Method for calculating contact stress of ball screw

Abstract

The application discloses a kind of ball screw contact stress calculation methods, solve the existing entity steel ball simulation exists and is assembled with the problem such as big, loaded law disorder, low solving efficiency etc. of discrete error, the method does not need rolling body, only through screw and nut modeling constructs assembly body, adopts spring to replace steel ball and is established finite element model in coordination Python batch processing, through function accurate control contact point, batch export spring normal contact force and coordinate before and after deformation, after conversion actual contact angle, contact stress is calculated in combination with Hertz contact theory.The application avoids initial assembly and discrete error, reduces the number of contact pairs, improves solving speed and stability, without repeatedly debugging model, greatly reduce research and development cost, shorten product iteration cycle, applicable to EMB braking system etc. the performance analysis of automobile field ball screw.

Description

Technical Field

[0001] This invention relates to a method for calculating the contact stress of a ball screw. Background Technology

[0002] With the accelerated transformation of automobiles towards electrification and intelligence, electromechanical braking (EMB) systems have become the core development direction of next-generation automotive braking technology due to their advantages such as fast response speed, high control precision, and strong structural integration. As a key component in EMB systems for energy transfer and force amplification, the ball screw's application scope is continuously expanding, with increasing penetration in new energy vehicles and high-end passenger vehicles. However, current specialized mechanical analysis of ball screws in EMB braking systems remains relatively weak, especially in simulation studies of contact stress, a key performance indicator. The industry commonly uses a solid steel ball modeling scheme; this scheme faces multiple technical bottlenecks in practice: the modeling stage requires accurate fitting of the arc-shaped contact surface between the steel ball and the raceway, which easily introduces geometric errors; during assembly, ensuring the uniform distribution of multiple steel balls between the screw and nut makes spatial positioning deviations difficult to avoid; and when discretizing the mesh, the mesh density and partitioning method of the contact area directly affect the calculation accuracy, further amplifying the cumulative error effect. These issues ultimately led to severe disruptions in the load characteristics of the steel balls in the simulation results. Some steel balls exhibited abnormal peak loads far exceeding the design threshold due to the cumulative effect of errors, while others were almost unloaded, which is seriously inconsistent with the uniform load characteristics in actual operation. To obtain reasonable simulation results, engineers need to repeatedly debug geometric model parameters, adjust assembly clearances, and optimize mesh generation strategies. The entire process not only requires a significant investment of manpower, but a single simulation calculation often takes several hours or even days, significantly extending the product development cycle. Against the backdrop of increasingly stringent requirements for braking system reliability and lightweighting in the automotive industry, developing efficient and accurate ball screw simulation analysis methods can not only reduce R&D costs and shorten iteration cycles, but also provide key technical support for the performance optimization and safety assurance of EMB systems, highlighting its growing importance. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention provides a method for calculating the contact stress of ball screws, replacing experiments and traditional simulations. By establishing a near-realistic finite element spring loading model, the contact force and coordinates are extracted, and Hertzian contact stress between the steel ball, screw, and nut is calculated using Hertzian theory.

[0004] To achieve the above objectives, the present invention provides a method for calculating the contact stress of a ball screw, comprising the following steps:

[0005] Step 1: Use 3D drawing software to model the lead screw and nut and construct the assembly;

[0006] Step 2: Establish a finite element model. Use finite element preprocessing software to mesh the three-dimensional digital model to obtain a mesh model. During meshing, make two rows of nodes connected at the center of the groove curvature of the raceway.

[0007] Step 3, Import and Parameter Definition: Import the discretized mesh model into the finite element analysis software, define the material properties of the lead screw and nut, and calculate the coordinates of the center points of the raceways of the lead screw and nut corresponding to the contact points of each steel ball using the known coordinates of the first steel ball in the initial design and the lead screw design parameters. Confirm the coordinate points of the two curvature centers of the spring. The specific coordinate calculation process is as follows: Let OXYZ be a fixed coordinate system, with the Z-axis coinciding with the lead screw axis, and the ball center motion trajectory being a helix. Establish a Frenet frame coordinate system O´τnb at any point O´ on the helix, where the τ-axis coincides with the tangent direction of the helix at O´, and the n-axis coincides with the radial direction of the lead screw at O´. The coordinate transformation relationship between the two coordinate systems is:

[0008]

[0009] in The helix angle, The pitch circle diameter of the ball screw. Let O' be the rotation angle of point O' relative to the starting point of the spiral;

[0010] Based on geometric relationships, any point on the normal section of the screw raceway surface at point O' can be obtained. The coordinates in the coordinate system O´τnb are:

[0011]

[0012] Therefore, the surface equation of any point on the raceway surface of the screw in the fixed coordinate system OXYZ is:

[0013]

[0014] Similarly, the surface equation of the nut raceway in the coordinate system OXYZ can be expressed as:

[0015]

[0016] Step 4: Use Python to batch establish the curvature reference points at the contact points of the lead screw, nut, and steel ball, and establish spring contact pairs at the corresponding positions to obtain the finite element model. The nonlinear stiffness of the spring is completely consistent with the contact stiffness of the solid steel ball, and its stiffness data is obtained by calculation using Hertzian contact theory.

[0017] Step 5: Set boundary conditions, apply fixed constraints to the end face of the lead screw, and apply the actual load required by the lead screw to the end face of the nut;

[0018] Step 6: Submit the finite element model for solution calculation. After the solution is completed, use the post-processing function to batch export the normal contact force of each spring and the position coordinate data of each contact pair before and after deformation.

[0019] Step 7: Set boundary conditions. Apply a fixed constraint to the end face of the lead screw and apply the actual load required by the lead screw to the end face of the nut.

[0020] Step 8: Submit the finite element model for solution calculation. After the solution is completed, use the post-processing function to batch export the normal contact force of each spring and the position coordinate data of each contact pair before and after deformation. Using the exported normal contact force and position coordinate data, calculate the actual contact angle of each steel ball when in contact through the preset functional relationship. Finally, combine the Hertzian contact theory to calculate the Hertzian contact stress between the steel ball and the lead screw, and between the steel ball and the nut.

[0021] The advantages of this setup are as follows: It eliminates the need for physical steel balls, avoiding initial geometric errors in the assembly of the steel balls with the lead screw and nut; replacing the steel balls with springs resolves discretization errors and initial contact issues after steel ball discretization, improving computational accuracy; it reduces the number of contact pairs in the analysis model, and the use of Python for batch processing of spring models significantly shortens modeling time; the solution process eliminates the need for repeated model adjustments, significantly reducing the time required for each solution. Employing digital spring modeling and precisely controlling each contact point through functions ensures the consistency and stability of the ball screw's contact state, preventing issues related to disordered load patterns. Efficient and accurate simulation analysis reduces manual debugging costs and computation time, shortens product development cycles, and provides reliable technical support for performance optimization of the EMB braking system. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of a three-dimensional model of the lead screw and nut assembly in an embodiment of the present invention;

[0023] Figure 2 This is an overall schematic diagram of the finite element model after mesh generation in an embodiment of the present invention;

[0024] Figure 3 This is an enlarged schematic diagram of the contact area node between the lead screw and the nut raceway in an embodiment of the present invention after processing.

[0025] Figure 4 This is a schematic diagram of the coordinate system and raceway normal section of the ball screw pair in an embodiment of the present invention, where a is a schematic diagram of the coordinate system and b is a schematic diagram of the raceway normal section.

[0026] Figure 5 This is a schematic diagram of curvature reference points created in batches using Python in an embodiment of the present invention;

[0027] Figure 6 This is a schematic diagram of the finite element model of the spring contact pair after its construction is completed in an embodiment of the present invention;

[0028] Figure 7 This is a spring stiffness curve diagram in an embodiment of the present invention;

[0029] Figure 8 This is a schematic diagram of the calculation results of the normal load on the steel ball in an embodiment of the present invention;

[0030] Figure 9 This is a schematic diagram showing the calculation results of the actual contact angle of the steel ball in an embodiment of the present invention;

[0031] Figure 10 This is a schematic diagram showing the calculation results of the Hertzian contact stress between the steel ball and the lead screw in an embodiment of the present invention;

[0032] Figure 11 This is a schematic diagram showing the calculation results of the Hertzian contact stress between the steel ball and the nut in an embodiment of the present invention. Detailed Implementation

[0033] This invention provides an embodiment of a method for calculating the contact stress of a ball screw, such as... Figures 1 to 11 As shown, the following steps are included in establishing a 3D digital model: Using SolidWorks 3D drawing software, based on the design parameters of the EMB braking system, such as the screw pitch circle diameter Dwp = 46.8 mm and the helix angle λ = 2°, 3D models of the screw and nut are drawn respectively. Then, the two are assembled to form an assembly. No steel balls are added during the assembly process; only the relative positions of the screw and nut are ensured to meet the design requirements, resulting in the model shown below. Figure 1 The three-dimensional assembly shown;

[0034] Finite element model creation: The 3D assembly was imported into HyperMesh preprocessing software. Tetrahedral elements were used to mesh the lead screw and nut, with a mesh size of 0.1 mm. In the contact area between the steel ball and the raceway, the mesh was locally refined, and sector division was used to ensure that the mesh nodes at the points where the lead screw and nut rolled were mutually corresponding. The enlarged view of the processed nodes is shown below. Figure 3 As shown, the overall mesh model is as follows Figure 2 As shown;

[0035] Import and Parameter Definition: Import the pre-defined mesh model into ABAQUS. Define the materials of the lead screw and nut as 20CrMo bearing steel, with an elastic modulus E = 210 GPa and Poisson's ratio μ = 0.278. Given the initial coordinates of the first steel ball as (-2.257108, 21.459568, -6.761318), and combining the main parameters such as the lead screw pitch circle diameter, helix angle, and contact angle, the software automatically calculates the coordinates of the center points of the lead screw and nut raceways at each steel ball contact point using the coordinate transformation formula and surface equation described in this invention. This determines the coordinates of the curvature center points at both ends of the spring. A schematic diagram of the coordinate calculation is shown below. Figure 4 As shown;

[0036] Spring contact pair construction: Write a Python script to call the ABAQUS API interface to batch establish curvature reference points at the center points of each raceway, such as... Figure 5 As shown, spring contact pairs are established between each reference point, with the number of springs matching the designed number of steel balls. The nonlinear stiffness of the springs is calculated using Hertzian contact theory, and the calculated spring stiffness curve is shown below. Figure 7 As shown, the completed finite element model is as follows: Figure 6 As shown;

[0037] In ABAQUS, a fixed constraint is applied to the right end face of the lead screw to restrict translation and rotation in the X, Y, and Z directions; an axial load is applied to the left end face of the nut to simulate the working load of the EMB braking system.

[0038] Set the solver to Abaqus Static General and submit the solution calculation. After the solution is completed, use the post-processing module to batch export the normal contact force data of the springs, as well as the coordinate data of the contact points at both ends of each spring before and after deformation.

[0039] Using Excel software, a function was written to convert the exported coordinate data into the actual contact angle of each steel ball. The calculation results are as follows: Figure 9 As shown, combined with the derived normal contact force, such as Figure 8 As shown, substituting into the Hertzian contact stress formula, the Hertzian contact stress between the steel ball and the lead screw is calculated, as follows: Figure 10 As shown, and the Hertzian contact stress between the steel ball and the nut, as... Figure 11 As shown.

[0040] The calculation results of this embodiment show that the normal contact force distribution of each steel ball is uniform, the contact angle deviation is controlled within ±0.5°, and the maximum contact stress is 3250MPa. The error with the actual test results is less than 5%, verifying the accuracy and reliability of the method of this invention. Furthermore, the modeling time of this embodiment is only 1 / 10 of that of traditional solid steel ball modeling, significantly shortening the solution time; and it eliminates the need for repeated model adjustments, significantly improving analysis efficiency.

[0041] The above examples are merely one preferred embodiment of the present invention. Ordinary variations and substitutions made by those skilled in the art within the scope of the technical solution of the present invention are all included within the protection scope of the present invention.

Claims

1. A ball screw contact stress calculation method characterized by: The method comprises the following steps: step one, modeling the screw rod and the nut by using three-dimensional drawing software and constructing an assembly; step two, establishing a finite element model; step three, importing and defining parameters; step four, using a python program to batch establish curvature reference points at the contact positions of the screw rod, the nut and the steel ball, and establishing spring contact pairs at the corresponding positions to obtain the finite element model; step five, setting boundary conditions, applying a fixed constraint to the end surface of the screw rod and applying the actual load required for calculation of the screw rod to the end surface of the nut; step six, submitting the finite element model for calculation, and after the calculation is completed, batch exporting the normal contact force of each spring and the position coordinate data of each contact pair before and after deformation by using a post-processing function; step seven, setting boundary conditions, applying a fixed constraint to the end surface of the screw rod and applying the actual load required for calculation of the screw rod to the end surface of the nut; step eight, submitting the finite element model for calculation, and after the calculation is completed, batch exporting the normal contact force of each spring and the position coordinate data of each contact pair before and after deformation by using a post-processing function; using the exported normal contact force and position coordinate data, the actual contact angle of each steel ball contact is converted through a preset function relationship, and finally the Hertz contact stress between the steel ball and the screw rod and the steel ball and the nut is calculated by using the Hertz contact theory.

2. The ball screw contact stress calculation method according to claim 1, characterized by: In the step two, the finite element model is established by using a finite element pre-processing software to divide the three-dimensional model into grids to obtain a grid model, and two rows of node connections are formed at the curvature centers of the raceways during the grid division.

3. The ball screw contact stress calculation method according to claim 1, characterized by: In the step three, the imported and defined parameters are the grid model after discretization is imported into the finite element analysis software, the material properties of the screw rod and the nut are defined, the coordinates of the center points of the screw rod and the nut at the contact positions of the steel balls are calculated by combining the design parameters of the screw rod with the known coordinate position of the first steel ball in the initial design of the model, and the coordinates of the two curvature centers of the spring are confirmed; the specific coordinate calculation process is as follows: assuming that OXYZ is a fixed coordinate system, the Z axis coincides with the axial direction of the screw rod, the center of the ball is a spiral line, an Frenet frame coordinate system O´τnb is established at any point O´ on the spiral line, the τ axis coincides with the tangent direction of the spiral line at the O´ point, the n axis coincides with the radial direction of the screw rod at the O´ point, and the coordinate conversion relationship between the two coordinate systems is: wherein is the helix angle, is the ball screw pitch diameter, is the rotation angle of the point O' relative to the start point of the helix. According to the geometric relationship, the coordinates of any point on the normal section of the ball screw raceway surface at point O' in the coordinate system O'xnb are: , in the coordinate system O'xnb. Therefore, the surface equation of any point on the screw rod raceway in the fixed coordinate system OXYZ is: Similarly, the surface equation of the nut raceway in the coordinate system OXYZ can be expressed as: 。 4. The ball screw contact stress calculation method according to claim 1, characterized by: In the step four, the non-linear stiffness of the spring and the contact stiffness of the solid steel ball are completely consistent, and the stiffness data are obtained by calculation and solving according to the Hertz contact theory.

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