A Grouping and Matching Method for Planetary Roller Screw Considering the Probability Distribution of Machining Errors

Abstract

The present invention provides a grouping and matching method for planetary roller screws considering the probability distribution of machining errors, including: constructing a relationship matrix of the assembled parts, and obtaining the sensitivity of the assembled parts according to the relationship matrix of the assembled parts; analyzing the sensitivity of the assembled parts based on the signal-to-noise ratio to determine the grouping reference tolerance; generating an initial matching scheme by using the initial grouping method according to the statistical analysis result of the actual machining errors; constructing a non-dominated sorting genetic optimization algorithm; constructing an optimization function with the qualified rate of grouping and the remaining rate of grouping as the objectives; based on the grouping reference tolerance, optimizing the grouping interval of the initial matching scheme according to the non-dominated sorting genetic optimization algorithm and the optimization function with the qualified rate of grouping and the remaining rate of grouping as the objectives to obtain a key tolerance design scheme; and performing grouping and matching design on the key tolerance design scheme based on the simulation assembly verification of the probability distribution of machining errors. The present invention solves the problem of the mismatch between the tolerance width and the machining accuracy of the planetary roller screw.

Description

Technical Field

[0001] The present invention relates to the field of optimized design of planetary roller screws, and particularly to a method for grouping and matching planetary roller screws considering the probability distribution of machining errors. Background Technique

[0002] A planetary roller screw is a screw drive mechanism that converts rotational motion into linear motion through the meshing of multiple pairs of helical surfaces between the screw, rollers, and nut. Its extremely high load-carrying capacity, stroke accuracy, transmission efficiency, axial stiffness, and high-speed performance characteristics make it mainly used in fields such as numerical control machine tools, aerospace, weaponry, and precision machinery. Benefiting from the higher unit density power that can be transmitted compared to the same-specification ball screw pair, the planetary roller screw has extremely high application potential under the trend of all-electricity, especially as the end actuator in an electro-mechanical actuator.

[0003] Especially in fields such as aerospace and weaponry, there are relatively high precision requirements for the application of planetary roller screws, and the tolerance design of its key components is a major difficulty in the research and development process. Compared with ordinary structural parts, precision drive mechanisms have extremely high requirements for the machining accuracy of parts. The limited machining accuracy conditions provided by production equipment in the ordinary machining production environment limit the machining accuracy grade of parts when designing precision drive mechanisms. The main contradiction in the machining production of planetary roller screws lies in that the machining ability and machining conditions are difficult to ensure product performance and product consistency. Therefore, the primary goal of grouping and matching is to meet the performance indicators of the assembled parts, and it is necessary to introduce a grouping and matching method to group the parts for assembly to meet the high-performance index requirements under general machining accuracy. Therefore, how to select a reasonable part size grouping under the premise of meeting the corresponding technical indicators is an issue that must be concerned when designing planetary roller screw products. Summary of the Invention

[0004] In order to overcome the deficiencies of the prior art, the purpose of the present invention is to provide a method for grouping and matching planetary roller screws considering the probability distribution of machining errors, and the present invention solves the problem of the mismatch between the tolerance width and machining accuracy of planetary roller screws.

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

[0006] A method for grouping and matching planetary roller screws considering the probability distribution of machining errors, including:

[0007] Construct a relationship matrix of the assembled part, and obtain the sensitivity of the assembled part according to the relationship matrix of the assembled part;

[0008] Analyze the sensitivity of the assembled part based on the signal-to-noise ratio to determine the grouping reference tolerance;

[0009] Generate an initial matching plan using the initial grouping method of midpoint positioning and bilateral expansion based on the statistical analysis results of actual processing errors;

[0010] Construct a non-dominated sorting genetic optimization algorithm;

[0011] Construct an optimization function with the grouping qualification rate and the grouping surplus rate as the objectives;

[0012] Based on the grouping reference tolerance, optimize the grouping interval of the initial matching plan according to the non-dominated sorting genetic optimization algorithm and the optimization function with the grouping qualification rate and the grouping surplus rate as the objectives to obtain a key tolerance design plan;

[0013] Based on the simulation assembly verification of the processing error probability distribution, conduct grouping matching design on the key tolerance design plan.

[0014] Preferably, the analysis of the sensitivity of the assembled part based on the signal-to-noise ratio to determine the grouping reference tolerance includes:

[0015] Divide the sensitivity of the assembled part into part-level sensitivity and dimension-level sensitivity;

[0016] Analyze the dimension-level sensitivity and part-level sensitivity of the assembled part based on the signal-to-noise ratio to determine the grouping reference tolerance.

[0017] Preferably, the calculation formula of the signal-to-noise ratio is:

[0018]

[0019] where, u and σ 2 are the mean and variance when assuming that the manufacturing error of the part geometric dimension is a random variable with a normal distribution within the tolerance zone, TU and TL are the original tolerance upper and lower bounds, and v represents the offset rate.

[0020] Preferably, the expression of the dimension-level sensitivity is:

[0021]

[0022] where, τ is the dimension-level sensitivity, the reciprocal of the signal-to-noise ratio is used as the correction coefficient, T m and T f are the manufacturing tolerance and the fit tolerance respectively.

[0023] Preferably, the part-level sensitivity is:

[0024]

[0025] where, Γ is the part-level sensitivity, and C is the manufacturing cost coefficient.

[0026] Preferably, the expression of the manufacturing cost is:

[0027] C = N / H;

[0028] Wherein, H is the qualified rate and N is the number of parts.

[0029] Preferably, the optimization function is:

[0030]

[0031] Wherein, C og represents the total number of assembled parts that do not meet the requirements of the axial clearance index in this matching scheme, x t i represents the right boundary position of the t-th grouping interval of the i-th part from small to large, D i represents the median diameter value of the i-th part, represents the lower deviation of the median diameter tolerance, represents the upper deviation of the median diameter tolerance.

[0032] According to the specific embodiments provided by the present invention, the following technical effects are disclosed:

[0033] The present invention provides a grouping and matching method for planetary roller screws considering the probability distribution of machining errors. By constructing a relationship matrix of assembled parts, the sensitivity of the assembled parts is obtained according to the relationship matrix of the assembled parts; based on the signal-to-noise ratio, the sensitivity of the assembled parts is analyzed to determine the grouping reference tolerance; according to the statistical analysis results of actual machining errors, an initial matching scheme is generated by using an initial grouping method of midpoint positioning and bilateral expansion; a non-dominated sorting genetic optimization algorithm is constructed; an optimization function with the grouping qualification rate and the grouping remainder rate as the objectives is constructed; based on the grouping reference tolerance, the initial matching scheme is optimized for the grouping interval according to the non-dominated sorting genetic optimization algorithm and the optimization function with the grouping qualification rate and the grouping remainder rate as the objectives to obtain a key tolerance design scheme; based on the simulation assembly verification of the probability distribution of machining errors, the key tolerance design scheme is subjected to grouping and matching design. The tolerance grouping of key components of the planetary roller screw is realized, and the assembly success rate of the planetary roller screw is improved on the premise of ensuring the machining accuracy. Description of the Drawings

[0034] 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 for use in the embodiments. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0035] Figure 1 is a flowchart of the grouping and matching method for the planetary roller screw in the embodiment of the present invention;

[0036] Figure 2 This is a schematic structural diagram of the planetary roller screw in the embodiment of the present invention;

[0037] Figure 3 This is a probability distribution diagram of the machining error distribution in the embodiment of the present invention;

[0038] Figure 4 This is a trend diagram of the average value change of the total number of unqualified assemblies in the embodiment of the present invention;

[0039] Figure 5 This is a trend diagram of the average value change of the total remaining number of parts in the embodiment of the present invention;

[0040] Figure 6 This is the Pareto solution set of multi-objective optimization in the embodiment of the present invention.

[0041] Description of the drawings: 1. Roller; 2. Screw; 3. Nut; 4. Internal gear ring; 5. Cage; 6. Cage baffle. Detailed implementation manners

[0042] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0043] The purpose of the present invention is to provide a grouping and matching method for planetary roller screws considering the probability distribution of machining errors, and the present invention solves the problem of mismatch between the tolerance width and machining accuracy of planetary roller screws.

[0044] 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 in conjunction with the accompanying drawings and specific implementation manners.

[0045] As Figure 1 shown, the present invention provides a grouping and matching method for planetary roller screws considering the probability distribution of machining errors, including:

[0046] Step 100: Construct a relationship matrix of the assembly, and obtain the assembly sensitivity according to the relationship matrix of the assembly;

[0047] Step 200: Analyze the assembly sensitivity based on the signal-to-noise ratio to determine the grouping reference tolerance;

[0048] Step 300: According to the statistical analysis results of the actual machining errors, use the initial grouping method of midpoint positioning and bilateral expansion to generate an initial matching scheme;

[0049] Step 400: Construct a non-dominated sorting genetic optimization algorithm;

[0050] Step 500: Construct an optimization function with the grouped qualification rate and the grouped remainder rate as the objectives;

[0051] Step 600: Based on the grouped reference tolerance, optimize the grouping interval of the initial mating scheme according to the non-dominated sorting genetic optimization algorithm and the optimization function with the grouped qualification rate and the grouped remainder rate as the objectives, and obtain a key tolerance design scheme;

[0052] Step 700: Conduct grouped mating design for the key tolerance design scheme based on the simulation assembly verification of the machining error probability distribution.

[0053] As Figure 2 shown, the planetary roller screw mainly consists of several parts including roller 1, screw 2, nut 3, internal gear ring 4, cage 5, and cage baffle 6. Among them, the parts directly affecting the stroke accuracy and axial clearance of the planetary roller screw are screw 2, roller 1, and nut 3; during operation, the rotational motion of screw 2 is converted into the linear motion of nut 3 through the meshing of multiple pairs of helical meshing surfaces between screw 2 and roller 1 and between nut 3 and roller 1. Table 1 is the structural dimension table of the key components of the planetary roller screw in the embodiment of the present invention, and Table 1 is as follows:

[0054] Table 1 Structural dimension table of the key components of the planetary roller screw:

[0055]

[0056] Furthermore, the analysis of the sensitivity of the assembled part based on the signal-to-noise ratio to determine the grouped reference tolerance includes:

[0057] Dividing the sensitivity of the assembled part into part-level sensitivity and dimension-level sensitivity;

[0058] Analyze the dimension-level sensitivity and part-level sensitivity of the assembled part based on the signal-to-noise ratio to determine the grouped reference tolerance.

[0059] Specifically, the sensitivity of the assembled part is divided into two layers from bottom to top: dimension-level sensitivity (τ) and part-level sensitivity (Γ). The signal-to-noise ratio, as an important indicator used to measure the robustness of design parameters in parameter design, is divided into target-seeking characteristics, smaller-the-better characteristics, and larger-the-better characteristics according to different usage objects. For the actual situation, the target-seeking characteristic is selected as the standard for measuring the volatility of manufacturing errors.

[0060] Specifically, the calculation formula of the signal-to-noise ratio is:

[0061]

[0062] where, u and σ2 When manufacturing errors of the geometric dimensions of the assumed parts are random variables that follow a normal distribution within the tolerance zone, the mean and variance are as follows. TU and TL are the original upper and lower tolerance limits, and v represents the offset rate, which is used to quantify the deviation degree between the dimension distribution center and the tolerance zone center.

[0063] Furthermore, the expression for the dimension layer sensitivity is:

[0064]

[0065] Among them, τ is the dimension layer sensitivity, and the reciprocal of the signal-to-noise ratio is used as the correction coefficient. T m and T f are the manufacturing tolerance and the fit tolerance respectively, which are corrected by the signal-to-noise ratio. The ratio of the manufacturing tolerance to the fit tolerance can reflect the influence of manufacturing errors on the fluctuation of fit errors.

[0066] Furthermore, the part layer sensitivity is used to quantify the influence degree of part failure on the assembly success rate. For parts in the planetary roller screw that can meet the design accuracy requirements and do not require selection and matching, such as the cage, internal gear ring, retaining ring, etc., their Γ = 0. Due to the non-negligible manufacturing cost, the part sensitive layer includes the manufacturing cost of the part and the sum of the sensitivity of each dimension layer. The part layer sensitivity is:

[0067]

[0068] Among them, Γ is the part layer sensitivity, and C is the manufacturing cost coefficient.

[0069] Furthermore, the part layer sensitivity is a comprehensive comparison of the dimension layer sensitivity and the manufacturing cost. For high-precision planetary roller screw pairs, the proportion of the manufacturing cost is slightly less than the proportion of the dimension layer sensitivity. The dimension layer sensitivity should be compared first. The only components in PRSM with Γ≠0 are the screw, roller, and nut, and the rest of the parts are assembled using the complete interchange method. Therefore, the main influencing factor for the part layer sensitivity ranking is the dimension layer sensitivity, specifically including:

[0070] For the pitch diameters of the screw, roller, and nut, the manufacturing cost can be calculated using the qualification rate as an index. The normal distribution expectation and standard deviation are obtained by fitting the distribution of the machining errors of each pitch diameter, and then interpolation is performed according to the tolerance zone. The expression for the manufacturing cost is:

[0071] C = N / H;

[0072] Among them, H is the qualification rate, and N is the number of parts.

[0073] The fitting data of the distribution probability of the assembled parts comes from the processing and inspection data of the parts of the same type of planetary roller screw pairs in a certain batch. Table 2 shows the dimensional deviation data of the parts. Table 2 shows the difference between the measured value and the theoretical value of the pitch diameter of the three types of parts, with the unit of mm. Table 2 is shown as follows:

[0074] Table 2 Dimensional deviation data of the parts

[0075]

[0076]

[0077] Based on the Kolmogorov-Smirnov test and the Anderson-Darling test methods, the distribution of the above dimensional deviation data is tested. Table 3 is the p-value table of the normal distribution test. Table 3 is shown as follows:

[0078] Table 3 p-values of the normal distribution test

[0079]

[0080] The calculated p-values obtained from the K-S test and the A-D test in Table 3 are both greater than the significance level of 5%. Then it is considered that its distribution is a normal probability distribution.

[0081] Through the detection and analysis of the processing errors of the previous processed samples, the distribution of the pitch diameter processing errors of the screw, roller, and nut is obtained as Figure 3 shown: The non-dominated sorting genetic algorithm is used to determine the optimal grouping interval. The non-dominated sorting algorithm is based on the Pareto dominance relationship defined in the multi-dimensional space, and the crowding distance is introduced to make the solution set evenly distributed. With these characteristics, NSGA-II can effectively solve the multi-objective optimization problem and find the Pareto optimal solution set.

[0082] By calculating the non-dominated sorting and crowding distance of the solutions, a set of Pareto optimal solution sets is generated to evaluate the quality of the solutions to the multi-objective problem. For the standard multi-objective optimization problem, generally its optimization function is shown as follows:

[0083] minF(X) = [f1(X), f2(X), …, f m (X)]

[0084] s.t.g i (X) ≤ 0, i = 1, 2, … k

[0085] h j (X) = 0, j = 1, 2, … l

[0086] where F(X) = [f1(X), f2(X), …, f m(X) is the problem target, and X = [x1, x2,..., x n is a given vector in R n space, called the decision space of the target problem, whose dimension n is equal to the number of variables involved in the problem, h j (X) = 0, j = 1, 2,..., l are equality constraints, g i (X) ≤ 0, i = 1, 2,..., k are inequality constraints.

[0087] Furthermore, the optimization function needs to achieve two goals: 1) the remaining number of parts within the group is the least; 2) the number of unqualified assembled machines is the least. The optimization function is:

[0088]

[0089] Among them, C og represents the total number of assembled parts that do not meet the axial clearance index requirements in this matching scheme, x t i represents the right boundary position of the t-th grouping interval of the i-th part from small to large, D i represents the median diameter value of the i-th part, represents the lower deviation of the median diameter tolerance, represents the upper deviation of the median diameter tolerance.

[0090] According to the center position of the reference part group, the center points of the remaining dimensions in the assembly dimension chain are located by the constraint conditions. For multi-fit precision matching, each fit precision grouping is established separately, and then each grouping situation is comprehensively subdivided. For complex matching with the number of fits being n a , the actual number of groups N RG adopts the following formula:

[0091]

[0092] In the formula, n o,i represents the total number of possible permutations and combinations of the sequence numbers of all grouping intervals of the i-th part, n a represents the total number of fits.

[0093] The remaining parts of the selected parts with multi-fit relationships are the sum of the remaining parts of each single grouping, calculated as follows:

[0094]

[0095] In the formula, δ(n a -1) represents the remaining part rate when considering n a -1 fits, represents the n-th aRemaining parts in each group. The selection criterion is determined through the sensitivity analysis of the part layer to ensure the minimum remaining rate of key parts.

[0096] Total number of unassembled parts C in the group nf Sum of all remaining parts calculated based on the part with the minimum assembly rate in the mating dimension chain:

[0097]

[0098] In the formula, n ij represents the total number of parts of the i-th part in the j-th mating plan in the assembly dimension chain, n g,j represents the total number of parts with the minimum assembly rate in the j-th grouping plan, p k represents the assembly ratio of the i-th part to the part with the minimum assembly rate, and M represents the total number of parts in a single assembly dimension chain.

[0099] The initial number of groups k is obtained as 5, the number of part types in a single mating dimension chain is 3, and 1000 groups of parts are generated for each grouping plan based on the standard deviation shown in Figure 3 The ratio of lead screw, roller, and nut in each group of parts is 1:10:1. The initial population of the NSGA-II multi-objective optimization algorithm is set to 200, the number of iterations is set to 500, and the crossover ratio is set to 0.8. To obtain better iteration results, the mutation rate is set to 0.8. After multiple repeated iterations, the objective function values are as shown in Figure 4 、 Figure 5 and tend to be stable. The Pareto solution set of the objective function of the final generation is as shown in Figure 6 shown.

[0100] The beneficial effects of the present invention are as follows:

[0101] Based on the sensitivity analysis of the assembled parts based on the signal-to-noise ratio, the grouping reference tolerance is determined. According to the statistical analysis results of the actual machining errors, the initial grouping method of midpoint positioning and bilateral expansion is used to generate the initial mating plan. The multi-objective directional optimization of the qualification rate and the remaining rate is carried out through the genetic optimization algorithm. Through the simulation assembly verification based on the probability distribution of machining errors, the grouping and mating design of the key tolerance design plan is carried out. The proposed grouping and mating can not only ensure the stroke accuracy index of the product after assembly under a relatively wide tolerance band, but also make full use of the existing parts, reduce the production cost, and improve the product economy at the same time.

[0102] The various embodiments in this specification are described in a progressive manner. The key points of each embodiment are the differences from other embodiments. The same and similar parts among the various embodiments can be referred to each other.

[0103] In this article, specific examples are used to elaborate on the principles and implementation modes of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea; 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 modes and application scopes. To sum up, the content of this specification should not be construed as a limitation to the present invention.

Claims

1. A method for grouped selection and matching of planetary roller screws considering the probability distribution of machining errors, characterized in that, Including: Construct a relationship matrix of the assembly, and obtain the assembly sensitivity according to the relationship matrix of the assembly; Analyze the assembly sensitivity based on the signal-to-noise ratio to determine the grouping reference tolerance; According to the statistical analysis results of the actual machining errors, generate an initial matching scheme by using the initial grouping method of midpoint positioning and bilateral expansion; Construct a non-dominated sorting genetic optimization algorithm; Construct an optimization function with the grouping pass rate and the grouping remaining rate as the objectives; Based on the grouping reference tolerance, optimize the grouping interval of the initial matching scheme according to the non-dominated sorting genetic optimization algorithm and the optimization function with the grouping pass rate and the grouping remaining rate as the objectives to obtain a key tolerance design scheme; Based on the simulation assembly verification of the machining error probability distribution, perform grouping matching design on the key tolerance design scheme.

2. A method for grouped selection and matching of planetary roller screws considering the probability distribution of machining errors according to claim 1, characterized in that The analysis of the assembly sensitivity based on the signal-to-noise ratio to determine the grouping reference tolerance includes: Divide the assembly sensitivity into part-level sensitivity and dimension-level sensitivity; Analyze the dimension-level sensitivity and part-level sensitivity of the assembly based on the signal-to-noise ratio to determine the grouping reference tolerance.

3. A method for grouped selection and matching of planetary roller screws considering the probability distribution of machining errors according to claim 2, characterized in that The calculation formula of the signal-to-noise ratio is: where u and σ 2 are the mean and variance when the manufacturing error of the assumed part geometric dimension is a random variable that follows a normal distribution within the tolerance zone, TU and TL are the original upper and lower tolerance limits, and v represents the offset rate.

4. A method for grouped selection and matching of planetary roller screws considering the probability distribution of machining errors according to claim 3, characterized in that The expression of the dimension-level sensitivity is: Among them, τ is the sensitivity of the dimensional layer, and the reciprocal of the signal-to-noise ratio is used as a correction coefficient, T m and T f are the manufacturing tolerance and the fit tolerance respectively.

5. A method for grouping and matching planetary roller screws considering the probability distribution of machining errors according to claim 4, characterized in that The part-level sensitivity is: Where Γ is the part-level sensitivity and C is the manufacturing cost coefficient.

6. A method for grouping and matching planetary roller screws considering the probability distribution of machining errors according to claim 5, characterized in that The expression of the manufacturing cost is: C = N / H; Where H is the pass rate and N is the number of parts.

7. A method for grouping and matching planetary roller screws considering the probability distribution of machining errors according to claim 5, characterized in that The optimization function is: Among them, C og represents the total number of assembled parts that do not meet the axial clearance index requirements in this optional assembly plan, and x t i represents the right boundary position of the t-th grouping interval of the i-th part from small to large, and D i represents the median diameter value of the i-th part, represents the lower deviation of the median diameter tolerance, represents the upper deviation of the median diameter tolerance.

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