CN110597177A - Numerical control machine tool precision control method based on precision mapping - Google Patents

Numerical control machine tool precision control method based on precision mapping Download PDF

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CN110597177A
CN110597177A CN201910882028.5A CN201910882028A CN110597177A CN 110597177 A CN110597177 A CN 110597177A CN 201910882028 A CN201910882028 A CN 201910882028A CN 110597177 A CN110597177 A CN 110597177A
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precision
motion
accuracy
mapping
layer
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CN110597177B (en
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金传喜
张根保
冉琰
王治超
黄广全
肖莉明
许文林
应广祺
李世霖
谷豪东
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Chongqing University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/19—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by positioning or contouring control systems, e.g. to control position from one programmed point to another or to control movement along a programmed continuous path
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/4097—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by using design data to control NC machines, e.g. CAD/CAM
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/45—Nc applications
    • G05B2219/45136—Turning, lathe

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Abstract

The invention discloses a numerical control machine tool precision control method based on precision mapping, which maps the design precision value of a total functional layer of a numerical control machine tool to the design precision value of a sub-functional layer in a direct transmission mode; mapping the design precision value of each functional layer to the positioning precision or the repeated positioning precision value of the main motion layer by adopting a characteristic root method; mapping the positioning precision or the repeated positioning precision value of the main motion layer to the positioning precision or the repeated positioning precision value of the secondary motion layer by adopting a fuzzy analytic hierarchy process and an interval gray system theory; mapping the positioning precision or repeated positioning precision value of the secondary motion layer to the motion precision value of the meta-action unit by adopting a sensitivity-based precision mapping mode; and then, performing precision control on the meta-action unit level and giving a precision control measure. The invention can design the precision of the element action unit on the basis of the known design requirement of the overall precision of the machine tool and control the precision on the element action layer.

Description

Numerical control machine tool precision control method based on precision mapping
Technical Field
The invention relates to improvement of precision control of a numerical control machine, in particular to a precision control method of the numerical control machine based on precision mapping, and belongs to the technical field of numerical control machines.
Background
The numerical control machine tool is a 'working master machine' in the equipment manufacturing industry, and the technical level and the product quality of the national machine tool industry are important marks for measuring the development level of the equipment manufacturing industry. Through the development of over thirty years, although the domestic numerical control machine tool makes certain progress, in the aspect of machine tool machining precision, the machining precision of the domestic numerical control machine tool is often more than one order of magnitude lower than that of foreign products, and the low precision not only can affect the quality of machined parts, but also can affect some performances of the numerical control machine tool, so that the precision of the numerical control machine tool is very necessary to be controlled.
At present, machining precision control methods of numerical control machine tools are mainly divided into the following five types: 1. controlling the self error of the numerical control machine; 2. controlling the processing technological error of the numerical control machine; 3. controlling the machining positioning error of the numerical control machine; 4. controlling the temperature and the thermal deformation of a process system to influence the machining precision; 5. and the resonance of the stepping motor and the numerical control machine tool influences the control of the machining precision. Most of the machining precision control methods are used for controlling the machining precision in the manufacturing and using stages of the machine tool, the precision is not controlled in the design process of the machine tool, the method belongs to a post-processing control method, and the precision of the numerical control machine tool cannot be well controlled from the source.
Disclosure of Invention
Aiming at the defects that the existing numerical control machine tool precision control method is mainly a post control method and does not control the precision of the numerical control machine tool from the source, the invention aims to provide a precision control method of the numerical control machine tool based on precision mapping.
The technical scheme of the invention is realized as follows:
a numerical control machine tool precision control method based on precision mapping comprises the steps of firstly obtaining the design precision of the total function of a numerical control machine tool, then mapping the design precision value of the total function of the numerical control machine tool layer by layer downwards until the value is mapped to the level of an element action unit, so that the motion precision required by each element action unit is obtained, and finally, precision control is carried out on the element action unit to meet the motion precision required by the element action unit, so that the precision control of the numerical control machine tool is realized.
The element action unit precision influence factors comprise the size precision, the position precision and the assembly precision of element action unit parts; in the design process, starting from the three aspects, corresponding precision control measures are given for different meta-action units.
Specifically, the invention maps the design precision value of the total function to the meta-action unit by adopting the following steps:
A. carrying out structural decomposition on the numerical control machine according to a 'function-motion-action' mode, decomposing into five levels of a total functional layer, a sub functional layer, a main motion layer, a secondary motion layer and a meta-action unit layer, and establishing a numerical control machine precision waterfall mapping chain model according to a structural decomposition model;
B. extracting design precision value DP of total functional layer of numerical control machine tool according to customer requirementsTFThe accuracy mapping from the total functional layer to the sub functional layers adopts a direct transmission mode, namely the design accuracy values of the sub functions of the sub functional layers are equal to the design accuracy value of the total function, so that the design accuracy matrix of the sub functional layers is DPF＝(DPTF，DPTF，…，DPTF)t；
In the formula: t represents that the numerical control machine tool has t sub-functions;
C. precision mapping of sub-function layers to main motion layers first takes into account the fact that each main motion is relative to a certain sub-function FxThe level of the precision requirement is calculated by adopting a characteristic root method to obtain a certain sub function FxLower dominant motion weight vectorThen divide the sub-function F according to the right distributionxIs mapped to the positioning accuracy or repeated positioning accuracy of the corresponding main motion layerNamely, it is
Obtaining the positioning accuracy or repeated positioning accuracy of the main motion layer under other sub-functions considering the accuracy requirement in the same mode, comparing, and selecting each main motion layer with high accuracy, thereby obtaining the positioning accuracy or repeated positioning accuracy matrix of the main motion layer considering the accuracy requirement
Then considering the complexity of the structure of each main motion part, and calculating by adopting a characteristic root method CRM to obtain a weight vector of a main motion layer considering the complexity of the structure of the part asThen, calculating according to the following formula to obtain a main motion layer positioning precision or repeated positioning precision matrix considering the structural complexity of the component
Finally will beAndcomparing, and obtaining the positioning accuracy or repeated positioning accuracy matrix SP of the main motion layerPM；
D. The precision mapping from the main motion layer to the secondary motion layer considers the complexity of each secondary motion structure, namely the influence of structural coupling between the secondary motions on the mapping process, and a certain main motion M is obtained by adopting a fuzzy analytic hierarchy process and an interval gray system theory to calculateiThe lower two-level motion layer mapping weight vector isThe main movement M is then represented by the following formulaiPositioning accuracy or repeated positioning accuracy ofMapping to obtain the positioning precision or repeated positioning precision of the corresponding secondary motion layer
Then, the same mapping mode is adopted to calculate the positioning precision or repeated positioning precision values of the secondary motion layers under other main motions, and finally, the positioning precision or repeated positioning precision values are integrated into a positioning precision or repeated positioning precision matrix SP of all the secondary motion layersSM；
E. The precision mapping from the secondary motion layer to the element action unit layer considers that each element action unit is of a chain structure, and the precision of each element action unit is calculated by adopting the following formula according to the sensitivity of the secondary motion positioning precision or the repeated positioning precision relative to the precision of each element action unit in the element action chain;
in the formula: p (A)k) For two-stage movement MicThe next kth element action unit precision; p (M)ic) Refers to a two-stage movement MicM represents a secondary motion MicComprises m element action units; pk(Mic) For two-stage movement MicA positioning accuracy or a repeated positioning accuracy component for the kth element action unit; Δ Fk(Mic) For two-stage movement MicA positioning error or a repeated positioning error component for the kth element action unit; zpkSensitivity of secondary motion positioning precision or repeated positioning precision to motion precision of the element action unit; zkThe variation coefficient of the second-level motion positioning error or the repeated positioning error component and the motion error of the element action unit;
thereby obtaining a certain secondary movement MicPrecision matrix formed by all element action unit precision
Finally, the element action unit precision matrix under all the second-level motionIntegrating to obtain a precision matrix SP consisting of all element action unit precisionsMA。
The unit action units of the invention are divided into two categories of a moving unit action unit and a rotating unit action unit, wherein the precision value of the moving unit action unit is the straightness of the movement of the unit executive component, and the precision value of the rotating unit action unit is the rotation precision of the unit executive component.
Compared with the prior art, the invention has the following beneficial effects:
the precision of the numerical control machine tool is controlled in the design stage, the precision of the meta-action unit is finally deduced through layer-by-layer decomposition on the basis of the known design requirement of the overall precision of the machine tool, the precision value is used as an actual control target, and corresponding control measures are taken to guarantee the precision value of the meta-action unit, so that the aim of controlling the precision of the numerical control machine tool from the source is fulfilled, and better precision control is realized.
Drawings
FIG. 1 is a flow chart of the method for controlling the accuracy of a numerically-controlled machine tool based on accuracy mapping.
FIG. 2 is a numerical control machine FMA structural decomposition model.
FIG. 3 is a numerical control machine accuracy waterfall mapping chain model.
FIG. 4 is a mapping coupling pair structure level quantization model.
Fig. 5 is a functional diagram of four whitening weight functions.
In fig. 3, TF — total functional layer; f-is divided into functional layers; PM-main motion layer; SM-secondary motion layer; MA-Meta action Unit layer; DPTF-overall functional design accuracy; DPF-designing a precision matrix in function; SPPM-a primary motion localization accuracy or a repeated localization accuracy matrix; SPSM-a secondary motion localization accuracy or a repeated localization accuracy matrix; MP (moving Picture experts group)MA-a meta motion accuracy matrix.
Detailed Description
The invention relates to a numerical control machine tool precision control method based on precision mapping, which has the general idea that: the method comprises the steps of firstly obtaining the design precision of the total function of the numerical control machine, then mapping the design precision value of the total function of the numerical control machine layer by layer downwards until the design precision value is mapped to the level of the element action unit, so that the motion precision required by each element action unit is obtained, and finally, the element action units are subjected to precision control to meet the motion precision required by the element action units, so that the precision control of the numerical control machine is realized.
The invention specifically adopts the following steps to map the design precision value of the total function to the meta-action unit, and the implementation process can be seen in fig. 1.
A. Carrying out structural decomposition on the numerical control machine according to a Function-Motion-Action (FMA) mode, and decomposing into five levels of a total Function layer, a sub Function layer, a main Motion layer, a secondary Motion layer and a meta-Action unit layer, wherein FIG. 2 is a schematic diagram of an FMA structural decomposition model of the numerical control machine, and establishing a precision waterfall mapping chain model of the numerical control machine according to the FMA structural decomposition model; FIG. 3 is a schematic diagram of a numerical control machine precision waterfall mapping chain model; table 1 shows the accuracy index of each layer of the accuracy waterfall mapping chain model;
TABLE 1 precision waterfall mapping chain model layer precision index description
B. Extracting design precision value DP of total functional layer of numerical control machine tool according to customer requirementsTFThe accuracy mapping from the total functional layer to the sub functional layers adopts a direct transmission mode, namely the design accuracy values of the sub functions of the sub functional layers are equal to the design accuracy value of the total function, so that the design accuracy matrix of the sub functional layers is DPF＝(DPTF，DPTF，…，DPTF)t；
In the formula: t represents t sub-functions of the numerical control machine tool;
C. precision mapping of sub-function layers to main motion layers first takes into account the fact that each main motion is relative to a certain sub-function FxThe accuracy requirement is high or low, and a certain sub-function F is calculated by adopting a Characteristic Root Method (CRM)xLower dominant motion weight vectorThen divide the sub-function F according to the right distributionxIs mapped to the positioning accuracy or repeated positioning accuracy of the corresponding main motion layerNamely, it is
Obtaining the positioning precision or repeated positioning precision of the main motion layer under other sub-functions considering the precision requirement by the same mode, and comparing the positioning precision or repeated positioning precision every timeThe selection precision of each main motion layer is high, so that a main motion layer positioning precision or repeated positioning precision matrix considering the precision requirement is obtained
Then considering the complexity of the structure of each main motion part, and calculating by adopting a characteristic root method CRM to obtain a weight vector of a main motion layer considering the complexity of the structure of the part asThen, calculating according to the following formula to obtain a main motion layer positioning precision or repeated positioning precision matrix considering the structural complexity of the component
Finally will beAndcomparing, and obtaining the positioning accuracy or repeated positioning accuracy matrix SP of the main motion layerPM；
D. The precision mapping from the main motion layer to the secondary motion layer considers the complexity of each secondary motion structure, namely the influence of structural coupling between the secondary motions on the mapping process, and a certain main motion M is calculated by adopting a Fuzzy Analytic Hierarchy Process (FAHP) and an Interval Gray System Theory (IGST)iThe lower two-level motion layer mapping weight vector isThe main movement M can be obtained by the following formulaiPositioning accuracy or repetition of positioningAccuracy of measurementMapping to obtain the positioning precision or repeated positioning precision of the corresponding secondary motion layer
Then, the same mapping mode is adopted to calculate the positioning precision or repeated positioning precision values of the secondary motion layers under other main motions, and finally, the positioning precision or repeated positioning precision values are integrated into a positioning precision or repeated positioning precision matrix SP of all the secondary motion layersSM；
E. The precision mapping from the secondary motion layer to the element action unit layer considers that each element action unit is of a chain structure, and the precision of each element action unit is calculated by adopting the following formula according to the sensitivity of the secondary motion positioning precision or the repeated positioning precision relative to the precision of each element action unit in the element action chain;
in the formula: p (A)k) For two-stage movement MicThe next kth element action unit precision; p (M)ic) Refers to a two-stage movement MicM represents a secondary motion MicComprises m element action units; pk(Mic) For two-stage movement MicA positioning accuracy or a repeated positioning accuracy component for the kth element action unit; Δ Fk(Mic) For two-stage movement MicA positioning error or a repeated positioning error component for the kth element action unit; zpkSensitivity of secondary motion positioning precision or repeated positioning precision to motion precision of the element action unit; zkThe variation coefficient of the second-level motion positioning error or the repeated positioning error component and the motion error of the element action unit;
thereby obtaining a certain secondary movement MicPrecision matrix formed by all element action unit precision
Finally, the element action unit precision matrix under all the second-level motionIntegrating to obtain a precision matrix (Mm P) composed of all the element action unitsMA。
Through the mapping of the four steps, the design precision of the whole machine can be mapped to the meta-action unit layer, the design input of the meta-action unit is obtained, and therefore a mapping mechanism of the whole machine precision is established.
The unit action units are divided into two categories of moving unit action units and rotating unit action units, wherein the precision value of the moving unit action unit is the straightness of the movement of the unit executive component, and the precision value of the rotating unit action unit is the rotation precision of the unit executive component. The precision of the unit executive component is jointly guaranteed by the dimensional precision, the position precision and the assembly precision of the component parts no matter whether the component parts move or rotate, and different precision control measures are given for different element action units in the design process from the three aspects.
The main precision control measures of the meta-action unit are as follows:
1. and selecting a proper assembly method according to the assembly characteristics. Different component action units are different in component parts and assembling characteristics, so that the assembling modes are different, and a proper assembling method needs to be selected according to the assembling characteristics.
2. And selecting a proper assembly standard. In the design process, different assembly references are selected, the precision values of the executive parts of the meta-motion units are different, and therefore, a proper assembly reference should be selected, so that the assembly error of the meta-motion units is minimized.
3. Reasonable design of machining allowance. In order to ensure that the dimensional accuracy of each component part can meet the requirements, reasonable machining allowance needs to be distributed to each part according to the machining mode and materials of the part.
4. The dimensional tolerances of the parts are reasonably distributed. According to design requirements, a process dimension chain of each part is established, and then, the dimension errors of the parts are reasonably distributed according to the process dimension chain, so that the dimension precision of each part can meet the requirements.
The invention is divided into two processes of precision mapping and precision control.
The precision mapping process is to map the design precision of the whole machine of the numerical control machine tool to the element action unit according to a precision waterfall mapping chain model, and the whole mapping process is divided into four steps:
and mapping the TF-F layer. The design precision value of the total function is mapped to the sub-function layers by adopting a direct transmission mode, so that the complete machine precision design target is favorably decomposed, and the design precision value of each sub-function is obtained;
and mapping the F-P layer. The design precision values of all sub-functions are mapped to the main motion layer in a characteristic root mode, the situation that the sub-functions share main motion and the complexity of the structure of each main motion part are considered in the whole mapping process, and the two factors are considered, so that the mapping result is more accurate;
and mapping the P-S layer. The positioning precision or the repeated positioning precision of the main motion layer is mapped to the secondary motion layer by adopting a fuzzy analytic hierarchy process and an interval gray system theory, the influence of the complexity of a secondary motion structure (namely the structural coupling relation between secondary motions) is considered in the mapping process, and the coupling relation is used as the influence factor of the mapping weight, so that the effect of eliminating the influence of the coupling relation on the mapping process is indirectly achieved;
and mapping the S-A layer. The positioning precision or the repeated positioning precision of the secondary motion is mapped to the element action units by adopting the sensitivity distribution and equal action principle, the chain structure is considered between the element action units in the mapping process, and the influence of the chain structure on the precision mapping can be eliminated by adopting the method for mapping, so that the mapping result is more accurate.
The precision control process mainly controls the precision of the element action units according to the design precision value obtained by mapping in the front, ensures that the precision value of the element action units can be maintained in a qualified range in the full life cycle range of the product, and ensures the precision values of all the element action units through control, so that the precision of the whole machine can be well ensured. The precision control method can control the precision of the whole numerical control machine from the source, and reduces the times of after-service maintenance, thereby achieving the effect of improving the quality and the reliability of the numerical control machine.
For better understanding of the present invention, the THM6380 processing center is used as a control object to perform precision control according to the control method of the present invention, and the specific process is as follows.
1) FMA structured decomposition of THM6380 with drill F in the machining center1Boring F2Hinge F3Tapping F4Milling F5And rough, fine machining F of the profile6Equal 6 sub-functions, with milling function F5For example, an FMA structural decomposition model is established, and a precision waterfall mapping chain model of the machining center is established according to the FMA structural decomposition model.
2) The total functional design precision value DP of the machining center extracted from the customer requirementsTFObtaining design precision matrix DP of functional layer by direct transmissionF＝(DPTF，DPTF，DPTF，DPTF，DPTF，DPTF)。
3) Consider the case where the primary motion is shared between the sub-functions. By a milling function F5For example, F is calculated by using CRM5Lower dominant motion layer mapping weightsSince CRM determines weights are common, it is not described here in detail. Obtaining F taking into account the common primary motion5Weight vector of lower dominant motion layerThen, the function F can be divided5Is mapped to the primary motion layer:
in the formula: DPTFIs divided into functions F5The value of the design accuracy of (a) is,to take account of F sharing a primary motion5A positioning accuracy or a repeated positioning accuracy matrix of the lower main motion layer.
The positioning accuracy or repeated positioning accuracy matrix of the main motion layer under other sub-functions can be obtained in the same way, then comparison is carried out, and high accuracy is selected, so that the positioning accuracy or repeated positioning accuracy matrix of the main motion layer sharing main motion under the consideration of the sub-functions is obtained
Consider the case of the structural complexity of each of the primary motion components. In the whole consideration, the weight vector of the main motion layer considering the complexity of the component structure is obtained by adopting CRM calculation aiming at a certain sub-functionThereby calculating the main motion layer positioning precision or repeated positioning precision vector considering the complexity of the component structure
In the formula: DPFA design precision value matrix for each functional layer.
Comparing the precision values of the main motions under the two conditions, selecting the matrix SP with high precision requirement, and finally obtaining the positioning precision or repeated positioning precision matrix SP of the main motion layerPM。
4) The positioning precision or the repeated positioning precision of the main motion layer is mapped to the secondary motion layer, the complexity (namely the structure coupling relation) of a secondary motion structure is considered, and the whole mapping process is divided into two steps:
a. and calculating the structural coupling degree based on FAHP. Now assume a certain primary motion MiIf there are m pairs of mapping coupling pairs, the mapping coupling pair set isWhereinRefers to a main movement MiThe mth mapping coupled pair of (1). The process of quantifying the mapping coupling pair using FAHP is as follows:
firstly, establishing a mapping coupling pair hierarchical structure quantization model. For the evaluation of the mapping coupling pair, the established criterion layer comprises H indexes such as coupling tightness, coupling degree, coupling stability and coupling reliability, so that the index set U is { U ═ U {1，u2，u3，…uhIn which uhRefers to the h-th quantization index. In the quantification process, there are W experts in total, and all the expert sets V ═ V1，v2，v3，…vwIn which v iswRefers to the w-th expert. The established mapping coupling pair hierarchical structure quantization model is shown in fig. 4.
Establishing FAHP quantization matrix language scale. For these indexes established, the higher the index is, the better the index is, so the linguistic scale of the quantization matrix is divided into 9 levels according to the 1-9 scaling method, and the specific fuzzy value assignment is shown in table 2.
And thirdly, establishing and integrating an expert quantization matrix. Order expert vyConsider a mapping coupling pairThe values of the degrees corresponding to the requirements of h indices are expressed as follows:whereinThe number is a triangular fuzzy number (x is 1,2 … M; y is 1,2 … W; j is 1,2 … H), and the number is obtained by adopting intuitive fuzzy entropy calculation
TABLE 2 fuzzy analytic hierarchy process quantization matrix linguistic scaling
Expert weight G ═ G (G)1，G2,…,Gw) Wherein G iswRefers to the weight of the w expert whose triangular fuzzy weighted average formula is:
in the formula: LT (LT)xhyRefer to the y-th expert as mapping the coupled pairsCorresponding to the first value of the degree value triangular blur number satisfying the h-th index requirement, MTxhy,UTxhyA second value and a third value, respectively.
Thereby the expert comprehensive quantization matrix obtained by calculation is:
in the formula:is the triangular fuzzy value after weighted average.
Fourthly, carrying out hierarchical single sequencing to obtain the mapping coupling pair quantity value. Mapping the coupled pairs b according to the expert quantization matrixx iThe comprehensive importance degree value correspondingly meeting the H indexes is as follows:
in the formula: sxIs the comprehensive importance degree value.
Two triangular blur numbers M1＝(l1，m1，μ1) And M2＝(l2，m2，μ2)，M2≥M1The degree of likelihood of (a) is:
if present, (x, y), and x>y，Then there is V (M)2≥M1) 1, wherein M1And M2For convex functions, the formula is as follows
The paste number of one punch is M higher than that of the rest k punchesi(i-1, 2, …, k) is highly probable to the extent that
V(M≥M1，M2，…，Mk)＝V(M≥M1)∪V(M≥M2)∪V(M≥M3)…V(M≥Mk)＝minV(M≥Mi)
Suppose d' (A)x)＝minV(Sx≥Sk),k＝1,2,…,M；k≠i，SxTo synthesize the importance measure, AxRepresenting the xth mapping couple pair, the magnitude of each mapping couple pair is W '═ d' (a)1)，d'(A2)，…，d'(Am))TAfter normalization, the magnitude of the final mapping couple pair is W ═ d' (a)1)，d'(A2)，…，d'(Am))TI.e. degree of mapping couplingThe mapping coupling degree is the structural coupling degree eta between two secondary motions.
b. Mapping weight calculation based on IGST. To calculate a main movement MiEach two-stage movement M oficThe structural coupling relation is used as the influence factor of the mapping weight, and the coupling weight of the c second-level motion mapping weight influence factor is calculated according to the obtained coupling degree eta
In the formula:refers to the coupling weight of the kth influencing factor of the c-th secondary motion,refers to the degree of coupling of the kth influencing factor of the c-th secondary motion.
In order to avoid the situation that the mapping weight is zero, the coupling weight is corrected by adopting an entropy weight method, and the calculation process is as follows:
in the formula: dckThe judgment value of the c secondary motion under the k influence factor is obtained; f. ofckThe specific gravity of the k-th influencing factor of the c-th secondary motion; hkIs the entropy value of the k-th influencing factor.
The corrected value entropy weight beta of each mapping weight influence factor can be obtained according to the formulak：
In the formula: k is the total number of the c second-stage motion influence factors;
the final mapping weight factor has the following weights:
in the formula:the weight of the k-th influencing factor for the c-th secondary motion,the corrected value entropy weight of the k-th influence factor of the c-th secondary motion.
Evaluation matrix of influence factors of I < th > expert on c < th > two-level motion mapping weightThe coupling relationship will have an effect on the mapping weight, and the gray class set to which the influence degree is evaluated is marked as X ═ X1，x2，…，xhDivide this influence into four categories, high, normal and low, i.e. h 4, X { X ═ X }1，x2，x3，x4High, normal, low. In combination with IGST, can obtainWeights belonging to the s-th classAnd s is 1-4, and the adopted method is a whitening weight function. Fig. 5(a) and 5(b) are functional graphs of four whitening weight functions, where P is the lower limit of the first class, G is the upper limit of the second class, Q is the upper limit of the third class, and Z is the upper limit of the fourth class, and the formula for calculating the whitening weight functions of each class is obtained from the graphs by setting { P, G, Q, Z } - {9, 7, 5, 2 }.
Ash numberThe calculation formula is as follows:
in the formula:the evaluation value of the kth influence factor of the mapping weight of the ith expert on the kth secondary motion is obtained;is composed ofWeights belonging to the s-th class.
Ash number-The calculation formula is as follows:
(iii) ash numberThe calculation formula is as follows:
ash numberThe calculation formula is as follows:
to obtainWeight in the s-th gray classThen, the gray statistic n of the judgment matrix can be obtainedcsAnd total grey statistics nc；
The evaluation value of the L-bit experts on each secondary motion is synthesized, and for the c-th secondary motion, the mapping weight influence factor k belongs to the s-th grey evaluation weight valueThe grey evaluation matrix for the c-th secondary motion can thus be obtained as:
grey evaluation matrix R for the c-th two-level motion(c)And a weight vector beta of the mapping weight influencing factors(c)After the determination, the comprehensive gray evaluation value of the c-th secondary motion can be obtained:
Z(c)＝w(c)·R(c)·DT
in the formula: z(c)Integrated gray scale estimate for the c-th secondary motion, DTD ═ P, G, Q, Z ═ 9, 7, 5, 2, w is the value corresponding to the four-level estimation method(c)Is the weight vector of the c-th secondary motion influencing factor.
In the same way, the main movement M can be obtainediThe combined gray assessment value of the other secondary motion, then the mapping weight of each secondary motion is
In the formulaIs a main movement MiWeight value of the next c second-order motion.
So that a main movement M can be obtainediThe lower two-level motion layer mapping weight vector isAssigning principal motion M according to weightiThe positioning accuracy or the repeated positioning accuracy is mapped to a secondary motion layer:
in the formula:is a main movement MiA lower two-level motion layer positioning accuracy or repeated positioning accuracy matrix,is a main movement MiOr a repeated positioning accuracy value.
Then, the same mapping mode is adopted to calculate the positioning precision or repeated positioning precision values of the secondary motion layers under other main motions, and finally, the positioning precision or repeated positioning precision values are integrated into a positioning precision or repeated positioning precision matrix SP of all the secondary motion layersSM。
5) And mapping the positioning precision or the repeated positioning precision of the secondary motion layer to the meta-action unit layer, wherein a chain structure is considered between the meta-action units. Now with a certain two-stage movement MicFor example, precision mapping is performed, the secondary motion comprises m element action units, and a precision mathematical model is established as follows:
sensitivity is highDegree refers to the ratio of the amount of change in the design output to the design input of a mechanical system in a steady state. Positioning precision or repeated positioning precision P (M) of secondary motionic) As a design output, the precision P (A) of each meta-action unitk) As a design input, then a two-stage motion MicPositioning accuracy or repeated positioning accuracy P (M)ic) Pair element action unit precision P (A)k) Sensitivity Z ofpkComprises the following steps:
and mapping the positioning precision or the repeated positioning precision of the secondary motion layer to the meta-action unit, and adopting a sensitivity-based distribution mode according to the equal action principle. The equal action rule is that when precision distribution is carried out, the positioning precision or repeated positioning precision variation of the two-stage motion and the precision variation of each element action unit satisfy the following relation:
according to the principle of equal action, two-stage motion positioning accuracy or repeated positioning accuracy P (M)ic) Precision P (A) of each element action unitk)、P(Ak+1)、…、P(Ak+m-1) Should satisfy the following relationship:
(ZPkP(Ak))2≈(ZP(k+1)P(Ak+1))2≈…≈(ZP(k+m-1)P(Ak+m-1))2
(P(Mic))2＝(ZPkP(Ak))2+(ZP(k+1)P(Ak+1))2+…+(ZP(k+m-1)P(Ak+m-1))2
so that the positioning accuracy or the repeated positioning accuracy of the secondary motion is mappedThe precision P (A) of each unit action unitk) Must satisfy:
in the formula: p (A)k) For two-stage movement MicThe next kth element action unit precision; p (M)ic) Refers to a two-stage movement MicM represents a secondary motion MicComprises m element action units; pk(Mic) For two-stage movement MicA positioning accuracy or a repeated positioning accuracy component for the kth element action unit; Δ Fk(Mic) For two-stage movement MicA positioning error or a repeated positioning error component for the kth element action unit; zpkSensitivity of secondary motion positioning precision or repeated positioning precision to motion precision of the element action unit; zkThe variation coefficient of the second-level motion positioning error or the repeated positioning error component and the motion error of the element action unit;
the equal sign calculation in the front of the formula obtains the precision P (A) of the element action unitk) Since the actual value cannot be accurately calculated, the value calculated by the equal action principle (hereinafter equal sign) is used as the final mapping value in a scaling manner to obtain the precision value P (A) of the meta-action unitk)。
To obtain a two-stage movement MicLower meta-action unit accuracy matrixAnd then, obtaining the meta-action unit precision matrix under other two-level motion in the same way. The integration is performed, so that an overall meta-action unit layer precision matrix MP can be obtainedMA。
Furthermore, it is necessary to control the precision value of each element action unit, and here, taking the gear rotating element action unit as an example, the precision control measures are as follows:
1. the gear rotating unit action units are assembled in a grouping and matching mode because most of parts obtained by the gear rotating unit action units belong to large-scale and mass-production and have high-precision small ring size.
2. In the design process, the outer circle outline of the gear shaft is selected as the assembly reference for the assembly reference of the gear, and other parts on the shaft can also take the outer circle outline of the gear shaft as the assembly reference.
3. When the gear shaft and the gear are machined, in order to ensure the precision of the gear shaft and the gear, reasonable machining allowances need to be distributed for the gear shaft and the gear.
4. The dimensional tolerances of the parts are reasonably distributed. According to design requirements, a process dimension chain of each part is established, and then, the dimension errors of the parts are reasonably distributed according to the process dimension chain, so that the dimension precision of each part can meet the requirements.
Finally, it should be noted that the above-mentioned embodiments of the present invention are only examples for illustrating the present invention, and are not intended to limit the embodiments of the present invention. Although the present invention has been described in detail with reference to preferred embodiments, it will be apparent to those skilled in the art that other variations and modifications can be made based on the above description. Not all embodiments are exhaustive. All obvious changes and modifications of the present invention are within the scope of the present invention.

Claims (4)

1. A numerical control machine tool precision control method based on precision mapping is characterized in that: the method comprises the steps of firstly obtaining the design precision of the total function of the numerical control machine, then mapping the design precision value of the total function of the numerical control machine layer by layer downwards until the design precision value is mapped to the level of the element action unit, so that the motion precision required by each element action unit is obtained, and finally, the element action units are subjected to precision control to meet the motion precision required by the element action units, so that the precision control of the numerical control machine is realized.
2. The accuracy control method of the numerical control machine tool based on the accuracy mapping according to claim 1, characterized in that: the influence factors of the accuracy of the element action unit comprise the size accuracy, the position accuracy and the assembly accuracy of the element action unit parts; in the design process, starting from the three aspects, corresponding precision control measures are given for different meta-action units.
3. The accuracy control method of the numerical control machine tool based on the accuracy mapping according to claim 1, characterized in that the design accuracy value of the total function is mapped to the meta-action unit by adopting the following steps:
A. carrying out structural decomposition on the numerical control machine according to a 'function-motion-action' mode, decomposing into five levels of a total functional layer, a sub functional layer, a main motion layer, a secondary motion layer and a meta-action unit layer, and establishing a numerical control machine precision waterfall mapping chain model according to a structural decomposition model;
B. extracting design precision value DP of total functional layer of numerical control machine tool according to customer requirementsTFThe accuracy mapping from the total functional layer to the sub functional layers adopts a direct transmission mode, namely the design accuracy values of the sub functions of the sub functional layers are equal to the design accuracy value of the total function, so that the design accuracy matrix of the sub functional layers is DPF＝(DPTF，DPTF，…，DPTF)t；
In the formula: t represents that the numerical control machine tool has t sub-functions;
C. precision mapping of sub-function layers to main motion layers first takes into account the fact that each main motion is relative to a certain sub-function FxThe level of the precision requirement is calculated by adopting a characteristic root method to obtain a certain sub function FxLower dominant motion weight vectorThen divide the sub-function F according to the right distributionxIs mapped to the positioning accuracy or repeated positioning accuracy of the corresponding main motion layerNamely, it is
Obtaining the positioning accuracy or repeated positioning accuracy of the main motion layer under other sub-functions considering the accuracy requirement in the same mode, comparing, and selecting each main motion layer with high accuracy, thereby obtaining the positioning accuracy or repeated positioning accuracy matrix of the main motion layer considering the accuracy requirement
Then considering the complexity of the structure of each main motion part, and calculating by adopting a characteristic root method CRM to obtain a weight vector of a main motion layer considering the complexity of the structure of the part asThen, calculating according to the following formula to obtain a main motion layer positioning precision or repeated positioning precision matrix considering the structural complexity of the component
Finally will beAndcomparing, and obtaining the positioning accuracy or repeated positioning accuracy matrix SP of the main motion layerPM；
D. The precision mapping from the main motion layer to the secondary motion layer considers the complexity of each secondary motion structure, namely the influence of structural coupling between the secondary motions on the mapping process, and a certain main motion M is obtained by adopting a fuzzy analytic hierarchy process and an interval gray system theory to calculateiThe lower two-level motion layer mapping weight vector isThe main movement M is then represented by the following formulaiPositioning accuracy or repeated positioning accuracy ofMapping to obtain the positioning precision or repeated positioning precision of the corresponding secondary motion layer
Then, the same mapping mode is adopted to calculate the positioning precision or repeated positioning precision values of the secondary motion layers under other main motions, and finally, the positioning precision or repeated positioning precision values are integrated into a positioning precision or repeated positioning precision matrix SP of all the secondary motion layersSM；
E. The precision mapping from the secondary motion layer to the element action unit layer considers that each element action unit is of a chain structure, and the precision of each element action unit is calculated by adopting the following formula according to the sensitivity of the secondary motion positioning precision or the repeated positioning precision relative to the precision of each element action unit in the element action chain;
in the formula: p (A)k) For two-stage movement MicThe next kth element action unit precision; p (M)ic) Refers to a two-stage movement MicM represents a secondary motion MicComprises m element action units; pk(Mic) For two-stage movement MicA positioning accuracy or a repeated positioning accuracy component for the kth element action unit; Δ Fk(Mic) For two-stage movement MicA positioning error or a repeated positioning error component for the kth element action unit; zpkFor two-stage movement positioning accuracy or repeated positioning accuracySensitivity to meta-action unit motion accuracy; zkThe variation coefficient of the second-level motion positioning error or the repeated positioning error component and the motion error of the element action unit;
thereby obtaining a certain secondary movement MicPrecision matrix formed by all element action unit precision
Finally, the element action unit precision matrix under all the second-level motionIntegrating to obtain a precision matrix SP consisting of all element action unit precisionsMA。
4. The precision control method of numerical control machine based on precision mapping according to claim 1, wherein the meta-action units are divided into two categories of moving meta-action units and rotating meta-action units, wherein the precision value of the moving meta-action unit is the straightness of the movement of the unit actuator, and the precision value of the rotating meta-action unit is the revolution precision of the unit actuator.
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