Ball screw contact characteristic calculation method and system

Abstract

The application discloses a kind of ball screw contact characteristic calculation method and system, input ball screw size parameter and external load, the correlation equation of preliminary establishment ball stress and axial load;Combined with the balance condition of force, the displacement variation of raceway contact point under axial load is solved;Add the rotational speed parameter of ball screw, calculate the position offset of raceway contact point when high speed rotates, and update the contact angle between ball and screw / nut;Through geometric constraint equation and kinematic analysis, the centrifugal force and gyroscopic moment generated by high-speed rotation of ball are quantified;On the basis of original static model, superimpose centrifugal force, gyroscopic effect and friction force of contact surface, and rebuild axial, radial stress balance equation containing dynamic factors;The geometric constraint equation is associated with multidimensional mechanics equation, numerical calculation is carried out using Newton iteration method, and finally the contact characteristics considering uneven load distribution and containing high-speed rotation influence are obtained.

Description

Technical Field

[0001] This invention belongs to the technical field of ball screw contact characteristics, specifically relating to a method and system for calculating ball screw contact characteristics. Background Technology

[0002] Machine tools are known as "mother machines" in the industrial field, and ball screws are crucial functional components of machine tools. Accurate analysis of the contact characteristics of ball screws for optimized design is essential for improving the positioning accuracy of machine tools and the machining quality of workpieces. However, due to the limitations of existing methods, it is impossible to accurately analyze the contact characteristics of ball screws based on their actual load conditions, which seriously hinders the development of the machine tool industry. Therefore, it is necessary to perform ball screw contact characteristic calculations that consider 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 Yong proposed a method combining coordinate system transformation to treat the contact angle as a function of the ball position angle, calculated the load distribution of a 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 was established between speed, axial load, lead, raceway curvature ratio, and ball screw stiffness. Zhen Ni treated the balls in the ball screw as uniformly loaded and analyzed the load distribution of the ball screw under different axial and radial loads. Mei Xuesong proposed a method for calculating non-uniform loads on 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 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 only analyze the contact characteristics of ball screws under single conditions of non-uniform loading or centrifugal effect, which does not reflect the actual working conditions of ball screws in machine tools. They neglect the influence of non-uniform loading and the centrifugal effect of the balls on the contact characteristics. 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 ball screws, which addresses the shortcomings of the prior art and solves the technical problem of accurately calculating the contact characteristics of ball screws under different speeds and different axial loads, taking into account non-uniform loading and centrifugal effects.

[0006] The present invention adopts the following technical solution:

[0007] A method for calculating the contact characteristics of a ball screw includes the following steps:

[0008] S1. Input the geometric parameters and axial load of the ball screw. Determine the force coordination equation between the ball contact load and the axial load based on Hertz contact theory, the deformation compatibility relationship between adjacent balls, Hooke's law, contact angle analysis, and axial internal force analysis.

[0009] S2. Based on the force coordination equation of ball contact load and axial load obtained in step S1 and the axial load balance equation of ball screw determined according to Newton's first law, solve for the displacement of raceway curvature center when axial load is applied.

[0010] S3. Input the rotational 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 based on the displacement of the raceway curvature center obtained in step S2, and determine the contact angles between the ball and the screw, and between the ball and the nut.

[0011] S4. Based on the contact angles between the ball and the screw, and between the ball and the nut obtained in step S3, calculate the geometric constraint equations for the center of curvature of the raceway; based on velocity analysis and coordinate transformation considerations, calculate the centrifugal force and gyroscopic torque of the ball based on Newton's second law and the acceleration formula for circular motion.

[0012] S5. Based on the centrifugal force and gyroscopic torque of the ball obtained in step S4, and the frictional 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 considering non-uniform loading and centrifugal effect.

[0013] S6. Combine the geometric constraint equations of the raceway curvature center 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 the Newton iteration method to solve for the ball screw contact characteristics considering non-uniform loading and centrifugal effect.

[0014] Preferably, step S1 specifically includes:

[0015] Calculated according to Hertzian contact theory Normal contact deformation of each ball and the Normal contact deformation of each ball Based on the deformation coordination relationship of adjacent balls; calculate Hooke's Law to calculate the first... Axial contact deformation of each ball When subjected to non-uniform loading, the contact angle between the balls and the raceways is calculated based on the geometric deformation relationship. ; Determine the first Axial internal forces of adjacent ball bearing units Based on the above steps, the force coordination equation between the ball contact load and the axial load is obtained.

[0016] Preferably, the force coordination equation between the ball contact load and the axial load is as follows:

[0017]

[0018] in, The helix angle of the ball screw. For the first Contact load of each ball For the first The contact angle of each ball. and For force compatibility coefficient, For the axial load of the ball screw, For the first Contact load of each ball For the first The contact angle of each ball. The contact angle between the ball and the raceway.

[0019] Preferably, step S2 specifically includes:

[0020] Calculate the axial load balance equation of the ball screw according to Newton's first law; solve for the raceway curvature center displacement under axial load based on the calculated ball contact characteristics. .

[0021] Preferably, step S3 specifically includes:

[0022] Calculate the axial distance between the center of curvature of the lead screw raceway and the center of curvature of the nut raceway. and the center of curvature of the lead screw raceway and the nut raceway The contact angle determined by comprehensively considering non-uniform loading and centrifugal effects is as follows:

[0023]

[0024] in, The contact angle between the ball and the lead screw. The contact angle between the ball and the nut. The diameter of the ball bearing is... This refers to the normal contact deformation between the ball and the lead screw. This refers to the normal contact deformation between the ball and the nut. The distance between the center of curvature of the nut raceway and the center of the ball is axial. The radial distance between the center of curvature of the nut raceway and the center of the ball. The radius of curvature of the lead screw raceway is... Let be the radius of curvature of the nut raceway.

[0025] Preferably, step S4 specifically includes:

[0026] The geometric constraint equations for the raceway curvature center are determined based on the Pythagorean theorem; then the mass moment of inertia of the balls is calculated. The gyro angle between the ball and the raceway And the sliding speed between the contact points of the balls and the lead screw raceways. Determine the relationship between the ball spin velocity, the ball rotational speed around the screw axis, and the screw rotational speed; calculate the centrifugal force of the ball based on Newton's second law and the acceleration formula for circular motion. Finally, the gyroscopic torque of the ball bearing is obtained. .

[0027] Preferably, the relationship between the ball spin speed, the ball rotation speed around the screw axis, and the screw speed is as follows:

[0028]

[0029] in, The contact angle between the ball and the lead screw. The contact angle between the ball and the nut. Let be the angular velocity of the ball about the screw axis. The rotational speed of the ball screw, The diameter of the ball bearing is... The pitch circle diameter of the leadscrew.

[0030] Preferably, step S5 specifically includes:

[0031] Calculate the friction between the ball and the screw raceway according to step S4. Friction between the ball and the nut raceway Then, the axial load balance equation and the radial force balance equation of the ball screw are calculated; finally, the axial load balance equation of the ball screw that takes into account non-uniform loading and centrifugal effect is calculated.

[0032] Preferably, the axial load balance equation for the ball screw, taking into account both non-uniform loading and centrifugal effects, is as follows:

[0033]

[0034] in, The equation for axial load balance on the screw side of the ball screw is as follows: The equation for axial load balance of the ball screw on the nut side is as follows: The contact angle between the ball and the lead screw. The contact angle between the ball and the nut. This refers to the contact load between the ball and the lead screw. The helix angle, and This is the raceway control coefficient. The friction between the ball and the lead screw. The number of balls in the ball screw. This refers to the contact load between the ball and the nut. The contact angle between the ball and the nut. This refers to the frictional force between the balls and the raceway of the nut.

[0035] Secondly, embodiments of the present invention provide a ball screw contact characteristic calculation system, comprising:

[0036] The input module takes the geometric parameters and axial load of the ball screw as input. Hertz contact theory, deformation compatibility relationship between adjacent balls, Hooke's law, contact angle analysis, and axial internal force analysis are used to determine the force compatibility equation between the ball contact load and the axial load.

[0037] The calculation module solves for the displacement of the raceway curvature center when the axial load is applied, based on the 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.

[0038] The distance module takes the rotational speed of the ball screw as input 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 based on the obtained raceway curvature center displacement, thereby determining the contact angles between the ball and the screw, and between the ball and the nut.

[0039] The torque module calculates the geometric constraint equation of the raceway curvature center based on the obtained contact angles between the ball and the lead screw, and between the ball and the nut; based on velocity analysis and coordinate transformation considerations, it calculates the centrifugal force and gyroscopic torque of the ball based on Newton's second law and the acceleration formula of circular motion.

[0040] The equation module calculates 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 effects, based on the obtained centrifugal force and gyroscopic torque of the ball and the friction between the ball and the raceway.

[0041] The output module combines the obtained raceway curvature center geometric constraint equations, ball axial load balance equations, radial force balance equations, and ball screw axial load balance equations. The Newton iteration method is then used to solve for the ball screw contact characteristics considering non-uniform loading and centrifugal effects.

[0042] Thirdly, a computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described ball screw contact characteristic calculation method.

[0043] Fourthly, embodiments of the present invention provide a computer-readable storage medium including a computer program, which, when executed by a processor, implements the steps of the above-described ball screw contact characteristic calculation method.

[0044] Fifthly, a chip includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described ball screw contact characteristic calculation method.

[0045] In a sixth aspect, embodiments of the present invention provide an electronic device, including a computer program, which, when executed by the electronic device, implements the steps of the above-described ball screw contact characteristic calculation method.

[0046] Compared with the prior art, the present invention has at least the following beneficial effects:

[0047] A method for calculating the contact characteristics of a ball screw is proposed. Based on the non-uniform loading of the ball screw, force coordination equations between the ball contact load and the axial load are established according to Hertzian contact theory, the deformation compatibility relationship between 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 the ball screw is established. The contact characteristics of the balls under non-uniform loading are calculated by simultaneously establishing the force coordination equations and the axial load balance equations. The displacement of the raceway curvature center is calculated according to the formula for calculating the raceway curvature center. Considering the non-uniform loading, the displacement attenuation of the raceway curvature center is introduced into the analysis of the raceway curvature center considering the centrifugal effect. Geometric constraint equations for the raceway curvature displacement during ball motion are established based on the Pythagorean theorem. Considering the centrifugal effect and the non-uniform loading, the ball rotation speed and the ball rotational speed around the screw axis are calculated based on the ball velocity analysis and coordinate transformation. Based on Newton's first law, centrifugal force analysis, and gyroscopic torque analysis, the axial load balance equation and radial force balance equation of the ball screw during its motion were established. Finally, the axial load balance equation of the ball screw during its motion was established. A process for calculating the contact characteristics of the ball screw based on non-uniform loading and centrifugal effect was given.

[0048] Furthermore, based on Hertzian contact theory, the deformation compatibility relationship between adjacent balls, axial contact deformation analysis, contact angle analysis, and axial internal force analysis, the force compatibility equation between contact load and axial load is obtained simultaneously.

[0049] Furthermore, the axial load balance equation of the ball screw is obtained through Newton's first law. Based on the geometric relationship analysis, the force coordination equation in step S1 and the axial load balance equation of the ball screw in step S2 are combined to obtain the displacement of the raceway curvature center under axial load.

[0050] Furthermore, based on the distance and geometric relationship between the curvature centers of the lead screw and nut raceways, a contact angle that comprehensively considers non-uniform loading and centrifugal effects is obtained.

[0051] Furthermore, based on the Pythagorean theorem, the geometric constraint equation of the raceway curvature center is obtained. Based on the mass moment of inertia of the ball, the gyro angle between the ball and the raceway, and velocity analysis, the ball spin velocity, the ball rotation speed around the screw axis, and the transformation relationship of the screw rotation speed are obtained. The gyro torque of the ball is obtained by combining these equations. The centrifugal force of the ball is obtained according to Newton's second law and the acceleration formula of circular motion.

[0052] Furthermore, based on the force analysis and the centrifugal force of the balls in step S4, the axial load balance equation 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 raceway in step S4, the axial load balance equation of the ball screw that comprehensively considers non-uniform loading and centrifugal effect is obtained.

[0053] It is understood that the beneficial effects of the second to sixth aspects mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0054] In summary, the method of the present invention can comprehensively consider the influence of non-uniform loading of the ball screw under axial load and the centrifugal effect on the displacement of the raceway curvature center during the motion process, and then calculate the contact characteristics that comprehensively consider non-uniform loading and centrifugal effect, providing guidance for the optimized design of ball screws and the dynamic characteristic analysis of ball screws during operation.

[0055] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0056] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments of this application will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0057] Figure 1 A schematic diagram of the load distribution of the balls when the ball screw is subjected to non-uniform load;

[0058] Figure 2 A schematic diagram of the raceway curvature center, taking into account both non-uniform loading and centrifugal effects;

[0059] Figure 3 For the calculation flowchart;

[0060] Figure 4 The diagram shows a comparison of the contact angle of the first ball between the lead screw and ball, and between the nut and ball in the method of the present invention and that in the prior art, at different rotational speeds.

[0061] Figure 5The diagram shows a comparison of the contact load between the lead screw and ball, and between the nut and ball in the method of the present invention and the existing method at different rotational speeds.

[0062] Figure 6 Diagrams showing the contact angles between the ball and nut at different rotational speeds;

[0063] Figure 7 The contact angle diagram between the ball and the lead screw at different rotational speeds;

[0064] Figure 8 Diagrams showing the contact load between the ball and nut at different rotational speeds;

[0065] Figure 9 The diagram shows the contact load between the ball and the lead screw at different rotational speeds.

[0066] Figure 10 A schematic diagram of a computer device provided in an embodiment of the present invention;

[0067] Figure 11 This is a block diagram of an electronic device according to an embodiment of the present invention.

[0068] Among them, 60. Computer equipment; 61. Processor; 62. Memory; 63. Computer program; 600. Electronic device; 610. Processing unit; 620. Storage unit; 6201. Random access memory unit; 6202. Cache memory unit; 6203. Read-only memory unit; 6204. Program / utility; 6205. Program module; 630. Bus; 640. Display unit; 650. Input / output interface; 660. Network adapter; 700. External device. Detailed Implementation

[0069] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0070] In the description of this invention, it should be understood that the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0071] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0072] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Additionally, the character " / " in this invention generally indicates that the preceding and following objects have an "or" relationship.

[0073] It should be understood that although terms such as first, second, third, etc., may be used in the embodiments of the present invention to describe the preset range, these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from one another. 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.

[0074] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0075] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0076] This invention provides a method for calculating the contact characteristics of ball screws. By inputting the dimensional parameters of the ball screw and the applied load, and using principles of materials mechanics and contact mechanics (Hertz theory, deformation compatibility relationships, etc.), a preliminary correlation equation between the ball force and the axial load is established. Combining the force equilibrium condition (Newton's first law), the displacement change of the raceway contact point under the axial load is solved, providing initial data for subsequent dynamic analysis. By adding the ball screw's rotational speed parameter, the positional offset (axial and radial distance) of the raceway contact point during high-speed rotation is calculated, and the contact angle between the ball and the screw / nut is updated. Through geometric constraint equations and kinematic analysis, the centrifugal force generated by the high-speed rotation of the ball is quantified. (Outward-throwing inertial force) and gyroscopic torque (resistance effect of rotational direction change); based on the original static model, centrifugal force, gyroscopic effect and contact surface friction are superimposed to reconstruct the axial and radial force balance equations that include dynamic factors; the geometric constraint equations are combined with the multidimensional mechanical equations, and Newton's iteration method is used for numerical calculation to finally obtain the contact characteristics (such as contact stress, contact angle change, etc.) that take into account both uneven load distribution and the influence of high-speed rotation; through a layered and progressive modeling approach, the model is gradually refined from static to dynamic, which solves the limitation of traditional methods that ignore high-speed rotation effects and significantly improves the calculation accuracy of ball screw contact characteristics under high-speed conditions.

[0077] Example 1

[0078] This invention discloses a method for calculating the contact characteristics of a ball screw, comprising the following steps:

[0079] S1. Input the geometric parameters and axial load of the ball screw. Determine the force coordination equation between the ball contact load and the axial load based on Hertz contact theory, the deformation compatibility relationship between adjacent balls, Hooke's law, contact angle analysis, and axial internal force analysis.

[0080] S101. Calculate the contact deformation between the ball and the raceway according to Hertz contact theory;

[0081]

[0082] in, It is the first Normal contact deformation of each ball, It is the first Contact load of each ball It is the first Normal contact deformation of each ball, It is the first Contact load of each ball and It is the Hertzian contact coefficient.

[0083] S102. Calculate the deformation compatibility relationship between adjacent balls;

[0084]

[0085] Among them, It is the first Axial contact deformation of each ball, It is the first Axial contact deformation of each ball, It is the first Axial contact deformation of the ball bearings.

[0086] S103, Calculation of the first based on Hooke's Law Axial contact deformation of the ball;

[0087]

[0088] in, It is the lead screw side The ball and the first The axial distance between the balls It is the nut side. The ball and the first The axial distance between the balls and It is the axial deformation coefficient.

[0089] S104. Under non-uniform loading, calculate the contact angle between the ball and the raceway based on the geometric deformation relationship;

[0090]

[0091] in, It is the distance between the centers of curvature of the raceway when it is unloaded. It is the contact angle between the ball and the raceway when unloaded.

[0092] S105. Determine the axial internal force of adjacent balls;

[0093] Figure 1 This diagram illustrates the load distribution of the balls when the ball screw is under load. Axial internal forces of adjacent ball bearing units for:

[0094]

[0095] Among them, For the first The axial internal force of each adjacent ball bearing unit, For the first Contact load of each ball For the first The contact angle of each ball. This refers to the axial load on the ball screw.

[0096] S106. Based on steps S101, S102, S103, S104, and S105, the force coordination equation between the ball contact load and the axial load is calculated.

[0097]

[0098] in, The helix angle of the ball screw. For the first Contact load of each ball For the first The contact angle of each ball. and This is the force compatibility coefficient.

[0099] S2. 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, solve for the displacement of the raceway curvature center when the axial load is applied.

[0100] S201. Calculate the axial load balance equation of the ball screw according to Newton's first law;

[0101]

[0102] in, This refers to the number of balls in the ball screw.

[0103] S202. Based on the ball contact characteristics calculated in steps S106 and S201, solve for the raceway curvature center displacement under axial load.

[0104]

[0105] S3. Input the rotational 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 based on the displacement of the raceway curvature center obtained in step S2, and determine the contact angles between the ball and the screw, and between the ball and the nut.

[0106] Please see Figure 2 This represents the change in the raceway curvature center considering both non-uniform loading and centrifugal effects. The specific calculation steps are as follows:

[0107] S301. Calculate the distance between the center of curvature of the lead screw raceway and the center of curvature of the nut raceway;

[0108]

[0109] in, This is the axial distance between the center of curvature of the lead screw raceway and the center of curvature of the nut raceway. The center of curvature of the lead screw raceway and the nut raceway, For the first The displacement of the raceway curvature center corresponding to each ball.

[0110] S302. Calculate the contact angle that takes into account both non-uniform loading and centrifugal effect according to step S301.

[0111]

[0112] in, The contact angle between the ball and the lead screw. The contact angle between the ball and the nut. The diameter of the ball bearing is... This refers to the normal contact deformation between the ball and the lead screw. This refers to the normal contact deformation between the ball and the nut. The distance between the center of curvature of the nut raceway and the center of the ball is axial. The radial distance between the center of curvature of the nut raceway and the center of the ball. The radius of curvature of the lead screw raceway is... Let be the radius of curvature of the nut raceway.

[0113] S4. Based on the contact angles between the ball and the screw, and between the ball and the nut obtained in step S3, calculate the geometric constraint equations for the center of curvature of the raceway; based on velocity analysis and coordinate transformation considerations, calculate the centrifugal force and gyroscopic torque of the ball based on Newton's second law and the acceleration formula for circular motion.

[0114] S401. Calculate the geometric constraint equation of the curvature center of the raceway based on the Pythagorean theorem.

[0115]

[0116] S402, Calculate the moment of inertia of the ball bearings;

[0117]

[0118] in, Let the moment of inertia of the ball be . The density of the ball bearing material, The diameter of the lead screw.

[0119] S403, Calculate the gyro angle between the ball and the raceway;

[0120]

[0121] in, The gyro angle between the ball and the raceway.

[0122] S404, Calculate the sliding speed between the contact points of the ball and the lead screw raceway;

[0123]

[0124] in, It is the sliding speed of the lead screw raceway and the balls on the ball side. It is the sliding speed of the lead screw raceway and the ball on the raceway side. It is the sliding speed between the ball and the raceway. It is a coordinate system fixed at the center of the ball to describe the movement of the ball. It is the angular velocity of the leadscrew. It is the angular velocity of the ball bearings around the axis of the leadscrew. It is the angular velocity of the ball's spin. It is the spin angular velocity of the ball. exist directional components, yes exist directional components, yes exist The directional component.

[0125] S405. Calculate the relationship between the ball spin speed, the ball rotation speed around the screw axis, and the screw rotation speed according to steps S403 and S404.

[0126]

[0127] S406. According to step S405, calculate the centrifugal force of the ball based on Newton's second law and the acceleration formula of circular motion.

[0128]

[0129] in, This refers to the centrifugal force of the ball bearings.

[0130] S407. Calculate the gyroscopic torque of the ball according to steps S402, S403, S404, and S405.

[0131]

[0132] in, The gyroscopic torque is the torque of the ball bearing.

[0133] S5. Based on the centrifugal force and gyroscopic torque of the ball obtained in step S4, and the frictional 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 considering non-uniform loading and centrifugal effect.

[0134] S501. Calculate the frictional force between the ball and the raceway according to step S4.

[0135]

[0136] in, This refers to the frictional force between the balls and the lead screw raceway. This refers to the frictional force between the balls and the raceways of the nut. and This is the raceway control coefficient.

[0137] S502. Calculate the axial load balance equation of the ball according to step S501.

[0138]

[0139] S503. Calculate the radial force balance equation of the ball according to steps S406 and S501.

[0140]

[0141] S504. Calculate the axial load balance equation of the ball screw that comprehensively considers non-uniform loading and centrifugal effect according to step S501.

[0142]

[0143] in, The equation for axial load balance on the screw side of the ball screw is as follows: The equation for axial load balance of the ball screw on the nut side is given.

[0144] S6. Combine the geometric constraint equations of the raceway curvature center 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 the Newton iteration method to solve for the ball screw contact characteristics considering non-uniform loading and centrifugal effect.

[0145] Those skilled in the art will understand that various aspects of the present invention can be implemented as systems, methods, or program products. Therefore, various aspects of the present invention can be specifically implemented in the following forms: a completely hardware implementation, a completely software implementation (including firmware, microcode, etc.), or a combination of hardware and software aspects, collectively referred to herein as a "circuit," "module," or "platform."

[0146] Example 2

[0147] This 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.

[0148] The input module takes in the geometric parameters and axial load of the ball screw and determines the force coordination equation between the ball contact load and the axial load based on Hertz contact theory, the deformation compatibility relationship between adjacent balls, Hooke's law, contact angle analysis, and axial internal force analysis.

[0149] The calculation module solves for the displacement of the raceway curvature center when the axial load is applied, based on the force coordination equation of the ball contact load and the axial load and the ball screw axial load balance equation determined according to Newton's first law.

[0150] The distance module takes the rotational speed of the ball screw as input 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 based on the obtained raceway curvature center displacement, thereby determining the contact angles between the ball and the screw, and between the ball and the nut.

[0151] The torque module calculates the geometric constraint equation of the raceway curvature center based on the obtained contact angles between the ball and the lead screw, and between the ball and the nut; based on velocity analysis and coordinate transformation considerations, it calculates the centrifugal force and gyroscopic torque of the ball based on Newton's second law and the acceleration formula of circular motion.

[0152] The equation module calculates 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 effects, based on the obtained centrifugal force and gyroscopic torque of the ball and the friction between the ball and the raceway.

[0153] The output module combines the obtained raceway curvature center geometric constraint equations, ball axial load balance equations, radial force balance equations, and ball screw axial load balance equations. The Newton iteration method is then used to solve for the ball screw contact characteristics considering non-uniform loading and centrifugal effects.

[0154] Example 3

[0155] This invention provides a terminal device comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, graphics processing units (GPUs), tensor processing units (TPUs), digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions to achieve a corresponding method flow or corresponding function. The processor described in this embodiment can be used for the operation of a ball screw contact characteristic calculation method, including:

[0156] Input the geometric parameters and axial load of the ball screw. Based on Hertzian contact theory, the deformation compatibility relationship between adjacent balls, Hooke's law, contact angle analysis, and axial internal force analysis, determine the force compatibility equations for the ball contact load and axial load. Determine the axial load balance equation of the ball screw based on Newton's first law. Based on the obtained force compatibility equations for the ball contact load and axial load, and the axial load balance equation of the ball screw, solve for the displacement of the raceway curvature center when the axial load is applied. Input the rotational speed of the ball screw. Combine the obtained raceway curvature center displacement to calculate the axial and radial distances between the raceway curvature centers of the screw and nut, and determine the contact angles between the ball and screw, and between the ball and nut. Based on the obtained ball-... The contact angle between the screw, ball, and nut is calculated using the geometric constraint equation of the raceway curvature center. Based on velocity analysis and coordinate transformation, the centrifugal force and gyroscopic torque of the ball are calculated using Newton's second law and the acceleration formula for circular motion. Based on the obtained centrifugal force and gyroscopic torque of the ball, and the frictional force between the ball and the raceway, the axial load balance equations, radial force balance equations, and ball screw axial load balance equations considering non-uniform loading and centrifugal effects are calculated. The obtained raceway curvature center geometric constraint equations, ball axial load balance equations, radial force balance equations, and ball screw axial load balance equations are solved simultaneously using Newton's iteration method to obtain the ball screw contact characteristics considering non-uniform loading and centrifugal effects.

[0157] Please see Figure 10 The terminal device is a computer device. In this embodiment, the computer device 60 includes a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61. When executed by the processor 61, the computer program 63 implements the ball screw contact characteristic calculation method in this embodiment; to avoid repetition, it will not be described in detail here. Alternatively, when executed by the processor 61, the computer program 63 implements the functions of each model / unit in the ball screw contact characteristic calculation system of this embodiment; to avoid repetition, it will not be described in detail here.

[0158] Computer device 60 can be a desktop computer, laptop, handheld computer, cloud server, or other computing device. Computer device 60 may include, but is not limited to, a processor 61 and a memory 62. Those skilled in the art will understand that... Figure 10 This is merely an example of computer device 60 and does not constitute a limitation on computer device 60. It may include more or fewer components than shown, or combine certain components, or different components. For example, computer device may also include input / output devices, network access devices, buses, etc.

[0159] The processor 61 may be a Central Processing Unit (CPU), or other general-purpose processors, graphics processing units (GPUs), tensor processing units (TPUs), digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0160] The memory 62 can be an internal storage unit of the computer device 60, such as a hard disk or RAM of the computer device 60. The memory 62 can also be an external storage device of the computer device 60, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc., provided on the computer device 60.

[0161] Furthermore, the memory 62 may include both internal storage units of the computer device 60 and external storage devices. The memory 62 is used to store computer programs and other programs and data required by the computer device. The memory 62 can also be used to temporarily store data that has been output or will be output.

[0162] Please see Figure 11 The terminal device is an electronic device 600, which is manifested 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 storage unit 620 and processing unit 610), a display unit 640, etc.

[0163] The storage unit stores program code, which can be executed by the processing unit 610 to perform the steps described in the method section of this specification according to various exemplary embodiments of the present invention. For example, the processing unit 610 can perform actions such as... Figure 3 The steps are shown in the figure.

[0164] Storage unit 620 may include a readable medium in the form of a volatile storage unit, such as random access memory (RAM) 6201 and / or cache memory 6202, and may further include a read-only memory (ROM) 6203.

[0165] Storage unit 620 may also include a program / utility 6204 having a set (at least one) program module 6205, such program module 6205 including but not limited to: operating system, one or more application programs, other program modules and program data, each or some combination of these examples may include an implementation of a network environment.

[0166] Bus 630 can represent one or more of several types of bus structures, including a memory cell bus or memory cell controller, a peripheral bus, a graphics acceleration port, a processing unit, or a local bus using any of the multiple bus structures.

[0167] Electronic device 600 can also communicate with one or more external devices 700 (e.g., keyboard, pointing device, Bluetooth device, etc.), and with one or more devices that enable a user to interact with electronic device 600, and / or with any device that enables electronic device 600 to communicate with one or more other computing devices (e.g., router, modem). This communication can be performed via input / output interface 650. Furthermore, electronic device 600 can also communicate with one or more networks (e.g., local area network, wide area network, and / or public network, such as the Internet) via network adapter 660. Network adapter 660 can communicate with other modules of electronic device 600 via bus 630. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with 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.

[0168] Example 4

[0169] This 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 understood that the computer-readable storage medium here can include both built-in storage media in the terminal device and extended storage media supported by the terminal device; it can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, the storage space also stores one or more instructions suitable for loading and execution by a processor, which can be one or more computer programs (including program code). More specific examples of the computer-readable storage medium include: an electrical connection with one or more wires, a portable disk, a hard disk, random access memory, read-only memory, erasable programmable read-only memory, optical fiber, portable compact disk read-only memory, optical storage device, magnetic storage device, or any suitable combination thereof.

[0170] Computer-readable storage media also include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable storage medium can also be any readable medium other than a readable storage medium that can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the readable storage medium can be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, radio frequency, etc., or any suitable combination thereof.

[0171] Program code for performing the operations of this invention can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, and conventional procedural programming languages ​​such as C or similar languages. The program code can execute entirely on the user's computing device, partially on the user's computing device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0172] One or more instructions stored in a computer-readable storage medium can be loaded and executed by a processor to implement the corresponding steps of the ball screw contact characteristic calculation method in the above embodiments; one or more instructions in the computer-readable storage medium are loaded and executed by the processor in the following steps:

[0173] Input the geometric parameters and axial load of the ball screw. Based on Hertzian contact theory, the deformation compatibility relationship between adjacent balls, Hooke's law, contact angle analysis, and axial internal force analysis, determine the force compatibility equations for the ball contact load and axial load. Determine the axial load balance equation of the ball screw based on Newton's first law. Based on the obtained force compatibility equations for the ball contact load and axial load, and the axial load balance equation of the ball screw, solve for the displacement of the raceway curvature center when the axial load is applied. Input the rotational speed of the ball screw. Combine the obtained raceway curvature center displacement to calculate the axial and radial distances between the raceway curvature centers of the screw and nut, and determine the contact angles between the ball and screw, and between the ball and nut. Based on the obtained ball-... The contact angle between the screw, ball, and nut is calculated using the geometric constraint equation of the raceway curvature center. Based on velocity analysis and coordinate transformation, the centrifugal force and gyroscopic torque of the ball are calculated using Newton's second law and the acceleration formula for circular motion. Based on the obtained centrifugal force and gyroscopic torque of the ball, and the frictional force between the ball and the raceway, the axial load balance equations, radial force balance equations, and ball screw axial load balance equations considering non-uniform loading and centrifugal effects are calculated. The obtained raceway curvature center geometric constraint equations, ball axial load balance equations, radial force balance equations, and ball screw axial load balance equations are solved simultaneously using Newton's iteration method to obtain the ball screw contact characteristics considering non-uniform loading and centrifugal effects.

[0174] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0175] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0176] Please see Figure 4The differences between the contact angle of the first ball between the lead screw and ball, and between the nut and ball in the method of this invention and existing methods were compared at different rotational speeds:

[0177] The ball screw parameters 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.

[0178] Existing methods maintain a constant contact angle between the ball and raceway at different rotational speeds. The contact angle curve of this invention varies with rotational speed and considers the different effects of centrifugal force on the ball-nut and ball-screw relationships. As the rotational speed gradually increases, the contact angle between the ball and nut gradually decreases, while the contact angle between the ball and screw gradually increases. When the rotational speed is less than 1000 rpm, the contact angles between the ball and screw and between the ball and nut are consistent with existing methods. As the rotational speed increases, the difference between the three curves gradually widens, demonstrating the necessity of considering the influence of centrifugal force on the contact angle in this invention.

[0179] Please see Figure 5 The differences between the contact load of the first ball between the lead screw and ball, and between the nut and ball in the method of this invention and existing methods were compared at different rotational speeds:

[0180] The ball screw parameters 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.

[0181] At different rotational speeds, the contact load calculated by existing methods is a constant. The contact load curve calculated by the method of this invention varies with the rotational speed.

[0182] When the rotational speed increases, the contact loads between the ball and the lead screw and between the ball and the nut are close when the rotational speed is less than 1000 rpm; when the rotational speed is greater than 1000 rpm, the contact loads between the ball and the lead screw and between the ball and the nut gradually decrease, with the former showing a greater change than the latter.

[0183] When the rotational speed is 0, the calculation results of the existing method are different from those of the present invention. This is because the existing method does not take into account the axial load balance and radial load balance of a single ball.

[0184] Furthermore, as the rotational speed increases, the three curves show significant differences, indicating the necessity of considering the influence of centrifugal effect on contact load in the method of the present invention.

[0185] Please see Figure 6 and Figure 7 The contact angle between the ball and the nut, and the contact angle between the ball and the lead screw at different speeds.

[0186] The ball screw parameters 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.

[0187] (1) When the rotational speed is fixed, the contact angle between the ball and the nut gradually decreases as the ball number increases. When the ball number increases, the contact angle between the ball and the screw gradually decreases when the rotational speed is low, but gradually increases when the rotational speed is high.

[0188] (2) With the ball number fixed, as the rotation speed increases, the contact angle between the ball and the nut gradually decreases and the contact angle between the ball and the screw gradually increases. The former decreases in the upward convex shape and the latter increases in the downward concave shape.

[0189] Simulation results demonstrate the complex coupling relationship between centrifugal effect and ball bearing number, verifying the necessity of considering the influence of centrifugal effect on contact angle in this invention.

[0190] Please see Figure 8 and Figure 9 The contact load between the ball and the nut, and the contact load between the ball and the lead screw at different speeds.

[0191] 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.

[0192] (1) When the rotation speed is fixed, as the ball number increases, the contact load between the ball and nut and between the ball and the screw gradually increases.

[0193] (2) When the ball number is determined, as the rotational speed increases, the contact load between the ball and the screw gradually decreases in an upward convex shape.

[0194] When the ball number is small, the contact load between the ball and the nut gradually decreases in an upward convex shape, and when the ball number is small, the contact load between the ball and the nut gradually increases in a downward concave shape.

[0195] Simulation results demonstrate the complex coupling relationship between the centrifugal effect and the ball bearing sequence, verifying the necessity of considering the influence of the centrifugal effect on the contact load in this invention.

[0196] In summary, the ball screw contact characteristic calculation method and system of the present invention can significantly reduce the optimization design cost of ball screws in the design stage and the dynamic characteristic analysis cost in the actual operation stage, improve the optimization design efficiency of ball screws and extend their service life, and reduce the time cost of optimization design for ball screw manufacturers and dynamic characteristic analysis for users.

[0197] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to 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 embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0198] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0199] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this invention can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0200] In the embodiments provided by this 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 merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0201] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0202] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0203] If the integrated module / unit is implemented as 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, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random-access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed 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 electrical carrier signals and telecommunication signals.

[0204] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus, and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1A device that provides the functions specified in one or more boxes.

[0205] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0206] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0207] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A method for calculating the contact characteristics of a ball screw, characterized in that, Includes the following steps: S1. Input the geometric parameters and axial load of the ball screw. Based on Hertzian contact theory, the deformation compatibility relationship between adjacent balls, Hooke's law, contact angle analysis, and axial internal force analysis, determine the force compatibility equation between the ball contact load and the axial load, specifically: Calculated according to Hertzian contact theory Normal contact deformation of each ball and the Normal contact deformation of each ball ; Based on the deformation coordination relationship of adjacent balls; calculate Hooke's Law to calculate the first... Axial contact deformation of each ball When subjected to non-uniform loading, the contact angle between the balls and the raceways is calculated based on the geometric deformation relationship. ; Determine the first Axial internal forces of adjacent ball bearing units Based on the above steps, the force compatibility equation between the ball contact load and the axial load is obtained. The force compatibility equation between ball contact load and axial load is as follows: in, The helix angle of the ball screw. For the first Contact load of each ball For the first The contact angle of each ball. and For force compatibility coefficient, For the axial load of the ball screw, For the first Contact load of each ball For the first The contact angle of each ball. The contact angle between the ball and the raceway; S2. Based on the force coordination equation of ball contact load and axial load obtained in step S1 and the axial load balance equation of ball screw obtained based on Newton's first law, solve for the displacement of raceway curvature center when axial load is applied. S3. Input the rotational 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 based on the displacement of the raceway curvature center obtained in step S2, and determine the contact angles between the ball and the screw, and between the ball and the nut. S4. Based on the contact angle between the ball and the screw, and between the ball and the nut obtained in step S3, calculate the geometric constraint equation of the raceway curvature center; based on velocity analysis and coordinate transformation considerations, calculate the centrifugal force and gyroscopic torque of the ball based on Newton's second law and the acceleration formula of circular motion. S5. Based on the centrifugal force and gyroscopic torque of the ball obtained in step S4, and the frictional 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 considering non-uniform loading and centrifugal effect. S6. Combine the geometric constraint equations of the raceway curvature center 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 the Newton-Raphson iteration method to solve for the ball screw contact characteristics considering non-uniform loading and centrifugal effect.

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

3. The method for calculating the contact characteristics of a ball screw according to claim 1, characterized in that, Step S3 is as follows: Calculate the axial distance between the center of curvature of the lead screw raceway and the center of curvature of the nut raceway. and the center of curvature of the lead screw raceway and the nut raceway The contact angle determined by comprehensively considering non-uniform loading and centrifugal effects is as follows: in, The contact angle between the ball and the lead screw. The contact angle between the ball and the nut. The diameter of the ball bearing is... This refers to the normal contact deformation between the ball and the lead screw. This refers to the normal contact deformation between the ball and the nut. The distance between the center of curvature of the nut raceway and the center of the ball is axial. The radial distance between the center of curvature of the nut raceway and the center of the ball. The radius of curvature of the lead screw raceway is... Let be the radius of curvature of the nut raceway.

4. The method for calculating the contact characteristics of a ball screw according to claim 1, characterized in that, Step S4 is as follows: The geometric constraint equations for the raceway curvature center are determined based on the Pythagorean theorem; then the mass moment of inertia of the balls is calculated. The gyro angle between the ball and the raceway And the sliding speed between the contact points of the balls and the lead screw raceways. ; Determine the relationship between the ball spin velocity, the ball rotational speed around the screw axis, and the screw rotational speed; calculate the centrifugal force of the ball based on Newton's second law and the acceleration formula for circular motion. Finally, the gyroscopic torque of the ball bearing is obtained. .

5. The method for calculating the contact characteristics of a ball screw according to claim 4, characterized in that, The relationship between the ball spin speed, the ball rotation speed around the screw axis, and the screw speed is as follows: in, The contact angle between the ball and the lead screw. The contact angle between the ball and the nut. Let be the angular velocity of the ball about the screw axis. The rotational speed of the ball screw, The diameter of the ball bearing is... The pitch circle diameter of the leadscrew.

6. The method for calculating the contact characteristics of a ball screw according to claim 1, characterized in that, Step S5 is as follows: Calculate the friction between the ball and the screw raceway according to step S4. Friction between the ball and the nut raceway Then, the axial load balance equation and the radial force balance equation of the ball screw are calculated; finally, the axial load balance equation of the ball screw that takes into account non-uniform loading and centrifugal effect is calculated.

7. The method for calculating the contact characteristics of a ball screw according to claim 6, characterized in that, The axial load balance equation for the ball screw, taking into account both non-uniform loading and centrifugal effects, is as follows: in, The equation for axial load balance on the screw side of the ball screw is as follows: The equation for axial load balance of the ball screw on the nut side is as follows: The contact angle between the ball and the lead screw. The contact angle between the ball and the nut. This refers to the contact load between the ball and the lead screw. The helix angle, and This is the raceway control coefficient. The friction between the ball and the lead screw. The number of balls in the ball screw. This refers to the contact load between the ball and the nut. The contact angle between the ball and the nut. This refers to the frictional force between the balls and the raceway of the nut.

8. A ball screw contact characteristic calculation system, characterized in that, include: The input module takes the geometric parameters and axial load of the ball screw as input. Based on Hertzian contact theory, the deformation compatibility relationship between adjacent balls, Hooke's law, contact angle analysis, and axial internal force analysis, the force compatibility equations for the ball contact load and axial load are determined, specifically: Calculated according to Hertzian contact theory Normal contact deformation of each ball and the Normal contact deformation of each ball ; Based on the deformation coordination relationship of adjacent balls; calculate Hooke's Law to calculate the first... Axial contact deformation of each ball When subjected to non-uniform loading, the contact angle between the balls and the raceways is calculated based on the geometric deformation relationship. ; Determine the first Axial internal forces of adjacent ball bearing units Based on the above steps, the force compatibility equation between the ball contact load and the axial load is obtained. The force compatibility equation between ball contact load and axial load is as follows: in, The helix angle of the ball screw. For the first Contact load of each ball For the first The contact angle of each ball. and For force compatibility coefficient, For the axial load of the ball screw, For the first Contact load of each ball For the first The contact angle of each ball. The contact angle between the ball and the raceway; The calculation module solves for the displacement of the raceway curvature center when the axial load is applied, based on the 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 takes the rotational speed of the ball screw as input 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 based on the obtained raceway curvature center displacement, thereby determining the contact angles between the ball and the screw, and between the ball and the nut. The torque module calculates the geometric constraint equation of the raceway curvature center based on the obtained contact angles between the ball and the screw, and between the ball and the nut; based on velocity analysis and coordinate transformation considerations, it calculates the centrifugal force and gyroscopic torque of the ball 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, taking into account non-uniform loading and centrifugal effects, based on the obtained centrifugal force and gyroscopic torque of the ball and the friction between the ball and the raceway. The output module combines the obtained raceway curvature center geometric constraint equations, ball axial load balance equations, radial force balance equations, and ball screw axial load balance equations. The Newton-Raphson iteration method is then used to solve for the ball screw contact characteristics considering non-uniform loading and centrifugal effects.

9. A computer-readable storage medium for storing one or more programs, characterized in that, The one or more programs include instructions that, when executed by a computing device, cause the computing device to perform the method of any one of claims 1 to 7.

10. A computing device, characterized in that, include: One or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the one or more programs including steps for performing the method of any one of claims 1 to 7.

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