Automatic generation method of thin-wall curved surface power spinning roller track

Abstract

The invention relates to the technical field of metal power spinning processing, and discloses a thin-wall curved surface power spinning spinning roller track automatic generation method, which comprises the following steps of S1, extracting a bus of a spinning core mold by adopting a vector method, S2, constructing a cubic NURBS curve of the bus of the core mold by adopting an interpolation method to obtain a control point and an NURBS curve section, S3, calculating a unit normal vector of the NURBS curve, and S4, calculating the unit normal vector of the NURBS curve. The method comprises the following steps of: (1) selecting an individual and deviating a specified distance along a normal vector, (2) fitting an equidistant line by adopting a minimum multiplication method, (5) constructing an objective function required by a differential evolution algorithm, and (6) carrying out differential variation and intersection on the individual, and obtaining the minimum objective function of the differential evolution algorithm through a greedy algorithm, so as to obtain a spinning roller center motion trail formed by fewest control points and NURBS curve segments. According to the method, the NURBS curve of the thin-wall curved surface power spinning roller track line is automatically generated, and the control point of the NURBS curve of the center of the spinning roller can be automatically calculated along with the difference of the machining precision and the center position of the spinning roller.

Description

Technical Field

[0001] The invention relates to the technical field of metal high-power spinning processing, in particular to a method for automatically generating a spinning wheel trajectory for high-power spinning of a thin-walled curved surface. Background Art

[0002] The metal high-power spinning process uses a spinning wheel to apply pressure to the blank. The blank rotates, and the spinning wheel makes a feeding motion, and local plastic deformation along the spinning core mold is performed to thin the blank, thereby forming a part of the required shape.

[0003] During the spinning process, the uneven gap between the center of the spinning wheel and the core mold will produce uneven plastic deformation and thus uneven residual stress. Due to the existence of residual stress, the parts are always in an unstable state. During the residual stress release process, the parts will deform and the processing accuracy will deteriorate, especially for thin-walled parts. Therefore, it is very necessary to make the spinning wheel trajectory equidistant from the mother curve of the forming mold. Summary of the invention

[0004] The present invention is to solve the above problems. In order to ensure the geometric continuity of the spinning wheel trajectory during the spinning process, the present invention 2 In order to achieve uniform plastic deformation in the entire spinning process and avoid forming defects, and to meet the requirements of machining accuracy, a minimum of control points are used to construct the approximate equidistant line of the spinning wheel to improve the calculation efficiency. Thus, a method for automatic generation of thin-walled surface high-power spinning wheel trajectory combining cubic NURBS (Non-Uniform Rational B-Splines) curve and differential evolution algorithm DE (Differential Evolution Algorithm) is proposed. That is, the differential evolution algorithm is used to optimize the control points and arc length S of the cubic NURBS curve to construct the motion trajectory of the spinning wheel center.

[0005] To achieve the above object, the present invention provides the following technical solution: a method for automatically generating a thin-walled curved surface high-power spinning wheel trajectory, the method comprising the following steps:

[0006] S1. Extract the generatrix of the spinning core mold using the vector method;

[0007] S2, constructing a cubic NURBS curve of the core mold busbar by using an interpolation method, and obtaining its control points and NURBS curve segments;

[0008] S3, calculating the unit normal vector of the NURBS curve, and deviating the specified distance along the normal vector;

[0009] S4, using the minimum multiplication method to fit the equidistant lines;

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

[0011] S6. Individuals perform differential mutation and crossover, and through a greedy algorithm, the differential evolution algorithm objective function is minimized, thereby obtaining the motion trajectory of the wheel center consisting of the least control points and NURBS curve segments.

[0012]

[0013]

[0014] Preferably, in step S2, the cubic NURBS curve segment S of the spinning wheel trajectory is composed of control vertices d ij (i=0,1,…,n-3,j=0,1,2,3) is determined, then its equation is

[0015]

[0016] Among them, 0≤u≤1,

[0017]

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

[0019] Preferably, the partial derivative of equation (1) is obtained as

[0020]

[0021] By r iu The normal vector of the curve is

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

[0023] N i (u) is normalized to obtain the unit normal vector corresponding to parameter u

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

[0025] Let R(u) be a line equidistant from r(u) by d, then

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

[0027] From the above calculation, we know that the numerator and denominator of N(u) are quintic polynomials about variable u, W i and are all unknown, the unit normal vector n i The representation of (u) is very complicated, which leads to R i (u) It is difficult to find the optimal solution.

[0028] Compared with the prior art, the present invention has the following beneficial effects:

[0029] 1. The present invention uses the same core mold generatrix curve, and the minimum control points and NURBS curve segments required for the spinning wheel center trajectory line are different under different spinning thickness processing accuracy;

[0030] 2. In the present invention, the minimum control points and NURBS curve segments required for the center trajectory of the spinning wheel are different when the distance between the center of the spinning wheel and the core mold is different while the same spinning thickness accuracy is adopted;

[0031] 3. The NURBS curve of the thin-walled surface high-force spinning wheel trajectory line is automatically generated. With the difference in processing accuracy and the center position of the spinning wheel, the control points of the NURBS curve of the spinning wheel center can be automatically calculated, and the minimum control points can be used to achieve it, which improves the efficiency of CNC programming and reduces the amount of calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 A simplified flow chart of the automatic generation method of the present invention;

[0033] Figure 2 This is a comparison chart of different accuracies for the same spacing of the present invention;

[0034] Figure 3 This is a comparison chart of different spacings with the same precision of the present invention. DETAILED DESCRIPTION

[0035] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0036] A method for automatically generating a thin-wall curved surface spinning wheel trajectory, the method comprising the following steps:

[0037] S1. Extract the generatrix of the spinning core mold using the vector method;

[0038] S2, constructing a cubic NURBS curve of the core mold busbar by using an interpolation method, and obtaining its control points and NURBS curve segments;

[0039] S3, calculating the unit normal vector of the NURBS curve, and deviating the specified distance along the normal vector;

[0040] S4, using the minimum multiplication method to fit the equidistant lines;

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

[0042] S6. Individuals perform differential mutation and crossover, and through a greedy algorithm, the differential evolution algorithm objective function is minimized, thereby obtaining the motion trajectory of the wheel center consisting of the least control points and NURBS curve segments.

[0043]

[0044]

[0045] In this embodiment, in step S2, a cubic NURBS curve segment S of the spinning wheel trajectory is composed of control vertices d ij (i=0,1,…,n-3,j=0,1,2,3) is determined, then its equation is

[0046]

[0047] Among them, 0≤u≤1,

[0048]

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

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

[0051]

[0052] By r iu The normal vector of the curve is

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

[0054] N i (u) is normalized to obtain the unit normal vector corresponding to parameter u

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

[0056] Let R(u) be a line equidistant from r(u) by d, then

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

[0058] From the above calculation, we know that the numerator and denominator of N(u) are quintic polynomials about variable u, W i and are all unknown, the unit normal vector n i The representation of (u) is very complicated, which leads to R i (u) It is difficult to find the optimal solution.

[0059] The differential evolution algorithm is a population-based adaptive global optimization algorithm. Compared with the genetic algorithm, the algorithm has a simple principle, few control parameters, only crossover probability and scaling factor, strong robustness and easy implementation.

[0060] In the differential evolution algorithm, the gene of each individual represents a candidate solution to the problem to be solved. Each iteration will first perform a mutation operation, select the genes of one or more individuals as the base, then select the differences of different individuals to form the differential gene, and finally add the genes as the base to the differential gene to obtain a new individual. The crossover operation crosses the new individual with the corresponding individual of the parent generation, and then performs an operation to compare the crossover individual with the corresponding individual of the parent generation, and select the better individual to be retained for the next generation. After the iteration is completed, the gene of the best individual in the population will be selected as the solution.

[0061] The process diagram of the automatic generation method is as follows: Figure 1 .

[0062] 1. Using the same core mold generatrix curve, the minimum control points and NURBS curve segments required for the spinning wheel center trajectory line are different under different spinning thickness processing accuracy.

[0063] For example, the distance between the center line of the spinning wheel and the core mold is 50mm. When the spinning thickness accuracy is 0.01mm, the center trajectory of the spinning wheel needs to be composed of at least 14 control points and 12 NURBS curve segments, such as Figure 2 (a); When the spinning thickness processing accuracy is 0.001mm, the spinning wheel center trajectory line needs to be composed of at least 28 control points and 26 NURBS curve segments, such as Figure 2 (b).

[0064] 2. When the same spinning thickness accuracy is used and the distance between the spinning wheel center and the core mold is different, the minimum control points and NURBS curve segments required for the spinning wheel center trajectory are different.

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

[0066] In summary, compared with the existing technology, this method can automatically generate the NURBS curve of the thin-walled surface high-force spinning wheel trajectory line. With the difference in processing accuracy and the center position of the spinning wheel, the control points of the NURBS curve of the spinning wheel center can be automatically calculated, and it can be achieved with the least control points, thereby improving the efficiency of CNC programming and reducing the amount of calculation.

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

[0068] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for automatically generating a thin-wall curved surface spinning wheel trajectory, characterized in that: The method comprises the following steps: S1. Extract the generatrix of the spinning core mold using the vector method; S2, constructing a cubic NURBS curve of the core mold busbar by using an interpolation method, and obtaining its control points and NURBS curve segments; S3, calculating the unit normal vector of the NURBS curve, and deviating the specified distance along the normal vector; S4, using the minimum multiplication method to fit the equidistant lines; S5. Construct the objective function required by the differential evolution algorithm; S6. Individuals perform differential mutation and crossover, and through a greedy algorithm, the differential evolution algorithm objective function is minimized, thereby obtaining the motion trajectory of the wheel center consisting of the least control points and NURBS curve segments.

2. The method for automatically generating a thin-wall curved surface spinning wheel trajectory according to claim 1, characterized in that: In step S2, the cubic NURBS curve segment S of the spinning wheel trajectory is composed of the control vertex d ij (i=0,1,…,n-3,j=0,1,2,3) is determined, then its equation is Among them, 0≤u≤1, W i =[ω i oh i+1 oh i+2 oh i+3 ] T 。 3. The method for automatically generating a thin-walled curved surface spinning wheel trajectory according to claim 2, characterized in that: The partial derivative of equation (1) is obtained By r iu The normal vector of the curve is N i (u)=-[r iu (u)] -1 (3) N i (u) is normalized to obtain the unit normal vector corresponding to parameter u n i (u)=N i (u) / |N i (u)| (4) Let R(u) be a line equidistant from r(u) by d, then R i (u)=r i (u)+d×n i (u) (5) From the above calculation, we know that the numerator and denominator of N(u) are quintic polynomials about variable u, W i and are all unknown, the unit normal vector n i The representation of (u) is very complicated, which leads to R i (u) It is difficult to find the optimal solution.

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