CN108399287B - Evaluation method of machine tool beam design scheme by adopting fuzzy hierarchical analysis - Google Patents
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Abstract
The invention discloses an evaluation method of a machine tool beam design scheme by adopting fuzzy hierarchical analysis, which comprises the following steps: determining the design requirement of the cross beam through research and consultation, mapping the design requirement to the engineering characteristic index of the cross beam, and converting the engineering characteristic index into a design factor of the cross beam; screening design element parameter combinations to formulate a cross beam candidate scheme, and performing three-dimensional modeling to obtain a cross beam engineering characteristic simulation value; and establishing a beam design scheme evaluation system, establishing a fuzzy judgment matrix by using fuzzy hierarchy analysis to calculate relative weight, and solving the difference influence degree of beam engineering characteristic indexes on each scheme, so as to obtain the final grade of the beam design scheme and determine the optimal scheme. The method focuses on customer requirements, comprehensively considers factor index weights influencing evaluation of the beam design scheme, effectively solves the problem of comprehensive evaluation of the beam design scheme with multiple layers and ambiguity, and has the characteristics of flexibility, simplicity, easiness in programming and the like.
Description
Technical Field
The invention belongs to the field of machine tool design, relates to an evaluation method of a machine tool key part design scheme, and particularly relates to an evaluation method of a machine tool beam design scheme by adopting fuzzy hierarchy analysis.
Background
The cross beam of the machine tool is used as an important part of the numerical control machine tool, the weight of key parts such as a sliding seat, a ram, a main shaft and the like is borne on the cross beam, the deformation and vibration of the cross beam caused by the self gravity and external load directly influence the whole machine performance of the machine tool, and further influence the geometric precision and the surface processing quality of a workpiece. In the traditional beam design, a real object is firstly processed by virtue of empirical design, then the beam is assembled on a machine tool for testing, various test results are synthesized to judge the superiority of the performance of the structural scheme, the modification scheme is determined, and then the processing test is carried out after the modification, so that the steps are repeated, and a large amount of manpower, material resources and time are consumed.
In recent years, with the continuous development and improvement of finite element analysis technology, technical researchers carry out optimization design on a beam structure through computer virtual modeling and simulation analysis technology, for example, patent CN103310064A introduces an optimization design method of a numerical control machine beam structure adopting extreme dimension adjustment; patent CN102819653A introduces an optimized design method for a beam of a PCB processing machine tool; patent CN201610100874.3 introduces a machine tool beam optimization design method based on BP neural network and genetic algorithm. The optimized design of the beam structure based on the method changes the mode of the traditional beam scheme design, so that the beam design scheme tends to be diversified day by day, and the comprehensive performance of the machine tool beam is improved to a certain extent. However, for a plurality of cross beam design schemes designed by adopting the structure optimization design method, a reasonable and effective evaluation means is still lacked at present. When the performance of the beam scheme is considered to be good or bad, the static and dynamic performance of the beam is used as an evaluation index, the static and dynamic performance is pursued to be improved on one side, the influence of customer requirement indexes such as cost and machining efficiency on the selection of the machine tool beam structure design scheme is not considered, and the market demand can not be met. Therefore, how to scientifically evaluate various beam design schemes and quickly and effectively select the optimal beam design scheme becomes an urgent problem to be solved in the research and development process of the numerical control machine tool.
In order to solve the problems existing in the evaluation and selection process of the existing cross beam design scheme and meet increasingly-intensified market competition and diversified customer requirements, an evaluation method of the machine tool cross beam design scheme by adopting fuzzy hierarchical analysis is provided.
Disclosure of Invention
The invention provides an assessment method for a machine tool beam design scheme by adopting fuzzy hierarchical analysis, which is oriented to customer requirements, comprehensively considers the relative weight of beam design requirements, the difference influence degree of engineering characteristic indexes on the design scheme and the conformity degree grading of each scheme on each design requirement, effectively solves the comprehensive judgment problem of the multi-level and fuzzy beam design scheme, and has the characteristics of flexibility, simplicity, easy programming and the like.
The technical scheme of the invention is as follows:
a method for evaluating a machine tool beam design scheme by adopting fuzzy hierarchical analysis mainly comprises the following steps:
determining the design requirement of a beam scheme on the basis of the requirements of research and consultation customers and the analysis of an internal database, mapping the design requirement to a beam engineering characteristic index, and further converting the design requirement into a design element of the beam scheme;
screening design element parameter combinations to form a beam candidate design scheme, establishing a beam three-dimensional entity model for finite element analysis, and obtaining a beam engineering characteristic index value;
step (3) establishing a beam design scheme evaluation system according to the investigation consult and analysis result, establishing a fuzzy judgment matrix by using fuzzy hierarchical analysis to calculate the weight, obtaining the relative weight of beam design requirements, the relative weight of beam engineering characteristic indexes and the conformity score of each scheme to each design requirement, determining whether each fuzzy judgment matrix has compatibility, if so, performing the next step, otherwise, reconstructing the fuzzy judgment matrix to calculate the weight;
step (4) normalization processing is carried out on the beam engineering characteristic index values, and the difference influence degree of the beam engineering characteristic index on each scheme is solved by combining the beam design requirement weight obtained in the step (3);
and (5) solving the final score of the beam design scheme, and determining the optimal scheme according to the calculation result.
Further, the weight calculation by establishing the fuzzy judgment matrix by adopting fuzzy hierarchical analysis comprises the following calculation steps:
a. establishing fuzzy complementary judging matrix
In a beam design scheme evaluation system, experts who engage in numerical control machine tool research and development and application for a long time are invited to compare every two importance degrees of each factor by adopting a 0.1-0.9 scale method to form a judgment matrix B:
in matrix B, if Bii＝0.5，bij+bjiWhen the value of 1, i, j is 1,2, … m, the decision matrix B is a fuzzy complement decision matrix.
b. Calculation of weights
Solving the fuzzy judgment matrix and determining the relative weight vector D ═ D of the fuzzy complementary judgment matrix B1 d2 … dm]The concrete formula is as follows:
wherein
c. Decision matrix satisfaction compatibility test
Order to
Then, the m-order matrix S ═ d is calledij)m×mIs a feature matrix of the fuzzy judgment matrix B.
The compatibility index of B and S is
And regarding the attitude alpha of the decision maker, when the compatibility index I (B, S) is less than or equal to alpha, the judgment matrix is considered to be satisfactory and consistent. The smaller the α, the higher the compatibility of the matrix, and the α is 0.2.
For the evaluation of a kind of practical problems of the beam design scheme, the evaluation is carried out by a plurality of expertsJudging, if there are k experts, there is fuzzy judgment matrix
The corresponding set of relative weight vectors is Dk＝[D1 D2 … Dt]The feature matrix is Sk＝(dk ij)m×m。
Then, t judgment matrixes B are respectively checked according to the formula (4)kAnd satisfactory compatibility among the judgment matrixes, if the two judgment matrixes are both satisfactory compatibility, the mean value of the t relative weight vector sets is reasonable and reliable as a final result, and the calculation is as follows:
respectively obtaining the final beam design requirement relative weight according to the formulas (1) to (5)
Beam engineering property index relative weight
And a conformity score matrix corresponding to each design requirement
Further, the difference influence degree of the beam engineering characteristic index on each scheme is calculated by the following steps:
step 1), normalization processing of beam engineering characteristic index value matrix
Assuming that l design schemes and m engineering characteristic indexes exist in the beam evaluation system, constructing a beam engineering characteristic index value matrix X according to three-dimensional modeling simulation data*：
In this evaluation model, some indexes are larger and more preferable, and some indexes are smaller and more preferable. Therefore, before evaluating the design scheme of the cross beam, corresponding data should be distinguished and processed firstly, which is as follows:
wherein r is 1,2, …, l; j is 1,2, …, m
And normalizing the matrix X by the beam engineering characteristic index value.
Step 2) calculating the differential influence degree I
Wherein
Then
Further, the calculation method of the final scoring vector F of the beam design scheme is as follows:
the scores of the schemes obtained by the formula (10) are ranked, and the scheme with the highest score is selected as the optimal design scheme.
The invention has the advantages that:
1) the assessment method for the machine tool beam design scheme by adopting the fuzzy hierarchy analysis emphasizes the customer requirements, comprehensively considers the factor index weight influencing the evaluation of the beam design scheme, has a more complete evaluation system, and can meet the market requirements.
2) By adopting fuzzy hierarchical analysis to calculate the relative weight of each factor index, the comprehensive evaluation problem of the multi-level and fuzzy beam design scheme is effectively solved, the method has the characteristics of flexibility, simplicity, easy programming and the like, the optimization of the beam design scheme is favorably and effectively completed, the product research and development period is shortened, and the design cost is reduced.
Drawings
FIG. 1 is a flow chart of an implementation of a method for evaluating a cross beam design of a machine tool;
FIG. 2 is a schematic structural diagram of design elements of a cross beam design;
FIG. 3 is a cross beam design evaluation system;
FIG. 4 is a schematic representation of a three-dimensional model of a preferred beam design.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings and detailed description.
Examples
The invention takes the evaluation of the beam design scheme of the bridge type planomiller as an example, and the implementation flow is shown in figure 1. On the basis of investigation and consultation and internal data analysis, the requirement of the beam design scheme is acquired as the machining precision R1And a processing efficiency R2And R is light3Vibration resistance R4Static performance R5Cost R6And the outer dimension R7Determining the mass E of the beam1Outer volume E2Maximum deformation amount E3Maximum equivalent stress E4First order natural frequency E5As an index for evaluating the engineering characteristics of the cross beam, design elements forming the design scheme of the cross beam are the layout of the cross beam structure, the rib plate structure, the thickness of the rib plate and the type of the guide rail, as shown in fig. 2(a) and (b). Screening design element combinations, determining beam candidate schemes, and performing three-dimensional modeling and simulation analysis, wherein the results are shown in table 1.
TABLE 1 simulation results of candidate design schemes for crossbeams
Then, a beam design scheme evaluation system as shown in fig. 3 is established, and a fuzzy judgment matrix is established by using fuzzy hierarchical analysis to calculate the relative weight.
Firstly, experts who are invited to research and development and application of the numerical control machine tool for a long time are invited to compare every two crossbeam design requirements by adopting a 0.1-0.9 scale method, and fuzzy judgment scale distribution is determined, as shown in a table 2.
TABLE 2 fuzzy judgment Scale assignment for Beam design requirements
On the basis of the table 2, fuzzy judgment matrixes B are respectively established according to the formula (1)1And B2The following are:
calculating the weight of the beam design requirement according to the formula (2) as follows:
D1＝(0.152 0.164 0.155 0.121 0.138 0.129 0.140)
D2＝(0.157 0.162 0.160 0.121 0.140 0.121 0.140)
then, B is obtained from (3) to (4)1And S1The compatibility index of (A) is:
I(B1,S1)＝0.128<0.2
B2and S2The compatibility index of (A) is:
I(B2,S2)＝0.141<0.2
fuzzy judgment matrix B capable of judging design requirements of beam scheme1And B2Are all satisfactorily identical, and their corresponding design requirements are relative to the weight vector D1、D2Is reasonable. Simultaneous checking of the fuzzy decision matrix B1And B2Satisfactory compatibility therebetween: i (B)1,B2)＝0.198<0.2, the fuzzy score matrix is considered to be satisfactorily consistent. Therefore, the final beam design requirement weight can be obtained according to the formula (5) as follows:
by adopting the same method, the beam engineering characteristic indexes and the fuzzy judgment matrix of the conformity score of each scheme corresponding to each design requirement can be constructed in sequence, the relative weight is calculated, and the compatibility judgment is carried out. Finally, the relative weight of the engineering characteristic indexes of the cross beam is obtained as follows:
the conformity score matrix of each scheme corresponding to each design requirement is as follows:
and (3) normalizing the beam engineering characteristic index values obtained by applying three-dimensional modeling simulation analysis in the table 1 according to the formulas (6) to (8) to obtain a normalized matrix X.
The difference influence degree I of the beam engineering characteristic indexes on the evaluation of each beam design scheme is obtained according to a formula (9) and is as follows:
I＝(0.701 0.635 0.644 0.639 0.673 0.655 0.538 0.653)T
and then, obtaining a final scoring vector F of the beam design scheme according to a formula (10) as follows:
F＝(93.481 77.326 80.201 81.618 86.959 82.901 60.445 82.229)
the scoring vector shows that the beam design scheme 1 is an optimal design scheme, namely the optimal design elements adopted by the beam design scheme are combined into a three-dimensional model of 'box-in-box-well-20 mm-line rail', and the three-dimensional model is shown in fig. 4.
In conclusion, the evaluation method for the cross beam design scheme comprehensively considers the weight of factor indexes influencing the evaluation of the cross beam design scheme, so that the evaluation system is more complete, the evaluation of the machine tool cross beam design scheme can be quickly and effectively finished, and the cross beam design scheme meeting the requirements of customers is obtained.
The above-mentioned embodiments are only one preferred embodiment of the present invention. The foregoing detailed description is to be considered as merely illustrative of the principles of the present invention, and not in limitation thereof. Therefore, any modification, equivalent replacement, improvement and the like made without departing from the spirit and scope of the present invention should be included in the protection scope of the present invention. Further, it is intended that the appended claims cover all such variations and modifications as fall within the scope and boundaries of the appended claims or the equivalents of such scope and boundaries.
Claims (2)
1. A method for evaluating a machine tool beam design scheme by adopting fuzzy hierarchy analysis is characterized by comprising the following steps of:
determining the design requirement of a beam scheme on the basis of the requirements of research and consultation customers and the analysis of an internal database, mapping the design requirement to a beam engineering characteristic index, and further converting the design requirement into a design element of the beam scheme; on the basis of investigation and consultation and internal data analysis, the requirements of a beam design scheme are machining precision R1, machining efficiency R2, light weight R3, vibration resistance R4, static performance R5, cost R6 and external dimension R7, the mass E1, the external volume E2, the maximum deformation E3, the maximum equivalent stress E4 and the first-order natural frequency E5 of the beam are determined as beam engineering characteristic evaluation indexes, and design elements forming the beam design scheme are beam structure layout, rib plate structures, rib plate thicknesses and guide rail types;
screening design element parameter combinations to form a beam candidate design scheme, establishing a beam three-dimensional entity model for finite element analysis, and obtaining a beam engineering characteristic index value;
step (3) establishing a crossbeam design scheme evaluation system according to the investigation consult and analysis result, establishing a fuzzy judgment matrix by using fuzzy hierarchical analysis to calculate the weight, and obtaining the relative weight of the crossbeam design requirement
Beam engineering property index relative weight
And the conformity score of each scheme to each design requirement
Determining whether each fuzzy judgment matrix has compatibility, if so, performing the next step, otherwise, reconstructing the fuzzy judgment matrix for weight calculation;
step (4) normalization processing is carried out on the beam engineering characteristic index values, and the difference influence degree of the beam engineering characteristic index on each scheme is solved by combining the beam design requirement weight obtained in the step (3);
step (5) solving the final score of the beam design scheme, and determining an optimal scheme according to a calculation result;
the method for calculating the difference influence degree of the beam engineering characteristic indexes on each scheme comprises the following steps:
wherein X is a beam engineering characteristic index normalization matrix.
2. The method for evaluating a cross-member design of a machine tool using fuzzy hierarchy analysis according to claim 1, wherein: the calculation method of the final scoring vector F of the beam design scheme comprises the following steps:
and then ranking the scores of all the obtained schemes, and selecting the scheme with the highest score as the optimal design scheme.
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