CN110489903A - Based on extension science-grey relational ideal solution lathe bed structure optimum design method - Google Patents
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Abstract
The invention discloses a kind of based on extension science-grey relational ideal solution lathe bed structure optimum design method comprising carries out finite element analysis to lathe bed, and calculates four kinds of reinforcing plate structures；The experimental factor that sensitivity analysis determination and orthogonal test are carried out to lathe bed inside dimension and external dimensions, determines evaluation index later；The value for setting experimental factor gusset thickness and lathe bed wall thickness constructs the horizontal orthogonal test table of three factor four using experimental factor and carries out Finite Element Simulation Analysis, picks out optimal parameter and combine the lathe bed alternative to be formed；Euclidean distance is based on using the improved AHP method and entropy assessment combination weighting and GC-TOPSIS method of extension theory and grey relational grade selects optimal conduct lathe bed structure scheme from lathe bed alternative；Lathe bed structure scheme is judged relative to former lathe bed structure, and whether comprehensive performance improves, if improving, exports lathe bed structure scheme, otherwise, returns to the value step of setting gusset thickness and lathe bed wall thickness.
Description
Technical field
The present invention relates to the optimization methods of machining apparatus, and in particular to one kind is based on extension science-grey correlation ideal solution
The lathe bed structure optimum design method of method.
Background technique
Currently, lathe is always the core of equipment manufacture in the machining of modernization, it is a kind of expensive
Electromechanical integration precision equipment.In each component part of planer-type milling machine, lathe bed is the important bearing part of planer-type milling machine, is risen
The effect of the various components of lathe is supported, weight accounts for the 20%~30% of complete machine total weight, the static and dynamic performance of lathe bed structure
Quality will directly influence the processing quality, machining accuracy and production efficiency of planer-type milling machine.And the interior tendon of gantry miller body
Whether hardened structure design is reasonable, largely determines the dynamic and static state performance of lathe bed structure.It therefore, is guarantee planer-type milling machine
At a high speed, efficiently, in high precision and high-intensitive design requirement, lathe bed must have enough static rigidities and good dynamic special
Property.
Theoretical by computer technology and finite element analysis, the structure design of bed piece has become lot of domestic and foreign
The research method largely about lathe exists in the prior art in the hot research problem of person, such as: Shen is remote etc. has studied forging machine
The corresponding parameter of bed, the lathe parameter optimized using genetic algorithm improve the structural behaviour of the lathe.What is listened by having
Finite element analysis has studied the dynamic stiffness weak spot of lathe bed, establishes a variety of lathe bed schemes based on lathe bed meta structure, finally excellent to have selected
Preferred plan improves the dynamic characteristic of bed piece.
These researchs are optimized just with machine tool structure parameter, are not selected parameter, also without complete
Face considers the combined influence of inside, shape and gusset to lathe bed of lathe bed, it is difficult to the structure of fully optimized lathe bed.
Summary of the invention
It is provided by the invention based on extension science-grey relational ideal solution bed for above-mentioned deficiency in the prior art
Body structure optimum design method using lathe bed gusset, inside and outer dimension structural parameters carry out finite element analysis, according to point
It analyses result and preferably goes out optimal machine tool structure scheme, improve the comprehensive performance of lathe bed.
In order to achieve the above object of the invention, the technical solution adopted by the present invention are as follows:
It provides a kind of based on extension science-grey relational ideal solution lathe bed structure optimum design method comprising:
S1, it constructs former Machine body and carries out Static finite element analysis and dynamic finite element analysis, determine that lathe bed rigidity is thin
Weak part structure, and four kinds of reinforcing plate structures are designed according to lathe bed rigidity vulnerable area structure；
S2, it is carried out respectively based on lathe bed inner structure size and external structure size to quality, maximum stress, maximum change
The sensitivity analysis of shape, first natural frequency, selecting, dynamic property quiet on lathe bed influences maximum critical size: gusset thickness
With lathe bed wall thickness；
S3, the experimental factor using reinforcing plate structure, gusset thickness and lathe bed wall thickness as orthogonal test, using lathe bed matter
Amount, maximum distortion, maximum stress and first natural frequency are as evaluation index；
S4, the value for setting gusset thickness and lathe bed wall thickness construct the horizontal orthogonal examination of three factor four using experimental factor
It tests table and carries out L16(43)=16 time Finite Element Simulation Analysis picks out optimal parameter and combines the lathe bed alternative to be formed；
It is S5, comprehensive using the improved AHP method and entropy assessment combination weighting Calculation Estimation index and lathe of extension theory
Close the comprehensive weight between performance；
S6, Euclidean distance and grey relational grade are based on from lathe bed alternative using comprehensive weight and GC-TOPSIS method
Optimal lathe bed alternative is selected as lathe bed structure scheme；
S7, according to maximum stress, maximum distortion and the first natural frequency of lathe bed structure scheme and former lathe bed structure, judgement
Whether lathe bed comprehensive performance improves, if improving, exports lathe bed structure scheme, otherwise, return step S4.
The invention has the benefit that this programme passes through the finite element analysis of static properties and dynamic property, it can be accurate
Ground determines the vulnerable area of lathe bed, and to realize targeted gusset design, the choosing of lathe bed prioritization scheme parameter can be improved in this way
The accuracy selected；Sensitivity analysis is carried out by lathe bed inside dimension and external dimensions later and determines orthogonal experiment factor and evaluation
Index enables the parameter chosen comprehensively to react the comprehensive performance of lathe bed, and the more of Orthogonal Experiment and Design below can be improved
The accuracy of kind lathe bed alternative.
This programme uses analytic hierarchy process (AHP) and entropy assessment host computer combination weights based on extension theory, considers simultaneously
Lathe bed is quiet, the collision problem between dynamic property raising and light-weight design and subjective and objective factor are to lathe bed performance evaluation band
The influence come, so that analysis result is truer.
Using combination weights and Euclidean distance is comprehensively considered using GC-TOPSIS method and grey relational grade determines lathe bed structure
Scheme, wherein the synthesis exchange premium degree based on Euclidean distance and grey relational grade can be respectively from positional distance and shape similarity
The comprehensive degree of closeness for obtaining lathe bed alternative Yu positive and negative ideal scheme ensure that the final lathe bed structure scheme preferably gone out
Accuracy, keep lathe bed evaluation more rationally reliable, more tally with the actual situation.
Detailed description of the invention
Fig. 1 is the flow chart based on extension science-grey relational ideal solution lathe bed structure optimum design method.
Fig. 2 is the perspective view of the lathe bed structure of this programme.
Fig. 3 is the side view of lathe bed structure width direction.
Fig. 4 is four kinds of lathe bed reinforcing plate structures of design, and wherein a is V-type reinforcing plate structure, and b is O-shaped reinforcing plate structure, and c is well type
Reinforcing plate structure, d are biomimetic type reinforcing plate structure.
Fig. 5 is to determine lathe bed structure side based on Euclidean distance and grey relational grade using comprehensive weight and GC-TOPSIS method
The flow chart of case.
Fig. 6 be in specific example each scheme and ideal scheme to the degree of correlation of each evaluation index.
Fig. 7 be in specific example each scheme and ill ideal solution to the degree of correlation of each evaluation index.
Fig. 8 is the tendency chart of each orthogonal experiment scheme exchange premium degree in specific example.
Specific embodiment
A specific embodiment of the invention is described below, in order to facilitate understanding by those skilled in the art this hair
It is bright, it should be apparent that the present invention is not limited to the ranges of specific embodiment, for those skilled in the art,
As long as various change is in the spirit and scope of the present invention that the attached claims limit and determine, these variations are aobvious and easy
See, all are using the innovation and creation of present inventive concept in the column of protection.
It shows with reference to Fig. 1, Fig. 1 based on extension science-grey relational ideal solution lathe bed structure optimum design method
Flow chart；As shown in Figure 1, this method S includes step S1 to step S7.
In step sl, it constructs former Machine body and carries out Static finite element analysis and dynamic finite element analysis, determine bed
Body rigidity vulnerable area structure, and four kinds of reinforcing plate structures are designed according to lathe bed rigidity vulnerable area structure.
As shown in figure 4, four kinds of reinforcing plate structures of this programme design are respectively V-type reinforcing plate structure, O-shaped reinforcing plate structure, well type
Reinforcing plate structure and the biomimetic type reinforcing plate structure for copying honeycomb structure to design.
In step s 2, based on lathe bed inner structure size and external structure size carry out respectively to quality, maximum stress,
The sensitivity analysis of maximum distortion, first natural frequency, selecting, dynamic property quiet on lathe bed influences maximum critical size: muscle
Plate thickness and lathe bed wall thickness.
As shown in Figures 2 and 3, it illustrates the lathe bed structure general structure that the application optimizes, letter L1 in Fig. 2,
L2, d, t and θ be respectively up and down pitch-row, front and rear gaps away from, gusset thickness bottom, lathe bed wall thickness and tilt angle, alphabetical H, L in Fig. 3 and
B is respectively total high, overall length of lathe bed, beam overall.
The lathe bed inner structure size of this programme includes gusset thickness, lathe bed wall thickness, front and rear gaps away from, upper and lower pitch-row and inclination
Angle, outer dimension (length, width, height) of the external structure having a size of lathe bed.
In step s3, the experimental factor using reinforcing plate structure, gusset thickness and lathe bed wall thickness as orthogonal test uses
Lathe bed quality, maximum distortion, maximum stress and first natural frequency are as evaluation index；Before wherein first natural frequency refers to lathe bed
After swing.
In step s 4, it is horizontal to construct three factor four using experimental factor for the value for setting gusset thickness and lathe bed wall thickness
Orthogonal test table carry out L16(43)=16 time Finite Element Simulation Analysis picks out optimal parameter and combines the lathe bed to be formed alternatively side
Case.
In orthogonal test table, first row to third column respectively reinforcing plate structure, gusset thickness and lathe bed wall thickness, and first
Row to fourth line is respectively V-type reinforcing plate structure, O-shaped reinforcing plate structure, well type reinforcing plate structure and biomimetic type reinforcing plate structure.
In one embodiment of the invention, further include data prediction before calculating comprehensive weight:
A1, the data of evaluation index are converted to initial data decision matrix V=(vij)m×n:
Wherein, vijIt is the achievement data of i-th of lathe bed alternative and j-th of evaluation index；I=1,2 ..., m, j=1,
2 ..., n, m are lathe bed alternative total number；N is evaluation index total number；
A2, the achievement data in initial data decision matrix is normalized to obtain normalized matrix:
When the achievement data in initial data decision matrix is positive index, located in advance using positive target function
Reason:
When the achievement data in initial data decision matrix is negative sense index, located in advance using negative sense target function
Reason:
A3, it constructs to form normalized matrix using the achievement data after normalization:
In step s 5, using the improved AHP method of extension theory and entropy assessment combination weighting Calculation Estimation index
With the comprehensive weight between lathe comprehensive performance.
When implementation, this programme preferably uses the improved AHP method of extension theory and the calculating of entropy assessment combination weighting to comment
Comprehensive weight between valence index and lathe comprehensive performance further comprises step D1 and step D2:
In step D1, according to evaluation index relative to the importance between lathe comprehensive performance, building can open up interval judgement
Matrix, and it includes step B1 to step B5 that calculating, which can open up the weight vector of Interval Judgment Matrix:
B1, basis can open up Interval Judgment Matrix A=< A-、A+> A is found out respectively-、A+Maximum eigenvalue and its corresponding
Normalization characteristic vector, wherein
B2,0 < kx of satisfaction is calculated-≤mx+All positive real numbers m, k value:
B3, judge whether k and m meets 0≤k≤1≤m, solve vector step if meeting and entering, otherwise correcting or rebuild can
Open up Interval Judgment Matrix；
B4, vector: S=(S is solved1, S1..., Snk)=(kx-, mx+), S in formulankIt is kth layer nth elements to upper one layer
The interval weight of element；
B5, weight is determined:
IfUtilize formula
IfJ=1,2 ..., n；V(Si≥Sj) >=0 (i ≠ j) is then
In formula, PiIt is i-th of element to upper one layer of weight sequencing；
To vector Pi=(P1, P2..., Pn) be normalized, each evaluation index is obtained to the weight vector of destination layer
W=(w1,w2,…,wn)。
In step d 2, according to normalized matrix and initial data decision matrix, using entropy assessment Calculation Estimation index
Entropy weight, later using the comprehensive weight between weight vector and entropy weight Calculation Estimation index and lathe comprehensive performance:
Wherein, WiFor comprehensive weight；W=(w1,w2,…,wn) it is weight vector；For entropy weight.
When implementation, this programme preferably uses the entropy weight concrete methods of realizing of entropy assessment Calculation Estimation index to include:
For canonical matrix Y, parameter value weight dij:
In lathe bed alternative selection course, entropy calculation formula are as follows:
Calculate the entropy weight of each evaluation index:
In step s 6, Euclidean distance is based on using comprehensive weight and GC-TOPSIS method and grey relational grade is standby from lathe bed
It selects and selects optimal lathe bed alternative in scheme as lathe bed structure scheme；
In one embodiment of the invention, step S6 (the general idea process of this step may refer to Fig. 5) is further
Include:
C1, standardization
Using initial data decision matrix V=(vij)m×nIn data do standardization, X=(x can be obtainedij)m×n's
Normalized matrix:
Wherein,I=1,2 ..., m；J=1,2 ..., n；
C2, weighting standard matrix is calculated using comprehensive weight
Enable uij=(Wixij)m×n, weighted normal matrix U=(u can be obtainedij)m×nAre as follows:
In formula, yijFor Y=(yij)m×nIn element, WiIt is the comprehensive weight of every evaluation index, i=1,2 ..., m, j
=1,2 ..., n；
C3, positive and negative ideal solution and its distance are determined
Positive ideal solutionIndicate ideal scheme, minus ideal resultIndicate ill ideal solution, expression formula is as follows:
In formula, J1For the set of profit evaluation model evaluation index, J2For the set of cost type evaluation index；
Calculate i-th of scheme to positive and negative ideal solution distanceIts calculation formula is as follows:
C4, each scheme and ideal and ill ideal solution grey relational grade size are calculated
C41, the grey relational grade for calculating i-th of scheme and ideal schemeUnder j-th of evaluation index, calculate i-th
The grey incidence coefficient of scheme and ideal scheme:
Wherein, ρ is resolution ratio, and ρ ∈ (0,1) takes ρ=0.5；
Grey incidence coefficient matrix is constructed using the grey incidence coefficient of i-th of scheme and ideal scheme are as follows:
Calculate the grey relational grade size of i-th of scheme and ideal scheme:
C42, the grey relational grade for calculating i-th of scheme and ill ideal solutionUnder j-th of evaluation index, i-th is calculated
The grey incidence coefficient of a scheme and ill ideal solution:
Wherein, ρ is resolution ratio, and ρ ∈ (0,1) takes ρ=0.5；
Grey incidence coefficient matrix is constructed using the grey incidence coefficient of i-th of scheme and ill ideal solution:
Calculate the grey relational grade size of i-th of scheme and ill ideal solution:
C5, the comprehensive extraction for calculating each scheme
It adjusts the distanceAnd grey relational gradeNondimensionalization processing, the public affairs of nondimensionalization processing are done respectively
Formula are as follows:
Wherein, HiIt respectively represents
Nondimensionalization distance and the degree of association are combined:
In formula, η1、η2It is policymaker to the preference of location and shape, η1+η2=1；It is alternative for each lathe bed
The degree of closeness of scheme and ideal scheme and ill ideal solution,More big then lathe bed alternative is more excellent,More big then lathe bed
Alternative is poorer, i=1,2 ..., m；
Calculate the comprehensive extraction of each lathe bed alternative:
C6, each lathe bed alternative is ranked up according to the size of comprehensive extraction, selects comprehensive extraction maximum
Scheme is as lathe bed structure scheme.
In the step s 7, intrinsic according to the maximum stress of lathe bed structure scheme and former lathe bed structure, maximum distortion and single order
Frequency, judges whether lathe bed comprehensive performance improves, if improving, exports lathe bed structure scheme, otherwise, return step S4.
It is illustrated below with reference to effect of the specific example to the lathe bed structure optimum design method of this programme:
Choose the value of gusset thickness and lathe bed wall thickness, the horizontal orthogonal test table (being shown in Table 1) of three factor of building four；
1 Orthogonal Experiment and Design of table
L is carried out according to lathe bed of the orthogonal experiment to different structure16(43)=16 time Finite Element Simulation Analysis, passes through lathe bed
Statics and model analysis obtain the evaluation such as design variable and lathe bed quality, maximum distortion, maximum stress and first natural frequency
The simulation numerical of index, as shown in table 2.Optimal parameter combination is picked out by orthogonal experiment, greatly reduces test number (TN),
It improves work efficiency.
2 lathe bed orthogonal test of table and simulation result
It is comprehensive using the improved AHP method and entropy assessment combination weighting Calculation Estimation index and lathe of extension theory
Comprehensive weight between performance:
Expert is constructed by being compared to each other two-by-two to quality, maximum stress, maximum distortion and first natural frequency
It is flexible out to open up Interval Judgment Matrix, as shown in table 3.
Table 3 can open up Interval Judgment Matrix
A is calculated based on Interval Judgment Matrix can be opened up-、A+Corresponding maximum eigenvalue and its corresponding feature vector x-、
x+:
x-=[0.3976,0.3164,0.1252,0.1607]T
x-=[0.3976,0.3164,0.1252,0.1607]T
K=0.925, m=1.076,0<k<1, m>1 can be obtained by the calculation formula of k, m, therefore the judgment matrix constructed meets
Coherence request.It can be calculated by the calculation formula in step B5:
S1=<0.3678,0.4104>S2=<0.2927,0.3409>
S3=<0.1158,0.1377>S4=<0.1486,0.1870>
V(S1≥S3)=9.135, V (S2≥S3)=6.422, V (S4≥S3)=2.362
P1=9.315, P2=6.422, P3=1, P4=2.362.
Normalized obtains weight vectors: P=(0.483,0.339,0.053,0.125)；
Use the entropy weight of entropy assessment Calculation Estimation index for
Evaluation formula acquires subjective and objective comprehensive weight:
To the imitative of 4 evaluation indexes (lathe bed quality, maximum stress, maximum distortion, first natural frequency) of bed piece
The initial data of true analysis result carries out data processing and obtains weighted normal matrix U:
Calculate positive and negative ideal solution
Calculate the distance of positive and negative ideal solution
Calculate the grey incidence coefficient matrix of each lathe bed alternative and ideal scheme:
The grey incidence coefficient matrix of each lathe bed alternative and ill ideal solution can similarly be obtained:
By analyzing the grey incidence coefficient size of each lathe bed alternative and ideal scheme and ill ideal solution, Ke Yiqing
Chu obtains each scheme and ideal scheme and ill ideal solution to each evaluation index (lathe bed quality mm, maximum stress σ, maximum change
The degree of correlation of shape δ and first natural frequency f), as shown in Figure 6,7.
The grey relational grade size of each scheme Yu ideal scheme and ill ideal solution is calculated using the calculation formula of step C4
Relatively positive approach degree and relatively negative approach degree are calculated using the calculation formula in step C5:
Relatively positive approach degree:
Relatively negative approach degree:
Based on the above calculated result, the synthesis exchange premium degree of each alternative of lathe bed is obtained by comprehensive extraction calculation formula
Size, as shown in table 4.As shown in Table 4, in each orthogonal experiment of lathe bed structure, best lathe bed scheme is scheme 4: reinforcing plate structure
" V " type, gusset thickness 35mm, lathe bed wall thickness 22mm.
The synthesis exchange premium degree of each scheme of table 4
Comprehensive extraction that this programme obtains while Euclidean distance and grey relational grade are considered, is able to reflect out each lathe bed
The similar sex differernce of alternative and the distance between ideal scheme and ill ideal solution positional relationship and data and curves, makes scheme
Evaluation is more accurate reasonable, and the trend of each alternative exchange premium degree is as shown in Figure 8.
By analyzing the average aggregate approach degree of each level of bed piece, by GC-TOPSIS it is found that comprehensive extraction is got over
Greatly, for the optimization aim corresponding to closer to optimal value, the average aggregate approach degree of each level is as shown in table 5.As shown in Table 5,
Lathe bed structure optimal combination parameter are as follows: reinforcing plate structure " V " type, gusset thickness 35mm, lathe bed wall thickness 22mm.
The average aggregate approach degree of each level of table 5
According to bed piece Orthogonal Optimum Design as a result, respectively to each water in the comprehensive extraction and table 5 of each scheme in table 4
The calculated result of flat average aggregate approach degree is analyzed, and the identical structural design of the machine body side of factor level parameter combination is obtained
Case, best lathe bed structure combination parameter just correspond to orthogonal experiment optimal case 4, can finally determine the optimal design side of lathe bed
Case: reinforcing plate structure " V " type, gusset thickness 35mm, lathe bed wall thickness 22mm.
In order to analyze the effect of optimization of preferred plan, the comparing result before and after each evaluation index optimization design of lathe bed is obtained
As shown in table 6.
6 optimization design comparing result of table
Shown by the optimization design comparing result of table 6: lathe bed structure after optimization design is in quality increase only 4.734%
In the case where, maximum stress decline 17.595%, maximum distortion decline 10.684%, and first natural frequency improves
16.417%, quiet, the dynamic property of the lathe bed are significantly improved；It can be seen that the optimization method designed by this programme
The comprehensive performance of lathe bed can be increased substantially.
Claims (8)
1. based on extension science-grey relational ideal solution lathe bed structure optimum design method characterized by comprising
S1, it constructs former Machine body and carries out Static finite element analysis and dynamic finite element analysis, determine lathe bed rigidity weak point
Separation structure, and four kinds of reinforcing plate structures are designed according to lathe bed rigidity vulnerable area structure；
S2, it is carried out respectively based on lathe bed inner structure size and external structure size to quality, maximum stress, maximum distortion, one
The sensitivity analysis of rank intrinsic frequency, selecting, dynamic property quiet on lathe bed influences maximum critical size: gusset thickness and lathe bed
Wall thickness；
S3, the experimental factor using reinforcing plate structure, gusset thickness and lathe bed wall thickness as orthogonal test, using lathe bed quality, most
Large deformation, maximum stress and first natural frequency are as evaluation index；
S4, the value for setting gusset thickness and lathe bed wall thickness construct the horizontal orthogonal test table of three factor four using experimental factor
Carry out L16(43)=16 time Finite Element Simulation Analysis picks out optimal parameter and combines the lathe bed alternative to be formed；
It is S5, comprehensive using the improved AHP method and entropy assessment combination weighting Calculation Estimation index and lathe of extension theory
Comprehensive weight between energy；
S6, it is chosen from lathe bed alternative using comprehensive weight and GC-TOPSIS method based on Euclidean distance and grey relational grade
Optimal lathe bed alternative is as lathe bed structure scheme out；
S7, according to maximum stress, maximum distortion and the first natural frequency of lathe bed structure scheme and former lathe bed structure, judge lathe bed
Whether comprehensive performance improves, if improving, exports lathe bed structure scheme, otherwise, return step S4.
2. it is according to claim 1 based on extension science-grey relational ideal solution lathe bed structure optimum design method,
It is characterized in that, four kinds of reinforcing plate structures are respectively V-type reinforcing plate structure, O-shaped reinforcing plate structure, well type reinforcing plate structure and copy honeycomb structure
The biomimetic type reinforcing plate structure of design.
3. it is according to claim 2 based on extension science-grey relational ideal solution lathe bed structure optimum design method,
It is characterized in that, in orthogonal test table, first row to third column respectively reinforcing plate structure, gusset thickness and lathe bed wall thickness, and the
A line to fourth line is respectively V-type reinforcing plate structure, O-shaped reinforcing plate structure, well type reinforcing plate structure and biomimetic type reinforcing plate structure.
4. it is according to claim 1 based on extension science-grey relational ideal solution lathe bed structure optimum design method,
It is characterized in that, further includes data prediction before calculating comprehensive weight:
A1, the data of evaluation index are converted to initial data decision matrix V=(vij)m×n:
Wherein, vijIt is the achievement data of i-th of lathe bed alternative and j-th of evaluation index；I=1,2 ..., m, j=1,
2 ..., n, m are lathe bed alternative total number；N is evaluation index total number；
A2, the achievement data in initial data decision matrix is normalized to obtain normalized matrix:
When the achievement data in initial data decision matrix is positive index, pre-processed using positive target function:
When the achievement data in initial data decision matrix is negative sense index, pre-processed using negative sense target function:
A3, it constructs to form normalized matrix using the achievement data after normalization:
5. it is according to claim 4 based on extension science-grey relational ideal solution lathe bed structure optimum design method,
It is characterized in that, it is comprehensive using the improved AHP method and entropy assessment combination weighting Calculation Estimation index and lathe of extension theory
Comprehensive weight between performance further comprises:
According to evaluation index relative to the importance between lathe comprehensive performance, building can open up Interval Judgment Matrix, and calculate and can open up
The weight vector of Interval Judgment Matrix；
According to normalized matrix and initial data decision matrix, using the entropy weight of entropy assessment Calculation Estimation index, later using power
Comprehensive weight between weight vector sum entropy weight Calculation Estimation index and lathe comprehensive performance:
Wherein, WiFor comprehensive weight；W=(w1,w2,…,wn) it is weight vector；For entropy weight.
6. it is according to claim 5 based on extension science-grey relational ideal solution lathe bed structure optimum design method,
It is characterized in that, the weight vector that calculating can open up Interval Judgment Matrix further comprises:
B1, basis can open up Interval Judgment Matrix A=< A-、A+> A is found out respectively-、A+Maximum eigenvalue and its corresponding normalizing
Change characteristic vector, wherein
B2,0 < kx of satisfaction is calculated-≤mx+All positive real numbers m, k value:
B3, judge whether k and m meets 0≤k≤1≤m, solve vector step if meeting and entering, area can be opened up by otherwise correcting or rebuilding
Between judgment matrix, and return step B1；
B4, vector: S=(S is solved1, S1..., Snk)=(kx-, mx+), S in formulankIt is kth layer nth elements to upper one layer of element
Interval weight；
B5, weight is determined:
IfUtilize formula
IfJ=1,2 ..., n；V(Si≥Sj) >=0 (i ≠ j) is then
In formula, PiIt is i-th of element to upper one layer of weight sequencing；
To vector Pi=(P1, P2..., Pn) be normalized, each evaluation index is obtained to the weight vector w=of destination layer
(w1,w2,…,wn)。
7. it is according to claim 5 based on extension science-grey relational ideal solution lathe bed structure optimum design method,
It is characterized in that, according to normalized matrix and initial data decision matrix, the entropy weight using entropy assessment Calculation Estimation index is further
Include:
For canonical matrix Y, parameter value weight dij:
In lathe bed alternative selection course, entropy calculation formula are as follows:
Calculate the entropy weight of each evaluation index:
8. any described based on extension science-grey relational ideal solution lathe bed structure optimization design according to claim 4-6
Method, which is characterized in that step S6 further comprises:
C1, standardization
Using initial data decision matrix V=(vij)m×nIn data do standardization, X=(x can be obtainedij)m×nStandard
Change matrix:
Wherein,
C2, weighting standard matrix is calculated using comprehensive weight
Enable uij=(Wixij)m×n, weighted normal matrix U=(u can be obtainedij)m×nAre as follows:
In formula, yijFor Y=(yij)m×nIn element, WiIt is the comprehensive weight of every evaluation index, i=1,2 ..., m, j=1,
2,…,n；
C3, positive and negative ideal solution and its distance are determined
Positive ideal solutionIndicate ideal scheme, minus ideal resultIndicate ill ideal solution, expression formula is as follows:
In formula, J1For the set of profit evaluation model evaluation index, J2For the set of cost type evaluation index；
Calculate i-th of scheme to positive and negative ideal solution distanceIts calculation formula is as follows:
C4, each scheme and ideal and ill ideal solution grey relational grade size are calculated
C41, the grey relational grade for calculating i-th of scheme and ideal schemeUnder j-th of evaluation index, i-th of scheme is calculated
With the grey incidence coefficient of ideal scheme:
Wherein, ρ is resolution ratio, and ρ ∈ (0,1) takes ρ=0.5；
Grey incidence coefficient matrix is constructed using the grey incidence coefficient of i-th of scheme and ideal scheme are as follows:
Calculate the grey relational grade size of i-th of scheme and ideal scheme:
C42, the grey relational grade for calculating i-th of scheme and ill ideal solutionUnder j-th of evaluation index, i-th of side is calculated
The grey incidence coefficient of case and ill ideal solution:
Wherein, ρ is resolution ratio, and ρ ∈ (0,1) takes ρ=0.5；
Grey incidence coefficient matrix is constructed using the grey incidence coefficient of i-th of scheme and ill ideal solution:
Calculate the grey relational grade size of i-th of scheme and ill ideal solution:
C5, the comprehensive extraction for calculating each scheme
It adjusts the distanceAnd grey relational gradeNondimensionalization processing, the formula of nondimensionalization processing are done respectively are as follows:
Wherein, HiIt respectively represents
Nondimensionalization distance and the degree of association are combined:
In formula, η1、η2It is policymaker to the preference of location and shape, η1+η2=1；For each lathe bed alternative
With the degree of closeness of ideal scheme and ill ideal solution,More big then lathe bed alternative is more excellent,More big then lathe bed is alternative
Scheme is poorer, i=1,2 ..., m；
Calculate the comprehensive extraction of each lathe bed alternative:
C6, each lathe bed alternative is ranked up according to the size of comprehensive extraction, selects the maximum scheme of comprehensive extraction
As lathe bed structure scheme.
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