An assembly sequence planning method

Abstract

The application discloses an assembly sequence planning method, and specifically comprises the following steps: obtaining three-dimensional model information of an assembly body and parts; extracting an interference matrix and a contact matrix of the assembly body, extracting information such as part quality, volume, geometric constraint quantity, assembly direction and assembly tool category in the assembly body, and calculating the connection constraint quantity and assembly operation difficulty of each part in the assembly body; selecting a base part of the assembly body; constructing an evaluation index of an assembly sequence cost; calculating the assembly sequence cost; solving a discrete optimization problem of assembly sequence planning by using a discrete artificial sparrow search algorithm to obtain an optimal assembly sequence with the minimum assembly sequence cost; and the planning method can reduce unfeasible assembly sequences, improve the rationality of the assembly sequence, and achieve the goals of reducing the assembly cost and improving the assembly efficiency.

Description

Technical Field

[0001] This invention relates to the field of assembly technology, and more specifically to an assembly sequence planning method. Background Technology

[0002] With the rapid development of digitalization and intelligentization in the equipment industry, reducing production costs, improving efficiency, and shortening product lifecycles during product design have become urgent problems for enterprises. Part assembly design, as the final and most crucial stage of product development, accounts for at least 40% of production time and cost, and 40-60% of production workload, throughout the entire process from a single part to the final product. Currently, traditional assembly processes still rely on manual experience for design, and the resulting assembly sequences largely depend on worker skill levels, making it difficult to guarantee the rationality and effectiveness of the assembly process and resulting in unnecessary cost waste. Therefore, how to utilize computer technology to improve product assembly efficiency and quality has always been a problem the industry has been committed to solving. To find the optimal assembly sequence that simultaneously satisfies both geometric feasibility constraints and assembly operation constraints, it is necessary to establish an intelligent assembly sequence planning model and conduct in-depth research on the problem of generating assembly sequences.

[0003] Sparrow Search (SMS) has been successfully applied in many fields due to its advantages of few parameters, fast search speed, and high accuracy. However, traditional SMS can only handle continuous optimization problems, and the initial population generated has low diversity. Assembly sequence planning, as an NP problem with a complex and variable discrete solution space and constraints, cannot be solved by traditional SMS alone, and it is difficult to guarantee the rationality and feasibility of the generated assembly sequence. Summary of the Invention

[0004] To overcome the shortcomings of low computational efficiency and low quality of assembly planning in existing assembly planning techniques, this invention provides an assembly sequence planning method based on the Discrete Artificial Sparrow Search Algorithm (DASSA). The aim is to reduce infeasible assembly sequences, improve the rationality and feasibility of assembly sequences, and at the same time reduce assembly costs and improve assembly efficiency.

[0005] The objective of this invention can be achieved through the following technical solutions:

[0006] An assembly sequence planning method includes the following steps:

[0007] S1: Establish an assembly information model and obtain the 3D model information of the assembly and parts;

[0008] S2: Extract the assembly interference matrix and contact matrix, extract information such as the mass, volume, number of geometric constraints, assembly direction, and assembly tool type of the parts in the assembly, and calculate the number of connection constraints and assembly operation difficulty of each part in the assembly.

[0009] S3: Select the basic component of the assembly based on the mass, volume, and number of geometric constraints of the parts in the assembly;

[0010] S4: Based on the mass, volume, number of geometric constraints, number of connection constraints, assembly direction, type of assembly tools, and difficulty of assembly operation of the parts in the assembly, construct an evaluation index for the cost of the assembly sequence, including assembly handling cost, assembly geometric constraint cost, assembly connection constraint cost, assembly direction change cost, assembly tool change cost, and assembly operation difficulty cost.

[0011] S5: Based on the assembly handling cost, assembly geometric constraint cost, assembly connection constraint cost, assembly direction change cost, assembly tool change cost, and assembly operation difficulty cost, design the corresponding weight coefficients for each evaluation index and calculate the assembly sequence cost.

[0012] S6: The discrete artificial sparrow search algorithm is used to solve the discrete optimization problem of assembly sequence planning. The discrete artificial sparrow search algorithm adds a discrete strategy and a feasible regularization strategy to the sparrow search algorithm, and adds four mutation strategies in the sparrow population evolution, including the Tent mapping strategy, the reverse learning strategy, the elite selection strategy and the dimension learning strategy, to obtain the optimal assembly sequence with the minimum assembly sequence cost.

[0013] Furthermore, for an assembly P = {p1, p2, ..., pn} consisting of n parts... n There exist several assembly sequences S = [s1, s2, ..., s2]. n The assembly sequence S describes the order in which parts are assembled to achieve the assembly process of assembly P. The i-th element s in the assembly sequence... i (i = 1, 2, ..., n) refers to the part number of the part to be assembled in the assembly body in the i-th assembly sequence operation of the assembly process.

[0014] Furthermore, the interference matrix is ​​used to describe part p in assembly P. i When assembling along a certain coordinate axis in a Cartesian coordinate system, and with part p... j The interference between parts reflects the spatial constraint relationship between the parts of the assembly and is used to determine the geometric feasibility of the assembly sequence.

[0015] For an assembly P = {p1, p2, ..., pn} consisting of n parts, ... n The interference matrix IM is defined as shown in equation (1). k :

[0016] IM k =[I ij k ] n×n (1)

[0017] In equation (1), the interference matrix element I ij k (i,j=1,2,…,n) represents part p i With part p j The interference relationship between them along the k-direction is described by equation (2) for the interference matrix element I. ij k (i,j=1,2,…,n):

[0018]

[0019] In equation (2), when part p i When assembling along the k direction with part p j Interference occurs, and part p j When assembled along the -k direction with part p i The interference occurs under the same conditions, therefore, according to the interference matrix IM with directions k = {+x,+y,+z}... k The interference matrix IM with directions k = {-x, -y, -z} can be obtained. -k , among which, I ij k =I ji -k ;

[0020] The contact matrix is ​​used to describe part p in the assembly. i With part p j The contact situation reflects the connection constraint relationship between parts;

[0021] For an assembly P = {p1, p2, ..., pn} consisting of n parts, n The contact matrix CM is defined as shown in equation (3):

[0022] CM = [C ij ] n×n (3)

[0023] In equation (3), the contact matrix element C ij (i,j=1,2,…,n) represents part p i With part p j The contact relationship between them is described by equation (4) for the contact matrix element C. ij (i,j=1,2,…,n):

[0024]

[0025] According to the definition of a contact matrix, the contact matrix CM is a symmetric matrix, i.e., C ij =C ji .

[0026] As the number of parts increases, the theoretical number of assembly sequences grows exponentially. Therefore, under the condition of satisfying the geometric feasibility of the assembly sequence, the screening and evaluation of the assembly sequence becomes extremely important. A reasonable method for evaluating assembly sequences is a prerequisite for outputting the optimal or near-optimal assembly sequence.

[0027] Assembly sequence cost reflects the efficiency and rationality of the assembly sequence. Assembly sequence planning is essentially a measure of the assembly cost incurred throughout the entire assembly process. This invention comprehensively considers the following assembly information: the interference matrix and contact matrix of the assembly, the mass, volume, number of geometric constraints, number of connection constraints, assembly direction, type of assembly tools, and assembly operation difficulty of the parts. During assembly, parts with larger mass and volume, and more geometric constraints, should be used as the foundation components of the assembly or prioritized for assembly. Therefore, these three types of assembly information are used to select the foundation components, and assembly handling cost and assembly geometric constraint cost are set as evaluation indicators. Parts with more connection constraints have a more stable assembly process and should be assembled first; therefore, assembly connection constraint cost is set as an evaluation indicator. The number of assembly direction changes and assembly tool changes should be minimized during assembly to save assembly time and cost; therefore, assembly direction change cost and assembly tool change cost are set as evaluation indicators. The assembly process should conform to the assembly operation difficulty of the parts. Parts with higher assembly operation difficulty have more complex assembly processes; if placed last for assembly, it will greatly increase the operational difficulty of the assembly process. Therefore, assembly operation difficulty cost is set as an evaluation indicator.

[0028] Furthermore, the assembly base component is the first part to be assembled in the assembly, characterized by large mass, large volume, and numerous geometric constraints with other parts. The assembly base component Base can be selected according to formula (5):

[0029] Base = argmax(B i (5)

[0030] In equation (5), B i Indicates part p in the assembly i The corresponding evaluation scores for the basic components of the assembly are shown in Equation (6):

[0031]

[0032] In equation (6), m i v i ci Let P = {p1, p2, ..., p3} represent the assembly P = {p1, p2, ..., p3} respectively. n The i-th part p in} i The mass, volume, and number of geometric constraints.

[0033] By summarizing the assembly rules in relevant materials and combining the assembly experience given by experts, the following six evaluation indicators for assembly sequences are defined. The assembly cost of the candidate assembly sequences is evaluated from six dimensions: assembly handling, assembly geometric constraints, assembly connection constraints, assembly direction change, assembly tool change, and assembly operation difficulty.

[0034] Furthermore, the assembly handling cost (ATC) can be described by equation (7):

[0035]

[0036] In equation (7), m i v i These represent the assembly sequence S = [s1, s2, ..., s...] n The i-th part s that needs to be assembled i In the assembly process, the larger the mass and volume of a part, the worse its assemblability. The time and cost of assembling such parts are also higher. Therefore, they should be prioritized for assembly.

[0037] The assembly geometric constraint cost AGCC can be described by equation (8):

[0038]

[0039] In equation (8), c i The assembly sequence S = [s1, s2, ..., s2] represents the assembly sequence. n The i-th part s that needs to be assembled i The number of geometric constraints is a factor in the assembly process. Parts with more geometric constraints have a more complex assembly process, resulting in higher assembly time and costs. Therefore, these parts should be prioritized for assembly. agcc The calculation of (i,u) is shown in equation (9):

[0040]

[0041] The assembly connection constraint cost ACCC can be described by equation (10):

[0042] (10)

[0044] In equation (10), conn i The assembly sequence S = [s1, s2, ..., s2] represents the assembly sequence. nThe i-th part s that needs to be assembled i The number of assembly connection constraints is important. During assembly, the more connection constraints a part has, the more stable the assembly process will be; therefore, these constraints should be prioritized for assembly. i The calculation is shown in equation (11):

[0045]

[0046] σ accc (i,u) is calculated as shown in equation (12):

[0047]

[0048] The assembly orientation change cost AOCC can be described by equation (13):

[0049]

[0050] In equation (13), aocc i The assembly sequence S = [s1, s2, ..., s2] represents the assembly sequence. n The i-th part s that needs to be assembled i The more times the assembly orientation is changed during assembly, the more complex the assembly process becomes, and the higher the assembly time and cost to complete the assembly. Therefore, the number of assembly orientation changes should be minimized. i The calculation is shown in equation (14):

[0051]

[0052] In equation (14), o i ∈{±x,±y,±z} represents the assembly part s i The assembly direction used at that time;

[0053] The assembly tool transformation cost ATCC can be described by equation (15):

[0054]

[0055] In equation (15), atcc i The assembly sequence S = [s1, s2, ..., s2] represents the assembly sequence. n The i-th part s that needs to be assembled i The more times assembly tools are changed during assembly, the more complex the assembly process becomes, and the higher the assembly time and cost to complete the assembly. Therefore, the number of tool changes should be minimized. i The calculation is shown in equation (16):

[0056]

[0057] In equation (16), t i ∈{tool1,tool2,,tool l} represents the assembly parts s i The assembly tool category used during assembly is l, which represents the total number of assembly tool categories used in the assembly process. Its value is determined by the total number of tool categories used in the actual assembly process.

[0058] Furthermore, the assembly operation difficulty cost calculation steps include:

[0059] S61: Establish assembly rules, including a first assembly rule, a second assembly rule, a third assembly rule, a fourth assembly rule, a fifth assembly rule, a sixth assembly rule, and a seventh assembly rule. The first assembly rule includes assembling the basic components of the assembly body; the second assembly rule includes assembling parts that are "heavy and large in volume"; the third assembly rule includes assembling parts that are "high precision"; the fourth assembly rule includes assembling parts with "many connecting parts"; the fifth assembly rule includes assembling parts with "interference fit"; the sixth assembly rule includes assembling parts at the "bottom layer of the assembly tree"; and the seventh assembly rule includes assembling parts that require heating or cooling and that are subject to extrusion or impact during the assembly process.

[0060] S62: Based on the above assembly rules, define the assembly sequence S = [s1, s2, ..., s62]. n The i-th part s that needs to be assembled i assembly operation difficulty pr i Specifically, it includes:

[0061] When part s i Satisfy the first assembly rule, pr i =1,

[0062] When part s i If the first assembly rule is not met, but rules three through six of the second, third, fourth, fifth, sixth, and seventh assembly rules are met, pr i =2,

[0063] When part s i If the first assembly rule is not met, but one or two of the second, third, fourth, fifth, sixth, and seventh assembly rules are met, pr i =3,

[0064] When part s iIf the first assembly rule is not met, and simultaneously the second, third, fourth, fifth, sixth, and seventh assembly rules are also not met, pr i =4,

[0065] S63: Obtain the assembly sequence S = [s1, s2, ..., s2] using the method described in S62. n The corresponding assembly operation difficulty sequence is Pr = [pr1, pr2, ..., pr...] n During the assembly process, the more difficult the assembly operation, the more complex the assembly process, and the higher the assembly time and cost. Therefore, these parts should be assembled first. As shown in formula (17), the assembly operation difficulty cost (AODC) of the assembly sequence S is calculated as follows:

[0066]

[0067] In equation (17), σ aodc (i,u) is calculated as shown in equation (18):

[0068]

[0069] Furthermore, for the assembly sequence set SS = [S1, S2, ..., S...] N The method for calculating the assembly sequence cost of one of the assembly sequences is shown in equation (19):

[0070] Cost=w1×ATC+w2×AGCC+w3×ACCC+w4×AOCC+w5×ATCC+w6×AODC (19)

[0072] In equation (19), w1, w2, w3, w4, w5, and w6 are the weighting coefficients corresponding to the assembly handling cost, assembly geometric constraint cost, assembly connection constraint cost, assembly direction change cost, assembly tool change cost, and assembly operation difficulty cost, respectively, and satisfy the following:

[0073] w1+w2+w3+w4+w5+w6=1 (20)

[0074] Furthermore, sparrow Defined as an assembly sequence of an assembly. It is initialized as an n-dimensional vector, where n is the number of parts contained in the assembly, and each sparrow The vector representation is as shown in equation (21):

[0075]

[0076] In equation (21), g = 0, 1, 2, ..., iter maxIter represents the current evolutionary iteration number of the sparrow population in the Discrete Artificial Sparrow Search Algorithm. max The maximum number of evolution iterations is preset for the discrete artificial sparrow search algorithm.

[0077] Furthermore, the specific steps for using the Discrete Artificial Sparrow Search algorithm to solve the discrete optimization problem of assembly sequence planning include:

[0078] S91: Parameter settings for the discrete artificial sparrow search algorithm, including setting the population size (pop) and the maximum number of evolutionary iterations (iter). max Warning value ST, the proportion of discoverers PD, the proportion of scouts SD, and the number of elite sparrows E;

[0079] S92: Use the Tent mapping strategy to generate half the population size. The initial sparrow population with continuous value encoding is generated, and then the resulting population (half the size of the initial population with continuous value encoding) is discretized using a discretization strategy to obtain... Assembly sequence;

[0080] S93: A reverse learning strategy is used to reverse learn the initial sparrow population with continuous value encoding of half the population size generated by the Tent mapping strategy in S82, and obtain... A sparrow population with continuous-value codes obtained through reverse learning is then discretized using a discretization strategy to obtain... The assembly sequence will be generated in S82. Strip assembly sequence and reverse learning generated The assembly sequences are merged to obtain the complete set of assembly sequences corresponding to the initial sparrow population;

[0081] S94: Generate the initial evolutionary search sparrow population with g=0: Calculate and initialize each sparrow in the initial sparrow population one by one. The corresponding assembly sequence Assembly sequence cost In the assembly sequence cost calculation, all infeasible assembly sequences are regenerated and feasiblely regularized based on a feasible regularization strategy. The assembly sequence cost of the regularized feasible assembly sequences is then calculated, thus obtaining the set of feasible assembly sequences for the initial evolutionary search sparrow population with g=0. The assembly sequence costs of all sparrows in the current sparrow population are sorted, and the sparrow with the minimum assembly sequence cost is selected to update X. best Select the sparrow update X with the maximum assembly sequence cost. worst ;

[0082] S95: Sparrow population evolution iterative search, specifically including:

[0083] S951: Based on each sparrow in the sparrow population during each evolutionary iteration Assembly sequence cost value Sort the sparrows from smallest to largest and divide them into two sets, discoverers and followers, according to a pre-set ratio PD. Sparrows with smaller assembly costs are discoverers, and sparrows with larger assembly costs are followers. Sparrows in the discoverer set correspond to better assembly sequences.

[0084] Using an elite selection strategy, pop×PD-E sparrows are selected from the discoverer population based on the assembly sequence cost, and updated using Equation (22):

[0085]

[0086] In equation (22), This represents the sparrow in the current g-th evolution iteration. The assembly sequence represented Given an n-dimensional random vector, For a random value between [0,1], Let be an n-dimensional random vector that follows a normal distribution;

[0087] Using an elite selection strategy, select pop×(1-PD)-E sparrows from the follower group based on the assembly sequence cost, and update them using equation (23):

[0088]

[0089] In equation (23), where, Let X be the sparrow in the sparrow population with the minimum assembly sequence cost in the current g-th evolutionary iteration. worst Let A be the sparrow with the maximum assembly sequence cost that has appeared in the sparrow population up to the current g-th evolutionary iteration. Let A be an n-dimensional vector with each element value randomly assigned a value of 1 or -1. + =A T (AA T ) -1 L is an n-dimensional vector consisting entirely of 1s. Let be an n-dimensional random vector that follows a normal distribution;

[0090] S952: The sparrow population updated by discoverers and followers is updated according to the dimensional learning strategy to obtain the sparrow population updated by dimensional learning. For the sparrow population updated by dimensional learning, some sparrows are randomly selected as scouts according to the scout ratio SD, and updated according to formula (24):

[0091]

[0092] In equation (24), Xbest This refers to the sparrow with the minimum assembly sequence cost that has appeared in the sparrow population up to the current g-th evolutionary iteration. For the sparrow in the sparrow population with the maximum assembly sequence cost in the g-th evolutionary iteration, the optimal update step size control parameter is... For random numbers that follow a standard normal distribution, It is a random number. To avoid the denominator being zero, σ is set to the smallest non-zero constant.

[0093] S953: Use a discretization strategy to discretize the sparrows in the current sparrow population, and calculate each sparrow in the current evolutionary iteration of the sparrow population one by one. The corresponding assembly sequence Assembly sequence cost In the assembly sequence cost calculation, all infeasible assembly sequences are regenerated and made feasible based on the feasible regularization strategy, and the assembly sequence cost of the regularized feasible assembly sequence is calculated.

[0094] S954: Select each sparrow in the current sparrow population. Assembly sequence cost The assembly sequence cost of its previous evolutionary iteration The assembly sequence cost is compared with that of the previous generation of sparrows. If the assembly sequence cost decreases, the current assembly sequence corresponding to that sparrow is maintained; if the assembly sequence cost increases, the assembly sequence corresponding to that sparrow is restored to the assembly sequence of the previous evolutionary iteration, thus obtaining a sparrow population adjusted and updated based on the comparison with the assembly sequence cost of the previous generation of sparrows. The assembly sequence costs of all sparrows in the current sparrow population are sorted, and the sparrow with the lowest assembly sequence cost in the current sparrow population is selected and compared with X. best Compare the assembly sequence costs. If the sparrow with the lowest assembly sequence cost in the current sparrow population has a lower assembly cost, then update X using that sparrow. best Similarly, select the sparrow with the highest assembly sequence cost in the current sparrow population, and X. worst Compare the assembly sequence costs. If the sparrow with the highest assembly sequence cost in the current sparrow population has a higher assembly cost, then update X using that sparrow. worst ;

[0095] S955: Increment the current evolution iteration count by 1, g = g + 1, if the current evolution iteration count g is less than the maximum evolution iteration count iter max If the result is positive, proceed to S951; otherwise, stop the evolutionary iterative search and output X. best The optimal assembly sequence is the one with the lowest cost found through evolutionary iteration.

[0096] Furthermore, the Tent mapping strategy is a chaotic mapping, and its expression is shown in equation (25):

[0097]

[0098] In equation (25), Generally, 0.5 is used, where pop is the population size of sparrows. The assembly sequence represented by the randomly generated sparrow i*. The Assembly sequence of individual parts The assembly sequence represented by the randomly generated sparrow i*. The assembly sequence with continuous value encoding obtained after Tent mapping is the first... The assembly sequence of the parts;

[0099] The discrete strategy is an assembly sequence that encodes continuous values ​​generated in the discrete artificial sparrow search algorithm. The element values ​​are arranged in ascending order. If the element values ​​are equal, they are arranged according to their order in the assembly sequence. Based on the element value sorting result, each assembly sequence... elements A corresponding integer sequence number is obtained, and the element value at the original position of the assembly sequence is replaced with the integer sequence number to generate a discrete assembly sequence, where each element represents the part number of the part to be assembled in the assembly body in the corresponding assembly sequence.

[0100] All steps involving calculating the assembly sequence cost require discretization of the assembly sequence using the discretization strategy for the continuously value-encoded assembly sequence before the assembly sequence cost can be calculated.

[0101] The feasibility of the assembly sequence is regularized using the aforementioned feasible regularization strategy, specifically including: placing the base component selected according to the assembly base component selection method in the first position of the assembly sequence; then, starting from the second position in the assembly sequence, judging whether there is interference in the current assembly sequence according to the assembly interference matrix; if there is interference, regenerating an assembly sequence and judging whether there is interference in the generated assembly sequence; if there is still interference, repeating the assembly sequence generation and interference judgment process until a feasible assembly sequence without interference is obtained.

[0102] The method for determining whether there is interference in the assembly sequence is as follows: For each part in the assembly sequence, the interference matrix corresponding to its assembly direction can be used to determine whether the part interferes with all the parts assembled earlier in the assembly sequence. If all the parts in the assembly sequence do not interfere with the parts assembled earlier, then it can be determined that there is no interference in the assembly sequence, which is feasible.

[0103] All steps involving the calculation of assembly sequence costs require the use of feasible regularization strategies to perform feasible regularization on the interference situations of the assembly sequence, and finally calculate the assembly sequence cost of a feasible assembly sequence that has no interference situations after feasible regularization.

[0104] Furthermore, the reverse learning strategy generates half the population size of the Tent mapping strategy in S92. The continuous value encoding of the initial sparrow population is used for reverse learning to generate... A reversed sparrow, the generation of which is shown in equations (26) to (28):

[0105]

[0106]

[0107]

[0108] In equations (26) to (28), Half the population size after Tent mapping The sparrow with the minimum assembly sequence cost in the initial sparrow population. This is its inverse solution, where lb and ub are the upper and lower bounds of the search space, respectively, and b is the information exchange control parameter. Let be an n-dimensional random vector that follows a normal distribution (0,1). The assembly sequence represented by the initial sparrow i* after reverse learning;

[0109] The elite selection strategy guides the sparrow population to generate assembly sequences with lower assembly costs. An elite is defined as the E assembly sequences with the lowest assembly cost in the sparrow population, where E is the number of elite sparrows. During each evolutionary iteration, the sparrow population maintains the E assembly sequences with the lowest assembly cost corresponding to the elite sparrows in the current g-th evolutionary iteration. The process proceeds directly to the next sparrow population evolution iteration, as shown in equation (29):

[0110]

[0111] Before each evolutionary iteration of the sparrow population's discoverers and followers, an elite selection strategy is needed to select a certain proportion of elite sparrows corresponding to the assembly sequence to directly enter the next evolutionary iteration.

[0112] The dimensional learning strategy simulates the evolutionary iteration of a sparrow population, where the evolution of each sparrow is influenced by several neighboring sparrows, i.e., each assembly sequence... The next evolutionary iteration is influenced by the set of nearest-neighbor assembly sequences. The influence of this is shown in equations (30) to (33) regarding the dimensional learning of sparrows:

[0113]

[0114]

[0115]

[0116]

[0117] In equations (30) to (33), Indicates the first Assembly sequence nearest neighbor radius, Indicates the current number The set of nearest neighbor sequences of an assembly sequence. This means randomly selecting a nearest neighbor sequence from the set of nearest neighbor sequences. This represents the nearest neighbor sequence after dimensional learning is performed according to the dimensional learning strategy.

[0118] Compared with the prior art, the present invention has the following technical effects:

[0119] (1) Before the algorithm evolution iteration process begins, the present invention uses the mass, volume and geometric constraint quantity information of the parts to select the assembly base part as the first part to be assembled, and fixes the assembly base part in the first position of the assembly sequence in the subsequent process as the basis for assembling other parts.

[0120] (2) A feasible regularization strategy was designed to ensure that the assembly sequences obtained by the algorithm are all feasible assembly sequences without interference. Based on the assembly information, assembly transportation cost, assembly geometric constraint cost, assembly connection constraint cost, assembly direction change cost, assembly tool change cost, and assembly operation difficulty cost were set as assembly cost evaluation indicators for the assembly sequence, and the optimal assembly sequence with the minimum assembly cost was selected.

[0121] (3) In order to better solve the optimization problem of assembly sequence planning, a discrete artificial sparrow search algorithm was proposed for the first time. Discrete strategy and feasible regularization strategy were designed in the traditional sparrow algorithm so that the traditional sparrow algorithm can be applied to the NP problem of assembly sequence planning with complex and variable discrete solution space and constraints. Furthermore, four mutation strategies were added to the sparrow population evolution: Tent mapping strategy, reverse learning strategy, elite selection strategy and dimension learning strategy, which greatly improved the diversity of the sparrow population and increased the possibility of the algorithm finding the optimal assembly sequence. Attached Figure Description

[0122] Figure 1 This is the overall flowchart of the present invention;

[0123] Figure 2 A 3D model of an example of axle box assembly;

[0124] Figure 3 This is a flowchart of the Discrete Artificial Sparrow Search Algorithm (DASSA). Detailed Implementation

[0125] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the invention, any modifications, equivalent substitutions, improvements, etc., made by those skilled in the art to all other embodiments obtained without creative effort should be included within the protection scope of the present invention.

[0126] The core idea of ​​this invention is as follows: Based on the geometric feasibility constraints and stability requirements of the assembly during the assembly process, interference matrices and contact matrices are designed respectively. On this basis, considering the mass, volume, number of geometric constraints, number of connection constraints, assembly direction, type of assembly tools, and difficulty of assembly operations of the parts in the assembly, an evaluation index for the assembly sequence cost is rationally constructed. This index includes assembly handling cost, assembly geometric constraint cost, assembly connection constraint cost, assembly direction change cost, assembly tool change cost, and assembly operation difficulty cost. Corresponding weight coefficients are designed for each evaluation index, and the assembly sequence cost is calculated to screen and evaluate the assembly sequence. Finally, a discrete artificial sparrow search algorithm is used to solve the discrete optimization problem of assembly sequence planning, obtaining the optimal assembly sequence with the minimum assembly sequence cost. This achieves the goal of outputting the optimal or near-optimal assembly sequence with the highest probability while satisfying all geometric feasibility and assembly stability requirements, shortening assembly time, reducing assembly costs, and improving the quality and efficiency of assembly sequence generation.

[0127] The following case study provides a detailed explanation of the algorithm, based on actual part processing requirements, models, and algorithms.

[0128] like Figure 1 As shown, an assembly sequence planning method includes the following steps:

[0129] S1: Establish an assembly information model and obtain the 3D model information of the assembly and parts;

[0130] S2: Extract the assembly interference matrix and contact matrix, extract information such as the mass, volume, number of geometric constraints, assembly direction, and assembly tool type of the parts in the assembly, and calculate the number of connection constraints and assembly operation difficulty of each part in the assembly.

[0131] S3: Select the basic component of the assembly based on the mass, volume, and number of geometric constraints of the parts in the assembly;

[0132] S4: Based on the mass, volume, number of geometric constraints, number of connection constraints, assembly direction, type of assembly tools, and difficulty of assembly operation of the parts in the assembly, construct an evaluation index for the cost of the assembly sequence, including assembly handling cost, assembly geometric constraint cost, assembly connection constraint cost, assembly direction change cost, assembly tool change cost, and assembly operation difficulty cost.

[0133] S5: Based on the assembly handling cost, assembly geometric constraint cost, assembly connection constraint cost, assembly direction change cost, assembly tool change cost, and assembly operation difficulty cost, design the corresponding weight coefficients for each evaluation index and calculate the assembly sequence cost.

[0134] S6: The discrete artificial sparrow search algorithm is used to solve the discrete optimization problem of assembly sequence planning. The discrete artificial sparrow search algorithm adds a discrete strategy and a feasible regularization strategy to the sparrow search algorithm, and adds four mutation strategies in the sparrow population evolution, including the Tent mapping strategy, the reverse learning strategy, the elite selection strategy and the dimension learning strategy, to obtain the optimal assembly sequence with the minimum assembly sequence cost.

[0135] For example Figure 2 The 3D model of the "axle box assembly" example shown is an implementation example illustrating the method of obtaining the optimal assembly sequence of the present invention:

[0136] (1) Assembly Information Acquisition Method

[0137] The axle box assembly contains 19 parts. The part numbers in the design BOM are used as the part numbers in the program, as shown in Table 1:

[0138] Table 1 Part Numbers of the Bearing Box Assembly

[0139]

[0140] 1) Extracting the interference matrix

[0141] An interference matrix (IM) represents the interference between each part and other parts when each part is assembled along a certain coordinate axis in a Cartesian coordinate system. It reflects the spatial constraint relationship between the parts in the assembly and is used to determine the geometric feasibility of the assembly sequence.

[0142] Open the 3D model of the axle box to be assembled in the CAD software. Enable the "Stop Operation on Collision" function. Select the corresponding parts in sequence and move them in the +x, +y, +z directions of the Cartesian coordinate system until they are detached from the entire assembly. During this disassembly process, detect dynamic collisions between parts and observe whether there is interference with other parts during dragging. Obtain the interference matrix IM of the assembly in the k = {±x, ±y, ±z} directions. k The interference matrix IM of the assembly in the +x direction. +x As shown in Equation (E-1), the interference matrix IM of the assembly in the +y direction is... +y As shown in Equation (E-2), the interference matrix IM of the assembly in the +z direction +z As shown in equation (E-3).

[0143] When part p i When assembled along the k direction, part p j Interference occurs and p j When assembled along the -k direction with part p i The interference occurs under the same conditions. Therefore, based on the interference matrix IM with directions k = {±x,±y,±z},... k The interference matrix IM with directions k = {-x, -y, -z} can be obtained. -k , among which, I ij k =I ji -k The interference matrix IM of the assembly in the -x direction. -x As shown in Equation (E-4), the interference matrix IM of the assembly in the -y direction is... -y As shown in Equation (E-5), the interference matrix IM of the assembly in the -z direction is... -z As shown in equation (E-6).

[0144]

[0145]

[0146]

[0147]

[0148]

[0149]

[0150] 2) Extract the contact matrix

[0151] The contact matrix (CM) represents the contact situation between a part and other parts in an assembly, reflecting the connection constraints between components. In CAD software, open the 3D model of the axle box that needs assembly planning, use the "Check Collision" function to detect contact collisions among all components, and obtain the contact matrix CM as shown in Equation (E-7):

[0152]

[0153] (2) Assembly sequence evaluation method based on assembly sequence cost

[0154] 1) Method for selecting basic components in the assembly sequence

[0155] The mass, volume, assembly tool type, assembly direction, and number of geometric constraints of each part in the assembly can be directly extracted from the CAD model file. This is based on the assembly's contact matrix CM = [C ij ] 19×19 The number of connection constraints for each part in the assembly can be obtained. Part p i The number of connection constraints conn for (i = 1, 2, ..., 19) i It can be calculated using the following formula (E-8):

[0156]

[0157] The assembly information table for the bearing housing is shown in Table 2:

[0158] Table 2 Assembly Information Table for Bearing Box

[0159]

[0160]

[0161] The assembly direction numbers in the assembly sequence are shown in Table 3:

[0162] Table 3 Assembly Direction Numbering

[0163]

[0164] The assembly tool category numbers in the assembly sequence are shown in Table 4:

[0165] Table 4 Assembly Tool Category Numbers

[0166]

[0167] Based on the mass, volume, and number of geometric constraints of each part in the assembly, part p is calculated using the following formula (E-9). i The corresponding basic component evaluation score is B. i :

[0168]

[0169] The calculation yields part p with part number i in the axle box assembly. i The corresponding basic component evaluation score is B. i As shown in Table 5:

[0170] Table 5. Evaluation scores of basic components in the axle box assembly.

[0171]

[0172]

[0173] Select the base component of the axle box assembly using the following formula (E-10):

[0174] Base = argmax(B i (E-10)

[0175] It can be determined that the base component of the bearing housing assembly is p1 bearing housing, and the part number is 1.

[0176] 2) Constructing an evaluation index for the cost of assembly sequence

[0177] The assembly difficulty of each part in the assembly can be obtained based on the following seven assembly rules:

[0178] First assembly rule: Assemble the "basic components";

[0179] Second assembly rule: Assemble parts that are "heavy and large in volume";

[0180] The third assembly rule: Assemble "high-precision" parts;

[0181] Fourth assembly rule: Assemble parts with many connectors;

[0182] Fifth assembly rule: Assemble parts with an interference fit;

[0183] Sixth assembly rule: Assemble the parts at the bottom of the assembly tree;

[0184] Seventh assembly rule: Assemble parts that require heating or cooling, or that are subject to compression or impact during the assembly process;

[0185] Based on the above 7 assembly rules, the assembly difficulty of the parts of the resulting axle box assembly is shown in Table 6:

[0186] Table 6. Assembly difficulty of parts in the bearing box assembly

[0187]

[0188]

[0189] By using information such as the mass, volume, number of geometric constraints, number of connection constraints, assembly direction, type of assembly tools, and difficulty of assembly operation of each part in the axle box assembly, the assembly sequence cost of the assembly sequence can be calculated.

[0190] Assuming the current assembly sequence is S = [1,17,16,3,7,4,5,6,18,19,15,14,13,8,9,2,10,11,12], the calculation steps for its assembly sequence cost are as follows:

[0191] ① Assembly Transportation Cost (ATC)

[0192] The assembly quality sequence corresponding to assembly sequence S is:

[0193] M=[211.99,0.013,0.1,12.954,1.655,10.809,6.169,3.925,0.0006,0.001,0.01,0.003,0.06,3.737,5.118,18.195,0.307,0.017,0.023]

[0194] The assembly volume sequence corresponding to assembly sequence S is:

[0195] V=[27,0.002,0.049,2,0.2105,1,0.7848,0.4994,0.0005,0.001,0.001,0.0003,0.008,0.4754,0.6512,2,0.039,0.002,0.003]

[0196] The assembly handling cost (ATC) of this assembly sequence S can be obtained according to the following formula (E-11):

[0197]

[0198] The assembly handling cost (ATC) for assembly sequence S was calculated to be 5.947.

[0199] ② Assembly Geometry Constraints Cost (AGCC)

[0200] The geometric constraint number sequence corresponding to assembly sequence S is C = [8,1,1,4,1,3,3,2,1,1,1,1,1,3,3,3,1,1,1]. The assembly geometric constraint cost AGCC of this assembly sequence S can be obtained according to the following formulas (E-12) to (E-13):

[0201]

[0202]

[0203] Where, σ agcc (i,u), i=1,2,...,19; u=1,2,...,19 can be determined by the matrix surface

[0204] 9.

[0205]

[0206] The assembly geometric constraint cost AGCC for the assembly sequence S was calculated to be 3.789.

[0207] ③ Assembly Connection Constraint Cost (ACCC)

[0208] The sequence of connection constraint numbers corresponding to assembly sequence S is as follows:

[0209] Conn = [10,1,1,2,3,5,5,1,1,1,1,2,5,2,1,3,2,2,2], the assembly connection constraint cost ACCC of this assembly sequence S can be obtained according to the following formulas (E-14) to (E-15):

[0210]

[0211]

[0212] Where, σ accc (i,u), i=1,2,...,19; u=1,2,...,19 can be determined by the matrix express:

[0213]

[0214] The assembly connection constraint cost ACCC for the assembly sequence S is calculated to be 6.053.

[0215] ④ Assembly Orientation Change Cost (AOCC)

[0216] The assembly direction sequence corresponding to assembly sequence S is:

[0217] O = [-2,-2,-2,+2,+2,+2,+2,+2,+2,+2,+1,+2,+2,-2,-2,-2,-2,-2,-2], and the assembly direction change cost AOCC of this assembly sequence S can be obtained according to the following formulas (E-16)~(E-17):

[0218]

[0219]

[0220] Among them, aocc i The values ​​of (i = 1, 2, ..., 19) can be obtained from the sequence aocc = [aocc1, ..., aocc 19 ]express:

[0221] aocc=[ / ,0,0,1,0,0,0,0,0,0,1,1,0,1,0,0,0,0,0]

[0222] The assembly direction change cost AOCC for the assembly sequence S is calculated to be 4.

[0223] ⑤ Assembly Tool Change Cost (ATCC)

[0224] The assembly tool category sequence corresponding to assembly sequence S is T = [1,3,1,2,1,1,1,2,1,3,1,1,3,1,2,2,1,1,3]. The assembly tool transformation cost (ATCC) of this assembly sequence S can be obtained according to the following formulas (E-18) to (E-19):

[0225]

[0226]

[0227] Among them, atcc i The values ​​of (i = 1, 2, ..., 19) can be obtained from the sequence atcc = [atcc1, ..., atcc] 19 ]express:

[0228] atcc=[ / ,1,1,1,1,0,0,1,1,1,1,0,1,1,1,0,1,0,1]

[0229] The assembly tooling transformation cost ATCC for this assembly sequence S is calculated to be 13.

[0230] ⑥ Assembly Operation Difficulty Cost (AODC)

[0231] The assembly operation difficulty sequence corresponding to assembly sequence S is:

[0232] Pr = [1,4,4,2,2,2,3,3,4,4,4,4,4,2,2,2,3,3,4], the assembly operation difficulty cost (AODC) of this assembly sequence S can be obtained according to the following formulas (E-20) to (E-21):

[0233]

[0234]

[0235] Where, σ aodc (i,u), i=1,2,...,19; u=1,2,...,19 can be determined by the matrix express:

[0236]

[0237] The assembly operation difficulty cost AODC for this assembly sequence S is calculated to be 4.632.

[0238] 3) Comprehensive evaluation method for assembly sequence cost

[0239] For assembly sequence S, the above indicators, including assembly handling cost, assembly geometric constraint cost, assembly connection constraint cost, assembly direction change cost, assembly tool change cost, and assembly operation difficulty cost, are weighted and summed. The assembly cost of this assembly sequence is calculated using the assembly sequence cost function (E-22) as follows, resulting in an assembly cost Cost of 5.713.

[0240] Cost=w1×ATC+w2×AGCC+w3×ACCC+w4×AOCC+w5×ATCC+w6×AODC (E-22)

[0241] The weighting coefficients are w1 = 0.1, w2 = 0.1, w3 = 0.25, w4 = 0.25, w5 = 0.1, and w6 = 0.2.

[0242] The assembly cost of the axle box assembly sequence can be obtained by following the steps shown above.

[0243] (3) Assembly sequence planning based on discrete artificial sparrow search algorithm

[0244] like Figure 3As shown, the assembly sequence planning for the axle box is based on the discrete artificial sparrow search algorithm. The steps are as follows:

[0245] S91. Discrete Artificial Sparrow Search Algorithm Parameter Settings: Population size pop = 30, maximum number of evolutionary iterations iter max =100, warning value ST=0.8, proportion of discoverers PD=20%, proportion of scouts SD=10%, number of elite sparrows E=3;

[0246] S92. Use the Tent mapping strategy to generate half the population size. The initial sparrow population with continuous value encoding is shown in Table 7; the generated initial sparrow population with continuous value encoding, which is half the size of the population, is discretized using a discretization strategy to obtain 15 assembly sequences, as shown in Table 8:

[0247] Table 7. Assembly sequences of 15 consecutive-value codes generated by the Tent mapping strategy.

[0248]

[0249] Table 8 shows the assembly sequences generated by the 15 Tent mapping strategies after discretization.

[0250]

[0251] S93. A reverse learning strategy is used to reverse learn the initial sparrow population with continuous value encoding (half the population size) generated in S92, resulting in 15 sparrow populations with continuous value encoding after reverse learning, as shown in Table 9. A discretization strategy is used to discretize the 15 continuous value sequences after reverse learning, resulting in 15 discrete assembly sequences after reverse learning, as shown in Table 10. The 15 discrete assembly sequences with half the population size generated in S92 are merged with the 15 discrete assembly sequences with half the population size generated by reverse learning to obtain the set of assembly sequences corresponding to all initial sparrow populations, as shown in Table 11.

[0252] Table 9 shows the assembly sequences of 15 continuous-value codes generated by the reverse learning strategy.

[0253]

[0254] Table 10 shows the assembly sequences generated by the 15 back-learning strategies after discretization.

[0255]

[0256] S94. Calculate the initialization of each sparrow in the sparrow population. The corresponding assembly sequence Assembly sequence cost A first-generation evolutionary search sparrow population with g=0 is generated. In calculating the assembly sequence cost, all infeasible assembly sequences are regenerated and feasiblely regularized based on a feasible regularization strategy, and the assembly sequence cost of the regularized feasible assembly sequences is calculated. Thus, the set of feasible assembly sequences for the first-generation evolutionary search sparrow population with g=0 is shown in Table 12, and the assembly sequence costs are shown in Table 13. The assembly sequence costs of all sparrows in the current sparrow population are sorted, and the sparrow with the lowest assembly sequence cost is selected to update X. best Select the sparrow update X with the maximum assembly sequence cost. worst .

[0257] X obtained using the method described above best =[1,3,7,4,5,6,16,18,19,15,17,14,13,8,9,2,10,11,12], assembly sequence X best The corresponding assembly handling cost is 5.4473, the assembly geometric constraint cost is 2.9474, the assembly connection constraint cost is 4.8947, the assembly direction change cost is 7, the assembly tool change cost is 13, the assembly operation difficulty cost is 3.7895, and the assembly sequence cost of this assembly sequence is 5.871.

[0258] The obtained X worst =[1,15,17,3,7,4,5,6,16,18,19,8,9,2,10,11,12,14,13], assembly sequence X worst The corresponding assembly handling cost is 5.5771, the assembly geometric constraint cost is 3.1579, the assembly connection constraint cost is 7, the assembly direction change cost is 7, the assembly tool change cost is 12, the assembly operation difficulty cost is 3.6842, and the assembly sequence cost of this assembly sequence is 6.3103.

[0259] Table 11 Set of assembly sequences for initializing the sparrow population

[0260]

[0261] Table 1. Set of feasible assembly sequences for the 2g=0 initial evolutionary search sparrow population.

[0262]

[0263] Table 13g=0 Initial Evolutionary Search for Assembly Sequence Costs of Sparrow Populations (Assembly Sequence Cost)

[0264]

[0265] S95. The following are the steps of sparrow population evolution and iteration:

[0266] This section uses the evolutionary iteration calculation of a sparrow population in the initial evolutionary search with g=0 as an example:

[0267] S951, based on each sparrow in the sparrow population during each evolutionary iteration Assembly sequence cost value Sort the sparrows by size from smallest to largest, and divide the entire sparrow population into two sets: discoverers and followers, according to a pre-set ratio of PD = 20%. Sparrows with smaller assembly costs are considered discoverers, and sparrows with larger assembly costs are considered followers. For the sparrow population in the first generation of evolutionary search with g = 0, the assembly sequences corresponding to the 6 discoverers are shown in Table 14, and the assembly sequences corresponding to the 24 followers are shown in Table 15.

[0268] Table 14. Set of assembly sequences for the discoverers

[0269]

[0270] Table 15 Set of assembly sequences for followers

[0271]

[0272] Using an elite selection strategy, select 3 sparrows from the discoverer population based on the assembly sequence cost, then pop×PD-E = 3 sparrows, and update them using the following formula (E-23):

[0273]

[0274] in, For the sparrow in the current evolution iteration number The assembly sequence represented, for n 3D random vector, For a random value between [0, 1], To follow a normal distribution n 3D random vector.

[0275] For the current computational instance, when g=0, the finder in the initial evolutionary search sparrow population is updated... as follows:

[0276]

[0277]

[0278]

[0279] The assembly sequence corresponding to the continuous value encoding after the discoverer's update is shown in Table 16.

[0280] Table 16 shows the assembly sequence of the updated six consecutive values ​​encoded by the elite selection strategy for the discoverer.

[0281]

[0282] Using an elite selection strategy, select 21 sparrows from the follower group based on the assembly sequence cost, then pop×(1-PD)-E = 21 sparrows, and update them using the following formula (E-24):

[0283]

[0284] in, Let X be the sparrow in the sparrow population with the minimum assembly sequence cost in the current g-th evolutionary iteration. worst Let A be the sparrow with the maximum assembly sequence cost that has appeared in the sparrow population up to the current g-th evolutionary iteration. Let A be an n-dimensional vector with each element value randomly assigned a value of 1 or -1. + =A T (AA T ) -1 L is an n-dimensional vector consisting entirely of 1s. Let be an n-dimensional random vector that follows a normal distribution.

[0285] For the current computational instance, when g=0, A and A' are updated in the first-generation evolutionary search sparrow population when followers are updated. + , as follows:

[0286] A=[1 1 1 1 -1 -1 -1 1 1 -1 1 -1 1 1 1 -1 1 -1 -1]

[0287] A + = [0.053 0.053 0.053 0.053 -0.053 -0.053 -0.053 0.053 0.053 -0.053 0.053 0.053 0.053 0.053 0.053 -0.053 -0.053]

[0288]

[0289] The assembly sequence of the continuous value encoding corresponding to the follower update is shown in Table 17:

[0290] Table 17 shows the assembly sequence of the updated 24 consecutive values ​​encoded by the elite selection strategy for followers.

[0291]

[0292] S952. The sparrow population updated with discoverers and followers is updated according to the dimensional learning strategy, resulting in the sparrow population updated with dimensional learning, as shown in Table 18. For the sparrow population updated with the dimensional learning strategy, some sparrows are randomly selected as scouts according to the scout ratio SD = 10%, namely the 4th, 18th, and 26th sparrows, as shown in Table 19. The population is then updated according to the following formula (E-25):

[0293]

[0294] Among them, X best This refers to the sparrow with the minimum assembly sequence cost that has appeared in the sparrow population up to the current g-th evolutionary iteration. For the sparrow in the sparrow population with the maximum assembly sequence cost in the g-th evolutionary iteration, the optimal update step size control parameter is... For random numbers that follow a standard normal distribution, It is a random number. To avoid zero in the denominator, σ is set to the smallest non-zero constant.

[0295] Table 18 shows the assembly sequence of the updated 30 continuous value codes for discoverers and followers using the dimensional learning strategy.

[0296]

[0297] Table 19: Set of assembly sequences for continuous value coding of scouts

[0298]

[0299] For the current computational instance, when g=0, the scout updates in the initial evolutionary search sparrow population. σ is as follows:

[0300]

[0301]

[0302] σ = 10e-8

[0303] The updated scouts are shown in Table 20, and the sparrow population after the scouts update is shown in Table 21.

[0304] Table 20 shows the assembly sequence for the updated three consecutive value codes of the scout.

[0305]

[0306] Table 21 Assembly Sequence of the 30 Updated Continuous Value Codes for the Scout

[0307]

[0308] S953. Discretize the sparrow population updated by the scout using a discrete strategy to obtain a discrete sparrow population, as shown in Table 22. Calculate the value of each sparrow in the current evolutionary iteration of the sparrow population. The corresponding assembly sequence Assembly sequence cost In the assembly sequence cost calculation, all infeasible assembly sequences are regenerated and made feasible based on the feasible regularization strategy, and the assembly sequence cost of the regularized feasible assembly sequences is calculated.

[0309] Table 22. 30 Discretized Scout Updated Assembly Sequences

[0310]

[0311] For the current computational instance, the set of assembly sequences adjusted by feasible regularization strategies is shown in Table 23; the cost of the assembly sequences adjusted by feasible regularization strategies is shown in Table 24.

[0312] Table 23 Set of assembly sequences after adjustment by feasible regularization strategies

[0313]

[0314] Table 24. Assembly sequence costs after adjustment using feasible regularization strategies.

[0315]

[0316] S954, Set the assembly sequence cost for each sparrow in the current population. The assembly sequence cost of its previous evolutionary iteration The assembly sequence cost is compared with that of the previous generation of sparrows. If the assembly sequence cost decreases, the current assembly sequence corresponding to that sparrow is maintained; if the assembly sequence cost increases, the assembly sequence corresponding to that sparrow is restored to the assembly sequence of the previous evolution iteration, thus obtaining the sparrow population adjusted and updated based on the comparison with the assembly sequence cost of the previous generation of sparrows. For the current computational instance, the sparrow population adjusted and updated based on the comparison with the assembly sequence cost of the previous generation of sparrows is shown in Table 25; the assembly sequence costs of the assembly sequences corresponding to all sparrows in the current sparrow population are sorted to obtain the sorted sparrow population, as shown in Table 26; the assembly sequence costs corresponding to the set of assembly sequences sorted by assembly sequence cost are shown in Table 27. The sparrow with the smallest assembly sequence cost in the current sparrow population is selected and compared with X. best Compare the assembly sequence costs. If the sparrow with the lowest assembly sequence cost in the current sparrow population has a lower assembly cost, then update X using that sparrow. best Similarly, select the sparrow with the highest assembly sequence cost in the current sparrow population, and X.worst Compare the assembly sequence costs. If the sparrow with the highest assembly sequence cost in the current sparrow population has a higher assembly cost, then update X using that sparrow. worst .

[0317] For the current computation instance, the obtained X best =[1,3,7,4,5,6,14,13,18,19,15,16,8,9,2,10,11,12,17], assembly sequence X best The corresponding assembly handling cost is 5.2634, assembly geometric constraint cost is 2.6316, assembly connection constraint cost is 3.2632, assembly direction change cost is 3, assembly tool change cost is 11, and assembly operation difficulty cost is 3.3158. The assembly sequence cost of this assembly sequence is 4.1184.

[0318] The obtained X worst =[1,15,17,16,3,7,4,5,6,18,19,8,9,2,10,11,12,14,13], assembly sequence X worst The corresponding assembly handling cost is 5.822, assembly geometric constraint cost is 3.5789, assembly connection constraint cost is 7.5789, assembly direction change cost is 5, assembly tool change cost is 13, and assembly operation difficulty cost is 4.1053. The assembly sequence cost of this assembly sequence is 6.2059.

[0319] S955, If the current evolution iteration number is less than the maximum evolution iteration number iter max If the result is positive, proceed to S951; otherwise, stop the evolutionary iteration and output the assembly sequence with the lowest assembly sequence cost in the current population.

[0320] Based on the discrete artificial sparrow search algorithm, the optimal assembly sequence of the axle box is [1,3,7,4,5,6,14,13,16,8,9,2,10,11,12,17,15,18,19].

[0321] The optimal assembly sequence for the axle box has an assembly handling cost of 4.684, an assembly geometric constraint cost of 1.684, an assembly connection constraint cost of 2.316, an assembly direction change cost of 4, an assembly tool change cost of 11, and an assembly operation difficulty cost of 1.895. The assembly sequence cost of this assembly sequence is 3.6947.

[0322] Table 25 shows the updated set of assembly sequences after adjustments based on a comparison with the assembly sequence cost of the previous generation of Sparrows.

[0323]

[0324] Table 26. Set of assembly sequences sorted by assembly sequence cost

[0325]

[0326] Table 27 shows the assembly sequence costs corresponding to the assembly sequence set sorted by assembly sequence cost.

[0327]

[0328] The above example of assembly sequence planning using the "axle box" assembly specifically includes:

[0329] First, information on 19 parts in the "axle-holding box" assembly is obtained. An interference matrix representing the spatial constraints between the parts and a contact matrix representing the connection constraints between the components are extracted. Based on this, assembly information for the "axle-holding box" is extracted, including the mass, volume, assembly tool type, assembly direction, and number of geometric constraints for each of the 19 parts. Second, based on the mass, volume, and number of geometric constraints of the 19 parts, the assembly base component of the "axle-holding box" assembly is selected as the axle-holding box, with part number 1. The number of assembly connection constraints for each part in the "axle-holding box" assembly is obtained based on the contact matrix. Finally, based on seven assembly rules, the number of connections between each component in the "axle-holding box" assembly is determined. The assembly operation difficulty of the components is assessed. Based on the mass, volume, number of geometric constraints, number of connection constraints, assembly direction, type of assembly tools, and assembly operation difficulty of the parts in the "axle box" assembly, an evaluation index for the assembly sequence cost of the "axle box" is constructed, including assembly handling cost, assembly geometric constraint cost, assembly connection constraint cost, assembly direction change cost, assembly tool change cost, and assembly operation difficulty cost. Then, based on the evaluation index of the "axle box" assembly sequence cost and the corresponding weight coefficients of each evaluation index, the assembly sequence cost of the "axle box" is calculated. Finally, the discrete artificial sparrow search algorithm is used to solve the discrete optimization problem of assembly sequence planning, and the optimal assembly sequence with the minimum assembly sequence cost of the "axle box" is obtained as the optimal assembly sequence of the "axle box" assembly. Further details are omitted.

[0330] Similarly, the method provided by this invention can be used to plan the assembly sequence for other assemblies and obtain the optimal assembly sequence with the minimum assembly sequence cost. Specific examples will not be given here.

[0331] In summary, the assembly sequence planning method based on the discrete artificial sparrow search algorithm proposed in this invention is feasible and practical. It can rationally plan the assembly sequence of parts in an assembly, eliminate infeasible assembly sequences, improve the rationality of the assembly sequence, reduce assembly costs, and improve assembly efficiency.

Claims

1. An assembly sequence planning method, characterized in that, The planning method includes the following steps: S1: Establish an assembly information model and obtain the three-dimensional model information of the assembly and parts; S2: Extract the interference matrix and contact matrix of the assembly, extract the mass, volume, number of geometric constraints, assembly direction, and assembly tool type information of the parts in the assembly, and calculate the number of connection constraints and assembly operation difficulty of each part in the assembly. S3: Select the basic component of the assembly based on the mass, volume, and number of geometric constraints of the parts in the assembly; S4: Based on the mass, volume, number of geometric constraints, number of connection constraints, assembly direction, type of assembly tools, and difficulty of assembly operation of the parts in the assembly, construct an evaluation index for the cost of the assembly sequence, including assembly handling cost, assembly geometric constraint cost, assembly connection constraint cost, assembly direction change cost, assembly tool change cost, and assembly operation difficulty cost. S5: Based on the assembly handling cost, assembly geometric constraint cost, assembly connection constraint cost, assembly direction change cost, assembly tool change cost, and assembly operation difficulty cost, design the corresponding weight coefficients for each evaluation index and calculate the assembly sequence cost. S6: The discrete artificial sparrow search algorithm is used to solve the discrete optimization problem of assembly sequence planning. The discrete artificial sparrow search algorithm adds a discrete strategy and a feasible regularization strategy to the sparrow search algorithm, and adds four mutation strategies in the sparrow population evolution, including the Tent mapping strategy, the reverse learning strategy, the elite selection strategy and the dimension learning strategy, to obtain the optimal assembly sequence with the minimum assembly sequence cost.

2. The assembly sequence planning method according to claim 1, characterized in that, For a given An assembly composed of individual parts There are several assembly sequences. Assembly sequence The implementation of this assembly is described. The assembly sequence of parts in the assembly process. For the first in the assembly sequence There are elements, among which This refers to the first step in the assembly process. The part numbers of the parts required for assembly in each assembly sequence operation within the assembly body.

3. The assembly sequence planning method according to claim 2, characterized in that, The interference matrix is ​​used to describe the assembly. Medium parts When assembling parts along a certain coordinate axis in a Cartesian coordinate system The interference between parts reflects the spatial constraint relationship between the parts of the assembly and is used to determine the geometric feasibility of the assembly sequence. For a given An assembly composed of individual parts The interference matrix is ​​defined as shown in equation (1). : ；（1） In equation (1), the interference matrix elements ,in , indicating parts With parts Between along The interference relationship in the direction is described by equation (2) for the elements of the interference matrix. : ；（2） In formula (2), when the part Along When assembling in a directional manner with the parts Interference occurs, and the parts Along When assembling in a directional manner with the parts The interference occurs under the same conditions, therefore, depending on the direction... Interference matrix You can get the direction Interference matrix ,in, ; The contact matrix is ​​used to describe the parts in the assembly. With parts The contact situation reflects the connection constraint relationship between parts; For a given An assembly composed of individual parts The contact matrix is ​​defined as shown in equation (3). : （3） In equation (3), the contact matrix elements ,in , indicating parts With parts The contact relationships between them are described by equation (4) for the contact matrix elements. : ；（4） According to the definition of the contact matrix, the contact matrix... It is a symmetric matrix, that is .

4. The assembly sequence planning method according to claim 3, characterized in that, The assembly base component is the first part to be assembled in the assembly. It is characterized by its large mass, large volume, and numerous geometric constraints with other parts. You can choose according to formula (5): ；（5） In equation (5), Indicates parts in an assembly The corresponding evaluation scores for the basic components of the assembly are shown in Equation (6): ； （6） In equation (6), , , Representing assemblies respectively The Middle One part The mass, volume, and number of geometric constraints.

5. The assembly sequence planning method according to claim 4, characterized in that, The assembly and handling cost This can be described by equation (7): ；（7） In equation (7), , Representing assembly sequence The Middle A part that needs to be assembled In the assembly process, the larger the mass and volume of a part, the worse its assemblability. The time and cost of assembling such parts are also higher. Therefore, they should be prioritized for assembly. The assembly geometric constraint cost This can be described by equation (8): ； （8） In equation (8), Indicates assembly sequence The Middle A part that needs to be assembled The number of geometric constraints is a factor in the assembly process. Parts with more geometric constraints have a more complex assembly process, resulting in higher assembly time and costs. Therefore, these parts should be prioritized for assembly. The calculation is shown in equation (9): ； （9） The assembly connection constraint cost This can be described by equation (10): ； （10） In equation (10), Indicates assembly sequence The Middle A part that needs to be assembled The number of assembly connection constraints is important. During assembly, the more connection constraints a part has, the more stable the assembly process will be. Therefore, parts with more connection constraints should be prioritized for assembly. The calculation is shown in equation (11): ； （11） The calculation is shown in equation (12): ；（12） The assembly direction change cost This can be described by equation (13): ； （13） In equation (13), Indicates assembly sequence The Middle A part that needs to be assembled The more times the assembly direction is changed, the more complex the assembly process becomes, and the higher the assembly time and cost to complete the assembly. Therefore, the number of assembly direction changes should be minimized. The calculation is shown in equation (14): ；（14） In equation (14), For assembling parts The assembly direction used at that time; The cost of changing the assembly tool This can be described by equation (15): ； （15） In equation (15), Indicates assembly sequence The Middle A part that needs to be assembled The more times assembly tools are changed during assembly, the more complex the assembly process becomes, and the higher the assembly time and cost to complete the assembly. Therefore, the number of tool changes should be minimized. The calculation is shown in equation (16): ； （16） In equation (16), Indicates assembly parts The type of assembly tools used at that time This represents the total number of assembly tool categories used in the assembly process, and its value is determined by the total number of tool categories actually used in the assembly process.

6. The assembly sequence planning method according to claim 5, characterized in that, The steps for calculating the difficulty and cost of the assembly operation include: S61: Establish assembly rules, including a first assembly rule, a second assembly rule, a third assembly rule, a fourth assembly rule, a fifth assembly rule, a sixth assembly rule, and a seventh assembly rule. The first assembly rule includes the basic components of the assembly body; the second assembly rule includes assembling parts that are "heavy and large in volume"; the third assembly rule includes assembling parts that are "high precision"; the fourth assembly rule includes assembling parts that have "many connecting parts"; the fifth assembly rule includes assembling parts that have "interference fit"; the sixth assembly rule includes assembling parts at the "bottom layer of the assembly tree"; and the seventh assembly rule includes assembling parts that require heating or cooling and that are subject to compression or impact during the assembly process. S62: Define the assembly sequence according to the above assembly rules. The Middle A part that needs to be assembled Assembly operation difficulty Specifically, it includes: When parts The first assembly rule is met. , When parts It does not meet the first assembly rule, but meets three to six of the second, third, fourth, fifth, sixth, and seventh assembly rules. , When parts It does not meet the first assembly rule, but meets one or two of the second, third, fourth, fifth, sixth, and seventh assembly rules. , When parts If the first assembly rule is not met, and simultaneously any one of the second, third, fourth, fifth, sixth, and seventh assembly rules is also not met. , S63: Obtain the assembly sequence according to the method in S62. Corresponding assembly operation difficulty sequence During the assembly process, the more difficult the assembly operation, the more complex the assembly process, and the higher the assembly time and cost of assembling such parts. Therefore, they should be assembled first, as shown in formula (17) to calculate the assembly sequence. Assembly operation difficulty and cost : ；（17） In equation (17), The calculation is shown in equation (18): （18）。 7. The assembly sequence planning method according to claim 6, characterized in that, For assembly sequence set The method for calculating the assembly sequence cost of one of the assembly sequences is shown in equation (19): ；（19） In equation (19), , , , , as well as These are the weighting coefficients corresponding to the assembly handling cost, assembly geometric constraint cost, assembly connection constraint cost, assembly direction change cost, assembly tool change cost, and assembly operation difficulty cost, respectively, and they satisfy the following: （20）。 8. The assembly sequence planning method according to claim 7, characterized in that, sparrow Defined as an assembly sequence of an assembly. It is initialized to a 3D vector For the number of parts contained in the assembly, each sparrow The vector representation is as shown in equation (21): ； （21） In equation (21), This represents the current number of sparrow population evolution iterations in the discrete artificial sparrow search algorithm. The maximum number of evolution iterations is preset for the discrete artificial sparrow search algorithm.

9. The assembly sequence planning method according to claim 8, characterized in that, The specific steps for solving the discrete optimization problem of assembly sequence planning using the discrete artificial sparrow search algorithm include: S91: Discrete Artificial Sparrow Search Algorithm Parameter Settings, Population Size Setting Maximum number of evolution iterations Warning value The proportion of discoverers The proportion of scouts Elite Sparrows ; S92: Use the Tent mapping strategy to generate half the population size. The initial sparrow population with continuous value encoding is generated, and then the resulting initial sparrow population with continuous value encoding, which is half the size of the population, is discretized using a discretization strategy to obtain... Assembly sequence; S93: A reverse learning strategy is used to reverse learn the initial sparrow population with continuous value encoding, which is half the population size generated by the Tent mapping strategy in S92, to obtain... A sparrow population with continuous-value codes obtained through reverse learning is then discretized using a discretization strategy to obtain... The assembly sequence will generate the sequence in S92. Strip assembly sequences and reverse learning generated The assembly sequences are merged to obtain the complete set of assembly sequences corresponding to the initial sparrow population; S94: Generation Initial evolutionary search of the sparrow population: Calculate and initialize each sparrow in the initial sparrow population one by one. The corresponding assembly sequence Assembly sequence cost In the assembly sequence cost calculation, based on the feasible regularization strategy, all infeasible assembly sequences are regenerated and feasible regularized, and the assembly sequence cost of the regularized feasible assembly sequences is calculated, thereby obtaining... The initial evolutionary search sets feasible assembly sequences for the sparrow population. The assembly sequence costs of all sparrows in the current population are sorted, and the sparrow with the lowest assembly sequence cost is selected for updating. Select the sparrow update with the maximum assembly sequence cost. ; S95: Sparrow population evolution iterative search, specifically including: S951: Based on each sparrow in the sparrow population during each evolutionary iteration Assembly sequence cost value Sort by size from smallest to largest, according to a pre-set ratio. The entire sparrow population is divided into two sets: discoverers and followers. Sparrows with lower assembly costs are considered discoverers, while sparrows with higher assembly costs are considered followers. The sparrows in the discoverer set correspond to the better assembly sequence. Using an elite selection strategy, after selecting from the discoverer population based on the assembly sequence cost... Each sparrow is updated using equation (22): ； （22） In equation (22), Indicates the current number Sparrow in secondary evolution iteration The assembly sequence represented, for 3D random vector, To take values ​​in Random values ​​between To follow a normal distribution 3D random vector; Using an elite selection strategy, select from the follower group based on the assembly sequence cost. Each sparrow is updated using equation (23): ； （23） In equation (23), where, For the current number The sparrow with the minimum assembly sequence cost in the sparrow population during the next evolutionary iteration. As of now The sparrow with the highest assembly sequence cost that appeared in the sparrow population during the next evolutionary iteration. Each element value is randomly assigned the value 1 or -1. dimensional vector, , For all 1s dimensional vector, To follow a normal distribution 3D random vector; S952: Update the sparrow population after updating the discoverers and followers using the dimensional learning strategy to obtain the sparrow population updated by dimensional learning. For the sparrow population updated by dimensional learning, the proportion of scouts is determined. Randomly select some sparrows as scouts and update them according to equation (24): ；（24） In equation (24), As of now The sparrow with the minimum assembly sequence cost that appeared in the sparrow population during the next evolutionary iteration. For the first In the next evolutionary iteration, the sparrow with the highest assembly sequence cost in the sparrow population is the optimal update step size control parameter. For random numbers that follow a standard normal distribution, It is a random number. To avoid zero in the denominator, set... It is the smallest non-zero constant; S953: Use a discretization strategy to discretize the sparrows in the current sparrow population, and calculate each sparrow in the current evolutionary iteration of the sparrow population one by one. The corresponding assembly sequence Assembly sequence cost In the assembly sequence cost calculation, all infeasible assembly sequences are regenerated and made feasible based on the feasible regularization strategy, and the assembly sequence cost of the regularized feasible assembly sequence is calculated. S954: Select each sparrow in the current sparrow population. Assembly sequence cost The assembly sequence cost of its previous evolutionary iteration The assembly sequence cost is compared with that of the previous generation of sparrows. If the assembly sequence cost decreases, the current assembly sequence corresponding to that sparrow is maintained; if the assembly sequence cost increases, the assembly sequence corresponding to that sparrow is restored to the assembly sequence of the previous evolutionary iteration, thus obtaining a sparrow population adjusted and updated based on the comparison with the assembly sequence cost of the previous generation of sparrows. The assembly sequence costs of all sparrows in the current sparrow population are sorted, and the sparrow with the lowest assembly sequence cost in the current sparrow population is selected and compared with... Compare the assembly sequence costs. If the sparrow with the lowest assembly sequence cost in the current sparrow population has an even lower assembly cost, then use that sparrow to update the system. Similarly, select the sparrow with the highest assembly sequence cost in the current sparrow population, and... Compare the assembly sequence costs. If the sparrow with the highest assembly sequence cost in the current sparrow population has a higher assembly cost, then use that sparrow to update the sequence. ; S955: Increment the current evolution iteration count by 1. If the current evolution iteration number Less than the maximum number of evolution iterations If the result is positive, proceed to S951; otherwise, stop the evolutionary iterative search and output the result. The optimal assembly sequence is the one with the lowest cost found through evolutionary iteration.

10. The assembly sequence planning method according to claim 9, characterized in that, The Tent mapping strategy is a chaotic mapping, and its expression is shown in equation (25): ； （25） In equation (25), , , For the population size of sparrows, Sparrows generated for random initialization The assembly sequence represented The Assembly sequence of individual parts Sparrows generated for random initialization The assembly sequence represented The assembly sequence with continuous value encoding obtained after Tent mapping is the first... The assembly sequence of the parts; The discrete strategy is an assembly sequence that encodes continuous values ​​generated in the discrete artificial sparrow search algorithm. The element values ​​are arranged in ascending order. If the element values ​​are equal, they are arranged according to their order in the assembly sequence. Based on the element value sorting result, each assembly sequence... elements A corresponding integer sequence number is obtained, and the element value at the original position of the assembly sequence is replaced with the integer sequence number to generate a discrete assembly sequence, where each element represents the part number of the part to be assembled in the assembly body in the corresponding assembly sequence. All steps involving calculating the assembly sequence cost require discretization of the assembly sequence using the discretization strategy for the continuously value encoded assembly sequence before the assembly sequence cost can be calculated. The feasibility of the assembly sequence is regularized using the aforementioned feasible regularization strategy, specifically including: selecting the basic components according to the method for selecting basic components of the assembly. Place it at the first position in the assembly sequence. Then, starting from the second position in the assembly sequence, determine whether there is interference in the current assembly sequence based on the assembly interference matrix. If there is interference, regenerate an assembly sequence and determine whether there is interference in the generated assembly sequence. If there is still interference, repeat the assembly sequence generation and interference judgment process until a feasible assembly sequence without interference is obtained. The method for determining whether there is interference in the assembly sequence is as follows: For each part in the assembly sequence, the interference matrix corresponding to its assembly direction can be used to determine whether the part interferes with all the parts assembled earlier in the assembly sequence. If all the parts in the assembly sequence do not interfere with the parts assembled earlier, then it can be determined that there is no interference in the assembly sequence, which is feasible. All steps involving the calculation of assembly sequence costs require the use of feasible regularization strategies to perform feasible regularization on the interference situations of the assembly sequence, and finally calculate the assembly sequence cost of a feasible assembly sequence that has no interference situations after feasible regularization.

11. The assembly sequence planning method according to claim 10, characterized in that, The reverse learning strategy generates half the population size of the Tent mapping strategy in S92. The continuous value encoding of the initial sparrow population is used for reverse learning to generate... A reverse sparrow, the generation of which is shown in equations (26) to (28): ；（26） ；（27） ； （28） In equations (26) to (28), , Half the population size after Tent mapping The sparrow with the minimum assembly sequence cost in the initial sparrow population. For its inverse solution, and These are the upper and lower limits of the search space, respectively. For information exchange control parameters, To obey A normal distribution 3D random vector, The initial sparrow after reverse learning The assembly sequence it represents; The elite selection strategy guides the sparrow population to generate assembly sequences with lower assembly costs, defining elites as those with the lowest assembly sequence costs within the sparrow population. Assembly sequence, To determine the number of elite sparrows, the sparrow population maintains the current number during each evolutionary iteration. The elite sparrow corresponding to the secondary evolutionary iteration Assembly sequences with lower cost The process proceeds directly to the next sparrow population evolution iteration, as shown in equation (29): ；（29） Before each evolutionary iteration of the sparrow population's discoverers and followers, an elite selection strategy is needed to select a certain proportion of elite sparrows corresponding to the assembly sequence to directly enter the next evolutionary iteration. The dimensional learning strategy simulates the evolutionary iteration of a sparrow population, where the evolution of each sparrow is influenced by several neighboring sparrows, i.e., each assembly sequence... The next evolutionary iteration is influenced by the set of nearest-neighbor assembly sequences. The influence of this, the dimensional learning of sparrows is shown in equations (30) to (33): ； （30） ；（31） ； （32） ；（33） In equations (30) to (33), , , Indicates the first Assembly sequence nearest neighbor radius, Indicates the current number The set of nearest neighbor sequences of an assembly sequence. This means randomly selecting a nearest neighbor sequence from the set of nearest neighbor sequences. This represents the nearest neighbor sequence after dimensional learning is performed according to the dimensional learning strategy.

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