimensional tire model represented by a plurality of finite elements to reproduce the tire comprising a viscoelastic material, at least, a tire inner pressure filling processing step and the two-dimensional tire model filling a predetermined internal pressure in the two-dimensional tire model The rolling resistance of a rolling tire is determined from the stress and strain obtained in the static finite element analysis method including a load loading step for applying a predetermined load to a three-dimensional tire model in which the tires are connected one turn, and the loss factor in that element. A tire rolling resistance evaluation method to be estimated,
In addition to the tire internal pressure filling step and the load loading step, a centrifugal force calculation step of calculating a centrifugal force generated when the tire is rolled and applying it to the two-dimensional tire model is performed.
Performing the centrifugal force calculation step before the load loading step;
A tire rolling resistance evaluation method comprising: performing a load loading step of applying a predetermined load to the three-dimensional tire model by using physical quantities including displacement, stress and strain obtained in the centrifugal force calculation step as initial conditions.   2. The tire rolling resistance according to claim 1, wherein the step of estimating the rolling resistance of the tire includes an operation of converting stress and strain of each finite element of the tire into stress and strain referring to a local coordinate system. Rolling resistance evaluation method.   The step of estimating the rolling resistance of the tire uses the stress and strain in each finite element of the tire and the loss factor of the finite element to calculate the area of the Lissajous waveform of the stress and strain hysteresis of each finite element, 3. The tire rolling resistance evaluation method according to claim 1, wherein the rolling resistance of the tire is estimated by a sum of all areas of the Lissajous waveforms of elements.   The tire rolling resistance evaluation method according to claim 1, wherein the tire internal pressure filling step is performed before the centrifugal force calculation step.   The estimation step of estimating the rolling resistance of the tire calculates the heat generation energy of the entire tire from the stress and strain of the tire calculated by performing the tire internal pressure filling step, the centrifugal force calculation step, and the load loading step. In addition, the tire internal pressure filling step, the centrifugal force calculating step, and the load applying step are performed to calculate a travel distance when the tire makes one rotation, and the calculated heat energy of the entire tire and the tire make one rotation The rolling resistance evaluation method for a tire according to any one of claims 1 to 4, wherein the rolling resistance of the tire is calculated based on a travel distance when the tire is run.   A tire evaluation system using the tire rolling resistance evaluation method according to any one of claims 1 to 5. A tire model generation unit for generating a two-dimensional tire model represented by a plurality of finite elements that reproduces a tire including a viscoelastic material, or a three-dimensional tire model obtained by connecting the two-dimensional tire models one turn ;
An internal pressure filling processing unit that fills the generated two-dimensional tire model with a predetermined internal pressure; a centrifugal force calculation unit that calculates a centrifugal force generated when the tire rolls and applies the two-dimensional tire model to the centrifugal force calculation unit; A stress and strain calculation unit comprising a load load processing unit for applying a predetermined load to the three-dimensional tire model;
A tire heat generation energy calculation unit that calculates heat generation energy of the entire tire from the stress and strain calculated in the stress and strain calculation unit and a loss coefficient in the tire constituent material;
A tire travel distance calculation unit that calculates a travel distance when the tire makes one rotation from the calculation result of the stress and strain calculation unit;
Tire rolling for calculating rolling resistance of the tire based on the heat generation energy of the whole tire calculated by the tire heat generation energy calculation unit and the travel distance when the tire makes one rotation calculated by the tire travel distance calculation unit A resistance calculation unit,
Before applying a predetermined load to the three-dimensional tire model by the load load processing unit, the centrifugal force generated when the tire is rolled by the centrifugal force calculation unit is calculated and applied to the two-dimensional tire model. ,
A tire evaluation system in which a predetermined load is applied to the three-dimensional tire model by the load load processing unit using physical quantities including displacement, stress and strain obtained by the centrifugal force calculation unit as initial conditions.   A computer-executable program for executing the tire rolling resistance evaluation method according to any one of claims 1 to 5.

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