Method for evaluating the critical slip distance

Abstract

The present disclosure provides a method for determining a critical sliding distance (CSD) of a sample, the method comprising: applying a force to the sample toward a sliding surface; sliding the sample n times along the sliding surface in a plurality of sections, the plurality of sections having different widths w, where n is an integer greater than or equal to 1; determining, for each width wi, a wear rate m(wi)=ΔM / (n*wi) for each of a plurality of wear rates m(w), where ΔM is the difference in weight of the sample after sliding the sample in the n sections of width wi compared to before sliding; and determining a CSD for width w0 based on the plurality of wear rates and each width, wherein the method is optional (I). [Equation 1] JPEG2025537032000016.jpg14127

Description

[Technical Field]

[0001] The present disclosure is generally directed to a method for determining the critical sliding distance (CSD) of a sample, which can be used, for example, to assess tire wear by determining the critical sliding distance of a tire contact patch. [Background technology]

[0002] Wear experiments at the tire level are complex and expensive. Several methods for predicting wear performance have been described in the prior art. In particular, simulations are often used for this purpose, but in order to properly calculate the energy leading to wear and to achieve reliable results from the simulation, appropriate inputs related to the actual contact conditions and the wear characteristics of the materials must be properly evaluated.

[0003] In particular, a fundamental input required by wear simulation is the "Critical Slip Distance" (CSD), i.e., the distance at which a tread block begins to exhibit a certain rate of wear, which cannot be easily and intuitively provided by standard friction and wear tests.

[0004] Currently, the characterization of material friction and wear is performed by sliding tests on small rubber wheels, which do not provide information about the actual contact conditions, or by using linear friction testers with rubber blocks tested in full sliding mode. Either way, these types of tests cannot provide information about CSD.

[0005] For this purpose, a new methodology was specifically designed to determine the CSD by linear friction tests using rubber samples under different test conditions. Summary of the Invention

[0006] According to a first aspect, the present disclosure provides a method for determining a critical sliding distance (CSD) of a sample. The method includes applying a force to the sample toward a sliding surface. The method includes sliding the sample along the sliding surface n times in a plurality of sections, the plurality of sections having different widths w, where n is an integer greater than or equal to 1, and each width w i For each of the multiple wear rates m(w), i )=ΔM / (n*w i ) where ΔM is the width w i and determining the CSD as a width w0 based on the plurality of wear rates and their respective widths, where for any w>w0, the CSD is as follows:

[0007]

number

[0008] According to one example of the first aspect, the widths w i is an integer that divides the total length of the sliding surface.

[0009] According to another example of the first aspect, the method includes: i The sample is slid over multiple sections of width w i The method may further include weighing the sample before and after sliding over n sections to obtain a weight difference ΔM, and determining a wear rate based on the weight difference ΔM and the total sliding distance.

[0010] According to another example of the first embodiment, the wear rate m is the weight loss per total sliding distance.

[0011] According to another example of the first embodiment, the total sliding distance is i are equal for each of the

[0012] According to another example of the first embodiment, the force is released after sliding the sample along each section, and the force is reapplied before sliding the sample along the subsequent section.

[0013] According to another example of the first embodiment, the sample is slid along the sliding surface at a substantially constant speed.

[0014] According to another example of the first aspect, the method further includes identifying a first distance at which the static friction force exceeds the sliding friction force, identifying a second distance at which the sliding friction force exceeds the static friction force, and determining the CSD further based on the first distance.

[0015] According to another example of the first aspect, the method further includes providing a sliding surface having a total length, sliding a sample on the sliding surface a plurality of times at each step of a plurality of widths w, and measuring a plurality of wear rates for each of the plurality of widths w.

[0016] According to another example of the first aspect, the CSD is measured based on any one of the following: sample geometry, sample material properties, sliding surface texture, amount of force, amount of sliding speed, amount of acceleration to reach the set sliding speed, and sample temperature.

[0017] According to a second aspect, the present disclosure provides a computer-implemented method for estimating tire wear, the method including: providing a tire wear model configured to convert frictional energy rate to wear, the wear model being based on moving and non-moving portions, the moving portions experiencing greater wear than the non-moving portions; segmenting the tire contact patch into moving and non-moving portions, the non-moving portions exhibiting substantially no movement relative to the tire substrate, and the moving portions exhibiting movement relative to the tire substrate; and estimating tire wear based on the wear model and the segmented contact patch.

[0018] According to one example of the second aspect, the non-moving part does not substantially cause wear.

[0019] According to another example of the second aspect, the non-movable portion has a first width, and the critical slip distance (CSD) is proportional to the first width.

[0020] According to another example of the second aspect, the CSD is determined experimentally prior to performing the computer-implemented method, and the CSD is used as an input variable for the computer-implemented method.

[0021] According to another example of the second aspect, the CSD is determined according to the method of the first aspect.

[0022] According to another example of the second aspect, the computer-implemented method is based on the finite element method (FEM). [Brief explanation of the drawings]

[0023] [Figure 1] 1 shows a tire segmented for wear simulation in the contact area and the division of the tire's contact patch in the tight and sliding areas. [Figure 2] 1 shows a sliding surface across which a sample is slid over a small section to determine CSD according to the present disclosure. [Figure 3] 3 is a graph showing the change in the coefficient of friction over the sliding time for sliding in a short section such as that shown in FIG. 2. [Figure 4] 1 shows a sliding surface across which a sample is slid over a large section to determine CSD according to the present disclosure. [Figure 5] 5 shows a graph illustrating the change in coefficient of friction over sliding time for sliding over a large section such as that shown in FIG. [Figure 6] 1 shows a flowchart of a method for determining the CSD of a sample according to the present disclosure. [Figure 7] 1 shows a graph illustrating the wear rate m(w) for different widths wi, including the bends that characterize CSD. [Figure 8]1 shows a graph illustrating the wear rate m(w) for different widths wi and different rubber compounds A, B, C and D, including the bend that characterizes the CSD. [Figure 9] 1 shows a graph illustrating the wear rate m(w) for different widths wi and different sample geometries from the same rubber compound, including the bend that characterizes the CSD. [Figure 10] 1 shows a flowchart of a computer-implemented method for estimating tire wear according to the present disclosure. [Figure 11] 1 illustrates a finite element mesh that can be used in a computer-implemented method according to the present disclosure. [Figure 12] 1 shows a graph comparing the accuracy of a standard simulation that does not consider CSD with the accuracy of a simulation that considers CSD.

[0024] The present disclosure provides a method for determining the CSD of a sample and a computer-implemented method for estimating tire wear.

[0025] 1 shows a tire segmented for wear simulation based on the finite element method (FEM) in the contact area and in the contact and sliding areas of the tire's ground contact patch. In this embodiment, a tire is used as a sample and the method is described in the context of estimating tire wear. However, it should be understood that the functionality described in this context can also be used for other samples, such as predicting the wear of shoe soles, rubber seals, especially rubber seals that are part of a rotating system, or any other rubber compound.

[0026] The tire 110 is segmented into a number of finite elements (=segments), for example segments 122 and 124. At contact patch 130, the tire 110 is in contact with the road surface 140. As the tire 110 moves in the indicated direction of travel 150, it begins to roll on the road surface 140, and after a time interval, segment 126 encounters the road surface 140 and thus becomes part of the road surface 140. Similarly, segment 128, which is initially in contact with the road surface 140, is lifted off the road and therefore moves off the road surface 130. Thus, during the rolling of the tire 110, the tire segments first encounter the road surface 140, then move through the road surface 140, and finally are lifted off the road surface 140 and move off the road surface 130.

[0027] When the segment encounters the road surface 140, i.e., at the very front of the contact patch 130, the segment does not move substantially relative to the road surface 140. Only as the segment approaches the very rear edge of the contact patch 130 does the segment begin to move relative to the road surface 140, i.e., the segment begins to slide on the surface.

[0028] Therefore, the contact patch can be divided into a contact region 132 where the segments do not move relative to the road surface, and a sliding region 134 where the segments move relative to the road surface.

[0029] Generally, when the tire is not moving, there is no movement relative to the road surface, and therefore the complete contact patch consists of one contact area 132 and no sliding area 134. As the tire begins to move, sliding areas 134 begin to form in the contact patch, and therefore the contact area 132 becomes smaller. Thus, as the rolling speed increases, the sliding area 134 becomes larger and the contact area 132 becomes smaller. The width of the contact area 132 can then be characterized as the critical sliding distance (CSD), i.e., the distance at which the adhesive portion of the sliding phenomenon begins to become irrelevant for calculating the accumulated wear energy per unit distance; therefore, after that threshold, the sliding phenomenon shows a constant trend with sliding distance.

[0030] CSD can be used as a new fundamental input for phenomenological models that serve as the basis for tire wear simulations in order to increase the level of confidence in the predictions provided by the simulations.

[0031] FIG. 2 shows a slide surface 210 across which a sample is slid over a small section to determine CSD according to the present disclosure.

[0032] 2 shows a sliding surface 210. A sample 220 is provided on the sliding surface 210, for example, at a starting position 230. In some embodiments, the sample 220 can be a rubber sample. The force F applied to the sliding surface z 240 is applied to the sample. For example, the force is gravity F z The force can be applied by applying a load to the sample such that a force presses the sample 220 against the slide surface 210. In other examples, the force may be applied hydraulically, pneumatically, or mechanically by a motor, e.g., an electric motor. In still other examples, the force may be generated by the weight of the sample, such that no external force needs to be applied.

[0033] Here, the horizontal force F xA horizontal force 250 can be applied to the sample, and the sample 220 is moved along the sliding surface 210 in a first section with a small width w1 until it reaches a second position 232. In the example shown, the small width w1 is 4 mm. However, other widths can be used. As shown in FIG. 2 , the lower portion 222 of the sample 220 is deformed by the horizontal force 250 and the friction of the sample 220 on the sliding surface 210, while the upper portion 224 of the sample 220 remains substantially undeformed. The deformation increases as long as the static friction force exceeds the sliding friction force. At the point of maximum deformation, the sliding friction force begins to exceed the static friction force, and the sample 220 begins to slide along the sliding surface 210. The sample 220 is then slid until it reaches the second position 232. Here, the sample may be stopped, the force 240 may be released to allow the deformation of the sample to disappear, and then the same procedure may be repeated after re-applying the force 240, causing the sample 220 to slide a second section of equal width w1 until it reaches a third position 234. This procedure may be repeated multiple times until the sample 220 reaches an end position 236.

[0034] In the above examples, the sample may be slid over the entire slide surface in multiple sections. In some examples, the sample may only be slid over a portion of the slide surface in one or more steps. In some examples, the sample may be slid over the same portion of the slide surface multiple times.

[0035] FIG. 3 shows a graph 300 illustrating the change in coefficient of friction over sliding time for sliding on a small section w1 as shown in FIG.

[0036] The abscissa of the graph 300 indicates the sliding time from one position to the next in the section w1, as shown in FIG. 2. The ordinate of the graph 300 indicates the respective coefficients of friction μ at the respective times. The coefficient of friction is determined by the horizontal force F x and normal force F z μ=F x / F zEach line on the graph shows the change in friction for one of the sections with width w1. The lines show the increasing friction over time until the break-off point 310. Beyond the break-off point 310, the friction coefficient drops slightly and then exhibits a substantially constant behavior. Thus, prior to the break-off point, there is an adhesion region 320 where the adhesion contribution exceeds the friction contribution, and a slip region 330 where the friction contribution exceeds the adhesion contribution.

[0037] FIG. 4 shows a slide surface 410 across which a sample is slid over a large distance to determine CSD according to the present disclosure.

[0038] 4 shows a sliding surface 410. A sample 420 is provided on the sliding surface 410, for example, at a starting position 430. In some embodiments, the sample 420 can be a rubber sample. The force F applied to the sliding surface 410 z 440 is applied to the sample 420. For example, the force 440 is the force of gravity F z This can be achieved by applying a load to the sample 420 so that the sample 420 is pressed against the sliding surface 410 .

[0039] Here again, the horizontal force F xA horizontal force 450 can be applied to the sample, and the sample 420 is slid along the sliding surface 410 in a first section at a larger width w2 until a second position 432 is reached. In the example shown, the larger width w2 is 24 mm. However, other widths can be used. As shown in FIG. 4 , the lower portion 422 of the sample 420 is deformed by the horizontal force 450 and the friction of the sample 420 on the sliding surface 410, while the upper portion 424 of the sample 420 remains substantially undeformed. The deformation increases as long as the static friction force exceeds the sliding friction force. At the point of maximum deformation, the sliding friction force begins to exceed the static friction force, and the sample 420 begins to slide. The sample 420 is then slid until the second position 432 is reached. Here, the sample may be stopped, force 440 may be removed to release the deformation of the sample, and then the same procedure may be repeated after reapplying force 440, causing sample 420 to slide a second section of equal width w2 until it reaches third position 434. This may be repeated multiple times until sample 420 reaches end position 436.

[0040] FIG. 5 shows a graph 500 illustrating the change in coefficient of friction over sliding time for sliding over a large section such as that shown in FIG.

[0041] As in Figure 3, in Figure 5, each line in graph 500 shows the change in friction for one of the sections having width w1. The lines show the increasing friction over time until break-off point 510. Beyond break-off point 510, the friction coefficient drops slightly and remains substantially constant. Thus, prior to break-off point 510, there is an adhesion region 520 where the adhesion contribution exceeds the friction contribution, and a slippage region 530 where the friction contribution exceeds the adhesion contribution.

[0042] Compared to graph 300 in Figure 3, graph 500 shows a breakaway point at approximately the same time as graph 300. However, because sample 420 in the case shown in Figure 4 moves much further than in the case shown in Figure 2, slip region 530 in Figure 5 is wider compared to slip region 330 in Figure 3. This therefore means that the adhesion-to-slip ratio of sample 220 / 420 is a function of sliding distance. A longer sliding distance results in a smaller contribution from adhesion region 320 / 520 compared to the contribution from slip region 330 / 530.

[0043] Since wear only occurs when there is relative movement (sliding) between the contacting bodies, this means that the wear rate (=total mass loss per unit sliding distance) is also a function of the section width: the shorter the section width, the lower the wear rate due to the larger contribution of adhesive areas, but by increasing the section width, adhesive areas become less important and the wear rate increases up to a virtually constant value. From this phenomenon, the CSD can be defined as the section width beyond which adhesive areas become negligible, i.e., the wear rate becomes constant. Therefore, the CSD can be determined by the method described below.

[0044] In the above examples, the sample may be slid over the entire slide surface in multiple sections. In some examples, the sample may only be slid over a portion of the slide surface in one or more steps. In some examples, the sample may be slid over the same portion of the slide surface multiple times.

[0045] FIG. 6 shows a flowchart of a method 600 for determining the CSD of a sample according to the present disclosure.

[0046] At 610, a force is applied to the sample toward the slide. In some embodiments, the sample can be a rubber sample. For example, the force can be a force of gravity F zThe normal force can be applied by applying a load to the sample such that the force pushes the sample toward the slide. In other examples, the force may be applied hydraulically, pneumatically, or mechanically by a motor, such as an electric motor, or in some other manner. In some examples, the force may be applied solely by the gravity of the sample itself, without any additional external force. The force toward the slide ensures adhesion between the sample and the slide. In some examples, the force may be varied throughout the experiment, and in other examples, the force may be kept constant over the course of the experiment. Because the normal force also generates a contact pressure proportional to the force, the magnitude of the force can be expressed in terms of the magnitude of the contact pressure generated by the normal force.

[0047] At 620, the sample is slid n times along the sliding surface along multiple sections, the multiple sections having different widths w, where n is an integer greater than or equal to 1. As described elsewhere herein, the sample can be slid on the sliding surface in sections of small width w1 (as described with reference to FIGS. 2 and 3), and then the sample can be slid on the sliding surface in sections of larger width w2 (as described with reference to FIGS. 4 and 5). For each section width, the sample can be slid in n steps over the total sliding distance, so that the total sliding distance for the ith section width is (n*w i )

[0048] In some instances, the sample may be slid over the entire slide surface in multiple sections. In some instances, the sample may only be slid over a portion of the slide surface in one or more steps. In some instances, the sample may be slid over the same portion of the slide surface multiple times.

[0049] In a preferred embodiment, the total sliding distance (n*w i ) is the width of all sections w i For example, the sample may be sampled n=6 times along a section of width w1=4 mm, then n=4 times along a section of width w2=6 mm, then n=3 times along a section of width w3=8 mm, etc. i ) is all wi About (n*w i ) = 24 mm. This setting can increase the comparability of the results by providing similar sliding conditions.

[0050] In some embodiments, the widths w of the sections i can divide the total length of the sliding surface by an integer.

[0051] In some embodiments, the method 600 includes: i The sample is slid over multiple sections of width w i The method may further include weighing the sample before and after sliding over n sections to obtain a weight difference ΔM, and determining a wear rate based on the weight difference ΔM and the total sliding distance.

[0052] In some embodiments, the force can be released after sliding the sample along one of the sections, and the force can be reapplied before sliding the sample along a subsequent section, allowing deformation of the sample to resolve between subsequent sliding steps.

[0053] In some embodiments, the sample can be slid along the slide surface at a substantially constant speed, which can increase the comparability of results. Furthermore, this allows for a speed series to be performed to examine the effect of speed on CSD.

[0054] In some embodiments, the method 600 may further include identifying a first distance at which the static friction force exceeds the sliding friction force, identifying a second distance at which the sliding friction force exceeds the static friction force, and determining the CSD further based on the first distance.

[0055] At 630, for each section width, a respective wear rate is determined. The wear rate for the ith section width is m(w i )=ΔM / (n*w i ) and ΔM is the interval width wi The difference in weight of the sample after sliding the sample n times over a period of time is compared to the weight before sliding.

[0056] (n*w i In the preferred embodiment of paragraph

[0058] , where m(w) is constant, the wear rate m(w) is directly proportional to the (absolute) weight difference ΔM.

[0057] In some embodiments, method 600 can further include providing a sliding surface having a total length, sliding a sample on the sliding surface multiple times at each step of a plurality of widths w, and measuring multiple wear rates for each of the plurality of widths w.

[0058] At 640, the CSD is determined based on a plurality of wear rates m(w) and their respective widths. Specifically, the CSD is determined as a width w0, and for any w greater than w0, is as follows:

[0059]

number

[0060] In some embodiments, the CSD can be determined based on any one of the sample geometry, the sample material properties, the sliding surface texture, the amount of force, the amount of sliding speed, the amount of acceleration to reach the set sliding speed, and the sample temperature, thereby enabling more accurate prediction of tire wear by using each determined CSD as an input for a tire wear simulation model.

[0061] In some examples, different rubber samples can be used to determine different CSD values. In some other examples, different substrates can be used to determine substrate-dependent CSD. In still other examples, different sliding speeds can be used to determine speed dependence of CSD. Preferably, a sliding speed of 1 mm / s to 5000 mm / s can be used. More preferably, a sliding speed of 5 mm / s to 1000 mm / s can be used. Most preferably, a sliding speed of about 5 mm / s can be used.

[0062] In some instances, different contact pressures can be used to determine the load dependence of CSD. As noted above, the magnitude of the contact pressure is proportional to the magnitude of the normal force. Preferably, a contact pressure of 1 bar to 20 bar can be used. More preferably, a contact pressure of 2 bar to 4 bar can be used. Most preferably, a contact pressure of about 3 bar can be used.

[0063] Figure 7 shows the CSD at different widths, w i 7 shows a graph 700 showing the wear rate m(w) versus the surface area.

[0064] The abscissa of the graph 700 shown in FIG. 7 indicates different section widths in [mm]. Each ordinate indicates a constant sliding distance (n*w i ) in units of [mg]. The graph shows two lines, both of which are equal except for the horizontal shift. The first graph, designated "nominal distance," shows the interval width corresponding to the movement of the upper portion 224 / 424 of the sample 220 / 420. The second graph, designated "actual distance," is shifted horizontally by the maximum deformation of the sample. Thus, the second graph corresponds to the movement of the contact surface of the lower portion 222 / 422 of the sample 220 / 420 on the sliding surface. The CSD is determined by the "actual distance," i.e., by the movement of the contact surface of the sample.

[0065] From graph 700, it can be seen that the line exhibits bilinear behavior with a distinct knee 710 at a particular value of section width, beyond which mass loss remains substantially constant with increasing section width. The width at which knee 710 is located thus corresponds to the CSD.

[0066] FIG. 8 shows the results of the different rubber compounds A, B, C, and D and different widths w i 8 shows a graph 800 illustrating the wear rate m(w) versus the surface area.

[0067] The abscissa of the graph 800 shown in FIG. 8 indicates different section widths in [mm]. Each ordinate indicates a constant sliding distance (n*w i ) in units of [mg]. Graph 800 includes four lines, labeled A, B, C, and D. Each line represents a measurement using a different rubber compound with different physical properties. Each measurement corresponds to the method described in Figures 2-6. The different compounds differ from each other in terms of stiffness, friction, and wear characteristics and were tested by maintaining the same sample geometry (rounded block). It can be seen that the initial slope of the curve is different for different materials and therefore different CSDs can be determined for different rubber compounds. For rubber part A, inflection 810 corresponds to a CSD of approximately 5 mm. For rubber part B, inflection 820 corresponds to a CSD of approximately 3 mm. For rubber part C, inflection 830 corresponds to a CSD of approximately 5 mm. For rubber part D, inflection 840 corresponds to a CSD of approximately 5 mm.

[0068] This allows for different wear performances. Generally, rubber compounds with a longer CSD result in lower wear rates. At the same time, the saturation level affects the overall wear of the tire, as it corresponds to the wear rate that occurs after each CSD is exceeded. Thus, rubber compound A has the highest CSD, but also the highest wear rate after the CSD is exceeded.

[0069] Figure 9 shows the CSD at different widths, w iand a graph 900 showing the wear rate m(w) for different sample geometries from the same rubber compound.

[0070] The abscissa of the graph 900 shown in FIG. 9 indicates different section widths in [mm]. Each ordinate indicates a constant sliding distance (n*w i ) in units of mg. Graph 900 shows four lines, each corresponding to a different sample shape, but all shapes formed from the same rubber compound. Each measurement using a different sample shape corresponds to the method described in Figures 2-6. The line for wheel shape 910 shows a bend 912 corresponding to a CSD of approximately 5 mm. The line for plain shape 920 shows a bend 922 corresponding to a CSD of approximately 12 mm. The line for lug shape 930 shows a bend 932 corresponding to a CSD of approximately 20 mm. The line for sipe shape 940 shows a bend 942 corresponding to a CSD of approximately 30 mm.

[0071] This allows for different wear performance. Generally, sample shapes exhibiting a longer CSD result in a lower wear rate. At the same time, the saturation level corresponds to the wear rate that occurs beyond each CSD, thus affecting the overall wear of the tire. Thus, sipe shape 940 has the largest CSD, but also the largest wear rate beyond the CSD.

[0072] FIG. 10 shows a flowchart 1000 of a computer-implemented method for estimating tire wear according to the present disclosure.

[0073] At 1010, a wear model is provided. The wear model can be configured to convert friction energy rate to wear. The wear model can be based on moving parts and non-moving parts. Moving parts can cause more wear than non-moving parts.

[0074] In some examples, the non-moving parts experience substantially no wear, which increases the simplicity of the computer-implemented method, thus allowing for savings in computational resources, while providing an accurate representation of realistic physical conditions.

[0075] At 1020, the tire contact patch is divided into moving and non-moving portions, where the non-moving portions do not exhibit substantial movement relative to the tire substrate, and in contrast, the moving portions can exhibit movement relative to the tire substrate.

[0076] In some examples, the non-moving portion can have a first width and the CSD can be proportional to the first width, which can improve the accuracy of the wear prediction provided by the computer-implemented method.

[0077] In some examples, the CSD can be determined prior to performing the computer-implemented method. In some examples, the CSD can be used as an input variable for the computer-implemented method.

[0078] In some examples, the CSD can be determined according to the method described in FIGS.

[0079] In some instances, multiple CSD values ​​can be used as input variables for a computer model. For example, different CSD values ​​can be used as input variables for different amounts of velocity. In other instances, different CSD values ​​can be used for different amounts of acceleration, different amounts of normal force, or different temperatures of the sample.

[0080] Using CSD as input to computer-implemented methods improves the quality of tire wear predictions by providing a more accurate model of how tire wear actually occurs.

[0081] At 1030, tire wear is estimated based on the wear model and the segmented contact patch.

[0082] In the following, an exemplary algorithm for estimating tire wear is described. The algorithm may be based on the finite element method (FEM), which may include geometric and / or material data of the simulated tire. To perform the method, the simulated tire may be discretized into a plurality of finite elements as described with respect to FIG. 1. Each finite element may be characterized by a set of nodes representing degrees of freedom in the model.

[0083] The following experimental data can be used as input parameters for the algorithm: Friction maps as a function of pressure, velocity, and temperature ●Critical slip distance (CSD) ●Abrasion parameters of rubber materials

[0084] For each node, we may require the following quantities as output from the simulation: ●Pressure ●Speed ●Slip

[0085] The finite elements can be represented by a finite element mesh 1110 as shown in Figure 11. The finite element mesh 1110 includes a number of contact elements represented by quadrilaterals. In this example, at a given time t n In Fig. 1, nodes 1120 and 1128 are not in contact with the road surface. Nodes 1121-1124 are in contact with the road surface and do not move relative to the road surface, i.e., they adhere to the road surface. Nodes 1125, 1126, and 1127 are also in contact with the road surface and move relative to the road surface, i.e., they slide on the road surface. Therefore, they exhibit nodal pressure p (p>0) and slide (γ>0).

[0086] Each node 1121-1127 that is in contact with the road surface has a corresponding node area. Illustrated in Figure 11 are node area 1135 of node 1125 and node area 1136 of node 1126. However, all other nodes that are in contact with the road also have corresponding node areas A. n It should be understood that

[0087] From the node data, we can define the corresponding friction stress τ. For the i-th node, the friction stress τ i can be defined as follows:

[0088]

number

[0089]

number

[0090]

number

[0091]

number

[0092] For closely-coupled nodes,

[0093]

number

[0094] In the transient framework, the nodal slippage γ for each node can be a direct output of the simulation framework and can be used to determine which part of the bilinear model is applied to each node. In the following, we also refer to the CSD as γ cr In this way, the friction energy rate can be calculated using the scaling factor f i The wear energy rate can be reduced by

[0095]

number

[0096]

number

[0097]

number

[0098] From the wear energy rate, the mass loss rate per node is calculated as follows:

[0099]

number

[0100]

number

[0101]

number

[0102] To generalize this to the full width of the tire, we can assume that the total wear is the sum of all the mass losses calculated at the nodes.

[0103] Therefore, the energy rate used in the wear phenomenon is calculated based on the nodal slip and critical slip distances obtained from the experiment, using the coefficient f i (γ) can be obtained.

[0104] Finally, the wear energy rate can be applied to the wear model to calculate the mass loss rate (or volume loss rate, depending on the units used) applied to the node. That is, the output of the framework makes it possible to evaluate the amount of mass worn off per unit time at all contacting nodes. This data can be further used to estimate mileage, evaluate irregular tread wear, and compare performance between geometries, materials, and rolling conditions, among others.

[0105] FIG. 12 shows a graph 1200 comparing the accuracy of a standard simulation that does not consider CSD with the accuracy of a simulation that does consider CSD.

[0106] The ordinate of graph 1200 shows the rank of the wear rate performance for different rubber compounds A, B, C, and D, as described with reference to FIG. 8. The wear rate performance in graph 1200 is given in units of [%] relative to compound C, with compound C corresponding to a value of 100%. The abscissa of graph 1200 shows the wear rate performance obtained in a preliminary wear test of the tire performed by the manufacturer, also in units of [%] relative to compound C. The data shown as circles represent the relationship between the experimental ranking and the simulation without CSD. The dotted line 1210 is the Pearson correlation coefficient squared R 2=0.6892. There is a significant discrepancy between data points 1216 and 1217 corresponding to compounds B and D and the respective simulation data, indicating poor quality of correlation.

[0107] The data shown in the squares represent the simulation results taking CSD into account. The dotted line 1220 represents the squared R of the Pearson correlation coefficient. 2 = 0.9417. As can be seen, when CSD is considered in the simulation, an increase in the experimental wear rate performance also leads to an increase in the simulated wear rate performance. As can be further seen from graph 1200, when CSD is considered in the simulation, the discrepancy between the experimental and simulated data is much lower and the quality of the correlation is higher.

Claims

1. 1. A method for determining the critical sliding distance (CSD) of a sample, comprising: applying a force to the sample toward a sliding surface; Sliding the sample n times along the sliding surface in a plurality of sections, the plurality of sections having different widths w, where n is an integer equal to or greater than 1; Each width w ｉ For each of the multiple wear rates m(w), ｉ ) = ΔM / (n * w ｉ ) wherein ΔM is the width w ｉ is a weight difference of the sample after sliding the sample over n sections compared to before sliding; Based on the plurality of wear rates and the respective widths, the CSD is divided into widths w ０ and determining as follows: ０ and [Equation 1]

2. The width w of the plurality of sections ｉ 2. The method of claim 1, wherein r divides the total length of the sliding surface by an integer.

3. Each width w ｉ Sliding the sample over a plurality of sections; Width w ｉ Obtaining the weight difference ΔM by weighing the sample before and after sliding in n sections; determining the wear rate based on the weight difference ΔM and the total sliding distance; The method of claim 1 or 2, further comprising:

4. The total sliding distance is the width w ｉ 4. The method of claim 3, wherein each of

5. the force is released after sliding the sample along each of the sections; The force is applied again before sliding the sample along a subsequent section. The method according to claim 3 or 4.

6. The sample is slid along the sliding surface at a substantially constant speed.

6. The method according to any one of claims 1 to 5.

7. Identifying a first distance at which the static friction force exceeds the sliding friction force; identifying a second distance at which the sliding friction force exceeds the static friction force; determining the CSD further based on the first distance; 7. The method of claim 1, further comprising:

8. providing a sliding surface having an overall length; Sliding the sample on the sliding surface a plurality of times at each step of the plurality of widths w; measuring the plurality of wear rates for each of the plurality of widths w; 8. The method of claim 1, further comprising:

9. The CSD is the geometry of the sample; material properties of said sample; a texture of the sliding surface; the amount of force, The amount of speed of the sliding; the amount of acceleration to reach the set sliding speed, and The method of claim 1 , wherein the temperature of the sample is measured based on any one of the following:

10. 1. A computer-implemented method for estimating tire wear, the method comprising: providing a wear model of the tire configured to convert frictional energy rate into wear, the wear model is based on moving and non-moving parts, the moving parts causing greater wear than the non-moving parts; Dividing the tire contact surface into a movable portion and a non-movable portion, the non-movable portion exhibits substantially no movement relative to the tire substrate; the movable part exhibits movement relative to the tire substrate; and estimating the wear of the tire based on the wear model and the segmented contact patch; 10. A computer-implemented method comprising:

11. The method of claim 10 , wherein the non-moving part exhibits substantially no wear.

12. The non-movable portion has a first width. a critical sliding distance (CSD) proportional to the first width; 12. The method according to claim 10 or 11.

13. the CSD is determined experimentally prior to performing the computer-implemented method; the CSD is used as an input variable of the computer-implemented method; The method of claim 12.

14. 14. The method of claim 12 or 13, wherein the CSD is determined according to a method according to any one of claims 1 to 10.

15. The method of any one of claims 10 to 14, wherein the computer-implemented method is based on the finite element method (FEM).

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