A planetary roller screw tolerance optimization method

Abstract

The present invention provides a method for optimizing the tolerances of a planetary roller screw, including extracting the variation amounts of design parameters based on Latin hypercube random sampling, randomly combining the extracted variation amounts of each design parameter to obtain a design parameter variation combination, establishing mathematical models for calculating the transmission accuracy, axial clearance, and fatigue life of the planetary roller screw considering the design parameter variation combination, evaluating the service risk probability of the planetary roller screw based on the service requirements of transmission accuracy, axial clearance, and fatigue life, according to the number of design parameter variation combinations and the number of combinations meeting the service requirements, taking the lowest service risk probability of the planetary roller screw and the largest width of the part tolerance interval as the objectives, and the minimum tolerance interval width limited by the part machining accuracy grade as the constraint, establishing a multi-objective optimization model for part tolerance parameters, and solving the multi-objective optimization model of tolerance parameters based on the non-dominated sorting genetic algorithm to achieve tolerance optimization driven by the transmission accuracy - axial clearance - fatigue life of the planetary roller screw.

Description

Technical Field

[0001] The present invention relates to the technical field of the design optimization of planetary roller screws, and in particular to a method for optimizing the tolerances of planetary roller screws. Background Art

[0002] A planetary roller screw is a new type of precision heavy-duty linear transmission mechanism, mainly composed of a screw, multiple rollers, and a nut, which realizes the efficient conversion of rotational motion and linear motion, and has broad application prospects in high-end equipment fields such as aerospace, weaponry, and intelligent manufacturing. Due to its transmission characteristics of "multiple points", "multiple pairs", and "multiple bodies", the service performance of planetary roller screws is highly sensitive to changes in design parameters, and the extremely high machining difficulty of the screw, rollers, and nut threads of the core parts endows significant significance to the tolerance parameter allocation of planetary roller screws.

[0003] Currently, the tolerance parameter design method based on the machining tolerance intervals of the optical axis and trapezoidal threads and engineering experience is the main design method for the tolerance parameters of planetary roller screws. This method fails to consider the transmission accuracy, axial clearance, and fatigue life service requirements of planetary roller screws in a coordinated manner while taking into account the machinability of parts, and cannot further reduce the service risk probability and improve the machinability of parts on the premise of meeting service performance requirements and machining capabilities. Therefore, it is very necessary to design a method for optimizing the tolerances of planetary roller screws. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for optimizing the tolerances of planetary roller screws, which can further reduce the service risk probability and improve the machinability of parts on the premise of meeting service performance requirements and machining capabilities, and is convenient for use.

[0005] To achieve the above purpose, the present invention provides the following solutions:

[0006] A method for optimizing the tolerances of planetary roller screws includes the following steps:

[0007] Step 1: Extract the design parameter variation within the initial tolerance interval based on the Latin hypercube random sampling method;

[0008] Step 2: Randomly combine the extracted design parameter variations of each item of the planetary roller screw to obtain a certain number of design parameter variation combinations;

[0009] Step 3: Establish a mathematical model for calculating the transmission accuracy, axial clearance, and fatigue life of the planetary roller screw considering the design parameter variation combinations;

[0010] Step 4: Based on the service requirements of transmission accuracy, axial clearance, and fatigue life, evaluate the service risk probability of the planetary roller screw according to the number of design parameter variation combinations and the number of combinations that meet the service requirements;

[0011] Step 5: Taking the lowest service risk probability of the planetary roller screw and the largest width of the part tolerance interval as the objectives, and taking the minimum tolerance interval width limited by the part machining accuracy grade as the constraint, establish a multi-objective optimization model for part tolerance parameters;

[0012] Step 6: Based on the non-dominated sorting genetic algorithm, solve the multi-objective optimization model of tolerance parameters to realize the tolerance optimization driven by the transmission accuracy - axial clearance - fatigue life of the planetary roller screw.

[0013] Optionally, in Step 1, the design parameter variation is extracted within the initial tolerance interval based on the Latin hypercube random sampling method, specifically:

[0014] Based on the initial tolerance interval of the design parameters of the planetary roller screw part, through the Latin hypercube random sampling method, the variation of the design parameters within the initial tolerance interval is sampled and simulated. Among them, the tolerance interval is divided into N S sub-sampling intervals according to the sampling quantity of the design parameter variation, and the design parameter variation sampling sample and the sub-sampling interval satisfy:

[0015]

[0016] In the formula, N LHS is the vector composed of Latin hypercube sub-sampling intervals, x d is the Latin hypercube sub-sampling interval, N S is the sampling quantity of the design parameter variation, and are the upper and lower bounds of the Latin hypercube sub-sampling interval respectively, F d (·) is the cumulative probability distribution function value, and x n is the random sampling individual of the design parameter variation within the Latin hypercube sub-sampling interval.

[0017] Optionally, in Step 2, the various design parameter variations of the randomly selected planetary roller screw are combined to obtain a certain number of design parameter variation combinations, specifically:

[0018] Randomly combine the sampling results of the design parameter variations of the screw, roller, nut eccentricity, pitch, mean diameter, and thread profile half angle of the planetary roller screw to obtain N S design parameter variation combinations, which are:

[0019]

[0020] In the formula, is the design parameter variation combination with the quantity of N S , Δ xX is the eccentricity design parameter variation of the screw, roller, and nut, and Δ pXis the variation of the pitch design parameter of the lead screw, roller, and nut, Δ dX is the variation of the pitch diameter design parameter of the lead screw, roller, and nut, Δ βX is the variation of the thread profile half-angle design parameter of the lead screw, roller, and nut. X represents the lead screw, roller, and nut of the planetary roller screw.

[0021] Optionally, in step 3, a mathematical model for calculating the transmission accuracy, axial clearance, and fatigue life of the planetary roller screw considering the combination of design parameter variations is established, specifically:

[0022] Establish a mathematical model for calculating the transmission accuracy, axial clearance, and fatigue life of the planetary roller screw considering the combination of design parameter variations of the lead screw, roller, and nut. Based on the mathematical model, calculate the stroke deviation, stroke variation, axial clearance, and fatigue life of the planetary roller screw under different combinations of design parameter variations Among them, the transmission accuracy mathematical model includes transmission error calculation, linear equation fitting of transmission error and lead screw rotation angle, and calculation of stroke deviation and stroke variation. Among them, the transmission error calculation is:

[0023]

[0024] In the formula, is the lead screw rotation angle is the transmission error of the planetary roller screw under is the lead screw rotation angle, and are the transmission errors caused by eccentricity and pitch design parameter variations respectively under the lead screw rotation angle and are the transmission errors caused by pitch diameter and thread profile half-angle design parameter variations respectively, p h is the lead of the planetary roller screw, l u is the effective operating range of the nut;

[0025] The linear fitting equation of the transmission error and the lead screw rotation angle is:

[0026]

[0027] In the formula, m e and c e are the undetermined coefficients of the linear fitting equation of the transmission error and the lead screw rotation angle, T E is the column vector composed of the transmission errors of the planetary roller screw at each lead screw rotation angle p is the column vector composed of 1s, and the dimension is the same as that of T E is the column vector composed of lead screw rotation angles, and the dimension is the same as that of T E

[0028] ​​​The travel deviation and travel variation are calculated as follows:

[0029]

[0030] In the formula, e a and v ua are the travel deviation and travel variation of the planetary roller screw respectively, and are the lead angles of the planetary roller screw corresponding to the maximum and minimum transmission errors respectively;

[0031] The mathematical model of the axial clearance is as follows:

[0032]

[0033] In the formula, is the lead angle of the screw The axial clearance of the planetary roller screw below;

[0034] The mathematical model of fatigue life includes the calculation of axial load of thread teeth, contact stress calculation, and fatigue life calculation. Among them, the calculation of axial load of thread teeth on the screw-roller and roller-screw sides is as follows:

[0035]

[0036] In the formula, δ BX 、δ TX and δ CX represent the axial deformation of the screw, roller, and nut shaft segments, the deformation of the thread teeth, and the contact deformation respectively, N t is the number of thread teeth of the roller (i, j = 1, 2,..., N t ), and k is the contact thread pair on the screw-roller and roller-nut sides;

[0037] The calculation of contact stress of thread teeth is as follows:

[0038]

[0039] In the formula, σ H is the Hertz contact stress of the thread teeth, F is the axial load of the thread teeth, and a and b are the lengths of the major and minor axes of the Hertz contact ellipse respectively;

[0040] The fatigue life calculation is as follows:

[0041] N = CS -m (9)

[0042] In the formula, N is the contact fatigue life of the thread teeth, C and m are the undetermined coefficients of the Basquin contact fatigue life calculation formula, and S is the Hertz contact stress of the thread teeth.

[0043] Optionally, in step 4, based on the service requirements of transmission accuracy, axial clearance, and fatigue life, evaluate the service risk probability of the planetary roller screw according to the number of combinations of design parameter variations and the number of combinations that meet the service requirements. Specifically:

[0044] Based on the service requirements of transmission accuracy, axial clearance, and fatigue life of the planetary roller screw, set the stroke deviation threshold e t , the stroke variation threshold v t , the axial clearance threshold A up and A down , and the fatigue life threshold t, and determine whether the combination of design parameter variations makes the planetary roller screw meet the service requirements, that is:

[0045]

[0046] In the formula, n u and n FCu are the combinations of design parameter variations that make the planetary roller screw meet the service requirements of transmission accuracy, axial clearance, and fatigue life, A m and A min are the average and minimum axial clearances of the planetary roller screw, and L f is the fatigue life of the planetary roller screw;

[0047] Based on the number of combinations of design parameter variations and the number of combinations of design parameters that make the planetary roller screw meet the service requirements, evaluate the service risk probability of the planetary roller screw as:

[0048] R sys =1-(∑n FCu ) / N s (u≤N s ) (11)

[0049] In the formula, R sys is the service risk probability of the planetary roller screw.

[0050] Optionally, in step 5, taking the lowest service risk probability of the planetary roller screw and the largest width of the part tolerance interval as the objectives, and taking the minimum tolerance interval width limited by the part machining accuracy grade as the constraint, establish a multi-objective optimization model for part tolerance parameters. Specifically:

[0051] Taking the lowest service risk probability of the planetary roller screw and the largest width of the part tolerance interval as the objectives, select the eccentricity, pitch, mean diameter, and thread profile half-angle tolerance parameters of the screw, roller, and nut as the design variables, and take the minimum tolerance interval width limited by the part machining accuracy grade as the constraint to establish a multi-objective optimization model for tolerance parameters. The objective function is:

[0052]

[0053] where, f 1 and f 2 are the objective functions, n is the design variable, and δ w is the weighted average of the tolerance interval widths, and are the tolerance interval widths of the eccentricity, pitch, mean diameter, and half tooth profile angle of the lead screw, roller, and nut. Among them, s lim = upper&lower;

[0054] The design variables are:

[0055]

[0056] where, and are the lower bounds of the tolerance intervals of the design parameters, and are the upper bounds of the tolerance intervals of the design parameters;

[0057] The design constraints are:

[0058]

[0059] where, ω limxX , ω limpX , ω limdX and ω limβX are the minimum tolerance interval widths of the eccentricity, pitch, mean diameter, and half tooth profile angle of the lead screw, roller, and nut under the machining accuracy grade limit.

[0060] Optionally, in step 6, based on the non-dominated sorting genetic algorithm, the multi-objective optimization model of the tolerance parameters is solved to realize the tolerance optimization driven by the transmission accuracy - axial clearance - fatigue life of the planetary roller screw, specifically including the following steps:

[0061] Step 601: Set the maximum number of iterations and population size of the non-dominated sorting genetic algorithm;

[0062] Step 602: Randomly generate an initial population N 1 ;

[0063] Step 603: Perform non-dominated sorting and crowding degree calculation on the optimization solutions in the population N 1 ;

[0064] Step 604: Set the crossover rate and mutation rate, and perform selection, crossover, and mutation operations to obtain the next generation population N 2 ;

[0065] Step 605: Perform non-dominated sorting and crowding degree calculation on the optimization solutions in the population N 2 ;

[0066] Step 606: Eliminate the inferior solutions in population N 2 so that the number of tolerance parameter solutions is the same as that of population N 1 to obtain a new population N 3 , and determine whether the number of iterations has reached the maximum value. If not, replace population N 3 with population N 1 , and repeat steps 603 - 606. Otherwise, output the tolerance parameter solution with the lowest front surface level in population N 3 as the Pareto optimization solution set z of ;

[0067] Step 607: Evaluate the tolerance parameter solutions in the Pareto optimization solution set z of using the Topsis comprehensive evaluation method to find the optimal tolerance parameters, which are:

[0068]

[0069] In the formula, and are the distances between the objective function values caused by the tolerance parameter solutions in the optimization solution set and the defined maximum and minimum values, and are the defined maximum and minimum values, z of is the objective function value caused by the tolerance parameter solution in the Pareto optimization solution set, S o is the comprehensive score of the tolerance parameter solutions in the solution set, f is the number of optimization objectives, and o is the number of tolerance parameter solutions in the Pareto optimization solution set.

[0070] According to the specific embodiments provided by the present invention, the following technical effects are disclosed: The planetary roller screw tolerance optimization method provided by the present invention uses Latin hypercube sampling to sample and simulate the variation of design parameters within the tolerance range, randomly combines the sampling results of the variation of the design parameters of the screw, roller, nut eccentricity, pitch, mean diameter, and thread profile half angle of the planetary roller screw to obtain a combination of design parameter variations, establishes a mathematical model for calculating the transmission accuracy, axial clearance, and fatigue life of the planetary roller screw considering the combination of design parameter variations of the screw, roller, and nut, calculates the stroke deviation, stroke variation, axial clearance, and fatigue life of the planetary roller screw under different combinations of design parameter variations, evaluates the service risk probability based on the number of combinations of design parameter variations and the number of combinations of design parameter variations that enable the planetary roller screw to meet the service requirements, takes the lowest service risk probability of the planetary roller screw and the largest width of the part tolerance range as the goal, uses the eccentricity, pitch, mean diameter, and thread profile half angle tolerance parameters of the screw, roller, and nut as design variables, and the minimum tolerance range width limited by the part machining accuracy grade as a constraint to establish a multi-objective optimization model for tolerance parameters, and solves the optimization model based on the non-dominated sorting genetic algorithm and Topsis comprehensive evaluation. On the premise of meeting the service performance requirements and machining capabilities, it further reduces the service risk probability while improving the machinability of parts, which has important research and engineering application significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0072] Figure 1 Schematic diagram of the process of the planetary roller screw tolerance optimization method in the embodiment of the present invention;

[0073] Figure 2 Schematic diagram of Latin hypercube sampling;

[0074] Figure 3 Schematic diagram of the calculation of the mathematical model of the transmission accuracy, axial clearance, and fatigue life of the planetary roller screw;

[0075] Figure 4 Schematic diagram of the service risk assessment of the planetary roller screw;

[0076] Figure 5 Schematic diagram of the solution process of the multi-objective optimization model for the tolerance parameters of the planetary roller screw;

[0077] Figure 6 Schematic diagram of the Pareto optimization solution set of the tolerance parameters of the planetary roller screw;

[0078] Figure 7 It is the effect diagram of the reduction of the service risk before and after the optimization of the planetary roller screw. Specific implementation manners

[0079] The purpose of the present invention is to provide a method for optimizing the tolerances of a planetary roller screw, which can further reduce the probability of service risk and improve the machinability of parts on the premise of meeting the service performance requirements and machining capabilities, and is convenient for use.

[0080] In order to make the above objects, features and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific implementation manners.

[0081] As Figure 1 shown, the method for optimizing the tolerances of the planetary roller screw provided by the embodiment of the present invention includes the following steps:

[0082] Step 1: Extract the design parameter variation within the initial tolerance interval based on the Latin hypercube random sampling method;

[0083] Step 2: Randomly combine the extracted design parameter variations of the planetary roller screw to obtain a certain number of design parameter variation combinations;

[0084] Step 3: Establish a mathematical model for calculating the transmission accuracy, axial clearance, and fatigue life of the planetary roller screw considering the design parameter variation combinations;

[0085] Step 4: Based on the service requirements of transmission accuracy, axial clearance, and fatigue life, evaluate the service risk probability of the planetary roller screw according to the number of design parameter variation combinations and the number of combinations that meet the service requirements;

[0086] Step 5: Take the lowest service risk probability of the planetary roller screw and the largest width of the part tolerance interval as the objectives, and take the minimum tolerance interval width limited by the part machining accuracy grade as the constraint, and establish a multi-objective optimization model for the part tolerance parameters;

[0087] Step 6: Based on the non-dominated sorting genetic algorithm, solve the multi-objective optimization model of the tolerance parameters to realize the tolerance optimization driven by the transmission accuracy - axial clearance - fatigue life of the planetary roller screw.

[0088] In Step 1, extracting the design parameter variation within the initial tolerance interval based on the Latin hypercube random sampling method is specifically as follows:

[0089] The sampling method is as Figure 2 shown. Based on the initial tolerance interval of the design parameters of the planetary roller screw part, the variation of the design parameters within the initial tolerance interval is sampled and simulated by the Latin hypercube random sampling method. Among them, the tolerance interval is divided into N according to the sampling quantity of the design parameter variationS The sub-sampling interval, the sampling sample of the design parameter variation amount, and the sub-sampling interval satisfy:

[0090]

[0091] In the formula, N LHS is a vector composed of Latin hypercube sampling sub-intervals, x d is a Latin hypercube sampling sub-interval, N S is the sampling quantity of the design parameter variation amount, and are the upper and lower bounds of the Latin hypercube sampling sub-interval respectively, F d (·) is the cumulative probability distribution function value, x n is a random sampling individual of the design parameter variation amount within the Latin hypercube sampling sub-interval.

[0092] In step 2, the variation amounts of each design parameter of the planetary roller screw randomly combined and extracted are obtained to get a certain number of design parameter variation combinations, specifically:

[0093] Randomly combine the sampling results of the variation amounts of the lead screw, roller, nut eccentricity, pitch, pitch diameter, and thread profile half angle design parameters of the planetary roller screw to obtain N S design parameter variation combinations, which are:

[0094]

[0095] In the formula, is the design parameter variation combination with the quantity of N S Δ xX is the eccentricity design parameter variation amount of the lead screw, roller, and nut, Δ pX is the pitch design parameter variation amount of the lead screw, roller, and nut, Δ dX is the pitch diameter design parameter variation amount of the lead screw, roller, and nut, Δ βX is the thread profile half angle design parameter variation amount of the lead screw, roller, and nut, X represents the lead screw, roller, and nut of the planetary roller screw;

[0096] The present invention provides an embodiment, and the initial tolerance parameter table is shown in Table 1;

[0097] Table 1 Initial Tolerance Parameter Table of a Certain Planetary Roller Screw

[0098]

[0099] In step 3, establish a mathematical model for calculating the transmission accuracy, axial clearance, and fatigue life of the planetary roller screw considering the design parameter variation combination, specifically:

[0100] Establish a mathematical model for calculating the transmission accuracy, axial clearance, and fatigue life of a planetary roller screw considering the combined changes in the design parameters of the screw, rollers, and nut. Based on the mathematical model, calculate the stroke deviation, stroke variation, axial clearance, and fatigue life of the planetary roller screw under different combinations of design parameter changes The stroke deviation, stroke variation, axial clearance, and fatigue life under different design parameter changes are calculated. Among them, the transmission accuracy mathematical model includes transmission error calculation, linear equation fitting of transmission error and screw rotation angle, and calculation of stroke deviation and stroke variation. Among them, the transmission error calculation is as follows:

[0101]

[0102] In the formula, is the screw rotation angle is the transmission error of the planetary roller screw under is the screw rotation angle, and are the transmission errors caused by the changes in eccentricity and pitch design parameters under the screw rotation angle respectively, and are the transmission errors caused by the changes in the pitch diameter and thread profile half angle design parameters respectively, p h is the lead of the planetary roller screw, l u is the effective operating range of the nut;

[0103] The linear fitting equation of the transmission error and the screw rotation angle is:

[0104]

[0105] In the formula, m e and c e are the undetermined coefficients of the linear fitting equation of the transmission error and the screw rotation angle, T E is the column vector composed of the transmission errors of the planetary roller screw at each screw rotation angle respectively, p is the column vector composed of 1, and the dimension is the same as T E is the column vector composed of the screw rotation angles, and the dimension is the same as T E

[0106] The calculation of the stroke deviation and the stroke variation is as follows:

[0107]

[0108] In the formula, e a and v ua are the stroke deviation and the stroke variation of the planetary roller screw respectively, and are the screw rotation angles corresponding to the maximum and minimum transmission errors of the planetary roller screw respectively;

[0109] ​​The mathematical model of the axial clearance is as follows:

[0110]

[0111] In the formula, is the lead screw rotation angle axial clearance of the lower planetary roller screw;

[0112] The mathematical model of fatigue life includes the calculation of axial load of thread teeth, contact stress calculation, and fatigue life calculation. Among them, the calculation of axial load of thread teeth on the lead screw-roller and roller-lead screw sides is:

[0113]

[0114] In the formula, δ BX , δ TX and δ CX respectively represent the axial deformation of the lead screw, roller, and nut shaft segments, the deformation of thread teeth, and the contact deformation, N t is the number of roller thread teeth (i, j = 1, 2,..., N t ), and k is the contact thread pair on the lead screw-roller and roller-nut sides;

[0115] The calculation of contact stress of thread teeth is:

[0116]

[0117] In the formula, σ H is the Hertz contact stress of thread teeth, F is the axial load of thread teeth, and a and b are the lengths of the major and minor axes of the Hertz contact ellipse respectively;

[0118] The fatigue life calculation is:

[0119] N = CS -m (9)

[0120] In the formula, N is the contact fatigue life of thread teeth, C and m are the undetermined coefficients of the Basquin contact fatigue life calculation formula, and S is the Hertz contact stress of thread teeth. By considering the mathematical models of the transmission accuracy, axial clearance, and fatigue life of the planetary roller screw considering the combination of design parameter variations, based on the embodiments of the present invention, calculate the planetary roller screw stroke deviation, stroke variation, axial clearance, and fatigue life under different combinations of design parameter variations as Figure 3 shown.

[0121] In step 4, based on the service requirements of transmission accuracy, axial clearance, and fatigue life, according to the number of combinations of design parameter variations and the number of combinations that meet the service requirements, evaluate the service risk probability of the planetary roller screw, specifically:

[0122] Based on the service requirements of the transmission accuracy, axial clearance, and fatigue life of the planetary roller screw, set the stroke deviation threshold e t , the stroke variation threshold v t , the axial clearance threshold A up and A down , and the fatigue life threshold t, and determine whether the combination of design parameter variations makes the planetary roller screw meet the service requirements, that is:

[0123]

[0124] In the formula, n u and n FCu are the combinations of design parameter variations that make the planetary roller screw meet the service requirements of transmission accuracy, axial clearance, and fatigue life, A m and A min are the average and minimum axial clearances of the planetary roller screw, and L f is the fatigue life of the planetary roller screw;

[0125] Among them, the present invention gives an embodiment, setting the stroke deviation threshold e t = 0.012 mm, the stroke variation threshold v t = 0.012 mm, the axial clearance threshold A up = 0.03 mm and A down = 0.02 mm, and the fatigue life threshold t = 350 h (the working speed of the screw is 3000 r / min, and the axial load is 15 kN)

[0126] The combination of design parameter variations that makes the planetary roller screw meet the service requirements is as Figure 4 shown. Based on the number of combinations of design parameter variations and the number of combinations of design parameters that make the planetary roller screw meet the service requirements, evaluate the service risk probability of the planetary roller screw as:

[0127] R sys = 1 - (∑n FCu ) / N s (u ≤ N s ) (11)

[0128] In the formula, R sys is the service risk probability of the planetary roller screw.

[0129] In step 5, taking the lowest service risk probability of the planetary roller screw and the largest width of the part tolerance interval as the objectives, and taking the minimum tolerance interval width limited by the part machining accuracy grade as the constraint, establish a multi-objective optimization model for part tolerance parameters, specifically:

[0130] Taking the lowest service risk probability of the planetary roller screw and the largest width of the part tolerance interval as the objectives, selecting the eccentricity, pitch, pitch diameter, and thread profile half-angle tolerance parameters of the screw, roller, and nut as the design variables, and the minimum tolerance interval width limited by the part machining accuracy grade as the constraint, a multi-objective optimization model of the tolerance parameters is established. The objective functions are as follows:

[0131]

[0132] In the formula, f 1 and f 2 are the objective functions, n is the design variable, δ w is the weighted average of the tolerance interval widths, and are the tolerance interval widths of the eccentricity, pitch, pitch diameter, and thread profile half-angle of the screw, roller, and nut. Among them, s lim = upper&lower;

[0133] The design variables are:

[0134]

[0135] In the formula, and are the lower bounds of the tolerance intervals of the design parameters, and are the upper bounds of the tolerance intervals of the design parameters;

[0136] The design constraints are:

[0137]

[0138] In the formula, ω limxX 、ω limpX 、ω limdX and ω limβX are the minimum tolerance interval widths of the eccentricity, pitch, pitch diameter, and thread profile half-angle of the screw, roller, and nut under the limitation of the machining accuracy grade;

[0139] The present invention provides an embodiment. The machining accuracies of the screw, roller, and nut of the planetary roller screw are IT6 level. The specific design constraints are:

[0140]

[0141] As Figure 5 shown, in step 6, based on the non-dominated sorting genetic algorithm, the multi-objective optimization model of the tolerance parameters is solved to realize the tolerance optimization driven by the transmission accuracy - axial clearance - fatigue life of the planetary roller screw, which specifically includes the following steps:

[0142] Step 601: Set the maximum number of iterations and population size of the non-dominated sorting genetic algorithm;

[0143] Step 602: Randomly generate an initial population N containing tolerance parameter solutions 1 ;

[0144] Step 603: Perform non-dominated sorting and crowding degree calculation on the optimal solutions in population N 1 ;

[0145] Step 604: Set the crossover rate and mutation rate, and perform selection, crossover, and mutation operations to obtain the next generation population N 2 ;

[0146] Step 605: Perform non-dominated sorting and crowding degree calculation on the optimal solutions in population N 2 ;

[0147] Step 606: Eliminate the inferior solutions in population N so that the number of tolerance parameter solutions is the same as that of population N 2 to obtain a new population N 1 , and judge whether the number of iterations reaches the maximum value. If not, replace population N 3 with population N 3 , and repeat steps 603 - 606. If so, output the tolerance parameter solution with the lowest front face level in population N 1 as the Pareto optimal solution set z 3 ; of ;

[0148] Step 607: Evaluate the tolerance parameter solutions in the Pareto optimal solution set z of using the Topsis comprehensive evaluation method to find the optimal tolerance parameter, which is:

[0149]

[0150] In the formula, and are the distances between the objective function values caused by the tolerance parameter solutions in the optimal solution set and the defined maximum and minimum values, and are the defined maximum and minimum values, z of is the objective function value caused by the tolerance parameter solution in the Pareto optimal solution set, and S o is the comprehensive score of the tolerance parameter solutions in the solution set. f is the number of optimization objectives, and o is the number of tolerance parameter solutions in the Pareto optimal solution set.

[0151] The optimal tolerance parameter solution can further reduce the service risk probability and improve the machinability of parts while meeting the service performance requirements and machining capabilities;

[0152] According to the above-provided embodiments of the present invention, an optimized solution set as shown in Figure 6 is obtained. As shown in Figure 6 , the tolerance parameter solution with the lowest leading surface level is the Pareto optimization solution set. After optimization, the service risk probability of the planetary roller screw is reduced from the original 89.25% to 57.61%, the weighted average value of the tolerance interval increases from 0.7683 to 1.5206, and the average width of the tolerance interval increases by 17.38%. The optimized tolerance parameters are shown in Table 2;

[0153] Table 2 Optimized Tolerance Parameters of a Certain Planetary Roller Screw

[0154]

[0155] As shown in Figure 7 , by substituting the optimized tolerance parameters, the service performance risk probability including the stroke deviation, stroke variation, axial clearance, and fatigue life of the planetary roller screw changes, resulting in a reduction in the service risk probability of the planetary roller screw.

[0156] The present invention provides a method for optimizing the tolerance of a planetary roller screw. This method uses Latin hypercube sampling to sample and simulate the variation of design parameters within the tolerance interval, randomly combines the sampling results of the variation of the lead screw, roller, nut eccentricity, pitch, mean diameter, and thread profile half angle design parameters of the planetary roller screw to obtain a combination of design parameter variations, establishes a mathematical model for calculating the transmission accuracy, axial clearance, and fatigue life of the planetary roller screw considering the combination of design parameter variations of the lead screw, roller, and nut, calculates the stroke deviation, stroke variation, axial clearance, and fatigue life of the planetary roller screw under different combinations of design parameter variations, evaluates the service risk probability based on the number of combinations of design parameter variations and the number of combinations of design parameters that enable the planetary roller screw to meet the service requirements, takes the lowest service risk probability of the planetary roller screw and the largest width of the part tolerance interval as the objectives, uses the eccentricity, pitch, mean diameter, and thread profile half angle tolerance parameters of the lead screw, roller, and nut as design variables, and the minimum tolerance interval width limited by the part processing accuracy grade as the constraint to establish a multi-objective optimization model for tolerance parameters. Based on the non-dominated sorting genetic algorithm and Topsis comprehensive evaluation to solve the optimization model, while meeting the service performance requirements and processing capabilities, it further reduces the service risk probability and improves the machinability of parts, which has important research and engineering application significance.

[0157] Specific examples are applied in the present invention to elaborate on the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation to the present invention.

Claims

1. A method for optimizing the tolerances of a planetary roller screw, characterized in that, it includes the following steps: Step 1: Based on the Latin hypercube random sampling method, extract the design parameter variations within the initial tolerance interval; Step 2: Randomly combine the extracted design parameter variations of each item of the planetary roller screw to obtain a certain number of design parameter variation combinations; Step 3: Establish a mathematical model for calculating the transmission accuracy, axial clearance, and fatigue life of the planetary roller screw considering the design parameter variation combinations; Step 4: Based on the service requirements of transmission accuracy, axial clearance, and fatigue life, evaluate the service risk probability of the planetary roller screw according to the number of design parameter variation combinations and the number of combinations that meet the service requirements; Step 5: Take the lowest service risk probability of the planetary roller screw and the largest width of the part tolerance interval as the objectives, and take the minimum tolerance interval width limited by the part machining accuracy grade as the constraint to establish a multi-objective optimization model for part tolerance parameters; Step 6: Based on the non-dominated sorting genetic algorithm, solve the multi-objective optimization model for tolerance parameters to realize the tolerance optimization driven by the transmission accuracy - axial clearance - fatigue life of the planetary roller screw; In the said Step 5, taking the lowest service risk probability of the planetary roller screw and the largest width of the part tolerance interval as the objectives, and taking the minimum tolerance interval width limited by the part machining accuracy grade as the constraint to establish a multi-objective optimization model for part tolerance parameters, specifically: Taking the lowest service risk probability of the planetary roller screw and the largest width of the part tolerance interval as the objectives, select the eccentricity, pitch, mean diameter, and thread profile half-angle tolerance parameters of the screw, roller, and nut as the design variables, and the minimum tolerance interval width limited by the part machining accuracy grade as the constraint to establish a multi-objective optimization model for tolerance parameters. The objective function is: where f 1 and f 2 are objective functions, n is a design variable, and δ w is the weighted average of the tolerance zone widths, and are the tolerance zone widths of the eccentricity, pitch, pitch diameter, and thread profile half angle of the lead screw, roller, and nut, where s lim = upper&lower; The design variables are: Wherein, and are the lower bounds of the tolerance intervals of the design parameters, and are the upper bounds of the tolerance intervals of the design parameters; The design constraints are: where ω limxX , ω limpX , ω limdX and ω limβX are the minimum tolerance interval widths of the eccentricity, pitch, pitch diameter, and half angle of the thread profile of the lead screw, roller, and nut under the limitation of the machining accuracy grade.

2. The method for optimizing the tolerances of a planetary roller screw according to claim 1, characterized in that, in Step 1, based on the Latin hypercube random sampling method, extract the design parameter variations within the initial tolerance interval, specifically: Based on the initial tolerance interval of the design parameters of the planetary roller screw parts, the variation of the design parameters within the initial tolerance interval is sampled and simulated by the Latin hypercube random sampling method. Among them, the tolerance interval is divided into N S sub-sampling intervals, and the sampling sample of the design parameter variation and the sub-sampling interval satisfy: where N LHS is a vector composed of Latin hypercube sampling subintervals, and x d is a Latin hypercube sampling subinterval, N S is the sampling quantity of the design parameter variation, and are the upper and lower bounds of the Latin hypercube sampling subinterval respectively, F d (·) is the cumulative probability distribution function value, and x n is a random sampling individual of the design parameter variation within the Latin hypercube sampling subinterval.

3. The method for optimizing the tolerances of a planetary roller screw according to claim 2, characterized in that, in Step 2, randomly combine the extracted design parameter variations of each item of the planetary roller screw to obtain a certain number of design parameter variation combinations, specifically: Randomly combine the sampling results of the changes in the design parameters of the lead screw, rollers, nut eccentricity, pitch, mean diameter, and thread profile half angle of the planetary roller screw to obtain N combinations of design parameter changes, which are as follows: S For: In the formula, is the combination of design parameter variations with the quantity of N S , Δ xX is the variation of the eccentricity design parameter of the lead screw, roller, and nut, Δ pX is the variation of the pitch design parameter of the lead screw, roller, and nut, Δ dX is the variation of the pitch diameter design parameter of the lead screw, roller, and nut, Δ βX is the variation of the thread profile half angle design parameter of the lead screw, roller, and nut, and X represents the lead screw, roller, and nut of the planetary roller screw.

4. The method for optimizing the tolerances of a planetary roller screw according to claim 3, characterized in that, in Step 3, establish a mathematical model for calculating the transmission accuracy, axial clearance, and fatigue life of the planetary roller screw considering the design parameter variation combinations, specifically: Establish a mathematical model for calculating the transmission accuracy, axial clearance, and fatigue life of a planetary roller screw considering the combined variations of the design parameters of the screw, roller, and nut. Based on the mathematical model, calculate the stroke deviation, stroke variation, axial clearance, and fatigue life of the planetary roller screw under different combinations of design parameter variations The stroke deviation, stroke variation, axial clearance, and fatigue life under different combinations of design parameter variations. Among them, the transmission accuracy mathematical model includes transmission error calculation, fitting of the linear equation between the transmission error and the screw rotation angle, and calculation of the stroke deviation and stroke variation. Among them, the transmission error calculation is as follows: Wherein, is the lead screw rotation angle the transmission error of the lower planetary roller screw,[ is the lead screw rotation angle,[ and are respectively the transmission errors caused by eccentricity and pitch design parameter variations at the lead screw rotation angle below,[ and are respectively the transmission errors caused by variations in the pitch diameter and thread profile half angle design parameters, p h is the lead of the planetary roller screw, l u is the effective operating range of the nut; The linear fitting equation between the transmission error and the screw rotation angle is: where m e and c e are the undetermined coefficients of the linear fitting equation of the transmission error and the lead screw rotation angle, T E is the column vector composed of the transmission errors of the planetary roller screw at each lead screw rotation angle , p is the column vector composed of 1s, and the dimension is the same as that of T E ; is the column vector composed of the lead screw rotation angles, and the dimension is the same as that of T E ; The calculation of the stroke deviation and the stroke variation is: where e a and v ua are the stroke deviation and stroke variation of the planetary roller screw, respectively, and are the screw angles of the planetary roller screw corresponding to the maximum and minimum transmission errors, respectively; The mathematical model of the axial clearance is: In the formula, is the lead screw rotation angle axial clearance of the lower planetary roller screw; The fatigue life mathematical model includes the calculation of the axial load of the thread tooth, the calculation of the contact stress, and the calculation of the fatigue life. Among them, the calculation of the axial load of the thread tooth on the screw-roller and roller-screw sides is: Where, δ BX , δ TX and δ CX respectively represent the axial deformation of the lead screw, roller, and nut shaft segments, the deformation of the thread teeth, and the contact deformation. N t is the number of roller thread teeth (i, j = 1, 2,..., N t ), and k is the contact thread pair on the lead screw-roller and roller-nut sides; The calculation of the contact stress of the thread tooth is: where σ H is the Hertz contact stress of the thread tooth, F is the axial load of the thread tooth, and a and b are the lengths of the major and minor axes of the Hertz contact ellipse, respectively; The calculation of the fatigue life is: N = CS -m (9) In the formula, N is the contact fatigue life of the thread tooth, C and m are the undetermined coefficients of the Basquin contact fatigue life calculation formula, and S is the Hertz contact stress of the thread tooth.

5. The method for optimizing the tolerances of a planetary roller screw according to claim 4, characterized in that, In step 4, based on the service requirements of transmission accuracy, axial clearance, and fatigue life, and according to the number of combinations of design parameter variations and the number of combinations that meet the service requirements, the service risk probability of the planetary roller screw is evaluated, specifically as follows: Based on the service requirements of the transmission accuracy, axial clearance, and fatigue life of the planetary roller screw, set the stroke deviation threshold e t , the stroke change threshold v t , the axial clearance threshold A up and A down , the fatigue life threshold t, and determine whether the combination of design parameter changes makes the planetary roller screw meet the service requirements, that is: where n u and n FCu are the combined design parameter variations that enable the planetary roller screw to meet the service requirements of transmission accuracy, axial clearance, and fatigue life. A m and A min are the average and minimum axial clearances of the planetary roller screw, and L f is the fatigue life of the planetary roller screw; Based on the number of combinations of design parameter variations and the number of design parameter variation combinations that enable the planetary roller screw to meet the service requirements, the service risk probability of the planetary roller screw is evaluated as: R sys = 1 - (∑n FCu ) / N s (u ≤ N s ) (11) Wherein, R sys is the service risk probability of the planetary roller screw.

6. The planetary roller screw tolerance optimization method according to claim 5, characterized in that, In step 6, based on the non-dominated sorting genetic algorithm, the multi-objective optimization model of tolerance parameters is solved to realize the tolerance optimization driven by the transmission accuracy - axial clearance - fatigue life of the planetary roller screw, specifically including the following steps: Step 601: Set the maximum number of iterations and population size of the non-dominated sorting genetic algorithm; Step 602: Randomly generate an initial population N containing tolerance parameter solutions 1 ; Step 603: Perform non-dominated sorting and crowding degree calculation on the optimal solutions in population N 1 ; Step 604: Set the crossover rate and mutation rate, and perform selection, crossover, and mutation operations to obtain the next generation population N 2 ; Step 605: Perform non-dominated sorting and crowding degree calculation on the optimal solutions in population N 2 ; Step 606: Eliminate the inferior solutions in population N 2 so that the number of tolerance parameter solutions is the same as that of population N 1 to obtain a new population N 3 , and determine whether the number of iterations has reached the maximum value. If not, replace population N 3 with population N 1 , and repeat steps 603 - 606. Otherwise, output the tolerance parameter solution with the lowest front surface level in population N 3 as the Pareto optimization solution set z of ; Step 607: Evaluate the tolerance parameter solutions in Pareto optimization solution set z by using the Topsis comprehensive evaluation method, and find the optimal tolerance parameters, which are: of in which, and the optimal tolerance parameters are: Wherein, and are the distances of the objective function values caused by the tolerance parameter solutions in the optimized solution set from the defined maximum and minimum values, and are the defined maximum and minimum values, z of is the objective function value caused by the tolerance parameter solution in the Pareto optimized solution set, S o is the comprehensive score of the tolerance parameter solutions in the solution set, f is the number of optimization objectives, and o is the number of tolerance parameter solutions in the Pareto optimized solution set.

Images