Method for evaluating critical slip distance

Abstract

The present disclosure relates to a method for determining a critical slip distance (CSD) for a sample, the method comprising: providing a force towards a sliding surface to the sample; sliding the sample along the sliding surface n times within a plurality of intervals, the plurality of intervals having different widths w, n being an integer > = 1; determining, for each width wi, a respective wear rate m (w) of a plurality of wear rates m (w) = [Delta] M / (n * wi), where [Delta] M is the weight difference of the sample after sliding the sample over n intervals of width wi compared to before the sliding; and determining the CSD as width w0 based on the plurality of wear rates and corresponding widths, where for any (I), # imgabs0 #

Description

Technical Field

[0001] The present disclosure generally relates to a method for determining a critical slip distance (CSD) for a sample. The method can be used, for example, to evaluate tire wear by determining the critical slip distance of a tire contact patch. Background Art

[0002] Tire-level wear experiments are complex and expensive. Several methods for predicting wear performance are described in the prior art. In particular, simulations are commonly used for this purpose, but the appropriate inputs related to actual contact conditions and the abrasive characteristics of the material must be properly evaluated in order to appropriately calculate the energy that causes wear and obtain reliable results from the simulation.

[0003] In particular, the basic input required for wear simulation is the "critical slip distance" (CSD), i.e., the distance at which the tread blocks show a constant wear rate, which cannot be simply and intuitively provided by standard friction and abrasion tests.

[0004] Currently, the friction and abrasion characterization of materials is carried out by sliding tests on small rubber wheels, which do not provide any information about actual contact conditions, or by using a linear friction tester with rubber blocks that are tested in a full-sliding mode. In any case, these types of tests do not provide any information about the CSD.

[0005] For this purpose, a new method for determining the CSD by performing linear friction tests on rubber samples under different test conditions has been specifically designed. Summary of the Invention

[0006] According to a first aspect, the present disclosure provides a method for determining a critical slip distance (CSD) for a sample. The method includes: applying a force to the sample towards a sliding surface. The method also includes: sliding the sample n times along the sliding surface in a plurality of intervals having different widths w, where n is an integer ≥ 1; for each width w i , determining the corresponding wear rate m(w i ) = ΔM / (n * w i ), where ΔM is the weight difference of the sample after sliding the sample in the n intervals of width w i ; and determining the CSD as width w0 based on the plurality of wear rates and the corresponding widths, where for any w > w0

[0007]

[0008] According to an example of the first aspect, the width w of the plurality of intervals iis an integer divisor of the total length of the sliding surface.

[0009] According to another example of the first aspect, the method may further include: sliding the sample in a plurality of intervals of each width w i to obtain a weight difference ΔM by weighing the sample before and after sliding in n intervals of width w i and determining the wear rate based on the weight difference ΔM and the total sliding distance.

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

[0011] According to another example of the first aspect, for each of these widths w i the total sliding distance is equal.

[0012] According to another example of the first aspect, the lifting force is increased after sliding the sample along each of these intervals and the force is reapplied before sliding the sample along a subsequent interval.

[0013] According to another example of the first aspect, the sample slides 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 exceeds the sliding friction, identifying a second distance at which the sliding friction exceeds the static friction, and further determining the CSD 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 the sample multiple times on the sliding surface in steps of each width of a plurality of widths w, and measuring the 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 of the following: the geometry of the sample, the material properties of the sample, the texture of the sliding surface, the amount of the force, the amount of the sliding speed, the amount of the acceleration to reach a set sliding speed, and the temperature of the sample.

[0017] According to a second aspect, the present disclosure provides a computer-implemented method for estimating tire wear. The method includes: providing a wear model of the tire, the wear model being configured to convert a friction energy rate into wear, wherein the wear model is based on a movable part and a non-movable part, and wherein the movable part provides higher wear compared to the non-movable part; dividing a contact surface of the tire into the movable part and the non-movable part, wherein the non-movable part exhibits substantially no movement relative to a base of the tire, and wherein the movable part exhibits movement relative to the base of the tire; estimating the wear of the tire based on the wear model and the divided contact surface.

[0018] According to an example of the second aspect, the non-movable part provides substantially no wear.

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

[0020] According to another example of the second aspect, the CSD is experimentally determined before 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). Description of the Drawings

[0023] Figure 1 Illustrates a tire in a contact area segmented for wear simulation, and the division of the contact surface of the tire into viscous and sliding parts.

[0024] Figure 2 Illustrates a sliding surface on which a sample slides at small intervals in order to determine the CSD according to the present disclosure.

[0025] Figure 3 Illustrates a graph showing the development of the coefficient of friction over sliding time while sliding at small intervals as depicted in Figure 2 is described.

[0026] Figure 4 Illustrates a sliding surface on which a sample slides at large intervals in order to determine the CSD according to the present disclosure.

[0027] Figure 5 Illustrates a graph showing the development of the coefficient of friction over sliding time while sliding at large intervals as depicted in Figure 4 is described.

[0028] Figure 6 Illustrates a flow chart of a method for determining CSD for a sample according to the present disclosure.

[0029] Figure 7 Illustrates a graph showing the wear rate m(w) for different widths w i including an inflection point characterizing the CSD.

[0030] Figure 8 Illustrates a graph showing the wear rate m(w) for different widths w i including an inflection point characterizing the CSD and for different rubber compounds A, B, C, and D.

[0031] Figure 9 Illustrates a graph showing the wear rate m(w) for different widths w i including an inflection point characterizing the CSD and for different sample shapes from the same rubber compound.

[0032] Figure 10 Illustrates a flow chart of a computer-implemented method for estimating tire wear according to the present disclosure.

[0033] Figure 11 Illustrates a finite element mesh as may be used in a computer-implemented method according to the present disclosure.

[0034] Figure 12 Illustrates a graph comparing the accuracy of a standard simulation not considering CSD with the accuracy of a simulation considering CSD. Detailed Description

[0035] The present disclosure provides a method for determining CSD for a sample and a computer-implemented method for estimating tire wear.

[0036] Figure 1 Illustrates a tire segmented in a contact area for wear simulation based on the finite element method (FEM), and the division of the contact surface of the tire into viscous and sliding portions. In the present embodiment, the tire is used as a sample, and the method is explained 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 (specifically rubber seals that are part of a rotating system), or any other rubber compound.

[0037] The tire 110 is segmented into a plurality of finite elements (= segments), such as segments 122 and 124. At the contact surface 130, the tire 110 contacts the road surface 140. When the tire 110 travels in the indicated travel direction 150, it begins to roll on the road surface 140 such that after a time interval, segment 126 will encounter the road surface 140 and will thus become part of the contact surface 130. Similarly, segment 128 that is initially in contact with the road surface 140 will lift from the road and will thus move out of the contact surface 130. Thus, during the rolling of the tire 110, the tire segments will first encounter the road surface 140, then will move through the contact surface 130, and will finally lift from the road surface 140 and leave the contact surface 130.

[0038] When encountering the road surface 140, i.e., in the foremost part of the contact surface 130, the segment does not experience substantial movement relative to the road surface 140. Only when the segment approaches the rearmost end of the contact surface 130 does the segment begin to experience some movement relative to the road surface 140, i.e., the segment will begin to slide on the road surface.

[0039] Thus, the contact surface can be divided into a viscous region 132 where the segment does not experience movement relative to the road surface and a sliding region 134 where the segment experiences movement relative to the road surface.

[0040] Typically, when the tire is not moving, there is no movement relative to the road surface, so the complete contact surface consists of a single viscous region 132 and there is no sliding region 134. As the tire begins to move, a sliding region 134 begins to form at the contact surface and the viscous region 132 thus becomes smaller. Thus, as the rolling speed increases, the sliding region 134 becomes larger and the viscous region 132 becomes smaller. Then, the width of the viscous region 132 can be characterized as the critical slip distance (CSD), i.e., the distance at which the adhesive part of the sliding phenomenon begins to become irrelevant to the calculation of the cumulative wear energy per unit distance, and thus after this threshold, the sliding phenomenon shows a constant trend relative to the sliding distance.

[0041] The CSD can be used as a new fundamental input for a phenomenological model that serves as the basis for tire wear simulation to increase the level of reliability of the predictions provided by the simulation.

[0042] Figure 2 A sliding surface 210 is illustrated in which samples slide at small intervals to determine the CSD according to the present disclosure.

[0043] Figure 2Depicts a sliding surface 210. On the sliding surface 210, for example, in the starting position 230, a sample 220 is provided. In some aspects, the sample 220 can be a rubber sample. A force F is provided to the sample towards the sliding surface z 240. For example, the force can be provided by applying a load to the sample such that the gravitational force F z presses the sample 220 against the sliding surface 210. In other examples, the force can be applied hydraulically, pneumatically, or mechanically by a motor (e.g., an electric motor). In still other examples, the force can be generated by the weight of the sample itself such that no external force needs to be applied.

[0044] Now, a horizontal force F x 250 can be provided to the sample such that the sample 220 moves along the sliding surface 210 within a first interval of a small width w1 until it reaches the second position 232. In the example depicted herein, the small width w1 is 4 mm. However, other widths can be used. As Figure 2 illustrated, the lower portion 222 of the sample 220 undergoes deformation due to 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. As long as the static friction exceeds the sliding friction, the deformation increases. At the maximum deformation point, the sliding friction begins to exceed the static friction such that the sample 220 begins to slide along the sliding surface 210. Then, the sample 220 slides until it reaches the second position 232. Here, the sample can be stopped, the force 240 can be lifted to relieve the deformation of the sample, and then the force 240 can be reapplied before repeating the same process, and the sample 220 can slide within a second interval of an equal width w1 until it reaches the third position 234. This process can be repeated multiple times until the sample 220 reaches the end position 236.

[0045] In the above example, the sample can slide across the entire sliding surface in multiple intervals. In some examples, the sample can slide only on a portion of the sliding surface in one or more steps. In some examples, the sample can slide multiple times on the same portion of the sliding surface.

[0046] Figure 3 Illustrates a graph 300 that shows the development of the coefficient of friction over time as the sample slides over a small interval w1 as Figure 2 depicted.

[0047] The abscissa of the graph 300 shows the sliding time from one position to the next within the interval w1 as Figure 2 depicted. The ordinate of the graph 300 shows the corresponding coefficient of friction μ for the corresponding time. The coefficient of friction can be defined as the ratio between the horizontal force F x and the vertical force F z such that μ = Fx / F z Each line in the curve graph shows the development of the friction of one interval in an interval having a width w1. These lines show that the friction increases over time until the break point 310. Beyond the break point 310, the coefficient of friction slightly decreases and then shows a substantially constant behavior. Thus, before the break point, there is an adhesion zone 320 and a slip zone 330, where the adhesion contribution exceeds the friction contribution in the adhesion zone and the friction contribution exceeds the adhesion contribution in the slip zone.

[0048] Figure 4 The sliding surface 410 is illustrated, and the sample slides in a large interval among the sliding surfaces to determine the CSD according to the present disclosure.

[0049] Figure 4 The sliding surface 410 is depicted. On the sliding surface 410, for example, in the starting positioning 430, the sample 420 is provided. In some aspects, the sample 420 can be a rubber sample. A force F is provided to the sample 420 towards the sliding surface 410 z 440. For example, the force 440 can be provided by applying a load to the sample 420 such that the gravitational force F z presses the sample 420 onto the sliding surface 410.

[0050] Now, similarly, a horizontal force F can be provided to the sample x 450 such that the sample 420 slides within a first interval of a large width w2 along the sliding surface 410 until it reaches the second positioning 432. In the example depicted herein, the large width w2 is 24 mm. However, other widths can also be used. As Figure 4 illustrated, the lower part 422 of the sample 420 undergoes deformation due to the horizontal force 450 and the friction of the sample 420 on the sliding surface 410, while the upper part 424 of the sample 420 remains substantially undeformed. As long as the static friction exceeds the sliding friction, the deformation increases. At the maximum deformation point, the sliding friction begins to exceed the static friction, causing the sample 420 to start sliding. Then, the sample 420 slides until it reaches the second positioning 432. Here, the sample can be stopped, the force 440 can be lifted to resolve the deformation of the sample, and then the force 440 can be reapplied before repeating the same process, and the sample 420 can slide within a second interval of an equal width w2 until it reaches the third positioning 434. This can be repeated multiple times until the sample 420 reaches the end positioning 436.

[0051] Figure 5 The curve graph 500 is illustrated, which shows the development of the coefficient of friction over the sliding time on a large interval as Figure 4 depicted.

[0052] Similar toFigure 3 , in Figure 5 , each line in graph 500 shows the development of friction for one of the intervals in an interval with width w1. These lines show that the friction increases over time until the break point 510. Beyond the break point 510, the coefficient of friction drops slightly and shows a substantially constant behavior. Thus, before the break point 510, there is an adhesion zone 520 and a slip zone 530, where the adhesion contribution exceeds the friction contribution at the adhesion zone and the friction contribution exceeds the adhesion contribution at the slip zone.

[0053] Compared with Figure 3 graph 300 of Figure 4 , the graph 500 shows a break point at approximately the same time as graph 300. However, since Figure 2 the sample 420 in the case illustrated moves much longer than Figure 5 the sample 220 in the case illustrated, the slip zone 530 of Figure 3 is extensive compared to the slip zone 330 of

[0054] Since abrasion only occurs when there is relative movement (slip) between the contacting bodies, this means that the wear rate (= total mass loss per unit of sliding distance) is also a function of the interval width: for shorter interval widths, the wear rate is lower due to the greater contribution of the adhesion part; while by increasing the interval width, the adhesion part becomes less important and the wear rate increases to a substantially constant value. Based on this phenomenon, the CSD can be defined as the interval width beyond which the adhesion part becomes negligible (i.e., when the wear rate becomes constant). Thus, the CSD can be determined by the method described below.

[0055] In the above example, the sample can slide over the entire sliding surface with multiple intervals. In some examples, the sample can slide over only a part of the sliding surface with one or more steps. In some examples, the sample can slide over the same part of the sliding surface multiple times.

[0056] Figure 6 Illustrates a flowchart of a method 600 for determining the CSD for a sample according to the present disclosure.

[0057] At 610, a force is provided to the sample towards the sliding surface. In some aspects, the sample can be a rubber sample. For example, the force can be provided by applying a load to the sample such that the gravitational force F zPress the sample towards the sliding surface. In other examples, a force may be applied hydraulically, pneumatically, mechanically, or in some other way by a motor (e.g., an electric motor). In some examples, the force may be applied only by the gravity of the sample itself, without any additional external force. The force towards the sliding surface ensures adhesion between the sample and the sliding surface. In some examples, the force may vary during the experiment, and in other examples, the force may remain constant during the experiment. Since the vertical force also generates a contact pressure proportional to the force, the magnitude of the force may be represented by the magnitude of the contact pressure generated by the vertical force.

[0058] At 620, slide the sample along the sliding surface n times within a plurality of intervals having different widths w, where n is an integer greater than or equal to 1. As discussed elsewhere herein, the sample may slide on the sliding surface in intervals of small width w1 (as discussed with reference to Figure 2 and Figure 3 ), and then the sample may slide on the sliding surface in intervals of larger width w2 (as discussed with reference to Figure 4 and Figure 5 ). For each interval width, the sample may slide in n steps over the total sliding distance, so the total sliding distance for the i-th interval width is (n * w i ).

[0059] In some examples, the sample may slide over the entire sliding surface in a plurality of intervals. In some examples, the sample may slide in one or more steps only on a portion of the sliding surface. In some examples, the sample may slide on the same portion of the sliding surface multiple times.

[0060] In a preferred embodiment, the total sliding distance (n * w i ) may be constant for all interval widths w i . For example, the sample may slide along intervals with width w1 = 4 mm n = 6 times, then along intervals with width w2 = 6 mm n = 4 times, then along intervals with w3 = 8 mm n = 3 times, etc., such that at (n * w i ) = 24 mm, for all w i , (n * w i ) is constant. This setting can increase the comparability of the results by providing similar sliding conditions.

[0061] In some aspects, the widths w i of the plurality of intervals may be integer divisors of the total length of the sliding surface.

[0062] In some aspects, method 600 may further include: sliding the sample within a plurality of intervals of each width w i , by sliding within intervals of width w iWeigh the sample before and after it slides within n intervals to obtain the weight difference ΔM, and determine the wear rate based on the weight difference ΔM and the total sliding distance.

[0063] In some aspects, after the sample slides along one of the intervals, the lifting force can be applied, and before the sample slides along a subsequent interval, the force can be reapplied. This allows the deformation of the sample to be resolved between subsequent sliding steps.

[0064] In some aspects, the sample can slide along the sliding surface at a substantially constant speed. This allows for increased comparability of the results. In addition, this allows a speed sequence to be performed to examine the effect of speed on the CSD.

[0065] In some aspects, method 600 may further include: identifying a first distance at which the static friction exceeds the sliding friction, identifying a second distance at which the sliding friction exceeds the static friction, and further determining the CSD based on the first distance.

[0066] At 630, a corresponding wear rate is determined for each interval width. The wear rate for the i-th interval width is defined as m(w i ) = ΔM / (n*w i ), where ΔM is the weight difference of the sample after it slides n times within the interval width w i compared to before the sliding.

[0067] In the preferred embodiment of paragraph

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

[0068] In some aspects, method 600 may further include: providing a sliding surface with a total length, sliding the sample multiple times in steps of each of a plurality of widths w on the sliding surface, and measuring a plurality of wear rates for each of the plurality of widths w.

[0069] At 640, the CSD is determined based on the plurality of wear rates m(w) and the corresponding widths. Specifically, the CSD is determined as the width w0, where for any w greater than w0:

[0070]

[0071] In other words, the CSD is determined as the interval width beyond which the wear rate remains constant as the interval width increases.

[0072] In some aspects, the CSD can be determined based on any of the following: the geometry of the sample, the material properties of the sample, the texture of the sliding surface, the amount of force, the amount of sliding speed, the amount of acceleration to reach a set sliding speed, and the temperature of the sample. This allows for a more precise prediction of tire wear by using the correspondingly determined CSD as an input to a tire wear simulation model.

[0073] 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 some other examples, different sliding speeds can be used to determine the speed dependence of CSD. Preferably, a sliding speed between 1 mm / s and 5000 mm / s can be used. More preferably, a sliding speed between 5 mm / s and 1000 mm / s can be used. Most preferably, a sliding speed of about 5 mm / s can be used.

[0074] In some examples, different contact pressures can be used to determine the load dependence of CSD. As indicated above, the magnitude of the contact pressure is proportional to the magnitude of the vertical force. Preferably, a contact pressure between 1 bar and 20 bar can be used. More preferably, a contact pressure between 2 bar and 4 bar can be used. Most preferably, a contact pressure of about 3 bar can be used.

[0075] Figure 7 Graph 700 is illustrated, which shows the wear rate m(w) for different widths w i including an inflection point characterizing the CSD.

[0076] Figure 7 The abscissa of the illustrated Graph 700 shows different interval widths in units of [mm]. The corresponding ordinate shows the weight loss in units of [mg] over a constant sliding distance (n*w i ). The graph shows two lines that are equal except for an offset in the horizontal direction. The first graph designated as "nominal distance" indicates the interval width corresponding to the movement of the upper part 224 / 424 of the sample 220 / 420. The second graph designated as "actual distance" is offset in the horizontal direction by the maximum deformation of the sample. Thus, the second graph corresponds to the movement of the contact surface on the lower part 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.

[0077] As can be seen from Graph 700, the lines show a bilinear behavior with a well-defined inflection point 710 at a certain value of the interval width, and beyond this inflection point, the mass loss is substantially constant as the interval width increases. Thus, the width at which the inflection point 710 is located corresponds to the CSD.

[0078] Figure 8 Illustrates a graph 800 that shows the wear rate m(w) for different widths w i , including the inflection points that characterize the CSD and for different rubber compounds A, B, C, and D.

[0079] Figure 8 The abscissa of the illustrated graph 800 shows different spacing widths in units of [mm]. The corresponding ordinate shows the weight loss in units of [mg] over a constant sliding distance (n*w i ). The graph 800 includes four lines, designated as A, B, C, and D respectively. Each line represents the measurement of a different rubber compound with different physical properties. The corresponding measurements have been made in accordance with the method described in Figures 2 to 6 . The different compounds differ from each other in terms of stiffness, friction, and abrasion characteristics and have been tested by maintaining the same sample geometry (circular block). It can be seen that the initial slope of the curves is different for different materials, and thus different CSDs for different rubber compounds can be determined. For rubber component A, the inflection point 810 corresponds to the CSD at approximately 5 mm. For rubber component B, the inflection point 820 corresponds to the CSD at approximately 3 mm. For rubber component C, the inflection point 830 corresponds to the CSD at approximately 5 mm. For rubber component D, the inflection point 840 corresponds to the CSD at approximately 5 mm.

[0080] Therefore, different wear performances can be obtained. Generally, a rubber compound showing a longer CSD will result in a lower wear rate. At the same time, the saturation level affects the overall wear of the tire because it corresponds to the wear rate that occurs beyond the corresponding CSD. Thus, although rubber compound A has the largest CSD, it also has the largest wear rate beyond the CSD.

[0081] Figure 9 Illustrates a graph 900 that shows the wear rate m(w) for different widths w i , including the inflection points that characterize the CSD and for different sample shapes from the same rubber compound.

[0082] Figure 9 The abscissa of the illustrated graph 900 shows different spacing widths in units of [mm]. The corresponding ordinate shows the weight loss in units of [mg] over a constant sliding distance (n*w i ). The graph 900 shows four lines, each corresponding to a different sample shape, while all shapes are formed from the same rubber compound. The corresponding measurements of the samples with different shapes have been made in accordance with Figures 2 to 6The lines for the shape of the wheel 910 show an inflection point 912 corresponding to a CSD of approximately 5 mm. The lines for the shape of the plane 920 show an inflection point 922 corresponding to a CSD of approximately 12 mm. The lines for the shape of the lug 930 show an inflection point 932 corresponding to a CSD of approximately 20 mm. The lines for the shape of the tread pattern 940 show an inflection point 942 corresponding to a CSD of approximately 30 mm.

[0083] Accordingly, different wear performances can be obtained. Generally, the sample shapes showing longer CSDs will 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 occurring beyond the corresponding CSD. Accordingly, although the tread pattern shape 940 has the largest CSD, it also has the largest wear rate beyond the CSD.

[0084] Figure 10 Flowchart 1000 illustrating a computer-implemented method for estimating the wear of a tire according to the present disclosure.

[0085] At 1010, a wear model is provided. The wear model can be configured to convert a friction energy rate into wear. The wear model can be based on a movable part and a non-movable part. The movable part can provide higher wear compared to the non-movable part.

[0086] In some examples, the non-movable part provides substantially no wear. This example provides increased simplicity of the computer-implemented method and thus allows for savings in computing resources while providing an accurate representation of realistic physical conditions.

[0087] At 1020, the contact surface of the tire is divided into a movable part and a non-movable part. The non-movable part exhibits substantially no movement relative to the base of the tire. In contrast, the movable part can exhibit movement relative to the base of the tire.

[0088] In some examples, the non-movable part can have a first width, and the CSD can be proportional to the first width. This allows for increased accuracy of the wear prediction provided by the computer-implemented method.

[0089] In some examples, the CSD can be determined before performing the computer-implemented method. In some examples, the CSD can be used as an input variable of the computer-implemented method.

[0090] In some examples, the CSD can be determined according to the method as Figures 2 to 6 described in.

[0091] In some examples, multiple CSD values can be used as input variables for a computer model. For example, different CSD values for different amounts of speed can be used as input variables. In other examples, different CSD values for different amounts of acceleration, different amounts of vertical force, or samples at different temperatures can be used.

[0092] Using CSD as an input value for a computer-implemented method improves the quality of the prediction of tire wear. This is achieved by providing a more accurate model of how tire wear occurs in reality.

[0093] At 1030, the wear of the tire is estimated based on the wear model and the divided contact surface.

[0094] Below, an exemplary algorithm for estimating tire wear is described. The algorithm can be based on the finite element method (FEM), which can include geometric data and / or material data for simulating the tire. To perform the method, the simulated tire can be discretized into multiple finite elements as described with respect to Figure 1 Each finite element can be characterized by a set of nodes that represent the degrees of freedom in the model.

[0095] The following experimental data can be used as input parameters for the algorithm:

[0096] · Friction map as a function of pressure, speed, and temperature

[0097] · Critical slip distance (CSD)

[0098] · Abrasiveness parameter for the rubber material

[0099] The following quantities may be required as outputs from the simulation for each node:

[0100] · Pressure

[0101] · Speed

[0102] · Slip

[0103] The finite element can be represented by a finite element mesh 1110 as illustrated in Figure 11 The finite element mesh 1110 includes a plurality of contact elements represented by quadrilaterals. In this example, at a given time t n , nodes 1120 and 1128 are not in contact with the road surface. Nodes 1121 to 1124 are in contact with the road surface and do not experience movement relative to the road surface, i.e., they are stuck to the road surface. Nodes 1125, 1126, and 1127 are also in contact with the road surface and do experience movement relative to the road surface, i.e., they slip on the road surface. Thus, they show a node pressure p (p > 0) and a slip (γ > 0).

[0104] Each of the nodes 1121 to 1127 in contact with the road surface has a corresponding node region. Figure 11 Exemplarily shown therein are the node region 1135 of node 1125 and the node region 1136 of node 1126. However, it should be understood that all other nodes in contact with the road also have corresponding node regions A n .

[0105] According to the node data, a corresponding frictional stress τ can be defined. For the i-th node, the frictional stress τ i can be defined as

[0106]

[0107] where is the corresponding friction coefficient that depends on the node pressure p and the slip velocity Then, the frictional energy rate (frictional energy per unit time) can be defined as

[0108]

[0109] A i is the node region of the i-th node.

[0110] For nodes in the viscous state, such that they do not contribute to the frictional energy rate. However, this formula is independent of the node slip γ, and thus, the contribution of the critical slip distance is not included therein. Therefore, according to the above formula, the result will be characterized by an unrealistic high wear rate.

[0111] In the transient framework, the node slip 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 applies to the corresponding node. Hereinafter, the CSD can also be regarded as γ cr . In this way, the frictional energy rate can be reduced by a scaling factor f i to obtain the wear energy rate as

[0112] where

[0113] If γ i <γ cr , then or

[0114] otherwise f i (γ i ) = 1.

[0115] According to the wear energy rate, the mass loss rate per node can be calculated as

[0116]

[0117] where k and n are material-specific abrasion parameters that have been discussed above as input parameters of the algorithm. According to the mass loss rate, the nodal mass loss q can be calculated as

[0118]

[0119] t r is the rolling time. The rolling time is the difference between the current analysis time t n and the previous time step t n-1 .

[0120] To generalize it to the total width of the tire, it can be assumed that the total abrasion is the sum of all mass losses calculated at the nodes.

[0121] Therefore, the energy rate used for the wear phenomenon can be obtained by a factor f i (γ) to be calculated based on the nodal slip and the critical slip distance obtained from experiments.

[0122] Finally, the wear energy rate can be applied to the wear model in order to calculate the mass loss rate (or volume loss rate, depending on the units used) to be applied at the nodes. That is, the output of the framework allows the evaluation of the amount of mass abraded per unit time at each contact node. This data can in particular be further used to estimate the mileage, evaluate the irregular wear in the tread, compare the performance between geometries, materials and rolling conditions.

[0123] Figure 12 Graph 1200 illustrates the comparison of the accuracy of a standard simulation without considering the CSD and the accuracy of a simulation considering the CSD.

[0124] The ordinate of Graph 1200 shows the ranking of the wear rate performance of different rubber compounds A, B, C and D, as discussed in the reference Figure 8 . The wear rate performance in Graph 1200 is given in [%] relative to compound C, such that compound C corresponds to a value of 100%. The abscissa of Graph 1200 shows the wear rate performance obtained in previous abrasion tests in tires performed by the manufacturer, also in [%] relative to compound C. The data represented by the circles shows the relationship between the experimental ranking and the simulation without using the CSD. The dashed line 1210 represents the square of the Pearson correlation coefficient R 2 = 0.6892. It can be seen that there are considerable differences between the data points 1216 and 1217 corresponding to compounds B and D and the corresponding simulation data, as well as the low quality of the correlation.

[0125] The data represented by the squares shows the simulation results considering the CSD. The dashed line 1220 represents the square of the Pearson correlation coefficient R2 = 0.9417. It can be seen that when CSD is considered in the simulation, the increase in the experimental wear rate performance also leads to an increase in the simulated wear rate performance. As can be further seen from the graph 1200, when CSD is considered in the simulation, the difference between the experimental data and the simulated data is significantly lower, with a higher correlation quality.

Claims

1. A method for determining a critical slip distance (CSD) for a sample, the method comprising: Applying a force to the sample towards a sliding surface; Sliding the sample along the sliding surface n times in a plurality of intervals, The plurality of intervals having different widths w, where n is an integer ≥ 1; For each width w i , determine the corresponding wear rate m(w) among the multiple wear rates m(w i ) = ΔM / (n*w i ), where ΔM is the weight difference of the sample after the sample slides within n intervals of width w i compared to before the sliding; And Based on the plurality of wear rates and corresponding widths, determining the CSD as a width w0, where for any w > w0, 2. The method according to claim 1, wherein the width w of the plurality of spaces i is an integer divisor of the total length of the sliding surface.

3. The method according to any one of the preceding claims, the method further comprising: Slide the sample within a plurality of intervals each having a width w i ; By weighing the sample before and after sliding in n intervals of width w i the weight difference ΔM is obtained; And Determining the wear rate based on the weight difference ΔM and the total sliding distance.

4. The method according to claim 3, wherein for each width w i in the widths, the total sliding distance is equal.

5. The method according to any one of claims 3 or 4, Wherein the force is increased after sliding the sample along each of the intervals; and The force is reapplied before sliding the sample along a subsequent interval.

6. The method according to any one of the preceding claims, Wherein the sample slides along the sliding surface at a substantially constant speed.

7. The method according to any one of the preceding claims, the method further comprising: Identifying a first distance at which the static friction exceeds the sliding friction; Identifying a second distance at which the sliding friction exceeds the static friction; And Further determining the CSD based on the first distance.

8. The method according to any one of the preceding claims, the method further comprising: Providing a sliding surface having a total length; Sliding the sample multiple times on the sliding surface in steps of each of the plurality of widths w; And Measuring the plurality of wear rates for each of the plurality of widths w.

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

10. A computer-implemented method for estimating tire wear, the computer-implemented method comprising: Providing a wear model for the tire, the wear model being configured to convert a friction energy rate into wear, Wherein the wear model is based on a movable part and a non-movable part, wherein the movable part provides higher wear compared to the non-movable part; Dividing the contact surface of the tire into a movable part and a non-movable part, Wherein the non-movable part exhibits substantially no movement relative to the base of the tire, and Wherein the movable part exhibits movement relative to the base of the tire; and Estimating the wear of the tire based on the wear model and the divided contact surface.

11. The method according to claim 10, wherein the non-movable part provides substantially no wear.

12. The method according to any one of claims 10 and 11, Wherein the non-movable part has a first width, Wherein the critical slip distance CSD is proportional to the first width.

13. The method according to claim 12, wherein the CSD is experimentally determined before performing the computer-implemented method, and wherein the CSD is used as an input variable of the computer-implemented method.

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

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

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