A method for predicting the frictional characteristics of rubber blocks on ice

Abstract

To provide a method for predicting the on-ice friction characteristics of a rubber block, capable of predicting the on-ice friction characteristics combined with the adhesive friction characteristics and the lubricating friction characteristics.SOLUTION: Disclosed is a method for predicting the on-ice friction characteristics of a rubber block of the present invention, which includes: an on-ice friction model-construction step of defining the on-ice friction as a function of the adhesion friction and the lubrication friction to construct an on-ice friction model; an adhesion friction characteristic calculation step of calculating the adhesion friction characteristics; a lubrication friction characteristic calculation step of calculating the lubrication friction characteristics; and an on-ice friction characteristic prediction step of predicting the on-ice friction characteristics of the rubber block based on the on-ice friction model, using the calculated adhesion friction characteristics and calculated lubrication friction characteristics.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a method for predicting the friction characteristics of a rubber block on ice, and more particularly to a method for predicting the friction characteristics of a rubber block defined by grooves in a tire contact area on ice. [Background technology]

[0002] It has been known to provide narrow grooves called sipes on the tread surface of tires (especially studless tires). The provision of sipes allows water that gushes out when ice melts on the tire's contact surface to be expelled outside the contact surface, thereby improving grip on ice.

[0003] In order to remove the water film on the contact surface and improve friction characteristics on ice, it is said that it is effective to remove water by using surface roughness, to break the water film with edges such as sipes, and to optimize ground pressure, but it is difficult to quantitatively evaluate the contribution and effect of these factors by observing and measuring the phenomena on the contact surface.

[0004] Therefore, in order to understand the phenomenon of the contact surface (friction surface on ice), analyze the contributions and effects of various factors, and consider ways to improve it, a method for predicting and analyzing the state of the ice friction surface is required. Conventional techniques for analyzing ice friction surfaces include those described in Non-Patent Documents 1 and 2. These documents present means for predicting and analyzing the friction characteristics (lubrication friction characteristics) due to the viscous resistance of a water film. [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] “An advanced viscous model for rubber-ice-friction”, C.Klapproth / Ostfalia Hochschule fur angewandte Wissenschaften, TMKessel, K.Wiese, B.Wies / Continental Reifen Deutscland GmbH, Tribology International 99(2016) 169-181 [Non-patent document 2] “Tire-ice model development for the simulation of rubber compounds effect on tire performance”, Hoda Mousavi, Corina Sandu / Virginia Tech, Journal of Terramechanics 91(2020) 97-115 Summary of the Invention [Problem to be solved by the invention]

[0006] However, friction phenomena on icy road surfaces are thought to involve not only lubricated friction via a water film, but also partial adhesive friction where the ice and tire contact surface come into direct contact. Therefore, the techniques described in Non-Patent Documents 1 and 2, which only consider lubricated friction, have the problem of being unable to analyze the contributions and effects of factors other than water removal, among the various factors that affect friction characteristics. Furthermore, as noted in the text of Non-Patent Document 1, there remain issues with the accuracy of predicting friction characteristics. Furthermore, these problems can arise not only in tires, but also in the friction characteristics of rubber blocks on ice.

[0007] Therefore, an object of the present invention is to provide a method for predicting the friction characteristics of a rubber block on ice, which is capable of predicting the friction characteristics on ice that are a combination of adhesive friction characteristics and lubricated friction characteristics. [Means for solving the problem]

[0008] The gist and configuration of the present invention are as follows. (1) A method for predicting the friction characteristics of a rubber block on ice, comprising: an ice friction model construction process in which friction on ice is defined as a function of adhesion friction in an adhesion region where the rubber block is in direct contact with the ice and lubrication friction in a lubrication region where the rubber block is in contact with the ice via a water film on the ice, and a friction model on ice is constructed; an adhesion friction characteristic calculation step of calculating adhesion friction characteristics; a lubrication friction characteristic calculation step of calculating lubrication friction characteristics; and an on-ice friction characteristic prediction step of predicting the on-ice friction characteristics of the rubber block based on the on-ice friction model using the adhesion friction characteristics calculated in the adhesion friction characteristic calculation step and the lubrication friction characteristics calculated in the lubrication friction characteristic calculation step.

[0009] (2) The method for predicting friction characteristics on ice described in (1) above, wherein the ice friction model takes into account the contribution rate of adhesive friction to the ice friction and the contribution rate of lubricated friction to the ice friction.

[0010] TIFF0007736498000001.tif41170

[0011] (4) A method for predicting frictional characteristics on ice described in any one of (1) to (3) above, wherein in the adhesion frictional characteristics calculation step, the adhesion frictional characteristics are calculated by assuming the dependence of the adhesion frictional characteristics on ground pressure and the dependence of the adhesion frictional characteristics on the frictional shear strength of ice.

[0012] (5) The contact pressure dependence of the adhesive friction characteristics is determined by the adhesive friction coefficient μ ad is expressed by a relational expression proportional to the power of the ground pressure P, The dependence of the adhesive friction characteristics on the friction shear strength of the ice is expressed as the adhesive friction coefficient μ ad The method for predicting frictional characteristics on ice described in (4) above, wherein is expressed by a relational expression proportional to the frictional shear strength s of the ice.

[0013] (6) A method for predicting frictional characteristics on ice according to (5) above, wherein the frictional shear strength s of the ice is expressed as a linear equation of the surface temperature Ts of the ice.

[0014] (7) A method for predicting frictional characteristics on ice described in any one of (4) to (6) above, in which the dependence of the adhesion frictional characteristics on ground pressure and the dependence of the frictional shear strength of the ice on the surface temperature of the ice are determined in advance by measurement.

[0015] (8) An elastic block model construction process for defining block rigidity based on elastic deformation of the rubber block having a rectangular shape in a plan view, which is partitioned by sipes, and constructing an elastic block model; a block rigidity calculation step of calculating block rigidity of the rubber block based on the elastic block model; and a block deformation model construction step of defining block deformation based on the block rigidity, the frictional force on ice acting in the sliding direction of the rubber block, and the ground contact pressure, and constructing a block deformation model. In the ice friction characteristic prediction step, (a) the on-ice friction force calculated based on the on-ice friction model using the adhesive friction characteristics calculated in the adhesive friction characteristics calculation step and the lubricating friction characteristics calculated in the lubricating friction characteristics calculation step; and (b) the block rigidity calculated in the block rigidity calculation step; The method for predicting frictional characteristics on ice described in (1) above, further comprising: calculating the block deformation on ice based on the block deformation model construction step using the above formula; and predicting the frictional characteristics on ice.

[0016] (9) The elastic block model is constructed by defining a reduction in the contact length of the rubber block due to elastic deformation of the rubber block, The method for predicting frictional characteristics on ice described in (8) above, in which the block deformation model is constructed by defining the block deformation as a function of the reduction in the contact length of the rubber block and the frictional force on ice calculated based on the contact length.

[0017] TIFF0007736498000002.tif56170

[0018] According to the present invention, it is possible to provide a method for predicting the friction characteristics of a rubber block on ice, which is capable of predicting the friction characteristics on ice that are a combination of adhesive friction characteristics and lubricated friction characteristics. [Brief explanation of the drawings]

[0019] [Figure 1] 1 is a conceptual diagram of a friction model on ice. [Figure 2] FIG. 1 is a flow diagram of a method for predicting friction characteristics on ice. [Figure 3] FIG. 10 is a diagram for explaining an adhesion rate. [Figure 4] FIG. 10 is a diagram showing an example of coefficients obtained by fitting. [Figure 5] FIG. 1 is a schematic diagram of the temperature distribution near the ice surface. [Figure 6] FIG. 10 is a conceptual diagram for explaining the balance of heat quantities. [Figure 7] FIG. 2 is a diagram mainly for explaining a lubrication region. [Figure 8] FIG. 1 is a diagram showing the tread patterns of three test tires with different sipe densities. [Figure 9] FIG. 1 is a diagram showing the change in coefficient of friction on ice depending on sipe density. [Figure 10] This is a sketch of the traces of the contact state remaining on the icy road surface and the observed contact state when the sipes are low density. [Figure 11] This is a sketch of the traces of contact with the icy road surface and the observed contact state when the sipes are densely packed. [Figure 12] FIG. 1 is a flow diagram of a method for predicting friction characteristics on ice when the influence of block rigidity is taken into account. [Figure 13] FIG. 10 is a diagram showing an elastic block model used in another embodiment. [Figure 14] 10A and 10B are diagrams for explaining the influence of block deformation on a friction surface. [Figure 15]FIG. 10 is a diagram showing a friction surface of a subsequent block when the blocks are coupled together. [Figure 16] FIG. 10 is a diagram showing predicted temperature distribution inside and on the surface of ice. [Figure 17] FIG. 10 is a diagram showing the predicted results of the sliding speed dependency of the friction coefficient on ice. [Figure 18] FIG. 10 is a diagram showing the predicted results of the relationship between the sipe edge density and the block rigidity and the coefficient of friction. DETAILED DESCRIPTION OF THE INVENTION

[0020] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

[0021] Figure 1 is a conceptual diagram of an on-ice friction model. Figure 2 is a flow diagram of a method for predicting on-ice friction characteristics. In a method for predicting on-ice friction characteristics of a rubber block according to one embodiment of the present invention, first, friction on ice is defined as a function of adhesive friction in an adhesive region where the rubber block (e.g., a rubber block of a tire partitioned by grooves) comes into direct contact with the ice, and lubricated friction in a lubricated region where the rubber block comes into contact with the ice via a water film on the ice, and an on-ice friction model is constructed (on-ice friction model construction process: step S101).

[0022] As shown in Figure 1, when a rubber block slides on ice, it first comes into direct contact with the ice, but frictional heat causes the ice to melt, creating a film of water on the ice. This means that the side of the contact length in the direction of travel (of the rubber block) becomes an adhesion region where the rubber block comes into direct contact with the ice, while the side of the contact length opposite the direction of travel becomes a lubrication region where the rubber block comes into contact with the ice via the film of water on the ice. Furthermore, at the ends of the contact length (the ends in the direction of travel (sliding direction)), the sipes act to break up the water film, creating digging resistance.

[0023] For these reasons, in step S101, friction on ice is defined as a function of adhesive friction in the adhesion region and lubricated friction in the lubricated region, and an ice friction model is constructed. First, we will explain the case where digging resistance due to sipes is not taken into account. The case where digging resistance is taken into account will be described later.

[0024] TIFF0007736498000003.tif48170

[0025]

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[0026] As shown in Figure 3, in the adhesion region, as the ice temperature increases (towards the direction opposite to the direction of travel), the adhesion friction coefficient μ ad In the lubricated region, the lubrication friction coefficient μ decreases as the thickness of the water film increases (in the opposite direction to the direction of travel). f is decreasing.

[0027] As expressed in Equation 1, to calculate the coefficient of friction on ice μ, the coefficient of adhesive friction, the coefficient of lubricated friction, and the adhesion rate must be calculated. For this reason, the method for predicting the friction characteristics of a rubber block on ice of this embodiment includes an adhesive friction characteristics calculation step (step S102) for calculating the adhesive friction characteristics, and a lubricated friction characteristics calculation step (step S103) for calculating the lubricated friction characteristics. In the adhesive friction characteristics calculation step (step S102), μ ad and α are calculated based on adhesive friction theory, thermodynamics, and heat transfer engineering. In the lubrication friction characteristic calculation step (step S103), μ f is calculated based on lubrication friction theory, thermodynamics, and heat transfer engineering. Specific methods for these calculations are explained below.

[0028] First, the calculation of adhesive friction characteristics will be explained. According to known adhesive friction theory, the adhesive friction coefficient depends on the contact pressure P and the frictional shear strength s of the ice. Therefore, in the adhesive friction calculation step (step S102), adhesive friction can be calculated by assuming the contact pressure dependence of adhesive friction and the frictional shear strength dependence of adhesive friction. In particular, according to known adhesive friction theory, the contact pressure dependence of adhesive friction characteristics depends on the adhesive friction coefficient μ ad The adhesion friction coefficient μ ad can be expressed as a relational expression proportional to the frictional shear strength s of ice. Therefore, the adhesion friction coefficient μ ad can be expressed by the following Equation 2. In Equation 2, k and n are coefficients.

[0029]

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[0030] As shown in Figure 3, adhesive friction can be defined by the following equation 3. In equation 3, L ad is the length of the adhesion region (the length measured in the direction of travel of the rubber block), and x is the distance from the end of the rubber block in the direction of travel.

[0031]

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[0032] Substituting Equation 2 into Equation 3, it can be seen that the integral of Equation 3 above can be solved analytically or numerically in a convergent manner, especially when the right-hand side of Equation 2 can be expressed relatively simply as a function of x.

[0033] It is known that the frictional shear strength s of ice depends on the ice temperature. The equation for the ice surface temperature Ts as a function of x can also be derived from known adhesive friction theory, thermodynamics, and heat transfer engineering, but as will be discussed later, this equation for the function of x is not simple. For the above reasons, in this embodiment, the frictional shear strength s of ice is expressed (as a simple formula) by a linear equation of the ice surface temperature Ts (Equation 4 below). In Equation 4, s0 is the frictional shear strength of ice at a temperature of 0°C, and ε is the temperature-dependent gradient of the frictional shear strength of ice.

[0034]

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[0035] Incidentally, when calculating the integral by substituting Equation 2 into Equation 3 to obtain the numerical value, it is necessary to determine the coefficients k, n, ε, and constant s0 in advance. For this reason, in this embodiment, the dependence of adhesion friction characteristics on contact pressure and the dependence of ice friction shear strength on ice surface temperature are determined in advance by measurement.

[0036] First, the adhesion friction characteristics are dependent on the contact pressure, and the adhesion friction coefficient μ ad The adhesive friction coefficient μ is measured, and k and n are identified by plotting a large number of them and fitting them using Equation 2. ad For example, the coefficient of friction measured under extremely low speed conditions (for example, sliding speed V of a rubber block = 0.01 km / h) where melting of ice due to frictional heat is extremely small can be determined as the coefficient of adhesive friction.

[0037] The dependence of ice frictional shear strength on ice surface temperature can be determined by measuring the ice surface temperature Ts and the ice frictional shear strength s, plotting a large number of these values, and then identifying s0 and ε by fitting using Equation 4. Figure 4 shows an example of coefficients determined by fitting, and in this way k, n, s0, and ε can be determined in advance.

[0038] In particular, if the ground pressure P is assumed to be independent of x, the adhesive friction coefficient μ ad can be expressed by the following Equation 5. In Equation 5, μ ad0 is a constant, and E is the gradient of the adhesion friction coefficient depending on the ice surface temperature.

[0039]

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[0040] Next, we will explain how to express the ice surface temperature Ts as a function of x. Figure 5 is a schematic diagram of the temperature distribution near the ice surface. Consider the temperature change near the ice surface when the surface temperature of a semi-infinite piece of ice, with a uniform initial temperature T0, is maintained at T=Ts from time t=0. In this case, the unsteady temperature change near the ice surface, the temperature distribution inside the ice, and the temperature gradient in the depth direction y can be expressed by the following equations 6, 7, and 8, respectively, based on known theories of thermodynamics and heat transfer engineering. Here, equation 6 is a basic equation when the temperature change is one-dimensional, in the depth direction y only. In addition, in equation 7, a is a coefficient, T0 is the ice temperature at t=0, z is the elapsed time t (= x / V), and the variable z=y / 2(at) is defined as the elapsed time t (= x / V) and the depth y. 1 / 2 =(y / 2)×(V / ax) 1 / 2 is.

[0041]

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[0042]

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[0043]

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[0044] Figure 6 is a conceptual diagram for explaining the balance of heat quantity. First, according to the known theory of thermodynamics and heat transfer engineering, the heat quantity q i can be expressed by the following equation 9. In equation 9, μ is the friction coefficient, and J is the thermal work equivalent. Furthermore, according to known theories of thermodynamics and heat transfer engineering, the amount of heat q0 conducted inside the ice can be expressed by the following equation 10. In equation 10, λ is the thermal conductivity, c is the specific heat of water, ρ is the density of water, and t0 is the elapsed time until the edge slides the distance x.

[0045]

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[0046]

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[0047] Heat generation amount qad i and the heat transferred to the ice qad o By setting μ equal to μ, we can obtain the following equation 11. ad0 is the adhesive friction coefficient of ice at a temperature of 0°C, E is the temperature-dependent gradient of the adhesive friction coefficient of ice, and K is a coefficient.

[0048]

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[0049] where μ ad0 and E is μ ad0 =ks0P n-1 , E=kεP n-1 , can be used. From the above, using Equation 2, Equation 3, Equation 4, and Equation 11, αμ ad It is possible to calculate L ad can be calculated as the contact area before Ts reaches 0°C in Equation 11.

[0050] Next, calculation of lubrication friction characteristics will be described. First, the lubrication region can be calculated as the contact region after Ts reaches 0°C in Equation 11. The lubrication friction characteristics can be obtained from known lubrication friction theories, thermodynamics, and heat transfer engineering. As explained below, the frictional heat in a small area within the lubrication region is assumed to be equal to the heat of melting of the ice, and the water film thickness and lubrication friction coefficient in that area are calculated. These are then integrated over the entire lubrication region, allowing the lubrication friction characteristics to be determined.

[0051] FIG. 7 is a diagram mainly for explaining the lubrication region. i can be expressed by the following formula 12. In formula 12, μ f is the lubrication friction coefficient, η is the viscous resistance of water, and h is the thickness of the water film at position x.

[0052]

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[0053] The amount of heat consumed as heat of melting ice, dqf0, can be expressed by the following formula 13: In formula 13, R is the latent heat of melting ice.

[0054]

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[0055] Here, the amount of heat generated by friction dqf i = Amount of heat consumed as heat of melting ice dqf0 + Amount of heat conducted into the ice dqf 02 " (However, since Ts=0℃ has been reached, dqf 02 is small, so we can simply use dqf i = dqf0), the following formula 14 can be derived. Formula 14 can be used to calculate the lubrication friction characteristics.

[0056]

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[0057] As described above, the adhesive friction characteristics calculated in the adhesive friction characteristics calculation step (step S102) and the lubricating friction characteristics calculated in the lubricating friction characteristics calculation step (step S103) are used to predict the on-ice friction characteristics of the rubber block (calculate the friction coefficient μ) based on the on-ice friction model (by substituting into Equation 1) (on-ice friction characteristics prediction step: step S104).

[0058] According to the method for predicting the frictional characteristics of a rubber block on ice of this embodiment, it is possible to calculate not only the lubrication frictional characteristics but also the adhesion frictional characteristics, and predict the frictional characteristics on ice that are a combination of these. As shown in the examples below, this makes it possible to predict the frictional characteristics on ice with higher accuracy than when only the lubrication frictional characteristics are considered. Examples of the frictional characteristics on ice are the μ-V characteristics and μ-P characteristics, as shown in the examples below.

[0059] As mentioned above, it is preferable that the ice friction model take into account the contribution of adhesive friction to ice friction and the contribution of lubricated friction to ice friction. In particular, it is preferable that the ice friction model be constructed by defining the coefficient of friction on ice using Equation 1. This is because it is possible to more accurately predict the friction characteristics on ice.

[0060] In addition, in the adhesive friction characteristic calculation step, it is preferable to calculate the adhesive friction characteristics by assuming the dependency of the adhesive friction characteristics on the ground pressure and the dependency of the adhesive friction characteristics on the friction shear strength of ice. In particular, the dependency of the adhesive friction characteristics on the ground pressure is calculated by assuming the dependency of the adhesive friction characteristics on the ground pressure and the friction shear strength of ice. ad is expressed by a relational expression proportional to the power of the contact pressure P, and the dependence of adhesion friction characteristics on the friction shear strength of ice is expressed by the adhesion friction coefficient μ ad is preferably expressed by a relational expression proportional to the shear strength s of the ice. According to known theory, adhesion friction characteristics are known to be expressed by the above relational expression, and therefore this is suitable for calculating adhesion friction characteristics.

[0061] It is also preferable to express the frictional shear strength s of ice as a linear equation of the ice surface temperature Ts, because this is suitable for solving the integral of Equation 3 in a convergent manner by analytical or numerical analysis.

[0062] In this embodiment, tire design parameters and friction conditions are set in advance. The tire design parameters are set as block dimensions. That is, the block length L described above is set. In addition to the block length, it is preferable to also set block height, edge density, etc. Furthermore, the ice temperature T0 at t = 0, the sliding speed V of the rubber block, and the ground contact pressure P are set as friction conditions.

[0063] In this embodiment, the dependence of adhesion friction characteristics on contact pressure and the dependence of ice friction shear strength on ice surface temperature are determined in advance by measurement. This allows the adhesion friction characteristics to be calculated using each formula. Specifically, the coefficients k and n in Formula 2 and the constant s0 and coefficient ε in Formula 4 are determined in advance by measurement.

[0064] Next, another embodiment will be described. In the other embodiment, particularly when the rubber blocks are partitioned by sipes of the tire, the influence of the sipes (the influence of the sipe density, the edge effect of the sipes, etc.) is further taken into consideration. Figure 8 is a diagram of the tread patterns of three test tires with different sipe densities. Figure 9 is a diagram showing the change in the coefficient of friction on ice depending on the sipe density. The results in Figure 9 are for a block height of 10 mm, a sipe depth of 8 mm, and an ice temperature of -5°C. As shown in Figures 8 and 9, providing sipes at a high density increases drainage capacity and improves grip performance on ice, but increasing the sipe density too much actually reduces grip performance on ice. For this reason, in another embodiment, we will clarify the effect of sipe density on block rigidity and grip performance on ice, the mechanism behind this, and quantitative indicators for these effects.

[0065] Figure 10 shows the traces of contact with the icy road surface and a sketch of the observed contact state when the sipes are low density, and Figure 11 shows the traces of contact with the icy road surface and a sketch of the observed contact state when the sipes are high density. Observations of actual block deformation and contact state, as shown in Figures 10 and 11, revealed that increasing the sipe density reduces block rigidity and causes the blocks to collapse and deform. When the blocks collapse and deform, the contact area decreases, resulting in reduced grip on ice.

[0066] Figure 12 is a flow diagram of a method for predicting friction characteristics on ice when the influence of block rigidity is taken into account. In consideration of the phenomena explained in Figures 10 and 11, the inventors have developed a modeling method for block rigidity and a modeling method for block deformation using block rigidity in order to predict friction characteristics on ice (especially grip performance on ice).

[0067] FIG. 13 is a diagram showing an elastic block model used in another embodiment. In this embodiment, the block rigidity is defined based on the elastic deformation of a rubber block that is rectangular in plan view and is partitioned by sipes, and an elastic block model is constructed (elastic block model construction process: step S105). In this example, the elastic block model of the rubber block is constructed by defining the amount of reduction in the contact length of the rubber block due to the elastic deformation of the rubber block. That is, as shown schematically in FIG. 13, the contact length of the rubber block is reduced (from block length L) to Lc due to the elastic deformation of the rubber block. At this time, the inclination angle of the rubber block with respect to the height direction is defined as θ for the elastic deformation of the rubber block.

[0068] As shown in Figure 13, the inclination angle θ of the beam can be calculated using a model in which the rubber block is regarded as a cantilever beam. The inclination angle θ can be expressed by the following equation 15. In equation 15, E is the elastic modulus (Young's modulus), I is the second moment of area (I=bL 3 / 12), k=3 / 2 (for rectangular cross section), A=bL, shear rigidity Gs=E / 3, F is the shear force acting on the block (=τ×bL), and f is F per unit width (=τ×L).

[0069]

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[0070] In addition, the block stiffness G θ can be expressed by the following Equation 16.

[0071]

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[0072] In another embodiment, the block rigidity of the rubber block is calculated based on the elastic block model (using Equation 16) (block rigidity calculation step: step S106). Here, since the length L of the block depends on the sipe density, the relationship between the sipe density and the block rigidity can be obtained using Equation 16.

[0073] In addition, the actual contact length Lc can be calculated from the balance of forces in the actual contact portion expressed by the following equation 17, where Ec is the compressive elastic modulus and P0 is the initial average contact pressure.

[0074]

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[0075] Thus, the block stiffness G θ A block deformation model is constructed by defining block deformation (actual contact length Lc) based on the frictional force on ice F acting in the longitudinal direction of the rubber block and the ground contact pressure P0 (block deformation model construction step: step S107). That is, the block deformation model is constructed by defining block deformation as a function of the reduction in the contact length Lc of the rubber block and the frictional force on ice F calculated based on the contact length Lc.

[0076] In consideration of Equations 15 to 17, in another embodiment, the block length in the sliding direction BL, block height (= sipe depth) H, sipe density SD, sipe thickness t, and rubber elastic modulus E' are set as tire design parameters. Here, sipe density SD = 1 / average sipe spacing (1 / mm). The length L of a rubber block separated by a sipe is the block length obtained by subtracting the sipe thickness t from the average sipe spacing. By setting these in advance, the inclination angle θ and block stiffness G required to predict friction characteristics on ice taking sipe density into consideration can be calculated. θ , and the actual contact length Lc can be calculated.

[0077] Next, we will explain how to calculate the friction force, which reflects the decrease in the actual contact length and the increase in contact pressure caused by the partial lifting of the contact surface due to block deformation. Figure 14 is a diagram for explaining the effect of block deformation on the friction surface.

[0078] First, the coefficient of friction on ice can be expressed by the following equation 18. The coefficient of adhesive friction can be expressed by the following equation 19 in the model shown in Figure 14. Furthermore, the coefficient of lubricated friction can be expressed by the following equation 20 in the model shown in Figure 14. In equation 20, P is the contact pressure after block deformation.

[0079]

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[0080]

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[0081]

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[0082] The ground pressure P after block deformation can be expressed by the following formula 21, or simply by the following formula 22.

[0083]

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[0084]

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[0085] Therefore, the friction coefficient μ that takes into account the reduction in the contact length can be calculated using Formulas 18 to 22. The calculation of the adhesive friction characteristics related to Formula 19 and the lubrication friction characteristics related to Formula 20 is the same as that described in the previous embodiment (except for the reduction in the actual contact length), so a repeated explanation will be omitted.

[0086] As described above, in another embodiment, in the on-ice friction characteristic prediction process (step S104), (a) the frictional force on ice calculated based on the on-ice friction model using the adhesion friction characteristics calculated in the adhesion friction characteristic calculation process and the lubrication friction characteristics calculated in the lubrication friction characteristic calculation process, and (b) the block rigidity calculated in the block rigidity calculation process are used to calculate block deformation on ice based on the block deformation model construction process, and to predict the on-ice friction characteristics.

[0087] Here, when frictional force is generated, block deformation occurs, the actual contact length decreases, and the frictional force decreases. When the frictional force decreases, the block deformation decreases, so the actual contact length and frictional force recover. When the frictional force recovers, the block deformation increases, and the actual contact length and frictional force decrease. In this way, frictional force, block deformation, and contact state interact with each other. The steady state where the friction force, block deformation, and ground contact state are balanced can be obtained by a convergence calculation incorporating a damping term.

[0088] Next, we will explain how to calculate the effect of sipe edge density on a continuous block consisting of a series of rubber blocks separated by sipes. First, we calculate the effect of edge pressure by calculating the effect of the sipe edges separating the preceding and succeeding blocks cutting ice that has been heated by friction of the preceding block in the continuous block.

[0089] The pressure on the edge (sipe edge) of the trailing block is P E [kPa]. And, "Edge pressure P E It is assumed that the edge penetrates and cuts to a depth d where the coefficient β is equal to the friction shear strength s of the ice. After cutting to that depth, the new ice surface temperature TE can be expressed as in Equation 24 below using Equation 23 below.

[0090]

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[0091]

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[0092] The cutting depth d by the sipe edge after passing the preceding block represents the ice temperature distribution in the following equation 25, T = T E , and calculate as y when x=Lc.

[0093]

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[0094] FIG. 15 is a diagram showing the friction surface of the following block when the blocks are coupled together. When rubber blocks separated by sipes are continuous within one block, the temperature of the ice surface on which the following block rubs rises due to friction with the preceding block. Therefore, it is preferable to calculate the friction force of the following block taking into account the temperature rise due to friction with the preceding block. The friction surface temperature Ts of the following block is calculated by the following equation (11): Ts = T E Assuming that friction begins at x = xe, the friction coefficients for the adhesion region from x = xe to xc and the lubrication region from x = xc to xe + Lc are integrated to calculate the average value of the friction coefficients for each region. In this way, it is possible to predict the friction characteristics on ice of the following block, taking into account the temperature rise caused by the preceding block.

[0095] TIFF0007736498000029.tif42170

[0096] By performing a sensitivity analysis of the coefficient of ice friction μ by varying each design parameter independently, it is possible to predict the effect of resolving the trade-off between each parameter, and to set optimization, design targets, and effective ranges. [Example]

[0097] Example 1 Figure 16 shows the temperature distribution inside and on the surface of the ice predicted using the above theory when T0 is -2°C, ground pressure P is 250 kPa, and the block length is 20 mm, based on the flow chart shown in Figure 2. As shown in Figure 16, the predicted results were obtained for a low sliding speed (2 km / h) and a high sliding speed (10 km / h). When the sliding speed is low (2 km / h), the friction coefficient is high but the amount of heat generated per unit time is low, which means that heat is easily diffused into the ice, resulting in a small temperature rise in the surface layer of the ice. Furthermore, when the sliding speed is high (10 km / h), the heat input is instantaneous, which means that little heat is conducted into the ice, resulting in only the surface layer of the ice melting.

[0098] Using a rubber block with L = 28 mm and W = 27 mm, and based on the flow shown in Figure 2 and the above theory, the dependence of the friction coefficient on ice on sliding speed at low and high temperatures was predicted, with the results shown in Figure 17. The results for low temperatures show that adhesive friction is dominant at low temperatures, resulting in a larger friction coefficient, and it can be assumed that the friction coefficient decreases as the sliding speed increases. The results for high temperatures show that lubricating friction is dominant at high temperatures, resulting in a decrease in the friction coefficient even as the sliding speed increases.

[0099] Example 2 Based on the flow chart shown in Figure 12, block stiffness and coefficient of friction were calculated and predicted using the above theory for the following conditions: ice temperature -2°C, ground pressure P of 250 kPa, block length of 30 mm, block height of 6.7 mm, and sipe spacing on the opposing lines of 6 mm, 5 mm, and 3.75 mm. The results are shown in Figure 18. We were able to predict the appropriate sipe density to improve the coefficient of friction on ice.

Claims

1. 1. A method for predicting frictional characteristics of a rubber block on ice, comprising: an ice friction model construction process in which friction on ice is defined as a function of adhesion friction in an adhesion region where the rubber block is in direct contact with the ice and lubrication friction in a lubrication region where the rubber block is in contact with the ice via a water film on the ice, and a friction model on ice is constructed. an adhesion friction characteristic calculation step of calculating adhesion friction characteristics; a lubrication friction characteristic calculation step of calculating lubrication friction characteristics; an on-ice friction characteristic prediction step of predicting the on-ice friction characteristics of the rubber block based on the on-ice friction model using the adhesive friction characteristics calculated in the adhesive friction characteristic calculation step and the lubricating friction characteristics calculated in the lubricating friction characteristic calculation step, In the adhesive friction characteristic calculation step, the adhesive friction characteristic is calculated by assuming a dependency of the adhesive friction characteristic on ground pressure and a dependency of the adhesive friction characteristic on ice friction shear strength, The dependency of the adhesive friction characteristic on the ground pressure is expressed by a relational expression in which the adhesive friction coefficient μ ad is proportional to the power of the ground pressure P, The dependency of the adhesive friction characteristics on the frictional shear strength of the ice is expressed by a relational expression in which the adhesive friction coefficient μ ad is proportional to the frictional shear strength s of the ice, A method for predicting frictional characteristics on ice, characterized in that the frictional shear strength s of the ice is expressed as a linear equation of the surface temperature Ts of the ice.

2. 2. The method for predicting frictional characteristics on ice according to claim 1, wherein the ice friction model takes into account the contribution of adhesive friction to the ice friction and the contribution of lubricated friction to the ice friction.

3.

4. The method for predicting frictional characteristics on ice according to any one of claims 1 to 3, wherein the dependence of the adhesion frictional characteristics on ground pressure and the dependence of the frictional shear strength of the ice on surface temperature are determined in advance by measurement.

5. A method for predicting the frictional characteristics of a rubber block on ice, comprising: an ice friction model construction process in which friction on ice is defined as a function of adhesion friction in an adhesion region where the rubber block is in direct contact with the ice and lubrication friction in a lubrication region where the rubber block is in contact with the ice via a water film on the ice, and a friction model on ice is constructed. an adhesion friction characteristic calculation step of calculating adhesion friction characteristics; a lubrication friction characteristic calculation step of calculating lubrication friction characteristics; an on-ice friction characteristic prediction step of predicting the on-ice friction characteristics of the rubber block based on the on-ice friction model using the adhesive friction characteristics calculated in the adhesive friction characteristic calculation step and the lubricating friction characteristics calculated in the lubricating friction characteristic calculation step, an elastic block model construction step of defining block rigidity based on elastic deformation of the rubber block having a rectangular shape in a plan view and partitioned by sipes, and constructing an elastic block model; a block rigidity calculation step of calculating block rigidity of the rubber block based on the elastic block model; and a block deformation model construction step of defining block deformation based on the block rigidity, the frictional force on ice acting in the sliding direction of the rubber block, and the ground contact pressure, and constructing a block deformation model. In the ice friction characteristic prediction step, (a) the on-ice friction force calculated based on the on-ice friction model using the adhesive friction characteristics calculated in the adhesive friction characteristics calculation step and the lubricating friction characteristics calculated in the lubricating friction characteristics calculation step; and (b) the block rigidity calculated in the block rigidity calculation step; and calculating the block deformation on ice based on the block deformation model construction step using the block deformation model to predict the frictional characteristics on ice.

6. the elastic block model is constructed by defining a reduction in the contact length of the rubber block due to elastic deformation of the rubber block; 6. The method for predicting frictional characteristics on ice described in claim 5, wherein the block deformation model is constructed by defining the block deformation as a function of the amount of reduction in the contact length of the rubber block and the frictional force on ice calculated based on the contact length.

7.

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