Multi-tolerance coupling mechanism precision analysis and tolerance distribution method

Abstract

The invention discloses a multi-tolerance coupling mechanism precision analysis and tolerance distribution method, which comprises the following steps of: analyzing an assembly structure of a mechanism to be processed: analyzing part composition of the mechanism and an assembly relationship among all parts, and determining key geometric features which influence functional requirement poses; determining the small displacement spinor of the key geometrical characteristics of each assembly surface, establishing a mechanism error transfer matrix, solving a functional requirement pose error accumulation transfer function, and analyzing the mechanism precision; fitting a function relationship between the tolerance and the actual variation interval of the small displacement spinor; establishing a reliability performance function of the tolerance, and carrying out reliability analysis; carrying out primary distribution on each tolerance when the output function requirement is known; and a PSO algorithm is adopted to optimize the tolerance, and a final tolerance value is determined, so that the to-be-machined mechanism is designed. While the final precision of the mechanism is predicted, the tolerance selection problem of each assembly key geometric feature can be guided, and finally the tolerance-machining cost optimization is realized.

Description

Technical Field

[0001] The invention relates to the technical field of tolerance allocation and component precision, and in particular to a multi-tolerance coupling mechanism precision analysis and tolerance allocation method. Background Art

[0002] The tolerance allocation problem is one of the most important tasks to be solved in mechanism design. It affects the function, service life and manufacturing cost of the mechanism and runs through the entire life cycle of the mechanism. Traditional tolerance design relies on consulting design manuals and workers' experience. At present, an assembly tolerance transfer model has been established on this basis. However, the variables in the assembly tolerance transfer model are only small displacement screws. The tolerance is not directly used as input and combined with Sobol global sensitivity and processing difficulty weight to scientifically guide tolerance allocation. A detailed analysis method combining systematic tolerance allocation with mechanism reliability and processing cost has not yet been established. Summary of the invention

[0003] In order to overcome the fact that the existing tolerance allocation technology has not yet formed a bottom-up research system, the present invention provides a multi-tolerance coupled mechanism accuracy analysis and tolerance allocation method. While predicting the final accuracy of the mechanism, the present invention can guide the tolerance selection of each key geometric feature of the assembly, and finally achieve tolerance-processing cost optimization.

[0004] Terminology explanation:

[0005] 1. SDT: Small Displacement Torsor.

[0006] 2. RSM: Response Surface Methodology.

[0007] 3. PSO: Particle Swarm Optimization, particle swarm algorithm.

[0008] 4. MSE: Mean Squared Error.

[0009] 5. R²: R-Square, coefficient of determination.

[0010] 6. Sobol: Sampling method for global sensitivity analysis.

[0011] The technical solution adopted by the present invention to overcome the technical problems is:

[0012] A method for analyzing the accuracy and allocating tolerances of a multi-tolerance coupled mechanism comprises the following steps:

[0013] S1. Analyze the assembly structure of the mechanism to be processed: analyze the component composition of the mechanism and the assembly relationship between the various parts, and determine the key geometric features that affect the functional requirements;

[0014] S2. Determine the small displacement spin of the key geometric features of each assembly surface, establish the mechanism error transfer matrix, solve the cumulative transfer function of the functional requirements posture error, and analyze the mechanism accuracy;

[0015] S3, the functional relationship between the fitting tolerance and the actual variation range of the small displacement screw;

[0016] S4. Establish the reliability function of tolerance and conduct reliability analysis; make initial allocation of each tolerance when the output function requirements are known; use PSO algorithm to optimize the tolerance and determine the final tolerance value;

[0017] S5. Based on the final tolerance value obtained in step S4, the processing mechanism is designed.

[0018] Further, step S1 includes the following:

[0019] S11. Analyze the component composition of the mechanism and the assembly relationship between the various components;

[0020] S12, finding the path of tolerance transfer in the process of parts assembly and establishing the tolerance transfer topology structure;

[0021] S13. According to the assembly sequence of parts, the features that affect the functional requirements during the assembly process are taken as the key geometric features of the mechanism to be analyzed.

[0022] Furthermore, in step S13, the key geometric features of the structure to be analyzed are described as follows:

[0023] )(1)

[0024] In formula (1), represents the number of key geometric features, where , , ··· The specific expressions are as follows:

[0025] =( , ··· )(2)

[0026] =( , ··· )(3)

[0027] ···

[0028] =( , ··· )(4)

[0029] Formula (2)-Formula (4), , ··· Respectively represent the number of tolerances contained in each key geometric feature.

[0030] Further, step S2 includes the following:

[0031] S21, determining the coordinate system of each key geometric feature;

[0032] S22, establish the small displacement screw of the key geometric features of each assembly surface;

[0033] S23, determine the expression of small displacement spins corresponding to different key geometric features;

[0034] S24, determine the constraint inequality of small displacement screw under the action of tolerance;

[0035] S25, establishing a homogeneous coordinate transformation matrix mathematical model of each key geometric feature;

[0036] S26. Establish the mechanism error transfer matrix and solve the cumulative transfer function of the functional required posture error to analyze the mechanism accuracy.

[0037] Furthermore, step S2 specifically includes the following:

[0038] S21. Determine the coordinate system of each key geometric feature, specifically establish a Cartesian coordinate system: according to the assembly order of the parts, establish a global theoretical coordinate system with the appropriate position of the key geometric feature initially assembled by the mechanism as the origin, and establish a local theoretical coordinate system with the appropriate position of the key geometric feature input by the remaining errors as the origin, wherein the appropriate position refers to the position that is convenient for calculating the cumulative error of the functional required posture, generally the center of the key geometric feature is selected as the origin, and the remaining errors refer to the errors of the key geometric features other than the initially assembled key geometric features;

[0039] S22. Establish the small displacement spin of the key geometric features of each assembly surface: According to the small displacement spin theory, the actual position of the key geometric features relative to the ideal position is changed by three rotation vectors C=[ ] and three translation vectors D=[ ] to indicate that, , , Respectively represent the small changes in rotation around the X-axis, Y-axis, and Z-axis. , , They represent the small changes in translation along the X-axis, Y-axis, and Z-axis respectively, and the total rotation is expressed as =[C,D]=[ ];

[0040] S23. Determine the expression of small displacement spin corresponding to different key geometric features: The key geometric features include plane, cylinder, axis and sphere. Assume that the degree of freedom of the plane is , then the small displacement spin corresponding to the plane is , assuming the degree of freedom of the cylindrical surface is , , then the small displacement spin corresponding to the cylindrical surface is , let the degree of freedom of the axis be , then the small displacement rotation corresponding to the axis is , assuming the degrees of freedom of the sphere is , then the small displacement spin corresponding to the sphere is ;

[0041] S24, determine the constraint inequality of the small displacement screw under the effect of tolerance: constrain the variation range of the small displacement screw with the tolerance size, and set the tolerance of each key geometric feature described in step S23 to be , the constraint inequalities corresponding to the plane, cylinder, axis and sphere are respectively expressed as formula (5), formula (6), formula (7) and formula (8), as follows:

[0042] , , (5)

[0043] , , , (6)

[0044] , , , (7)

[0045] (8)

[0046] Formula (5)-Formula (7), represents the length of the plane, represents the width of the plane, represents the length of the cylindrical surface, Indicates the length of the axis;

[0047] S25. Establish a mathematical model of homogeneous coordinate transformation matrix of each key geometric feature: Use homogeneous coordinate transformation theory to establish a homogeneous coordinate transformation matrix, the expression is as follows:

[0048] H = J K [ 0 ] I = 1 -γ β μ γ 1 -α ν -β α 1 ω 0 0 0 1 (9)

[0049] In formula (9), represents the rotation transformation matrix, represents the translational change matrix, is 1, [ 0 ] is [0, 0, 0];

[0050] S26. Establish the mechanism error transfer matrix and solve the cumulative transfer function of the functional requirements posture error. is the cumulative transfer matrix of the ideal pose of the key geometric features, is the cumulative transfer matrix of the actual pose of the key geometric features, is the cumulative error transfer matrix of the actual posture relative to the ideal posture, The pose matrix of the functional requirement pose in the local theoretical coordinate system, is the cumulative error matrix of the actual functional requirement posture relative to the ideal functional requirement posture. The specific expression is as follows:

[0051] (10)

[0052] (11)

[0053] (12)

[0054] (13)

[0055] (14)

[0056] (15)

[0057] Formula (10)-Formula (15), Represents the ideal pose transformation matrix of two key geometric features at the junction, Represents the transformation matrix of the actual pose of each key geometric feature relative to the ideal pose, express The number of express The number of , , are the coordinates in the X-axis, Y-axis, and Z-axis directions respectively. , , They are the errors of the actual functional requirement posture relative to the ideal functional requirement posture in the X-axis, Y-axis, and Z-axis directions, all of which contain small displacement spinors;

[0058] The error accumulation transfer function of the functional requirement posture is expressed as:

[0059] (16)

[0060] By calculating the formula (16) The value of is used to analyze the accuracy of the mechanism.

[0061] Further, step S3 includes the following:

[0062] S31. Using the Monte Carlo random sampling method, samples of independent variables and dependent variables are obtained, wherein the independent variable refers to the tolerance, and the dependent variable refers to the actual variation range of the small displacement spinor;

[0063] S32, using the RSM method, a quadratic polynomial without cross terms is used to fit the explicit function of the actual variation range and tolerance of each small displacement spinor;

[0064] S33, verifying the accuracy of the fitted explicit function: if the error exceeds a preset threshold, return to step S31 to refit; otherwise, execute step S4.

[0065] Furthermore, step S3 specifically includes the following:

[0066] S31, determine the value range of each small displacement screw, and set the maximum tolerance With minimum tolerance The two are divided equally intervals, select normal distribution as the tolerance distribution type, use Monte Carlo random sampling to obtain samples of independent variables and dependent variables, specifically, obtain the sample matrix of tolerance And the sample matrix of the actual variation range of the small displacement spinor ;

[0067] S32, through the RSM method, the actual change interval of each small displacement spinor is constructed using a quadratic polynomial without cross terms The explicit function between and tolerance is expressed as follows:

[0068] (17)

[0069] In formula (17), , , All represent the coefficients to be determined. Indicates A tolerance constraining small displacement screws, Indicates the number of constraints on a small displacement screw tolerance;

[0070] Use the least squares method to calculate the coefficients to be determined , , , the coefficient to be determined , , The three are expressed as , the expression is as follows:

[0071] (18)

[0072] In formula (18), express The transposed matrix of

[0073] and They are respectively expressed as follows:

[0074] (19)

[0075] (20)

[0076] In formula (19) and formula (20), , , , , , They represent the first tolerance value of the first interval constraint small displacement spinor, the first interval constraint small displacement spinor tolerance value, the first tolerance value of the second interval constraint small displacement spinor, the first tolerance value of the second interval constraint small displacement spinor Tolerance value, The first tolerance value, the second tolerance value, Interval Constrained Small Displacement Screw Tolerance values, , , They represent the actual variation range of the small displacement spinor corresponding to the first interval tolerance value, the actual variation range of the small displacement spinor corresponding to the second interval tolerance value, and the The actual variation range of the small displacement screw corresponding to the interval tolerance value;

[0077] The solved Replacement tolerance , and obtain the actual variation range of the small displacement spinor;

[0078] S33. Use mean square error MSE or determination coefficient R² to verify the accuracy of the fitted explicit function: if the error exceeds the preset threshold, return to step S31 and refit; otherwise, the relationship between the tolerance and the output accuracy is obtained, and then execute step S4.

[0079] Further, step S4 includes the following:

[0080] S41. Based on formulas (16) and (17), a tolerance reliability function is established to perform reliability analysis.

[0081] S42. The sensitivity of each tolerance to the output accuracy is calculated by using the Sobol global sensitivity analysis method, and the processing difficulty of each part feature is analyzed by using a triangular fuzzy judgment matrix. Then, the weight of each tolerance allocation is calculated, so that each tolerance is initially allocated when the output function requirements are known.

[0082] S43. Taking the error-cost function as the optimization objective function, the reliability and tolerance values ​​as constraints, the PSO algorithm is used to optimize the tolerance and determine the final tolerance value.

[0083] Furthermore, step S4 specifically includes:

[0084] S41. Based on formulas (16) and (17), establish the tolerance reliability function and conduct reliability analysis: Assume that the functional requirement accuracy is The reliability should not be less than , according to formula (16) the error accumulation transfer function is , establish the mechanism reliability function and reliability constraint inequalities are expressed as follows:

[0085] (twenty one)

[0086] (twenty two)

[0087] R τ =1- ∫ ⋯ ∫ u ∈ G u <0 V [G(u)] O (u)du (twenty three)

[0088] Formula (21) represents the mechanism reliability function, formula (22) represents the reliability constraint inequality; in formula (23), V [G(u)] represents the indicative function, when >0, ;when <0, ; express The joint probability density function involving the error variables, is the independent variable of formula (23);

[0089] S42, according to the error accumulation transfer function obtained And the actual variation range of each small displacement spinor , using the Sobol global sensitivity analysis method, the sensitivity weight coefficient of each tolerance to the output accuracy is obtained ,in , the calculation formula is:

[0090] The first-order impact index formula is as follows:

[0091] (twenty four)

[0092] (25)

[0093] (26)

[0094] Formula (24)-Formula (26), represents the independent variable, represents the variance of the dependent variable, and All represent independent variable matrices, Represented by matrix Middle Column substitution matrix Middle The resulting matrix is , , Respectively represent matrices ,matrix ,matrix The function value of represents the number of first-order influence indices, Indicates the number of function values;

[0095] The triangular fuzzy judgment matrix is ​​used to analyze the processing difficulty weight coefficient of each part feature tolerance. First, the fuzzy judgment matrix is ​​constructed and the median matrix is ​​extracted. And Perform a consistency check as follows:

[0096] (27)

[0097] (28)

[0098] In formula (27) and formula (28), Represents the consistency index, express The maximum eigenvalue of express The dimension of represents the random consistency ratio, represents the average consistency index;

[0099] Constructing fuzzy evaluation factor matrix , and calculate the adjustment judgment matrix , and finally calculate the processing difficulty weight coefficient , the calculation formula is as follows:

[0100] (29)

[0101] (30)

[0102] (31)

[0103] In formula (30) and formula (31), represents the evaluation index weight, Representation Matrix No. Line Column elements, Representation Matrix The number of columns;

[0104] According to the calculated and , and then find the weights of each tolerance allocation as follows:

[0105] (32)

[0106] Assign weights to each tolerance, so that each tolerance can be initially assigned when the output functional requirements are known;

[0107] S43, taking the tolerance processing cost function as the optimization objective function, the reliability and tolerance value as the constraint conditions, and using the PSO algorithm to optimize the tolerance to determine the final tolerance value, as follows:

[0108] There are at least 6 tolerance processing cost models, which are shown as follows:

[0109] (1) The function of the plane dimension tolerance processing cost model is:

[0110] (33)

[0111] (2) The function of the flatness tolerance processing cost model is:

[0112] (34)

[0113] (3) The function of the inner hole size tolerance processing cost model is:

[0114] (35)

[0115] (4) The function of the external circle dimension tolerance processing cost model is:

[0116] (36)

[0117] (5) The function of the position tolerance processing cost model is:

[0118] (37)

[0119] (6) The function of the verticality tolerance processing cost model is:

[0120] (38).

[0121] The beneficial effects of the present invention are:

[0122] 1. The tolerance allocation research system has been improved, which can reasonably analyze the design accuracy of the mechanism, so that the accuracy of the mechanism can be clearly grasped in the early stage of design, thereby improving production efficiency and product qualification rate.

[0123] 2. Provide effective guidance for tolerance selection, change the previous situation of tolerance selection based on experience or lack of systematic basis, and improve product quality.

[0124] 3. Using the method of the present invention to perform reasonable tolerance allocation helps to accurately control processing costs, improve economic benefits, and enhance the competitiveness of products in the market.

[0125] 4. The content of the present invention involves key links common to many manufacturing fields, and is expected to be widely used in many industries such as mechanical manufacturing that require structural accuracy, and promote the common progress of related industries in product manufacturing accuracy and cost control. BRIEF DESCRIPTION OF THE DRAWINGS

[0126] Figure 1The present invention is a flowchart of a method for analyzing the accuracy of a multi-tolerance coupled mechanism and allocating tolerances according to an embodiment of the present invention.

[0127] Figure 2 It is a structural schematic diagram of the parallel four-bar mechanism described in an embodiment of the present invention.

[0128] Figure 3 This is a sample flow chart of using the Monte Carlo sampling method to obtain the actual variation range of the independent variable tolerance and the dependent variable small displacement spinor according to an embodiment of the present invention.

[0129] Figure 4 This is a posture transformation diagram describing the small displacement spinor along the three coordinate axes of X, Y, and Z as described in an embodiment of the present invention.

[0130] Figure 5 It is a coordinate system diagram in the cross-sectional view of the base plate, head plate, sleeve and pull rod described in the embodiment of the present invention.

[0131] Figure 6 It is a coordinate system diagram in the side view of the parallel four-bar mechanism described in the embodiment of the present invention.

[0132] Figure 7 This is a plane tolerance coupling diagram used to describe the plane microscopic changes of a part after machining, as described in an embodiment of the present invention.

[0133] Figure 8 The cylindrical tolerance coupling diagram described in the embodiment of the present invention is used to describe the microscopic changes of the cylindrical surface after the part is processed. DETAILED DESCRIPTION

[0134] In order to facilitate those skilled in the art to better understand the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. The following is only exemplary and does not limit the protection scope of the present invention.

[0135] The present invention discloses a method for analyzing the precision of a multi-tolerance coupled mechanism and allocating tolerances, such as Figure 1 As shown, the following steps are included:

[0136] S1. Analyze the assembly structure of the mechanism to be processed: analyze the component composition of the mechanism and the assembly relationship between the various parts, and determine the key geometric features that affect the functional requirements;

[0137] S2. Determine the small displacement spin of the key geometric features of each assembly surface, establish the mechanism error transfer matrix, solve the cumulative transfer function of the functional requirements posture error, and analyze the mechanism accuracy;

[0138] S3, the functional relationship between the fitting tolerance and the actual variation range of the small displacement screw;

[0139] S4. Establish the reliability function of tolerance and conduct reliability analysis; make initial allocation of each tolerance when the output function requirements are known; use PSO algorithm to optimize the tolerance and determine the final tolerance value;

[0140] S5. Based on the final tolerance value obtained in step S4, the processing mechanism is designed.

[0141] In order to better understand the above technical solution, the exemplary embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings. These are only exemplary embodiments of the present invention. However, it should be understood that the present invention can also be implemented in various forms and is not limited to the embodiments described herein. These embodiments are intended to enable those skilled in the art to understand the present invention more clearly and thoroughly.

[0142] The method for analyzing the precision and allocating the tolerances of a multi-tolerance coupling mechanism described in this embodiment takes a parallel four-bar mechanism as a research object. Figure 2 As shown, it includes a bottom plate 1, a head plate 2, a tail plate 3, a sleeve 4, four tie rods 5, and a middle plate 6, wherein the head plate 2, the tail plate 3, and the sleeve 4 are connected into a whole through the four tie rods 5 and fixed on the bottom plate 1, and the middle plate 6 can slide back and forth with the tie rods 5 as guide rails. The goal of this embodiment is to ensure that the parallelism between the four tie rods does not exceed the specified tolerance range. After analysis, the change in the parallelism of the four tie rods can be converted into the relative change of the axis at both ends of a tie rod, and then simplified to the change of the axis at one end of a tie rod.

[0143] The specific steps include:

[0144] S1. Analyze the assembly structure of the mechanism to be processed: analyze the component composition of the mechanism and the assembly relationship between the various parts, and determine the key geometric features that affect the functional requirements and posture.

[0145] Specifically, in this embodiment, the key geometric features of the assembly contact surface are: the upper plane of the bottom plate, the bottom surface of the head plate, the head plate hole, the outer cylindrical surface of the sleeve, the inner hole surface of the sleeve and the outer cylindrical surface of the pull rod; the tolerances included in each key geometric feature are the size tolerances of the bottom plate , Floor flatness , Flatness of the bottom surface of the head plate , Head plate hole size tolerance , Head plate hole position , sleeve outer circle dimension tolerance , Verticality of the outer axis of the sleeve , sleeve inner circle dimension tolerance , Verticality of the inner axis of the sleeve , Tie rod size tolerance , Verticality of Tie Rod .

[0146] S2. Determine the small displacement rotation of the key geometric features of each assembly surface, establish the mechanism error transfer matrix, solve the cumulative transfer function of the functional requirements, and analyze the mechanism accuracy. The details are as follows:

[0147] (1) Determine the coordinate system of each key geometric feature, specifically establish a Cartesian coordinate system:

[0148] In this embodiment, the geometric center of the contact surface between the bottom plate and the head plate is used as the coordinate origin to establish a global theoretical coordinate system, and local theoretical coordinate systems are established at the bottom surface of the head plate, the head plate hole, the inner and outer circles of the sleeve, and the positions of the pull rod, such as Figure 5 and Figure 6 As shown, They represent the coordinate systems of the upper surface of the base plate, the bottom surface of the head plate, the head plate hole, the outer circle of the sleeve, the inner circle of the sleeve, and the tie rod. Figure 5 and Figure 6 The dimensions are in mm.

[0149] (2) Establish the small displacement spin of the key geometric features of each assembly surface: According to the small displacement spin theory, the actual position of the key geometric features relative to the ideal position is changed by three rotation vectors C=[ ] and three translation vectors D=[ ] to indicate that, , , Respectively represent the small changes in rotation around the X-axis, Y-axis, and Z-axis. , , They represent the small changes in translation along the X-axis, Y-axis, and Z-axis respectively, and the total rotation is expressed as =[C,D]=[ ].

[0150] In this embodiment, the small variation and small displacement rotation under the tolerance coupling are expressed as follows: Figure 4 , Figure 7 , Figure 8 And as shown in Table 1. Figure 4 In the figure, the black coordinate system represents the ideal pose, and the red coordinate system represents the change of the actual pose relative to the ideal coordinate system. Figure 7 middle, represents the flatness tolerance, It represents the dimensional tolerance. The upper and lower red lines represent the upper and lower boundary surfaces of the plane variation respectively. Figure 8 middle, , Respectively represent the upper and lower limits of the cylindrical surface variation; Indicates the diameter of the cylinder; Indicates dimensional tolerance; Indicates the verticality tolerance; the black solid line indicates the ideal position of the cylindrical surface, and the black dotted line indicates the ideal position of the cylindrical axis; the blue solid line indicates the actual position of the cylindrical surface, and the blue dotted line indicates the actual position of the cylindrical axis; the red dotted line indicates the upper and lower limits of the variation of the cylindrical axis and the cylindrical surface, that is, Figure 8 shown and .

[0151] Table 1 Shape, degree of freedom and SDT expression corresponding to different geometric features

[0152]

[0153] (3) Establishing the mechanism error transfer matrix: Specifically, establishing the cumulative transfer matrix of the ideal position of key geometric features between coordinate systems and the cumulative transfer matrix of the actual pose of the key geometric features , calculated Matrix, since the change in the X-axis direction has no effect on the parallelism of the mechanism rod, it can be ignored. The specific mathematical expression omitting high-order small terms is as follows:

[0154]

[0155]

[0156]

[0157] The error accumulation transfer function of the functional required posture is obtained as follows:

[0158] F

[0159] get The value of can be used to analyze the accuracy of the mechanism.

[0160] S3. Functional relationship between fitting tolerance and actual variation range of small displacement screw. Specifically include the following:

[0161] (1) Determine the value range of each small displacement screw. In this embodiment, the maximum tolerance is preferably With minimum tolerance The interval between the two is equally divided into 200 intervals, and the normal distribution is selected as the tolerance distribution type. The Monte Carlo method is used for random sampling, such as Figure 3As shown, we get samples of independent variables and dependent variables, specifically, we get the sample matrix of the tolerance And the sample matrix of the actual variation range of the small displacement spinor In this embodiment, the number of samples extracted for each assembly feature is The more samples there are, the more accurate the calculation result will be, but the calculation speed will be slower.

[0162] (2) Using the RSM method, a quadratic polynomial without cross terms is used to construct the actual variation interval of each small displacement spinor and the tolerance, and then the least squares method is used to calculate the coefficients in the explicit function.

[0163] Finally, the functional relationship between the actual variation range of the small displacement spinor and the tolerance of each key geometric feature on the target position is obtained as follows:

[0164] 1) Base plate Corresponding actual change range: ;

[0165] 2) Bottom plate Corresponding actual change range: ;

[0166] 3) Bottom plate Corresponding actual change range: ;

[0167] 4) Bottom of head panel Corresponding actual change range: ;

[0168] 5) Bottom of head panel Corresponding actual change range: ;

[0169] 6) Head plate hole and Corresponding actual change range: ;

[0170] 7) Outer cylindrical surface of sleeve and Corresponding actual change range: ;

[0171] 8) Inner cylindrical surface of sleeve and Corresponding actual change range: ;

[0172] 9) Outer cylindrical surface of sleeve and Corresponding actual change range: ;

[0173] 10) Inner cylindrical surface of sleeve and Corresponding actual change range: ;

[0174] 11) Tie rod and Corresponding actual change range: ;

[0175] 12) Tie rod and Corresponding actual change range: .

[0176] The actual variation range of each small displacement spinor is as follows:

[0177] 1) , , ;

[0178] 2) , ;

[0179] 3) , ;

[0180] 4) , , , ;

[0181] 5) , , , ;

[0182] 6) , , , .

[0183] (3) The coefficient of determination (R²) was used to verify the accuracy of the fitted explicit function. The R² value was evaluated to be 0.78, which is between 0 and 1 and meets the fitting accuracy requirements.

[0184] S4. Establish the reliability function of tolerance and conduct reliability analysis; make initial allocation of each tolerance when the output function requirements are known; use the PSO algorithm to optimize the tolerance and determine the final tolerance value.

[0185] Specifically, assuming that the reliability of the function requirement accuracy is less than 0.16 mm shall not be less than 97.3%, according to the error accumulation transfer function obtained in step S2, the mechanism reliability function function and the reliability constraint inequality are established as shown in the following formulas:

[0186]

[0187]

[0188] (3) Using the Sobol global sensitivity analysis method, the sensitivity weight coefficient of each tolerance to the output accuracy can be obtained ; Use triangular fuzzy judgment matrix and fuzzy evaluation factor matrix to calculate the weight coefficient of processing difficulty The triangular fuzzy judgment matrix and fuzzy evaluation factor matrix are calculated according to Table 2 and Table 3, respectively. In Table 2 and Table 3, and The distance between indicates the degree of blur. It indicates the processing difficulty of the latter factor relative to the former factor.

[0189] Table 2 Triangular fuzzy judgment matrix

[0190]

[0191] Table 3 Fuzzy evaluation factor matrix

[0192]

[0193] The triangular fuzzy judgment matrix is ​​used to analyze the processing difficulty weight coefficient of each part feature tolerance. First, the fuzzy judgment matrix is ​​constructed and the median matrix is ​​extracted. And Perform a consistency check as follows:

[0194]

[0195]

[0196] In the above formula, Represents the consistency index, express The maximum eigenvalue of express The dimension of represents the random consistency ratio, represents the average consistency index. In this embodiment, the median matrix The maximum eigenvalue of , , , ,in, It is calculated based on the median matrix. According to Table 4 The value can be obtained by looking up the table, and after calculation, it can be known that , it can be considered that the judgment matrix has satisfactory consistency. The weight coefficients of the difficulty of machining each tolerance are calculated and shown in Table 5.

[0197] Table 4 value

[0198]

[0199] Table 5 Weight coefficients of machining difficulty for each tolerance

[0200]

[0201] According to the sensitivity weight coefficient of tolerance to output accuracy and the weight coefficient of processing difficulty, the weight of each tolerance allocation is obtained. , weights are assigned to each tolerance, so that each tolerance can be initially assigned when the output functional requirements are known.

[0202] The total tolerance machining cost is:

[0203]

[0204] The cost of product quality loss is:

[0205] The total cost is:

[0206] The tolerance processing cost function of each key geometric feature is used as the optimization objective function, and the reliability and tolerance value range are used as constraints. The particle swarm algorithm (PSO) is used to optimize the tolerance to obtain the final tolerance value. The results are shown in Table 6.

[0207] Table 6 Final tolerance values

[0208]

[0209] S5. Based on the final tolerance value obtained in step S4, the processing mechanism is designed.

[0210] The above only describes the basic principles and preferred embodiments of the present invention. Those skilled in the art may make many changes and improvements based on the above description, and these changes and improvements should fall within the protection scope of the present invention.

Claims

1. A method for precision analysis and tolerance allocation of a multi-tolerance coupling mechanism, characterized in that: The steps include: S1. Analyze the assembly structure of the mechanism to be processed: analyze the component composition of the mechanism and the assembly relationship between the various parts, and determine the key geometric features that affect the functional requirements; S2. Determine the small displacement spin of the key geometric features of each assembly surface, establish the mechanism error transfer matrix, solve the cumulative transfer function of the functional requirements posture error, and analyze the mechanism accuracy; S3, the functional relationship between the fitting tolerance and the actual variation range of the small displacement screw; S4. Establish the reliability function of tolerance and conduct reliability analysis; make initial allocation of each tolerance when the output function requirements are known; use PSO algorithm to optimize the tolerance and determine the final tolerance value; S5. Based on the final tolerance value obtained in step S4, the processing mechanism is designed.

2. The method for precision analysis and tolerance allocation of multi-tolerance coupling mechanism according to claim 1, characterized in that: Step S1 includes the following: S11. Analyze the component composition of the mechanism and the assembly relationship between the various components; S12, finding the path of tolerance transfer in the process of parts assembly and establishing the tolerance transfer topology structure; S13. According to the assembly sequence of parts, the features that affect the functional requirements during the assembly process are taken as the key geometric features of the mechanism to be analyzed.

3. The method for precision analysis and tolerance allocation of multi-tolerance coupling mechanism according to claim 2, characterized in that: In step S13, the key geometric features of the structure to be analyzed are described as follows: ）（1） In formula (1), represents the number of key geometric features, where , ··· The specific expressions are as follows: =（ 、 ··· ）（2） =（ 、 ··· ）（3） ··· =（ 、 ··· ）（4） Formula (2)-Formula (4), , ··· Respectively represent the number of tolerances contained in each key geometric feature.

4. The method for precision analysis and tolerance allocation of multi-tolerance coupling mechanism according to claim 1, characterized in that: Step S2 includes the following: S21, determining the coordinate system of each key geometric feature; S22, establish the small displacement screw of the key geometric features of each assembly surface; S23, determine the expression of small displacement spins corresponding to different key geometric features; S24, determine the constraint inequality of small displacement screw under the action of tolerance; S25, establishing a homogeneous coordinate transformation matrix mathematical model of each key geometric feature; S26. Establish the mechanism error transfer matrix and solve the cumulative transfer function of the functional required posture error to analyze the mechanism accuracy.

5. The method for precision analysis and tolerance allocation of multi-tolerance coupling mechanism according to claim 4, characterized in that: Step S2 specifically includes the following: S21. Determine the coordinate system of each key geometric feature, specifically establish a Cartesian coordinate system: according to the assembly order of the parts, establish a global theoretical coordinate system with the appropriate position of the key geometric feature of the initial assembly of the mechanism as the origin, and establish a local theoretical coordinate system with the appropriate position of the key geometric feature of the remaining error input as the origin, wherein the appropriate position refers to the position that is convenient for calculating the cumulative error of the functional requirement posture, and the remaining error refers to the error of the key geometric feature other than the initial assembly key geometric feature; S22. Establish the small displacement spin of the key geometric features of each assembly surface: According to the small displacement spin theory, the actual position of the key geometric features relative to the ideal position is changed by three rotation vectors C=[ ] and three translation vectors D=[ ] to indicate that, , , Respectively represent the small changes in rotation around the X-axis, Y-axis, and Z-axis. , , They represent the small changes in translation along the X-axis, Y-axis, and Z-axis respectively, and the total rotation is expressed as =[C,D]=[ ]; S23. Determine the expression of small displacement spin corresponding to different key geometric features: The key geometric features include plane, cylinder, axis and sphere. Assume that the degree of freedom of the plane is , then the small displacement spin corresponding to the plane is , assuming the degree of freedom of the cylindrical surface is , , then the small displacement spin corresponding to the cylindrical surface is , assuming the degree of freedom of the axis is , then the small displacement rotation corresponding to the axis is , assuming the degrees of freedom of the sphere is , then the small displacement spin corresponding to the sphere is ; S24, determine the constraint inequality of the small displacement screw under the effect of tolerance: constrain the variation range of the small displacement screw with the tolerance size, and set the tolerance of each key geometric feature described in step S23 to be , the constraint inequalities corresponding to the plane, cylinder, axis and sphere are respectively expressed as formula (5), formula (6), formula (7) and formula (8), as follows: ， ， （5） ， ， ， （6） ， ， ， （7） （8） Formula (5)-Formula (7), represents the length of the plane, represents the width of the plane, represents the length of the cylindrical surface, Indicates the length of the axis; S25. Establish a mathematical model of homogeneous coordinate transformation matrix of each key geometric feature: Use homogeneous coordinate transformation theory to establish a homogeneous coordinate transformation matrix, the expression is as follows: （9） In formula (9), represents the rotation transformation matrix, represents the translational change matrix, is 1, is [0, 0, 0]; S26. Establish the mechanism error transfer matrix and solve the cumulative transfer function of the functional requirements posture error. is the cumulative transfer matrix of the ideal pose of the key geometric features, is the cumulative transfer matrix of the actual pose of the key geometric features, is the cumulative error transfer matrix of the actual posture relative to the ideal posture, The pose matrix of the functional requirement pose in the local theoretical coordinate system, is the cumulative error matrix of the actual functional requirement posture relative to the ideal functional requirement posture. The specific expression is as follows: （10） （11） （12） （13） （14） （15） Formula (10)-Formula (15), Represents the ideal pose transformation matrix of two key geometric features at the junction, Represents the transformation matrix of the actual pose of each key geometric feature relative to the ideal pose, express The number of express The number of , , are the coordinates in the X-axis, Y-axis, and Z-axis directions respectively. , , They are the errors of the actual functional requirement posture relative to the ideal functional requirement posture in the X-axis, Y-axis, and Z-axis directions, all of which contain small displacement spinors; The error accumulation transfer function of the functional requirement posture is expressed as: （16） By calculating formula (16) The value of is used to analyze the accuracy of the mechanism.

6. The method for precision analysis and tolerance allocation of multi-tolerance coupling mechanism according to claim 5, characterized in that: Step S3 includes the following: S31. Using the Monte Carlo random sampling method, samples of independent variables and dependent variables are obtained, wherein the independent variable refers to the tolerance, and the dependent variable refers to the actual variation range of the small displacement spinor; S32, using the RSM method, a quadratic polynomial without cross terms is used to fit the explicit function of the actual variation range and tolerance of each small displacement spinor; S33, verifying the accuracy of the fitted explicit function: if the error exceeds a preset threshold, return to step S31 to refit; otherwise, execute step S4.

7. The method for precision analysis and tolerance allocation of multi-tolerance coupling mechanism according to claim 6, characterized in that: Step S3 specifically includes the following: S31, determine the value range of each small displacement screw, and set the maximum tolerance With minimum tolerance The two are divided equally intervals, select normal distribution as the tolerance distribution type, use Monte Carlo random sampling to obtain samples of independent variables and dependent variables, specifically, obtain the sample matrix of tolerance And the sample matrix of the actual variation range of the small displacement spinor ; S32, through the RSM method, the actual change interval of each small displacement spinor is constructed using a quadratic polynomial without cross terms The explicit function between and tolerance is expressed as follows: （17） In formula (17), , , All represent the coefficients to be determined. Indicates A tolerance constraining small displacement screws, Indicates the number of constraints on a small displacement screw tolerance; Use the least squares method to calculate the coefficients to be determined , , , the coefficient to be determined , , The three are expressed as , the expression is as follows: （18） In formula (18), express The transposed matrix of and They are respectively expressed as follows: （19） （20） In formula (19) and formula (20), , , , , , They represent the first tolerance value of the first interval constraint small displacement spinor, the first interval constraint small displacement spinor tolerance value, the first tolerance value of the second interval constraint small displacement spinor, the first tolerance value of the second interval constraint small displacement spinor Tolerance value, The first tolerance value, the second tolerance value, Interval Constrained Small Displacement Screw Tolerance values, , , They represent the actual variation range of the small displacement spinor corresponding to the first interval tolerance value, the actual variation range of the small displacement spinor corresponding to the second interval tolerance value, and the The actual variation range of the small displacement screw corresponding to the interval tolerance value; The solved Replacement tolerance , and obtain the actual variation range of the small displacement spinor; S33. Use mean square error MSE or determination coefficient R² to verify the accuracy of the fitted explicit function: if the error exceeds the preset threshold, return to step S31 and refit; otherwise, the relationship between the tolerance and the output accuracy is obtained, and then execute step S4.

8. The method for precision analysis and tolerance allocation of multi-tolerance coupling mechanism according to claim 7, characterized in that: Step S4 includes the following: S41. Based on formulas (16) and (17), a tolerance reliability function is established to perform reliability analysis. S42. The sensitivity of each tolerance to the output accuracy is calculated by using the Sobol global sensitivity analysis method, and the processing difficulty of each part feature is analyzed by using a triangular fuzzy judgment matrix. Then, the weight of each tolerance allocation is calculated, so that each tolerance is initially allocated when the output function requirements are known. S43. Taking the error-cost function as the optimization objective function, the reliability and tolerance values ​​as constraints, the PSO algorithm is used to optimize the tolerance and determine the final tolerance value.

9. The method for precision analysis and tolerance allocation of multi-tolerance coupling mechanism according to claim 8, characterized in that: Step S4 specifically includes: S41. Based on formulas (16) and (17), establish the tolerance reliability function and conduct reliability analysis: Assume that the functional requirement accuracy is The reliability should not be less than , according to formula (16) the error accumulation transfer function is , establish the mechanism reliability function and reliability constraint inequalities are expressed as follows: （21） （22） （23） Formula (21) represents the mechanism reliability function, formula (22) represents the reliability constraint inequality; in formula (23), represents the indicative function, when >0, ;when <0, ; express The joint probability density function involving the error variables, is the independent variable of formula (23); S42, according to the error accumulation transfer function obtained And the actual variation range of each small displacement spinor , using the Sobol global sensitivity analysis method, the sensitivity weight coefficient of each tolerance to the output accuracy is obtained ,in , the calculation formula is: The first-order impact index formula is as follows: （24） （25） （26） Formula (24)-Formula (26), represents the independent variable, represents the variance of the dependent variable, and All represent independent variable matrices, Represented by matrix Middle Column substitution matrix Middle The resulting matrix is , , Respectively represent matrices ,matrix ,matrix The function value of represents the number of first-order influence indices, Indicates the number of function values; The triangular fuzzy judgment matrix is ​​used to analyze the processing difficulty weight coefficient of each part feature tolerance. First, the fuzzy judgment matrix is ​​constructed and the median matrix is ​​extracted. And Perform a consistency check as follows: （27） （28） In formula (27) and formula (28), Represents the consistency index, express The maximum eigenvalue of express The dimension of represents the random consistency ratio, represents the average consistency index; Constructing fuzzy evaluation factor matrix , and calculate the adjustment judgment matrix , and finally calculate the processing difficulty weight coefficient , the calculation formula is as follows: （29） （30） （31） In formula (30) and formula (31), represents the evaluation index weight, Representation Matrix No. Line Column elements, Representation Matrix The number of columns; According to the calculated and , and then find the weights of each tolerance allocation as follows: （32） Assign weights to each tolerance, so that each tolerance can be initially assigned when the output functional requirements are known; S43, taking the tolerance processing cost function as the optimization objective function, the reliability and tolerance value as the constraint conditions, and using the PSO algorithm to optimize the tolerance to determine the final tolerance value, as follows: There are at least 6 tolerance processing cost models, which are shown as follows: (1) The function of the plane dimension tolerance processing cost model is: （33） (2) The function of the flatness tolerance processing cost model is: （34） (3) The function of the inner hole size tolerance processing cost model is: （35） (4) The function of the external circle dimension tolerance processing cost model is: （36） (5) The function of the position tolerance processing cost model is: （37） (6) The function of the verticality tolerance processing cost model is: （38）。

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