System and method for indirect tire wear modeling and prediction based on tire specifications
Through comparative model technology, the tire parameters of various types of tires are scaled to the corresponding values of tires that lack finite element models to generate an indirect tire wear model, which solves the problem of difficult to quickly and accurately predict the tire wear status in the prior art, and realizes reasonable wear prediction when complex models are unavailable.
Patent Information
- Application Number
- CN202380074476.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Priority Date
- 2022-10-27
- Filing Date
- 2023-10-02
- Publication Date
- 2025-06-20
- Estimated Expiration
- 2043-10-02
AI Technical Summary
The prior art is difficult to predict tire wear status quickly and accurately, especially when complex finite element analysis models are not available.
By iteratively developing a comparative model, the tire parameters of multiple types of tires are scaled to the corresponding values of tires that lack the finite element model, and an indirect tire wear model is generated to predict the tire wear status.
The rapid development and implementation of tire wear models in the absence of complex finite element models is achieved, providing relatively low accuracy but still reasonable wear predictions.
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Figure CN120188023A_ABST
Abstract
Description
Technical Field
[0001] The present invention generally relates to the estimation and prediction of the condition of tires of wheeled vehicles. More specifically, embodiments of the present invention as disclosed herein relate to systems and methods for indirectly developing and implementing a tire wear model based on general tire specifications for characterizing and predicting the state and condition of tires of wheeled vehicles, including but not limited to motorcycles, consumer vehicles (e.g., passenger cars and light trucks), commercial vehicles, and off - road (OTR) vehicles. Background Art
[0002] The prediction of tire wear is an important tool for anyone who owns or operates a vehicle, especially in the context of fleet management. At a certain point, understanding how the tire condition changes over time becomes crucial because insufficient tire tread can create unsafe driving conditions. However, irregular tread wear can occur for a variety of reasons, which may cause the user to replace the tires earlier than otherwise necessary. The vehicle, the driver, the driving conditions, and any number of other factors can cause the tires to wear at very different rates. That is, it is not desirable to rely on measurements of tread depth and other such metrics of the current tire wear state, at least because such measurements may be difficult to obtain in real - time and / or inaccurate, and further because such measurements alone cannot predict future tire wear states.
[0003] Accordingly, tire wear models for prediction implementation have been developed to enable, for example, prediction of the tire wear state of a tire over its corresponding life cycle. However, tire wear is a complex modeled phenomenon. Accurate models currently exist that utilize finite element analysis (FEA), but these simulations typically take weeks to complete. If it is desired to simulate the wear rate at several different tread depths, this will further take months for computationally expensive simulations.
[0004] There is a desire to develop additional tire wear models that can indirectly model tires for which the corresponding and complex FEA (or equivalent) models are not available, or otherwise provide reasonably accurate tire wear modeling during periods when such complex models are not yet available. Summary of the Invention
[0005] Embodiments of the method for indirect tire wear modeling and implementation as disclosed herein are based on or supplement the existence of various accessible finite element models and corresponding direct tire wear models for each of various types of tires. A comparative model is iteratively developed that scales the values of multiple tire parameters of a selected comparison tire among multiple types of tires having corresponding accessible finite element models to the corresponding values of multiple tire parameters of any type of tire lacking the corresponding accessible finite element model. For a first type of tire provided that lacks the corresponding accessible finite element model, the corresponding values of multiple tire parameters are obtained, and an indirect tire wear model for the first type of tire is generated based on the first comparative model, the corresponding direct tire wear model, and the values of the first type of tire with respect to the multiple tire parameters.
[0006] In one exemplary aspect according to the above embodiment, the tire wear state of a first tire of the first type installed on a vehicle at one or more future times can be predicted at least in part based on the indirect tire wear model of the first type of tire.
[0007] In another exemplary aspect according to the above embodiment, the type of vehicle and / or the application of the tire can be provided as an input to the indirect tire wear model for predicting the tire wear state at one or more future times.
[0008] In another exemplary aspect according to the above embodiment, the actual tire performance values of the first tire can be monitored over time, and the monitored actual tire performance values are applied to determine the current wear state of the first tire based on the indirect tire wear model of the first type of tire.
[0009] In another exemplary aspect according to the above embodiment, the determined current wear state of the first tire can be provided as feedback for iteratively developing another tire wear model for the first type of tire.
[0010] In another exemplary aspect according to the above embodiment, the replacement time of the first tire can be predicted based on a comparison of the current wear state or the predicted tire wear state with a tire wear threshold associated with the first type of tire.
[0011] In another exemplary aspect according to the above embodiment, the step of generating the indirect tire wear model can include determining the frictional energy associated with the first type of tire at least in part based on the first comparative model and the values of the first type of tire with respect to the multiple tire parameters.
[0012] In another exemplary aspect according to the above embodiment, the frictional energy associated with the first type of tire can be related to the wear energy according to the determined elasticity of the corresponding tread compound.
[0013] In another exemplary aspect according to the above-described embodiments, the step of developing the comparison model may further include determining an empirical relationship between the wear energy at zero force and the values of a plurality of tire parameters using one or more coefficients extrapolated from one or more accessible finite element models among a plurality of accessible finite element models. The step of generating the indirect tire wear model may further include correlating the frictional energy associated with the first type of tire with the wear energy based at least in part on the determined empirical relationship.
[0014] In another exemplary aspect according to the above-described embodiments, the comparison model may include one or more scale factors for applying to the associated tire parameters related to the tread stiffness and / or carcass stiffness of a selected comparison tire.
[0015] In another embodiment, a system for indirect tire wear modeling and implementation is disclosed herein, and the system includes: a data storage network on which accessible finite element models and corresponding direct tire wear models for each of a plurality of types of tires are stored; and a computing network functionally linked to the data storage network. The computing network is configured to direct the execution of operations in a method according to the above-described embodiments and optionally according to any one or more of the aspects thereof.
[0016] For those skilled in the art, many of the objects, features, and advantages of the embodiments described herein will become apparent when the following disclosure is read in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS
[0017] Figure 1 is a block diagram representing an exemplary embodiment of a system as disclosed herein.
[0018] Figure 2 is a flowchart representing an exemplary embodiment of a method as disclosed herein.
[0019] Figure 3 is a graphical plot representing the relationship between the zero-force wear intensity of a given tire determined based on a direct (e.g., FEA) model and the zero-force wear intensity of the given tire determined based on an indirect model as disclosed herein.
[0020] Figure 4 includes four graphical plots representing the relationship between the lateral force results using a direct (e.g., FEA) model and using an indirect model as disclosed herein. DETAILED DESCRIPTION
[0021] General Reference Figures 1 to 4, various exemplary embodiments of the present invention will now be described in detail. In cases where various embodiments sharing various common elements and features may be described in the various figures, similar elements and features are given the same reference numerals, and redundant descriptions thereof may be omitted hereinafter.
[0022] In various embodiments, an indirect tire wear model as disclosed herein may, for example, have a relatively low accuracy but still provide reasonable wear predictions while being able to be quickly and easily developed and implemented using only publicly available basic tire specification data.
[0023] Various embodiments of the systems as disclosed herein may include a centralized computing node (e.g., a cloud server) that functionally communicates with a plurality of distributed data collectors and computing nodes (e.g., associated with respective fleet management entities, end users, vehicles, tires, etc.) to effectively develop and implement the models as disclosed herein.
[0024] First referring to Figure 1 , an exemplary embodiment of system 100 includes at least a server network 110 and a data storage network 120, and also includes or is functionally linked to one or more public tire data sources 130, a tire monitoring network 140 (including, for example, sensors and intermediate devices mounted on tires), in-vehicle computing devices (including a user interface 150 for each of a plurality of vehicles in a defined vehicle fleet, for example), endpoint computing devices 160 for each of a plurality of users (such as fleet management administrators), and the like. One or more of the foregoing components may be connected or otherwise functionally linked via a communication network (not shown), which in various embodiments may include, in whole or in part, the Internet, a public network, a private network, or any other communication medium capable of transmitting electronic communications.
[0025] In various exemplary embodiments, any or all of the computing devices 110, 150, 160 can be implemented as at least one of a server computer, a server device, a desktop computer, a laptop computer, a smart phone, or other equivalent electronic devices capable of executing program instructions. The server network can include a processor 112, a memory 114 on which program logic resides, and a communication unit 116 for selectively linking one or more servers in the network to other components such as those described above. In certain embodiments, the server network 110, the data storage network 120, and multiple in-vehicle computing devices or program modules residing thereon can jointly define a host system for tire wear monitoring of tires installed on a vehicle associated with the in-vehicle computing device 150. The in-vehicle computing device 150 can be portable or otherwise modular as part of a distributed vehicle data collection and control system, or can otherwise be provided integrally with respect to a central vehicle data collection control system (not shown).
[0026] Other vehicle components communicating with the in-vehicle computing device 150 can typically include, for example, one or more sensors linked to a Controller Area Network (CAN) bus network and thereby providing signals to a local processing unit, such as, for example, a body accelerometer, a gyroscope, an Inertial Measurement Unit (IMU), a position sensor such as a Global Positioning System (GPS) transponder, sensors mounted on the tires, a Tire Pressure Monitoring System (TPMS) sensor transmitter, and associated in-vehicle receivers, etc.
[0027] Based on the following discussion, other sensors for collecting and transmitting vehicle data such as those related to speed, acceleration, braking characteristics, etc. will become sufficiently obvious to those of ordinary skill in the art and will not be discussed further herein. A variety of bus interfaces, protocols, and associated networks are well known in the art for transmitting vehicle dynamics data, etc. between the respective data sources and local computing devices, and those skilled in the art will recognize a wide range of such tools and the means for implementing these tools.
[0028] In an embodiment, the vehicle and tire sensors are also provided with unique identifiers, where the on-vehicle computing device 150 can distinguish between signals provided from the corresponding sensors on the same vehicle, and further in some embodiments, where the central server 110 and / or the fleet maintenance supervisor client device 160 can distinguish between signals provided from the tires and associated vehicles and / or tire sensors on multiple vehicles. In other words, in various embodiments, for the purposes of on-vehicle or remote / downstream data storage and for the specific implementation of the computations as disclosed herein, the sensor output values can be associated with a specific tire, a specific vehicle, and / or a specific tire-vehicle system. The on-vehicle device processor can communicate directly with the hosting server network 110, as Figure 1 shown, or alternatively, the driver's mobile device or a computing device mounted on the truck can be configured to receive the on-vehicle device output data and process / transmit it to the hosting server and / or the fleet management server / device.
[0029] As Figure 1 shown, the data storage network 120 can include, for example, multiple databases or equivalent storage media for retrievably storing the models 122, 124, 126, 128 and the input data for their development. Vehicle data, sensed tire data, data from the public tire data source 130, etc., once transmitted to the hosting server network 110 via the communication network, can be stored accordingly in, for example, the database associated therewith. The system 100 can include or otherwise selectively retrieve at least the FEA model 122, the direct tire wear model 124, the scaling model 126, and / or the new tire (indirect) wear model for processing the input.
[0030] It should be noted that the embodiment of the system 100 as Figure 1 shown does not limit the scope of the system or method 200 as disclosed herein, and in an alternative embodiment, one or more of the models as disclosed herein can be implemented locally at the on-vehicle computing device 150 (e.g., an electronic control unit) of the vehicle or at the other endpoint device 160 (such as a fleet management device or server), rather than at the central (host) server level 110. For example, one or more of the models as disclosed herein can be generated and trained over time at the host server level 110 and downloaded to the on-vehicle computing device 150 and / or the endpoint device 160 for local execution of one or more steps or operations as disclosed herein.
[0031] In an embodiment, the estimated or predicted tire state can be provided as an output from the model to one or more downstream models or applications. As for example in Figure 1As represented, a feedback signal corresponding to a predicted tire wear state (e.g., a predicted tread depth at a given distance, time, etc.) can be provided to an in-vehicle computing device 150 associated with the vehicle itself or to a mobile device 160 associated with a user, such as a mobile device integrated with a user interface configured to provide an alert or notification / recommendation that a tire should or soon will need to be replaced.
[0032] Next, referring to Figure 2 , an exemplary implementation of a method 200 for developing and implementing an indirect tire wear model for new tires can be described as follows.
[0033] Initially, method 200 can include providing or otherwise defining access to a plurality of existing FEA models for corresponding types of tires and optionally access to corresponding direct tire wear models. In this context, a "direct" tire wear model can generally refer to a tire wear model for a specific tire developed based on an FEA model of the corresponding type of tire, and it can accordingly be considered to be very accurate, but is costly and time-consuming to develop, as previously described. If a tire wear model for an existing type of tire is subsequently requested from system 100 via, for example, a tire selection or input 232, where an "existing" type of tire in this context means a tire type for which an existing or otherwise accessible FEA model is available (i.e., in response to a query in step 230 being "yes"), then system 100 can accordingly use conventional techniques to retrieve or otherwise develop a tire wear model for the tire based on the corresponding FEA model.
[0034] If a tire wear model for a new type of tire is requested from system 100, or in other words, if a new type of tire is selected or otherwise input / presented to the system in step 232, where a "new" type of tire in this context means a tire type for which an existing or otherwise accessible FEA model is not available (i.e., in response to a query in step 230 being "no"), then method 200 of the present disclosure also involves obtaining various tire parameters of the tire (step 240) at least in part based on publicly available specifications 242 of the tire (such as from an online data source), and further generating a new and "indirect" tire wear model (step 250) according to a determined relationship, examples of which can be as follows.
[0035] Considering, for example, that the wear energy of a tire is related to the forces and slips experienced at the tire / road contact interface, the average frictional energy experienced by the tire can be calculated separately for front / rear and lateral forces / slips as:
[0036] E fx =F x s x =F xK (Equation 1)
[0037] E fy = F y s y = F y α (Equation 2)
[0038] where K is the slip ratio and α is the slip angle experienced by the tire.
[0039] This can be further simplified by assuming a small amount of slip (i.e., linear force - slip relationship) by including the slip / side - slip stiffness of the tire. The offset due to ply - steer in the lateral case and rolling resistance in the front / rear cases can be further considered, where the equation for frictional energy becomes:
[0040]
[0041] where k κ is the slip stiffness, k α is the side - slip stiffness, C RR is the rolling resistance coefficient, and α0 is the slip angle due to ply - steer.
[0042] The camber angle may also cause additional frictional energy, and its equation is
[0043]
[0044] where γ is the camber angle and k γ is the camber thrust stiffness of the tire. Then, the wear energy can be related to the frictional energy by multiplying by the elasticity of the tread rubber, which is a function of the tangent increment of the rubber.
[0045] The above equations indicate that when zero lateral / front / rear forces are applied to the tire, the wear energy will also be zero. Those skilled in the art can understand that this is not the case, as some areas of the tire footprint (contact patch) are in a "pushing" or "pulling" state, where the net result is zero force. To explain this issue, an empirical relationship between the wear energy at zero force and some of the previously mentioned tire parameters can be determined or otherwise explained, which is given by:
[0046]
[0047] where in this illustrative case, the coefficients c1, c2, and c3 shown are found by fitting to several FEA models of different sizes and types of tires, and exemplary results are shown in Figure 3
[0048] Using a simple model that relates various tire size and stiffness parameters to the parameters in the above equations, one or more comparative (i.e., scaled) models can be developed (step 220), which models include the scaling factors of the corresponding selected comparative tires that have previously been modeled using a more accurate FEA method and can be defined, for example, using the following relationships:
[0049]
[0050]
[0051] where R is the outer radius, h is the tread height, E is the tread rubber modulus, kr is the radial stiffness, ks is the lateral stiffness, and b is the tire width, and the subscript 0 refers to the corresponding comparative tire, while 1 refers to the tire of interest in a given application of the corresponding comparative model. Rt is the scale factor applied to the tread stiffness of the comparative tire, and Rc is the scale factor applied to the carcass stiffness of the corresponding comparative tire.
[0052] The slip stiffness of the tire can be assumed to be equal to the tread stiffness, while the cornering stiffness is related to the carcass and the tread by assuming two springs in series such that:
[0053]
[0054] Further illustratively referring to Figure 4 , several tire models created using the FEA method are compared with similar tire models developed according to an embodiment of method 200 as disclosed herein, where relevant tire parameters of a particular tire of interest are obtained using online and publicly available resources (e.g., www.tirerack.com ).
[0055] Exemplary tire parameters that are inputs to the developed models include the original tread depth, tread width, section width, outer diameter, and rim diameter, and each of these parameters can be obtained directly from the publicly available specifications of the tire of interest.
[0056] Additional exemplary tire parameters that are inputs to the developed models can include the predicted operating load and inflation pressure, which can be determined indirectly or otherwise predicted, for example, based on the vehicle type and / or application type (e.g., mid-size SUV, pickup truck, delivery, etc.).
[0057] Still other exemplary tire parameters that are inputs to the developed models can include tread rubber parameters (such as elasticity, where elasticity is a function of the tangent increment of the tread rubber as described above), and can be determined or otherwise predicted, for example, based on the tire type and / or grade (e.g., standard all-season touring, high-performance summer, etc., and / or Uniform Tire Quality Grading (UTQG), tread wear warranty, etc.).
[0058] In some embodiments, method 200 and more specifically step 250 may include a tire wear model selection step that may, for example, depend on application-related factors such as the wheel mounting location of the tire in question and take into account any known or predicted relevant dependencies of the applied loads based on such wheel mounting differences.
[0059] As Figure 4 shown, the relative accuracy of the indirectly developed tire model, in combination with the relative ease of model development, demonstrates the potential utility of method 200 disclosed herein.
[0060] Utilizing the new tire wear model generated according to step 250 (in some embodiments, the new tire wear model may be a general tire wear model for a particular type of tire or a tire wear model for a specific tire developed from a general model of the tire type in question), method 200 can proceed, i.e., predict the tire wear state of the particular tire and / or the determined tire-vehicle combination and / or tire application at one or more future times (step 260).
[0061] System 100 can collect inputs associated with tire usage over time and further process the inputs to further develop a tire wear model for a particular tire, or in some embodiments, an indirect tire model for the tire type itself, at least in part based on a comparison of the actual tire wear state at a specified time point relative to the previously predicted tire wear state at the same time point. For example, actual measurements can be used to update the model related to tire wear prediction over time, where the system can selectively "correct" the model predictions using each measurement made on a particular tire element and / or the vehicle tire system. To the extent that the tire wear model can be at least partially probabilistic in nature, allowing for a potential time series or similar progression curve over time and attempting to incorporate or otherwise account for all such possibilities and related uncertainties when predicting future tire wear and associated events, including a feedback loop of actual tire wear values or corresponding inputs can correspondingly allow system 100 to effectively rule out or minimize the relevance of certain such model components relative to a given tire or even relative to the tire type.
[0062] In an embodiment, the comparison may further consider one or more wear-causing factors specific to the tire in question and not considered (or at least not fully considered) at the start of the prediction. These factors can include, for example, driving style, vehicle alignment settings, driving route, road surface, environmental conditions, tire manufacturing variability, etc., to represent known causes of tire wear life variation among other equivalent tires.
[0063] During operation of a vehicle on which the discussed tire is mounted, method 200 may further include step 270: determining or otherwise predicting a tire intervention and recommending the tire intervention to a relevant user of system 100. For example, a feedback signal corresponding to a predicted tire wear state may be provided via an interface to an on-vehicle device 150 associated with the vehicle itself, or to a mobile device 160 associated with the user, such as a mobile device integrated with a user interface configured to provide warnings or notifications / recommendations of intervention events, such as that one or more tires should or will soon need to be replaced, rotated, aligned, inflated, etc.
[0064] Throughout the specification and claims, unless the context dictates otherwise, the following terms have at least the meanings explicitly associated herein. The meanings identified below do not necessarily limit the terms, but merely provide illustrative examples of the terms. The meanings of "a", "an", and "the" may include plural referents, and the meaning of "in" may include "in" and "on". As used herein, the phrase "in one embodiment" does not necessarily refer to the same embodiment, although it may be.
[0065] The various illustrative logical blocks, modules, and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both. To clearly illustrate this interchangeability of hardware and software, various illustrative components, blocks, modules, and steps have been described above generally in terms of their functionality. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the overall system. The described functionality may be implemented in different ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present disclosure.
[0066] The various illustrative logical blocks and modules described in connection with the embodiments disclosed herein may be implemented or executed by a machine, such as a general-purpose processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general-purpose processor may be a microprocessor, but in the alternative, the processor may be a controller, microcontroller, or state machine, combinations thereof, etc. The processor may also be implemented as a combination of computing devices, such as a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration.
[0067] The steps of the methods, processes, or algorithms described in connection with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of both. The software modules may reside in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, a hard disk, a removable disk, a CD-ROM, or any other form of computer-readable medium known in the art. An exemplary computer-readable medium may be coupled to the processor such that the processor can read information from, and write information to, the memory / storage medium. In an alternative, the medium may be integrated into the processor. The processor and the medium may reside in an ASIC. The ASIC may reside in a user terminal. In an alternative, the processor and the medium may reside as discrete components in a user terminal.
[0068] Unless otherwise specifically stated or otherwise understood within the context in which it is used, conditional language used herein, such as "can", "could", "may", "for example", etc., is generally intended to convey that certain embodiments include certain features, elements, and / or states, while other embodiments do not include certain features, elements, and / or states. Thus, such conditional language is generally not intended to imply that the features, elements, and / or states are in any way required for one or more embodiments or that one or more embodiments necessarily include logic for deciding, with or without author input or prompting, whether these features, elements, and / or states are included in any particular embodiment or whether they will be performed in any particular embodiment.
[0069] The foregoing detailed description has been provided for purposes of illustration and description. Accordingly, while specific embodiments of a new and useful invention have been described, these references are not to be construed as limitations on the scope of the invention, except as set forth in the following claims.
Claims
1. A method for indirect tire wear modeling and implementation, the method comprising: Provide an accessible finite element model and a corresponding direct tire wear model for each of a plurality of types of tires; Iteratively develop a comparison model that scales the values of a plurality of tire parameters of a selected comparison tire among the plurality of types of tires having corresponding accessible finite element models to the corresponding values of the plurality of tire parameters of any type of tire lacking a corresponding accessible finite element model; For a first type of tire provided that lacks a corresponding accessible finite element model, obtain the corresponding values of the plurality of tire parameters; And Based on a first comparison model, the corresponding direct tire wear model, and the obtained values of the first type of tire with respect to the plurality of tire parameters, generate an indirect tire wear model for the first type of tire.
2. The method according to claim 1, the method further comprising predicting a tire wear state of a first tire of the first type installed on a vehicle at one or more future times, at least in part based on the indirect tire wear model of the first type of tire.
3. The method according to claim 2, wherein a type of the vehicle and / or an application of the tire is provided as an input to the indirect tire wear model for predicting the tire wear state at the one or more future times.
4. The method according to claim 2, the method further comprising monitoring actual tire performance values of the first tire over time and applying the monitored actual tire performance values to determine a current wear state of the first tire based on the indirect tire wear model of the first type of tire.
5. The method according to claim 4, the method comprising providing the determined current wear state of the first tire as feedback for iteratively developing another tire wear model of the first type of tire.
6. The method according to claim 4, the method further comprising predicting a replacement time of the first tire based on a comparison of the current wear state or the predicted tire wear state with a tire wear threshold associated with the first type of tire.
7. The method according to claim 1, wherein the step of generating the indirect tire wear model comprises determining a frictional energy associated with the first type of tire, at least in part based on the first comparison model and the obtained values of the first type of tire for the plurality of tire parameters.
8. The method according to claim 7, wherein the frictional energy associated with the first type of tire is related to a wear energy according to the determined elasticity of the corresponding tread compound.
9. The method according to claim 7, wherein: The step of developing the comparison model further includes determining an empirical relationship between the wear energy at zero force and the values of the plurality of tire parameters using one or more coefficients extrapolated from one or more of the plurality of accessible finite element models; and The step of generating the indirect tire wear model further includes correlating the frictional energy associated with the first type of tire with the wear energy based at least in part on the determined empirical relationship.
10. The method according to claim 1, wherein the comparison model comprises one or more scale factors for applying to associated tire parameters related to the tread stiffness and / or carcass stiffness of the selected comparison tire.
11. A system for indirect tire wear modeling and implementation, the system comprising: A data storage network on which accessible finite element models and corresponding direct tire wear models for each of a plurality of types of tires are stored; And A computing network functionally linked to the data storage network and configured to direct the execution of the steps of the method according to one of claims 1 to 10.
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