CN113111466A - TOPSIS and MGA-based clamp clamping layout method - Google Patents

TOPSIS and MGA-based clamp clamping layout method Download PDF

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CN113111466A
CN113111466A CN202110472688.3A CN202110472688A CN113111466A CN 113111466 A CN113111466 A CN 113111466A CN 202110472688 A CN202110472688 A CN 202110472688A CN 113111466 A CN113111466 A CN 113111466A
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秦国华
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王华敏
叶海潮
林锋
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Nanchang Hangkong University
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Abstract

A clamp clamping layout method and a control method based on TOPSIS and MGA comprise the following steps: constructing a hierarchical analysis structure model of a positioning scheme according to a TOPSIS method, and sequencing candidate positioning datum planes according to the candidate positioning datum planes and the ideal solution proximity value from large to small; sequencing according to the candidate positioning datum planes, and determining and selecting the number of the layout positioning points on each positioning datum plane according to a generative point-by-point design method of a positioning scheme; constructing a hierarchical structure model of a clamping scheme according to a TOPSIS method, and sequencing candidate clamping surfaces from large to small according to the proximity value of the candidate clamping surfaces and an ideal solution; the optimal sequencing of the positioning datum plane and the clamping plane is objectively found out by adopting a TOSIS (transmitter optical system interface) evaluation method, the number of positioning points on the positioning datum plane is found out by adopting a point-by-point design method of a positioning scheme, and the positioning points, the coordinates of the clamping points and the size of the clamping force are optimized by adopting an MGA (media gateway architecture) based on evolution, so that a scientific basis is provided for the design of a complicated part clamping layout scheme.

Description

TOPSIS and MGA-based clamp clamping layout method
Technical Field
The invention relates to the technical field of clamp design, in particular to a clamp clamping layout method based on TOPSIS and MGA.
Background
In the actual part machining process, a plurality of clamp designers select a clamp clamping layout scheme according to experience, which often results in low clamping reliability, low positioning accuracy, low machining precision and large clamping deformation, and has greater influence on relatively complex aviation parts which need high precision. Therefore, the determination of a reasonable and scientific clamping layout scheme is of great importance in the machining process of complex aviation parts.
Disclosure of Invention
In order to solve the defects in the prior art, the invention provides a clamp clamping layout method based on TOPSIS and MGA. The technical scheme is as follows:
the invention provides a TOPSIS and MGA-based clamp clamping layout method, which comprises the following steps:
step 1: constructing a hierarchical analysis structure model of a positioning scheme according to a TOPSIS method, and sequencing candidate positioning datum planes according to the candidate positioning datum planes and the ideal solution proximity value from large to small;
step 2: sequencing according to the candidate positioning datum planes, and determining the number of the selected layout positioning points on each positioning datum plane according to a generative point-by-point design method of a positioning scheme;
and step 3: constructing a hierarchical structure model of a clamping scheme according to a TOPSIS method, and sequencing candidate clamping surfaces from large to small according to the proximity value of the candidate clamping surfaces and an ideal solution;
and 4, step 4: under the constraint condition of static balance, the MGA is adopted to find out the corresponding positioning point, the position of the clamping point and the clamping force according to the larger positioning and clamping stability and the smaller clamping force.
Further, the method for constructing the hierarchical analysis structure model of the positioning scheme in step 1 is to establish a positioning reference selection hierarchical structure model, which is composed of a target layer, an index layer and a scheme layer, wherein the scheme layer is all candidate positioning reference surfaces, the index layer is the characteristics of the candidate positioning reference surfaces, and the target layer is the characteristics of the candidate positioning reference surfacesSorting the advantages and the disadvantages, and finding out the optimal positioning reference plane combination according to the sorting; constructing index layer characteristic factor UiThe expression of (1); constructing a judgment matrix U; judging matrix consistency test; according to the judgment matrix, the weight of each index of the index layer is calculated; constructing a decision matrix Z array between the scheme layer and the index layer; obtaining a normalized decision matrix C; constructing a weighted normalized decision matrix D ═ Dij]m×n(ii) a Solving for the ideal solution E+Value and negative ideal solution E-A value; calculating the distance from each positioning scheme to the positive ideal solution and the negative ideal solution respectively
Figure BDA0003046106710000021
And
Figure BDA0003046106710000022
solving the scheme corresponding to each positioning reference surface and the ideal solution proximity value Fi。
Further, the method for determining the number of the layout positioning points on each selected positioning reference surface in step 2 is to determine the number of the layout positioning points on each positioning reference surface according to the relationship between the theoretical constraint degree of freedom and the processing requirement.
Further, the method for sorting the candidate clamping surfaces according to the closeness value of the candidate clamping surfaces and the ideal solution from large to small in the step 3 is to establish a clamping scheme hierarchical structure model, and the clamping scheme hierarchical structure model consists of a target layer, an index layer and a scheme layer, wherein the clamping scheme is all candidate clamping surfaces, the index layer is the characteristics of the candidate clamping surfaces, the target layer is the quality sorting of the candidate clamping surfaces, and the optimal clamping surface combination is found out according to the sorting; factor V of construction index layeriThe expression of (1); constructing a judgment matrix V of a clamping scheme hierarchical structure model; judging matrix consistency test; according to the judgment matrix V; constructing a decision matrix G array between the scheme layer and the index layer; obtaining a normalized decision matrix H; constructing a weighted normalized decision matrix L ═ Lij]m×n(ii) a Solving for the ideal solution P+Value and negative ideal solution P-A value; calculating the distance from each clamping scheme to the positive ideal solution and the negative ideal solution respectively
Figure BDA0003046106710000023
And
Figure BDA0003046106710000024
solving the scheme corresponding to each clamping surface and the ideal solution proximity value OiAccording to OiThe candidate positioning reference surfaces are ranked according to the value of (1), and the larger the value is, the better the value is taken as the clamping surface.
Furthermore, the method for finding out the position of the corresponding positioning point, the position of the corresponding clamping point and the magnitude of the corresponding clamping force in the step 4 is that under the constraint condition of static balance, the workpiece machining process is in a stable state, and the contact force vector F of the positioning elementdCan be obtained by a static equilibrium equation; constructing an evaluation target of the layout of the positioning element; and the scheme of clamp clamping layout is optimized by adopting MGA.
The TOPSIS and MGA-based clamp clamping layout method disclosed by the invention objectively finds out the optimal sequence of the positioning reference surface and the clamping surface by adopting a TOSIS evaluation method, finds out the number of the positioning points on the positioning reference surface by adopting a point-by-point design method of a positioning scheme, optimizes the positioning points, the coordinates of the clamping points and the clamping force by adopting an MGA based on evolution, and provides a scientific basis for the design of a complicated part clamping layout scheme.
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In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a model analysis diagram of a positioning reference selection hierarchical structure of the TOPSIS and MGA based clamp clamping layout method of the present invention;
FIG. 2 is a graph of a model analysis of a clamping scheme hierarchy structure of the TOPSIS and MGA based clamp clamping layout method of the present invention;
FIG. 3 is a structural diagram of a two-dimensional workpiece of the TOPSIS and MGA based clamp clamping layout method of the present invention;
FIG. 4 is a part drawing and candidate locating and clamping surfaces of a three-dimensional workpiece of the TOPSIS and MGA based clamp clamping layout method of the present invention;
FIG. 5 is an analysis diagram of an example of a positioning reference selection hierarchical structure model of the TOPSIS and MGA-based clamp clamping layout method of the present invention;
FIG. 6 is an analysis diagram of an example of a clamping scheme hierarchical structure model of the TOPSIS and MGA-based clamp clamping layout method of the present invention;
fig. 7 is a diagram of the optimized result of the clamp clamping layout method based on toposis and MGA of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail with reference to the accompanying drawings.
The invention provides a TOPSIS and MGA-based clamp clamping layout method, which comprises the following steps:
step 1: according to the TOPSIS method, a positioning scheme hierarchical analysis structure model is constructed, and candidate positioning datum planes are ranked according to the similarity value of the candidate positioning datum planes and the ideal solution from large to small.
And S01, establishing a positioning reference selection hierarchical structure model which is composed of a target layer, an index layer and a scheme layer as shown in figure 1, wherein for the selection of the positioning scheme, the scheme layer is all candidate positioning reference surfaces, the index layer is the characteristics of the candidate positioning reference surfaces, the target layer is the quality sequence of the candidate positioning reference surfaces, and the optimal positioning reference surface combination is found out according to the sequence.
S02 construction index layer characteristic factor UiThe expression (c) is mainly considered from the aspects of contact precision, reference superposition, reference unification, contact area, surface characteristics and the like.
Structural contact accuracy factor U1The expression is as follows
Figure BDA0003046106710000041
Wherein R isaThe surface roughness of the candidate positioning reference surface is usually 0.012, 0.025, 0.05, 0.1, 0.2, 0.4, 0.8, 1.6, 3.2, 6.3, 12.5, 25, 50, 100, etc.
Constructing a reference coincidence factor U2The expression is as follows
Figure BDA0003046106710000042
Wherein Δ is a reference misalignment error, which indicates an error value between a positioning reference and a process reference in a machining request direction;
t is the processing requirement, namely the process dimension tolerance;
construction reference unity factor U3The expression is as follows
Figure BDA0003046106710000043
Wherein N is the dimensional coefficient of correlation between the selected positioning reference and the machined feature
Structural contact area factor U4The expression is as follows
Figure BDA0003046106710000044
Wherein SiFor the area of the ith positioning reference plane, where max (S)j) The positioning reference plane with the largest area in all the candidate positioning reference planes is taken as the positioning reference plane.
Structural surface characteristic factor U5The expression is as follows
Figure BDA0003046106710000051
S03: constructing a judgment matrix U, comparing every two indexes of the index layer according to a 1-9 scaling method, and obtaining a comparison result UijThe judgment matrix is constructed so as to solve each index with respect to a certain criterionThe priority weight of the user. Index U of index layer1,U2,…,UnThe judgment matrix is U ═ Uij]n×nIts property satisfies UijUji＝1,Uij＞0,UiiThe expression of U is as follows ═ 1
Figure BDA0003046106710000052
The judgment matrix is obtained by pairwise comparison according to a 1-9 scale method, so that the judgment matrix has high subjectivity and uncertainty, consistency check needs to be carried out on the judgment matrix U, and a consistency ratio CR, a matrix consistency index CI and an average random consistency index RI are introduced. Wherein:
Figure BDA0003046106710000053
in the formula, λmaxThe maximum eigenvalue of the matrix U is judged, and n is the order of the judgment matrix U.
Figure BDA0003046106710000054
The value of RI in the formula is different with the change of the order of the judgment matrix U, the value of RI is shown in Table 1, the consistency of the judgment matrix U is checked, the smaller the value of CR is, the better the consistency of the judgment matrix U is, generally CR is less than or equal to 0.1, and the consistency of each element in the judgment matrix is considered to be better.
TABLE 1 values corresponding to the variation of the average random consistency index RI with the order
Order of the scale 1 2 3 4 5 6 7 8 9 10 11 12 13
RI 0 0 0.58 0.89 1.12 1.26 1.36 1.41 1.46 1.49 1.52 1.54 1.56
S04: judging matrix consistency test; calculating the maximum eigenvalue lambda of the judgment matrix UmaxIf CR > 0.1, it is indicated that the elements in the decision matrix U have poor consistency, and it is necessary to go back to S03 to construct a new decision matrix U ', and calculate a new maximum eigenvalue λ ' from the decision matrix U 'maxAnd until CR 'is less than 0.1, the consistency of each element in the judgment matrix U' is better.
S05: according to the judgment matrix, the weight of each index of the index layer is calculated; solving and solving the weight coefficient of the judgment matrix by using a sum method, firstly carrying out normalization processing on each column of the judgment matrix, then solving the row average value of the normalization matrix, wherein the corresponding value is the weight value of each index of the index layer, and the weight value W is equal to (W)1,w2,…,wn)TConstantly have
Figure BDA0003046106710000061
According to the judgment matrix U', the weight of each index of the index layer is calculated; weight value thereof
W＝(w1,w2,w3,w4,w5)T
S06: constructing a decision matrix Z array between the scheme layer and the index layer, wherein the decision matrix Z expression is as follows
Figure BDA0003046106710000062
And m is the number of the candidate positioning reference surfaces, and n is the number of the index factors in the index layer.
S07: obtaining a normalized decision matrix C, which aims to eliminate the incoherence of indexes in the decision matrix and make the indexes be compared with each other, wherein the normalized decision matrix C is [ C ]ij]m×nThe calculation process of the element elements in (1) is as follows
Figure BDA0003046106710000063
S08: constructing a weighted normalized decision matrix D ═ Dij]m×nThe element calculation rule is as follows
dij＝wi·cij(i＝j)
S09: solving for the ideal solution E+Value and negative ideal solution E-The value, rule is as follows
Figure BDA0003046106710000064
Figure BDA0003046106710000065
S10: calculating the distance from each positioning scheme to the positive ideal solution and the negative ideal solution respectively
Figure BDA0003046106710000066
And
Figure BDA0003046106710000067
Figure BDA0003046106710000071
Figure BDA0003046106710000072
s11: solving the scheme corresponding to each positioning reference surface and the ideal solution proximity value FiAccording to FiThe value of (2) is used for sorting the candidate positioning reference plane, and the larger the value is, the more suitable the value is as the reference plane.
Figure BDA0003046106710000073
Step 2: and sequencing according to the candidate positioning reference surfaces, and determining the number of the selected layout positioning points on each positioning reference surface according to a generative point-by-point design method of the positioning scheme.
And S12, determining the number of the layout positioning points on each positioning reference surface according to the following 3 definitions according to the relationship between the theoretical constraint freedom degree and the processing requirement.
Definition 1: if rank (ξ)y)+rank(J)-rank(Jξy) If the number is less than 6, the positioning scheme is called under positioning.
Definition 2: if rank (J) < k, the positioning scheme is called over-positioning.
Definition 3: if rank (ξ)y)+rank(J)-rank(Jξy) The positioning scheme is called full positioning, 6, and rank (j) k.
Xi is a base vector and is determined by actual processing requirements, J is a positioning Jacobian matrix, and k is the number of positioning points. In particular, when k is 6, such a full position is referred to as a unique position; and when k <6, this full positioning is called partial positioning.
And step 3: according to the TOPSIS method, a hierarchical structure model of the clamping scheme is constructed, and candidate clamping surfaces are ranked according to the closeness value of the candidate clamping surfaces and the ideal solution from large to small.
And S13, establishing a clamping scheme hierarchical structure model which is composed of a target layer, an index layer and a scheme layer as shown in figure 2, wherein for the selected clamping scheme, the clamping scheme is all candidate clamping surfaces, the index layer is the characteristics of the candidate clamping surfaces, the target layer is the quality sequence of the candidate clamping surfaces, and the best clamping surface combination is found out according to the sequence.
S14 construction of factors V of index layeriThe expression of (1); factors are considered primarily from the points of normal datum, near machining features, and clamping surface features.
Constructing a reference surface factor V of a pointing method1The expression is as follows
Figure BDA0003046106710000081
Structural machining characteristic factor V2The expression is as follows
Figure BDA0003046106710000082
K in formula (19)iIs the distance from the centroid of the ith clamping surface to the centroid of the phi 10 hole, KjThe largest distance from the centroid of all clamping surfaces to the centroid of the phi 10 hole.
Structural surface feature factor V3The expression is as follows
Figure BDA0003046106710000083
S15: constructing a judgment matrix V of a clamping scheme hierarchical structure model, comparing every two indexes of the index layer according to a 1-9 scaling method, and obtaining a comparison result VijThe judgment matrix is constructed in such a way as to solve the priority weight of each index with respect to a certain criterion.
S16: judging matrix consistency test; calculating the maximum eigenvalue lambda of the judgment matrix VmaxAnd CR, judging whether CR is less than or equal to 0.1, if CR is less than or equal to 0.1, judging that the consistency of each element in the matrix V is better, if CR is more than 0.1, judging that the consistency of each element in the matrix V is poorer, and reconstructing a new judgment matrix V ' until CR ' meets the condition that CR ' is less than or equal to 0.1.
S17: according to the judgment matrix V, weights of indexes of the index layers are obtained, and the weighted values are as follows
W＝(w1,w2,w3)T
S18: constructing a decision matrix G array between the scheme layer and the index layer, wherein the decision matrix G is [ G ]ij]m×nThe expression is as follows
Figure BDA0003046106710000091
S19: obtaining a normalized decision matrix H, in order to eliminate the incoherence of the indexes in the decision matrix and make the indexes mutually comparableComparing the normalized decision matrix H ═ Hij]m×nThe calculation process of the element elements in (1) is as follows
Figure BDA0003046106710000092
S20: constructing a weighted normalized decision matrix L ═ Lij]m×nThe element calculation rule is as follows
lij＝wi·cij
S21: solving for the ideal solution P+Value and negative ideal solution P-The value, rule is as follows
Figure BDA0003046106710000093
Figure BDA0003046106710000094
S22: calculating the distance from each clamping scheme to the positive ideal solution and the negative ideal solution respectively
Figure BDA0003046106710000095
And
Figure BDA0003046106710000096
Figure BDA0003046106710000097
Figure BDA0003046106710000098
s23: solving the scheme corresponding to each clamping surface and the ideal solution proximity value OiAccording to OiThe candidate positioning reference surfaces are ranked according to the value of (1), and the larger the value is, the better the value is taken as the clamping surface. O isiIs calculated as follows
Figure BDA0003046106710000101
And 4, step 4: under the constraint condition of static balance, aiming at the larger positioning and clamping stability and the smaller clamping force, the MGA is adopted to find out the corresponding positioning point, the clamping point position and the clamping force.
S24: under the constraint of static balance, the workpiece is in stable state in machining process, and the contact force vector F of the positioning elementdThe static equilibrium equation can be used to obtain:
GdFd+GjFj＝We
in the formula, GdFor positioning the layout matrix of the components, GjFor clamping a layout matrix of elements, FdFor positioning the contact force vector of the element, FjIs the contact force vector of the clamping element, WeThe external force is the amount of rotation (considering gravity).
Figure BDA0003046106710000102
Figure BDA0003046106710000103
Figure BDA0003046106710000104
GNFN＝We
FN＝Fd+Fj＝(F1,F2,…,Fu,Fu+1,…,Fu+v)T＞0
In which u and v are the number of positioning points and the number of clamping points, ri(i is more than or equal to 1 and less than or equal to u + v) is the coordinate of the positioning point or the clamping point, ni(i is more than or equal to 1 and less than or equal to u + v) is a normal vector of a positioning point or a clamping point, GNTo position the clamping matrix.
S25: evaluation target for constructing positioning element layout
(1) Constructing the maximum target of clamping stability
In the machining process, all degrees of freedom of the workpiece are eliminated by a reasonable positioning and clamping scheme, the clamping stability of different reasonable schemes is different, and the stronger the clamping stability is, the stronger the external force resisting spiral capacity is. From a mechanical point of view, the clamp can balance any loaded external force spiral by using positive contact force. It is noted that the ability to resist the external force screw varies from contact layout to contact layout, and it is clearly important to find the optimum fixture element contact layout for more stable clamping positioning, using GNFN＝WeDefining a positioning and clamping stability index, the expression of which is as follows
Figure BDA0003046106710000111
Index omegaSThe larger the value of (A), the less singular the contact layout matrix of the clamp elements, which means that the ability of this positional clamping to resist helical interference from external forces on the workpiece is stronger.
Define stability index ΩRThe expression is
Figure BDA0003046106710000112
Wherein k is1Is a non-negative constant, ΩRThe smaller the value of (A), the better the stability of the positioning and clamping scheme, and the stronger the interference capability of the workpiece against the external force screw.
(2) Establishing a minimum clamping force target
In the process of processing a workpiece, under the constraint of static balance, the clamp provides a clamping force with a proper size to resist external forces such as cutting force, cutting torque and the like, so that the workpiece and the positioning element always keep positive supporting force, and the clamping force directly influences the reliability, the processing precision, the positioning accuracy and the clamping deformation of the workpiece clamping.
Different positioning and clamping schemes and different external force screws have different required clamping force, and the actual processing process of the workpieceIn the middle, the clamping force is usually dependent on personal experience of workers, the randomness is large, and sufficient theoretical data support is lacked. The magnitude of the clamping force varies from contact layout to contact layout, and it is clearly important to find the optimum clamp element contact layout for achieving a positional clamping with less clamping force. According to GdFd+GjFj＝WeDefining the clamping force index omegaFExpression of
Figure BDA0003046106710000113
Wherein k is2And the constant is a constant larger than zero, and the minimum clamping force is obtained in different positioning and clamping schemes under the condition of meeting the constraint condition of static balance.
S26: scheme for optimizing clamping layout of clamp by using MGA
A large number of combination modes are provided for positioning points and clamping points in the clamp, the algorithm is required to have strong searching capability, and a multi-objective evolutionary algorithm (MOEAD) based on decomposition is adopted to solve the following multi-objective functions.
find[r1,…,ru,ru+1,…,ru+v,Fu+1,…,Fu+v]
Figure BDA0003046106710000121
s.t.
Figure BDA0003046106710000122
Sj(xi,yi,zi) 0 represents that the ith positioning point is on the jth positioning reference plane, and J is the number of candidate reference planes;
SCq(xh,yh,zh) 0 denotes the h-th clamping point on the Q-th clamping surface, and Q is the number of candidate clamping surfaces.
Specifically, referring to fig. 1 to 7, an optimal clamp clamping layout scheme is designed by taking a case that an enterprise produces oblique insertion frames in a large scale and processes phi 10 holes.
Step 1: according to the TOPSIS method, the candidate positioning datum planes are ranked according to the similarity value between the candidate positioning datum planes and the ideal solution.
Establishing a location reference selection hierarchy model, as shown in FIG. 5
The expression of the judgment matrix U, U is constructed as follows
Figure BDA0003046106710000123
Judging matrix consistency test; calculating the maximum eigenvalue lambda of the judgment matrix UmaxWhen CR is 5.54 and CR is 0.13 > 0.1, it means that the consistency of each element in the judgment matrix U is poor, and the judgment matrix needs to be reconstructed, and the expression of the new judgment matrix U ', U' is as follows
Figure BDA0003046106710000131
Calculating the maximum eigenvalue lambda of the judgment matrix UmaxWhen CR is 5.0166, CR is 0.0037 < 0.1, indicating that the elements in the determination matrix U' are more consistent.
According to the judgment matrix U', the weight of each index of the index layer is calculated; weight value thereof
W＝(w1,w2,w3,w4,w5)T＝(0.106，0.263,0.420,0.107,0.104)T
Constructing a scheme index numerical table shown in Table 2 according to information of the parts of the inclined insertion frame
TABLE 2 scheme index numerical table
Figure BDA0003046106710000132
Constructing a decision matrix Z between the scheme layer and the index layer, wherein the expression of the decision matrix Z is as follows
Figure BDA0003046106710000133
Obtain a normalized decision matrix C
Figure BDA0003046106710000141
Constructing a weighted normalized decision matrix D ═ Dij]m×n
Figure BDA0003046106710000142
Solving for the ideal solution E+Value and negative ideal solution E-Value of
Figure BDA0003046106710000143
Figure BDA0003046106710000144
Solving the corresponding scheme and ideal solution of each positioning reference surface to obtain a proximity value Fi,
TABLE 3 alternative proximity values to ideal solutions
Figure BDA0003046106710000145
As can be seen from the data in Table 3, the alternatives are ranked F from greater closeness to the ideal closeness3＞F4＞F1＞F2＞F5So that the optimal positioning reference plane selection order is A3、A4、A1、A2、A5。
Step 2: determining the number of positioning points on the selected positioning reference surface
In order to ensure a phi 10 via hole, according to the relation between the theoretical constraint freedom and the processing requirementMachining requirements, theoretical constraint of degree of freedom δ qwXi · λ, where the base vector xi ═ xi #y(ξy＝[0,1,0,0,0,0]T) Arbitrary vector λ ═ λy(ii) a Then, the sequence is selected according to the optimal selection of the candidate positioning reference surface, in A3Laying out the first locating point on the internal cylindrical surface, calculating Jacobian matrix J, supplementing
Ji＝-[ni T,(ni×ri w)T]
In the formula niIs the normal vector of the ith anchor point, ri wFor the position coordinates of the ith positioning point in the workpiece coordinate system
J＝[J1 T,J2 T,…Jk T]T
Figure BDA0003046106710000151
r1 w＝[x1,y1,z1]T
Figure BDA0003046106710000152
Figure BDA0003046106710000153
Thus, rank (J) ═ 1 ═ k, rank (J ξ)y)＝1,rank(ξy)+rank(J)-rank(Jξy) 1 <6, under-positioned according to definition 1.
According to definition 1, it can be known that the positioning scheme belongs to an under-positioning mode, and for an unreasonable positioning scheme, the effective number of positioning points is insufficient, so that A should be on the same positioning reference3Laying out the second positioning point, calculating Jacobian matrix J
Figure BDA0003046106710000154
Thus, rank (J) ═ 2 ═ k, rank (J ξ)y)＝1，rank(ξy)+rank(J)-rank(Jξy) 2 <6, under-positioned according to definition 1.
According to definition 1, it can be known that the positioning scheme belongs to an under-positioning mode, and for an unreasonable positioning scheme, the effective number of positioning points is insufficient, so that A should be on the same positioning reference3Laying out a third positioning point, calculating a Jacobian matrix J,
Figure BDA0003046106710000161
thus, rank (J) ═ 3 ═ k, rank (J ξ)y)＝1，rank(ξy)+rank(J)-rank(Jξy) 3 <6, under-positioned according to definition 1.
According to definition 1, it can be known that the positioning scheme belongs to an under-positioning mode, and for an unreasonable positioning scheme, the effective number of positioning points is insufficient, so that A should be on the same positioning reference3Laying out the fourth positioning point and calculating a Jacobian matrix J
Figure BDA0003046106710000162
Thus, rank (J) ═ 4 ═ k, rank (J ξ)y)＝1，rank(ξy)+rank(J)-rank(Jξy) 4 <6, under-positioned according to definition 1.
According to definition 1, it can be known that the positioning scheme belongs to an under-positioning mode, and for an unreasonable positioning scheme, the effective number of positioning points is insufficient, so that A should be on the same positioning reference3Laying out the fifth positioning point and calculating the Jacobian matrix J
Figure BDA0003046106710000171
Thus, rank (j) < 5 ═ k, according to definition 2, the positioning scheme is over-positioning (for the positioning reference plane a)3In other words, over-positioning); rank (J xi)y)＝1，rank(ξy)+rank(J)-rank(Jξy) 4 <6, the positioning scheme is under-positioned according to definition 1, and thus under-positioned for the entire positioning scheme.
The effective number of the positioning points is not enough and the layout is not reasonable as known from the insufficient positioning. A needs to be selected according to the reference coincidence principle and the candidate reference surface ideality proximity value sorting4The surface is the second positioning reference, and the fifth positioning point is arranged on the newly selected positioning reference A4In the above, the Jacobian matrix J is calculated
Figure BDA0003046106710000172
Thus, rank (J) ═ 5 ═ k, rank (J ξ)y)＝1,rank(ξy)+rank(J)-rank(Jξy) 5 <6, under-positioned according to definition 1.
According to definition 1, it can be known that the positioning scheme belongs to an under-positioning mode, and for an unreasonable positioning scheme, the effective number of positioning points is insufficient, so that A should be on the same positioning reference4Laying out the fifth positioning point and calculating the Jacobian matrix J
Figure BDA0003046106710000181
Thus, rank (j) <6 ═ k, according to definition 2, the positioning scheme is over-positioning (for the positioning reference plane a)4In other words, for over-positioning), rank (J ξ)y)＝1，rank(ξy)+rank(J)-rank(Jξy) 5 <6, the positioning scheme is under-positioned according to definition 1, and thus under-positioned for the entire positioning scheme.
The effective number of the positioning points is not enough and the layout is not reasonable as known from the insufficient positioning. Selecting A according to the principle of reference coincidence and the sequence of the candidate reference surface ideality close values1The surface is a third positioning reference, and a sixth positioning point is arranged on the newly selected positioning reference A1In the above, the Jacobian matrix J is calculated
Figure BDA0003046106710000182
Thus, rank (J) ═ 6 ═ k, rank (J ξ)y)＝1，rank(ξy)+rank(J)-rank(Jξy) As 6, full position according to definition 1. In conclusion, the positioning scheme is "4-1-1"
And step 3: according to the TOPSIS method, candidate clamping surfaces are ranked from large to small proximity to ideality values
Establishing a clamping scheme hierarchy model, which is shown in FIG. 6
Construct the judgment matrix V
Figure BDA0003046106710000191
Judging the consistency of the matrix V for inspection; calculating the maximum eigenvalue lambda of the judgment matrix VmaxWhen CR is 3.05 and CR is 0.045 < 0.1, it means that the elements in the matrix V are judged to be consistent well.
According to the judgment matrix V, weights of indexes of the index layers are obtained, and the weighted values are as follows
W＝(w1,w2,w3)T＝(0.472,0.377,0.151)T
Constructing a recipe index numerical table shown in Table 4 based on information on parts of the inclined insertion frame
TABLE 4 scheme index numerical table
Figure BDA0003046106710000192
Constructing a decision matrix G array between the scheme layer and the index layer, wherein the decision matrix G is [ G ]ij]m×nThe expression is as follows
Figure BDA0003046106710000193
Obtain a normalized decision matrix H
Figure BDA0003046106710000194
Constructing a weighted normalized decision matrix L ═ Lij]m×n
Figure BDA0003046106710000201
Solving for the ideal solution P+Value and negative ideal solution P-Value of
Figure BDA0003046106710000202
Figure BDA0003046106710000203
Calculating the closeness degree O between the scheme corresponding to each clamping surface and the ideal solutioni
TABLE 5 closeness of alternatives to ideal solution
Figure BDA0003046106710000204
As can be seen from the data in Table 5, the alternatives are ranked from greater closeness to ideal closeness O1＞O2＞O3＝O4So that the optimal positioning reference plane selection order is B1、B2、A2＝A5。
And 4, step 4: under the constraint condition of static balance, the larger the clamping stability is and the smaller the clamping force is, the corresponding positioning point, the clamping point coordinate and the clamping force are found out
From the first, the second and the third steps, take the processing of the phi 10 hole oblique inserting frame as an example, in A3Layout of 4 dot sites on the face, A4Arranging 1 positioning point on the surface, wherein A is11 positioning point is arranged on the surface, and firstly, B1Arranging 1 clamping point on the surface, inserting obliquelyThe barycentric coordinate of the frame is rg＝[24mm,-70mm,0mm]Gravity is Fg150N, external force screw W for processing phi 10 holeq＝[-85-20015004998.753.47]The information of each positioning point and clamping point is shown in Table 6
TABLE 6 locating and clamping point coordinates and normal vector information
Figure BDA0003046106710000211
Firstly, B is1Arranging a clamping point on the surface, setting the range of the clamping force to be (0N,2000N), and judging whether the static balance constraint can be met
find[r1,r2,r3,r4,r5,r6,r7,F7]
Figure BDA0003046106710000212
s.t.
Figure BDA0003046106710000213
For the formula (66), MOEAD algorithm is adopted for operation, the size of the population individual is set to be 1500, the number of pareto leading edge individuals is set to be 1500, the maximum iteration number is 1500, the cross probability is 0.9, and k is set1＝0，k20.1, the abscissa represents ΩRThe ordinate represents ΩFIf the positioning clamping layout point which meets the constraint condition does not exist, namely the static balance can not be met, two fitness values omega are set and outputRAnd ΩFIs a very large value, then ΩR＝1×1012，ΩF＝1×1012(ii) a And if the requirement can be met, outputting the specific numerical value on the pareto front surface. The result of solving equation (58) is shown in fig. 7.
As can be seen from FIG. 7, the description is only on the first clamping surface B1The static balance condition can be met by arranging a clamping point, and all results in fig. 7 are fullThe best clamp clamping layout scheme meets the clamp clamping layout scheme with high clamping stability and small clamping force, so that the best clamp clamping layout scheme needs to be selected from feasible schemes at the lower left corner of figure 7 when two target values (omega) are requiredR，ΩF) When the coordinate of the positioning point is (1920,2250), the coordinates of the positioning point are respectively A (-10, 0,25), B (8.7634, -4.8169, -25), C (4.0901, 9.1253, -25), D (-0.8547, 9.9634, 25), E (14.5692, 9.6944, -25), F (52, -120, 40); the coordinates of the clamping points are G (-13.7289, -10.8508, 25); b is1Face clamping force F7150N. Therefore, the positioning points, the coordinates of the clamping points and the clamping force are adopted, and the clamping layout scheme of the clamp has high stability and small clamping force.
The TOPSIS and MGA-based clamp clamping layout method disclosed by the invention objectively finds out the optimal sequence of the positioning reference surface and the clamping surface by adopting a TOSIS evaluation method, finds out the number of the positioning points on the positioning reference surface by adopting a point-by-point design method of a positioning scheme, optimizes the positioning points, the coordinates of the clamping points and the clamping force by adopting an MGA based on evolution, and provides a scientific basis for the design of a complicated part clamping layout scheme.
Compared with the prior art, the TOPSIS and MGA-based clamp clamping layout method provided by the invention has the advantages that (1) a general clamp clamping design scheme only considers a positioning scheme and directly provides a clamping scheme, the clamping scheme is lack of objectivity in the first time, and the clamping scheme and the positioning scheme are not necessarily matched very in the second time, so that the clamp clamping layout scheme is lack of persuasion.
(2) The traditional clamp design cases are mostly simple and regular parts, a 3-2-1 positioning scheme is mostly adopted, but the actually processed parts are irregular and complex parts, the traditional positioning scheme is not always satisfied, the invention only needs to obtain the basic information of the workpiece to be processed, indexes the information respectively, and can obtain the clamp clamping layout scheme through a reasonable mathematical modeling method, thereby greatly increasing the applicability of the invention to the parts.
(3) The traditional clamp clamping layout scheme mostly adopts a single evaluation index, and the invention evaluates one scheme from two dimensions of clamping stability and clamping force and can simultaneously take more indexes into consideration.
(4) In the design of the clamp clamping layout scheme, the positioning and clamping are considered, the distribution of the number of the positioning points on the positioning reference surface is also considered, the positioning points, the clamping point positions and the clamping force are also considered, and the factors which are more comprehensive than the common clamping layout scheme and are more in line with the actual clamping layout scheme are considered.
(5) The design of the traditional clamp clamping layout scheme only optimizes one or two indexes of a positioning point position, a clamping point position and a clamping force, which is not reasonable, and the invention simultaneously optimizes the positioning point position, the clamping point position and the clamping force, which is a factor actually needed to be optimized simultaneously, so that the optimal clamping layout scheme can be obtained through optimization.
(6) All technical schemes of the invention are derived in a mathematical modeling mode, and hundred percent programming processing can be realized in the whole process, so that a solid theoretical basis is provided for the design of a clamping layout scheme of a modularized, digital and intelligent clamp. Therefore, only basic information of the part to be processed needs to be input, and the clamp clamping layout scheme which is scientific and reasonable and suitable for the part can be provided.
The terms "first" and "second" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implying a number of the indicated technical features. Thus, a defined feature of "first", "second", may explicitly or implicitly include one or more of that feature. In the description of the present invention, "a plurality" means two or more unless otherwise specified.
The above-mentioned serial numbers of the embodiments of the present invention are merely for description and do not represent the merits of the embodiments.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (5)

1. A clamp clamping layout method based on TOPSIS and MGA is characterized by comprising the following steps:
step 1: constructing a hierarchical analysis structure model of a positioning scheme according to a TOPSIS method, and sequencing candidate positioning datum planes according to the candidate positioning datum planes and the ideal solution proximity value from large to small;
step 2: sequencing according to the candidate positioning datum planes, and determining the number of the selected layout positioning points on each positioning datum plane according to a generative point-by-point design method of a positioning scheme;
and step 3: constructing a hierarchical structure model of a clamping scheme according to a TOPSIS method, and sequencing candidate clamping surfaces from large to small according to the proximity value of the candidate clamping surfaces and an ideal solution;
and 4, step 4: under the constraint condition of static balance, the MGA is adopted to find out the corresponding positioning point, the position of the clamping point and the clamping force according to the larger positioning and clamping stability and the smaller clamping force.
2. The method according to claim 1, wherein the step 1 of constructing the hierarchical analysis structure model of the positioning solution selects a hierarchical structure model for establishing a positioning reference, and the hierarchical structure model is composed of a target layer, an index layer and a solution layer, wherein the solution layer is all candidate positioning reference planes, the index layer is the features of the candidate positioning reference planes, the target layer is the order of superiority and inferiority of the candidate reference planes, and the best positioning reference plane combination is found according to the order; constructing index layer characteristic factor UiThe expression of (1); constructing a judgment matrix U; judging matrix consistency test; according to the judgment matrix, the weight of each index of the index layer is calculated; constructing a decision matrix Z array between the scheme layer and the index layer; obtaining a normalized decision matrix C; constructing a weighted normalized decision matrix D ═ Dij]m×n(ii) a Solving for the ideal solution E+Value and negative ideal solution E-A value; calculating the distance from each positioning scheme to the positive ideal solution and the negative ideal solution respectively
Figure FDA0003046106700000011
And
Figure FDA0003046106700000012
solving the scheme corresponding to each positioning reference surface and the ideal solution proximity value Fi。
3. The method according to claim 1, wherein the step 2 of determining the number of the selected layout positioning points on each positioning reference surface is to determine the number of the layout positioning points on each positioning reference surface according to a relationship between the theoretical constraint degree of freedom and the processing requirement.
4. The method according to claim 1, wherein the candidate clamping surfaces are ranked according to the closeness value of the candidate clamping surfaces to the ideal solution from large to small in the step 3 by establishing a clamping scheme hierarchical structure model, which is composed of a target layer, an index layer and a scheme layer, wherein the clamping scheme is the clamping surfaces of all candidates, the index layer is the characteristics of the candidate clamping surfaces, the target layer is the ranking of the advantages and the disadvantages of the candidate clamping surfaces, and the best clamping surface combination is found according to the ranking; factor V of construction index layeriThe expression of (1); constructing a judgment matrix V of a clamping scheme hierarchical structure model; judging matrix consistency test; according to the judgment matrix V; constructing a decision matrix G array between the scheme layer and the index layer; obtaining a normalized decision matrix H; constructing a weighted normalized decision matrix L ═ Lij]m×n(ii) a Solving for the ideal solution P+Value and negative ideal solution P-A value; calculating the distance from each clamping scheme to the positive ideal solution and the negative ideal solution respectively
Figure FDA0003046106700000021
And
Figure FDA0003046106700000022
solving the scheme corresponding to each clamping surface and the ideal solution proximity value OiAccording to OiThe value of (A) is used for sorting the candidate positioning reference planes, and the larger the value isThe more preferred is as the clamping surface.
5. The method of claim 1, wherein the step 4 of finding the corresponding positions of the positioning point and the clamping force is to set the workpiece machining process in a stable state under the constraint of static equilibrium, and the contact force vector F of the positioning element isdCan be obtained by a static equilibrium equation; constructing an evaluation target of the layout of the positioning element; and the scheme of clamp clamping layout is optimized by adopting MGA.
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