A bending process planning method based on improved NSGA-II

Abstract

The application discloses a kind of based on the bending process planning method of improved NSGA-Ⅱ, step one, input processing information: including workpiece information, die library information, machine tool processing parameters;Step two, workpiece manufacturability check: check whether workpiece can be completed processing under existing bending equipment, if not, jump to step six;Step three, NSGA-Ⅱ initialization: set algorithm parameters, generate initial population;Step four, genetic evolution: the iterative process of strategy optimization algorithm using adaptive adjustment crossover mutation probability;Step five, result processing: according to the priority of optimization target from the pareto optimal solution set output in step four Optimal bending process is selected;Step six, output process scheduling results: if workpiece is manufacturable, output bending sequence, positioning sequence;Otherwise, output workpiece is not manufacturable.The application can obtain high processing efficiency bending process under the condition of meeting interference constraint, precision constraint and processing constraint.

Description

Technical Field

[0001] This invention belongs to the field of CNC bending machine control algorithms, specifically involving an intelligent process planning method based on the Elitist Non-dominated Sorting Genetic Algorithm (NSGA-Ⅱ). Background Technology

[0002] Bending is the most crucial process in sheet metal forming, significantly impacting the dimensional accuracy and shape profile of the finished product. Due to the combined effects of complex workpiece shapes, discrete processing steps, and diverse bending tools, bending process planning becomes a multi-objective optimization process. NSGA-II, as a multi-objective swarm intelligence algorithm, offers advantages such as independence from expert knowledge bases and model parameters, as well as high computational efficiency. Compared to single-objective genetic algorithms (SGA), its output Pareto optimal solution set lacks objective bias. Summary of the Invention

[0003] Purpose of the Invention: Sheet metal bending process planning is a complex multi-objective optimization process. A well-planned bending process can significantly reduce auxiliary time and improve bending accuracy. To improve bending efficiency, a process optimization model is established based on the constraints of bending operations, and a process planning method based on a fast non-dominated sorting genetic algorithm is designed. To improve bending accuracy and optimize the workpiece operation process, a back gauge positioning selection method that comprehensively considers interference collisions, accuracy requirements, and workpiece shape is proposed. To address the convergence instability problem of the algorithm, the crossover and mutation probabilities are adaptively adjusted based on the virtual fitness value to optimize the evolutionary process.

[0004] Technical solution: A bending process planning method based on the improved NSGA-II, characterized by the following steps:

[0005] Step 1: Input machining information: including workpiece information, mold library information, and machine tool machining parameters;

[0006] Step 2, Workpiece Manufacturability Check: Check whether the workpiece can be processed using existing bending equipment. If not, proceed to Step 6.

[0007] Step 3, NSGA-II Initialization: Set algorithm parameters and generate the initial population;

[0008] Step 4, Genetic Evolution: Optimize the algorithm iterative process using a strategy that adaptively adjusts the crossover and mutation probabilities;

[0009] Step 5: Result Processing: Select the optimal bending process from the Pareto optimal solution set output in Step 4 based on the priority of the optimization objectives;

[0010] Step 6: Output process arrangement results: If the workpiece is manufacturable, output the bending sequence and positioning sequence; otherwise, output that the workpiece is not manufacturable.

[0011] Furthermore, the workpiece information in step one specifically includes the sheet thickness, the width of each flange face between bending angles, and the material mechanical properties; the mold library information includes the upper mold fillet radius, the lower mold width, and other geometric dimensions used for interference checks; the machine tool information includes processing parameters and geometric dimensions.

[0012] Furthermore, the algorithm parameters in step three include the maximum number of generations G, the population size P, the encoding method, the selection operator, the crossover operator, and the mutation operator.

[0013] Furthermore, the genetic evolution process in step four is implemented as follows:

[0014] Step (1): Determine the back gauge positioning sequence based on the bending sequence, and further calculate the objective function value. The current evolution generation g = 1.

[0015] Step (2): Sort the population into non-dominated groups and stratify them according to the values ​​of each objective function until all populations are stratified.

[0016] Step (3): Based on the virtual fitness value, perform selection, adaptive crossover and mutation operations to generate a new population, g = g + 1;

[0017] The method for adaptively adjusting the crossover and mutation probabilities based on the virtual fitness value is as follows: NSGA-II uses a strategy of fixed crossover and mutation probabilities to control the population iteration process, and its convergence result depends on the values ​​of the crossover and mutation probabilities. In order to preserve the patterns of better individuals, accelerate the convergence of the solution space to the Pareto front, and improve the distribution of the Pareto optimal solution in the target space, the sigmoid function is used to fit the adaptive crossover and mutation probability curves. The formula for adaptively adjusting the crossover and mutation probabilities based on the virtual fitness value is as follows:

[0018]

[0019]

[0020] In equation (1-2): P c1 Minimum crossover rate; P c2 P represents the maximum crossover rate. m1 P represents the minimum rate of variation. m2 The maximum rate of variation is K; K is a constant; F is the maximum rate of variation. m F represents the maximum virtual fitness value of the population. a This represents the average virtual fitness value of the population.

[0021] Step (4): If g≤G, then jump to step (2); otherwise, output the Pareto optimal solution set.

[0022] Furthermore, the optimization objective in step five is as follows: N (N≥1) in the following text represents the number of bending segments of the workpiece;

[0023] (1) Number of mold changes D: The smaller the value, the better the process. The calculation method is as follows:

[0024]

[0025] In equation (3): D is the total number of die changes in the bending sequence; UD is the number of times the upper die is changed; LD is the number of times the lower die is changed;

[0026]

[0027] In equation (4): BA is the bending angle, BA∈(-180°,0)∪(0,180°); UA is the upper die fillet.

[0028]

[0029] In formula (5): PS is the workpiece positioning length, mm; LS is the lower die width, mm;

[0030] (2) Number of workpiece adjustments M: This includes two operations: flipping and turning. The smaller the value, the better the process. The calculation method is as follows:

[0031]

[0032] In equation (6): R is the number of times the workpiece is flipped; T is the number of times the workpiece is turned around;

[0033]

[0034]

[0035] In formula (8): PM is the back gauge positioning position, reflecting its position relative to the workpiece, 0≤PM≤N+1; BM is the current bending position, 1≤BM≤N;

[0036] (3) Relative movement path length W of the workpiece: Taking the contact position between the upper die and the workpiece as a reference, the workpiece can be regarded as moving between different bending positions. The shorter the relative movement distance, the higher the execution efficiency of the process. The calculation method is as follows:

[0037]

[0038] In equation (9): w iLet L be the distance the workpiece moves relative to the workpiece during the i-th bend; L is the unfolded length of the workpiece, calculated as follows:

[0039]

[0040] In formula (10): l i Let Δl be the side length of the i-th workpiece segment. j This is the transition length between the (j-1)th and jth segments of the workpiece.

[0041] Furthermore, the objective function includes f1, f2, and f3, corresponding to the number of mold changes, the number of workpiece adjustments, and the relative movement path length of the workpiece, respectively. To avoid the algorithm getting trapped in local optima and to optimize the distribution of the Pareto optimal solution in the target space, bending sequences that do not meet geometric constraints are also included in the genetic evolution process. To distinguish whether a sequence is feasible based on the objective function value, the objective function value of the interfering sequence is forced to be greater than the maximum value of the non-interfering sequence; this value can be pre-calculated from the workpiece information. The objective functions f1, f2, and f3 are calculated as follows:

[0042]

[0043] In equation (11): the maximum number of times the upper mold can be replaced is N; s ij Let i be the number of times the lower die can be changed from feasible positioning positions i to j on the workpiece. Therefore, the maximum number of times the lower die can be changed is:

[0044]

[0045] In equation (12): d ij n is the unfolded length corresponding to the feasible positioning positions i to j on the workpiece; L This represents the total number of sub-modules;

[0046]

[0047]

[0048] Furthermore, the process of determining the back gauge positioning sequence based on the bending sequence in step six is ​​as follows: In order to ensure positioning accuracy and reliability, back gauge positioning is generally selected from the already processed bends or both ends of the sheet metal. Therefore, there are at most N+2 feasible positioning options for a workpiece with N bends.

[0049] Step 1): Input the bending sequence B, and set the counter i = 1;

[0050] Step 2): Determine b L b R b L b R b is the current bending position of the workpiece. CThe nearest completed bends are on the left and right sides. If there are no completed bends, then they are at both ends of the workpiece.

[0051] Step 3): Using b respectively L and b R Perform an interference check for back gauge positioning, and return the interference check results. If interference occurs in both checks, proceed to step 5.

[0052] Step 4): Select the positioning position. If there is interference, select the positioning position without interference. Otherwise, select the positioning position according to the proximity conditions, accuracy requirements and workpiece shape, i = i + 1. If i ≤ N, jump to step 2).

[0053] Step 5): Output the results, if each is expressed in terms of b L and b R If interference occurs during back gauge positioning, the output process will collide; otherwise, the positioning sequence will be output.

[0054] Furthermore, the interference check process in step six is ​​as follows:

[0055] Step 1): Input the bending sequence B, and set the counter i = 1;

[0056] Step 2): Calculate the relative bending b at each point of the unfolded and formed workpiece. i The coordinates;

[0057] Step 3): Generate a set of graphic elements for the workpiece in its unfolded and formed states based on the bending angle symbol;

[0058] Step 4): Perform interference analysis on the elements in the workpiece element set and the element sets of the upper mold, lower mold, and machine tool respectively. If there is no interference, then i = i + 1, and jump to step 2); otherwise, jump to step 5.

[0059] Step 5): Output results: If there is interference, output the interference position information according to the source of the interference primitive; otherwise, output that the workpiece does not interfere.

[0060] Furthermore, the process for selecting the positioning position based on proximity conditions, accuracy requirements, and workpiece shape is as follows, where b G For the final bending positioning, p C For the current bend b C Precision requirements on both sides;

[0061]

[0062] (1) When b L With b C Adjacent and b R With b C When they are not adjacent:

[0063]

[0064] (2) When b L With b C Not adjacent and b R With b C When adjacent:

[0065]

[0066] (3) When b L and b R Both with b C When they are not adjacent:

[0067] b G =J(b) C ,b L ,b R (18);

[0068] (4) When b L and b R Both with b C When adjacent:

[0069]

[0070] Furthermore, the method for determining the positioning position based on the workpiece shape is as follows: In bending processes, to facilitate placement and positioning, it is necessary to ensure that the complex parts of the workpiece are located on the worker's side; a shape determination function is designed. (1≤i≤N) is used to determine the positioning position of the backstop based on the shape of the workpiece, where & is a logical AND operation, X ML X MR These represent the current bend b. C Based on the reference, the maximum horizontal projection length of the left and right parts of the workpiece relative to the current bend; Y ML Y MR These represent the current bend b. C Based on the reference, the maximum vertical projection length of the left and right parts of the workpiece relative to the current bend;

[0071] (1) When X ML ≠X MR hour:

[0072]

[0073] (2) When X ML =X MR hour:

[0074]

[0075] (3) When X ML =XMR And Y ML =Y MR At the same time, the positioning position of the current bend is selected based on the positioning of the previous bend to avoid the additional workpiece turning operation caused by random positioning.

[0076]

[0077] Beneficial Effects: This invention uses an improved adaptive NSGA-II design algorithm for bending process planning. The Pareto optimal solution set output by the algorithm is sorted according to the priority of the objective function to determine the optimal solution. By improving the backgauge positioning selection method, high-efficiency bending processes can be obtained while satisfying interference constraints, accuracy constraints, and processing constraints. For discrete permutation coding problems like bending process planning, the adaptive crossover and mutation evolution strategy based on the sigmoid function can effectively preserve the patterns of superior bending sequences and accelerate algorithm convergence. The bending process planning method based on the improved NSGA-II overcomes the shortcomings of SGA-based process planning methods in terms of accuracy and convergence stability. Furthermore, because the Pareto optimal solution set is uniformly distributed in the objective space, it can output different bending processes according to different decision preferences, making it more suitable for sheet metal bending manufacturing scenarios with diverse products. Attached Figure Description

[0078] Figure 1 This is a schematic diagram of the workpiece in an embodiment of the present invention;

[0079] Figure 2 This is a schematic diagram of the adaptive crossover probability adjustment curve in an embodiment of the present invention;

[0080] Figure 3 A schematic diagram of the process for selecting the back gauge positioning;

[0081] Figure 4 A schematic diagram for workpiece positioning;

[0082] Figure 5 This is a schematic diagram of the interference inspection process in an embodiment of the present invention;

[0083] Figure 6 This is a schematic diagram of a bending process planning method based on the improved NSGA-II in an embodiment of the present invention. Detailed Implementation

[0084] The technical solutions in the embodiments of the present invention will be clearly and completely described below, so that those skilled in the art can better understand the advantages and features of the present invention, thereby making a clearer definition of the scope of protection of the present invention. The embodiments described in this invention are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0085] Example

[0086] A bending process planning method based on the improved NSGA-II includes the following steps:

[0087] Step 1: Input machining information: including workpiece information, mold library information, and machine tool machining parameters;

[0088] Step 2, Workpiece Manufacturability Check: Check whether the workpiece can be processed using existing bending equipment. If not, proceed to Step 6.

[0089] Step 3, NSGA-II Initialization: Set algorithm parameters and generate the initial population;

[0090] Step 4, Genetic Evolution: Optimize the algorithm iterative process using a strategy that adaptively adjusts the crossover and mutation probabilities;

[0091] Step 5: Result Processing: Select the optimal bending process from the Pareto optimal solution set output in Step 4 based on the priority of the optimization objectives.

[0092] Step 6: Output process arrangement results: If the workpiece is manufacturable, output the bending sequence and positioning sequence; otherwise, output that the workpiece is not manufacturable.

[0093] like Figure 1 The diagram shown is a schematic of the workpiece in an embodiment of the present invention, where the positional accuracy of the mark Δ is required to be high.

[0094] Specifically, the algorithm parameters in step three are as follows: population size is 100, maximum number of generations is 50, encoding method is permutation encoding, and tournament selection operator, partial matching crossover operator and reverse mutation operator are used.

[0095] Specifically, the parameter for adaptively adjusting the crossover mutation probability in step four is set as: minimum crossover rate P. c1 =0.5, maximum crossover rate P c2 =0.9, minimum rate of variation P m1 =0.05, maximum variation rate P m2 =0.1, constant K = 31.691. For example... Figure 2The diagram shows an adaptive crossover probability adjustment curve. During a certain generation of evolution, when the virtual fitness value F1 of an individual is less than F... a When the maximum crossover rate is used, the probability of generating new genes is increased; when F1 ≥ F2, the probability of generating new genes is increased. a At that time, due to the characteristics of the sigmoid function, even if F a and F m Even with significant differences, the adaptive crossover probability curve will not degenerate into a linear curve, especially when it approaches F. a The crossover rate changes relatively little and remains close to its maximum value, allowing individuals with low fitness to maintain a high crossover probability; near F m The crossover rate also changes little and remains close to a minimum, which can minimize the disruption of the pattern of high-fit individuals. The adaptive mutation probability adjustment process is similar.

[0096] Specifically, the priority of the objective function in step five is f1 > f2 > f3. During the bending process, the time consumed by mold replacement (corresponding to f1) is the longest, followed by workpiece adjustment (corresponding to f2), and finally workpiece movement (corresponding to f3). Therefore, the Pareto optimal solutions are sorted according to the priority of f1 > f2 > f3, and the solution with the smallest objective function value is selected as the optimal solution.

[0097] The genetic evolution process in step four is implemented as follows:

[0098] Step 1: Determine the back gauge positioning sequence based on the bending sequence, and further calculate the objective function value. The current evolution generation g = 1.

[0099] Step 2: Sort the population into non-dominated groups and stratify them according to the objective function values ​​until all populations are stratified.

[0100] Step 3: Based on the virtual fitness value, perform selection, adaptive crossover, and mutation operations to generate a new population, g = g + 1;

[0101] Step 4: If g≤G, then jump to step (2); otherwise, output the Pareto optimal solution set.

[0102] The process for determining the back gauge positioning sequence based on the bending sequence is as follows:

[0103] Step 1: Input the bending sequence B, and set the counter i = 1;

[0104] Step 2: Determine b L b R b L b R b is the current bending position of the workpiece. C The nearest completed bends are on the left and right sides. If there are no completed bends, then they are at both ends of the workpiece.

[0105] Step 3: Using b respectively L and b R Perform an interference check for back gauge positioning, and return the interference check results. If interference occurs in both checks, proceed to step 5.

[0106] Step 4: Select the positioning position. If interference exists, select a positioning position without interference; otherwise, select a positioning position based on proximity conditions, accuracy requirements, and workpiece shape, i = i + 1. If i ≤ N, jump to step 2).

[0107] Step 5: Output the results. If we use b respectively... L and b R If interference occurs during back gauge positioning, the output process will collide; otherwise, the positioning sequence will be output.

[0108] like Figure 4 The diagram shown is a simplified illustration, with the candidate location b. L and b R All are related to the current bending b C Adjacent, and workpiece l L and l R Given the same precision requirements for the segments, X ML >X MR Y ML >Y MR It is known that the shape on the left side of the workpiece is more complex, therefore, option b is chosen in this case. R For back gauge positioning, such as Figure 4 As shown in (a).

[0109] The interference check process is as follows:

[0110] Step 1: Input the bending sequence B, and set the counter i = 1;

[0111] Step 2: Calculate the relative bending b at each point of the unfolded and formed workpiece. i The coordinates;

[0112] Step 3: Generate a set of primitives for the workpiece in its unfolded and formed states based on the bending angle symbol;

[0113] Step 4: Perform interference analysis on the elements in the workpiece element set and the element sets of the upper mold, lower mold, and machine tool respectively. If there is no interference, then i = i + 1, and jump to step 2); otherwise, jump to step 5.

[0114] Step 5: Output results: If interference occurs, output the interference location information based on the source of the interfering primitive; otherwise, output that the workpiece does not interfere.

[0115] In this embodiment, the final bending sequence of the workpiece is 1,7,8,17,15,16,6,4,2,5,10,11,14,3,9,12,13; the positioning sequence is 0,0,7,18,17,17,1,1,1,4,8,10,15,2,8,14,14; the objective functions are f1 = 6, f2 = 10, and f3 = 3.655. This bending sequence first completes bending 14 with bending 15 as the positioning, and then completes bending 13 with bending 14 as the positioning, thus meeting the accuracy requirements.

[0116] Sheet metal bending is a discrete processing procedure. The bending operation intervals require manual intervention to adjust the workpiece. A reasonable bending sequence can significantly improve bending efficiency. This invention designs a bending process planning algorithm based on an improved adaptive NSGA-II. The algorithm sorts the Pareto optimal solution set according to the priority of the objective function to determine the optimal solution. By improving the backgauge positioning selection method, high-efficiency bending processes can be obtained while satisfying interference constraints, accuracy constraints, and processing constraints. For discrete permutation coding problems like bending process planning, an evolutionary strategy based on adaptive crossover and mutation using the sigmoid function can effectively preserve the patterns of better bending sequences and accelerate algorithm convergence. The bending process planning method based on the improved NSGA-II overcomes the shortcomings of SGA-based process planning methods in terms of accuracy and convergence stability. Furthermore, because the Pareto optimal solution set is uniformly distributed in the target space, it can output different bending processes according to different decision preferences, making it more suitable for sheet metal bending manufacturing scenarios with diverse products.

Claims

1. A bending process planning method based on the improved NSGA-II, characterized in that: Includes the following steps: Step 1: Input machining information: including workpiece information, mold library information, and machine tool machining parameters; Step 2, Workpiece Manufacturability Check: Check whether the workpiece can be processed using existing bending equipment. If not, proceed to Step 6. Step 3, NSGA-II Initialization: Set algorithm parameters and generate the initial population; Step 4, Genetic Evolution: Optimize the algorithm iterative process using a strategy that adaptively adjusts the crossover and mutation probabilities; Step 5: Result Processing: Select the optimal bending process from the Pareto optimal solution set output in Step 4 based on the priority of the optimization objectives; Step 6: Output the process arrangement results: If the workpiece is manufacturable, output the bending sequence and positioning sequence; otherwise, output that the workpiece is not manufacturable. The workpiece information in step one specifically includes the sheet thickness, the width of each flange face between bending angles, and the material mechanical properties; the mold library information includes the upper mold fillet radius, the lower mold width, and other geometric dimensions used for interference checks; the machine tool information includes processing parameters and geometric dimensions. The algorithm parameters in step three include the maximum number of generations G, the population size P, the encoding method, the selection operator, the crossover operator, and the mutation operator; The genetic evolution process in step four is implemented as follows: Step (1): Determine the back gauge positioning sequence based on the bending sequence, and further calculate the objective function value. The current evolution generation g = 1. Step (2): Sort the population into non-dominated categories and stratify them according to the values ​​of each objective function until all populations are stratified. Step (3): Based on the virtual fitness value, perform selection, adaptive crossover and mutation operations to generate a new population, g = g + 1; The method for adaptively adjusting the crossover and mutation probabilities based on the virtual fitness value is as follows: NSGA-II uses a strategy of fixed crossover and mutation probabilities to control the population iteration process, and its convergence result depends on the values ​​of crossover and mutation probabilities. In order to preserve the patterns of better individuals, accelerate the convergence of the solution space to the Pareto front, and improve the distribution of the Pareto optimal solution in the target space, the sigmoid function is used to fit the adaptive crossover and mutation probability curves. The formula for adaptively adjusting the crossover and mutation probabilities based on the virtual fitness value is as follows: In equation (1-2): P c1 Minimum crossover rate; P c2 P represents the maximum crossover rate. m1 P represents the minimum rate of variation. m2 The maximum rate of variation is K; K is a constant; F is the maximum rate of variation. m F represents the maximum virtual fitness value of the population. a This represents the average virtual fitness value of the population. Step (4): If g≤G, then jump to step (2); otherwise, output the Pareto optimal solution set. The optimization objective in step five is as follows: N (N≥1) in the following text represents the number of bending segments of the workpiece; (1) Number of mold changes D: The smaller the value, the better the process. The calculation method is as follows: In equation (3): D is the total number of die changes in the bending sequence; UD is the number of times the upper die is changed; LD is the number of times the lower die is changed; In equation (4): BA is the bending angle, BA∈(-180°,0)∪(0,180°); UA is the upper die fillet, UA∈(0,180°); In formula (5): PS is the workpiece positioning length, in mm; LS is the lower die width, in mm; (2) Number of workpiece adjustments M: This includes two operations: flipping and turning. The smaller the value, the better the process. The calculation method is as follows: In equation (6): R is the number of times the workpiece is flipped; T is the number of times the workpiece is turned around; In formula (8): PM is the back gauge positioning position, reflecting its position relative to the workpiece, 0≤PM≤N+1; BM is the current bending position, 1≤BM≤N; (3) Relative movement path length W of the workpiece: Taking the contact position between the upper die and the workpiece as a reference, the workpiece can be regarded as moving between different bending positions. The shorter the relative movement distance, the higher the execution efficiency of the process. The calculation method is as follows: In equation (9): w i Let L be the distance the workpiece moves relative to the workpiece during the i-th bend; L is the unfolded length of the workpiece, calculated as follows: In formula (10): l i Let Δl be the side length of the i-th workpiece segment. j This is the transition length between the (j-1)th and jth segments of the workpiece; The objective function includes f1, f2, and f3, corresponding to the number of mold changes, the number of workpiece adjustments, and the relative movement path length of the workpiece, respectively. To avoid the algorithm getting trapped in local optima and to optimize the distribution of the Pareto optimal solution in the objective space, bending sequences that do not meet geometric constraints are also included in the genetic evolution process. To distinguish whether a sequence is feasible based on the objective function value, the objective function value of the interference sequence is forced to be greater than the maximum value of the non-interference sequence; this value can be pre-calculated from the workpiece information. The objective functions f1, f2, and f3 are calculated as follows: In equation (11): the maximum number of times the upper mold can be replaced is N; s ij Let i be the number of times the lower die can be changed from feasible positioning positions i to j on the workpiece. Therefore, the maximum number of times the lower die can be changed is: In equation (12): d ij n is the unfolded length corresponding to the feasible positioning positions i to j on the workpiece; L This represents the total number of sub-modules; The process of determining the back gauge positioning sequence based on the bending sequence in step six is ​​as follows: In order to ensure positioning accuracy and reliability, back gauge positioning is generally selected from the already processed bends or both ends of the sheet metal. Therefore, there are at most N+2 feasible positioning options for a workpiece with N bends. Step 1): Input the bending sequence B, and set the counter i = 1; Step 2): Determine b L b R :b L b R b is the current bending position of the workpiece. C The nearest completed bends are on the left and right sides. If there are no completed bends, then they are at both ends of the workpiece. Step 3): Using b respectively L and b R Perform an interference check for back gauge positioning, and return the interference check results. If interference occurs in both checks, proceed to step 5. Step 4): Select the positioning position. If there is interference, select the positioning position without interference. Otherwise, select the positioning position according to the proximity conditions, accuracy requirements and workpiece shape, i = i + 1. If i ≤ N, jump to step 2). Step 5): Output the results, if each is expressed in terms of b L and b R If interference occurs during back gauge positioning, the output process will collide; otherwise, the positioning sequence will be output. The interference check process in step six is ​​as follows: Step 1): Input the bending sequence B, and set the counter i = 1; Step 2): Calculate the relative bending b at each point of the unfolded and formed workpiece. i The coordinates; Step 3): Generate a set of graphic elements for the workpiece in its unfolded and formed states based on the bending angle symbol; Step 4): Perform interference analysis on the elements in the workpiece element set and the element sets of the upper mold, lower mold, and machine tool respectively. If there is no interference, then i = i + 1, and jump to step 2); otherwise, jump to step 5. Step 5): Output results: If interference occurs, output the interference location information based on the source of the interference primitive; otherwise, output that the workpiece does not interfere. The process for selecting the positioning position based on proximity conditions, accuracy requirements, and workpiece shape is as follows, where b G For the final bending positioning, p C For the current bend b C Precision requirements on both sides; (1) When b L With b C Adjacent and b R With b C When they are not adjacent: (2) When b L With b C Not adjacent and b R With b C When adjacent: (3) When b L and b R Both with b C When they are not adjacent: b G =J(b C ,b L ,b R ) (18); (4) When b L and b R Both with b C When adjacent: The method for determining the positioning position based on the workpiece shape is as follows: In bending processes, to facilitate placement and positioning, it is necessary to ensure that the complex parts of the workpiece are on the worker's side; design a shape determination function. Used to determine the positioning position of the backstop based on the shape of the workpiece, where & is a logical AND operation, X ML X MR These represent the current bend b. C Based on the reference, the maximum horizontal projection length of the left and right parts of the workpiece relative to the current bend; Y ML Y MR These represent the current bend b. C Based on the reference, the maximum vertical projection length of the left and right parts of the workpiece relative to the current bend; (1) When X ML ≠X MR hour: (2) When X ML =X MR hour: (3) When X ML =X MR And Y ML =Y MR At the same time, the positioning position of the current bend is selected based on the positioning of the previous bend to avoid the additional workpiece turning operation caused by random positioning.

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