Ball screw pair raceway wear evolution simulation system based on multi-physical field coupling

Abstract

The application relates to the technical field of ball screw pair wear simulation, and particularly discloses a ball screw pair raceway wear evolution simulation system based on multi-physical field coupling, which collects raceway cross-section parameters, material parameters, lubricant parameters, load speed and initial profile coordinate point sets; according to the profile coordinates and the load distribution, the cross section is divided into a load-bearing wear active area and a geometric sensitive transition area, and independent grids with non-coinciding interface nodes are respectively generated; a Lagrange multiplier field is arranged on the interface, and a weak balance constraint of only transmitting surface force and heat flux is established; according to the constraint, the active area is independently solved to obtain contact stress, friction heat and wear depth, grid reconstruction and field quantity remapping are triggered only in the active area, the transition area grid and field quantity remain unchanged, the output equivalent surface force and heat flux are applied to the transition area interface through the Lagrange multiplier field to update the boundary state and serve as the initial condition of the next round of iteration, and the process is repeated until the total wear depth reaches a set limit value.

Description

Technical Field

[0001] This invention relates to the field of ball screw pair wear simulation technology, specifically to a simulation system for the wear evolution of ball screw raceways based on multi-physics field coupled ball screw pairs. Background Technology

[0002] As a core component of precision mechanical transmission, the ball screw pair suffers from progressive wear of its raceway due to the cyclic contact and relative sliding of the rolling elements during service. This wear directly leads to loss of transmission accuracy and decline in fatigue life. Accurately predicting the evolution of raceway wear is of great significance for high-reliability design.

[0003] Currently, numerical simulation methods based on multi-physics coupling have become the main means of studying this type of wear problem. By simultaneously considering the interaction of multiple physical fields such as contact mechanics, frictional heat effect, lubrication state and material constitutive model, the raceway section is discretized using the finite element method and the material removal process is simulated using an explicit node offset strategy. Combined with adaptive mesh re-meshing technology to handle mesh distortion caused by large deformation, the numerical tracking of the raceway profile evolution over time can be achieved.

[0004] In existing simulations of wear evolution of ball screw pairs, the use of a uniform mesh re-division trigger threshold and shape function interpolation strategy across the entire field leads to the loss of curvature fidelity of the wear groove sidewalls and deviation of the contact angle calculation benchmark, making it impossible to achieve geometrically faithful evolution of the wear profile. Summary of the Invention

[0005] The purpose of this invention is to provide a simulation system for the wear evolution of the ball screw raceway of a ball screw pair based on multi-physics field coupling, so as to solve the problems mentioned above.

[0006] The objective of this invention can be achieved through the following technical solutions: A simulation system for the wear evolution of ball screw raceways based on multi-physics coupled ball screw pairs includes: The data acquisition module collects the arc radius, contact angle, material elastic modulus, Poisson's ratio, yield strength, thermal conductivity, specific heat capacity, lubricant viscosity-pressure coefficient, rated dynamic load and speed time series data of the cross-section of the screw raceway, and obtains the initial contour coordinate point set of the raceway surface; The partitioned mesh generation module divides the cross section into a bearing wear active zone and a geometrically sensitive transition zone along the raceway arc length direction based on the contour coordinate point set and load distribution. It generates initial meshes that are spatially independent and whose nodes at the interface do not overlap for the two zones, so that the two zones have their own mesh density and offset threshold. The interface weak equilibrium constraint definition module sets up a Lagrange multiplier field on the interface to establish a weak equilibrium constraint that only transmits surface forces and heat flux without forcing displacement continuity, and stores the multiplier degrees of freedom as the basis for subsequent interface coupling boundary updates. The wear evolution solution and independent update module independently solves the contact stress, frictional heat and wear depth in the active region based on the weak equilibrium constraint. It triggers mesh reconstruction and stress field remapping only in the active region according to the preset local offset threshold, while keeping the mesh and field constant in the transition region. It also outputs the equivalent surface force and heat flux density generated in the active region at the interface. The interface coupling and iterative control module applies the equivalent surface force and heat flux density to the interface of the transition zone through a Lagrange multiplier field, updates the boundary load and heat flux of the transition zone, and uses the updated interface state as the initial condition for the next round of time-series iteration. The wear evolution solution and independent update module are repeated until the total wear depth reaches the set limit.

[0007] As a further aspect of the present invention: the division of the cross-section into a bearing wear active zone and a geometrically sensitive transition zone along the raceway arc length direction specifically includes: The geometric center line and radius of curvature of the raceway arc are fitted based on the set of contour coordinate points. The projection width of the contact ellipse on the raceway cross section is calculated in combination with the load distribution. The predetermined arc length is extended to both sides based on the center point of the projection width to define the boundary of the active wear zone. The arc segment between the boundary of the active wear zone and the starting point of the shoulders on both sides of the raceway is defined as the geometrically sensitive transition zone. An interface is formed between the active wear zone and the geometrically sensitive transition zone. The interface extends continuously along the raceway axis and its position is dynamically adjusted with the load sequence.

[0008] As a further aspect of the present invention: the arrangement of Lagrange multiplier fields on the interface specifically includes: Extract the boundary node coordinates on the side of the interface that belongs to the active bearing wear zone and the boundary node coordinates on the side that belongs to the geometrically sensitive transition zone, and pair the boundary nodes on both sides according to their spatial proximity. A Lagrange multiplier degree of freedom is introduced between each node pair. The Lagrange multiplier degree of freedom is stored at the center point of the interface and assigned two independent components, normal and tangential. Weak equilibrium constraints are established by taking the product of the surface force difference and heat flux difference on the node pair and the corresponding multiplier components as the integral of zero on the interface, and storing the current value of the multiplier degree of freedom as the initial value for the next interface coupling iteration.

[0009] As a further aspect of the present invention: the introduction of a Lagrange multiplier degree of freedom between each node pair specifically includes: Select the boundary node coordinates belonging to the active bearing wear zone and the boundary node coordinates belonging to the geometrically sensitive transition zone in each node pair, and take the weighted average of the two coordinates as the position of the center point of the interface corresponding to the boundary node pair. Based on the local normal direction and tangential direction of the interface at the center point, normal multiplier components and tangential multiplier components are constructed respectively. The normal multiplier components are used to constrain the continuous transmission of normal surface forces, and the tangential multiplier components are used to constrain the continuous transmission of tangential surface forces. The values ​​of the normal and tangential multiplier components calculated at the current time are saved as the initial boundary state of the node pair for interface coupling iteration at the next time step.

[0010] As a further aspect of the present invention: the step of triggering mesh reconstruction and stress field remapping within the active region based on a preset local offset threshold specifically includes: Monitor the cumulative offset of each node in the active bearing wear zone. When the cumulative offset of any node reaches the preset local offset threshold of the active bearing wear zone, mark the element where the node is located as the area to be reconstructed and record the stress and temperature values ​​on all old nodes in the active bearing wear zone. Delete the old mesh in the area to be reconstructed, and regenerate new nodes and construct new elements based on the current deformed contour coordinates of the active wear zone. The recorded stress and temperature values ​​on the old nodes are extracted, and weighted interpolation is performed using the reciprocal of the spatial distance between the old and new nodes as the weight to obtain the initial stress and initial temperature values ​​on the new nodes. The interpolation operation is limited to occur only within the active bearing wear zone, and the interpolation results are not transmitted to the geometrically sensitive transition zone across the interface.

[0011] As a further aspect of the present invention: the construction of the new unit specifically includes: Extract the coordinates of all old nodes and their corresponding elements in the active bearing wear zone of the region to be reconstructed. Store the old node coordinates as a temporary list and then delete all old elements and old nodes in the active bearing wear zone. Based on the current deformed contour coordinates of the active wear zone, new nodes are arranged at equal intervals along the contour arc length direction in a predetermined number. Adjacent nodes are then connected sequentially in the order of the new nodes in the arc length direction to form a boundary chain. Using the boundary chain as a reference, new units are generated layer by layer into the material. The stress and temperature values ​​of each node in the new unit are temporarily set to the state of waiting to be filled. Calculate the spatial distance from each new node to all old nodes in the temporary list. Use the reciprocal of the obtained distance as the weight to perform a weighted summation of the stress and temperature values ​​on the old nodes. Assign the summation result to the stress and temperature values ​​of the new node.

[0012] As a further aspect of the present invention: the application of equivalent surface force and heat flux density to the transition region interface through a Lagrange multiplier field specifically includes: Extract the current values ​​of the Lagrange multiplier degrees of freedom corresponding to each node pair on the interface, and assign the equivalent surface force output by the bearing wear active zone to the normal multiplier component and tangential multiplier component of the corresponding node pair respectively. The heat flux density output from the active wear zone is assigned to the corresponding node pair and used as the heat flux boundary condition of the interface. The assigned normal and tangential multiplier components are converted into equivalent nodal loads of the boundary nodes at the interface of the geometrically sensitive transition zone, respectively. The heat flux is converted into the equivalent heat flow rate of the boundary nodes at the interface of the geometrically sensitive transition zone. The boundary loads and heat flux of the geometrically sensitive transition zone are updated with the converted equivalent nodal loads and equivalent heat flow rates. The updated boundary loads and heat flux are saved as the initial boundary states for the next time-series iteration.

[0013] As a further aspect of the present invention: the conversion of the assigned normal multiplier components and tangential multiplier components into equivalent nodal loads of the boundary nodes at the interface of the geometrically sensitive transition zone specifically includes: Extract the coordinates of all boundary nodes on the interface of the geometrically sensitive transition zone, and determine the local normal direction and tangent direction of each boundary node on the interface; Based on the normal multiplier components and tangential multiplier components at each center point, the boundary node with the closest spatial distance to the center point is selected as the target node. The normal multiplier components are projected and assigned values ​​along the local normal direction of the target node, and the tangential multiplier components are projected and assigned values ​​along the local tangential direction of the target node. The direction vectors obtained after projection assignment are synthesized into the equivalent nodal load of the target node.

[0014] The beneficial effects of this invention are: (1) By dividing the cross section of the raceway into a bearing wear active zone and a geometrically sensitive transition zone along the arc length, and generating independent meshes with non-overlapping nodes at the interface of the two zones, the bottom region with severe wear can independently perform mesh reconstruction and field remapping, while the side wall transition zone with minimal wear always maintains the original mesh and field unchanged. This avoids the non-physical protrusion artifacts caused by the false stretching of the side wall region due to the global unified mesh reconstruction, thereby ensuring the simulation fidelity of the raceway wear groove profile curvature and its stress gradient, and making the subsequent ball contact angle calculation value closer to the real service state.

[0015] (2) By setting up a Lagrange multiplier field on the interface between the active wear zone and the geometrically sensitive transition zone and establishing a weak equilibrium constraint that only transmits surface force and heat flux, the two zones can still maintain force balance and thermal continuity on the interface under the condition that the mesh nodes do not coincide and the displacement is discontinuous. The interpolation operation during mesh reconstruction in the active zone is strictly limited to the active zone. Its interpolation error will not cross the interface and contaminate the stress field and temperature field of the transition zone. This ensures that the transition zone, as the geometric reference for contact angle calculation, always maintains its initial high accuracy. At the same time, the active zone can independently adopt a finer mesh and a more frequent reconstruction strategy without increasing the computational burden of the transition zone. Attached Figure Description

[0016] The invention will now be further described with reference to the accompanying drawings.

[0017] Figure 1 This is a system block diagram of the present invention; Figure 2 This is a flowchart illustrating how the cross-section is divided into a wear-prone zone and a geometrically sensitive transition zone along the raceway arc length in this invention. Figure 3 This is a flowchart illustrating the process of arranging Lagrange multiplier fields on the interface in this invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] Please see Figure 1 As shown, this invention is a simulation system for the wear evolution of the raceway of a ball screw pair based on multi-physics field coupling, comprising the following steps: The data acquisition module collects the arc radius, contact angle, material elastic modulus, Poisson's ratio, yield strength, thermal conductivity, specific heat capacity, lubricant viscosity-pressure coefficient, rated dynamic load and speed time series data of the cross-section of the screw raceway, and obtains the initial contour coordinate point set of the raceway surface; The partitioned mesh generation module divides the cross section into a bearing wear active zone and a geometrically sensitive transition zone along the raceway arc length direction based on the contour coordinate point set and load distribution. It generates initial meshes that are spatially independent and whose nodes at the interface do not overlap for the two zones, so that the two zones have their own mesh density and offset threshold. The interface weak equilibrium constraint definition module sets up a Lagrange multiplier field on the interface to establish a weak equilibrium constraint that only transmits surface forces and heat flux without forcing displacement continuity, and stores the multiplier degrees of freedom as the basis for subsequent interface coupling boundary updates. The wear evolution solution and independent update module independently solves the contact stress, frictional heat and wear depth in the active region based on the weak equilibrium constraint. It triggers mesh reconstruction and stress field remapping only in the active region according to the preset local offset threshold, while keeping the mesh and field constant in the transition region. It also outputs the equivalent surface force and heat flux density generated in the active region at the interface. The interface coupling and iterative control module applies the equivalent surface force and heat flux density to the interface of the transition zone through a Lagrange multiplier field, updates the boundary load and heat flux of the transition zone, and uses the updated interface state as the initial condition for the next round of time-series iteration. The wear evolution solution and independent update module are repeated until the total wear depth reaches the set limit.

[0020] The data acquisition module collects the arc radius, contact angle, material elastic modulus, Poisson's ratio, yield strength, thermal conductivity, specific heat capacity, lubricant viscosity-pressure coefficient, rated dynamic load, and speed time series data of the lead screw raceway cross-section. It also obtains the initial contour coordinate point set of the raceway surface, specifically including: The radius of the arc and the contact angle of the raceway cross section of the lead screw are obtained by measuring the profile of the raceway cross section of the lead screw sample to be simulated. Specifically, an optical profilometer is used to scan at least three cross sections at equal intervals along the axis of the lead screw. The obtained profile data is imported into computer-aided design software to fit the arc segment. The arithmetic mean of the fitted arc radius of each cross section is taken as the arc radius. The average angle between the line connecting the center of the fitted arc of each cross section and the center of rotation of the lead screw and the center line of symmetry of the raceway is taken as the contact angle.

[0021] The elastic modulus, Poisson's ratio, yield strength, thermal conductivity, and specific heat capacity of the material can be obtained by consulting the material handbook corresponding to the grade of the lead screw to be simulated, or by cutting standard specimens from the same batch of material samples and measuring the above parameters by uniaxial tensile test and laser thermal conductivity meter respectively.

[0022] The viscosity-pressure coefficient of the lubricant was measured using a high-pressure viscometer within the temperature and pressure range of the simulated working conditions. After obtaining the experimental curve of viscosity changing with pressure, the value of the viscosity-pressure coefficient of the lubricant was determined by fitting the slope of the curve at the pressure point corresponding to the rated dynamic load.

[0023] The rated dynamic load is obtained directly from the rated dynamic load specification value of the lead screw sample. The speed time series data is extracted from the historical data of speed change over time obtained by converting the feed rate and lead screw of the machine tool CNC system. During extraction, the complete data points of acceleration, constant speed and deceleration periods are retained to form a speed sequence that changes over time.

[0024] The initial profile coordinate point set of the raceway surface is scanned point by point using a stylus-type profilometer along at least five generatrices at equal angular intervals along the circumference of the raceway. Samples are taken at equal intervals along the axial direction on each generatrice, with a sampling interval of no more than 0.1 mm. The position values ​​of each sampling point in the axial and radial coordinates are recorded. The coordinate values ​​of all sampling points are summarized to form the initial profile coordinate point set of the raceway surface.

[0025] Please see Figure 2 As shown, in the partitioned mesh generation module, based on the contour coordinate point set and load distribution, the cross-section is divided into a bearing wear active zone and a geometrically sensitive transition zone along the raceway arc length direction. Initial meshes are generated for each zone, ensuring they are spatially independent and that the nodes at the interface do not overlap. This gives each zone its own mesh density and offset threshold, specifically including: The geometric center line and radius of curvature of the raceway arc are fitted based on the set of contour coordinate points. Specifically, the least squares method is used to fit each sampling point on the continuous arc segment at the bottom of the raceway in the set of contour coordinate points into an arc. The center coordinates and radius of this arc are used as the position of the geometric center line and the radius of curvature of the raceway arc at this cross section. Repeat the above fitting operation section by section along the lead screw axis to obtain the position of the geometric center line and the radius of curvature at each section. Then, use cubic spline interpolation to construct a continuous spatial curve of the geometric center line along the axis and a continuous distribution curve of the radius of curvature along the axis.

[0026] The load distribution is input into the Hertzian contact theory calculation formula, which outputs the values ​​of the major and minor semi-axes of the contact ellipse based on the contact load, ball diameter, and radius of curvature distribution at the current moment. Twice the value of the minor semi-axe is taken as the projection width of the contact ellipse on the raceway cross section.

[0027] Using the center point of the projected width as a reference, which is the projection position of the center of the contact ellipse on the cross-section of the raceway, a predetermined distance is extended from the center point along the arc length of the raceway to both sides. The predetermined distance is 1.5 times the value of the minor semi-axis. The range of the arc segment covered after the extension is defined as the boundary of the active wear zone.

[0028] The arc lengths between the boundary of the active wear zone and the starting point of the shoulder on both sides of the raceway are respectively defined as geometrically sensitive transition zones, wherein the starting point of the shoulder is taken as the position point at the tangent point between the raceway arc and the outer cylindrical surface of the lead screw.

[0029] An interface is formed between the active wear zone and the geometrically sensitive transition zone. This interface is a spatial curve that extends continuously along the raceway axis. At each cross-section, the position of this interface on the raceway cross-section is taken as the endpoint position of the boundary of the active wear zone on that cross-section. As the load changes over time, the value of the minor semi-axis of the contact ellipse at each cross-section changes, the predetermined distance changes accordingly, and the position of the boundary of the active wear zone also changes accordingly. The position of the spatial curve of the interface is dynamically updated with the recalculated position of the boundary of the active wear zone at each moment.

[0030] Please see Figure 3 As shown, in the interface weak equilibrium constraint definition module, a Lagrange multiplier field is set up on the interface to establish a weak equilibrium constraint that only transmits surface forces and heat flux without forcing displacement continuity, and the multiplier degrees of freedom are stored as the basis for subsequent boundary updates of interface coupling. Specifically, this includes: Extract all boundary nodes on the interface belonging to the active bearing wear zone and record their spatial coordinates. Simultaneously, extract all boundary nodes on the interface belonging to the geometrically sensitive transition zone and record their spatial coordinates as well. Number the boundary nodes belonging to the active bearing wear zone according to their axial arrangement on the interface, and number the boundary nodes belonging to the geometrically sensitive transition zone according to the same axial arrangement, ensuring a one-to-one spatial proximity between the two groups of nodes. Select the two boundary nodes with the same axial position number and the closest spatial distance, one from the active bearing wear zone and the other from the geometrically sensitive transition zone, and pair them as a node pair. Repeat this process for all axial positions to obtain all node pairs.

[0031] For each node pair, take the coordinates of the boundary node belonging to the active bearing wear zone and the boundary node belonging to the geometrically sensitive transition zone, and calculate the position of the interface center point corresponding to the node pair. The calculation expression is as follows: ; in, This indicates the coordinates of the center point of the interface corresponding to this node. This indicates the spatial coordinates of the node belonging to the boundary node on the side of the active wear zone in the bearing pair. This represents the first weighting coefficient assigned to this node. This indicates the spatial coordinates of the node belonging to the boundary node on one side of the geometrically sensitive transition zone. This represents the second weighting coefficient assigned to the node; the first weighting coefficient is 0.5, and the second weighting coefficient is 0.5, that is, the arithmetic mean of the position coordinates of the two boundary nodes is taken as the position coordinate of the center point of the interface; the above operation is performed on each node pair in sequence to obtain the spatial position coordinates of the center point of each interface.

[0032] After obtaining the positions of the center points of each interface, the local normal direction and local tangent direction of the interface at each center point are determined based on the spatial orientation of the interface at that center point. Specifically, the direction of the line connecting the two adjacent center points before and after the current center point is taken as the local tangent direction of the interface at that point, and the cross product of this tangent direction and the normal direction of the raceway cross section is taken as the local normal direction of the interface at that point. At each center point, based on the surface force transmission requirements of the node to which the point belongs to the boundary nodes on both sides, a normal multiplier component and a tangential multiplier component are established. The direction of action of the normal multiplier component is along the local normal direction at the center point, and the direction of action of the tangential multiplier component is along the local tangent direction at the center point.

[0033] Weak equilibrium constraints are established by integrating the products of the normal force difference and tangential force difference on all node pairs with their corresponding normal multiplier components and tangential multiplier components at the interface until the integral is zero. Specifically, the normal force output by the boundary node on the active wear zone side at each center point is subtracted from the normal force borne by the boundary node on the geometrically sensitive transition zone side to obtain the normal force difference. This difference is multiplied by the normal multiplier component at the center point, and the sum is made up along the interface axis over each center point and then set to zero. Similarly, the tangential force output by the boundary node on the active wear zone side at each center point is subtracted from the tangential force borne by the boundary node on the geometrically sensitive transition zone side to obtain the tangential force difference. This difference is multiplied by the tangential multiplier component at the center point, and the sum is made up along the interface axis over each center point and then set to zero.

[0034] The heat flux density output from the boundary node on the side of the active wear zone at each center point is subtracted from the heat flux density borne by the boundary node on the side of the geometrically sensitive transition zone to obtain the heat flux difference. This difference is then multiplied by the corresponding normal and tangential multiplier components, and summed at the interface. The result is set to zero, thus forming the heat flux continuity constraint. The above constraints together constitute the weak equilibrium constraint.

[0035] Calculate and update the values ​​of the normal and tangential multiplier components at each center point. The calculation expression is as follows: ; in, This represents the updated value of the multiplier components at the current time. This represents the value of the multiplier component saved at the previous time step. This represents the preset relaxation factor. This represents the surface force component at the center point of the boundary node on one side of the active wear zone. The relaxation factor represents the surface force component at the center point of a boundary node on one side of the geometrically sensitive transition zone. The value is set to 0.8; the surface force component value is taken as the normal surface force value when the normal multiplier component is updated, and as the tangential surface force value when the tangential multiplier component is updated. The above calculation expression is substituted with the normal surface force value and the tangential surface force value respectively, and the normal multiplier component value and the tangential multiplier component value are updated synchronously. The updated normal multiplier component value and tangential multiplier component value are stored as the initial boundary state of the node pair for the interface coupling iteration at the next time step.

[0036] In the wear evolution solution and independent update module, based on weak equilibrium constraints, the contact stress, frictional heat, and wear depth are solved independently in the active region according to time sequence. Mesh reconstruction and stress field remapping are triggered only in the active region according to a preset local offset threshold, while keeping the mesh and field constant in the transition region. The equivalent surface force and heat flux density generated at the interface in the active region are output, specifically including: After each time-series solution step, the spatial position changes of all nodes in the active bearing wear zone are monitored. The spatial coordinates of each node at the current moment are subtracted from its initial spatial coordinates, and the absolute value of the projection of the difference onto the raceway normal direction is taken as the cumulative offset of that node. The preset local offset threshold for the active bearing wear zone is set to 20% of the initial element size of that zone.

[0037] When the cumulative offset of any node in the active wear zone reaches the local offset threshold, the element containing that node is marked as the region to be reconstructed. At the same time, all elements in the active wear zone are traversed, and the stress component values ​​and temperature values ​​at all integration points on each element are extracted and stored in the temporary storage area in the order of element number, forming a complete record of the old node stress value and the old node temperature value.

[0038] When deleting old meshes within the area to be reconstructed, firstly, extract the spatial coordinate data of all old nodes within the area and the element number information of each old node. Arrange the extracted spatial coordinate data of the old nodes in order of node number and store them in a temporary coordinate list. Then, delete all old elements and all old nodes within the area to be reconstructed, creating a blank area within the active bearing wear zone. Subsequently, regenerate new nodes and construct new elements based on the current deformed contour coordinates of the active bearing wear zone. Specifically, the endpoint positions of the arc segments covered by the region to be reconstructed are extracted from the current deformed contour coordinates. New nodes are then placed along the arc segments from one endpoint to the other at equal arc length intervals, with the equal arc length interval being half the initial element size of the region. The placed new nodes are then connected sequentially along the arc length direction to form a boundary chain. This boundary chain serves as the upper boundary, and the material interior direction is used as the advancing direction. New elements are generated layer by layer, with the advancing distance of each layer being the initial element size of the region, until the depth range of the entire blank area is covered. All the newly generated new nodes and new elements constitute the reconstructed mesh. The stress and temperature values ​​of each new node after reconstruction are temporarily set to the unfilled state.

[0039] After obtaining the reconstructed new nodes, stress and temperature values ​​are assigned to each new node: the spatial straight-line distance from the new node to each old node in the temporary coordinate list is calculated, and the first 8 old nodes are selected as the set of old nodes to participate in the interpolation after arranging all old nodes in ascending order of distance; the reciprocal of the spatial straight-line distance from the new node to each of the 8 old nodes to participate in the interpolation is calculated, and the eight reciprocals are divided by the sum of the eight reciprocals to obtain the normalized weight corresponding to each old node; the stress component values ​​and temperature values ​​on each old node are multiplied by their corresponding normalized weights and summed, and the sum is used as the initial stress and initial temperature values ​​of the new node.

[0040] The above interpolation operation is performed only within the active wear zone, and the interpolated initial stress and temperature values ​​are not transmitted to the geometrically sensitive transition zone.

[0041] In the interface coupling and iterative control module, the equivalent surface force and heat flux density are applied to the interface of the transition zone through a Lagrange multiplier field, updating the boundary load and heat flux of the transition zone. The updated interface state is used as the initial condition for the next round of time-series iteration. The wear evolution solution and independent update module are repeated until the total wear depth reaches the set limit. Specifically, this includes: After each time-series solution step is completed, the current values ​​of the Lagrange multiplier degrees of freedom corresponding to each node pair on the interface are extracted. Specifically, this includes extracting the values ​​of the normal multiplier components and the tangential multiplier components stored at the current time at each center point.

[0042] The equivalent surface force calculated at each center point of the interface in the current time-series solution step of the active wear zone is decomposed into normal and tangential components. The normal component is the projection value of the equivalent surface force on the local normal direction at the center point, and the tangential component is the projection value of the equivalent surface force on the local tangential direction at the center point. The decomposed normal component is assigned to the normal multiplier component at the center point, and the decomposed tangential component is assigned to the tangential multiplier component at the center point, so that the value of the multiplier component is updated to the value of the equivalent surface force component at the current time.

[0043] The equivalent heat flux density calculated at each center point of the interface in the current time-series solution step of the active wear zone is assigned to that center point as the heat flux boundary condition value at the interface.

[0044] After assigning values ​​to the normal and tangential multiplier components, the coordinates of all boundary nodes on the interface of the geometrically sensitive transition zone are extracted, and the local normal direction and local tangential direction of each boundary node on the interface are determined. The local normal direction of the boundary node is taken from the normal direction of the interface at that node, and the local tangential direction of the boundary node is taken from the tangential direction of the interface at that node. The direction determination method is the same as that at the center point.

[0045] For each center point, the boundary node with the closest spatial distance to that center point is selected as the target node. The spatial straight-line distance from the center point to each boundary node on the interface is calculated, and the boundary node corresponding to the smallest distance is selected as the target node for that center point. The normal multiplier component at the center point is projected along the local normal direction of the target node, and the value of the normal multiplier component is multiplied by the unit direction vector of the local normal direction of the target node to obtain the normal projection vector. The tangential multiplier component at the center point is projected along the local tangent direction of the target node, and the value of the tangential multiplier component is multiplied by the unit direction vector of the local tangent direction of the target node to obtain the tangential projection vector. The normal projection vector and the tangential projection vector are added together to synthesize the equivalent nodal load of the target node. After traversing all center points in the above manner, each target node obtains its corresponding equivalent nodal load.

[0046] The equivalent heat flux density at each center point is converted into the equivalent heat flux rate at the boundary nodes of the interface of the geometrically sensitive transition zone. Specifically, the boundary node closest to the center point in space is selected as the target node, and the equivalent heat flux density value at the center point is directly assigned to the target node as its equivalent heat flux ratio. When multiple center points correspond to the same target node, the arithmetic mean of the multiple equivalent heat flux density values ​​is taken and assigned to the target node. The boundary loads of each boundary node on the interface of the geometrically sensitive transition zone are updated with the converted equivalent node loads, and the heat flux of each boundary node on the interface of the geometrically sensitive transition zone is updated with the converted equivalent heat flux ratios. The updated boundary loads and heat fluxes are stored as the boundary state data of the geometrically sensitive transition zone at the current time.

[0047] The updated boundary loads and heat fluxes are saved as the initial boundary states for the next time-series iteration. Specifically, the updated equivalent nodal loads and equivalent heat fluxes of each boundary node are written into the state storage area at the current moment. When the next two time-series solution steps are started, the data in this storage area is read as the initial values ​​of the boundary conditions of the interface of the geometrically sensitive transition zone.

[0048] After each time series iteration, the cumulative offset of all nodes in the active wear zone is calculated, and the maximum offset is taken as the characterization value of the current total wear depth. This characterization value is compared with a preset termination limit. The preset termination limit is 50% of the initial element size of the active wear zone. When the maximum offset is less than the termination limit, the next time series iteration continues. When the maximum offset reaches or exceeds the termination limit, the iteration stops, and the physical field data at the current moment are output as the final simulation result.

[0049] The working principle of this invention is as follows: The arc radius, contact angle, material parameters, lubricant viscosity coefficient, rated dynamic load, rotational speed time series data, and initial profile coordinate point set of the raceway cross-section are collected. Based on the profile coordinate point set and load distribution, the cross-section is divided into a bearing wear active zone and a geometrically sensitive transition zone along the raceway arc length. Initial meshes with non-overlapping nodes at the interface are generated for each zone, giving each zone its own mesh density and offset threshold. A Lagrange multiplier field is deployed at the interface to establish a weak equilibrium constraint that only transmits surface forces and heat flux without forcing continuous displacement. Based on this constraint, the contact stress, frictional heat, and wear depth are solved independently in the active region according to the time series. Mesh reconstruction and stress field remapping are triggered only in the active region according to the preset local offset threshold, while keeping the mesh and field constant in the transition region. The equivalent surface force and heat flux density generated in the active region at the interface are output. The equivalent surface force and heat flux density are applied to the interface of the transition region through the Lagrange multiplier field to update the boundary load and heat flux of the transition region. The updated interface state is used as the initial condition for the next time series iteration. The process is repeated until the total wear depth reaches the set limit.

[0050] The foregoing has provided a detailed description of one embodiment of the present invention, but this description is merely a preferred embodiment and should not be construed as limiting the scope of the invention. All equivalent variations and modifications made within the scope of the claims of this invention should still fall within the patent coverage of this invention.

Claims

1. A simulation system for the wear evolution of the raceway of a ball screw pair based on multi-physics coupled fields, characterized in that, include: The data acquisition module collects the arc radius, contact angle, material elastic modulus, Poisson's ratio, yield strength, thermal conductivity, specific heat capacity, lubricant viscosity-pressure coefficient, rated dynamic load and speed time series data of the cross-section of the screw raceway, and obtains the initial contour coordinate point set of the raceway surface; The partitioned mesh generation module divides the cross section into a bearing wear active zone and a geometrically sensitive transition zone along the raceway arc length direction based on the contour coordinate point set and load distribution. It generates initial meshes that are spatially independent and whose nodes at the interface do not overlap for the two zones, so that the two zones have their own mesh density and offset threshold. The interface weak equilibrium constraint definition module sets up a Lagrange multiplier field on the interface to establish a weak equilibrium constraint that only transmits surface forces and heat flux without forcing displacement continuity, and stores the multiplier degrees of freedom as the basis for subsequent interface coupling boundary updates. The wear evolution solution and independent update module independently solves the contact stress, frictional heat and wear depth in the active region based on the weak equilibrium constraint. It triggers mesh reconstruction and stress field remapping only in the active region according to the preset local offset threshold, while keeping the mesh and field constant in the transition region. It also outputs the equivalent surface force and heat flux density generated in the active region at the interface. The interface coupling and iterative control module applies the equivalent surface force and heat flux density to the interface of the transition zone through a Lagrange multiplier field, updates the boundary load and heat flux of the transition zone, and uses the updated interface state as the initial condition for the next round of time-series iteration. The wear evolution solution and independent update module are repeated until the total wear depth reaches the set limit.

2. The simulation system for the wear evolution of the ball screw raceway based on multi-physics coupled ball screw pair according to claim 1, characterized in that, The division of the cross-section into a high-wear-bearing zone and a geometrically sensitive transition zone along the raceway arc length direction specifically includes: The geometric center line and radius of curvature of the raceway arc are fitted based on the set of contour coordinate points. The projection width of the contact ellipse on the raceway cross section is calculated in combination with the load distribution. The predetermined arc length is extended to both sides based on the center point of the projection width to define the boundary of the active wear zone. The arc segment between the boundary of the active wear zone and the starting point of the shoulders on both sides of the raceway is defined as the geometrically sensitive transition zone. An interface is formed between the active wear zone and the geometrically sensitive transition zone. The interface extends continuously along the raceway axis and its position is dynamically adjusted with the load sequence.

3. The simulation system for the wear evolution of the ball screw raceway of a ball screw pair based on multi-physics coupled field as described in claim 1, characterized in that, The arrangement of Lagrange multiplier fields on the interface specifically includes: Extract the boundary node coordinates on the side of the interface that belongs to the active bearing wear zone and the boundary node coordinates on the side that belongs to the geometrically sensitive transition zone, and pair the boundary nodes on both sides according to their spatial proximity. A Lagrange multiplier degree of freedom is introduced between each node pair. The Lagrange multiplier degree of freedom is stored at the center point of the interface and assigned two independent components, normal and tangential. Weak equilibrium constraints are established by taking the product of the surface force difference and heat flux difference on the node pair and the corresponding multiplier components as the integral of zero on the interface, and storing the current value of the multiplier degree of freedom as the initial value for the next interface coupling iteration.

4. The simulation system for the wear evolution of the ball screw raceway based on multi-physics coupled ball screw pair according to claim 3, characterized in that, The introduction of a Lagrange multiplier degree of freedom between each node pair specifically includes: Select the boundary node coordinates belonging to the active bearing wear zone and the boundary node coordinates belonging to the geometrically sensitive transition zone in each node pair, and take the weighted average of the two coordinates as the position of the center point of the interface corresponding to the boundary node pair. Based on the local normal direction and tangential direction of the interface at the center point, normal multiplier components and tangential multiplier components are constructed respectively. The normal multiplier components are used to constrain the continuous transmission of normal surface forces, and the tangential multiplier components are used to constrain the continuous transmission of tangential surface forces. The values ​​of the normal and tangential multiplier components calculated at the current time are saved as the initial boundary state of the node pair for interface coupling iteration at the next time step.

5. The simulation system for wear evolution of ball screw raceway based on multi-physics coupled ball screw pair according to claim 1, characterized in that, The step of triggering mesh reconstruction and stress field remapping within the active region based on a preset local offset threshold specifically includes: Monitor the cumulative offset of each node in the active bearing wear zone. When the cumulative offset of any node reaches the preset local offset threshold of the active bearing wear zone, mark the element where the node is located as the area to be reconstructed and record the stress and temperature values ​​on all old nodes in the active bearing wear zone. Delete the old mesh in the area to be reconstructed, and regenerate new nodes and construct new elements based on the current deformed contour coordinates of the active wear zone. The recorded stress and temperature values ​​on the old nodes are extracted, and weighted interpolation is performed using the reciprocal of the spatial distance between the old and new nodes as the weight to obtain the initial stress and initial temperature values ​​on the new nodes. The interpolation operation is limited to occur only within the active bearing wear zone, and the interpolation results are not transmitted to the geometrically sensitive transition zone across the interface.

6. The simulation system for the wear evolution of the ball screw raceway based on multi-physics coupled ball screw pair according to claim 5, characterized in that, The construction of the new unit specifically includes: Extract the coordinates of all old nodes and their corresponding elements in the active bearing wear zone of the region to be reconstructed. Store the old node coordinates as a temporary list and then delete all old elements and old nodes in the active bearing wear zone. Based on the current deformed contour coordinates of the active wear zone, new nodes are arranged at equal intervals along the contour arc length direction in a predetermined number. Adjacent nodes are then connected sequentially in the order of the new nodes in the arc length direction to form a boundary chain. Using the boundary chain as a reference, new units are generated layer by layer into the material. The stress and temperature values ​​of each node in the new unit are temporarily set to the state of waiting to be filled. Calculate the spatial distance from each new node to all old nodes in the temporary list. Use the reciprocal of the obtained distance as the weight to perform a weighted summation of the stress and temperature values ​​on the old nodes. Assign the summation result to the stress and temperature values ​​of the new node.

7. The simulation system for the wear evolution of the ball screw raceway of a ball screw pair based on multi-physics coupled field as described in claim 1, characterized in that, The application of equivalent surface force and heat flux density to the transition region interface via a Lagrange multiplier field specifically includes: Extract the current values ​​of the Lagrange multiplier degrees of freedom corresponding to each node pair on the interface, and assign the equivalent surface force output by the bearing wear active zone to the normal multiplier component and tangential multiplier component of the corresponding node pair respectively. The heat flux density output from the active wear zone is assigned to the corresponding node pair and used as the heat flux boundary condition of the interface. The assigned normal and tangential multiplier components are converted into equivalent nodal loads of the boundary nodes at the interface of the geometrically sensitive transition zone, respectively. The heat flux is converted into the equivalent heat flow rate of the boundary nodes at the interface of the geometrically sensitive transition zone. The boundary loads and heat flux of the geometrically sensitive transition zone are updated with the converted equivalent nodal loads and equivalent heat flow rates. The updated boundary loads and heat flux are saved as the initial boundary states for the next time-series iteration.

8. The simulation system for wear evolution of ball screw raceway based on multiphysics coupled ball screw pair according to claim 7, characterized in that, The process of converting the assigned normal and tangential multiplier components into equivalent nodal loads for the boundary nodes of the geometrically sensitive transition zone interface specifically includes: Extract the coordinates of all boundary nodes on the interface of the geometrically sensitive transition zone, and determine the local normal direction and tangent direction of each boundary node on the interface; Based on the normal multiplier components and tangential multiplier components at each center point, the boundary node with the closest spatial distance to the center point is selected as the target node. The normal multiplier components are projected and assigned values ​​along the local normal direction of the target node, and the tangential multiplier components are projected and assigned values ​​along the local tangential direction of the target node. The direction vectors obtained after projection assignment are synthesized into the equivalent nodal load of the target node.

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