Ball screw contact characteristic calculation method and system

Abstract

The invention discloses a ball screw contact characteristic calculation method and system, and the method comprises the steps: inputting a size parameter and an external load of a ball screw, and preliminarily building a related equation of a ball stress and an axial load; solving the displacement change of the raceway contact point under the action of the axial load according to the balance condition of the binding force; adding rotating speed parameters of the ball screw, calculating position offset of a raceway contact point during high-speed rotation, and updating a contact angle between the ball and the screw / nut; the centrifugal force and gyroscopic moment generated by high-speed rotation of the ball are quantified through a geometric constraint equation and kinematics analysis; on the basis of an original static model, centrifugal force, gyroscopic effect and contact surface friction force are superposed, and axial and radial stress balance equations containing dynamic factors are reconstructed; and a geometric constraint equation and a multi-dimensional mechanical equation are combined, numerical calculation is carried out by adopting a Newton iteration method, and finally, the contact characteristic which not only considers uneven load distribution but also contains the influence of high-speed rotation is obtained.

Description

Background Art

[0002] Machine tools are called "industrial mother machines" in the industrial field, and ball screws are important functional components of machine tools. Accurate analysis of the contact characteristics of ball screws for optimal design is crucial to improving the positioning accuracy of machine tools and the processing quality of workpieces. However, due to the shortcomings of existing methods, it is impossible to accurately analyze the contact characteristics of ball screws based on their actual load conditions, which seriously affects the development of the machine tool industry. Therefore, it is necessary to calculate the contact characteristics of ball screws taking into account non-uniform loading and centrifugal effects.

[0003] Jones proposed a method for calculating bearing contact load and contact angle considering centrifugal effect based on coordinate transformation. Chen Yongjiang proposed a method of considering contact angle as a function of ball position angle in combination with coordinate system transformation, calculated the load distribution of double-nut ball screw, and analyzed the distribution of ball normal load and contact angle under different ball screw geometric parameters and speeds. Finally, a nonlinear mapping relationship between speed, axial load, lead, raceway curvature ratio and ball screw stiffness was established. Zhen Ni regarded the balls in the ball screw as uniformly loaded and analyzed the load distribution of the ball screw under different axial loads and radial loads. Mei Xuesong proposed a method for calculating uneven loading of ball screws based on Hooke's law, and analyzed the influence of machining errors on load distribution. Zhao Jiajia proposed a method for calculating the load distribution of ball screws under combined axial loads and radial loads based on Hooke's law, and analyzed the influence of ball machining errors on the positioning accuracy of ball screws under combined loads.

[0004] However, the above studies are only based on the single condition of non-uniform loading or centrifugal effect to analyze the contact characteristics of ball screws, which does not conform to the actual working conditions of ball screws in machine tools. The influence of non-uniform loading and ball centrifugal effect on contact characteristics is ignored. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a method and system for calculating the contact characteristics of a ball screw in response to the deficiencies in the above-mentioned prior art, so as to solve the technical problem of accurately calculating the contact characteristics of a ball screw taking into account non-uniform loading and centrifugal effects at different speeds and different axial loads.

[0006] The present invention adopts the following technical solutions: A method for calculating contact characteristics of a ball screw comprises the following steps: S1. Input the geometric parameters and axial load of the ball screw, and determine the force coordination equation of the ball contact load and axial load based on Hertz contact theory, the coordination relationship of adjacent ball deformations, Hooke's law, contact angle analysis, and axial internal force analysis; S2, based on the force coordination equation of the ball contact load and the axial load obtained in step S1 and the axial load balance equation of the ball screw determined according to Newton's first law, solving the center displacement of the raceway curvature when the axial load is applied; S3, input the rotation speed of the ball screw, calculate the axial distance and radial distance between the center of curvature of the screw raceway and the center of curvature of the nut raceway in combination with the displacement of the center of curvature of the raceway obtained in step S2, and determine the contact angles between the ball-screw and the ball-nut; S4, calculating the geometric constraint equation of the center of curvature of the raceway based on the contact angles between the ball-screw and the ball-nut obtained in step S3; calculating the centrifugal force and gyroscopic moment of the ball based on Newton's second law and the acceleration formula of circular motion based on velocity analysis and coordinate transformation; S5, according to the centrifugal force and gyroscopic moment of the ball obtained in step S4, and the friction force between the ball and the raceway, calculate the ball axial load balance equation, radial force balance equation, and ball screw axial load balance equation taking into account non-uniform loading and centrifugal effect; S6. Combine the raceway curvature center geometric constraint equation obtained in step S4 with the ball axial load balance equation, radial force balance equation, and ball screw axial load balance equation obtained in step S5, and use Newton's iteration method to solve them to obtain the contact characteristics of the ball screw considering non-uniform loading and centrifugal effects.

[0007] Preferably, step S1 specifically includes: According to Hertz contact theory, the Normal contact deformation of a ball and Normal contact deformation of a ball ; Based on the deformation coordination relationship of adjacent balls; Calculate the Hooke's law to calculate the Axial contact deformation of a ball ; When the load is non-uniform, the contact angle between the ball and the raceway is calculated based on the geometric deformation relationship ; Determine the Axial internal forces of adjacent ball units ; Based on the above steps, the force coordination equation between the ball contact load and the axial load is obtained.

[0008] Preferably, the force coordination equation between the ball contact load and the axial load is as follows:

[0009] in, is the helix angle of the ball screw, For the The contact load of each ball, For the The contact angle of the ball, and is the force coordination coefficient, is the axial load of the ball screw, For the The contact load of each ball, For the The contact angle of the ball, is the contact angle between the ball and the raceway.

[0010] Preferably, step S2 specifically includes: Calculate the axial load balance equation of the ball screw according to Newton's first law; solve the center displacement of the raceway curvature under axial load based on the calculated ball contact characteristics .

[0011] Preferably, step S3 specifically includes: Calculate the axial distance between the center of curvature of the screw raceway and the center of curvature of the nut raceway and the center of curvature of the screw raceway and the nut raceway ; The contact angle considering the non-uniform loading and centrifugal effect is determined as follows:

[0012] in, is the contact angle between the ball and the screw, is the contact angle between the ball and the nut, is the ball diameter, is the normal contact deformation between the ball and the screw, is the normal contact deformation between the ball and the nut, is the axial distance between the center of curvature of the nut raceway and the center of the ball, is the radial distance between the center of curvature of the nut raceway and the center of the ball, is the curvature radius of the screw raceway, is the curvature radius of the nut raceway.

[0013] Preferably, step S4 is specifically: Determine the geometric constraint equation of the center of curvature of the raceway based on the Pythagorean theorem; then calculate the mass moment of inertia of the ball , the gyroscopic angle between the ball and the raceway , and the sliding speed between the contact points between the ball and the screw raceway ; Determine the transformation relationship between the ball spin speed, the ball speed around the screw axis, and the screw speed; Calculate the centrifugal force of the ball based on Newton's second law and the acceleration formula of circular motion ; Finally, the gyroscopic moment of the ball is obtained .

[0014] Preferably, the transformation relationship among the ball spin speed, the ball rotation speed around the screw axis, and the screw rotation speed is as follows:

[0015] in, is the contact angle between the ball and the screw, is the contact angle between the ball and the nut, is the angular velocity of the ball around the screw axis, is the speed of the ball screw, is the ball diameter, is the pitch diameter of the screw.

[0016] Preferably, step S5 is specifically: Calculate the friction between the ball and the screw raceway according to step S4 and the friction between the ball and the nut raceway ; Then calculate the axial load balance equation of the ball and the radial force balance equation of the ball; Finally, calculate the axial load balance equation of the ball screw that comprehensively considers non-uniform loading and centrifugal effects.

[0017] Preferably, the axial load balance equation of the ball screw taking into account the non-uniform loading and centrifugal effect is as follows:

[0018] in, is the axial load balance equation of the ball screw on the screw side, is the axial load balance equation of the ball screw on the nut side, is the contact angle between the ball and the screw, is the contact angle between the ball and the nut, is the contact load between the ball and the screw, is the helix angle, and is the raceway control coefficient, is the friction between the ball and the screw, is the number of balls in the ball screw, is the contact load between the ball and the nut, is the contact angle between the ball and the nut, is the friction between the ball and the nut raceway.

[0019] In a second aspect, an embodiment of the present invention provides a ball screw contact characteristic calculation system, comprising: Input module, input the geometric parameters of the ball screw, axial load, Hertz contact theory, deformation coordination relationship of adjacent balls, Hooke's law, contact angle analysis, axial internal force analysis to determine the force coordination equation of ball contact load and axial load; A calculation module, which solves the displacement of the center of curvature of the raceway when the axial load is applied based on the obtained force coordination equation of the ball contact load and the axial load and the axial load balance equation of the ball screw determined according to Newton's first law; The distance module inputs the rotation speed of the ball screw, and calculates the axial and radial distances between the center of curvature of the screw raceway and the center of curvature of the nut raceway in combination with the obtained displacement of the center of curvature of the raceway, and determines the contact angles between the ball-screw and the ball-nut; The torque module calculates the geometric constraint equation of the center of raceway curvature based on the contact angles between the ball-screw and the ball-nut; based on the consideration of velocity analysis and coordinate transformation, the centrifugal force and gyroscopic torque of the ball are calculated based on Newton's second law and the acceleration formula of circular motion; The equation module calculates the ball axial load balance equation, radial force balance equation, and ball screw axial load balance equation considering non-uniform loading and centrifugal effect based on the obtained centrifugal force and gyroscopic moment of the ball and the friction between the ball and the raceway; The output module combines the geometric constraint equation of the raceway curvature center and the ball axial load balance equation, radial force balance equation, and ball screw axial load balance equation, and uses Newton's iteration method to solve the ball screw contact characteristics considering non-uniform loading and centrifugal effects.

[0020] In a third aspect, a computer device comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above-mentioned ball screw contact characteristic calculation method when executing the computer program.

[0021] In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium, comprising a computer program, which, when executed by a processor, implements the steps of the above-mentioned ball screw contact characteristic calculation method.

[0022] In a fifth aspect, a chip comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above-mentioned ball screw contact characteristic calculation method when executing the computer program.

[0023] In a sixth aspect, an embodiment of the present invention provides an electronic device, comprising a computer program, which, when executed by the electronic device, implements the steps of the above-mentioned ball screw contact characteristic calculation method.

[0024] Compared with the prior art, the present invention has at least the following beneficial effects: A method for calculating contact characteristics of ball screws is proposed. Based on the non-uniform loading of ball screws, the force coordination equation between ball contact load and axial load is established according to Hertz contact theory, deformation coordination relationship of adjacent balls, Hooke's law, contact angle analysis, and axial internal force analysis. Based on Newton's first law, the axial load balance equation of ball screw is established. The contact characteristics of balls under non-uniform loading are calculated by the combined force coordination equation and axial load balance equation. The displacement of the center of curvature of the raceway is calculated according to the calculation formula of the center of curvature of the raceway; on the basis of considering non-uniform loading, the displacement attenuation of the center of curvature of the raceway is introduced into the analysis of the center of curvature of the raceway considering the centrifugal effect, and the geometric constraint equation of the curvature displacement of the raceway during ball motion is established according to the Pythagorean theorem; on the basis of considering the centrifugal effect and non-uniform loading, the self-rotation speed of the ball and the speed of the ball around the axis of the screw are calculated according to the speed analysis and coordinate transformation of the ball. Based on Newton's first law, centrifugal force analysis, and gyroscopic torque analysis, the ball axial load balance equation and radial force balance equation during ball motion were established, and finally the axial load balance equation during ball screw motion was established; the process of calculating the contact characteristics of the ball screw based on non-uniform loading and centrifugal effect was given.

[0025] Furthermore, based on the Hertz contact theory, the deformation coordination relationship of adjacent balls, axial contact deformation analysis, contact angle analysis, and axial internal force analysis, the force coordination equation between the contact load and the axial load is obtained jointly.

[0026] Furthermore, the axial load balance equation of the ball screw is obtained by Newton's first law, and the center displacement of the raceway curvature under the axial load is obtained by analyzing the geometric relationship and simultaneously calculating the force coordination equation in step S1 and the axial load balance equation of the ball screw in step S2.

[0027] Furthermore, based on the distance and geometric relationship between the centers of curvature of the screw and nut raceways, the contact angle that comprehensively considers non-uniform loading and centrifugal effects is obtained.

[0028] Furthermore, the geometric constraint equation of the center of curvature of the raceway is obtained based on the Pythagorean theorem, and the ball spin speed, the speed of the ball around the screw axis, and the transformation relationship of the screw speed are obtained based on the mass inertia moment of the ball, the gyroscopic angle between the ball and the raceway, and the velocity analysis. The gyroscopic torque of the ball is obtained together, and the centrifugal force of the ball is obtained according to Newton's second law and the acceleration formula of circular motion.

[0029] Furthermore, based on the force analysis and the centrifugal force of the balls in step S4, the axial load balance equation of the balls and the radial force balance equation of the balls are established. Based on the overall force analysis of the ball screw and the friction between the balls and the raceways in step S4, the axial load balance equation of the ball screw is obtained which comprehensively considers the non-uniform loading and centrifugal effects.

[0030] It can be understood that the beneficial effects of the second to sixth aspects mentioned above can be found in the relevant description of the first aspect mentioned above, and will not be repeated here.

[0031] In summary, the method of the present invention can comprehensively consider the influence of the non-uniform loading of the ball screw under the action of axial load and the centrifugal effect during its movement on the displacement of the center of curvature of the raceway, and then calculate the contact characteristics that comprehensively consider the non-uniform loading and centrifugal effects, providing guidance for the optimal design of the ball screw and the dynamic characteristics analysis of the ball screw during operation.

[0032] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following is a brief introduction to the drawings required for use in the embodiments of the present application. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0034] Figure 1 This is a schematic diagram of the load distribution of the ball when the ball screw is non-uniformly loaded; Figure 2 Schematic diagram of the center of curvature of the raceway considering the non-uniform loading and centrifugal effect; Figure 3 is the calculation flow chart; Figure 4 The figure is a comparison diagram of the contact angle of the first ball between the screw-ball and the nut-ball of the method of the present invention and the existing method at different rotation speeds; Figure 5 The figure is a comparison diagram of the contact load of the first ball between the screw-ball and the nut-ball of the method of the present invention and the existing method at different speeds; Figure 6 The contact angle diagram between ball and nut at different speeds; Figure 7 The contact angle diagram between ball and screw at different speeds; Figure 8 The contact load diagram between ball and nut at different speeds; Fig. 9 The contact load diagram between ball and screw at different speeds; Fig.10 A schematic diagram of a computer device provided by an embodiment of the present invention; Fig.11 The present invention is a block diagram of an electronic device provided according to an embodiment.

[0035] Among them, 60. computer equipment; 61. processor; 62. memory; 63. computer program; 600. electronic device; 610. processing unit; 620. storage unit; 6201. random access storage unit; 6202. cache storage unit; 6203. read-only storage unit; 6204. program / utility; 6205. program module; 630. bus; 640. display unit; 650. input / output interface; 660. network adapter; 700. external device. DETAILED DESCRIPTION

[0036] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0037] In the description of the present invention, it should be understood that the terms “include” and “comprises” indicate the presence of described features, wholes, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or collections thereof.

[0038] It should also be understood that the terms used in the present specification are only for the purpose of describing specific embodiments and are not intended to limit the present invention. As used in the present specification and the appended claims, unless the context clearly indicates otherwise, the singular forms "a", "an" and "the" are intended to include plural forms.

[0039] It should be further understood that the term "and / or" used in the present specification and the appended claims refers to any combination of one or more of the associated listed items and all possible combinations, and includes these combinations. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. In addition, the character " / " in the present invention generally indicates that the associated objects are in an "or" relationship.

[0040] It should be understood that, although the terms first, second, third, etc. may be used to describe preset ranges, etc. in the embodiments of the present invention, these preset ranges should not be limited to these terms. These terms are only used to distinguish preset ranges from each other. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0041] The word "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining" or "in response to detecting", depending on the context. Similarly, the phrases "if it is determined" or "if (stated condition or event) is detected" may be interpreted as "when it is determined" or "in response to determining" or "when detecting (stated condition or event)" or "in response to detecting (stated condition or event)", depending on the context.

[0042] Various structural schematic diagrams of the embodiments disclosed in the present invention are shown in the accompanying drawings. These figures are not drawn to scale, and some details are magnified and some details may be omitted for the purpose of clear expression. The shapes of various regions and layers shown in the figures and the relative sizes and positional relationships therebetween are only exemplary, and may deviate in practice due to manufacturing tolerances or technical limitations, and those skilled in the art may additionally design regions / layers with different shapes, sizes, and relative positions according to actual needs.

[0043] The present invention provides a method for calculating the contact characteristics of a ball screw. The dimensional parameters and external load of the ball screw are input, and the correlation equation between the ball force and the axial load is preliminarily established through the principles of material mechanics and contact mechanics (Hertz theory, deformation coordination relationship, etc.); the displacement change of the raceway contact point under the action of the axial load is solved in combination with the force balance condition (Newton's first law), so as to provide initial data for subsequent dynamic analysis; the speed parameter of the ball screw is added to calculate the position offset (axial and radial distance) of the raceway contact point during high-speed rotation, and update the contact angle between the ball and the screw / nut; the centrifugal force generated by the high-speed rotation of the ball is quantified through geometric constraint equations and kinematic analysis. (outward inertial force) and gyroscopic torque (resistance effect of change in rotation direction); on the basis of the original static model, the centrifugal force, gyroscopic effect and contact surface friction are superimposed to reconstruct the axial and radial force balance equations containing dynamic factors; the geometric constraint equations are combined with the multi-dimensional mechanical equations, and the Newton iteration method is used for numerical calculation, and finally the contact characteristics (such as contact stress, contact angle change, etc.) that take into account both the uneven load distribution and the influence of high-speed rotation are obtained; through a hierarchical and progressive modeling method, the modeling is gradually refined from static to dynamic, which solves the limitation of the traditional method that ignores the high-speed rotation effect, and significantly improves the calculation accuracy of the contact characteristics of the ball screw under high-speed conditions.

[0044] Example 1 A method for calculating contact characteristics of a ball screw according to the present invention comprises the following steps: S1. Input the geometric parameters and axial load of the ball screw, and determine the force coordination equation of the ball contact load and axial load based on Hertz contact theory, the coordination relationship of adjacent ball deformations, Hooke's law, contact angle analysis, and axial internal force analysis; S101. Calculate the contact deformation between the ball and the raceway according to Hertz contact theory;

[0045] in, It is The normal contact deformation of a ball is It is The contact load of each ball, It is The normal contact deformation of a ball is It is The contact load of each ball, and is the Hertz contact coefficient.

[0046] S102, calculating the deformation coordination relationship of adjacent balls;

[0047] in, It is The axial contact deformation of each ball, It is The axial contact deformation of each ball, It is Axial contact deformation of the balls.

[0048] S103, based on Hooke's law, calculate Axial contact deformation of each ball;

[0049] in, The screw side The first ball and the The axial distance between the balls, The nut side The first ball and the The axial distance between the balls, and is the axial deformation coefficient.

[0050] S104. When the load is non-uniform, the contact angle between the ball and the raceway is calculated based on the geometric deformation relationship;

[0051] in, is the distance from the center of curvature of the raceway when unloaded, It is the contact angle between the ball and the raceway when unloaded.

[0052] S105, determining the axial internal force of adjacent balls; Figure 1It shows the load distribution diagram of the ball when the ball screw is loaded. Axial internal forces of adjacent ball units for:

[0053] in, For the The axial internal force of adjacent ball units, For the The contact load of each ball, For the The contact angle of the ball, is the axial load of the ball screw.

[0054] S106. According to step S101, step S102, step S103, step S104 and step S105, a force coordination equation between the ball contact load and the axial load is calculated.

[0055]

[0056] in, is the helix angle of the ball screw, For the The contact load of each ball, For the The contact angle of the ball, and is the force coordination coefficient.

[0057] S2, solving the displacement of the center of curvature of the raceway when the axial load is applied based on the force coordination equation between the ball contact load and the axial load obtained in step S1 and the axial load balance equation of the ball screw determined according to Newton's first law; S201. Calculate the axial load balance equation of the ball screw according to Newton's first law;

[0058] in, is the number of balls in the ball screw.

[0059] S202, according to the ball contact characteristics calculated in step S106 and step S201, solving the raceway curvature center displacement under axial load.

[0060]

[0061] S3, input the rotation speed of the ball screw, calculate the axial distance and radial distance between the center of curvature of the screw raceway and the center of curvature of the nut raceway in combination with the displacement of the center of curvature of the raceway obtained in step S2, and determine the contact angles between the ball-screw and the ball-nut; See also Figure 2 , which represents the change of the center of curvature of the raceway taking into account the non-uniform loading and centrifugal effect. The specific calculation steps are as follows: S301, calculating the distance between the center of curvature of the screw raceway and the center of curvature of the nut raceway;

[0062] in, is the axial distance between the center of curvature of the screw raceway and the center of curvature of the nut raceway, is the curvature center of the screw raceway and the nut raceway, For the The displacement of the center of curvature of the raceway corresponding to each ball.

[0063] S302. According to step S301, the contact angle taking into account the non-uniform load and the centrifugal effect is calculated.

[0064]

[0065] in, is the contact angle between the ball and the screw, is the contact angle between the ball and the nut, is the ball diameter, is the normal contact deformation between the ball and the screw, is the normal contact deformation between the ball and the nut. is the axial distance between the center of curvature of the nut raceway and the center of the ball, is the radial distance between the center of curvature of the nut raceway and the center of the ball, is the curvature radius of the screw raceway, is the curvature radius of the nut raceway.

[0066] S4, calculating the geometric constraint equation of the center of curvature of the raceway based on the contact angles between the ball-screw and the ball-nut obtained in step S3; calculating the centrifugal force and gyroscopic moment of the ball based on Newton's second law and the acceleration formula of circular motion based on velocity analysis and coordinate transformation; S401. Calculate the geometric constraint equation of the center of curvature of the raceway based on the Pythagorean theorem;

[0067] S402, calculating the mass moment of inertia of the ball;

[0068] in, is the mass moment of inertia of the ball, is the material density of the ball, is the diameter of the screw.

[0069] S403, calculating the gyro angle between the ball and the raceway;

[0070] in, is the gyroscopic angle between the ball and the raceway.

[0071] S404, calculating the sliding speed between the contact points between the ball and the screw raceway;

[0072] in, is the sliding speed of the screw raceway and the ball on the ball side, is the sliding speed of the screw raceway and the ball on the raceway side, is the sliding speed between the ball and the raceway, It is a coordinate system fixed at the center of the ball and used to describe the motion of the ball. is the angular velocity of the screw, is the angular velocity of the ball around the screw axis, is the ball spin angular velocity, is the ball spin angular velocity exist The direction of the component, yes exist The direction component, yes exist The direction component.

[0073] S405, calculating the conversion relationship between the ball spin speed, the ball speed around the screw axis, and the screw speed according to step S403 and step S404;

[0074] S406, according to step S405, calculating the centrifugal force of the ball based on Newton's second law and the acceleration formula of circular motion;

[0075] in, is the centrifugal force of the ball.

[0076] S407. Calculate the gyroscopic moment of the ball according to step S402, step S403, step S404 and step S405.

[0077]

[0078] in, is the gyroscopic torque of the ball.

[0079] S5, according to the centrifugal force and gyroscopic moment of the ball obtained in step S4, and the friction force between the ball and the raceway, calculate the ball axial load balance equation, radial force balance equation, and ball screw axial load balance equation taking into account non-uniform loading and centrifugal effect; S501, calculating the friction force between the ball and the raceway according to step S4;

[0080] in, is the friction between the ball and the screw raceway, is the friction between the ball and the nut raceway, and is the raceway control coefficient.

[0081] S502, calculating the axial load balance equation of the ball according to step S501;

[0082] S503, calculating the radial force balance equation of the ball according to step S406 and step S501;

[0083] S504. According to step S501, calculate the axial load balance equation of the ball screw that comprehensively considers the non-uniform loading and the centrifugal effect.

[0084]

[0085] in, is the axial load balance equation of the ball screw on the screw side, is the axial load balance equation of the ball screw on the nut side.

[0086] S6. Combine the raceway curvature center geometric constraint equation obtained in step S4 with the ball axial load balance equation, radial force balance equation, and ball screw axial load balance equation obtained in step S5, and use Newton's iteration method to solve them to obtain the contact characteristics of the ball screw considering non-uniform loading and centrifugal effects.

[0087] It will be appreciated by those skilled in the art that various aspects of the present invention may be implemented as systems, methods or program products. Therefore, various aspects of the present invention may be specifically implemented in the following forms, namely: complete hardware implementation, complete software implementation (including firmware, microcode, etc.), or a combination of hardware and software implementations, which may be collectively referred to herein as "circuits", "modules" or "platforms".

[0088] Example 2 The present invention provides a ball screw contact characteristic calculation system, which can be used to implement the above-mentioned ball screw contact characteristic calculation method. Specifically, the ball screw contact characteristic calculation system includes an input module, a calculation module, a distance module, a torque module, an equation module and an output module.

[0089] Among them, the input module inputs the geometric parameters and axial load of the ball screw, and determines the force coordination equation of the ball contact load and the axial load based on the Hertz contact theory, the coordination relationship of the deformation of adjacent balls, Hooke's law, the contact angle analysis, and the axial internal force analysis; A calculation module, which solves the displacement of the center of curvature of the raceway when the axial load is applied based on the obtained force coordination equation of the ball contact load and the axial load and the axial load balance equation of the ball screw determined according to Newton's first law; The distance module inputs the rotation speed of the ball screw, and calculates the axial and radial distances between the center of curvature of the screw raceway and the center of curvature of the nut raceway in combination with the obtained displacement of the center of curvature of the raceway, and determines the contact angles between the ball-screw and the ball-nut; The torque module calculates the geometric constraint equation of the center of raceway curvature based on the contact angles between the ball-screw and the ball-nut; based on the consideration of velocity analysis and coordinate transformation, the centrifugal force and gyroscopic torque of the ball are calculated based on Newton's second law and the acceleration formula of circular motion; The equation module calculates the ball axial load balance equation, radial force balance equation, and ball screw axial load balance equation considering non-uniform loading and centrifugal effect based on the obtained centrifugal force and gyroscopic moment of the ball and the friction between the ball and the raceway; The output module combines the geometric constraint equation of the raceway curvature center and the ball axial load balance equation, radial force balance equation, and ball screw axial load balance equation, and uses Newton's iteration method to solve the ball screw contact characteristics considering non-uniform loading and centrifugal effects.

[0090] Example 3 The present invention provides a terminal device, which includes a processor and a memory, wherein the memory is used to store a computer program, the computer program includes program instructions, and the processor is used to execute the program instructions stored in the computer storage medium. The processor may be a central processing unit (CPU), or other general-purpose processors, graphics processors (GPU), tensor processors (TPU), digital signal processors (DSP), application specific integrated circuits (ASIC), field programmable gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc., which are the computing core and control core of the terminal, which are suitable for implementing one or more instructions, and are specifically suitable for loading and executing one or more instructions to implement corresponding method processes or corresponding functions; the processor described in the embodiment of the present invention can be used for the operation of the ball screw contact characteristic calculation method, including: Input the geometric parameters and axial load of the ball screw, and determine the force coordination equation of the ball contact load and the axial load based on Hertz contact theory, the coordination relationship of adjacent ball deformations, Hooke's law, contact angle analysis, and axial internal force analysis. Determine the axial load balance equation of the ball screw based on Newton's first law; solve the displacement of the center of curvature of the raceway when the axial load is applied based on the obtained force coordination equation of the ball contact load and the axial load and the axial load balance equation of the ball screw; input the rotation speed of the ball screw, and calculate the axial and radial distances between the center of curvature of the screw raceway and the center of curvature of the nut raceway in combination with the obtained displacement of the center of curvature of the raceway, and determine the contact angles between the ball-screw and the ball-nut; based on the obtained ball- The contact angle between the screw and the ball-nut is used to calculate the geometric constraint equation of the center of raceway curvature; based on velocity analysis and coordinate transformation, the centrifugal force and gyroscopic moment of the ball are calculated based on Newton's second law and the acceleration formula of circular motion; the ball axial load balance equation, radial force balance equation, and ball screw axial load balance equation considering non-uniform loading and centrifugal effects are calculated based on the obtained centrifugal force and gyroscopic moment of the ball and the friction force between the ball and the raceway; the geometric constraint equation of the center of raceway curvature and the ball axial load balance equation, radial force balance equation, and ball screw axial load balance equation are combined and solved using Newton's iteration method to obtain the contact characteristics of the ball screw considering non-uniform loading and centrifugal effects.

[0091] See also Fig.10, the terminal device is a computer device, and the computer device 60 of this embodiment includes: a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61. When the computer program 63 is executed by the processor 61, the ball screw contact characteristic calculation method in the embodiment is implemented. To avoid repetition, it is not described one by one here. Alternatively, when the computer program 63 is executed by the processor 61, the functions of each model / unit in the ball screw contact characteristic calculation system in the embodiment are implemented. To avoid repetition, it is not described one by one here.

[0092] The computer device 60 may be a computing device such as a desktop computer, a notebook, a PDA, or a cloud server. The computer device 60 may include, but is not limited to, a processor 61 and a memory 62. Those skilled in the art will appreciate that Fig.10 This is only an example of the computer device 60 and does not constitute a limitation of the computer device 60. It may include more or fewer components than shown in the figure, or a combination of certain components, or different components. For example, the computer device may also include input and output devices, network access devices, buses, etc.

[0093] The processor 61 may be a central processing unit (CPU), or other general-purpose processors, graphics processing units (GPU), tensor processing units (TPU), digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or the processor may be any conventional processor, etc.

[0094] The memory 62 may be an internal storage unit of the computer device 60, such as a hard disk or memory of the computer device 60. The memory 62 may also be an external storage device of the computer device 60, such as a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, etc., equipped on the computer device 60.

[0095] Furthermore, the memory 62 may include both an internal storage unit of the computer device 60 and an external storage device. The memory 62 is used to store computer programs and other programs and data required by the computer device. The memory 62 may also be used to temporarily store data that has been output or is to be output.

[0096] See also Fig.11 The terminal device is an electronic device 600, which is in the form of a general-purpose computing device. The components of the electronic device may include, but are not limited to: at least one processing unit 610, at least one storage unit 620, a bus 630 connecting different platform components (including the storage unit 620 and the processing unit 610), a display unit 640, etc.

[0097] The storage unit stores program codes, which can be executed by the processing unit 610, so that the processing unit 610 performs the steps according to various exemplary embodiments of the present invention described in the above method section of this specification. For example, the processing unit 610 can perform the following steps: Figure 3 Follow the steps shown in .

[0098] The storage unit 620 may include a readable medium in the form of a volatile storage unit, such as a random access memory unit (RAM) 6201 and / or a cache memory unit 6202 , and may further include a read-only memory unit (ROM) 6203 .

[0099] The storage unit 620 may also include a program / utility 6204 having a set (at least one) of program modules 6205, such program modules 6205 including but not limited to: an operating system, one or more application programs, other program modules, and program data, each of which or some combination may include an implementation of a network environment.

[0100] Bus 630 may represent one or more of several types of bus structures, including a memory unit bus or memory unit controller, a peripheral bus, an accelerated graphics port, a processing unit, or a local bus using any of a variety of bus architectures.

[0101] The electronic device 600 may also communicate with one or more external devices 700 (e.g., keyboards, pointing devices, Bluetooth devices, etc.), may also communicate with one or more devices that enable a user to interact with the electronic device 600, and / or communicate with any device that enables the electronic device 600 to communicate with one or more other computing devices (e.g., routers, modems). Such communication may be performed via an input / output interface 650. In addition, the electronic device 600 may also communicate with one or more networks (e.g., local area networks, wide area networks, and / or public networks, such as the Internet) via a network adapter 660. The network adapter 660 may communicate with other modules of the electronic device 600 via a bus 630. It should be understood that, although not shown in the figure, other hardware and / or software modules may be used in conjunction with the electronic device 600, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage platforms, etc.

[0102] Example 4 The present invention also provides a storage medium, specifically a computer-readable storage medium, which is a memory device in a terminal device for storing programs and data. It is understandable that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and the extended storage medium supported by the terminal device, and can be any tangible medium containing or storing a program, which can be used by an instruction execution system, device or device or used in combination with it. The computer-readable storage medium provides a storage space, which stores the operating system of the terminal. In addition, one or more instructions suitable for being loaded and executed by a processor are also stored in the storage space, and these instructions can be one or more computer programs (including program codes). It should be noted that more specific examples of the computer-readable storage medium here include: an electrical connection with one or more wires, a portable disk, a hard disk, a random access memory, a read-only memory, an erasable programmable read-only memory, an optical fiber, a portable compact disk read-only memory, an optical storage device, a magnetic storage device, or any suitable combination of the above.

[0103] Computer readable storage media also include data signals propagated in baseband or as part of a carrier wave, which carry readable program code. Such propagated data signals can take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. The readable storage medium can also be any readable medium other than a readable storage medium, which can send, propagate or transmit a program for use by or in conjunction with an instruction execution system, device or device. The program code contained on the readable storage medium can be transmitted using any appropriate medium, including but not limited to wireless, wired, optical cable, radio frequency, etc., or any suitable combination of the above.

[0104] Program code for performing the operations of the present invention may be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java, C++, etc., and conventional procedural programming languages ​​such as "C" or similar programming languages. The program code may be executed entirely on the user computing device, partially on the user device, as a separate software package, partially on the user computing device and partially on a remote computing device, or entirely on a remote computing device or server. In the case of a remote computing device, the remote computing device may be connected to the user computing device through any type of network, including a local area network or a wide area network, or may be connected to an external computing device (e.g., through the Internet using an Internet service provider).

[0105] The processor may load and execute one or more instructions stored in a computer-readable storage medium to implement the corresponding steps of the ball screw contact characteristic calculation method in the above embodiment; the processor may load and execute the following steps: Input the geometric parameters and axial load of the ball screw, and determine the force coordination equation of the ball contact load and the axial load based on Hertz contact theory, the coordination relationship of adjacent ball deformations, Hooke's law, contact angle analysis, and axial internal force analysis. Determine the axial load balance equation of the ball screw based on Newton's first law; solve the displacement of the center of curvature of the raceway when the axial load is applied based on the obtained force coordination equation of the ball contact load and the axial load and the axial load balance equation of the ball screw; input the rotation speed of the ball screw, and calculate the axial and radial distances between the center of curvature of the screw raceway and the center of curvature of the nut raceway in combination with the obtained displacement of the center of curvature of the raceway, and determine the contact angles between the ball-screw and the ball-nut; based on the obtained ball- The contact angle between the screw and the ball-nut is used to calculate the geometric constraint equation of the center of raceway curvature; based on velocity analysis and coordinate transformation, the centrifugal force and gyroscopic moment of the ball are calculated based on Newton's second law and the acceleration formula of circular motion; the ball axial load balance equation, radial force balance equation, and ball screw axial load balance equation considering non-uniform loading and centrifugal effects are calculated based on the obtained centrifugal force and gyroscopic moment of the ball and the friction force between the ball and the raceway; the geometric constraint equation of the center of raceway curvature and the ball axial load balance equation, radial force balance equation, and ball screw axial load balance equation are combined and solved using Newton's iteration method to obtain the contact characteristics of the ball screw considering non-uniform loading and centrifugal effects.

[0106] The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. The non-relational database may include a distributed database based on blockchain, etc., but is not limited thereto. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but is not limited thereto.

[0107] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. The components of the embodiments of the present invention described and shown in the drawings here can usually be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0108] See also Figure 4, the difference between the contact angle of the first ball between the screw-ball and the nut-ball of the method of the present invention and the existing method at different speeds is compared: The parameters of the ball screw are: nominal diameter 42mm, ball diameter 7.14mm, lead 16mm, number of columns × number of rows 2.5 × 1, contact angle 45°, number of balls 46, and axial load 1690N.

[0109] In the existing method, the contact angle between the ball and the raceway is a constant at different speeds. The contact angle curve of the method of the present invention changes with the speed, and takes into account the different effects of the centrifugal effect on the ball-nut and ball-screw. When the speed gradually increases, the contact angle between the ball-nut gradually decreases, and the contact angle between the ball-screw gradually increases. When the speed is less than 1000rpm, the contact angle between the ball-screw and the ball-nut is consistent with the existing method. As the speed increases, the difference between the three curves gradually increases, which shows the necessity of considering the influence of the centrifugal effect on the contact angle in the method of the present invention.

[0110] See also Figure 5 , the difference between the contact load of the first ball between the screw-ball and the nut-ball of the method of the present invention and the existing method at different speeds is compared: The parameters of the ball screw are: nominal diameter 42mm, ball diameter 7.14mm, lead 16mm, number of columns × number of rows 2.5 × 1, contact angle 45°, number of balls 46, and axial load 1690N.

[0111] At different rotation speeds, the contact load calculated by the existing method is a constant. The contact load curve calculated by the method of the present invention changes with the rotation speed.

[0112] When the speed increases, when the speed is less than 1000rpm, the contact loads between the ball-screw and the ball-nut are close; when the speed is greater than 1000rpm, the contact loads between the ball-screw and the ball-nut gradually decrease, and the former has a greater change amplitude than the latter.

[0113] When the rotation speed is 0, the calculation results of the existing method and the method of the present invention are different. This is because the existing method does not consider the axial load balance and radial load balance of a single ball.

[0114] In addition, when the rotation speed increases, the three curves show significant differences, which shows the necessity of considering the influence of centrifugal effect on contact load in the method of the present invention.

[0115] See also Figure 6 and Figure 7 , the contact angle between ball and nut, and the contact angle between ball and screw at different speeds.

[0116] The parameters of the ball screw are: nominal diameter 42mm, ball diameter 7.14mm, lead 16mm, number of columns × number of rows 2.5 × 1, contact angle 45°, number of balls 46, and axial load 1690N.

[0117] (1) When the speed is fixed, the contact angle between the ball and the nut gradually decreases as the ball number increases. When the ball number increases, when the speed is low, the contact angle between the ball and the screw gradually decreases, and when the speed is high, the contact angle between the ball and the screw gradually increases.

[0118] (2) When the ball number is fixed, as the speed increases, the contact angle between the ball and the nut gradually decreases, while the contact angle between the ball and the screw gradually increases. The former decreases in a convex shape, while the latter increases in a concave shape.

[0119] The simulation results show the complex coupling relationship between the centrifugal effect and the ball number, verifying the necessity of considering the influence of the centrifugal effect on the contact angle in the present invention.

[0120] See also Figure 8 and Fig. 9 , contact load between ball and nut, contact load between ball and screw at different speeds.

[0121] The parameters of the ball screw are: nominal diameter 42mm, ball diameter 7.14mm, lead 16mm, number of columns × number of rows 2.5 × 1, contact angle 45°, number of balls 46, and axial load 1690N.

[0122] (1) When the speed is fixed, as the ball number increases, the contact load between the ball-nut and the ball-screw gradually increases.

[0123] (2) When the ball number is determined, as the rotation speed increases, the contact load between the ball and the screw gradually decreases in a convex shape.

[0124] When the ball number is small, the contact load between the ball and the nut gradually decreases in a convex shape. When the ball number is small, the contact load between the ball and the nut gradually increases in a concave shape.

[0125] The simulation results show the complex coupling relationship between the centrifugal effect and the ball serial number, verifying the necessity of considering the influence of the centrifugal effect on the contact load in the present invention.

[0126] In summary, the present invention provides a method and system for calculating contact characteristics of a ball screw, which can significantly reduce the optimization design cost of the ball screw in the design stage and the dynamic characteristics analysis cost in the actual operation stage, improve the optimization design efficiency of the ball screw and extend its service life, and reduce the time cost of optimization design and dynamic characteristics analysis of ball screw manufacturers.

[0127] The technicians in the relevant field can clearly understand that for the convenience and simplicity of description, only the division of the above-mentioned functional units and modules is used as an example for illustration. In practical applications, the above-mentioned function allocation can be completed by different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiment can be integrated in a processing unit, or each unit can exist physically separately, or two or more units can be integrated in one unit. The above-mentioned integrated unit can be implemented in the form of hardware or in the form of software functional units. In addition, the specific names of the functional units and modules are only for the convenience of distinguishing each other, and are not used to limit the scope of protection of this application. The specific working process of the units and modules in the above-mentioned system can refer to the corresponding process in the aforementioned method embodiment, which will not be repeated here.

[0128] In the above embodiments, the description of each embodiment has its own emphasis. For parts that are not described or recorded in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0129] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed in the present invention can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0130] In the embodiments provided by the present invention, it should be understood that the disclosed devices / terminals and methods can be implemented in other ways. For example, the device / terminal embodiments described above are only schematic. For example, the division of the modules or units is only a logical function division. There may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0131] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0132] In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0133] If the integrated module / unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the present invention implements all or part of the processes in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium, and the computer program can implement the steps of the above-mentioned various method embodiments when executed by the processor. Among them, the computer program includes computer program code, and the computer program code can be in source code form, object code form, executable file or some intermediate form. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, U disk, mobile hard disk, disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electric carrier signal, telecommunication signal and software distribution medium, etc. It should be noted that the content contained in the computer-readable medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electric carrier signals and telecommunication signals.

[0134] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices, and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of the processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0135] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0136] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0137] The above contents are only for explaining the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. A method for calculating contact characteristics of a ball screw, characterized in that: The following steps are involved: S1. Input the geometric parameters and axial load of the ball screw, and determine the force coordination equation of the ball contact load and axial load based on Hertz contact theory, the coordination relationship of adjacent ball deformations, Hooke's law, contact angle analysis, and axial internal force analysis; S2, solving the displacement of the center of curvature of the raceway when the axial load is applied based on the force coordination equation of the ball contact load and the axial load obtained in step S1 and the axial load balance equation of the ball screw obtained based on Newton's first law; S3, input the rotation speed of the ball screw, calculate the axial distance and radial distance between the center of curvature of the screw raceway and the center of curvature of the nut raceway in combination with the displacement of the center of curvature of the raceway obtained in step S2, and determine the contact angles between the ball-screw and the ball-nut; S4, calculating the geometric constraint equation of the center of curvature of the raceway based on the contact angles between the ball-screw and the ball-nut obtained in step S3; Based on the consideration of velocity analysis and coordinate transformation, the centrifugal force and gyroscopic moment of the ball are calculated based on Newton's second law and the acceleration formula of circular motion; S5, according to the centrifugal force and gyroscopic moment of the ball obtained in step S4, and the friction force between the ball and the raceway, calculate the ball axial load balance equation, radial force balance equation, and ball screw axial load balance equation taking into account non-uniform loading and centrifugal effect; S6. Combine the raceway curvature center geometric constraint equation obtained in step S4 with the ball axial load balance equation, radial force balance equation, and ball screw axial load balance equation obtained in step S5, and use Newton's iteration method to solve them to obtain the contact characteristics of the ball screw considering non-uniform loading and centrifugal effects.

2. The method for calculating contact characteristics of a ball screw according to claim 1, characterized in that: Step S1 is specifically as follows: According to Hertz contact theory, the Normal contact deformation of a ball and Normal contact deformation of a ball ; Based on the deformation coordination relationship of adjacent balls; calculate the Hooke's law to calculate the Axial contact deformation of a ball ; When the load is non-uniform, the contact angle between the ball and the raceway is calculated based on the geometric deformation relationship ; Determine Axial internal forces of adjacent ball units ; Based on the above steps, the force coordination equation between the ball contact load and the axial load is obtained.

3. The method for calculating contact characteristics of a ball screw according to claim 2, characterized in that: The force coordination equation between the ball contact load and the axial load is as follows: in, is the helix angle of the ball screw, For the The contact load of each ball, For the The contact angle of the ball, and is the force coordination coefficient, is the axial load of the ball screw, For the The contact load of each ball, For the The contact angle of the ball, is the contact angle between the ball and the raceway.

4. The method for calculating contact characteristics of a ball screw according to claim 1, characterized in that: Step S2 is specifically as follows: Calculate the axial load balance equation of the ball screw according to Newton's first law; solve the center displacement of the raceway curvature under axial load based on the calculated ball contact characteristics .

5. The method for calculating contact characteristics of a ball screw according to claim 1, characterized in that: Step S3 is specifically as follows: Calculate the axial distance between the center of curvature of the screw raceway and the center of curvature of the nut raceway and the center of curvature of the screw raceway and the nut raceway ; The contact angle considering the non-uniform loading and centrifugal effect is determined as follows: in, is the contact angle between the ball and the screw, is the contact angle between the ball and the nut, is the ball diameter, is the normal contact deformation between the ball and the screw, is the normal contact deformation between the ball and the nut, is the axial distance between the center of curvature of the nut raceway and the center of the ball, is the radial distance between the center of curvature of the nut raceway and the center of the ball, is the curvature radius of the screw raceway, is the curvature radius of the nut raceway.

6. The method for calculating contact characteristics of a ball screw according to claim 1, characterized in that: Step S4 is specifically as follows: Determine the geometric constraint equation of the center of curvature of the raceway based on the Pythagorean theorem; then calculate the mass moment of inertia of the ball , the gyroscopic angle between the ball and the raceway , and the sliding speed between the contact points between the ball and the screw raceway ; Determine the transformation relationship between the ball spin speed, the ball speed around the screw axis, and the screw speed; calculate the centrifugal force of the ball based on Newton's second law and the acceleration formula of circular motion ; Finally, the gyroscopic moment of the ball is obtained .

7. The method for calculating contact characteristics of a ball screw according to claim 6, characterized in that: The conversion relationship between the ball spin speed, the speed of the ball around the screw axis, and the screw speed is as follows: in, is the contact angle between the ball and the screw, is the contact angle between the ball and the nut, is the angular velocity of the ball around the screw axis, is the speed of the ball screw, is the ball diameter, is the pitch diameter of the screw.

8. The method for calculating contact characteristics of a ball screw according to claim 1, characterized in that: Step S5 is specifically as follows: Calculate the friction between the ball and the screw raceway according to step S4 and the friction between the ball and the nut raceway ; Then calculate the axial load balance equation of the ball and the radial force balance equation of the ball; Finally, calculate the axial load balance equation of the ball screw that comprehensively considers non-uniform loading and centrifugal effects.

9. The method for calculating contact characteristics of a ball screw according to claim 8, characterized in that: The axial load balance equation of the ball screw taking into account the non-uniform loading and centrifugal effect is as follows: in, is the axial load balance equation of the ball screw on the screw side, is the axial load balance equation of the ball screw on the nut side, is the contact angle between the ball and the screw, is the contact angle between the ball and the nut, is the contact load between the ball and the screw, is the helix angle, and is the raceway control coefficient, is the friction between the ball and the screw, is the number of balls in the ball screw, is the contact load between the ball and the nut, is the contact angle between the ball and the nut, is the friction between the ball and the nut raceway.

10. A ball screw contact characteristic calculation system, characterized in that: include: Input module, input the geometric parameters and axial load of the ball screw, and determine the force coordination equation of the ball contact load and the axial load based on Hertz contact theory, the coordination relationship of adjacent ball deformations, Hooke's law, contact angle analysis, and axial internal force analysis; A calculation module, which solves the displacement of the center of curvature of the raceway when the axial load is applied based on the obtained force coordination equation of the ball contact load and the axial load and the axial load balance equation of the ball screw determined according to Newton's first law; The distance module inputs the rotation speed of the ball screw, and calculates the axial and radial distances between the center of curvature of the screw raceway and the center of curvature of the nut raceway in combination with the obtained displacement of the center of curvature of the raceway, and determines the contact angles between the ball-screw and the ball-nut; The torque module calculates the geometric constraint equation of the center of curvature of the raceway based on the contact angles between the ball-screw and the ball-nut; Based on the consideration of velocity analysis and coordinate transformation, the centrifugal force and gyroscopic moment of the ball are calculated based on Newton's second law and the acceleration formula of circular motion; The equation module calculates the ball axial load balance equation, radial force balance equation, and ball screw axial load balance equation considering non-uniform loading and centrifugal effect based on the obtained centrifugal force and gyroscopic moment of the ball and the friction between the ball and the raceway; The output module combines the geometric constraint equation of the raceway curvature center and the ball axial load balance equation, radial force balance equation, and ball screw axial load balance equation, and uses Newton's iteration method to solve the ball screw contact characteristics considering non-uniform loading and centrifugal effects.

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