A hole shaft assembly simulation analysis method

Abstract

The application discloses a kind of assembly simulation analysis methods of hole shaft group, which comprises the following steps: S1: using Monte Carlo method to convert the design parameters of hole shaft group into hole shaft simulation data;S2: based on hole shaft simulation data, the mathematical model of hole shaft movable circle intersection angle is established, the assembly possibility of hole shaft group is predicted, when hole shaft movable circle contains actual intersection, it can be determined that the simulation data can be assembled, enter S3 step;Otherwise, there is no possibility of assembly, after adjusting hole shaft group design parameters, return S1 step;S3: using GRO gold panning optimization algorithm, obtain the assembly simulation position point of suitable assembly hole shaft group.The method provides a simulation result of hole shaft group assembly by evolutionary algorithm, to simulate the actual assembly result;Further, by calculating simulation data, the distribution of assembly error and the limit assembly condition are provided, the tolerance analysis process is accelerated, the design cycle is reduced and the yield is improved.

Description

Technical Field

[0001] This invention discloses an assembly simulation analysis method for hole-shaft assemblies, belonging to the field of tolerance analysis technology. Background Technology

[0002] Tolerance analysis is the process of calculating assembly tolerances from known part tolerances. However, if the final analysis results do not meet the design quality requirements, the part tolerances need to be adjusted. To reduce production costs and improve part quality, multiple assembly tolerance analyses are often required during the production design process to finally determine the optimal and reasonable values ​​for part tolerances.

[0003] As a commonly used assembly structure, the hole-shaft assembly plays an important role in the tolerance transfer process of the dimensional chain. When the tolerance of the parts is constantly modified, the calculation of the impact of the error generated by the hole-shaft assembly structure on the final control object of the entire design is very large. As a result, in the machining process, the focus is often on improving the machining accuracy to ensure the yield, rather than obtaining a reasonable tolerance value at the design end. Summary of the Invention

[0004] The purpose of this invention is to provide an assembly simulation analysis method for hole-shaft assemblies. This method addresses the shortcomings of existing technologies by helping tolerance designers obtain the possible assembly results of the designed hole-shaft assemblies during the actual assembly process. It provides a simulation result of the hole-shaft assemblies assembly through an evolutionary algorithm, thereby simulating the actual assembly results. At the same time, it provides the distribution of assembly errors and limit assembly conditions by calculating simulation data, thereby accelerating the tolerance analysis process, reducing the design cycle, and improving the yield.

[0005] To achieve the above objectives, the present invention provides an assembly simulation analysis method for a hole-shaft assembly, characterized in that the method includes the following steps:

[0006] S1: The Monte Carlo method is used to convert the design parameters of the hole-shaft assembly into hole-shaft simulation data;

[0007] S2: Based on the simulation data of the hole shaft, establish a mathematical model of the intersection angle of the movable circles of the hole shaft, and predict the assembly possibility of the hole shaft group. When the movable circles of the hole shaft all contain actual intersections, it can be determined that the simulation data can be assembled, and proceed to step S3; otherwise, there is no possibility of assembly, and after readjusting the design parameters of the hole shaft group, return to step S1.

[0008] S3: The GRO gold mining optimization algorithm is used to obtain the simulation position points of the hole and shaft assembly suitable for assembly.

[0009] Furthermore, the specific process of converting the design parameters of the hole-shaft assembly into hole-shaft simulation data using the Monte Carlo method in step S1 is as follows:

[0010] Based on the design parameters of the hole-shaft pair, including bilateral tolerances ES, EI, es, ei, axis position Pos, and axis relative coordinates (x, y), in each simulation, the Monte Carlo method is used to generate the hole axis manufacturing offset ri, the shaft axis manufacturing offset Ri, the simulated maximum material radius r of the hole, and the simulated maximum material radius R of the shaft for each hole-shaft pair.

[0011] Secondly, the relative positions of the simulated hole and shaft axes are calculated. The manufacturing offset direction θri of the hole axis and the manufacturing offset direction θRi of the shaft axis are obtained by random numbers. In polar coordinates, the simulated position (X1,Y1) / (X2,Y2) of the hole / shaft axis is obtained by the manufacturing offset ri / Ri of the hole / shaft axis and the manufacturing offset direction θri / θRi of the hole / shaft axis.

[0012] Furthermore, the specific process of establishing a mathematical model of the intersection angle of the movable circles of the hole and shaft based on the hole and shaft simulation data in step S2, and predicting the assembly possibility of the hole and shaft assembly, is as follows:

[0013] First, for each pair of hole-shafts in the hole-shaft group, the movable circle radius R of the hole-shaft is calculated by subtracting the simulated maximum solid radius r of the shaft from the simulated maximum solid radius R of the hole. a Secondly, based on the simulated position of the hole / shaft axis, the relative position of the hole with respect to the shaft is calculated, and the axis positions of all movable circles of the hole / shaft group are made to coincide, thus obtaining the set of movable circles of the hole / shaft group.

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[0018] Secondly, for each movable circle of the bore shaft, calculate its intersection with every other movable circle of the bore shaft. This is done by calculating the angle of intersection of the two circles in their polar coordinate system using formulas 1-4, where D is the distance between the centers of the two circles, and r1 and r2 are the radii of the two circles, respectively. This gives the range θ of the angle between the current movable circle of the bore shaft and every other movable circle of the bore shaft. si and θ eiFollowing this method, calculate the range of intersection angles between the current movable circle of the hole shaft and each of the other N movable circles of the hole shaft. Then determine whether there is an intersection among all the intersection angle ranges. If there is an intersection, it is determined that the movable circle of the hole shaft intersects with each circle and there may be assembly possibilities. Repeat the above process. When all the movable circles of the hole shaft contain actual intersections, it can be determined that the simulation data can be assembled, and proceed to step S3. Otherwise, there is no possibility of assembly. After readjusting the hole shaft group design parameters, return to step S1.

[0019] In formulas 1 to 4, θ′ i Let be the angle between the line connecting the i-th movable circle of the hole shaft and the positive x-axis; x1 and y1 are the x and y coordinates of the simulated position of the axis of the current movable circle of the hole shaft, respectively; x2 and y2 are the x and y coordinates of the simulated position of the axis of the i-th movable circle of the hole shaft, respectively; D is the distance between the centers of the current movable circle of the hole shaft and the i-th movable circle of the hole shaft; R a1 R is the radius of the movable circle of the current hole shaft. a2 Let θ be the radius of the movable circle of the i-th hole shaft; H is the length of the line connecting the intersection point of the current movable circle of the hole shaft and the movable circle of the i-th hole shaft; ti Let θ be the angle between the intersection point of the current movable circle of the hole shaft and the movable circle of the i-th hole shaft and the positive x-axis; si θ is the lower limit of the angle range between the current movable circle of the hole shaft and the i-th movable circle of the hole shaft; ei This is the upper limit of the angle range between the current movable circle of the hole shaft and the movable circle of the i-th hole shaft.

[0020] Furthermore, the specific process of obtaining the suitable assembly simulation position points for the hole-shaft assembly using the GRO gold mining optimization algorithm in step S3 is as follows:

[0021] By randomly scattering points with radii r to R and directions between 0 and 2π in polar coordinates, the fitness of each point is calculated to obtain an initial point group of a certain size;

[0022] The GRO Gold Mining optimization algorithm is used to estimate the best point as the point with the highest fitness. Then, the position of each point is updated through three operations: migration operation, moving towards the best point; gold mining operation, searching for another possible point near a randomly selected point; and cooperative operation, cooperating with two randomly selected points to find a new point.

[0023] After the operation is performed, if the fitness of the new position point is better than the current position, the point is moved to the new position; otherwise, it remains unchanged. The position and fitness of the point are continuously adjusted in this way. The maximum number of iterations and the weights of the three operations are set to calculate a point that meets all the movable range of the hole and shaft, which is a suitable simulation position point for the assembly of the hole and shaft group, as a possible assembly situation of the hole and shaft group.

[0024] Furthermore, the assembly simulation analysis method for the hole-shaft assembly further includes step S4: obtaining the movable range and limit assembly conditions of the hole-shaft assembly by calculating simulation data.

[0025] First, by traversing the intersection of each movable circle of the hole shaft relative to other movable circles of the hole shaft obtained in S2, that is, the angular range of each movable circle of the hole shaft relative to other movable circles of the hole shaft, the starting point and ending point of the arc are calculated by using this angular range and its radius. All cases where the starting and ending points coincide are traversed and calculated. Only one closed line is found in the combination of multiple arcs. The area enclosed by the closed line is the movable range of the hole shaft group.

[0026] Secondly, for the limit assembly point, by traversing all the arcs on this closed line, the farthest distance from each arc to the farthest point is calculated, and the point farthest from the origin on this closed line is the limit assembly point.

[0027] Furthermore, the assembly simulation analysis method for a hole-shaft assembly further includes step S5: based on the movable range of the hole-shaft assembly obtained in step S4 and the simulation data obtained in step S1, calculating the assembly error distribution and the translation matrix of the limit assembly:

[0028] In step S4, the intersection of each hole shaft movable circle with respect to other hole shaft movable circles is obtained. The distance between the farthest point from the axis coincidence point and the origin within the intersection range is the maximum error. The x and y coordinates of the farthest point in Cartesian coordinates are directly used as the translation matrix of the limit assembly in a simulation.

[0029] Secondly, the movable range of the hole and shaft assembly is divided in polar coordinates with the origin as the center, using the radius as the independent variable, to obtain the distribution of the movable range with respect to the error, i.e., the assembly error distribution.

[0030] The present invention has the following advantages or beneficial effects:

[0031] This paper proposes an assembly simulation analysis method for hole-shaft assemblies, helping tolerance designers obtain the possible assembly results of the designed hole-shaft assembly tolerances during the actual assembly process. An evolutionary algorithm provides a simulation result of the hole-shaft assembly, thus simulating the actual assembly result. This invention also provides the distribution of assembly errors and limit assembly conditions through simulation data calculation, effectively accelerating the tolerance analysis process and solving the practical problem of obtaining reasonable tolerance values ​​during the tolerance design of hole-shaft assemblies. It significantly reduces the long tolerance design cycle of hole-shaft assemblies and improves the yield rate, providing designers with an intuitive understanding of the distribution of assembly errors and limit assembly conditions after manufacturing. Attached Figure Description

[0032] The accompanying drawings are provided to further illustrate embodiments of the present invention and form part of the specification. They are used together with the following detailed description to explain the embodiments of the present invention, but do not constitute a limitation thereof. In the drawings:

[0033] Figure 1 This is a schematic diagram of an embodiment of the assembly simulation analysis method for a hole-shaft assembly according to the present invention;

[0034] Figure 2 illustrates (a) the movable circle of the hole shaft and (b) the assembly of movable circles of the hole shaft group of the present invention;

[0035] Figure 3 This describes the movable range and limit assembly point of the hole-shaft assembly in this invention;

[0036] Figure 4 This illustrates that the present invention uses an evolutionary algorithm to calculate possible assembly scenarios;

[0037] Figure 5 This is a schematic diagram of another embodiment of the assembly simulation analysis method for a hole-shaft assembly according to the present invention;

[0038] Figure 6 This is a schematic diagram of another embodiment of the assembly simulation analysis method for a hole-shaft assembly according to the present invention. Detailed Implementation

[0039] To better understand the above-mentioned objects, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Many specific details are set forth in the following description to provide a thorough understanding of the present invention; however, the present invention may also be implemented in other ways different from those described herein. Therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0040] like Figure 1 As shown, an embodiment of the present invention provides an assembly simulation analysis method for a hole-shaft assembly, comprising the following steps:

[0041] S1: The Monte Carlo method is used to convert the design parameters of the hole-shaft assembly into hole-shaft simulation data.

[0042] Based on the design parameters of the hole-shaft pair, including bilateral tolerances ES, EI, es, ei, axis position Pos, and axis relative coordinates (x, y), in each simulation, the manufacturing offset ri of the hole axis, the manufacturing offset Ri of the shaft axis, the simulated maximum material radius r of the hole, and the simulated maximum material radius R of the shaft are generated for each hole-shaft pair using the Monte Carlo method. Next, the relative positions of the simulated hole-shaft axes are calculated. The manufacturing offset directions θri of the hole axis and θRi of the shaft axis are obtained using random numbers. In polar coordinates, the simulated positions (x1, y1) / (x2, y2) of the hole / shaft axis are obtained using the manufacturing offset ri / Ri and the manufacturing offset directions θri / θRi, and the hole-shaft simulation data is recorded.

[0043] S2: Based on the simulation data of the hole and shaft, establish a mathematical model of the intersection angle of the movable circles of the hole and shaft to predict the assembly possibility of the hole and shaft assembly.

[0044] First, for each pair of hole-shafts in the hole-shaft group, the movable circle radius R of the hole-shaft is calculated by subtracting the simulated maximum solid radius r of the shaft from the simulated maximum solid radius R of the hole. a (That is, the radius of the movable circle relative to the hole), as shown in Figure 2(a). Next, based on the simulated position of the hole / shaft axis, the relative position of the hole with respect to the shaft is calculated. By using this method, the axis positions of all movable circles of the hole / shaft group are made to coincide, thus obtaining the set of movable circles of the hole / shaft group, as shown in Figure 2(b).

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[0049] Secondly, assuming there are N+1 movable circles in the aforementioned set of movable circles of the hole shaft group, for each movable circle of the hole shaft (hereinafter referred to as the current movable circle of the hole shaft), calculate its intersection with each of the other N movable circles of the hole shaft (hereinafter referred to as the i-th movable circle of the hole shaft, i∈N, i and N are natural numbers, N≥1). The process is to calculate the angle of the intersection of the two circles in their polar coordinate system using formulas 1 to 4, thus obtaining the range θ of the angle of intersection between the current movable circle of the hole shaft and the i-th movable circle of the hole shaft. si ~θ ei Following this method, calculate the range of intersection angles between the current movable circle of the hole shaft and each of the other N movable circles of the hole shaft. Then, determine whether any of the intersection angle ranges intersect. If an intersection exists, it is determined that the movable circle of the hole shaft intersects with each of the other N circles and there is a possibility of assembly. Figure 3 The black border of the shaded area represents the actual intersection of a movable circle. Repeating this process, when all movable circles of the hole and shaft contain actual intersections, it can be determined that the simulation data can be assembled, and the process proceeds to step S3; otherwise, assembly is not possible, and the hole and shaft assembly design parameters are readjusted before returning to step S1.

[0050] In formulas 1 to 4, θ′ i Let be the angle between the line connecting the i-th movable circle of the hole shaft and the positive x-axis; x1 and y1 are the x and y coordinates of the simulated position of the axis of the current movable circle of the hole shaft, respectively; x2 and y2 are the x and y coordinates of the simulated position of the axis of the i-th movable circle of the hole shaft, respectively; D is the distance between the centers of the current movable circle of the hole shaft and the i-th movable circle of the hole shaft; R a1 R is the radius of the movable circle of the current hole shaft. a2 Let θ be the radius of the movable circle of the i-th hole shaft; H is the length of the line connecting the intersection point of the current movable circle of the hole shaft and the movable circle of the i-th hole shaft; ti Let θ be the angle between the intersection point of the current movable circle of the hole shaft and the movable circle of the i-th hole shaft and the positive x-axis; si θ is the lower limit of the angle range between the current movable circle of the hole shaft and the i-th movable circle of the hole shaft; ei This is the upper limit of the angle range between the current movable circle of the hole shaft and the movable circle of the i-th hole shaft.

[0051] S3: Using the GRO Gold Mining optimization algorithm, suitable simulation positions for the hole-shaft assembly are obtained.

[0052] By randomly scattering points with radii r to R and directions between 0 and 2π in polar coordinates (these randomly scattered points are the projections of the axis of the shaft group center relative to the hole group center onto the reference plane), an initial point group of size 100 is obtained. The fitness of the initial point group is calculated using formulas 5 to 6. Figure 4 The points are marked with an asterisk (*). This embodiment uses the GRO Gold Mining optimization algorithm, estimating the optimal point as the point with the highest fitness (the point with the largest T-value). Then, three operations are used to update the position of each point: migration (moving towards the optimal point, as shown in formulas 7-10); gold mining (searching for another possible point near a randomly selected point, as shown in formulas 11-13); and cooperation (collaborating with two randomly selected points to find a new point, as shown in formulas 14-15). After each operation, if the fitness of the new position is better than the current position, the point moves to the new position; otherwise, it remains unchanged. This process continuously corrects the point's position and fitness. With a maximum iteration count of 100, the weights of the three operations in this embodiment are 0.2, 0.7, and 0.1, respectively, to calculate a point that satisfies all the movable ranges of the hole-shaft assembly, i.e., the suitable simulation position point for the hole-shaft assembly, as shown below. Figure 4 The triangular markers in the diagram represent a possible assembly configuration for the hole-shaft assembly.

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[0065] In formulas 5 and 6, T represents the fitness of a random point; t i This refers to the fitness component of that point relative to the movable circle of the i-th hole shaft; R a The radius of the movable circle of the finger-hole shaft; P i This refers to the distance between the point and the center of the movable circle of the i-th hole shaft.

[0066] In formulas 7-10, The distance traveled under the migration strategy; To control the random vector coefficients; It is the optimal individual in each iteration process, that is, the position of the point closest to satisfying all the movable ranges of the hole shaft; This refers to the position of the point that is being modified in this iteration; Random1 and Random2 are random numbers between 0 and 1; The new point location under the migration strategy; The vector coefficients used to control convergence; This represents the convergence factor, obtained from Equation 16.

[0067] In formulas 11 to 13, The distance traveled under the gold mining strategy; This refers to the position of the point that is being modified in this iteration; This refers to the position of another random individual in the current iteration (i.e., a point in another current iteration); To determine the new location under the gold mining strategy; The vector coefficients used to control convergence; This represents the convergence factor, obtained from formula 16; Random1 is a random number between 0 and 1.

[0068] In formulas 14 and 15, The distance traveled under the cooperative strategy; It refers to a random individual in the current iteration, that is, a point in the current iteration; Refers to another random individual in the current iteration, that is, a point in another current iteration; To establish new point locations under the cooperation strategy; This refers to the position of the point that is being modified in this iteration; Random1 is a random number between 0 and 1.

[0069] In formula 16, The convergence factor is , and when the subscript e = 1, it is . When the subscript e = 2, it is... max iter `iter` represents the maximum number of iterations; `iter` represents the current number of iterations.

[0070] like Figure 5 As shown, another embodiment of the present invention provides an assembly simulation analysis method for a hole-shaft assembly. In addition to the steps S1-S3 described above, it also includes the following step: S4: Obtain the movable range and limit assembly condition of the hole-shaft assembly by calculating simulation data.

[0071] First, by traversing the intersection of each movable circle of the hole shaft relative to other movable circles obtained in S2, i.e., the angular range of each movable circle of the hole shaft relative to other movable circles of the hole shaft, the start and end points of the arc are calculated using this angular range and its radius. This process is repeated for all cases where the start and end points coincide, and then a unique closed line is found among multiple arc combinations. This closed line is as follows: Figure 3 The black border section of the movable range. Figure 3 The area enclosed by the black border in the diagram represents the movable range of the hole-shaft assembly. Secondly, for the limit assembly point, by traversing all arcs on this closed line, the farthest distance from each arc to the origin is calculated. The point on this closed line farthest from the origin is precisely the limit assembly point, as shown in the diagram. Figure 3 The intersection of the markers.

[0072] like Figure 6As shown, another embodiment of the present invention provides an assembly simulation analysis method for a hole-shaft assembly. In addition to the steps S1-S4 described above, it also includes the following step: S5: Calculate the assembly error distribution and the translation matrix of the limit assembly using the movable range of the hole-shaft assembly and simulation data.

[0073] First, since the origin coincides with the axis, the distance between the farthest point from the axis coincidence point within the intersection range in S4 and the origin can be directly used as the translation matrix for the limit assembly in a simulation. Second, in polar coordinates with the origin as the center, the movable range of the hole-shaft assembly is divided with the radius as the independent variable to obtain the distribution of errors within the movable range. After processing, the distribution of assembly errors can be obtained.

[0074] The embodiments of this application have been described above with reference to the accompanying drawings. However, this application is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of this application without departing from the spirit and scope of the claims. All of these forms are within the protection scope of this application.

Claims

1. A method for assembling simulation analysis of a hole shaft group, characterized by, The method includes the following steps: S1: The Monte Carlo method is used to convert the design parameters of the hole-shaft assembly into hole-shaft simulation data; S2: Based on the simulation data of the hole shaft, establish a mathematical model of the intersection angle of the movable circles of the hole shaft, and predict the assembly possibility of the hole shaft group. When the movable circles of the hole shaft all contain actual intersections, it can be determined that the simulation data can be assembled, and proceed to step S3; otherwise, there is no possibility of assembly, and after readjusting the design parameters of the hole shaft group, return to step S1. S3: Use the GRO gold mining optimization algorithm to obtain the simulation position points for the hole and shaft assembly that are suitable for assembly. The specific process of converting the design parameters of the hole-shaft assembly into hole-shaft simulation data using the Monte Carlo method in step S1 is as follows: Based on the design parameters of the hole-shaft pair, including bilateral tolerances ES, EI, es, ei, axis position Pos, and axis relative coordinates (x, y), the Monte Carlo method is used to generate the hole axis manufacturing offset ri, the shaft axis manufacturing offset Ri, the simulated maximum material radius r of the hole, and the simulated maximum material radius R of the shaft for each hole-shaft pair. Second, the relative position of the hole axis and the shaft axis is calculated, the hole axis manufacturing offset direction θri and the shaft axis manufacturing offset direction θRi are obtained by random numbers, and the hole / axis axis simulation position is obtained by the hole / axis axis manufacturing offset ri / Ri and the hole / axis axis manufacturing offset direction θri / θRi in polar coordinates , ) / ( , ); In step S2, the specific process of establishing a mathematical model of the intersection angle of the movable circles of the hole and shaft based on the hole and shaft simulation data, and predicting the assembly possibility of the hole and shaft assembly, is as follows: First, for each pair of hole-axes in the hole-axis set, the simulated maximum solid radius R of the axis is subtracted from the simulated maximum solid radius r passing through the hole to calculate the hole-axes movable circle radius Second, based on the simulated position of the hole / axis axis, the relative position of the hole with respect to the axis is calculated, and the axis positions of all the movable circles in the hole-axis set are made to coincide to obtain the hole-axis set movable circle set; Secondly, for each movable circle of the bore shaft, calculate its intersection with every other movable circle of the bore shaft. This is done by calculating the angle of intersection of the two circles in their polar coordinate system using formulas 1-4, where D is the distance between the centers of the two circles, and r1 and r2 are the radii of the two circles, respectively. This gives the range of angles between the current movable circle of the bore shaft and every other movable circle of the bore shaft. and Following this method, calculate the range of intersection angles between the current movable circle of the hole shaft and each of the other N movable circles of the hole shaft. Then determine whether there is an intersection among all the intersection angle ranges. If there is an intersection, it is determined that the movable circle of the hole shaft intersects with each circle and there may be assembly possibilities. Repeat the above process. When all the movable circles of the hole shaft contain actual intersections, it can be determined that the simulation data can be assembled, and proceed to step S3. Otherwise, there is no possibility of assembly. After readjusting the hole shaft group design parameters, return to step S1. In formulas 1-4, Let be the angle between the line connecting the i-th movable circle of the hole shaft to the current movable circle of the hole shaft and the positive x-axis; and Let x and y be the simulated positions of the axis of the movable circle of the current hole shaft. and Let x and y be the abscissa and ordinate of the simulated position of the axis of the i-th movable circle of the hole shaft; D is the distance between the centers of the current movable circle of the hole shaft and the i-th movable circle of the hole shaft. 1 represents the radius of the movable circle of the current hole shaft. 2 is the radius of the movable circle of the i-th hole shaft; H is the length of the line connecting the intersection point of the current movable circle of the hole shaft and the movable circle of the i-th hole shaft; The angle between the intersection point of the current movable circle of the hole shaft and the movable circle of the i-th hole shaft and the positive x-axis; This is the lower limit of the angle range between the current movable circle of the hole shaft and the i-th movable circle of the hole shaft; This represents the upper limit of the angle range between the current movable circle of the hole shaft and the i-th movable circle of the hole shaft; The specific process of obtaining the suitable assembly simulation position points for the hole-shaft assembly using the GRO gold mining optimization algorithm in step S3 is as follows: By randomly scattering points with radii r to R and directions between 0 and 2π in polar coordinates, the fitness of each point is calculated to obtain an initial point group of a certain size; The GRO Gold Mining optimization algorithm is used to estimate the best point as the point with the highest fitness. Then, the position of each point is updated through three operations: migration operation, moving towards the best point; gold mining operation, searching for another possible point near a randomly selected point; and cooperative operation, cooperating with two randomly selected points to find a new point. After the operation is performed, if the fitness of the new position point is better than the current position, the point is moved to the new position; otherwise, it remains unchanged. The position and fitness of the point are continuously adjusted in this way. The maximum number of iterations and the weights of the three operations are set to calculate a point that meets all the movable range of the hole and shaft, which is a suitable simulation position point for the assembly of the hole and shaft group, as a possible assembly situation of the hole and shaft group.

2. The assembly simulation analysis method for a hole-shaft assembly according to claim 1, characterized in that, It also includes step S4: obtaining the movable range and limit assembly conditions of the hole-shaft assembly by calculating simulation data. First, by traversing the intersection of each movable circle of the hole shaft relative to other movable circles of the hole shaft obtained in S2, that is, the angular range of each movable circle of the hole shaft relative to other movable circles of the hole shaft, the starting point and ending point of the arc are calculated by using this angular range and its radius. All cases where the starting and ending points coincide are traversed and calculated. Only one closed line is found in the combination of multiple arcs. The area enclosed by the closed line is the movable range of the hole shaft group. Secondly, for the limit assembly point, by traversing all the arcs on this closed line, the farthest distance from each arc to the farthest point is calculated, and the point farthest from the origin on this closed line is the limit assembly point.

3. The assembly simulation analysis method for a hole-shaft assembly according to claim 2, characterized in that, The process also includes step S5: Based on the movable range of the hole-shaft assembly obtained in step S4 and the simulation data obtained in step S1, calculate the assembly error distribution and the translation matrix for the limit assembly. In step S4, the intersection of each hole shaft movable circle with respect to other hole shaft movable circles is obtained. The distance between the farthest point from the axis coincidence point and the origin within the intersection range is the maximum error. The x and y coordinates of the farthest point in Cartesian coordinates are directly used as the translation matrix of the limit assembly in a simulation. Secondly, the movable range of the hole and shaft assembly is divided in polar coordinates with the origin as the center, using the radius as the independent variable, to obtain the distribution of the movable range with respect to the error, i.e., the assembly error distribution.

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