An automatic generation method for the trajectory of a spinning wheel in thin-walled surface power spinning

Abstract

The present invention relates to the technical field of metal power spinning processing, and discloses an automatic generation method for the trajectory of a power spinning roller for thin-walled curved surfaces. The method includes the following steps: S1, extracting the generatrix of the spinning mandrel by the vector method; S2, constructing a cubic NURBS curve of the mandrel generatrix by the interpolation method to obtain its control points and NURBS curve segments; S3, calculating the unit normal vector of the NURBS curve and deviating a specified distance along the normal vector; S4, fitting the offset curve by the least squares method; S5, constructing the objective function required for the differential evolution algorithm; S6, performing differential mutation and crossover on individuals, and obtaining the minimum of the objective function of the differential evolution algorithm through the greedy algorithm, so as to obtain the trajectory of the roller center composed of the least number of control points and NURBS curve segments. The present invention realizes the automatic generation of the NURBS curve of the trajectory line of the power spinning roller for thin-walled curved surfaces, and can automatically calculate the control points of the NURBS curve of the roller center according to different processing accuracies and the positions of the roller center.

Description

Technical Field

[0001] The present invention relates to the technical field of metal power spinning processing, and particularly to an automatic generation method for the trajectory of a power spinning roller for thin-walled curved surfaces. Background Art

[0002] In the metal power spinning processing technology, a roller is pressed against a blank. The blank rotates, and the roller makes a feeding movement, and local plastic deformation occurs along the spinning mandrel to make the blank thinner, thereby forming a part with the required shape.

[0003] During the spinning process, unequal gaps between the center of the roller and the mandrel will cause uneven plastic deformation, resulting in uneven residual stress. Due to the existence of residual stress, the part is always in an unstable state. During the release process of the residual stress, the part will deform, deteriorating the processing accuracy, especially for thin-walled parts. Therefore, it is very necessary that the trajectory of the spinning roller is equidistant from the mother curve of the forming die. Summary of the Invention

[0004] To solve the above problems, the present invention ensures the geometric continuity G of the roller trajectory during the spinning process 2 and the uniformity of the gap between the center of the roller and the die during the spinning process, realizes uniform plastic deformation throughout the spinning process and avoids the generation of forming defects, and constructs an approximate equidistant line of the roller with as few control points as possible within the allowable range of processing accuracy to improve the calculation efficiency. Thus, an automatic generation method for the trajectory of a power spinning roller for thin-walled curved surfaces combining cubic NURBS (Non-Uniform Rational B-Splines) curves and the differential evolution algorithm DE (Differential Evolution Algorithm) is proposed, that is, the control points and arc length S of the cubic NURBS curve are optimized by the differential evolution algorithm to construct the movement trajectory of the center of the power spinning roller.

[0005] To achieve the above object, the present invention provides the following technical solution: An automatic generation method for the trajectory of a power spinning roller for thin-walled curved surfaces, the method comprising the following steps:

[0006] S1. Extract the generatrix of the spinning mandrel by the vector method;

[0007] S2. Construct a cubic NURBS curve of the generatrix of the mandrel by the interpolation method to obtain its control points and NURBS curve segments;

[0008] S3. Calculate the unit normal vector of the NURBS curve and deviate a specified distance along the normal vector;

[0009] S4. Fit the equidistant line by the least squares method;

[0010] S5. Construct the objective function required for the differential evolution algorithm;

[0011] S6. The individual performs differential mutation and crossover, and through the greedy algorithm, the minimum of the objective function of the differential evolution algorithm is obtained, so as to obtain the center trajectory line of the spinning wheel composed of the fewest control points and NURBS curve segments. The following is the DN-NURBS algorithm for the center trajectory line of the spinning wheel.

[0012]

[0013]

[0014] Preferably, let the cubic NURBS curve segment S of the spinning wheel trajectory be determined by the control vertices d ij (i = 0, 1, …, n - 3, j = 0, 1, 2, 3), then its equation is

[0015]

[0016] where 0 ≤ u ≤ 1,

[0017]

[0018] W i = [ω i ω i+1 ω i+2 ω i+3 T .

[0019] Preferably, taking the partial derivative of equation (1) gives

[0020]

[0021] From r iu the normal vector of the curve can be obtained

[0022] N i (u) = -[r iu (u)] -1 (3)

[0023] Normalizing N i (u) gives the unit normal vector corresponding to the parameter u

[0024] n i (u) = N i (u) / |N i (u)| (4)

[0025] Let R(u) be the offset curve at a distance d from r(u), then

[0026] R i (u) = r i (u) + d × n i ​(u) (5)

[0027] As can be seen from the above calculations, the numerator and denominator of N(u) are both fifth-degree polynomials with respect to the variable u, and W i and are both unknown, and the expression of the unit normal vector n i (u) is very complex, resulting in difficult optimization of R i (u).

[0028] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0029] 1. The present invention uses the same core die bus curve, and the minimum number of control points and NURBS curve segments required for the center locus line of the spinning wheel are different under different spinning thickness processing precisions;

[0030] 2. The present invention uses the same spinning thickness precision, and the minimum number of control points and NURBS curve segments required for the center locus line of the spinning wheel are different when the distance between the spinning wheel center and the core die is different;

[0031] 3. It realizes the automatic generation of the NURBS curve of the spinning wheel locus line for the thin-walled surface power spinning. With different processing precisions and spinning wheel center positions, it can automatically calculate the control points of the NURBS curve of the spinning wheel center, and it is realized with the minimum number of control points, improving the numerical control programming efficiency and reducing the calculation amount. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 is a flow diagram of the automatic generation method of the present invention;

[0033] Figure 2 is a comparison diagram of the same distance and different precisions of the present invention;

[0034] Figure 3 is a comparison diagram of the same precision and different distances of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0035] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0036] An automatic generation method for the spinning wheel locus of thin-walled surface power spinning, the method comprising the following steps:

[0037] S1. Extract the bus of the spinning core die by the vector method;

[0038] S2. Construct a cubic NURBS curve for the core mold busbar using the interpolation method to obtain its control points and NURBS curve segments;

[0039] S3. Calculate the unit normal vector of the NURBS curve and deviate a specified distance along the normal vector;

[0040] S4. Fit the offset curve using the least squares method;

[0041] S5. Construct the objective function required for the differential evolution algorithm;

[0042] S6. Perform differential mutation and crossover on individuals, and through the greedy algorithm, obtain the minimum of the objective function of the differential evolution algorithm, so as to obtain the center track line of the spinning wheel composed of the fewest control points and NURBS curve segments. The following is the DN-NURBS algorithm for the center track line of the spinning wheel.

[0043]

[0044]

[0045] In this embodiment: Let the cubic NURBS curve segment S of the spinning wheel track be determined by the control vertices d ij (i = 0, 1, …, n - 3, j = 0, 1, 2, 3), then its equation is

[0046]

[0047] where 0 ≤ u ≤ 1,

[0048]

[0049] W i = [ω i ω i+1 ω i+2 ω i+3 T .

[0050] In this embodiment: Taking the partial derivative of equation (1) gives

[0051]

[0052] From r iu the normal vector of the curve can be obtained

[0053] N i (u) = -[r iu (u)] -1 (3)

[0054] Normalizing N i (u) gives the unit normal vector corresponding to the parameter u ​

[0055] n i N(u) = N i N(u) / |N i |N(u)| (4)

[0056] Let R(u) be the offset curve at a distance d from r(u), then

[0057] R i R(u) = r i (u) + d × n i R(u) (5)

[0058] From the above calculations, the numerator and denominator of N(u) are both fifth-degree polynomials with respect to the variable u, and W i and are both unknown. The expression of the unit normal vector n i (u) is very complex, which makes it difficult to optimize R i (u).

[0059] Differential evolution algorithm is a population-based adaptive global optimization algorithm. Compared with genetic algorithm, this algorithm has a simple principle, few control parameters (only the crossover probability and the scaling factor), strong robustness, and is easy to implement.

[0060] In the differential evolution algorithm, the gene of each individual represents a candidate solution to the problem to be solved. In each iteration, the mutation operation will be performed first. One or more individuals' genes are selected as the basis, and then the differences of different individuals are selected to form the differential genes. Finally, the gene used as the basis is added to the differential genes to obtain a new individual. The crossover operation will cross the new individual with the corresponding individual of the parent generation, and then perform the operation. Compare the crossed individual with the corresponding individual of the parent generation, and select the better individual to be retained in the next generation. After the iteration is completed, the gene of the optimal individual in the population will be selected as the solution.

[0061] The flow diagram of its automatic generation method is as shown in Figure 1 .

[0062] 1. Using the same core die bus curve, the minimum number of control points and the number of NURBS curve segments required for the roller center locus line are different under different spinning thickness processing precisions.

[0063] For example, the distance between the roller center line and the core die is 50 mm. When the spinning thickness precision is 0.01 mm, the roller center locus line requires at least 14 control points and 12 NURBS curve segments, as shown in Figure 2 (a); when the spinning thickness processing precision is 0.001 mm, the roller center locus line requires at least 28 control points and 26 NURBS curve segments, as shown in Figure 2 (b).

[0064] 2. With the same precision of spinning thickness, when the distance between the center of the spinning wheel and the core mold is different, the minimum number of control points and NURBS curve segments required for the center locus line of the spinning wheel are different.

[0065] For example, when the machining precision is 0.01 mm and the distance between the center line of the spinning wheel and the core mold is 10 mm, the center locus line of the spinning wheel needs to be composed of at least 9 control points and 7 NURBS curve segments, as shown in Figure 3 a; when the distance between the center line of the spinning wheel and the core mold is 100 mm, the center locus line of the spinning wheel needs to be composed of at least 17 control points and 15 NURBS curve segments, as shown in Figure 3 b.

[0066] In summary, compared with the prior art, this method realizes the automatic generation of the NURBS curve of the spinning wheel locus line for the powerful spinning of thin-walled surfaces. With different machining precisions and the positions of the center of the spinning wheel, it can automatically calculate the control points of the NURBS curve of the center of the spinning wheel, and achieve it with the least number of control points, improving the CNC programming efficiency and reducing the calculation amount.

[0067] It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements not only includes those elements, but also includes other elements not expressly listed, or also includes elements inherent to such process, method, article or device.

[0068] Although the embodiments of the present invention have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principle and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. An automatic generation method for the trajectory of a spinning wheel in thin-wall curved surface power spinning, characterized in that: The method includes the following steps: S1. Extract the generatrix of the spinning mandrel by the vector method; S2. Construct the cubic NURBS curve of the mandrel generatrix by the interpolation method to obtain its control points and NURBS curve segments; S3. Calculate the unit normal vector of the NURBS curve and deviate a specified distance along the normal vector; S4. Fit the offset curve by the least square method; S5. Construct the objective function required for the differential evolution algorithm; S6. The individuals perform differential mutation and crossover, and through the greedy algorithm, the minimum of the objective function of the differential evolution algorithm is obtained, so as to obtain the spinning wheel center trajectory line composed of the least number of control points and NURBS curve segments. The following is the DN-NURBS algorithm for the spinning wheel center trajectory line; 2. The automatic generation method of the spinning wheel trajectory for the thin-walled curved surface power spinning according to claim 1, characterized in that: Let the cubic NURBS curve segment S of the spinning roller trajectory be determined by the control vertices d ij (i = 0, 1, …, n - 3, j = 0, 1, 2, 3), then its equation is where, 0 ≤ u ≤ 1, W i = [ω i ω i+1 ω i+2 ω i+3 T 。​ 3. An automatic generation method for the spinning wheel trajectory of thin-wall curved surface power spinning according to claim 2, characterized in that: Taking the partial derivative of Equation (1) gives From r iu the normal vector of the curve can be obtained N i (u) = -[r iu (u)] -1 (3) Let N i (u) The unit normal vector corresponding to the parameter u is obtained by unitizing it n i (u) = N i (u) / |N i (u) | (4) Let R(u) be the offset curve at a distance d from r(u), then R i r(u) = i r(u) + d×n i r(u)(5) As known from the above calculations, N i The numerator and denominator of (u) are both fifth-degree polynomials with respect to the variable u, and W i and are both unknown. The expression of the unit normal vector n i (u) is very complex, making it difficult to optimize R i (u).

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