Intelligent matching method for ball screw pair

Abstract

The application discloses a kind of intelligent matching methods for ball screw pair.The axial stiffness model of ball screw pair is constructed according to the nominal structure parameters and part error parameters of the ball screw pair to be analyzed;Using high-speed ball screw pair friction torque test bench and pre-tightening force adjustable device, the no-load friction torque under different pre-tightening force, speed and lubrication state is collected, the law of dynamic friction coefficient changing with working condition is obtained, and it is introduced into the relationship between no-load friction torque and pre-tightening force, to construct pre-tightening force model.On this basis, combined with part error statistical distribution, candidate grouping matching scheme is generated by Monte Carlo simulation, to maximize assembly qualification rate, minimize matching precision quality loss and minimize axial stiffness-pre-tightening force performance quality loss as target for multi-objective optimization, to obtain target ball diameter, part grouping boundary and inter-group matching rule, so as to improve part utilization, assembly quality, matching efficiency and ball screw pair performance consistency.

Description

Technical Field

[0001] This invention relates to the fields of precision transmission component assembly, selective assembly, and intelligent manufacturing technology, and more specifically to an intelligent selection method for ball screw pairs. Background Technology

[0002] Ball screw assemblies are widely used in CNC machine tools, industrial robots, and precision equipment. Their assembly condition directly affects axial clearance, preload, axial stiffness, frictional torque, and load-bearing capacity. Due to machining errors in the pitch diameter, lead, and raceway radius of the screw and nut, as well as manufacturing and grouping errors in the ball diameter, different combinations of parts often exhibit different contact states and performance. Furthermore, in engineering practice, preload is typically calculated based on the no-load frictional torque. However, the coefficient of friction varies with preload, rotational speed, and lubrication conditions; using fixed empirical values ​​can easily lead to errors in preload prediction.

[0003] Current manufacturing methods primarily rely on improving the machining accuracy of individual parts and narrowing tolerance zones to ensure assembly quality, resulting in high manufacturing costs and difficulty in eliminating the effects of multiple cumulative errors. Traditional assembly selection methods often involve grouping and matching based on dimensional tolerances, focusing mainly on geometric fits and rarely considering preload, axial stiffness, and friction performance simultaneously. Considering that variations in ball diameter affect the initial clearance, initial interference, and contact angle between the ball and the lead screw raceway and nut raceway, the ball diameter is used as the main control parameter in intelligent matching to improve assembly performance deviations caused by manufacturing errors in the lead screw and nut. Furthermore, batch assembly must also consider assembly pass rate, parts utilization rate, and performance consistency, and different application scenarios have different requirements for fit accuracy, axial stiffness, preload, and load-bearing capacity.

[0004] Therefore, it is necessary to provide an intelligent selection method for ball screw pairs based on measured part errors, performance prediction, and multi-objective optimization. Summary of the Invention

[0005] In view of this, the present invention provides an intelligent selection method for ball screw pairs to solve the problems of existing selection methods that mainly rely on dimensional tolerances and manual experience, making it difficult to simultaneously consider fit accuracy, axial stiffness and preload, as well as the low assembly qualification rate and parts utilization rate during batch selection.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A method for intelligent selection and matching of ball screw pairs includes: S1. Obtain the nominal structural parameters and component error parameters of the ball screw pair to be analyzed, and establish the axial stiffness model of the ball screw pair. S2. Based on the high-speed ball screw pair friction torque test bench and the adjustable preload device, obtain friction torque and preload data under different preload, speed and lubrication conditions, and establish a dynamic friction coefficient model and a ball screw pair preload model. S3. Collect the measured parameters of the lead screw, nut and ball to be selected. Use the stiffness output by S1 and the upper and lower limits of the preload output by S2 as hard constraint indicators to determine the intelligent selection target and constraint conditions, and determine the statistical distribution of the error parameters of each part to obtain the set of candidate ball diameters and the statistical distribution of part errors. S4. Generate candidate grouping matching schemes based on the candidate ball diameter set, part error statistical distribution and part grouping rules, and calculate the fitting accuracy, axial stiffness, preload and assembly qualification rate corresponding to each candidate grouping matching scheme; S5. Establish optimization objectives, build and solve the intelligent selection multi-objective optimization model of ball screw pairs, and obtain the target selection scheme; S6. Output the target ball diameter or ball diameter range corresponding to the target matching scheme, the lead screw group boundary, the nut group boundary, the ball group boundary, the inter-group matching rules and the predicted assembly performance.

[0007] Preferably, the nominal structural parameters in S1 include the nominal diameter of the ball, the mean diameter of the lead screw, the mean diameter of the nut, the lead, the raceway radius, the initial contact angle, the helix angle, the effective number of bearing balls, the elastic modulus of the material, and Poisson's ratio; the component error parameters include the ball diameter error, the mean diameter error of the lead screw, the lead screw lead error, the raceway radius error of the lead screw, the mean diameter error of the nut, the lead error of the nut, and the raceway radius error of the nut. Based on the degree of influence of each error parameter on the contact state between the ball and the lead screw raceway and the nut raceway, the pitch diameter error, lead error and raceway radius error of the lead screw and nut are converted into the corresponding equivalent ball diameter error. The initial contact position, initial contact angle, and initial clearance or initial interference between the ball and the screw raceway and nut raceway are determined based on the equivalent ball diameter error. The contact load-contact deformation relationship of a single ball is established based on Hertzian contact theory. A multi-ball load distribution model is established based on the force balance relationship and displacement coordination relationship among multiple bearing balls. The normal contact load of each bearing ball and the axial deformation of the ball screw pair are solved under different axial loads to obtain the axial load-axial deformation relationship and establish an axial stiffness model.

[0008] Preferably, the multi-ball load distribution model considers the lead error, raceway radius error, contact angle variation, and load distribution unevenness of each bearing ball. The axial stiffness of the ball screw pair is determined according to the axial load-axial deformation curve, and the axial stiffness is the first derivative of the axial load with respect to the axial displacement.

[0009] Preferably, in step S2, multiple known preload forces are preset, and the no-load friction torque is collected under different speeds and lubrication conditions. The dynamic friction coefficient is obtained based on the known preload forces, no-load friction torque, and ball screw pair structural parameters. The dynamic friction coefficient is fitted with the law of change of working conditions, and a ball screw pair preload force model is established.

[0010] Preferably, the S2 high-speed ball screw pair friction torque test bench includes a bed, a test screw drive device, a friction torque measuring device, a limiting device, a drag chain device, and a worktable drive device. The adjustable preload device includes a main nut, a secondary nut, a sleeve, a force sensor, a flat key, a washer, two disc springs, and two round nuts. The secondary nut has an external thread at its tail. By adjusting the round nuts to compress the disc springs, a preload is generated between the main nut and the secondary nut.

[0011] Preferably, step S4 generates a candidate ball diameter set based on the ball manufacturing specifications, stocked ball diameters, and intelligent selection targets, and sets the lead screw group boundary, nut group boundary, and ball group boundary according to the part error magnitude. Using group boundaries and inter-group matching relationships as decision variables, Monte Carlo sampling is performed based on the statistical distribution of part errors to generate virtual assembly combinations. The assembly qualification rate and assembly performance distribution of each candidate scheme are determined using the axial stiffness model and the preload model.

[0012] Preferably, step S5 uses candidate ball diameter, lead screw group boundary, nut group boundary, ball group boundary and inter-group matching relationship as decision variables, and establishes a multi-objective optimization model with the optimization objectives of maximizing assembly qualification rate, minimizing fit accuracy quality loss and minimizing axial stiffness-preload performance quality loss; the quality loss is determined by the deviation between assembly performance parameters and corresponding target values.

[0013] Preferably, the multi-objective optimization model is solved using the scenario-adaptive NSGA-III algorithm. The distribution of reference points and the priority of constraints are adjusted according to the application scenario to obtain the Pareto optimal solution set. The target configuration scheme is determined by combining the assembly qualification rate, quality loss, parts utilization rate and ball bearing inventory.

[0014] As can be seen from the above technical solution, compared with the prior art, the present invention provides an intelligent selection method for ball screw pairs, which has the following beneficial effects: 1) This invention converts the pitch diameter error, lead error, and raceway radius error of the lead screw and nut into equivalent ball diameter error, so that the machining errors of different types of parts can be processed in a unified ball-raceway contact model.

[0015] 2) This invention establishes a multi-ball load distribution model that considers lead error, raceway radius error, contact angle variation and uneven load distribution, thereby improving the rationality of the prediction of axial stiffness of the ball screw pair.

[0016] 3) This invention utilizes an adjustable preload device and a high-speed ball screw pair friction torque test bench to obtain test data under different working conditions, establishes a dynamic friction coefficient model that varies with working conditions, and reduces the preload prediction error caused by using a fixed empirical friction coefficient.

[0017] 4) This invention combines the statistical distribution of part errors with Monte Carlo simulation to predict the assembly pass rate and assembly performance distribution of different candidate grouping matching schemes before actual assembly.

[0018] 5) This invention simultaneously uses assembly qualification rate, fit accuracy quality loss and axial stiffness-preload performance quality loss as optimization targets, which can take into account the fit accuracy of parts, assembly performance, part utilization rate and batch product performance consistency.

[0019] 6) This invention can adjust the evaluation priority and optimize the search direction according to different application scenarios, thereby improving the pertinence of the intelligent selection scheme for ball screw pairs. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0021] Figure 1 The overall flowchart of the intelligent selection method for ball screw pairs provided by the present invention.

[0022] Figure 2 This is a schematic diagram illustrating the construction process of the axial stiffness model of the ball screw pair provided by the present invention.

[0023] Figure 3 A schematic diagram of the high-speed ball screw pair friction torque test bench provided by the present invention.

[0024] Figure 4 This is a schematic diagram of the preload adjustable device provided by the present invention.

[0025] Figure 5 A schematic diagram of the intelligent selection process for ball screw pairs provided by the present invention. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] like Figure 1 As shown in the figure, an embodiment of the present invention discloses an intelligent selection method for ball screw pairs, including: S1. Obtain the nominal structural parameters and component error parameters of the ball screw pair to be analyzed, and establish the axial stiffness model of the ball screw pair. S2. Based on the high-speed ball screw pair friction torque test bench and the adjustable preload device, obtain friction torque and preload data under different preload, speed and lubrication conditions, and establish a dynamic friction coefficient model and a ball screw pair preload model. S3. Collect the measured parameters of the lead screw, nut and ball to be selected. Use the stiffness output by S1 and the upper and lower limits of the preload output by S2 as hard constraint indicators to determine the intelligent selection target and constraint conditions, and determine the statistical distribution of the error parameters of each part to obtain the set of candidate ball diameters and the statistical distribution of part errors. S4. Generate candidate grouping matching schemes based on the candidate ball diameter set, part error statistical distribution and part grouping rules, and calculate the fitting accuracy, axial stiffness, preload and assembly qualification rate corresponding to each candidate grouping matching scheme; S5. Establish optimization objectives, build and solve the intelligent selection multi-objective optimization model of ball screw pairs, and obtain the target selection scheme; S6. Output the target ball diameter or ball diameter range corresponding to the target matching scheme, the lead screw group boundary, the nut group boundary, the ball group boundary, the inter-group matching rules and the predicted assembly performance.

[0028] In a specific embodiment of the present invention, the underlying mechanical equilibrium axiom for axial stiffness modeling is first given, and then the error parameters of S1 are substituted, deformation coordination equations are solved, and the stiffness expression is derived. It is clearly shown that all operations of S1 serve to solve the equilibrium equation and establish the mapping relationship between error and axial stiffness.

[0029] Specifically, the nominal structural parameters in S1 include the nominal diameter of the ball, the mean diameter of the lead screw, the mean diameter of the nut, the lead, the raceway radius, the initial contact angle, the helix angle, the effective number of bearing balls, the material's elastic modulus, and Poisson's ratio; the component error parameters include the ball diameter error, the lead screw mean diameter error, the lead screw lead error, the lead screw raceway radius error, the nut mean diameter error, the nut lead error, and the nut raceway radius error. Based on the degree of influence of each error parameter on the contact state between the ball and the lead screw raceway and the nut raceway, the pitch diameter error, lead error and raceway radius error of the lead screw and nut are converted into the corresponding equivalent ball diameter error. The initial contact position, initial contact angle, and initial clearance or initial interference between the ball and the screw raceway and nut raceway are determined based on the equivalent ball diameter error. The contact load-contact deformation relationship of a single ball is established based on Hertzian contact theory. A multi-ball load distribution model is established based on the force balance relationship and displacement coordination relationship among multiple bearing balls. The normal contact load of each bearing ball and the axial deformation of the ball screw pair are solved under different axial loads to obtain the axial load-axial deformation relationship and establish an axial stiffness model.

[0030] In a specific embodiment of the present invention, such as Figure 2 As shown, the geometric errors of the lead screw and nut are converted into equivalent ball diameter errors according to their influence on the ball-raceway contact state. The equivalent ball diameter error can be expressed as:

[0031] in, For the equivalent ball diameter error, To account for ball diameter error, and These are the lead screw pitch diameter error and the nut pitch diameter error, respectively. and These are the lead screw lead error and the nut lead error, respectively. and These are the lead screw raceway radius error and the nut raceway radius error, respectively. , , , , and This represents the corresponding error equivalent coefficient.

[0032] Based on the equivalent ball diameter error, determine the first... The initial clearance between the balls and the screw raceway and nut raceway is calculated, and the corresponding contact angle is determined. Based on Hertzian contact theory, the normal contact load in a single ball contact area can be expressed as:

[0033] in, For the first Normal contact load of the ball bearings For the first The normal contact deformation of each ball. For the first The Hertzian contact stiffness coefficient corresponding to each ball.

[0034] The multiple load-bearing balls satisfy the axial force balance relationship:

[0035] in, The axial load borne by the ball screw assembly. To effectively support the number of balls, This represents the contact angle between the j-th ball and the raceways of the lead screw and nut. This indicates the helix angle of the lead screw / nut raceway.

[0036] At the same time, displacement coordination equations for each bearing ball are established based on the geometric relationship between the lead screw, nut, and ball bearings.

[0037]

[0038] Among them, the axial deformation of the lead screw and nut is and , For the first Axial deformation of each ball; The Hertzian contact equation, the axial force balance equation, and the displacement compatibility equation are combined to form a set of nonlinear equations for multiple balls. The Newton-Raphson iteration method is then used to solve for the normal contact load, normal contact deformation, and contact angle of each ball.

[0039] Gradually change axial load Calculate the corresponding axial deformation. This allows us to obtain the axial load-axial deformation curve. The axial stiffness of the ball screw pair at the specified operating point is:

[0040] in, For axial stiffness, This represents the difference in axial load. This represents the difference in axial deformation.

[0041] This establishes a mapping relationship between the ball diameter error, the geometric errors of the lead screw and nut, and the axial stiffness of the ball screw pair.

[0042] Specifically, the multi-ball load distribution model considers the lead error, raceway radius error, contact angle variation, and load distribution unevenness of each bearing ball. The axial stiffness of the ball screw pair is determined based on the axial load-axial deformation curve, and the axial stiffness is the first derivative of the axial load with respect to the axial displacement.

[0043] Specifically, in S2, multiple known preloads are preset, and the no-load friction torque is collected under different speeds and lubrication conditions. The dynamic friction coefficient is obtained based on the known preloads, no-load friction torques, and ball screw pair structural parameters. The dynamic friction coefficient is fitted with the law of change of the working condition, and a ball screw pair preload model is established.

[0044] Specifically, the S2 high-speed ball screw pair friction torque test bench includes a bed, a test screw drive device, a friction torque measuring device, a limit device, a drag chain device, a worktable drive device, and a data acquisition and processing unit. The adjustable preload device includes a main nut, a secondary nut, a sleeve, a force sensor, a flat key, a washer, two disc springs, and two round nuts. The secondary nut has an external thread at its tail. By adjusting the round nuts to compress the disc springs, a preload is generated between the main nut and the secondary nut.

[0045] In a specific embodiment of the present invention, such as Figure 3 As shown, the ball screw under test is mounted on the machine bed via a fixed-end support component and a support-end support component. The drive device for the ball screw under test drives it to rotate at a set speed. The friction torque measuring device is connected to the nut assembly and is used to limit the rotation of the nut assembly and measure the reaction torque acting on the nut assembly. The table drive device moves the friction torque measuring device along the axial direction of the ball screw, keeping it synchronized with the nut assembly.

[0046] like Figure 4 As shown, the adjustable preload device includes a main nut, a secondary nut, a sleeve, a force sensor, a washer, a first disc spring, a second disc spring, a first round nut, and a second round nut. The secondary nut has an external thread at its tail, and the first and second round nuts are connected to this external thread.

[0047] By rotating the round nut, the round nut is axially displaced along the tail of the auxiliary nut. The axial force is transmitted to the main nut flange through the first disc spring, the second disc spring, the washer, the force sensor, and the sleeve, so that the main nut and the auxiliary nut form a preload along the direction of separation.

[0048] The first and second disc springs are mainly used to buffer the impact during the adjustment of the round nut, compensate for the small axial displacement of the device, and reduce the preload fluctuation caused by vibration and temperature rise during the test. The force sensor is used to measure the actual preload between the main nut and the auxiliary nut in real time.

[0049] During the experiment, multiple preload levels were set sequentially, and at each preload level, multiple rotational speeds and different lubrication conditions were set. The no-load friction torque was collected within the stable operating range under each set of test conditions. This forms the experimental dataset.

[0050] The general relationship between no-load frictional torque, preload, and dynamic friction coefficient can be expressed as follows:

[0051] in, For the preload of the ball screw assembly, The contact angle between the ball and the nut raceway. The coefficient of dynamic friction is the ratio of the balls to the raceway in contact area. The radius of the leadscrew shaft, The radius of the ball bearing is given.

[0052] By substituting the dynamic friction coefficient model into the relationship between no-load friction torque and preload, an improved preload model is obtained. During intelligent assembly, this preload model predicts the preload of the corresponding assembly combination.

[0053] In another specific embodiment of the present invention, the application scenario is determined based on the equipment and working conditions of the ball screw pair. The application scenarios include precision grinding machines, small and medium-sized high-speed machining centers, and large or heavy-duty machining centers. For precision grinding machines, priority is given to fit accuracy, axial stiffness, and preload stability; for small and medium-sized high-speed machining centers, priority is given to high-speed friction torque, operating temperature rise, and dynamic stiffness; for large or heavy-duty machining centers, priority is given to axial stiffness under working load, load-bearing capacity, and contact stress.

[0054] Set target accuracy according to application scenario Target axial stiffness Target preload It also determines the allowable deviations and the constraints such as assembly clearance, preload, friction torque, and contact load.

[0055] The selected lead screws, nuts, and ball bearings are inspected, and the part numbers are stored in relation to the measured error data. The statistical distribution of each error parameter is determined based on the batch measured data. Taking a normal distribution as an example, for any error parameter... It can be represented as:

[0056] In the formula, The mean of the error parameter is... Let be the standard deviation of the error parameter. When the error is constrained by the upper and lower limits of the tolerance, a truncated normal distribution is used; when the measured data does not conform to the typical parameter distribution, an empirical distribution or kernel density estimation method is used to determine the statistical distribution of the error.

[0057] Specifically, step S4 generates a candidate ball diameter set based on the ball manufacturing specifications, stocked ball diameters, and intelligent selection targets, and sets the lead screw group boundary, nut group boundary, and ball group boundary according to the part error magnitude. Using group boundaries and inter-group matching relationships as decision variables, Monte Carlo sampling is performed based on the statistical distribution of part errors to generate virtual assembly combinations. The assembly qualification rate and assembly performance distribution of each candidate scheme are determined using the axial stiffness model and the preload model.

[0058] In a specific embodiment of the present invention, a set of candidate ball diameters is generated based on the ball manufacturing specifications, the stock ball diameters, and the target preload, and the lead screw group boundary, nut group boundary, and ball group boundary are set according to the size of the part error.

[0059] The matching relationship between the lead screw assembly, nut assembly, and ball bearing assembly is represented as a ternary decision variable: , indicating the first lead screw Group, Nut Group and ball bearing Groups are allowed to match; , indicating the first lead screw Group, Nut Group and ball bearing Groups are not allowed to match.

[0060] Monte Carlo random sampling is performed based on the part error statistical distribution obtained in step S3 to generate virtual lead screws, virtual nuts and virtual balls, and virtual ball screw pairs are formed according to the candidate grouping boundaries and inter-group matching relationships.

[0061] For each virtual assembly, calculate its initial clearance, and then use the axial stiffness model established in step S1 to calculate the axial stiffness. And call the preload model established in step S2 to calculate the preload. When the fitting accuracy, axial stiffness, preload, and other constraints of the virtual assembly meet the requirements, it is judged as a qualified assembly sample.

[0062] Repeat After the virtual assembly, the assembly qualification rate of the candidate group matching scheme is:

[0063] In the formula, To improve the assembly pass rate, The number of qualified virtual assembly samples. This represents the total number of virtual assembly samples. Simultaneously, the mean, standard deviation, and distribution range of the fitting accuracy, axial stiffness, and preload for each candidate scheme are statistically analyzed.

[0064] Specifically, S5 uses candidate ball diameter, lead screw group boundary, nut group boundary, ball group boundary and inter-group matching relationship as decision variables, and establishes a multi-objective optimization model with the optimization objectives of maximizing assembly qualification rate, minimizing fit accuracy quality loss and minimizing axial stiffness-preload performance quality loss; the quality loss is determined by the deviation between assembly performance parameters and corresponding target values.

[0065] Specifically, the multi-objective optimization model is solved using the scenario-adaptive NSGA-III algorithm. The distribution of reference points and the priority of constraints are adjusted according to the application scenario to obtain the Pareto optimal solution set. The target selection scheme is determined by combining the assembly qualification rate, quality loss, parts utilization rate and ball bearing inventory.

[0066] In a specific embodiment of the present invention, such as Figure 5 As shown, using candidate ball diameter, screw group boundary, nut group boundary, ball group boundary, and inter-group matching relationship as decision variables, and with the optimization objectives of maximizing assembly pass rate, minimizing fit accuracy quality loss, and minimizing axial stiffness-preload performance quality loss, a multi-objective optimization model is established:

[0067] in:

[0068] In the formula, Let the objective function be the assembly pass rate. To compensate for the loss of precision and quality, The axial stiffness-preload performance mass loss; , and The first The fitting accuracy, axial stiffness, and preload of a virtual assembly sample; , and These are the corresponding target values; , and This is the mass loss coefficient; and The evaluation weights for axial stiffness and preload are set according to the application scenario.

[0069] The multi-objective optimization model should also meet constraints such as ordered group boundaries, no intersection between adjacent groups, the number of parts in each group meets the assembly requirements, the diameter of candidate balls is within the inventory or manufacturable range, and the fit accuracy, axial stiffness, preload, friction torque and contact stress are within the allowable range.

[0070] The scenario-adaptive NSGA-III algorithm is used to solve the multi-objective optimization model. For the three optimization objectives, the NSGA-III algorithm generates reference points on the unit simplex. The algorithm iteratively solves the problem through population initialization, crossover, mutation, non-dominated sorting, objective normalization, and reference point association, adjusting the reference point distribution and constraint processing priority according to different application scenarios. The computation stops when a preset number of iterations is reached or the Pareto solution set changes less than a set threshold for several consecutive generations, thus obtaining the Pareto optimal solution set.

[0071] Based on the assembly qualification rate, fit accuracy quality loss, axial stiffness-preload performance quality loss, parts utilization rate, and ball bearing inventory, the Pareto optimal solution set is evaluated a second time to determine the target matching scheme.

[0072] Furthermore, the target matching scheme obtained in step S5 is output in the form of a data table. The output data table includes the scheme number, lead screw group number and range, nut group number and range, ball group number and range, target ball diameter, inter-group matching relationship, predicted assembly qualification rate, predicted fit accuracy, predicted axial stiffness, and predicted preload.

[0073] During actual assembly, the lead screw, nut, and ball bearings are assigned to the corresponding groups according to the part number and the measured error, and then selected for assembly according to the inter-group matching rules in the output data table.

[0074] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0075] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for intelligent selection and matching of ball screw pairs, characterized in that, include: S1. Obtain the nominal structural parameters and component error parameters of the ball screw pair to be analyzed, and establish the axial stiffness model of the ball screw pair. S2. Based on the high-speed ball screw pair friction torque test bench and the adjustable preload device, obtain friction torque and preload data under different preload, speed and lubrication conditions, and establish a dynamic friction coefficient model and a ball screw pair preload model. S3. Collect the measured parameters of the lead screw, nut and ball to be selected. Use the stiffness output by S1 and the upper and lower limits of the preload output by S2 as hard constraint indicators to determine the intelligent selection target and constraint conditions, and determine the statistical distribution of the error parameters of each part to obtain the set of candidate ball diameters and the statistical distribution of part errors. S4. Generate candidate grouping matching schemes based on the candidate ball diameter set, part error statistical distribution and part grouping rules, and calculate the fitting accuracy, axial stiffness, preload and assembly qualification rate corresponding to each candidate grouping matching scheme; S5. Establish optimization objectives, build and solve the intelligent selection multi-objective optimization model of ball screw pairs, and obtain the target selection scheme; S6. Output the target ball diameter or ball diameter range corresponding to the target matching scheme, the lead screw group boundary, the nut group boundary, the ball group boundary, the inter-group matching rules and the predicted assembly performance.

2. The intelligent selection method for ball screw pairs according to claim 1, characterized in that, The nominal structural parameters in S1 include the nominal diameter of the ball, the mean diameter of the lead screw, the mean diameter of the nut, the lead, the raceway radius, the initial contact angle, the helix angle, the effective number of bearing balls, the elastic modulus of the material, and Poisson's ratio; the component error parameters include the ball diameter error, the mean diameter error of the lead screw, the lead screw lead error, the raceway radius error of the lead screw, the mean diameter error of the nut, the lead error of the nut, and the raceway radius error of the nut. Based on the degree of influence of each error parameter on the contact state between the ball and the lead screw raceway and the nut raceway, the pitch diameter error, lead error and raceway radius error of the lead screw and nut are converted into the corresponding equivalent ball diameter error. The initial contact position, initial contact angle, and initial clearance or initial interference between the ball and the screw raceway and nut raceway are determined based on the equivalent ball diameter error. The contact load-contact deformation relationship of a single ball is established based on Hertzian contact theory. A multi-ball load distribution model is established based on the force balance relationship and displacement coordination relationship among multiple bearing balls. The normal contact load of each bearing ball and the axial deformation of the ball screw pair are solved under different axial loads to obtain the axial load-axial deformation relationship and establish an axial stiffness model.

3. The intelligent selection method for ball screw pairs according to claim 2, characterized in that, The multi-ball load distribution model considers the lead error, raceway radius error, contact angle variation, and load distribution unevenness of each bearing ball. The axial stiffness of the ball screw pair is determined based on the axial load-axial deformation curve, and the axial stiffness is the first derivative of the axial load with respect to the axial displacement.

4. The intelligent selection method for ball screw pairs according to claim 1, characterized in that, In S2, multiple known preloads are preset, and the no-load friction torque is collected under different speeds and lubrication conditions. The dynamic friction coefficient is obtained based on the known preloads, no-load friction torques, and ball screw pair structural parameters. The dynamic friction coefficient is fitted with the law of change of the working condition, and a ball screw pair preload model is established.

5. The intelligent selection method for ball screw pairs according to claim 1, characterized in that, The S2 medium-high speed ball screw pair friction torque test bench includes a bed, a test screw drive device, a friction torque measuring device, a limit device, a drag chain device, and a worktable drive device. The ball screw under test is mounted on the bed via a fixed end support component and a support end support component. The ball screw drive device drives the ball screw to rotate at a set speed. The friction torque measuring device is connected to the nut assembly. The worktable drive device drives the friction torque measuring device to move along the axial direction of the ball screw, so that it moves synchronously with the nut assembly. The adjustable preload device includes a main nut, a secondary nut, a sleeve, a force sensor, a flat key, a washer, two disc springs, and two round nuts. The secondary nut has an external thread at its tail. By adjusting the round nuts to compress the disc springs, a preload is generated between the main nut and the secondary nut.

6. The intelligent selection method for ball screw pairs according to claim 1, characterized in that, S4 generates a candidate ball diameter set based on the ball manufacturing specifications, stocked ball diameters, and intelligent selection targets, and sets the lead screw group boundary, nut group boundary, and ball group boundary according to the part error magnitude. Using group boundaries and inter-group matching relationships as decision variables, Monte Carlo sampling is performed based on the statistical distribution of part errors to generate virtual assembly combinations. The assembly qualification rate and assembly performance distribution of each candidate scheme are determined using the axial stiffness model and the preload model.

7. The intelligent selection method for ball screw pairs according to claim 1, characterized in that, S5 uses candidate ball diameter, lead screw group boundary, nut group boundary, ball group boundary and inter-group matching relationship as decision variables, and establishes a multi-objective optimization model with the optimization objectives of maximizing assembly qualification rate, minimizing fit accuracy quality loss and minimizing axial stiffness-preload performance quality loss; the quality loss is determined by the deviation between assembly performance parameters and corresponding target values.

8. The intelligent selection method for ball screw pairs according to claim 7, characterized in that, The multi-objective optimization model is solved using the scenario-adaptive NSGA-III algorithm. The distribution of reference points and the priority of constraints are adjusted according to the application scenario to obtain the Pareto optimal solution set. The target configuration scheme is determined by combining the assembly qualification rate, quality loss, parts utilization rate and ball bearing inventory.

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