Matching method for assembling key transmission mechanism dimension chain of RV speed reducer

Abstract

The invention provides a matching method for assembling a dimension chain of a key transmission mechanism of an RV speed reducer. The method comprises the following steps: establishing a size chain for a first-stage speed reduction transmission mechanism and a second-stage speed reduction transmission mechanism of an RV speed reducer, performing size measurement on key parts, and establishing a part size database; taking the closed dimension chain deviation of the first-stage speed reduction transmission mechanism and the second-stage speed reduction transmission mechanism as an optimal solution objective function; and the optimal combination of the sun gear, the planet gear, the cycloidal gear and the pin wheel housing is realized through a rapid elite multi-objective genetic algorithm. According to the method, optimal matching combination of key parts of the RV speed reducer is achieved, it is guaranteed that the assembling errors of the RV speed reducer are reduced in the assembling process, and theoretical support is provided for manufacturing enterprises for assembling the high-precision RV speed reducer in batches.

Description

Technical Field

[0001] The invention relates to the technical field of RV reducer design and assembly, and in particular to a method for selecting and matching primary and secondary reduction transmission parts. Background Art

[0002] As a key component of industrial robots, the demand for high-precision RV reducers is increasing. However, the efficiency of installing finished products by manual selection and installation in the assembly process is not particularly ideal. Therefore, on the basis of improving the processing accuracy, it is also necessary to improve the assembly efficiency and assembly accuracy of RV reducers.

[0003] At present, the selection method of RV reducer using genetic algorithm is mainly optimized in terms of quality, transmission accuracy, transmission efficiency, production and geometric errors of core components. There is no optimization from the assembly relationship between parts, resulting in low assembly efficiency and accuracy. In addition, the selection method of RV reducer is mainly concentrated in the secondary reduction mechanism. Therefore, in order to make the selection of RV reducer more comprehensive, it is necessary to consider the key transmission parts of primary and secondary reduction.

[0004] In order to solve the above technical defects and improve the batch assembly efficiency of RV reducer related manufacturing enterprises, under the existing parts processing capabilities, high-precision parts and assembly conditions, the key parts in the primary and secondary reduction transmission mechanisms of the RV reducer are selected and assembled to improve the assembly efficiency and assembly accuracy of the RV reducer. Therefore, a selection method for the assembly of the dimension chain of the key transmission mechanism of the RV reducer is invented. Summary of the invention

[0005] The purpose of the present invention is to provide a method for selecting and assembling a dimension chain of a key transmission mechanism of an RV reducer, so as to ensure that the RV reducer manufacturing enterprise can improve the assembly efficiency of the enterprise while ensuring that the product accuracy is within an allowable range during the assembly process.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] Establishing a database of the dimension chain of key transmission mechanisms includes the following steps:

[0008] By measuring the dimensions of the parts in the key transmission mechanism of the RV reducer, the actual dimensions of the parts are obtained, and the dimension chain of the key transmission mechanism is established; the parts of the key transmission mechanism include the sun gear and planetary gear in the first-stage reduction, and the cycloid gear and pinion gear in the second-stage reduction; according to the assembly dimension chain relationship of the first-stage reduction and the second-stage reduction transmission, the dimension chain closed loop deviation is established; the dimension chain deviation of the first-stage reduction is δ1, and the assembly dimension chain of the second-stage reduction is δ2, δ3, δ4;

[0009] Primary transmission assembly dimension chain deviation:

[0010] δ1=r1+r2+e1-L2-e(1)

[0011] Among them, e represents the eccentricity of the cycloid wheel; e1 represents the eccentricity of the eccentric shaft; r1 represents the pitch circle radius of the involute gear; r2 represents the pitch circle radius of the input shaft; L2 represents the distance between the geometric center of the cycloid wheel bearing hole and the geometric center of the cycloid wheel center circle.

[0012] Secondary transmission assembly dimension chain deviation:

[0013]

[0014] Among them, r z Indicates the radius of the needle teeth; R z Indicates the center circle radius of the pinion housing; r f Indicates the root circle radius of the cycloid gear; r a It represents the radius of the top circle of the cycloid wheel; e1 represents the eccentricity of the eccentric shaft; L1 represents the distance between the geometric center of the center circle of the pinion housing and the geometric center of the bearing hole on the planet carrier.

[0015] The special fixture is fixed and placed directly below the detection head of the altimeter. When measuring, the cycloid wheel can be quickly placed on the special fixture, and the altimeter measures the overall height. The measured value is transmitted to the computer through the RS232 output interface of the altimeter. The actual measured dimension relationship diagram is as follows:

[0016]

[0017] Among them, a represents the size of the fixed gauge block on the fixture (i.e., the width of the rectangular gauge block), a1 represents the size of the part fixed on the fixture to determine the position of the cycloidal wheel (i.e., the shortest distance between the bottom edge of the rectangular gauge block and the needle teeth); θ1 represents the pitch angle of the teeth on the top of the cycloidal wheel; θ2 represents the pitch angle of the teeth under the cycloidal wheel.

[0018] According to formula (3), the radius r of the cycloid gear root circle can be derived: f And the radius of the cycloid pinwheel tooth tip circle r a :

[0019]

[0020] Among them, r p Indicates the radius of the center circle of the pinion teeth meshing with the cycloid wheel; r rp Indicates the radius of the grinding wheel tooth when machining the cycloid wheel; Δr p Indicates the modification amount of the radius of the center circle of the needle teeth; Δr rp Indicates the amount of grinding wheel arc radius modification.

[0021] Determine the constraints: The closed loop deviation must meet the closed loop tolerance while the fluctuation of the geometric closed loop deviation must be within the specified range. The fluctuation of the closed loop deviation is determined based on the variance of several closed loop deviations:

[0022]

[0023] The constraints for RV reducer assembly are:

[0024]

[0025] Among them, δ represents the minimum actual deviation of a reducer assembly, that is, δ = min{δ1,δ2,δ3,δ4}; ω represents the maximum allowable fluctuation of the closed loop deviation; σ1 and σ2 represent the upper and lower tolerances of the closed loop of a reducer assembly, respectively.

[0026] Objective function determination

[0027] The sun gear, planetary gear, pin gear and cycloid gear are randomly assembled according to the model pairing and form a combination. And a set of assembly schemes divided by model is formed according to the combination. The average assembly accuracy of all the formed assemblies and the residual parts rate that do not meet the assembly accuracy requirements are used as the objective function of the selection model. The average assembly accuracy function can be expressed as:

[0028]

[0029] Among them, δ j represents the minimum actual deviation of the jth reducer assembly (determined according to equations (5) and (6)).

[0030] The remaining parts rate (the rate of parts that do not meet the assembly accuracy) can be expressed as:

[0031]

[0032] Among them, n represents the number of reducers that meet the assembly accuracy in a set of assembly plans; N represents the number of reducers that can be assembled in a set of assembly plans in theory.

[0033] The final objective function can be expressed as:

[0034]

[0035] According to the constraints and objective function, the final matching model is determined as follows:

[0036]

[0037] Among them, y represents the objective function composed of two objective component functions minF1 and minF2.

[0038] The matching algorithm is designed based on the fast elite multi-objective genetic algorithm (NSGAII). The specific matching algorithm execution process is as follows: Figure 4 The specific implementation process is as follows:

[0039] ① According to the structural characteristics of the RV reducer, the parts of a reducer include: 1 pin gear housing, 2 cycloid wheels, 2 eccentric shafts, and 1 planet carrier. Each part is coded with a non-negative integer. When assembling N reducers at the same time, the following parts need to be prepared: N pin gear housings, 2N cycloid wheels, 2N eccentric shafts, and N planet carriers. The coding used in the present invention uses 1, 2, ..., N for part numbering. The present invention uses a set of assembly schemes to theoretically assemble 20 RV reducers (N = 20).

[0040] ② Randomly select and combine the parts according to the assembly requirements to generate the initial population; call the part sizes in the database and judge whether the part combination is reasonable based on the constraints of formula (6); calculate the objective function of the initial population that meets the constraints (i.e., calculate formulas (9) and (10)).

[0041] ③ Repeat step ② M times to obtain a population of size M (M chromosomes, ie, M assembly methods). The present invention sets the population size to M=40.

[0042] ④ Perform a fast non-dominated sort on the obtained M chromosomes and use them as the initial population P n .

[0043] ⑤ Perform rotation, crossover, and mutation operations on the M chromosomes in the initial population to generate a population size of M offspring Q n The present invention randomly selects a partial number sequence from two randomly selected parent chromosomes, and sorts the numbers selected in one chromosome according to the sequence of the numbers selected in the other chromosome to obtain two new chromosomes. The new chromosomes are compared with the parent chromosomes in sequence. If they are the same, they continue to be numbered. If they are different, they are used as offspring chromosomes. Repeat the operation to obtain M offspring chromosomes to form an offspring population Q n .

[0044] ⑥ Parent P n With offspring Q n Merge to get a population R of size 2M n , perform fast non-dominated sorting and crowding calculation, and select the first M combinations as the new parent population P n+1 .

[0045] ⑦ Repeat steps ⑤ and ⑥. After N iterations (i.e., iterations according to the number of reducer assemblies), the algorithm is terminated when the optional combinations of all parts have been calculated, and the optimal non-dominated solution is obtained and the results are output to achieve the purpose of optimizing the optional combination of the key transmission of the RV reducer.

[0046] In summary, the present invention measures the dimensions of the key parts of the RV reducer and establishes the variance of the closed dimension chain of the sun gear-planetary gear, cycloid gear-pin gear housing-pin gear as the objective function; realizes the optimal matching of parts through a fast elite multi-objective genetic algorithm; and solves the optimal matching combination with the fluctuation of the closed deviation and the assembly tolerance range as constraints to achieve the purpose of reducing the assembly error and improve the transmission accuracy of the finished RV reducer. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 Schematic diagram of primary assembly dimension chain

[0048] Figure 2 Schematic diagram of secondary assembly dimension chain

[0049] Figure 3 Schematic diagram of actual measurement of the two-stage reduction mechanism

[0050] Figure 4 Matching algorithm execution flow chart

[0051] Figure 5 Fast Non-Dominated Sorting Flowchart

[0052] Figure 6 Cross diagram

[0053] Figure 7 Comparison chart of manual combination and selection method combination DETAILED DESCRIPTION

[0054] The present invention is further described below with reference to the accompanying drawings and specific implementations:

[0055] The purpose of the present invention is to provide a method for selecting and assembling a dimension chain of a key transmission mechanism of an RV reducer, so as to ensure that the RV reducer manufacturing enterprise can improve the assembly efficiency of the enterprise while ensuring that the product accuracy is within an allowable range during the assembly process.

[0056] To achieve the above object, the present invention provides the following technical solutions:

[0057] Establishing a database of the dimension chain of key transmission mechanisms includes the following steps:

[0058] S1. By measuring the dimensions of the parts in the key transmission mechanism of the RV reducer, the actual dimensions of the parts are obtained, and the dimension chain of the key transmission mechanism is established; the parts of the key transmission mechanism include the sun gear and planetary gear in the first-stage reduction, and the cycloid gear and pinion gear in the second-stage reduction; according to the assembly dimension chain relationship of the first-stage reduction and the second-stage reduction transmission, the dimension chain closed loop deviation is established; the dimension chain deviation of the first-stage reduction is δ1, and the assembly dimension chain of the second-stage reduction is δ2, δ3, δ4;

[0059] S2. According to Figure 1 The primary assembly dimension chain diagram can establish the primary transmission assembly dimension chain deviation:

[0060] δ1=r1+r2+e1-L2-e(11)

[0061] Among them, e represents the eccentricity of the cycloid wheel; e1 represents the eccentricity of the eccentric shaft; r1 represents the pitch circle radius of the involute gear; r2 represents the pitch circle radius of the input shaft; L2 represents the distance between the geometric center of the cycloid wheel bearing hole and the geometric center of the cycloid wheel center circle.

[0062] S3. According to Figure 2 As shown in the schematic diagram of the secondary assembly dimension chain, O b Indicates the geometric center of the center circle of the pinion housing; O g Indicates the geometric center of the cycloid wheel center circle; O a Indicates the geometric center of the bearing hole on the cycloid wheel; O c Indicates the geometric center of the bearing hole on the planet carrier. Establish the secondary transmission assembly dimension chain deviation:

[0063]

[0064] Among them, r z Indicates the radius of the needle teeth; R z Indicates the center circle radius of the pinion housing; r f represents the root circle radius of the cycloid gear; represents the top circle radius of the cycloid gear; e1 represents the eccentricity of the eccentric shaft; L1 represents the distance between the geometric center of the center circle of the pinion gear housing and the geometric center of the bearing hole on the planet carrier.

[0065] S4. Fix the special fixture just below the altimeter detection head. When measuring, the cycloid wheel can be quickly placed on the special fixture. The altimeter measures the overall height. The measured value is transmitted to the computer through the RS232 output interface of the altimeter. The actual measurement is performed by Figure 3 As shown. Figure 3 The schematic diagram of the dimensional relationship during measurement shows:

[0066]

[0067] Among them, according to Figure 3 As shown, a represents the size of the fixed gauge block on the fixture (i.e., the width of the rectangular gauge block), a1 represents the size of the part fixed on the fixture to determine the position of the cycloidal wheel (i.e., the shortest distance between the bottom edge of the rectangular gauge block and the needle teeth); θ1 represents the pitch angle of the teeth on the top of the cycloidal wheel; θ2 represents the pitch angle of the teeth under the cycloidal wheel.

[0068] According to formula (13) and Figure 3 The geometric relationship can be used to deduce the radius r of the cycloid gear root circlef And the radius of the cycloid pinwheel tooth tip circle r a :

[0069]

[0070] Among them, r p Indicates the radius of the center circle of the pinion teeth meshing with the cycloid wheel; r rp Indicates the radius of the grinding wheel tooth when machining the cycloid wheel; Δr p Indicates the modification amount of the radius of the center circle of the needle teeth; Δr rp Indicates the amount of grinding wheel arc radius modification. S5.(1) Determine the constraint conditions: The closed loop deviation must meet the closed loop tolerance while the fluctuation of the geometric closed loop deviation must be within the specified range. The fluctuation of the closed loop deviation is determined based on the variance of several closed loop deviations:

[0071]

[0072] The constraints for RV reducer assembly are:

[0073]

[0074] Among them, δ represents the minimum actual deviation of a reducer assembly, that is, δ = min{δ1,δ2,δ3,δ4}; ω represents the maximum allowable fluctuation of the closed loop deviation; σ1 and σ2 represent the upper and lower tolerances of the closed loop of a reducer assembly, respectively.

[0075] (2) Determination of objective function

[0076] The sun gear, planetary gear, pinion gear housing and cycloid gear are randomly assembled according to the model pairing and form a combination. A set of assembly schemes divided by model is formed according to the combination. The average assembly accuracy of all the formed assemblies and the residual parts rate that do not meet the assembly accuracy requirements are used as the objective function of the selection model. The average assembly accuracy function can be expressed as:

[0077]

[0078] Among them, δ j represents the minimum actual deviation of the jth reducer assembly (determined according to equations (15) and (16)).

[0079] The remaining parts rate (the rate of parts that do not meet the assembly accuracy) can be expressed as:

[0080]

[0081] Among them, n represents the number of reducers that meet the assembly accuracy in a set of assembly plans; N represents the number of reducers that can be assembled in a set of assembly plans in theory.

[0082] The final objective function can be expressed as:

[0083]

[0084] According to the constraints and objective function, the final matching model is determined as follows:

[0085]

[0086] Among them, y represents the objective function composed of two objective component functions minF1 and minF2.

[0087] S6. Design of matching algorithm based on fast elite multi-objective genetic algorithm (NSGA II). The specific matching algorithm execution process is as follows: Figure 4 The specific implementation process is as follows:

[0088] S6.1 According to the structural characteristics of the RV reducer, the parts of a reducer include: 1 pinion housing, 2 cycloid wheels, 2 eccentric shafts, and 1 planet carrier. Each part is encoded with a non-negative integer. When assembling N reducers at the same time, the following parts need to be prepared: N pinion housings, 2N cycloid wheels, 2N eccentric shafts, and N planet carriers. The coding used in the present invention uses 1, 2, ..., N to number the parts. The present invention uses a set of assembly schemes that can theoretically assemble 20 RV reducers (N=20). The assembly combination is numbered with the original parts provided by the manufacturer. The specific numbering is as follows:

[0089]

[0090] S6.2 randomly selects and combines the parts according to the assembly requirements to generate an initial population; calls the part sizes in the database and determines whether the part combination is reasonable based on the constraints of formula (16); calculates the objective function of the initial population that meets the constraints (i.e., calculates formulas (19) and (20)).

[0091] S6.3 Repeat step (S6.2) M times to obtain a population of size M (M chromosomes, ie, M assembly methods). The present invention sets the population size to M=40.

[0092] S6.4 Perform a fast non-dominated sort on the obtained M chromosomes to form an initial population P n .

[0093] Among them according to Figure 5 It can be obtained that the specific implementation of the algorithm flow for fast non-dominated sorting of each chromosome is as follows:

[0094] ①Define an empty set S;

[0095] ② For each individual p in the population, compare p with other individuals one by one. If any individual that dominates p appears, p is ignored; if there is no individual that dominates p in the population, p is stored in the set S;

[0096] ③ Take the set S as the set of first-level (highest-level) non-dominated individuals and assign a

[0097] The same non-dominated series Rank = 1;

[0098] ④ Continue to perform the above classification operation on the individuals other than those in the set S and determine their corresponding non-dominated Rank (rank increasing) until all individuals are classified.

[0099] S6.5 performs rotation, crossover, and mutation operations on the M chromosomes in the initial population to generate a population size of M offspring Q n The present invention randomly selects a partial number sequence from two randomly selected parent chromosomes, sorts the numbers selected in one chromosome according to the sequence of the numbers selected in the other chromosome, and obtains two new chromosomes. The new chromosomes are compared with the parent chromosomes, and the new chromosomes that are different are used as offspring chromosomes. Repeat the operation to obtain M offspring chromosomes to form an offspring population Q n The cross diagram is as follows Figure 6 shown.

[0100] S6.6 Parent P n With offspring Q n Merge to get a population R of size 2M n , perform fast non-dominated sorting and crowding calculation, and select the first M combinations as the new parent population P n+1 .

[0101] S6.7 Repeat operation steps (S6.5) and (S6.6). After N iterations (i.e., iterations based on the number of reducer assemblies), the algorithm is terminated when all the optional combinations of parts have been calculated, and the optimal non-dominated solution is obtained and the result is output to achieve the purpose of optimizing the optional combination of the key transmission of the RV reducer.

[0102] According to the above steps, the algorithm was written in MATLAB, and the matching results of a group (N=20) were obtained by using the matching algorithm and random simulated artificial combination. Figure 7 It can be seen that in the manual matching combination, the gaps between the assemblies fluctuate greatly, and the difference between the maximum and minimum assembly gaps is 18.3um; while in the combination obtained by the matching algorithm, the fluctuations between the assemblies are small, and the difference between the maximum and minimum assembly gaps is 3.8um.

[0103] In summary, the present invention measures the dimensions of the key parts of the RV reducer and establishes the variance of the closed dimension chain of the sun gear-planetary gear, cycloid gear-pin gear housing-pin gear as the objective function; realizes the optimal matching of parts through a fast elite multi-objective genetic algorithm; and solves the optimal matching combination with the fluctuation of the closed deviation and the assembly tolerance range as constraints to achieve the purpose of reducing the assembly error and improve the transmission accuracy of the finished RV reducer.

Claims

1. A method for selecting and assembling the dimension chain of the key transmission mechanism of an RV reducer, characterized in that: The steps include: S1. Establish a database of key transmission mechanism dimension chains By measuring the dimensions of the parts in the key transmission mechanism of the RV reducer, the actual dimensions of the parts are obtained, and the dimension chain of the key transmission mechanism is established; The key transmission mechanism parts include the sun gear and planetary gear in the first-stage reduction gear, and the cycloid gear and pinion gear in the second-stage reduction gear. According to the assembly dimension chain relationship of the first-stage reduction gear and the second-stage reduction gear, the dimension chain closed loop deviation is established. The dimension chain deviation of the first-stage reduction gear is δ1, and the dimension chain of the second-stage reduction gear assembly is δ2, δ3, and δ4. The sun gear meshes with two involute gears at the same time. The two involute gears are installed symmetrically at 180°. The dimension chain of the primary reducer is established based on the sun gear and one involute gear. The assembly deviation of the dimension chain of the primary reducer is expressed as: δ1=r1+r2+e1-L2-e(1) Wherein, e represents the eccentricity of the cycloid wheel; e1 represents the eccentricity of the eccentric shaft; r1 represents the pitch circle radius of the involute gear; r2 represents the pitch circle radius of the input shaft; L2 represents the distance between the geometric center of the cycloid wheel bearing hole and the geometric center of the cycloid wheel center circle; The assembly deviation of the dimension chain of the secondary reduction is expressed as: Among them, r z Indicates the radius of the needle teeth; R z Indicates the center circle radius of the pinion housing; r f Indicates the root circle radius of the cycloid gear; r a represents the radius of the tooth top circle of the cycloid wheel; e1 represents the eccentricity of the eccentric shaft; L1 represents the distance between the geometric center of the center circle of the pinion gear housing and the geometric center of the bearing hole on the planet carrier; For the dimension measurement in each dimension chain, the secondary reduction transmission structure is measured by a gauge block fixture; according to the geometric relationship during measurement, it is obtained: Where a represents the size of the fixed gauge block on the fixture; a1 represents the size of the part fixed on the fixture to determine the position of the cycloid wheel; θ1 represents the pitch angle of the teeth on the top of the cycloid wheel; θ2 represents the pitch angle of the teeth under the cycloid wheel; According to formula (3) and the geometric relationship during measurement, the radius of the cycloid pinwheel tip circle r is derived: a and tooth root radius r f : Among them, r p Indicates the radius of the center circle of the pinion teeth meshing with the cycloid wheel; r rp Indicates the radius of the grinding wheel tooth when machining the cycloid wheel; Δr p Indicates the modification amount of the radius of the center circle of the needle teeth; Δr rp Indicates the amount of grinding wheel arc radius modification; S2. Establishment of matching model (1) Determine the constraints: The closed loop deviation must meet the closed loop tolerance while the fluctuation of the geometric closed loop deviation must be within the specified range; the fluctuation of the closed loop deviation is determined based on the variance of several closed loop deviations: The constraints for RV reducer assembly are: Among them, δ represents the minimum actual deviation of a reducer assembly, that is, δ = min{δ1,δ2,δ3,δ4}; ω represents the maximum allowable fluctuation of the closed loop deviation; σ1 and σ2 represent the upper and lower tolerances of the assembly closed loop respectively; (2) Determination of objective function The average assembly accuracy function is expressed as: Among them, δ j represents the minimum actual deviation of the jth reducer assembly. According to equations (5) and (6) Decide; The remaining parts rate is expressed as: Where n represents the number of reducers that meet the assembly accuracy in a set of assembly solutions; N represents the number of reducers that can be assembled in a set of assembly solutions in theory; The final objective function is expressed as: According to the constraints and objective function, the final matching model is determined as follows: Among them, y represents the objective function composed of two objective component functions, minF1 and minF2; S3. Design of matching algorithm based on fast elite multi-objective genetic algorithm S3.1 According to the structural characteristics of the RV reducer, the parts of a reducer include: 1 pin gear housing, 2 cycloid wheels, 2 eccentric shafts, and 1 planet carrier; each part is encoded with a non-negative integer; when assembling N reducers at the same time, the parts required are: N pin gear housings, 2N cycloid wheels, 2N eccentric shafts, and N planet carriers; Use 1, 2, ..., N for part numbering; N = 20; S3.2 randomly selects and combines the parts according to the assembly requirements to generate an initial population; calls the part sizes in the database and determines whether the part combination is reasonable based on the constraints of formula (6); calculates the objective function of the initial population that meets the constraints, that is, calculates formulas (9) and (10); S3.3 Repeat step (S3.2) M times to obtain a population of size M (M chromosomes, i.e., M assembly methods); set the population size to M=40; S3.4 Perform a fast non-dominated sort on the obtained M chromosomes and use them as the initial population P n ; S3.5 performs rotation, crossover, and mutation operations on the M chromosomes in the initial population to generate a population size of M offspring Q n ; Randomly select some number sequences from two randomly selected parent chromosomes, sort the numbers selected in one chromosome according to the sequence of numbers selected in the other chromosome, and obtain two new chromosomes; compare the sequences of the new chromosomes with the parent chromosomes, if they are the same, continue to number them, if they are different, they are used as daughter chromosomes; repeat the operation to obtain M daughter chromosomes to form the daughter population Q n ; S3.6 Parent P n With offspring Q n Merge to get a population R of size 2M n , perform fast non-dominated sorting and crowding calculation, and select the first M combinations as the new parent population P n+1 ; S3.7 Repeat steps S3.5 and S3.

6. After N iterations, when all the optional combinations of parts have been calculated, the algorithm is terminated, the optimal non-dominated solution is obtained and the result is output.

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