System and method for determining wear

Abstract

Embodiments determine wear. One such embodiment obtains a finite element mesh representing a first object in a memory associated with a processor. For a given node of the obtained grid, wear variables are associated and linked to contact constraints associated with the node. A simulation of contact between the first object and a second object is performed in a movement increment to determine wear at the node. A wear distance for a given increment is iteratively determined using the grid, the associated variables, and the constraints. The position of the node in the grid is iteratively updated based on the determined wear distance for the given increment until the wear distance for each of the increments is determined. The wear at the node is determined based on the determined wear distance for each of the increments. An indication of the determined wear is output.

Description

Background Art

[0001] There are many existing products and simulation systems available on the market for designing and simulating objects (e.g., vehicles). Such systems typically employ computer-aided design (CAD) and computer-aided engineering (CAE) programs. These systems allow users to build, manipulate, and simulate complex three-dimensional models of objects or assemblies of objects. These CAD and CAE systems provide a model representation of an object (e.g., a real-world object) using edges or lines (and in some cases faces). Lines, edges, faces, or polygons may be represented in a variety of ways (e.g., non-uniform rational basis splines (NURBS)).

[0002] Such systems manage parts or assemblies of parts of modeled objects, which are mainly specifications of geometric shapes. Specifically, CAD files contain specifications from which geometric shapes are generated. A three-dimensional CAD model or model representation is generated from the geometric shapes.

[0003] The emergence of CAD and CAE has made objects have a wider range of representation possibilities. Examples of computer-based models used by CAD and CAE systems include CAD models and finite element models (i.e., meshes). Computer-based models can be programmed so that the model has the properties (e.g., physical, material, or other physics-based) of one or more underlying real-world objects represented by the model. Example properties include stiffness (ratio of force to displacement), plasticity (irreversible strain), and viscosity (resistance to flow of one layer on an adjacent layer) and other examples. When CAD or other such computer-based models as known in the art are programmed in this way, they can be used to perform simulations of objects represented by the model. For example, mesh-based models can be used to represent the inner cavity of a vehicle, an acoustic fluid surrounding a structure, or any number of real-world objects. In addition, CAD and CAE systems and computer-based models can be used to simulate engineering systems, such as real-world physical systems, such as cars, airplanes, buildings, and bridges, as well as other examples. Further, CAE systems can be used to simulate any changes and combinations of the behavior of these physics-based systems, such as noise and vibration.

[0004] A common behavior modeled using CAD and CAE systems is wear. Wear is the removal or deformation of material at a solid surface. Wear can occur at different rates (e.g., gradually) and can be destructive. For example, in machine elements, wear can cause degradation of functional surfaces, ultimately leading to material failure and / or loss of function. Summary of the invention

[0005] A technical problem in existing computer-based systems (e.g., finite element systems) for modeling surface wear is how to simultaneously handle the interdependencies between wear distance, contact stress, and contact slip of implicit finite element simulations to enhance accuracy and robustness without changing the connectivity of contact constraints and with minimal changes to the code flow. Another technical problem in conventional systems is how to avoid the artificial requirement that surfaces that may experience wear must act as subsurfaces (i.e., surfaces in which contact constraints are specified so that constrained wear can be output as node wear). Past implementations of modeling surface wear have not addressed these challenges. Therefore, there is a need for improved accuracy, robustness, and efficiency. The implementation provides such functionality.

[0006] An example embodiment relates to a computer-implemented method for determining wear. The method begins by obtaining a finite element mesh representing a first object in a memory associated with a processor. Next, for a given node of the obtained finite element mesh, the method associates a wear variable and links the associated wear variable to a plurality of contact constraints associated with the given node. Next, the method performs a simulation of contact between the first object and the second object in a plurality of movement increments to determine wear at the given node. Performing the simulation includes iteratively (i) determining a wear distance for a given movement increment using the finite element mesh, the associated wear variable, and the plurality of contact constraints, and (ii) updating a position of a given node in the finite element mesh based on the determined wear distance for the given movement increment until a wear distance for each of the plurality of movement increments is determined. Performing the simulation also includes determining the wear at the given node based on the determined wear distance for each of the plurality of movement increments. Then, the method outputs an indication of the determined wear.

[0007] In an example embodiment, determining the wear distance for a given move increment may include executing a Newton iteration scheme to determine the wear distance until a convergence check is satisfied. According to another example embodiment, executing the Newton iteration scheme may include: in each iteration of the Newton iteration scheme, for each contact constraint in a plurality of contact constraints, determining at least one of: (i) a constraint wear value, (ii) a modified clearance value, (iii) a contact stress value, and (iv) a wear increment value.

[0008] According to an example embodiment, for a given iteration, the position of a given node in the finite element mesh used in determining the wear distance may be an updated position of the given node from a previous iteration. In another example embodiment, for a given iteration, the updating may include modifying the updated position of the given node from a previous iteration based on the wear distance determined for the given iteration.

[0009] In another example embodiment, the obtained finite element mesh may be a first finite element mesh. Further, in such embodiments, at least one contact constraint in the plurality of contact constraints may include (i) at least one node of the first finite element mesh and (ii) at least one node of a second finite element mesh representing a second object.

[0010] According to an example embodiment, determining the wear distance for a given move increment may include calculating a total constraint contribution based on a plurality of contact constraints and constraint coefficient values.Determining the wear distance for a given move increment may also include determining the wear distance based on the calculated total constraint contribution.

[0011] Another example embodiment relates to a computer-based system for determining wear. The system includes: a processor; and a memory having computer code instructions stored thereon. The processor and the memory are configured with the computer code instructions to cause the system to implement any embodiment or combination of embodiments described herein.

[0012] Yet another embodiment relates to a computer program product for determining wear. The computer program product includes a non-transitory computer-readable medium having computer code instructions stored thereon. The computer code instructions are configured to, when executed by a processor, cause a device associated with the processor to implement any embodiment or combination of embodiments described herein.

[0013] It should be noted that the method, system, and computer program product embodiments may be configured to implement any embodiment or combination of embodiments described herein. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] The foregoing will be apparent from the following more particular description of example embodiments, as illustrated in the accompanying drawings in which like reference numerals refer to the same parts throughout the different views. The drawings are not necessarily drawn to scale, emphasis instead being placed upon illustrating the embodiments.

[0015] Figure 1 An example finite element model system is illustrated in which contact between two objects is affected by multiple constraints.

[0016] Figure 2 is a flow chart of an example method of implicit wear modeling according to an embodiment.

[0017] Figure 3 The working principle of an example ball bearing that can be simulated using embodiments is illustrated.

[0018] FIG. 4A to FIG. 4E Stages of an example simulation of surface wear of a torsion block according to an embodiment are illustrated.

[0019] Figure 5Example simulation results of a surface wear simulation of a torsion block according to another embodiment are illustrated.

[0020] Figure 6 An example of surface wear of a torsion block determined using yet another embodiment is illustrated.

[0021] 7A to 7F Stages of an example simulation of surface wear of a slider according to an embodiment are illustrated.

[0022] Figure 8 This example uses a common scale. 7A to 7F Example simulation of wear distance results.

[0023] Fig. 9 is a graph of wear distance and wear coefficient determined using an embodiment.

[0024] Fig.10 This example shows the use of multiple scales 7A to 7F Example simulation of wear distance results.

[0025] Fig.11 Example simulation results of surface wear of a slider according to another embodiment are illustrated.

[0026] Fig.12 According to the implementation plan Fig.10 and Fig.11 A graph of the number of physical cycles and the maximum wear distance for an example.

[0027] Fig.13A and Fig. 13B An example of the contact pressure of the sliding block determined using the embodiment is illustrated.

[0028] Fig.14 An example system is illustrated in which wear occurs at the corners of a sliding block according to an embodiment.

[0029] Fig.15 Example finite elements and associated contact penetration distances that may be used in embodiments are illustrated.

[0030] Fig.16 is a flow chart of a method for determining wear according to an example embodiment.

[0031] Fig.17 is a schematic diagram of a computer network in which embodiments may be implemented.

[0032] Fig.18 It is an example Fig.17 A block diagram of an example implementation of a computer node in a computer network of FIG. DETAILED DESCRIPTION

[0033] A description of example implementations follows.

[0034] Introduction, shortcomings of existing methods and comparison with implementation plans

[0035] The incremental wear distance occurring within a time interval at a particular surface location may depend on the local contact stress state and the incremental slip distance. Conversely, the local contact stress state and the incremental slip distance may depend on the local incremental wear distance of the contacting surface. In the context of nonlinear implicit finite element simulation programs, it may be challenging to effectively and accurately handle the interdependencies between wear, contact stress state, and incremental slip distance. Embodiments provide novel functionality that can accurately and effectively handle these interdependencies between wear distance, contact stress, and contact slip.

[0036] Other non-limiting examples of functionality provided by embodiments include:

[0037] a) consider the contact constraints that each node participates in (e.g., all contact constraints);

[0038] b) making algorithmic decisions about contact constraint values ​​without regard to which contacting surfaces are susceptible to wear; and

[0039] c) Avoid subjective determination of a single representative value for incremental slip (and other contact constraint quantities) at nodes involved in multiple contacts.

[0040] Furthermore, the embodiments are not limited to the case of small wear distances relative to the size of the underlying finite elements in contact with the surface. The embodiments can further be applied to larger wear distances that also affect the underlying finite element calculations because a significant volume fraction of these elements is eroded due to surface wear.

[0041] Embodiments may address numerical design aspects associated with simultaneous implicit processing of the interdependencies between wear distance, contact stress, and contact slip to improve accuracy, robustness, and efficiency. Additionally, embodiments may be used for finite element simulations including the effects of surface wear.

[0042] A conventional approach for modeling the effects of ablation or wear (where material is eroded at a boundary) is arbitrary Lagrangian-Eulerian (ALE) adaptive meshing. Using this existing approach (i.e., ALE), the incremental wear distance (which affects the next simulation increment) can depend on the converged values ​​of the contact stress and contact slip (and other quantities). However, a limitation of this approach is that the contact stress and contact slip (and other quantities) have a delayed ("explicit") dependence on the incremental wear distance, rather than a simultaneous ("implicit") dependence.

[0043] Another existing finite element system has many disadvantages, including, for example:

[0044] a) The system cannot simultaneously satisfy the interdependencies between wear distance, contact stress, and contact slip in each solution increment, leading to inaccuracies and convergence problems.

[0045] b) The wear calculation for a given node can ignore all contact constraints in which the node participates.

[0046] c) Instruct the user to adjust the value based on which surface or surfaces of the interface are prone to wear.

[0047] d) The implementation of surface wear is also not elegant in terms of requiring the user to adjust the basic role of the surfaces in the contact definition depending on which or both surfaces of the contact interface are likely to experience wear.

[0048] i. In contrast, when the methods of the embodiments are employed, wear can occur on surfaces regardless of their "primary" and "secondary" roles in the contact formulation.

[0049] e) For a given simulation increment, based on a fixed (previously determined / hysteresis) wear distance, the existing system starts performing Newton iterations by varying the load conditions as usual. When this iterative sequence converges, the system calculates and applies the incremental wear distance based on the predicted contact stress, slip increment, etc. fields.

[0050] f) After adjusting the wear distance, the prior art system performs additional Newton iterations with the wear distance fixed at the new value. These iterations may not converge, in part due to the loss of equilibrium that occurs when changing the wear distance. If the iterations do not converge, the system re-attempts the simulation increment with a smaller increment size. This means that if these iterations do converge, the wear distance is not updated with the latest contact stress, slip increment, etc. fields. In other words, the prior art system does not simultaneously handle the interdependencies between the wear distance, contact stress, and contact slip.

[0051] g) Existing system wear capabilities affect both contact elements and underlying elements. The impact on underlying elements is similar to the pre-existing ALE adaptive meshing described above to model the effects of ablation or wear.

[0052] h) The interleaved treatment of the interdependencies between wear distance, contact stress and contact slip in existing systems is prone to convergence problems.

[0053] i. In contrast, embodiments may handle these interdependencies simultaneously during Newton iterations to provide better convergence behavior and reduce the dependence of results on the size of the simulation increment.

[0054] i) The existing system has an undesirable dependence on user-controlled numerical details (whether one, the other, or both surfaces in contact are susceptible to wear). As a result, users of the system are diverted toward performing wear calculations on nodes based on so-called "secondary" surfaces. The reason for this diversion appears to be that the existing system assumes that the nodal contact stresses, slip, etc. that appear in the wear rate equations for a given node are each associated with a single (preferably) contact constraint, even though each node is typically involved in multiple contact constraints.

[0055] i. In contrast, embodiments may avoid such undesirable complexity and consider the contribution to node wear of all contact constraints in which a node participates.

[0056] The existing wear model is the Archard model (or Archard's law) developed in 1953. The Archard equation is a simple model for describing sliding wear and is based on asperity contact theory.

[0057] This equation uses of the form, where:

[0058] a) Q is the total volume of wear debris generated;

[0059] b) K is a dimensionless constant;

[0060] c) W is the total normal load;

[0061] d) L is the sliding distance; and

[0062] e) H is the hardness of the softest contact surface.

[0063] A related model from 2004 describes a series of simulations in which the researchers calculated the incremental wear distance between simulations. This 2004 model is another example in which contact stress and contact slip (and other quantities) have a delayed ("explicit") dependence on incremental wear distance, rather than a simultaneous ("implicit") dependence.

[0064] Another related model from 2008 describes the correlation between material hardness and material yield strength. The original Archard wear model involved material hardness. However, material yield strength data is usually easier to obtain than hardness, so other references to wear models mention substituting yield strength into the wear model.

[0065] Discussion of Example Implementations

[0066] Considered by The evolution of the wear distance at a given surface position S, using the trapezoidal rule, is given by the following incremental form:

[0067]

[0068] In the above equation:

[0069] a) t+Δt refers to a value or expression evaluated for the current number of increments of the simulation.

[0070] b) t refers to a value or expression evaluated for the previous number of increments of the simulation.

[0071] c) ΔW is the incremental wear distance.

[0072] d) is a unitless wear coefficient that depends on the wear distance of the surface s, the contact pressure, the temperature and the field variables in the current increment.

[0073] e)μ fric is the friction coefficient at the node, which itself depends on the contact pressure, temperature, contact slip value, and field variables in the current increment.

[0074] f)σ P (h,W) is the contact pressure, which depends on the current penetration h and the wear distance W.

[0075] g)σ y is the yield stress of the material of the wear surface.

[0076] h) Δγ is the slip increment.

[0077] Thus, incremental wear and / or wear evolution may depend on the current contact stress, which in turn may depend on the current wear distance.Such cyclic dependencies may apply to other variations of the wear model that may still employ embodiments.

[0078] In addition to discretizing contact constraints on secondary surfaces, finite elements may also involve discretizing contact surfaces into element faces and nodes. Ultimately, contact node forces may be combined from a single contact constraint to solve for equilibrium. Any modeling of contact-based wear on both secondary and primary surfaces may require accumulated wear values ​​at the nodes. For example, accumulated wear at a contact constraint may be limited to the secondary surface, and constrained wear may not be a node value for output purposes. For example, in order to accumulate wear at a primary node, if the face connected to the node is in the shadow of the constraint-attached region projected onto the primary surface, the primary node may have contributions from multiple constraints.

[0079] Figure 1 An example finite element system 100 is illustrated that illustrates contributions from multiple constraints. Figure 1 As shown, a node 102a on a two-dimensional (2D) primary surface 104a has wear contributions 106a-106c from participating in three contact constraints 108a-108c centered at three secondary nodes 102b1-102b3 on a secondary surface 104b.

[0080] Thus, the finite element system 100 illustrates that nodal wear can have contributions from multiple constraints (e.g., 108a-108c), while a single constraint clearance can be modified by interpolated wear from multiple nodes (e.g., 102b1-102b3). With implicit processing, such bidirectional dependencies can lead to tight coupling between contact constraints (e.g., 108a-108c), thereby undermining the basic architecture of the finite element code, in which individual constraint contributions (e.g., 106a-106c) are combined without relying on information from other constraints. A novel approach is described below in which embodiments achieve such fully implicit wear processing with minimal changes to existing architecture and / or code flow.

[0081] Embodiments may include two exemplary aspects described below for fully implicit processing to accumulate wear on the minor and major surfaces (eg, 104a and 104b ), respectively.

[0082] In an embodiment, a first exemplary aspect may be that the sub-surface and W are K Nodal wear is introduced as an unknown at each node (e.g., 102a and 102b1 to 102b3) on the major surfaces (e.g., 104a and 104b). These additional unknowns may require additional equations, one for each node, and they may be Here is how the node incremental wear can be calculated Next, you can use The current value of the continuous wear field is interpolated, where is the node wear shape function. The contact stress can be calculated by the current constraint penetration, which can be modified as Here, on the (secondary or primary) surface J, (e.g., 104a or 104b) can be a constrained average quantity. Therefore, when the increment converges, the contact stress can be consistent with the current node wear value.

[0083] According to an embodiment, a second exemplary aspect may be to decompose the incremental node wear into the sum of contributions (e.g., 106a to 106c) from individual contact constraints (e.g., 108a to 108c) in which the node (e.g., 102a) participates via constraint coefficients. To this end, the current incremental wear on the primary or secondary surface (e.g., 104a or 104b, respectively) at node K may be defined as the average over the attached area, where is the shape function associated with the node, so that the node shape functions within the element face add up to 1 (one). The denominator can be equated to the node area AK .

[0084]

[0085] Embodiments may use a pull shape function for a single constraint I on a subsurface (e.g., 104b) to decompose the numerator into the sum of constraints. In addition, can be applied within each subsurface. Therefore, the following equation applies:

[0086]

[0087] In one embodiment, each constraint contribution may be approximated as:

[0088]

[0089] According to another embodiment, ΔW in the above equation I can be the constraint wear increment given by:

[0090]

[0091] Further, according to yet another embodiment, the above constraint value can be calculated with constraint coefficient c according to the following equation: IK Distributed to both secondary nodes and primary nodes (e.g., 102b1 to 102b3 and 102a), respectively:

[0092]

[0093] Therefore, in the implementation scheme, the current node wear This can be done by applying the known wear from previous increments Add to the independent constraint contribution ΔW I c IK The independent constraint contributions can be combined in any known way to combine any number of nodes in a finite element.

[0094] According to another embodiment, in order to solve the canonical equilibrium equations with the additional nodal wear equations introduced above, the Newton scheme can be used in most finite element codes. In yet another embodiment, the Newton scheme can include the derivatives of the governing equations that produce the stiffness matrix. For example, the derivatives of the additional wear equations can give the following equation:

[0095]

[0096] In an embodiment, the above summation terms over a single contact constraint may result in independent stiffness contributions for each constraint, which may be combined in any known manner for combining any nodal quantities in a finite element.

[0097] Figure 2 2 is a flow chart of an example method 200 for implicit wear modeling using Newton's method to solve equations according to an embodiment. The method 200 is computer-implemented and can be implemented using any computing device (e.g., a processor) or combination of computing devices known to those skilled in the art. In an embodiment, the method 200 can be implemented using an existing finite element code via coding changes.

[0098] The method 200 begins at step 201 by inputting wear attributes and assigning the wear attributes to contact surfaces (e.g., 104a and 104b ( Figure 1 )). At steps 202a to 202n, the method 200 loops through one or more increments. Specifically, at step 203, the method 200 starts a given increment. At steps 204a to 204n, the method 200 performs one or more iterations i of the given increment.

[0099] continue Figure 2 At step 205, for the current iteration i, method 200 performs the following operations:

[0100] a) combining the forces and stiffnesses of the canonical elements in any known way of combining any nodal quantities in a finite element;

[0101] b) For each constraint I, additionally calculate:

[0102] i. Constraint wear from the previous iteration i–1

[0103] ii. Based on the modified gap equation and Modification of clearance and contact stresses; and

[0104] iii. The wear increment at the current iteration i from the value at the previous iteration i–1 based on the equation

[0105] c) Based on the equation ΔW K =ΔW K +ΔW I c IK , distributing the constraint wear increment contribution to nodes (e.g., 102a( Figure 1 ));as well as

[0106] d) Generate the stiffness term K WW ,K UW ,K WU .

[0107] Continue again Figure 2At step 206, the method 200 determines whether the current iteration i has converged. If not, at step 207, the method 200 proceeds to the next iteration i+1. Otherwise, at step 208, the method 200 ends the given increment. At step 209, the method 200 outputs the wear result.

[0108] Figure 3 The working principle of an example ball bearing 300 that can be simulated using embodiments is illustrated. Figure 3 The illustrated example ball bearing 300 includes balls 312a to 312h, an inner race 314a, an outer race 314b, and a hub 316. A ball bearing (e.g., 300) is a rolling element bearing that uses balls (e.g., 312a to 312h) to maintain the spacing between bearing races (e.g., 314a and 314b). The purpose of a ball bearing (e.g., 300) is to reduce rotational friction and support radial and axial loads. The ball bearing achieves this purpose by using at least two races (e.g., 314a and 314b) to accommodate balls (e.g., 312a to 312h) and transmit loads through the balls. In most applications, one race (e.g., 314b) is fixed, while the other race (e.g., 314a) is attached to a rotating component (e.g., a hub or shaft 316). When one bearing race (e.g., 314a) rotates, it causes the balls (e.g., 312a to 312h) to rotate as well. Because the balls (e.g., 312a to 312h) are rolling, they have a much lower coefficient of friction than when two flat surfaces slide against each other. Figure 3 , arrow 318 shows the direction of rotation of the example ball bearing 300 .

[0109] As the balls 312a-312h move around races 314a and 314b during one or more sample cycles, embodiments may be used to simulate the wear of the balls 312a-312h of the example ball bearing 300. For example, in embodiments, the simulation may include moving each of the balls 312a-312h one-eighth of the distance around races 314a and 314b during a single sample cycle and determining the wear as a result of the movement.

[0110] Example Results

[0111] FIG. 4A to FIG. 4E Stages 400a to 400e of an example simulation of surface wear of torsion blocks 422a and 422b, respectively, are illustrated, performed in accordance with an embodiment. In an embodiment, FIG. 4A to FIG. 4E The example simulates incremental 90° twisting of block 422a relative to block 422b, with each increment being approximately 1° of twist. Other known increment sizes are also suitable. FIG. 4A to FIG. 4EIn the example simulation of FIG. 4 , according to another embodiment, blocks 422a and 422b may have the same material, part size, and / or assigned surface wear properties, but may have unequal mesh refinements.

[0112] Figure 4A An initial stage 400a of an example simulation is shown before twisting of block 422a relative to block 422b begins, according to an embodiment. Figure 4B A second stage 400b of the example simulation is shown in which block 422a has been twisted a certain number of increments relative to block 422b. Figure 4C A third stage 400c of the example simulation is shown, in which block 422a has been twisted an additional increment relative to block 422b (ie, beyond stage 400b). Figure 4D A fourth stage 400d of the example simulation is shown, in which block 422a has been twisted by a greater increment relative to block 422b (ie, beyond stage 400c). Figure 4E The final stage 400e of the example simulation is shown, in which block 422a has completed a 90° twist relative to block 422b (i.e., relative to its Figure 4A of the initial position in stage 400a).

[0113] Figure 4E Also shown are finite element mesh blocks 424a and 424b and shaded reference numeral 426. Finite element mesh blocks 424a and 424b are used in an embodiment to perform the FIG. 4A to FIG. 4E Model of the illustrated simulation. It should be noted that blocks 424a and 424b have different mesh refinements, with block 424a having a finer mesh than block 424b. Finite element mesh blocks 424a and 424b graphically depict the varying wear distance along the surfaces of blocks 422a and 422b, respectively, after the final stage 400e of the example simulation. As shown by finite element mesh block 424a with reference to shaded label 426 for block 422a, in an embodiment, region 428a may have a wear distance of approximately 0.000000 to 0.000063, region 428b may have a wear distance of approximately 0.000063 to 0.000126, region 428c may have a wear distance of approximately 0.000126 to 0.000189, region 428d may have a wear distance of approximately 0.000189 to 0.000252, region 428e may have a wear distance of approximately 0.000252 to 0.000315, and region 428e may have a wear distance of approximately 0.000315 to 0.000378. Likewise, finite element mesh block 424b and shading 426 show that block 422b has the same level of wear distance as block 422a at final stage 400e. It should be noted that in embodiments, different wear distances may be shown by color coding rather than shading; other known indicia are also suitable.

[0114] FIG. 4A to FIG. 4E The results of the example simulations indicate consistent wear distance values ​​for the two blocks 422a and 422b (ie, Figure 4E 424a and 424b (as graphically shown in FIG. 426 by finite element mesh blocks 424a and 424b). According to an embodiment, a small amount of wear may occur after each quarter turn. Further, in yet another embodiment, about 5% of a component (e.g., block 422a or 422b) may be worn away after 1,000 turns. FIG. 4A to FIG. 4E The results of the example simulation also reflect the ability of embodiments to model wear on two surfaces that are in contact interaction (e.g., the surfaces of both block 422a and block 422b). In addition, the results demonstrate how embodiments can minimize or eliminate dependence on numerical details such as mesh refinement (e.g., the example simulation is not affected by unequal mesh refinement of finite element mesh models 424a and 424b), secondary / primary roles, etc.

[0115] Figure 5 Example simulation 500 results for a surface wear simulation of a torsion block according to an embodiment are illustrated. FIG. 4A to FIG. 4E , by simulating block 422a relative to block 422b ( Figure 4A ) to generate the results from simulation 500, except that the results of example simulation 500 were obtained using varying increments, each increment size up to about 8° of twist, and an average of about 2.8° of twist per increment. Other known variations in increment size are also suitable. Figure 5As shown, finite element mesh block 524a and corresponding shaded reference numeral 526a display the wear distance of block 422a upon completion of example simulation 500, while finite element mesh block 524b and corresponding reference numeral 526b display a similar wear distance of block 422b. The finite element mesh block 524a and the corresponding shaded label 526a show an area 528a1 with a wear distance of approximately 0.000000 to 0.000063, an area 528a2 with a wear distance of approximately 0.000063 to 0.000126, an area 528a3 with a wear distance of approximately 0.000126 to 0.000189, an area 528a4 with a wear distance of approximately 0.000189 to 0.000252, an area 528a5 with a wear distance of approximately 0.000252 to 0.000315, and an area 528a6 with a wear distance of approximately 0.000315 to 0.000378. Similarly, finite element mesh block 524b and corresponding shaded label 526b show an area 528b1 with a wear distance of approximately 0.000000 to 0.000064, an area 528b2 with a wear distance of approximately 0.000064 to 0.000128, an area 528b3 with a wear distance of approximately 0.000128 to 0.000192, an area 528b4 with a wear distance of approximately 0.000192 to 0.000257, an area 528b5 with a wear distance of approximately 0.000257 to 0.000321, and an area 528b6 with a wear distance of approximately 0.000321 to 0.000385.

[0116] From Figure 5 and Figure 4E The results of the illustrated example simulations show that the wear distances from the embodiments are very consistent with each other. The results may also show that the wear distances predicted by the embodiments may not be particularly sensitive or even completely insensitive to the details of the increments. It should be noted that in embodiments, the increment size may need to be small enough to accurately accumulate the node contact energy that affects the wear.

[0117] Figure 6 An example of simulation 600 results of surface wear of a torsion block according to yet another embodiment is illustrated. Figure 6 In the implementation scheme, similar to FIG. 4A to FIG. 4E , example 600 illustrates the simulation results from block 422a relative to block 422b ( Figure 4A ), except that example 600 simulates only a 45° twist, i.e., FIG. 4A to FIG. 4E The example simulates half of a 90° twist. Other known twist magnitudes are also suitable. Figure 6As shown, the finite element model 624 and corresponding shaded labels 626 display the wear distance results for the block 422b upon completion of the example simulation 600. The finite element model 624 and corresponding shaded labels 626 show a region 628a with a wear distance of approximately 0.000000 to 0.000032, a region 628b with a wear distance of approximately 0.000032 to 0.000065, a region 628c with a wear distance of approximately 0.000065 to 0.000097, a region 628d with a wear distance of approximately 0.000097 to 0.000129, a region 628e with a wear distance of approximately 0.000129 to 0.000162, and a region 628f with a wear distance of approximately 0.000162 to 0.000194.

[0118] Figure 6 The results shown show that FIG. 4A to FIG. 4E The wear value for the 90° twist of the example simulation can be approximately twice the wear value for the 45° twist of the example simulation 600. For example, multiplying the upper limit of region 628f, 0.000194, by two yields a value of 0.000388, which differs from the upper limit of region 428f, 0.000378, by only 0.000010 ( Figure 4E ). Embodiments may utilize the foregoing approximation when simulating representative wear cycles.

[0119] 7A to 7F Stages 700a to 700f of an example simulation of surface wear of sliders 722a and 722b, respectively, are illustrated according to an embodiment. 7A to 7F In FIG. 7 , the wear distance is indicated by color code 726. According to an embodiment, 7A to 7F An example simulation of can approximate the accumulated wear during, for example, 160,000 physical cycles or load cycles by directly simulating, for example, seven sample cycles, where each individual cycle may include sliding block 722a along the surface of block 722b from one end of block 722b to the other end. Other numbers of physical cycles and / or sample cycles are also suitable. 7A to 7F In an example simulation, according to an embodiment, an initial step may be performed to push the top block 722a into the bottom block 722b. Further, according to yet another embodiment, a second step may then include establishing boundary conditions (e.g., displacement and / or velocity boundary conditions) for the simulation, followed by simulating the cycle of sliding block 722a along the surface of block 722b. In an embodiment, one or more wear properties may be specified for the example simulation. For example, defining wear properties may include specifying a wear coefficient and / or its dependence on wear distance, contact pressure, surface temperature, and / or other field variables for each contacting surface, as well as other examples. According to another embodiment, 7A to 7FThe example simulation may also adjust the number of physical cycles represented by each sample cycle and repeat the second step described above until a stop condition (eg, a target maximum wear value) is met.

[0120] Fig. 7A A first stage 700a of the example simulation is shown before block 722a begins sliding along block 722b, with block 722a in an initial position. Figure 7B A second stage 700b of the example simulation is shown, wherein block 722a has slid toward a first end of block 722b. Figure 7C A third stage 700c of the example simulation is shown, wherein block 722a has slid toward the second end of block 722b. Fig.7D A fourth stage 700d of the example simulation is shown, wherein block 722a has again slid toward the first end of block 722b. Fig. 7E A fifth stage 700e of the example simulation is shown, wherein block 722a has again slid toward the second end of block 722b. Figure 7F The final stage 700f of the example simulation is shown, where block 722a has returned to the Fig. 7A The initial position is shown in .

[0121] Figure 8 The use of a common scale 826 is illustrated 7A to 7F Example simulation of wear distance results. Figure 8 In FIG. 1 , the wear distance results are illustrated via finite element models 824a and 824b (corresponding to blocks 722a and 722b, respectively) and shaded number 826. Referring to shaded number 826, finite element models 824a and 824b graphically depict the wear distance results in FIG. 7A to 7F The final stage of the example simulation is 700f ( Figure 7F ) followed by blocks 722a and 722b ( Fig. 7A As indicated by finite element models 824a and 824b and reference numeral 826, region 828a has a wear distance of about 0.000 to 0.002, region 828b has a wear distance of about 0.002 to 0.004, region 828c has a wear distance of about 0.004 to 0.007, region 828d has a wear distance of about 0.007 to 0.009, region 828e has a wear distance of about 0.009 to 0.011, region 828f has a wear distance of about 0.011 to 0.013, region 828g has a wear distance of about 0.013 to 0.016, and region 828h has a wear distance of about 0.016 to 0.018.

[0122] Fig. 9 FIG. 9 is a graph 900 of wear coefficient 934 versus wear distance 932 according to an embodiment. Fig. 9, used to perform simulations (e.g. 7A to 7F The wear coefficient 934 of the example simulation of (for example, in 7A to 7F Still in graph 900, dashed line 938 indicates a varying wear factor 934 that may be used in embodiments (e.g., as described below with respect to Fig.11 900 shows that at point 942, when the wear distance is 0 (zero), a simulation using the wear coefficient given by lines 936 and 938 may have a wear coefficient of 2.5x10 -10 According to an embodiment, when the simulated wear distance 932 using the wear coefficient given by line 938 reaches a threshold value (e.g., 0.01), a transition 944 to a new higher value of the wear coefficient 934 may occur at point 946. In another embodiment, the wear coefficient 934 value at point 946 may be, for example, ten times the initial value, such as 2.5x10 -9 Other known wear coefficients and / or critical wear distance values ​​are also suitable. Next, after reaching the threshold wear distance value, the simulated wear coefficient 934 using the wear coefficient given by line 938 remains at the new higher value, as shown in region 948. In contrast, the simulated wear coefficient 934 using the wear coefficient given by line 936 remains constant even after reaching or exceeding the threshold wear distance value, as shown in region 952.

[0123] Fig.10 The use of multiple scales 1026a and 1026b is illustrated. 7A to 7F Example simulation of wear distance results. Fig.10 , wear distance results are illustrated via finite element models 1024a and 1024b and corresponding shaded labels 1026a and 1026b. Fig.10 The example shows that a constant wear factor is used to perform, for example, 160,000 physical cycles. 7A to 7F The wear distance results after the example simulation of Fig. 9 Referring to the corresponding reference numerals 1026a and 1026b, the finite element models 1024a and 1024b respectively graphically depict the 7A to 7F The final stage of the example simulation is 700f ( Figure 7F ) followed by blocks 722a and 722b ( Fig. 7A) of the surface. As indicated by the finite element model 1024b and the corresponding shaded number 1026b, for block 722b, region 1028b1 has a wear distance of about 0.000 to 0.002, region 1028b2 has a wear distance of about 0.002 to 0.003, region 1028b3 has a wear distance of about 0.003 to 0.005, region 1028b4 has a wear distance of about 0.005 to 0.006, and region 1028b5 has a wear distance of about 0.006 to 0.008. Similarly, as indicated by the finite element model 1024a and the corresponding shaded number 1026a, for block 722a, region 1028a4 has a wear distance of about 0.011 to 0.014, and region 1028a5 has a wear distance of about 0.014 to 0.018. It should be noted that according to an embodiment, the finite element model 1024a does not have wear corresponding to the region 1028a1 (wear distance is approximately 0.000 to 0.004), the region 1028a2 (wear distance is approximately 0.004 to 0.007), and / or the region 1028a3 (wear distance is approximately 0.007 to 0.011).

[0124] Fig.11 An example simulation 1100 of surface wear of a slider according to another embodiment is illustrated. 7A to 7F , Figure 8 and Fig. 9 , example 1100 also illustrates blocks 722a and 722b ( ) that accumulate during a physical cycle or load cycle by directly simulating a sample cycle. Fig. 7A ), except that example 1100 illustrates approximate wear simulation results for, for example, 111,498 physical cycles, and wherein a varying wear coefficient is used, as described above with respect to Fig. 9 As described in line 938. Other numbers of physical cycles are also suitable. Fig.11As shown, the wear distance results of blocks 722a and 722b after completing the example simulation 1100 are illustrated via finite element models 1124a and 1124b and corresponding shaded labels 1126a and 1126b. For block 722b, the finite element model 1124b and corresponding shaded labels 1126b show an area 1128b1 with a wear distance of approximately 0.000 to 0.001, an area 1128b2 with a wear distance of approximately 0.001 to 0.002, an area 1128b3 with a wear distance of approximately 0.002 to 0.003, an area 1128b4 with a wear distance of approximately 0.003 to 0.005, and an area 1128b5 with a wear distance of approximately 0.005 to 0.006. Likewise, for block 722a, finite element model 1124a and corresponding shaded reference 1126a show region 1128a3 with a wear distance of approximately 0.013 to 0.020, region 1128a4 with a wear distance of approximately 0.020 to 0.027, and region 1128a5 with a wear distance of approximately 0.027 to 0.033. It should be noted that, according to an embodiment, block 1124a does not include region 1128a1 (wear distance of approximately 0.000 to 0.007) and / or region 1128a2 (wear distance of approximately 0.007 to 0.013).

[0125] From Fig.11 The results of the example simulation 1100 shown are presented with the Fig.10 Compared to the results of the illustrated simulation, greater wear occurs on the top block 722a in fewer cycles. For example, Fig.11 For region 1128a5, the upper limit value is 0.033, which is greater than that for Fig.10 The comparable value of area 1028a5 is 0.018. This increase in wear may be due to Fig.11 The results from the example simulation 1100 show that in Fig.10 and Fig.11 In both cases, the wear on the bottom block 722b remains below the transition threshold. Specifically, area 1028b5 ( Fig.10 )'s upper limit value 0.008 and the comparable value 0.006 of region 1128b5 are less than the transition threshold, e.g. Fig. 9 0.01 as shown in the graph 900. In addition, the latter value 0.006 is lower than the former value 0.008 because Fig.10 The results shown are compared to the simulation obtained for example 160,000 cycles Fig.11 The result is a smaller number of cycles, such as 111,498 cycles.

[0126] Fig.12 According to the implementation plan Fig.10 and Fig.11An example of a graph 1200 of a simulated maximum wear distance 1256 versus the number of physical cycles 1254. In graph 1200, Fig.10 An example simulation of is shown by solid line 1236 and includes, for example, points 1258a1 to 1258a7 for seven sample cycles. Further, in graph 1200, Fig.11 An example simulation of is shown by dashed line 1238 and includes, for example, points 1258b1 to 1258b7 for seven sample cycles. As shown at point 1258a7 of solid line 1236, simulating seven sample cycles results in approximately, for example, 160,000 physical cycles 1254 and reaches a maximum wear distance 1256 of, for example, 0.018. In graph 1200, it can be observed that when the maximum wear distance 1256 of simulation 1238 reaches or exceeds a threshold value (e.g., 0.01) at point 1258b4, then, as described above with reference to Fig. 9 As described, simulation 1238 transitions to a new, higher wear coefficient value. This transition also causes simulation 1238 to have a final maximum wear distance 1256 greater than simulation 1236, e.g., 0.033 at point 1258b7 and 0.018 at point 1258a7. Conversely, after such transition (e.g., at point 1258b4), simulation 1238 also approximates a smaller number of physical cycles during each remaining sample cycle (e.g., between points 1258b4 and 1258b7). Therefore, approximating fewer physical cycles causes the final number of physical cycles 1254 of simulation 1238 to be lower than the final number of physical cycles of simulation 1236, e.g., 160,000 cycles at point 1258a7 and 111,498 cycles at point 1258b7.

[0127] Fig.13A and Fig. 13B The embodiment according to the present invention is illustrated Fig.11 Examples 1300a and 1300b of the contact pressure of the sliding block in the simulation. Fig.13A As shown, the finite element model 1324a and the shaded number 1326a illustrate the simulation 1100 ( Fig.11 ) before block 722a( Fig. 7A ) contact pressure. As indicated by finite element model 1324a and shaded numeral 1326a, for block 722a, region 1328a4 has a contact pressure of approximately 20.064 to 26.752, and region 1328a5 has a contact pressure of approximately 26.752 to 33.440. It should be noted that Fig.13AIn the embodiment of the present invention, the finite element model 1324a does not include a region 1328a1 indicating a contact pressure of about 0.000 to 6.688, a region 1328a2 indicating a contact pressure of about 6.688 to 13.376, and / or a region 1328a3 indicating a contact pressure of about 13.376 to 20.064. Fig. 13B As shown, according to an embodiment, the contact pressure of block 722a after simulation 1100 is performed to approximate, for example, 111,498 physical cycles is illustrated via finite element model 1324b and shaded reference numeral 1326b. As indicated by finite element model 1324b and shaded reference numeral 1326b, for block 722a, region 1328b4 has a contact pressure of approximately 18.926 to 25.235, and region 1328b5 has a contact pressure of approximately 25.235 to 31.543. It should be noted that in Fig. 13B In the embodiment of the present invention, the finite element model 1324b does not include a region 1328b1 indicating a contact pressure of about 0.000 to 6.309, a region 1328b2 indicating a contact pressure of about 6.309 to 12.617, and / or a region 1328b3 indicating a contact pressure of about 12.617 to 18.926. Fig.13A and Fig. 13B As shown, wear caused by performing simulation 1100 may result in a change in contact pressure values, for example, from an upper limit of 33.440 in region 1328a5 in example 1300a to an upper limit of 31.543 in region 1328b5 in example 1300b.

[0128] Fig.14 An example system 1400 is illustrated in which wear occurs at the corners of a slider, according to an embodiment. Fig.14 Depicts the wear that occurs at corners 1462a and 1462b when block 1422a slides along the surface of 1422b. According to another embodiment, increasing the wear at corners 1462a and 1462b can correspondingly reduce stress concentration. For example, when right-angle corners (e.g., 1462a and / or 1462b) are in contact, stress peaks in contact pressure may occur at and / or around the corners, and those areas may experience greater wear. This may be because Archard's law and the physical behavior simulated therefrom show that the wear rate is directly dependent on the contact pressure value. Therefore, the contact pressure peak may mean a greater wear rate and an overall greater wear distance. As the corners begin to wear at a faster rate, the original right-angle corner shape may change, and for this modified shape, the contact pressure may begin to decline.

[0129] In an embodiment, the node wear distance may evolve according to Archard's law or a suitable known variation thereof. According to another embodiment, among suitable known variations of Archard's law, the most intuitive variation may have an incremental node wear distance proportional to the incremental node friction energy density, for example, as expressed by the following relationship:

[0130]

[0131] In the above relationship:

[0132] a)Δw i is the incremental wear due to the movement increment at node “i”.

[0133] b) is the friction contribution due to constraint ‘j’ at node ‘i’.

[0134] c) Δγ j is the slip increment of constraint “j”.

[0135] d) A j is the constraint region of constraint “j”.

[0136] In yet another embodiment, the contact penetration distance h may be affected by the wear distance, for example, as expressed by the following equations and relationships:

[0137]

[0138]

[0139] h≤h no_werar

[0140] σ P =K pnlty h, where h>0

[0141] In the above equations and relations:

[0142] a)x s Indicates the position of the "secondary" node.

[0143] b) Represents the position of the projection of the secondary node on the "primary" surface in the normal direction n.

[0144] c)w s is the wear distance of the secondary node.

[0145] d)h no_werar is the penetration distance excluding wear.

[0146] e)σ P is the contact pressure.

[0147] f)K pnlty Contact penalty stiffness.

[0148] Fig.15 An example finite element 1500 and associated contact penetration distance according to an embodiment are illustrated. According to such embodiments, Fig.15 As shown, finite element 1500 includes nodes 1502a and 1502b and edge 1569. Finite element 1500 has an associated contact penetration distance 1564 before being affected by the wear distance, secondary node location 1566, and normal vector 1568.

[0149] Exemplary Method Implementations

[0150] Fig.16 is a flow chart of a method 1600 for determining wear according to an embodiment. The method 1600 is computer-implemented and may be performed using any computing device (eg, a processor) or combination of computing devices known to those skilled in the art.

[0151] Method 1600 begins at step 1601: obtaining a representation of a first object (eg, 422a ( Figure 4A )、722a( Fig. 7A ) or 1422a( Fig.14 Next, at step 1602, for a given node (e.g., 102a ( Figure 1 )、102b1 to 102b3( Figure 1 ) or 1502a to 1502b( Fig.15 )), method 1600 associates wear variables and links the associated wear variables to multiple contact constraints (e.g., 108a to 108c ()) associated with a given node. Figure 1 )). At step 1603, the method 1600 then performs a first object and a second object (eg, 422b ( Figure 4A )、722b( Fig. 7A ) or 1422b( Fig.14)) to determine wear at a given node. Executing the simulation includes iteratively (i) using the finite element mesh, the associated wear variables, and the plurality of contact constraints to determine a wear distance for a given move increment, and (ii) updating a position of a given node in the finite element mesh based on the determined wear distance for the given move increment until a wear distance for each of a plurality of move increments is determined. Executing the simulation also includes determining wear at a given node based on the determined wear distance for each of the plurality of move increments. Then, at step 1604, the method outputs an indication of the determined wear.

[0152] As described above, method 1600 is computer-implemented, and therefore, the functions and effective operations (e.g., obtaining (1601), associating and linking (1602), executing (1603), and outputting (1604)) are automatically performed by one or more digital processors. Method 1600 may also be implemented using any computer device or combination of computing devices known in the art. In other examples, method 1600 may be implemented using the following description of Fig.17 and Fig.18 The computer / device 50 and / or 60 described above may be used to implement the invention.

[0153] In an embodiment of method 1600, determining the wear distance for a given move increment may include executing a Newton iteration scheme to determine the wear distance until a convergence check is satisfied. According to another embodiment of method 1600, executing the Newton iteration scheme may include: in each iteration of the Newton iteration scheme, for each contact constraint in a plurality of contact constraints, determining at least one of: (i) a constraint wear value, (ii) a modified clearance value, (iii) a contact stress value, and (iv) a wear increment value.

[0154] According to an embodiment of method 1600, for a given iteration, the position of a given node in the finite element mesh used in determining the wear distance may be an updated position of the given node from a previous iteration. In another embodiment of method 1600, for a given iteration, updating may include modifying the updated position of the given node from a previous iteration based on the wear distance determined for the given iteration.

[0155] In an embodiment of method 1600, the obtained finite element mesh may be a first finite element mesh. At least one contact constraint of the plurality of contact constraints may include (i) at least one node of the first finite element mesh and (ii) at least one node of a second finite element mesh representing a second object.

[0156] According to an embodiment of method 1600, determining the wear distance for a given move increment may include calculating a total constraint contribution based on a plurality of contact constraints and constraint coefficient values. Determining the wear distance for a given move increment may also include determining the wear distance based on the calculated total constraint contribution.

[0157] Embodiments (e.g., method 1600) may be used as part of a manufacturing method. For example, method 1600 may be used in an optimization loop, wherein method 1600 is used to evaluate the wear of a real-world object. In such embodiments, based on the determined wear, the design of the real-world object may be approved, or defects may be identified. In response to identifying defects, changes may be made to the design, for example, in a finite element model, and after making these changes, the new design may be evaluated using method 1600. This process may be repeated until a design that meets the requirements is identified. After determining a design that meets the requirements, a real-world object that meets the requirements may be manufactured. Further, embodiments may begin by measuring or obtaining data about a real-world object and creating a finite element model representing the real-world object. The finite element model may then be used in embodiments to determine the wear characteristics of the real-world object. Further, the finite element model may also be used in the aforementioned optimization loop to (i) determine an improved design for the real-world object, and (ii) manufacture an improved version of the real-world object, for example, a version that meets the wear requirements.

[0158] Exemplary Advantages

[0159] Embodiments can simultaneously handle the interdependencies between wear distance, contact stress, and contact slip for implicit finite element simulations, which improves accuracy because contact wear and other contact quantities are consistent.

[0160] Further, embodiments may determine the incremental wear distance at a surface node of the finite element model by considering all contact constraints involved in the node.

[0161] The implementation of the embodiment also does not require any changes to the code architecture of any implicit finite element code.

[0162] Furthermore, embodiments are not limited by the need to distinguish between "primary" and "secondary" numerical contributions to contact surfaces.

[0163] The embodiment is operable even with a balanced primary-secondary role allocated.

[0164] Computer Support

[0165] The implementation can be implemented in existing software and CAD and CAE platforms. For example, the implementation can use 3DS features and functionality of the software, including those provided by applicant-assignee Dassault Systèmes Americas Corporation Applications and other examples.

[0166] Fig.17 is a schematic diagram of a computer network in which embodiments may be implemented. Client computers / devices 50 and server computers 60 provide processing, storage, and input / output devices for executing application programs, etc. Client computers / devices 50 may also be linked to other computing devices, including other client devices / processors 50 and server computers 60, via a communications network 70. Communications network 70 may be a remote access network, a global network (e.g., the Internet), a cloud computing server or service, a global collection of computers, a local area network or a wide area network, and a currently used corresponding protocol (e.g., TCP / IP, Other electronic device / computer network architectures are also suitable.

[0167] Fig.18 It is an example Fig.17 70 . Each computer node 50, 60 contains a system bus 79, where a bus is a set of hardware lines used for data transfer between components of a computer or processing system. The system bus 79 is essentially a shared pipe that connects the different elements of the computer system (e.g., processor, disk storage device, memory, I / O ports, network ports, etc.), which enables information to be passed between the elements. Attached to the system bus 79 is an I / O device interface 82 for connecting various input and output devices (e.g., keyboard, mouse, display, printer, speakers, etc.) to the computer node 50, 60. The network interface 86 allows the computer node to connect to a network attached to the network (e.g., Fig.17 The memory 90 is used to implement the embodiments of the present disclosure (for example, the method 200 ( Figure 2 ), method 1600( Fig.16 ) etc.) provide volatile storage for computer software instructions 92a and data 94a. Disk storage 95 provides non-volatile storage for computer software instructions 92b and data 94b for implementing the embodiments of the present disclosure. The central processor unit 84 is also attached to the system bus 79 and provides execution of computer instructions.

[0168] In one embodiment, the processor routines 92a to 92b and data 94a to 94b are computer program products (generally referred to as 92) that include a non-transitory computer-readable medium (e.g., a removable storage medium such as a DVD-ROM, CD-ROM, floppy disk, tape, etc.) that provides at least a portion of the software instructions for the disclosed system. The computer program product 92 can be installed by any suitable software installation program known in the art. In another embodiment, at least a portion of the software instructions can also be downloaded via a cable, communication and / or wireless connection. In other embodiments, the disclosed program is a computer program propagation signal product contained on a propagation medium (e.g., radio waves, infrared waves, laser waves, sound waves, or radio waves propagated through a global network such as the Internet or other networks). Such carrier media or signals provide at least a portion of the software instructions for the disclosed routines / programs 92.

[0169] In alternative embodiments, the propagated signal is an analog carrier wave or a digital signal carried on a propagation medium. For example, the propagated signal may be transmitted through a global network (e.g., the Internet), a telecommunications network, or other network (such as Fig.17 In one embodiment, the propagated signal is a signal transmitted over a propagation medium over a period of time, such as instructions for a software application sent in packets over a network over a period of milliseconds, seconds, minutes, or longer. In another embodiment, the computer readable medium of the computer program product 92 is a propagation medium that can be received and read by the computer system 50, such as by receiving the propagation medium and identifying the propagation signal contained in the propagation medium, as described above for the computer program propagation signal product.

[0170] Generally speaking, the term "carrier medium" or transient carrier encompasses the aforementioned transient signals, propagation signals, propagation media, storage media, etc.

[0171] In other embodiments, program product 92 may be implemented as so-called software as a service (SaaS) or other installation or communication support for end users.

[0172] Exemplary Specifications for Surface Wear Factors

[0173] In implementation, the surface wear coefficient can be specified to Abaqus using the following keyword interface for general contact:

[0174] *Surface property, name = WEAR1

[0175] * Wear Surface Properties, FricCoefDep = No, Unitless = No, Reference Stress = 150

[0176] 1. E-6

[0177] **

[0178] *Surface, name=WearSurf1

[0179] Elset1,

[0180] * Surface, Name = WearSurf2

[0181] Elset2,

[0182] *touch

[0183] *Contact included, all external

[0184] *Surface attribute assignment, attribute = wear

[0185] WearSurf1, WEAR1

[0186] WearSurf2, WEAR1

[0187] According to the implementation scheme, the surface wear coefficient can be specified to Abaqus using the following keyword interface for the contact pair:

[0188] *Surface property, name = WEAR1

[0189] * Wear Surface Properties, FricCoefDep = No, Unitless = No, Reference Stress = 150

[0190] 1. E-6

[0191] *Surface interaction, name = DfltContProp

[0192] **

[0193] *Surface, name=WearSurf1, properties=WEAR1

[0194] Elset1,

[0195] *Surface, name=WearSurf2, properties=WEAR1

[0196] Elset2,

[0197] *Contact pair, type = surface, interaction = DfltContProp

[0198] Surf1, Surf2

[0199] The embodiments or aspects thereof may be implemented in the form of hardware, including but not limited to hardware circuitry, firmware, or software. If implemented in software, the software may be stored on any non-transitory computer-readable medium configured to enable a processor to load the software or a subset of its instructions. The processor then executes the instructions and is configured to operate or cause the device to operate in the manner described herein.

[0200] Further, hardware, firmware, software, routines or instructions may be described herein as performing certain actions and / or functions of a data processor. However, it should be understood that such descriptions included herein are only for convenience and such actions are actually caused by a computing device, processor, controller or other device executing firmware, software, routines, instructions.

[0201] It should be understood that flow charts, block diagrams, and network diagrams may include more or fewer elements, be arranged in different ways, or be presented in different ways. However, it should be further understood that certain embodiments may indicate block diagrams and network diagrams and the number of block diagrams and network diagrams that illustrate the execution of an embodiment implemented in a particular manner.

[0202] Therefore, additional embodiments may also be implemented in a variety of computer architectures, physical computers, virtual computers, cloud computers and / or some combination thereof, and thus the data processor described herein is intended only for illustrative purposes and not as a limitation of the embodiments.

[0203] The teachings of all patents, published applications, and references cited herein are incorporated by reference in their entirety.

[0204] While example embodiments have been particularly shown and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the embodiments as encompassed by the appended claims.

[0205] For example, for purposes of illustration and not limitation, the foregoing description and details of the embodiments in the accompanying drawings relate to applicant-assignee (Dassault Systèmes Americas Corporation) and Dassault Systèmes tools and platforms. Other similar tools and platforms are also suitable.

Claims

1. A computer-implemented method for determining wear, the computer-implemented method comprising: obtaining, in a memory associated with the processor, a finite element mesh representing a first object; For a given node of the obtained finite element mesh, associating a wear variable and linking the associated wear variable to a plurality of contact constraints associated with the given node; performing a simulation of contact between the first object and the second object in a plurality of move increments to determine wear at the given node, performing the simulation comprising: iteratively (i) determining a wear distance for a given move increment using the finite element mesh, the associated wear variables, and the plurality of contact constraints, and (ii) updating a position of the given node in the finite element mesh based on the determined wear distance for the given move increment until a wear distance for each of the plurality of move increments is determined; and determining wear at the given node based on the determined wear distance for each of the plurality of move increments; and An indication of the determined wear is output.

2. The computer-implemented method of claim 1 , wherein determining the wear distance for the given move increment comprises: A Newton iteration scheme is performed to determine the wear distance until a convergence check is met.

3. The computer-implemented method of claim 2, wherein executing the Newton iteration scheme comprises, in each iteration of the Newton iteration scheme: For each contact constraint of the plurality of contact constraints, at least one of: (i) a constraint wear value, (ii) a modified clearance value, (iii) a contact stress value, and (iv) a wear increment value is determined.

4. The computer-implemented method of claim 1, wherein for a given iteration, the position of the given node in the finite element mesh used in determining wear distance is an updated position of the given node from a previous iteration.

5. The computer-implemented method of claim 4, wherein for the given iteration, the updating comprises: The updated position of the given node from the previous iteration is modified based on the wear distance determined for the given iteration.

6. The computer-implemented method of claim 1 , wherein the obtained finite element mesh is a first finite element mesh, and wherein at least one contact constraint of the plurality of contact constraints comprises (i) at least one node of the first finite element mesh and (ii) at least one node of a second finite element mesh representing the second object.

7. The computer-implemented method of claim 1 , wherein determining the wear distance for the given move increment comprises: calculating a total constraint contribution based on the plurality of contact constraints and the constraint coefficient values; and The wear distance is determined based on the calculated total constraint contribution.

8. A computer-based system for determining wear, the computer-based system comprising: processor; as well as a memory having computer code instructions stored thereon, the processor and the memory being configured with the computer code instructions to cause the computer-based system to: obtaining in the memory a finite element mesh representing a first object; For a given node of the obtained finite element mesh, associating a wear variable and linking the associated wear variable to a plurality of contact constraints associated with the given node; performing a simulation of contact between the first object and the second object in a plurality of move increments to determine wear at the given node, performing the simulation comprising: iteratively (i) determining a wear distance for a given move increment using the finite element mesh, the associated wear variables, and the plurality of contact constraints, and (ii) updating a position of the given node in the finite element mesh based on the determined wear distance for the given move increment until a wear distance for each of the plurality of move increments is determined; and determining wear at the given node based on the determined wear distance for each of the plurality of move increments; and An indication of the determined wear is output.

9. The computer-based system of claim 8, wherein in determining the wear distance for the given movement increment, the processor and the memory are configured with the computer code instructions to cause the system to: A Newton iteration scheme is performed to determine the wear distance until a convergence check is met.

10. The computer-based system of claim 9, wherein when executing the Newton iteration scheme, the processor and the memory are configured with the computer code instructions to cause the system, in each iteration of the Newton iteration scheme: For each contact constraint of the plurality of contact constraints, at least one of: (i) a constraint wear value, (ii) a modified clearance value, (iii) a contact stress value, and (iv) a wear increment value is determined.

11. The computer-based system of claim 8, wherein for a given iteration, the position of the given node in the finite element mesh used in determining wear distance is an updated position of the given node from a previous iteration.

12. The computer-based system of claim 11, wherein for the given iteration, in updating the position of the given node, the processor and the memory are configured with the computer code instructions to cause the system to: The updated position of the given node from the previous iteration is modified based on the wear distance determined for the given iteration.

13. The computer-based system of claim 8, wherein the obtained finite element mesh is a first finite element mesh, and wherein at least one contact constraint of the plurality of contact constraints comprises (i) at least one node of the first finite element mesh and (ii) at least one node of a second finite element mesh representing the second object.

14. The computer-based system of claim 8, wherein in determining the wear distance for the given movement increment, the processor and the memory are configured with the computer code instructions to cause the system to: calculating a total constraint contribution based on the plurality of contact constraints and constraint coefficient values; and The wear distance is determined based on the calculated total constraint contribution.

15. A computer program product for determining wear, the computer program product comprising a non-transitory computer readable medium having computer code instructions stored thereon, the computer code instructions being configured to, when executed by a processor, cause a device associated with the processor to: obtaining in a memory a finite element mesh representing a first object; For a given node of the obtained finite element mesh, associating a wear variable and linking the associated wear variable to a plurality of contact constraints associated with the given node; performing a simulation of contact between the first object and the second object in a plurality of move increments to determine wear at the given node, performing the simulation comprising: iteratively (i) determining a wear distance for a given move increment using the finite element mesh, the associated wear variables, and the plurality of contact constraints, and (ii) updating a position of the given node in the finite element mesh based on the determined wear distance for the given move increment until a wear distance for each of the plurality of move increments is determined; and determining wear at the given node based on the determined wear distance for each of the plurality of move increments; and An indication of the determined wear is output.

16. The computer program product of claim 15, wherein in determining the wear distance for the given move increment, the computer code instructions, when executed by the processor, cause the device associated with the processor to: A Newton iteration scheme is performed to determine the wear distance until a convergence check is met.

17. The computer program product of claim 16, wherein when executing the Newton iterative scheme, the computer code instructions, when executed by the processor, cause the device associated with the processor to, in each iteration of the Newton iterative scheme: For each contact constraint of the plurality of contact constraints, at least one of: (i) a constraint wear value, (ii) a modified clearance value, (iii) a contact stress value, and (iv) a wear increment value is determined.

18. The computer program product of claim 15, wherein for a given iteration, the position of the given node in the finite element mesh used in determining wear distance is an updated position of the given node from a previous iteration.

19. The computer program product of claim 18, wherein for the given iteration, in updating the position of the given node, the computer code instructions, when executed by the processor, cause the device associated with the processor to: The updated position of the given node from the previous iteration is modified based on the wear distance determined for the given iteration.

20. The computer program product of claim 15, wherein the obtained finite element mesh is a first finite element mesh, and wherein at least one contact constraint of the plurality of contact constraints comprises (i) at least one node of the first finite element mesh and (ii) at least one node of a second finite element mesh representing the second object.

Images