This disclosure relates to computer modeling of rolling tires, including through finite element analysis.
The computational resources required to perform finite element analyses of tires are significant. Maximizing the amount of information extracted from the data generated in any particular analysis can increase the benefit to the engineer or researcher performing the analysis, and would do so at a lower cost than would be incurred by performing additional analyses of a tire model. A particularly costly type of analysis in terms of the computational resources required is that of a rolling tire on a road surface. Thus, maximizing the information obtained from the data concerning, for example, the interaction of the tire with the road surface is beneficial.
A system and method for modeling a distribution of a tire footprint boundary include inputting a finite element model of a tire rolling against a road surface described by discrete road surface coordinates into a finite element analysis system. A finite element analysis simulation of tire model rolling against the road surface for a plurality of time increments is performed. A plurality of tire footprint boundary data are generated, each having road surface coordinates on which a footprint boundary overlaps during a unique one of a second plurality of time increments. The number of second plurality of time increments during which the footprint boundary overlaps the each of the discrete road surface coordinates is determined for each of time increments of the simulation. For each coordinate, the number of the second plurality of time increments may be associated with a color scale or grayscale.
In the accompanying drawings, structures and methods are illustrated that, together with the detailed description provided below, describe exemplary embodiments of systems and methods for determining statistical distributions of rolling tire footprint boundaries. One of ordinary skill in the art will appreciate that a single component may be designed as multiple components or that multiple components may be designed as a single component.
Further, in the accompanying drawings and description that follow, like parts are indicated throughout the drawings and written description with the same reference numerals, respectively. The figures are not drawn to scale and the proportions of certain parts have been exaggerated for convenience of illustration.
In a preferred embodiment, FEA system 100 performs the methods disclosed herein through use of an FEA software package installed upon the computer readable medium 104 having instructions that can be executed by processor 102. When executed by processor 102, the FEA software package is configured to receive an FEA model of a tire and perform an FEA analysis of the tire model. An FEA model may incorporate a variety of aspects of a tire, such as tread design, tire size, tire shape, material properties of the tread and underlying structures, such as belt plies, and inflation level. While tire models are exemplary, the teachings herein may be applied to a model of any type of deformable structure rolling over a surface, such as a rubber disk rolling on a flat plane. As used herein, the term “tread” refers to that portion of the tire that comes into contact with the road under normal load. The FEA model may be introduced to the FEA system 100 by the user through user interface 106, or by selection and retrieval of a previously composed model stored on computer readable medium 104 or on a storage device accessible though the network. Processor 102 generates results of the FEA analysis in the form of data that is written to and stored on the computer readable medium 104. The data generated by the FEA analysis may, for example, be displayed on output device 112, or may be processed further.
For nonplanar road surface, three dimensional Cartesian coordinates, or non-Cartesian coordinates may be used to describe coordinates on the road surface. The simulated road surface may be described completely by a set of discrete coordinates, such that any point on the road surface may be described by one of the discrete coordinates. For example, the simulated road surface may be divided into N rows along the X-coordinate, and M columns along the Y coordinate, where N and M are positive integers. Each discrete coordinate in the road surface plane may be uniquely described by a two numbers, the first corresponding to a particular row, from 1 to N, and the second corresponding to a particular column, from 1 to M.
With further reference to
As seen in
According to the present disclosure, there are multiple ways to assign a numerical value corresponding to the occurrence of boundary overlap at particular coordinates of the simulated road surface. In one example of obtaining a numerical boundary overlap value, an aggregate number of overlapping time increments is calculated, similar to a histogram. In another example, the boundary overlap value may be given as a density measured as the boundary overlap occurrences per unit time.
The determination of the number of time increments during which boundary 202 overlaps a particular coordinate as described with respect to
Where Oj (x, y) is equal to 1 if the boundary overlaps with coordinate (x, y) at time increment j times Δt, and 0 if the boundary does not overlap with coordinate (x, y) at time increment j times Δt. In one preferred embodiment, the index j runs from 0 to (T/Δt). However, in alternative embodiments, Sum(x, y) may be a sum taken over a different range of index variable j. For example, the index may have a lower bound greater than 0, which corresponds to the starting point of the FEA simulation. For example, the lower bound may be selected so that index spans only those time increments after which the tire model has achieved steady state motion. Likewise, the upper bound may be selected to be less than (T/Δt), such that time increments during which the model has left a steady state are not included in Sum(x,y). In other alternative embodiments, the sum may be taken over an index taken at different evenly spaced time increments, such as (0, 2Δt, 4Δt, 6Δt, . . . ) or (0, 3Δt, 6Δt, 9Δt, . . . ), up to a selected upper bound. In a preferred embodiment, the time increments over which Sum(x,y) is performed are evenly spaced in order to prevent disproportionate weight to be given to any particular time span and the number of increments may represent a characteristic roll distance such as a integer multiple of tread pattern pitches.
In an embodiment where the road surface is planar having rows 1 to N and columns 1 to M, there will be M times N unique coordinates on which boundary 202 may overlap at each time increment. Where an FEA simulation runs from a time t=0 to T, there will be (T/Δt)+1 footprints for which FEA system 100 may determine the coordinates on which boundary 202 overlaps, including the initial conditions of the model at t=0. In a preferred embodiment, FEA system 100 determines the number of time increments for which boundary 202 overlaps each discrete coordinate in the road surface plane and records this data to computer readable medium 104.
At step 640, FEA system 100 calculates, for each coordinate on the simulated road surface, the number of time increments during which the border overlaps with the particular coordinate, for example by processor 102 executing instructions to calculate the Sum(x, y) given above for each coordinate in the simulated road surface. In practice, boundary 200 will be limited to a subset of the possible coordinates in the simulated road surface. As such, FEA system may limit the x and y coordinates over which it performs the summation Sum(x, y) to only those coordinates identified by the user, or in another example only to those coordinates that have at least one instance of a boundary overlap during at least one time interval during a simulation.
In step 660, FEA system 100 associates a visual representation to the various values of Sum(x,y) obtained in step 640. For example, FEA system 100 may associate a gradually darker shade of gray to increasing values, or ranges of values, of Sum(x,y). An example of such an association is shown in
The information provided by FEA system 100 and the exemplary method 600 described herein allows a user to have a graphical representation of tire boundary behavior over the course of an FEA simulation. For example, a user may be able to visualize regions of a tire footprint 200 having undesirably large ranges of movement over the course of a simulation, which in turn may be indicative of premature tire wear, undesirable handling and poor noise characteristics. As a result, the user is able to change the tire model, and perform method 600 on the altered model in order to determine whether the characteristics of the modeled tire are improved. Such simulations and alterations to the tire model may be performed iteratively to determine an optimum tire design.
It will be appreciated that the exemplary embodiments described above and illustrated in the drawings represent a few of the many ways of implementing and applying finite element analysis to calculate boundary overlap sums and frequencies and obtain a boundary distribution plot. The present disclosure is not limited to the specific methods and systems disclosed herein, but may be applied to any field that uses finite element analysis to calculate boundary overlap sums and frequencies and boundary distribution plots. The methods described and illustrated in the present disclosure may be modified in any manner that accomplishes the functions described herein. It is to be understood that the methods and apparatuses described herein may be distributed in any manner among any quantity (e.g., one or more) of hardware and/or software modules or units, computer or processing systems or circuitry.
Software for implementing the methods disclosed herein may be integrated within a stand-alone computer system or may execute separately and be coupled to any number of devices, workstation computers, server computers or data storage devices via any communications medium (e.g., network, modem, direct connection, etc.). The processes described herein may be implemented by any quantity of devices and/or any quantity of personal or other type of devices, computers or processing system (e.g., Windows based PCs, Apple computers, UNIX workstations and servers, laptops, desktops, etc.). In addition, the processes described herein may be implemented by users stationed remotely from FEA system 100. For example, a user may interact with a user interface that communicates with an FEA system 100 at a remote location over a network connection. The FEA system 100 may include any commercially available operating system (e.g., Windows, Mac Lion, Unix, Linux, etc.), any commercially available and/or custom FEA software and any types of input and/or output devices (e.g., keyboard, mouse, displays, printers, etc.).
It is to be understood that the software having instructions for implementing the processes described herein may be implemented in any desired computer language, and could be developed by one of ordinary skill in the computer and/or programming arts based on the functional description contained herein. For example, in one exemplary embodiment, the processes disclosed herein can be written using the Python programming language, however, the present disclosure is not limited to being implemented in any specific programming language. The various instructions and data sets may be stored in any quantity or types of file, data or database structures. Moreover, the software for performing the steps described herein may be distributed on any suitable medium (e.g., stored on devices such as CD-ROM and diskette, downloaded from the Internet or other network (e.g., via packets and/or carrier signals), downloaded from a bulletin board (e.g., via carrier signals), or other conventional distribution mechanisms).
The software for implementing the methods described herein may be installed and executed on a computer system in any conventional or other manner (e.g., an install program, copying files, entering an execute command, etc.). The functions associated with an FEA system 100 that performs the steps described herein may be performed on any quantity of computers or other processing systems. Further, the specific functions may be assigned to one or more of the computer systems in any desired fashion.
Further, any references herein of software performing various functions generally refer to computer systems or processors performing those functions under software control. The computer system may alternatively be implemented by hardware or other processing circuitry. The various functions of the methods described herein may be distributed in any manner among any quantity (e.g., one or more) of hardware and/or software modules or units, computer or processing systems or circuitry, where the computer or processing systems may be disposed locally or remotely of each other and communicate via any suitable communications medium (e.g., LAN, WAN, Intranet, Internet, hardwire, modem connection, wireless, etc.). The software and/or processes described above and illustrated in the flow charts and diagrams may be modified in any manner that accomplishes the functions described herein.
For the purposes of this disclosure and unless otherwise specified, “a” or “an” means “one or more.” To the extent that the term “includes” or “including” is used in the specification or the claims, it is intended to be inclusive in a manner similar to the term “comprising” as that term is interpreted when employed as a transitional word in a claim. Furthermore, to the extent that the term “or” is employed (e.g., A or B) it is intended to mean “A or B or both.” When the applicants intend to indicate “only A or B but not both” then the term “only A or B but not both” will be employed. Thus, use of the term “or” herein is the inclusive, and not the exclusive use. See, Bryan A. Garner, A Dictionary of Modern Legal Usage 624 (2d. Ed. 1995). Also, to the extent that the terms “in” or “into” are used in the specification or the claims, it is intended to additionally mean “on” or “onto.” As used herein, “about” will be understood by persons of ordinary skill in the art and will vary to some extent depending upon the context in which it is used. If there are uses of the term which are not clear to persons of ordinary skill in the art, given the context in which it is used, “about” will mean up to plus or minus 10% of the particular term. From about A to B is intended to mean from about A to about B, where A and B are the specified values.
While the present disclosure illustrates various embodiments, and while these embodiments have been described in some detail, it is not the intention of the applicant to restrict or in any way limit the scope of the claimed invention to such detail. Additional advantages and modifications will be apparent to those skilled in the art. Therefore, the invention, in its broader aspects, is not limited to the specific details and illustrative examples shown and described. Accordingly, departures may be made from such details without departing from the spirit or scope of the applicant's claimed invention. Moreover, the foregoing embodiments are illustrative, and no single feature or element is essential to all possible combinations that may be claimed in this or a later application.
Filing Document | Filing Date | Country | Kind |
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PCT/US13/33661 | 3/25/2013 | WO | 00 |
Number | Date | Country | |
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61622300 | Apr 2012 | US |