CN110955940B - AHP-based mechanical device design model selection method - Google Patents

AHP-based mechanical device design model selection method Download PDF

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CN110955940B
CN110955940B CN201911186304.0A CN201911186304A CN110955940B CN 110955940 B CN110955940 B CN 110955940B CN 201911186304 A CN201911186304 A CN 201911186304A CN 110955940 B CN110955940 B CN 110955940B
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李海涛
龙新佳妮
杜岳峰
毛恩荣
高偌霖
魏文军
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Abstract

The invention relates to the field of mechanical design theory and method, in particular to a mechanical device design model selection method based on AHP. And analyzing experimental data obtained in the existing literature, and constructing a relation matrix of each type of all parts of the mechanical device on the performance index of the mechanical device. And according to each user requirement, assigning a corresponding mechanical device performance index judgment matrix, and solving the performance index attribute weight under each user requirement by using AHP. A similarity calculation formula of a performance index relation matrix of each part obtained based on experimental data and a performance index attribute weight matrix obtained by AHP is deduced, and a model selection scheme which best meets the user requirements is obtained by comparison. The subjective selection is converted into quantitative analysis, accurate model selection at the initial stage of the design of a multi-component and multi-type complex mechanical device of each component can be realized, and a quantitative evaluation method is provided for the design of the complex multifunctional mechanical device.

Description

AHP-based mechanical device design model selection method
Technical Field
The invention relates to the field of mechanical design theory and method, in particular to an AHP-based mechanical device design model selection method, which is suitable for multi-component mechanical device model selection with multiple performance evaluation index bases and various types of mechanical devices in each component.
Background
The mechanical design is an important component of mechanical engineering, is the first step of mechanical production, and is a purposeful, planned and organized activity for organizing intellectual scientific and technological achievements into mechanical devices. The aim of machine design is to design the best machine under various limited conditions, such as user requirements, mechanical strength criteria, reliability, green design criteria, economic benefits and the like, and the method is a complex multi-level multi-objective decision optimization process. Traditional mechanical design mostly stays in research on a mechanical device body, and people optimize the structure and the performance of the mechanical device through mature theoretical knowledge and experimental schemes, so that different parts in one mechanical device can have various structural variants aiming at different requirements and different performances. However, modern mechanical design requires intensive design theory and methodology and focuses on global design. The optimization of parameters and structure is the optimization of local problems, the optimization of the overall design requires standing on the macroscopic height, and the overall design of the mechanical device is continuously evaluated and modified from the aspects of user requirements, mechanical bodies, social economy and the like. Particularly, in the scheme model selection stage at the initial stage of mechanical design, the judgment standard has the characteristics of multiple targets, multiple factors, unquantifiable parts of factors and the like, and enterprises or scientific research units mostly determine the model selection scheme by artificial subjective experience and lack the scientificity and reliability of decision making. Therefore, there is a need to find a method for designing a mechanical device that can objectively quantify the user's needs to a model selection scheme.
The mechanical device design selection belongs to the scheme design stage at the initial stage of mechanical design, and the patent CN109408869A discloses a reciprocating compressor selection design method, which selects matched cylinders and a proper operating condition range in steps by calculating or initially calculating key parameters. However, the process from requirement to type selection only relates to a few calculation formulas, other potential requirement factors are easily ignored, product performance evaluation at the later stage of mechanical design cannot be associated, the application range is narrow, and the method is only suitable for component types which can be calculated through formulas and have fixed numerical value options according to specific numerical values. Patent CN109034503A discloses an AHP-GRAP-based open pit mine crushing station layout scheme optimization method, which is to select an optimal open pit mine crushing station position layout scheme by constructing a hierarchical structure model and using an AHP method. The AHP and the GRAP are combined, so that the subjective assumed components are reduced, and the scientificity of decision making is improved. However, the method is only suitable for site selection of the coal mine crushing station, and has strong speciality and low generalization. At present, the problem of lack of universal design theory and method research exists in the initial design stage of a mechanical device, a design type selection method suitable for user requirements in the early design stage and performance evaluation in the later design stage is explored aiming at a mechanical device design type selection method with evaluation indexes having the characteristics of multiple targets, multiple factors and unquantifiable parts, and key technical support is provided for quick, efficient and accurate design of a multi-part complex mechanical device with various parts.
Disclosure of Invention
The invention aims to provide a mechanical device design model selection method based on AHP. And analyzing experimental data obtained in the existing literature, and constructing a relation matrix of each type of all parts of the mechanical device on the performance index of the mechanical device. And according to each user requirement, assigning a corresponding mechanical device performance index judgment matrix, and solving the performance index attribute weight under each user requirement by using AHP. A similarity calculation formula of a performance index relation matrix of each part obtained based on experimental data and a performance index attribute weight matrix obtained by AHP is deduced, and a model selection scheme which best meets the user requirements is obtained by comparison. The subjective selection is converted into quantitative analysis, and the design efficiency and accuracy are improved. The technical scheme adopted for achieving the purpose of the invention is as follows:
1) analyzing the experimental data to construct a performance index relation matrix of each type of each component of the mechanical device, which is specifically as follows:
a) the parts of the mechanical device are classified according to types, such as part A with type Aj (j is 1,2, …, m).
b) Making required performance index K according to user requirements in the early stage of design, constraints in the middle stage of design and mechanical device evaluation indexes in the later stage of designi(i＝1,2,…,n)。
c) According to the experimental data and conclusions in the existing literature, the importance degree G of the performance index corresponding to different types of each part is set, and the grade of the importance degree gradually increases from 1 to (n + 1). Let the jth type Aj of the component A correspond to the mechanical device performance index KiIs of grade GAjKi, Performance index for each group of ComponentsRelationship matrix Gw(w is 1,2, …, d.d is the number of parts). The relationship matrix defining component a with respect to performance indicators is as follows:
Figure GDA0003534847380000021
note that if a certain performance index does not affect a certain component type, the degree of importance G is defined to ∞, taking into account the calculation limit of the third major step.
2) According to the user requirement, an AHP is used for solving the attribute weight of the performance index of the mechanical device required by the user, and the attribute weight is as follows:
a) according to different performance indexes K corresponding to the mechanical device by the useriRespectively determining a pair-wise comparison judgment matrix D ═ D (D) required for calculating the attribute weightsij) The following. Wherein d isijIndicates the performance index KiRelative to the performance index KjThe degree of importance of.
Figure GDA0003534847380000022
b) Calculating the maximum eigenvalue lambda of the judgment matrix DoCorresponding eigenvector λ ═ λ1 λ2 … λi … λn]TNormalizing lambda to obtain weight vector W ═ W1 w2 … wi … wn]TI.e. the obtained attribute weight corresponding to the performance index of the mechanical device is obtained by quantifying the user requirement.
c) And carrying out consistency check on the judgment matrix. The process is as follows:
c-1) calculating a consistency index:
Figure GDA0003534847380000031
where n is the order of the judgment matrix
c-2) calculating an average random consistency index R.I;
c-3) calculating the consistency ratio:
Figure GDA0003534847380000032
when the C.R. < 0.1, the judgment matrix D is judged to pass the consistency test, namely the next step is implemented; if not, returning to the a) small item of the item 2), readjusting the user requirement, and determining a new judgment matrix.
3) Comparing the performance index relation matrix of each type of each component of the mechanical device with the performance index weight vector of the mechanical device based on user requirements to obtain a group of component types with the maximum similarity between the performance index ratios, which is concretely as follows:
a) carrying out pairwise ratio on each element in the weight vector W based on user requirements to obtain a weight ratio vector
Figure GDA0003534847380000033
Wherein
Figure GDA0003534847380000034
Figure GDA0003534847380000035
b) Carrying out pairwise ratio on each element in each row vector in the performance index relation matrix to obtain a weight ratio vector of each row vector, and forming a ratio matrix R of the performance index relation matrixw(w is 1,2, …, d.d is the number of parts). The ratio matrix of the performance index relationship matrix of component a is found as follows:
Figure GDA0003534847380000036
wherein
Figure GDA0003534847380000037
c) A ratio matrix R of the performance index relation matrixwEach row vector of (a) is represented as RwjW represents a part identifier, j represents RwI.e. different types under the same component. Calculation of RwjSimilarity with weight ratio vector P
Figure GDA0003534847380000041
Wherein
Figure GDA0003534847380000042
Constructing similarity matrix S of each part of mechanical devicew(w is 1,2, …, d.d is the number of parts), Sw＝[sim(Rw1,P),sim(Rw2,P),...,sim(Rwm,P)]T。
d) Get Sw(simi) Maximum value of (d):
Figure GDA0003534847380000043
then Sw(simo) is a similarity matrix S from the parts of the machinewAnd selecting the component type corresponding to the value with the maximum similarity, namely the component type which best meets the requirements of the user.
The method has the advantages that the AHP is utilized to combine qualitative user requirements at the early stage of mechanical design with the performance indexes of the multiple factors which cannot be quantified at the later stage of design, the qualitative user requirements are converted into quantitative data, and the design efficiency and accuracy are improved. Accurate model selection in the early stage of design of a multi-component and multi-type complex mechanical device is realized, and a key technical reference is provided for modern mechanical design theories and methods.
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FIG. 1 is a flow chart of an AHP based mechanical device design selection method;
FIG. 2 is a block diagram of a multi-part mechanism with various types of components;
FIG. 3 is a schematic view of a corn husker apparatus;
Detailed Description
The following description of the embodiments of the present invention will be made with reference to the accompanying drawings. The specific embodiments described herein are merely illustrative of the invention and are not intended to be limiting.
Taking a corn husker device as an example, the corn husker is used as a main mechanical device for husking corn ears, and the overall design method of the corn husker is short of systematic theoretical research. The research on the corn husker device at home and abroad mostly stays in the research on the corn husker device body, and the corn husker device is divided into two aspects: on the first hand, from the physical angle, the mechanical relationship between the fruit ears and the peeling device structure is analyzed, the existing mechanical structure is improved, and the peeling performance is improved; in the second aspect, aiming at a certain variety of corn ears, the influence of different influence factors on peeling performance is analyzed by an orthogonal test method, and better structural parameters and motion parameters are obtained. Due to the fact that the demand positioning of users in the early stage is diversified, for example, corn planting varieties, agricultural and harvesting modes and regional climate differences are obvious, and the physical and mechanical characteristics of corn ears in the harvest period are different greatly, the configuration mode, the structural types of all parts, the motion parameters and the like of the peeling mechanism are different, and the research result aiming at the peeling machine body is limited. The design and selection scheme of the corn husker device is as follows:
1) analyzing related documents and existing experimental data to construct a performance index relation matrix of each component of the corn husker device, which is concretely as follows:
a) the corn husker device is classified into 4 parts A, B, C and D according to the functional structure of the corn husker device, and the part A is 3 types A1,A2,A3(ii) a Part B has 4 types B1,B2,B3,B4(ii) a The component C being of type 4C1,C2,C3,C4(ii) a The component D has 3 types D1,D2,D3。
b) A corn husker device belongs to agricultural harvesting machinery, and a performance index K is set according to relevant literature research, experimental data and market user requirementsi(i ═ 1,2,3,4), where K is1As kernel loss rate, K2Is the kernel breakage rate, K3Is impurity content, K4The non-peeled rate of the ears is shown.
c) According to literature research conclusions and experimental data of the corn husker device body, the importance degrees of performance indexes corresponding to different types of the components A, B, C and D are set as follows:
Figure GDA0003534847380000051
constructing a relation matrix of each part about the performance indexes as follows:
Figure GDA0003534847380000052
Figure GDA0003534847380000053
2) according to the user requirements, an AHP is used for solving the attribute weight of the performance index of the corn husker device required by the user, and the method specifically comprises the following steps:
a) determining a paired comparison judgment matrix D of performance indexes according to user requirements, setting that the grain loss rate is as important as the grain breakage rate, the grain loss rate is 2 times more important than the impurity rate, the non-ear-peeling rate is 3 times more important than the grain loss rate, the impurity rate is 1.5 times more important than the grain breakage rate, the non-ear-peeling rate is 1.6 times more important than the grain breakage rate, and the impurity rate is 2 times more important than the impurity rate. The following table is then obtained by pairwise comparison:
Figure GDA0003534847380000061
the constructed judgment matrix D is:
Figure GDA0003534847380000062
b) calculating the maximum eigenvalue lambda of the judgment matrix Do＝4.20，44λoCorresponding feature vector
Figure GDA0003534847380000065
Normalizing the lambda to obtain a weight vector
Figure GDA0003534847380000066
I.e., the attribute weight of the corn husker device performance index obtained by quantifying the user requirements.
c) And carrying out consistency check on the judgment matrix D.
c-1) calculating a consistency index:
Figure GDA0003534847380000063
c-2) calculating an average random consistency index R.I., and the following table shows the average random consistency index when the matrix with 1 to 10 dimensions is repeatedly calculated for 1000 times:
dimension number 1 2 3 4 5 6 7 8 9 10
R.I. 0 0 0.52 0.89 1.12 1.26 1.36 1.41 1.46 1.49
So, this time, r.i. ═ 0.89 is taken;
c-3) calculating the consistency ratio:
Figure GDA0003534847380000064
the decision matrix D passes the consistency check.
3) Comparing the performance index relation matrix of each type of each component of the corn husker device with the mechanical device performance index weight vector based on user requirements to obtain a group of component types with the maximum similarity, wherein the specific steps are as follows:
a) carrying out pairwise ratio on each element in the weight vector W to obtain a weight ratio vector:
Figure GDA0003534847380000071
and calculating to obtain:
P＝[1.1625 1.1695 0.5264 1.0059 0.4529 0.4502]T；
b) carrying out pairwise ratio on each element in each row vector in 4 individual performance index relationship matrixes A, B, C and D to obtain a weight ratio vector of each row vector, wherein the ratio matrix for forming the performance index relationship matrix is as follows:
Figure GDA0003534847380000072
Figure GDA0003534847380000073
c) calculating a ratio matrix R of the performance index relation matrix of the components A, B, C and DA,RB,RC,RDEach row vector R ofAj,RBj,RCj,RDjSimilarity with weight ratio vector P
Figure GDA0003534847380000074
Then there are:
Figure GDA0003534847380000075
Figure GDA0003534847380000076
Figure GDA0003534847380000077
Figure GDA0003534847380000078
carry in values, obtain results and construct similarity matrix S for corn husker device components A, B, C, DwThe following were used:
SA＝[1.4778 0.2401 0.2642]
SB＝[0.0805 0.7640 1.0370 0.4935]
SC＝[1.2926 1.3548 1.1354 1.1354]
SD＝[0.9268 1.3515 0.8825]；
d) get Sw(simi) The component type corresponding to the medium and maximum value is the component model most meeting the user requirement:
max SA＝SA11.4778, part A debarking roller assembly selection part type A1Namely a peeling roller assembly arranged in a groove shape;
max SB＝SB31.0370, part B debarking roller selection part type B3Namely a rubber spiral peeling roller;
max SC＝SC21.3548, component C Press-feeder selection component type C2A star wheel type pressure transmitter;
max SD＝SD21.3515, component D grain recovery device selection component type D2Namely a spiral conveying type grain recovery device.
The invention provides a mechanical device design model selection method based on AHP, which combines qualitative user requirements at the early stage of mechanical design with the performance indexes that multiple factors are not quantifiable at the later stage of design by the AHP and converts the qualitative user requirements into quantitative data, thereby improving the design efficiency and accuracy. Based on the method, accurate model selection of multiple components and parts with multiple types at the initial stage of the design of the complex mechanical device can be realized, a quantitative evaluation method can be provided for the design of the complex multifunctional mechanical device, a key technical reference is provided for modern mechanical design theories and methods, and the method has very wide social significance.

Claims (1)

1. The mechanical device design model selection method based on AHP is characterized by comprising the following steps:
step 1: analyzing the experimental data to construct a performance index relation matrix of each type of each component of the mechanical device, which is specifically as follows:
a) classifying according to types of each component of the mechanical device, wherein the component A has a type Aj，j＝1,2,…,m；
b) Making required performance index K according to user requirements in the early stage of design, constraints in the middle stage of design and mechanical device evaluation indexes in the later stage of designi，i＝1,2,…,n；
c) According to experimental data and conclusions in the existing literature, setting the importance degree G of the performance index corresponding to different types of each part, wherein the level of the importance degree is gradually increased from 1 to n; let the jth type A of component AjCorresponding to the performance index K of the mechanical deviceiIs of grade GAjKiConstructing a performance index relationship matrix G for each group of componentsAA is 1,2, …, d, d is the number of components; the relationship matrix defining component a with respect to performance indicators is as follows:
Figure FDA0003534847370000011
note that if a certain performance index does not affect a certain component type, the degree of importance G ═ infinity is defined in consideration of the calculation limit of step 3;
step 2: according to the user requirement, an AHP is used for solving the attribute weight of the performance index of the mechanical device required by the user, and the attribute weight is as follows:
a) according to different performance indexes K corresponding to the mechanical device by the useriRespectively determining a pair-wise comparison judgment matrix D ═ D (D) required for calculating the attribute weightsij) In which d is as followsijIndicates the performance index KiRelative to the performance index KjThe degree of importance of;
Figure FDA0003534847370000012
b) calculating the maximum eigenvalue lambda of the judgment matrix DoCorresponding eigenvector λ ═ λ1 λ2…λi…λn]TNormalizing lambda to obtain weight vector W ═ W1 w2…wi…wn]TThat is, the attribute weight corresponding to the performance index of the mechanical device is obtained by quantifying the user requirement;
c) and (3) carrying out consistency check on the judgment matrix, wherein the process is as follows:
c-1) calculating a consistency index:
Figure FDA0003534847370000021
wherein n is the order of the judgment matrix;
c-2) calculating an average random consistency index R.I;
c-3) calculating the consistency ratio:
Figure FDA0003534847370000022
when C.R. < 0.1, the judgment matrix D is considered to be openAfter consistency check, implementing the next step; if the judgment matrix does not pass the inspection, returning to the sub-item in the step (a) of the step (2), readjusting the user requirements, and determining a new judgment matrix;
and step 3: comparing the performance index relation matrix of each type of each component of the mechanical device with the performance index weight vector of the mechanical device based on user requirements to obtain a group of component types with the maximum similarity between the performance index ratios, which is concretely as follows:
a) carrying out pairwise ratio on each element in the weight vector W based on user requirements to obtain a weight ratio vector
Figure FDA0003534847370000023
Wherein
Figure FDA0003534847370000024
b) Carrying out pairwise ratio on each element in each row vector in the performance index relation matrix to obtain a weight ratio vector of each row vector, and forming a ratio matrix R of the performance index relation matrixAWhere a is 1,2, …, d, d is the number of components, and the ratio matrix for finding the performance index relationship matrix for component a is as follows:
Figure FDA0003534847370000025
wherein
Figure FDA0003534847370000026
c) A ratio matrix R of the performance index relation matrixAIs represented as each row vector of
Figure FDA0003534847370000028
A represents a part identifier, j represents RAThe number of rows of (a), i.e., different types under the same component; computing
Figure FDA0003534847370000029
And the weight valueSimilarity of ratio vector P
Figure FDA0003534847370000027
Wherein
Figure FDA0003534847370000031
Constructing a similarity matrix SA of each part of the mechanical device, wherein A is 1,2, …, d and d are the number of the parts,
Figure FDA0003534847370000033
d) get SAMaximum value of
Figure FDA0003534847370000032
Then SA(simo) At SAThe component type corresponding to the position in (1) is the component model which best meets the requirements of users.
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