CN108710725B - Complex assembly dimension chain solving method based on multicolor set theory - Google Patents
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Abstract
A complicated assembly dimension chain solving method based on a multicolor set theory belongs to the technical field of machining and assembly, and comprises the steps of firstly analyzing an assembly drawing of an assembly body or a component, obtaining and recording the assembly dimension, the design dimension, the auxiliary dimension and the assembly characteristic of the component in a form; then establishing a multicolor graph model of the assembly size, and solving the transmission coefficient and the proportionality coefficient of each component ring by using node information in the multicolor graph model; and finally, establishing a surrounding road matrix type of the assembly size according to the transmission coefficient and the proportionality coefficient and solving the surrounding road matrix type. By using the size chain solving method, all size relations can be expressed by one lane matrix type, and the sizes of all closed rings can be solved at one time, so that the size chain solving efficiency is improved, and an effective method is provided for solving a complex size chain.
Description
Technical Field
The invention relates to a size chain solving method, belongs to the technical field of machining and assembly, and particularly relates to a complicated assembly size chain solving method based on a multicolor set theory.
Background
Dimensional chain analysis is an important method for ensuring the quality of the machine assembly. In general, we can use the principle of the dimension chain to find each assembly dimension by disassembling the dimension chain. However, in the assembly of mechanical components, if the number of assembled components is large and the size relationship is complex, the representation and solution of the size chain is difficult, cumbersome and error-prone, and even the assembled size cannot be solved by the conventional size chain method.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a matrix solving method for a complex assembly dimension chain, which can improve the solving efficiency of the dimension chain.
The method provided by the invention comprises the following specific design steps:
step 1: analyzing an assembly drawing of the assembly or the component, and acquiring and recording the assembly size, the design size, the auxiliary size and the assembly characteristic of the part of the assembly or the component in a form;
step 2: establishing a multicolor chart model of the assembly size, acquiring the characteristics corresponding to each node of the assembly chart in the step 1, sequencing the characteristics from left to right,k=1,2,…,nidentifying on the multicolor chart model of the assembly size;
and step 3: for the closed ring in the multicolor chart model of the assembly size established in the step 2X Ni Respectively using serial numberi=1,2,…,nIdentifying on the multicolor chart model of the assembly size;
and 4, step 4: obtaining a component ring in the assembly design drawing in step 1L j In turn usingj=1,2,…,nIdentifying on the multicolor chart model of the assembly size;
and 5: acquiring the auxiliary design size and the auxiliary assembly size in the assembly design drawing in the step 1, and marking the auxiliary design size and the auxiliary assembly size on a multicolor drawing model of the assembly size;
and 6: a method for solving the transmission coefficient of component ring in multi-color model is disclosed, that is, the component ring opposite to the closed ring is an augmented ring and the transmission coefficientξ ij = +1, component ring in the same direction with closed ring is reduction ring, transmission coefficientξ ij =1, wherein,ξ ij indicating a serial number ofiThe closed ring is in the size chain with the serial number ofjThe transmission coefficient of the combined ring can be judged according to the method to obtain the value of the transmission coefficient, and the value of the transmission coefficient is marked on the multicolor graph model of the assembly size;
and 7: by observing the established multicolor diagram model of the assembly sizeiA ring containing a closed ringX N1 ~X Ni The ring being numbered respectivelyi=1,2,…,nMarking on the multicolor graph model of the assembly size;
and 8: by further analyzing the polychrome map model and the assembly map, the proportionality coefficient is obtainedk ij And scaling the value of the proportionality coefficientOn a multicolor chart model of the fitting size;
and step 9: using multicolor set to describe multicolor graph model of assembly size and corresponding each node to edge formed by featuresc m Respectively by serial numberm=1,2,…,qMarking on the multicolor graph model;
step 10: if an assembly size multicolor chart model containsiA ring including a closed ring and having a design size ofL 1 ~L j In an assembly size ofX N1 ~X Ni Then there is an assembly dimension chain matrix equationX Ni ] T =[ξ ij k ij ][L j ] T In the formula (I), wherein,k ij is a coefficient of proportionality constituting the size of the ringX Ni ] T For assembling the column vectors of the dimensionsi×1，[L j ] T Designing a dimensional column vector matrix for a partj×1，[ξ ij k ij ]Is a matrix of size chain coefficientsi×jThe dimension chain coefficient matrix establishes a linear relation between the assembly dimension and the design dimension;
step 11: by the transfer coefficient obtained in step 6ξ ij And the scale factor obtained in step 8k ij Obtaining a matrix of the dimensional chain coefficientξ ij k ij ]；
Step 12: from the dimensional chain coefficient matrix provided in step 11 and the assembled dimensional chain matrix equation provided in step 10, the assembled dimensional chain matrix equation can be solved using the mathematical software MATLAB R2014 a.
The invention has the beneficial effects that:
by using the size chain solving method, all size relationships can be represented by one lane matrix type, and the sizes of all closed rings can be solved at one time, so that the size chain solving efficiency is improved, and an effective method is provided for solving a complex size chain.
Drawings
FIG. 1 is an assembly view of a roller assembly to be analyzed.
Fig. 2 is a multi-color map model of the set-up dimensions established according to fig. 1.
Detailed Description
The invention is described in further detail below with reference to the figures and the specific embodiments.
First, the definitions of the terms and their compositions and characteristics are introduced below:
and (3) ring: listing each size of the size chain;
a closed ring: the last naturally formed loop in the dimensional chain during assembly or processing;
forming a ring: all loops in the size chain that have an effect on the closed loop;
ring addition: meaning a component ring whose variation causes the closed ring to vary in the same direction;
ring reduction: meaning a component ring whose variation causes the closed ring to vary in the opposite direction;
multi-color set: the collection itself and its constituent elements can be simultaneously painted with different "colors" to indicate the nature of the study and its elements;
color: in the multicolor set theory, colors represent abstractions and generalizations of technical concepts such as properties, attributes, parameters, characteristics, indexes and the like;
coloring: in the multi-color set theory, coloring means that "color" is given to nodes and edges;
a surrounding road: abstractions and generalizations of technical concepts such as object properties, attributes, parameters, features and metrics, to replace the purely mathematical term "color" with the concept of a corridor when modeling real-world systems with multi-color collections and multi-color maps;
general diagram: the common figure is marked asG=(A,C) In whichAIs a collection of nodes that are to be considered,Cis a collection of edges connecting nodes, but such conventional graph theory tools cannot depict both the composition of nodes and edges of a graph, and the different properties of nodes and edges of a graph;
a monochromatic picture: the monochromatic graph enlarges the simulation function of the common graph, but any node and edge in the monochromatic graph can only be coated with a certain unique color, and the simulation function is limited;
multicolor chart: in a multi-color graph, any node and any edge may be painted with some different "color" at the same time;
extraction: a binary logic operator in the logic and mathematical concepts represents the meaning of 'OR' and is represented by a V-shaped symbol, and the operation method is that if a true value of two variables is 'true', the result is 'true', the two variables are 'false' at the same time, and the result is 'false';
blending: a binary logical operator in the logical and mathematical concepts, denoted by the symbol "Λ", operates by setting a true value of two variables to "false", the result to "false", both variables to "true", and the result to "true";
this embodiment takes as an example the analysis of the assembly drawing of the roller member shown in fig. 1.
A complex assembly dimension chain solving method based on a multicolor set theory comprises the following steps:
step 1: analyzing the assembly drawing of the roller component shown in fig. 1, obtaining and recording the assembly size, design size and auxiliary size of the assembly or component and the assembly characteristics of the part in a table, as shown in the following table:
| design size (component ring size) | Assembly size (closed ring size) | Design-aided dimension | Auxiliary assembly dimension | Assembly features (nodes relating to assembly size and design size) |
| L 1 =15mm | X N1 | L * 1 =15mm | X * N1 | A S |
| L 2 =38mm | X N2 | L * 6 =10mm | B S | |
| L 3 =50mm | X N3 | C S | ||
| L 4 =80mm | D S | |||
| L 5 =80.2mm | E S | |||
| L 6 =10mm | O D | |||
| L 7 =15mm | O d | |||
| L 8 =40mm | O S | |||
| L 9 =0mm | F S | |||
| G S | ||||
| H S | ||||
| I S | ||||
| J S | ||||
| KS |
Step 2: establishing a multicolor chart model of the assembly size as shown in FIG. 2, acquiring the characteristics corresponding to each node of the assembly chart in the step 1, sequencing the characteristics from left to right, and sequentially using the characteristicsk=1,2, \ 8230, 14 is marked on a polychrome map model of the fitting size;
and step 3: for the closed ring in the multicolor chart model of the assembly size established in the step 2X Ni Respectively using serial numberi=1,2,3 is identified on a polychromatography model of the assembly size as shown in fig. 2, the thick solid line in fig. 2 representing the assembly size, i.e. the closed loop. (ii) a
And 4, step 4: obtaining the component rings in the assembly design drawing in step 1L j In turn usingj=1,2, \ 8230, 9 is marked on the polychromatography model in the set-up size as shown in fig. 2;
and 5: acquiring an auxiliary design size and an auxiliary assembly size in the assembly design drawing in the step 1, and marking the auxiliary design size and the auxiliary assembly size on a multicolor drawing model of the assembly size as shown in FIG. 2;
step 6: a method for solving the transmission coefficient of component ring in multi-color model is disclosed, that is, the component ring opposite to the closed ring is an augmented ring and the transmission coefficientξ ij = +1, the component ring in the same direction with the closed ring is a reduction ring, and the transmission coefficientξ ij =1, wherein,ξ ij indicating a serial number ofiThe closed ring is in the size chain with the serial number ofjThe value of the transmission coefficient can be judged and obtained according to the method, and the value of the transmission coefficient is marked on the multicolor graph model of the assembly size shown in figure 2;
and 7: 3 rings containing closed rings can be found by observing the established assembly size polychrome graph modelX N1 ~X N3 The ring being numbered respectivelyi=1,2,3 is marked on the polychromatography model of the set-up size as shown in fig. 2;
and 8: by further analyzing the multicolor chart model and the assembly chart, the method can be knownX * N1 =X N1 Closed loop in ring 1 corresponds to 2X N1 To be provided withX N1 As closed rings, the proportionality coefficients of the constituent ringsk ij The values are all divided by 2,L * 6 =L 6 ，L * 1 =L 1 therefore, it isk 11 =1，k 21 =1/2，k 13 =1/2，k 16 =1, all the proportionality coefficients can be obtained by the same methodk ij And the values of the scaling factors are plotted on a multicolor map model of the fitting size as shown in fig. 2;
and step 9: the multicolor map model of the fit size is described using multicolor sets as follows:
multicolor picturePGAs a multicoloured aggregatePSThe graphical representation of (A) consists of three parts:
PG=(F(G),PS A , PS C )
PS A =(A,F(a),F(A),[A×F(a)],[A×F(A)],[A×A(F)])
PS C =(C,F(c),F(C),[C×F(c)],[C×F(C)],[C×C(F)])
in the formula (I), the compound is shown in the specification,F(G) The color is the uniform coloring of the whole multicolor image and the uniform color of the whole multicolor set;
in the formula (I), the compound is shown in the specification,PS A is a multi-color set of nodes, whereinA ={a 1 , a 2 ,…, a 14 Is a set of nodes, i.e. assembly features of the part,a 1 ~a 14 respectively correspond toA S ，B S ，C S ，D S ，E S ，O D ，O d ，O S ，F S ，G S ，H S ，I S ，J S ，K S Elements ofa i (i=1,2, \8230;, 14) represents a multicolor chartPGNode of (i.e. of parts)iThe number of the individual features of the assembly,F(a)={f 1 (a), f 2 (a), f 3 (a), f 4 (a), f 5 (a), f 6 (a), f 7 (a), f 8 (a) Is the individual color of the element, i.e., the set of part assembly feature types, in this example, the part assembly feature types include point, straight line, plane, curve, virtual point, virtual straight line, virtual plane, and virtual curve, corresponding to point, straight line, plane, and curve, respectivelyf 1 (a)，f 2 (a)，f 3 (a)，f 4 (a)，f 5 (a)，f 6 (a)，f 7 (a)，f 8 (a) Elements ofa i To (1) ajIndividual color isf j (a i ) I.e. of the partsiA first of the assembly featuresjA type;
in this example, the uniform coloring of a multi-color setF(A)={F 1 (A), F 2 (A), F 3 (A), F 4 (A), F 5 (A), F 6 (A), F 7 (A), F 8 (A) I.e. the types of assembling characteristics of the parts and assemblies, specifically including points, straight lines, planes, curves, virtual points, virtual straight lines, virtual planes and virtual curves, which respectively correspond to the points, straight lines, planes, curves, virtual points, virtual straight lines, virtual planes and virtual curvesF 1 (A)，F 2 (A)，F 3 (A)，F 4 (A)，F 5 (A)，F 6 (A)，F 7 (A)，F 8 (A) That is, in the present example,F(A)=F(a)；
in this example, the set of nodesASet of assembling feature types with parts and assembliesF(A) Formed into a Boolean matrixA×F(A)]Can be expressed as:
in the Boolean matrixA×F(A)]In, ifF j (A)∈F(a i ) Then, thenc ij =1, otherwisec ij =0, i.e. if the second characteristic of the assembly of the component and the assemblyjOf the type in the first partiA set of assembly feature types, thenc ij =1, otherwisec ij =0，c ij Is shown as Boolean paper matrix [ 2 ]A×F(A)]To middleiGo to the firstjThe element values of the columns;
in the formula (I), the compound is shown in the specification,PS C is a multi-color set of edges, wherein the set of edgesC={c 1 , c 1 ,…, c 17 }={a i a j , i<j,i,j∈1,2,…,14}，CIn isASet of ordered and unordered pairs of middle nodes, edgec k And ordered idol< a i a j >Related, as directed edges, i.e. design, assembly and auxiliary dimensions of the part, whereina i Is called asc k The start node of (a) is,a j is called asc k The terminating node of (2), the set of edgesCMarked on the multi-color map model shown in fig. 2, in particular, when the two features are equally positioned (e.g., in an assembly tolerance design, only the dimensions of the two assembled features need to be specified and their references do not need to be specified), the edge connecting the two features is a non-directional edge, i.e., an edgec k And disorder couple< a i a j >Associating;
in this example, there are 3 rings comprising a closed ring, consisting ofL 3 、L 3 /2、L 3 The ring composed of/2 does not contain a closed ring, does not relate to the assembly relation, and is not considered, wherein the sidec 17 =a 8 a 12 =a 12 a 8 Is composed ofCOnly one of which, in this example, the polychrome setUnified coloring of blendsF(C)={F 1 (C), F 2 (C), F 3 (C), F 4 (C), F 5 (C) The sizes of the parts and the assembly body and the assembly size chain specifically comprise a part design size, an assembly size, an auxiliary design size, an auxiliary assembly size and an assembly size chain, which respectively correspond to the parts design size, the assembly size, the auxiliary assembly size and the assembly size chainF 1 (C),F 2 (C),F 3 (C),F 4 (C),F 5 (C)；
In this example, the set of edgesCSet of part design size typesF(C) Formed boolean matrix [ 2 ]C×F(C)]Can be expressed as:
in the Boolean matrixC×F(C)]In, ifF j (C)∈F(C i ) Then, thend ij =1, otherwised ij =0, i.e. if part is dimensionedjThe property being in the first partiA set of design-sized attributes, thend ij =1, otherwised ij =0，d ij Expressed by a Boolean matrix [ 2 ]C×F(C)]To middleiGo to the firstjThe element values of the columns;
set of if edgesCSeveral elements ofc i ∈CUniform color when coexistingF j (C) Are present then these elements are presentc i ∈CThe collection of compositions is called uniform colorF j (C) To (1)kIndividual, record asC k (F j ) The process of the present invention, in this case,C(F 5 ) = C 1 (F 5 )∪C 2 (F 5 )∪C 3 (F 5 ) Wherein, in the step (A),C 1 (F 5 ) = (c 5 ∧c 7 ∧c 8 ∧c 9 ∧c 10 ∧c 14 ∧c 15 ∧c 16 ) 1 ，C 2 (F 5 ) = (c 3 ∧c 4 ∧c 17 ) 2 ，C 3 (F 5 ) = (c 1 ∧c 2 ∧c 6 ∧c 11 ∧c 12 ) 3 and therefore, the first and second electrodes are,C(F 5 ) = (c 5 ∧c 7 ∧c 8 ∧c 9 ∧c 10 ∧c 14 ∧c 15 ∧c 16 ) 1 ∨(c 3 ∧c 4 ∧c 17 ) 2 ∨(c 1 ∧c 2 ∧c 6 ∧c 11 ∧c 12 ) 3 this means if the elementc 5 ，c 7 ，c 8 ，c 9 ，c 10 ，c 14 ，c 15 ，c 16 Co-exist of, or elementsc 3 ，c 4 ，c 17 Co-exist of, or elementsc 1 ，c 2 ，c 6 ，c 11 ，c 12 Existing simultaneously, then the dimensional chain is assembledF 5 (C) Is present;
step 10: the assembly size polychrome model, as shown in figure 2, comprises 3 rings, including a closed ring, designed to have a sizeL 1 ~L 9 In an assembly size ofX N1 ~X N3 Then, the matrix equation with the assembly dimension chain is as follows:
[X Ni ] T =[ξ ij k ij ][L j ] T
in the formula (I), the compound is shown in the specification,k ij is a coefficient of proportionality constituting the size of the ringX Ni ] T For assembling the column vectors of the dimensionsi×1，[L j ] T Designing a dimensional column vector matrix for a partj×1，[ξ ij k ij ]Is a matrix of size chain coefficientsi×jThe dimension chain coefficient matrix establishes a linear relation between the assembly dimension and the design dimension;
step 11: by the transfer coefficient obtained in step 6ξ ij And the scale factor obtained in step 8k ij Obtaining a dimension chain coefficient matrixξ ij k ij ]As follows:
step 12: from the dimension chain coefficient matrix of step 11 and the assembled dimension chain matrix equation provided in step 10, the assembled dimension chain matrix equation can be solved using MATLAB R2014a, as follows:
<xnotran> MATLAB R2014a , A = [ -1, -1/2,1/2,0,0,1,0,0,0;0,0,0, -1,1,0,0,0,0;0,0,1/2,0,0,0,1, -1,1 </xnotran>]Then inputting a part design dimension column vector matrix B = [15]Finally, the matrix multiplication command C is input=A B can obtain the closed loop column vector of the assembly size chain as follows:
therefore, the roller memberThe assembly dimensions of (a) are: clearance between the roller 3 and the frame 1X N1 Is equal to 1mm(ii) a Gap between frame 1 and nut 6X N2 Is equal to 0.2mm(ii) a The distance between the axial line of 26+0.021 0 in the big aperture of the rack 1 and the middle plane between the two end faces vertical to the axial line in the roller 3X N3 Is equal to 0mmI.e., require that both be coplanar;
while the invention has been described in further detail with reference to specific preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (1)
1. A complex assembly dimension chain solving method based on a multicolor set theory is characterized by comprising the following steps:
step 1: analyzing an assembly drawing of the assembly body or the component, and acquiring and recording the assembly size, the design size, the auxiliary size and the assembly characteristic of the part of the assembly body or the component in a form;
step 2: establishing a multicolor diagram model of the assembly size, acquiring the characteristics corresponding to each node of the assembly diagram in the step 1, and sequencing the characteristics from left to right, wherein k =1,2, \ 8230;
and step 3: for the closed ring X in the multicolor chart model of the assembly size established in the step 2 Ni Respectively using serial numbers i =1,2, \8230, n is marked on a multicolor diagram model of the assembly size;
and 4, step 4: obtaining a composition ring L in the assembly design drawing in the step 1 j Sequentially marked on the multicolor chart model of the assembly size with j =1,2, \ 8230;, n;
and 5: acquiring an auxiliary design size and an auxiliary assembly size in the assembly design drawing in the step 1, and marking the auxiliary design size and the auxiliary assembly size on a multicolor drawing model of the assembly size;
step (ii) of6: a method for solving the transmission coefficient of component ring in multi-color model features that the component ring reverse to the closed ring is an incremental ring and the transmission coefficient xi ij = +1, the component ring in the same direction with the closed ring is a reduction ring, and the transmission coefficient xi ij = -1, wherein xi ij Representing the transmission coefficient of a composition ring with the serial number j in a size chain in which the closed ring with the serial number i is positioned, judging according to the method to obtain the value of the transmission coefficient, and marking the value of the transmission coefficient on a multicolor graph model of the assembly size;
and 7: the closed ring X is formed by observing the established multicolor diagram model of the assembly size to find i circular rings containing the closed ring N1 ～X Ni The rings are marked on the multicolor chart model of the assembly size with serial numbers i =1,2, \8230;, n, respectively;
and 8: by further analyzing the multicolor chart model and the assembly chart, the proportionality coefficient k is obtained ij And marking the value of the proportionality coefficient on a multicolor graph model of the assembly size;
and step 9: using multicolor set to describe multicolor graph model of assembly size and corresponding each node to edge c formed by features m The multicolor chart model is marked with the serial numbers m =1,2, \8230;, q, respectively;
step 10: if an assembly-size multicolor chart model comprises i rings including closed rings, the design size is L 1 ～L j Assembly size X N1 ～X Ni Then there is an assembly dimension chain matrix equation [ X Ni ] T ＝[ξ ij k ij ][L j ] T In the formula, k ij As a coefficient of proportionality of the dimensions of the constituent rings, [ X ] Ni ] T To assemble the dimension column vector i × 1, [ L ] j ] T Design the size column vector matrix for the part, j × 1, [ xi ] ij k ij ]Establishing a linear relation between the assembly size and the design size for a size chain coefficient matrix i multiplied by j;
step 11: passing through the transfer coefficient ξ obtained in step 6 ij And the scaling factor k obtained in step 8 ij Obtain a size chain coefficient matrix xi ij k ij ]；
Step 12: solving the assembly dimension chain matrix equation by using mathematical software MATLAB R2014a according to the dimension chain coefficient matrix provided in the step 11 and the assembly dimension chain matrix equation provided in the step 10.
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