CN110597177A - A precision control method for CNC machine tools based on precision mapping - Google Patents

Abstract

The invention discloses a CNC machine tool precision control method based on precision mapping. The design precision value of the general function layer of the CNC machine tool is mapped to the design precision value of the sub-function layer by means of direct transfer; the characteristic root method is used to map the design precision value of the sub-function layer The design accuracy value is mapped to the positioning accuracy or repeat positioning accuracy value of the main motion layer; the positioning accuracy or repeat positioning accuracy value of the main motion layer is mapped to the positioning accuracy or repeat positioning accuracy value of the secondary motion layer by using fuzzy analytic hierarchy process and interval gray system theory Positioning accuracy value; use sensitivity-based precision mapping to map the positioning accuracy or repeat positioning accuracy value of the second-level motion layer to the motion accuracy value of the meta-action unit; then perform precision control at the level of the meta-action unit, and give precision control measures. The invention can design the precision of the meta-action unit on the basis of the known overall precision design requirements of the machine tool, and control the precision at the meta-action layer.

Description

A precision control method for CNC machine tools based on precision mapping

technical field

The invention relates to the improvement of precision control of numerical control machine tools, in particular to a precision control method of numerical control machine tools based on precision mapping, and belongs to the technical field of numerical control machine tools.

Background technique

CNC machine tools are the "working machine" of the equipment manufacturing industry. The technical level and product quality of a country's machine tool industry are important symbols to measure the development level of its equipment manufacturing industry. After more than 30 years of development, although domestic CNC machine tools have made some progress, in terms of machining accuracy, the machining accuracy of domestic CNC machine tools is often an order of magnitude worse than that of foreign products. Low precision will not only affect the quality of processed parts , and will affect some properties of the CNC machine tool itself, so it is necessary to control the accuracy of the CNC machine tool.

At present, the machining accuracy control methods of CNC machine tools are mainly divided into the following five types: 1. The control of the error of the CNC machine tool itself; 2. The control of the machining process error of the CNC machine tool; 3. The control of the positioning error of the CNC machine tool; The thermal deformation of the process system affects the control of the machining accuracy; 5. The control of the resonance of the stepper motor and the CNC machine tool affects the machining accuracy. Most of these machining accuracy control methods are controlled during the manufacturing and use stages of the machine tool. The accuracy is not controlled during the design process of the machine tool. It belongs to a post-event control method and cannot control the accuracy of the CNC machine tool from the source. .

Contents of the invention

In view of the fact that the existing CNC machine tool precision control method is mainly an after-the-fact control method, and there is no shortage of controlling the CNC machine tool precision from the source, the purpose of this invention is to propose a CNC machine tool precision control method based on precision mapping. The design stage is to control the precision of CNC machine tools, so as to achieve the purpose of controlling the precision of CNC machine tools from the source, so as to achieve better precision control.

Technical scheme of the present invention is realized like this:

A precision control method for CNC machine tools based on precision mapping. Firstly, the design precision of the general function of the CNC machine tool is obtained, and then the design precision value of the general function of the CNC machine tool is mapped down layer by layer until it is mapped to the level of the meta-action unit, so that each The motion precision required by the meta-action unit, and finally the precision control of the meta-action unit is carried out to meet the required motion precision, so as to realize the precision control of the CNC machine tool.

Among them, the factors affecting the accuracy of the meta-action unit include the dimensional accuracy, position accuracy and assembly accuracy of the parts of the meta-action unit; in the design process, starting from these three aspects, the corresponding precision control measures are given for different meta-action units. Can.

Specifically, the present invention uses the following steps to map the design accuracy value of the total function to the meta-action unit:

A. Structurally decompose the CNC machine tool according to the "function-movement-action" mode, and decompose it into five levels: total function layer, sub-function layer, main motion layer, secondary motion layer and meta-action unit layer, according to the structural decomposition The model establishes the precision waterfall mapping chain model of CNC machine tools;

B. Extract the design accuracy value DP _TF of the general function layer of the CNC machine tool according to customer needs, and the precision mapping from the total function layer to the sub-function layer adopts the method of direct transfer, that is, the design accuracy value of each sub-function in the sub-function layer is equal to the total function Design precision value, thus obtain the design precision matrix of sub-functional layer as DP _F = (DP _TF , DP _TF ,..., DP _TF ) _t ;

In the formula: t means that the CNC machine tool has t sub-functions;

C. The accuracy mapping from the sub-function layer to the main motion layer first considers the accuracy requirements of each main motion relative to a certain sub-function F _x , and uses the characteristic root method to calculate the main motion weight vector under a certain sub-function F _x Then map the design accuracy value of the sub-function _Fx to the positioning accuracy or repeat positioning accuracy of the corresponding main motion layer according to the weight distribution which is

Use the same method to obtain the positioning accuracy or repeat positioning accuracy of the main motion layer under other sub-functions considering the accuracy requirements, and then compare them. Each main motion layer is selected with high precision, so as to obtain the positioning accuracy of the main motion layer considering the accuracy requirements or repeat positioning accuracy matrix

Then, considering the complexity of the structure of each main moving part, the weight vector of the main moving layer considering the complexity of the part structure is calculated by using the characteristic root method CRM as Then calculate according to the following formula to obtain the main motion layer positioning accuracy or repeat positioning accuracy matrix considering the complexity of the component structure

Finally will and For comparison, each main motion layer selects the one with high precision requirements, so as to obtain the positioning accuracy or repeat positioning accuracy matrix SP _PM of the main motion layer;

D. The precision mapping from the main motion layer to the secondary motion layer considers the complexity of each secondary motion structure, that is, the influence of the structural coupling between the secondary motions on the mapping process, and is calculated by fuzzy analytic hierarchy process and interval gray system theory The weight vector of secondary motion layer mapping under a certain main motion M _i is Then the positioning accuracy or repeat positioning accuracy of the main motion M _i is determined by the following formula Mapping to obtain the positioning accuracy or repeat positioning accuracy of the corresponding secondary motion layer

Then use the same mapping method to calculate the positioning accuracy or repeat positioning accuracy values of the secondary motion layers under other main motions, and finally integrate them into the positioning accuracy or repeat positioning accuracy matrix SP _SM of all secondary motion layers;

E. The accuracy mapping from the second-level motion layer to the meta-action unit layer. Considering that there is a chain structure between the meta-action units, according to the accuracy of the second-level motion positioning accuracy or repeat positioning accuracy relative to the accuracy of each meta-action unit in the meta-action chain The sensitivity of each element action unit is calculated by the following formula;

In the formula: P(A _k ) is the accuracy of the kth meta-action unit under the secondary motion M _ic ; P(M _ic ) refers to the precision value of the secondary motion M _ic , and m means that the secondary motion M _ic includes m meta-action unit; P ^k (M _ic ) is the positioning accuracy or repeatability component of the second-level motion M _ic for the k-th meta-action unit; ΔF ^k (M _ic ) is the k-th meta-action for the second-level motion M _ic The positioning error or repetitive positioning error component of the unit; Z _pk is the sensitivity of the secondary motion positioning accuracy or repetitive positioning accuracy to the motion accuracy of the meta-action unit; Z _k is the secondary motion positioning error or repetitive positioning error component and the motion error of the meta-action unit coefficient of variation;

In this way, the precision matrix formed by the precision of all meta-action units under a certain level-2 motion M _ic can be obtained

Finally, the meta-action unit precision matrix under all secondary motions After the integration, the precision matrix SP _MA formed by the precision of all meta-action units is obtained.

The unit action unit of the present invention is divided into two categories: the moving unit action unit and the rotation unit action unit. The precision of the movement unit action unit is the straightness of the movement of the unit actuator, and the precision value of the rotation unit action unit is the rotation accuracy of the unit execution unit. .

Compared with the prior art, the present invention has the following beneficial effects:

In the design stage, the present invention controls the precision of the CNC machine tool. On the basis of the known overall precision design requirements of the machine tool, through layer-by-layer decomposition, the precision of the element action unit is finally deduced, and this precision value is used as the actual control target, and Take corresponding control measures to ensure the precision value of the element action unit, so as to achieve the purpose of controlling the precision of CNC machine tools from the source and achieve better precision control.

Description of drawings

Fig. 1 is a flow chart of the implementation of the accuracy control method of the CNC machine tool based on the accuracy mapping in the present invention.

Figure 2 is the FMA structured decomposition model of the CNC machine tool.

Fig. 3 is the cascade mapping chain model of CNC machine tool precision.

Figure 4 shows the quantitative model of mapping coupling to structure hierarchy.

FIG. 5 is a function graph of four whitening weight functions.

In Figure 3, TF-total functional layer; F-sub-functional layer; PM-main motor layer; SM-secondary motor layer; MA-meta-action unit layer; DP _TF -total function design accuracy; DP _F -divided function design Precision Matrix; SP _PM - Primary Motion Positioning Accuracy or Repeatability Matrix; SP _SM - Secondary Motion Positioning Accuracy or Repeatability Matrix; MP _MA - Metamotion Motion Precision Matrix.

Detailed ways

The precision control method of CNC machine tools based on precision mapping in the present invention has the general idea as follows: first obtain the design precision of the general function of the CNC machine tool, and then map the design precision value of the general function of the CNC machine tool down layer by layer until it is mapped to where the element action unit is located. Level, so as to obtain the motion accuracy required by each element action unit, and finally perform precision control on the element action unit to meet the required motion accuracy, thereby realizing the precision control of the CNC machine tool.

The present invention specifically adopts the following steps to map the design accuracy value of the total function to the meta-action unit, and the implementation process can be referred to in FIG. 1 .

A. Structurally decompose the CNC machine tool according to the "Function-Motion-Action" (Function-Motion-Action, FMA) model, and decompose it into the total functional layer, sub-functional layer, main motion layer, secondary motion layer and meta-action unit There are five layers. Figure 2 is a schematic diagram of the FMA structural decomposition model of CNC machine tools. According to the FMA structured decomposition model, the precision waterfall mapping chain model of CNC machine tools is established; Figure 3 is a schematic diagram of the precision waterfall mapping chain model of CNC machine tools; Table 1 is the precision waterfall mapping Description of the accuracy indicators of each layer of the chain model;

Table 1 Description of the precision indicators of each layer of the precision waterfall mapping chain model

B. Extract the design accuracy value DP _TF of the general function layer of the CNC machine tool according to customer needs, and the precision mapping from the total function layer to the sub-function layer adopts the method of direct transfer, that is, the design accuracy value of each sub-function in the sub-function layer is equal to the total function Design precision value, thus obtain the design precision matrix of sub-functional layer as DP _F = (DP _TF , DP _TF ,..., DP _TF ) _t ;

In the formula: t represents t sub-functions of the CNC machine tool;

C. The accuracy mapping from the sub-function layer to the main motion layer first considers the accuracy requirements of each main motion relative to a certain sub-function F _x , and uses the characteristic root method (Characteristic Root Method, CRM) to calculate the accuracy under a certain sub-function F _x main motion weight vector Then map the design accuracy value of the sub-function _Fx to the positioning accuracy or repeat positioning accuracy of the corresponding main motion layer according to the weight distribution which is

Use the same method to obtain the positioning accuracy or repeat positioning accuracy of the main motion layer under other sub-functions considering the accuracy requirements, and then compare them. Each main motion layer is selected with high precision, so as to obtain the positioning accuracy of the main motion layer considering the accuracy requirements or repeat positioning accuracy matrix

Then, considering the complexity of the structure of each main moving part, the weight vector of the main moving layer considering the complexity of the part structure is calculated by using the characteristic root method CRM as Then calculate according to the following formula to obtain the main motion layer positioning accuracy or repeat positioning accuracy matrix considering the complexity of the component structure

Finally will and For comparison, each main motion layer selects the one with high precision requirements, so as to obtain the positioning accuracy or repeat positioning accuracy matrix SP _PM of the main motion layer;

D. The precision mapping from the main motion layer to the secondary motion layer considers the complexity of each secondary motion structure, that is, the influence of the structural coupling between the secondary motions on the mapping process, and adopts Fuzzy Analytic Hierarchy Process (FAHP) and the interval gray system theory (Interval Gray System Theory, IGST) to calculate the secondary motion layer mapping weight vector under a certain main motion M _i is Then the positioning accuracy or repeat positioning accuracy of the main motion M _i can be obtained by the following formula Mapping to obtain the positioning accuracy or repeat positioning accuracy of the corresponding secondary motion layer

Then use the same mapping method to calculate the positioning accuracy or repeat positioning accuracy values of the secondary motion layers under other main motions, and finally integrate them into the positioning accuracy or repeat positioning accuracy matrix SP _SM of all secondary motion layers;

E. The accuracy mapping from the second-level motion layer to the meta-action unit layer. Considering that there is a chain structure between the meta-action units, according to the accuracy of the second-level motion positioning accuracy or repeat positioning accuracy relative to the accuracy of each meta-action unit in the meta-action chain The sensitivity of each element action unit is calculated by the following formula;

In the formula: P(A _k ) is the accuracy of the kth meta-action unit under the secondary motion M _ic ; P(M _ic ) refers to the precision value of the secondary motion M _ic , and m means that the secondary motion M _ic includes m meta-action unit; P ^k (M _ic ) is the positioning accuracy or repeatability component of the second-level motion M _ic for the k-th meta-action unit; ΔF ^k (M _ic ) is the k-th meta-action for the second-level motion M _ic The positioning error or repetitive positioning error component of the unit; Z _pk is the sensitivity of the secondary motion positioning accuracy or repetitive positioning accuracy to the motion accuracy of the meta-action unit; Z _k is the secondary motion positioning error or repetitive positioning error component and the motion error of the meta-action unit coefficient of variation;

In this way, the precision matrix formed by the precision of all meta-action units under a certain level-2 motion M _ic can be obtained

Finally, the meta-action unit precision matrix under all secondary motions After the integration, the precision matrix MP _MA formed by the precision of all meta-action units is obtained.

Through the mapping of the above four steps, the design accuracy of the whole machine can be mapped to the meta-action unit layer, and the design input of the meta-action unit can be obtained, so as to establish the mapping mechanism of the whole machine precision.

The meta-action unit is divided into two categories: the mobile meta-action unit and the rotational meta-action unit. The precision of the mobile meta-action unit is the straightness of the motion of the unit actuator, and the precision of the rotational meta-action unit is the rotation accuracy of the unit actuator. Whether it is moving or rotating, the accuracy of the unit actuator is jointly guaranteed by the dimensional accuracy, position accuracy and assembly accuracy of the component parts. In the design process, starting from these three aspects, for different meta-action units, given Different precision control measures.

The main precision control measures of the meta-action unit are:

1. Select the appropriate assembly method according to the assembly characteristics. Different meta-action units have different component parts and different assembly characteristics, resulting in different assembly methods. Therefore, it is necessary to choose an appropriate assembly method according to the assembly characteristics.

2. Select the appropriate assembly benchmark. In the design process, the accuracy of the actuators of the meta-action unit is different when different assembly datums are selected, so an appropriate assembly datum should be selected to minimize the assembly error of the meta-action unit.

3. Design a reasonable machining allowance. In order to ensure that the dimensional accuracy of each component part can meet the requirements, it is necessary to allocate a reasonable machining allowance to each part according to the processing method and material of the part.

4. Reasonably allocate the dimensional tolerances of each part. According to the design requirements, the process size chain of each part is established, and then the dimensional errors of the parts are reasonably distributed according to the process size chain, so as to ensure that the dimensional accuracy of each part can meet the requirements.

The present invention is divided into two processes of precision mapping and precision control.

The precision mapping process is to map the design precision of the CNC machine tool to the meta-action unit according to the precision waterfall mapping chain model. The whole mapping process is divided into four steps:

Mapping of TF-F layers. The design accuracy value of the overall function is reflected to the sub-function layer by direct transfer, which is beneficial to decompose the design target of the accuracy of the whole machine, so as to obtain the design accuracy value of each sub-function;

Mapping of the F-P layer. The design accuracy value of each sub-function is mapped to the main motion layer in the way of characteristic root. In the whole mapping process, the situation of sharing the main motion among the sub-functions and the complexity of the structure of each main moving part are considered. Taking into account two factors can make the mapping results more accurate;

Mapping of the P-S layer. Using fuzzy analytic hierarchy process and interval gray system theory to map the positioning accuracy or repeated positioning accuracy of the main motion layer to the secondary motion layer, the complexity of the secondary motion structure is considered in the mapping process (that is, the structure between the secondary motion Coupling relationship), the coupling relationship is used as the influencing factor of the mapping weight, so as to indirectly achieve the effect of eliminating the influence of the coupling relationship on the mapping process;

S-A layer mapping. The positioning accuracy or repetitive positioning accuracy of the secondary motion is mapped to the meta-action unit by using the principle of sensitivity distribution and equal action. During the mapping process, it is considered that there is a chain structure between the meta-action units. Using the above method for mapping can eliminate The impact of this chain structure on precision mapping makes the mapping result more accurate.

The precision control process is mainly to control the precision of the meta-action unit based on the design precision value obtained from the previous mapping, so as to ensure that the precision value of the meta-action unit can be maintained in a qualified range within the entire life cycle of the product. Through control, If the precision values of all meta-action units are guaranteed, then the precision of the whole machine can be well guaranteed. This precision control method can control the precision of the CNC machine tool from the source, reducing the number of maintenance after the event, so as to improve the quality and reliability of the CNC machine tool.

In order to better understand the present invention, the following takes THM6380 machining center as the control object to carry out precision control according to the control method of the present invention, and the specific process is as follows.

1) FMA structural decomposition of THM6380, the machining center has 6 sub-functions of drilling F ₁ , boring F ₂ , reaming F ₃ , tapping F ₄ , milling F ₅ and contour roughing and finishing F ₆ . The milling function _F5 is taken as an example to establish the FMA structured decomposition model, and the accuracy waterfall mapping chain model of the machining center is established according to the FMA structured decomposition model.

2) The total functional design accuracy value DP _TF of the machining center extracted from the customer's requirements is directly transferred to obtain the design accuracy matrix DP _F = (DP _TF , DP _TF , DP _TF , DP _TF , DP _TF , DP _TF ).

3) Consider the case where the main motion is shared between sub-functions. Taking the milling function F ₅ as an example, the main motion layer mapping weight under F ₅ is calculated by using CRM Since it is common for CRM to determine weights, details will not be repeated here. Get the weight vector of the main motion layer under F ₅ considering the shared main motion After that, the design accuracy value of sub-function F ₅ can be mapped to the main motion layer:

In the formula: DP _TF is the design accuracy value of sub-function F ₅ , It is the positioning accuracy or repeat positioning accuracy matrix of the main motion layer under F ₅ considering the common main motion.

In the same way, the positioning accuracy or repetitive positioning accuracy matrix of the main motion layer under other sub-functions can be obtained, and then compared, and the high-precision one is selected, so as to obtain the positioning accuracy or repetitive positioning accuracy of the main motor layer considering the sharing of the main motion by the sub-functions matrix

Consider the complexity of the structure of each main moving part. At this time, the overall consideration does not need to be specific to a certain sub-function. The weight vector of the main motion layer considering the complexity of the component structure is calculated by using CRM as In this way, the positioning accuracy or repeat positioning accuracy vector of the main motion layer is calculated considering the complexity of the component structure

In the formula: DP _F is the design accuracy value matrix of the functional layer.

Comparing the accuracy values of the main motions in these two cases, select the one with high accuracy requirements, and finally obtain the positioning accuracy or repeat positioning accuracy matrix SP _PM of the main motion layer.

4) Map the positioning accuracy or repetitive positioning accuracy of the main motion layer to the secondary motion layer, considering the complexity of the secondary motion structure (that is, the structural coupling relationship). The whole mapping process is divided into two steps:

a. Calculation of structural coupling degree based on FAHP. Assuming that there are m pairs of mapping coupling pairs for a certain main motion M _i , then the set of mapping coupling pairs is in refers to the m- _th mapped coupling pair of the main motion Mi. The process of quantifying mapping coupled pairs using FAHP is as follows:

① Establish a quantitative model of mapping coupling pair hierarchy. For the evaluation of mapping coupled pairs, the established criterion layer includes H indicators, such as coupling tightness, coupling degree, coupling stability and coupling reliability, etc., so the index set U={u ₁ , u ₂ , u ₃ ,...u _h }, where u _h refers to the hth quantitative index. There are a total of W experts in the quantization process, all expert sets V={v ₁ , v ₂ , v ₃ ,...v _w }, where v _w refers to the wth expert. The established mapping coupling pair hierarchy quantization model is shown in Figure 4.

②Establish the language scale of FAHP quantization matrix. For these established indicators, the higher the better, so the language scale of the quantization matrix is divided into 9 levels according to the 1-9 scale method, and the specific fuzzy value distribution is shown in Table 2.

③Establish and synthesize the expert quantitative matrix. Let expert v _y think that the mapping coupled pair The value corresponding to the degree of meeting the requirements of h indicators is expressed as follows: in It is a triangular fuzzy number (x=1,2...M; y=1,2...W; j=1,2...H), calculated by using intuitionistic fuzzy entropy

Table 2 Fuzzy AHP Quantification Matrix Linguistic Scale

Expert weight G=(G ₁ , G ₂ ,...,G _w ), where G _w refers to the weight of the wth expert, and its triangular fuzzy weighted average formula is:

In the formula: LT _xhy refers to the yth expert thinks that the mapping coupling pair Corresponding to the first value of the degree value triangular fuzzy number that meets the requirements of the h-th index, MT _xhy and UT _xhy are the second and third values respectively.

Thus, the expert comprehensive quantification matrix is calculated as:

In the formula: is the triangular fuzzy value after weighted average.

④Perform hierarchical single sorting to obtain the value of the mapping coupling pair. According to the expert quantification matrix, the value of the comprehensive importance of mapping coupling pair b _x ⁱ corresponding to H indicators is:

In the formula: S _x is the comprehensive importance value.

Two triangular fuzzy numbers M ₁ =(l ₁ ,m ₁ ,μ ₁ ) and M ₂ =(l ₂ ,m ₂ ,μ ₂ ), the degree of possibility of M ₂ ≥M ₁ is:

If (x,y) exists, and x>y, Then there is V(M ₂ ≥M ₁ )=1, where M ₁ and M ₂ are convex functions, and the formula is expressed as follows

The probability that a convex fuzzy number is larger than the other k convex fuzzy numbers M _i (i=1,2,...,k) is

V(M≥M ₁ , M ₂ ,...,M _k )=V(M≥M ₁ )∪V(M≥M ₂ )∪V(M≥M ₃ )...V(M≥M _k )=minV( M≥M _i )

Suppose d'(A _x )=minV(S _x ≥S _k ), k=1,2,...,M; k≠i, S _x is the comprehensive importance value, A _x represents the xth mapping coupling pair, then The magnitude of each mapping coupling pair is W'=(d'(A ₁ ), d'(A ₂ ),...,d'(A _m )) ^T , after normalization, the magnitude of the final mapping coupling pair W=(d'(A ₁ ), d'(A ₂ ),...,d'(A _m )) ^T , that is, the mapping coupling degree The mapping coupling degree is the structural coupling degree η between the two secondary motions.

b. IGST-based mapping weight calculation. In order to calculate the mapping weight of each secondary motion M _ic under the main motion M _i , the structural coupling relationship is used as the influencing factor of the mapping weight, and the coupling of the cth secondary motion mapping weight influencing factor is calculated by the obtained coupling degree η Weights

In the formula: refers to the coupling weight of the kth influencing factor of the cth secondary movement, Refers to the coupling degree of the kth influencing factor of the cth secondary motion.

In order to avoid the situation where the mapping weight is zero, the entropy weight method is used to correct the coupling weight, and the calculation process is as follows:

In the formula: d _ck is the judgment value of the c-th secondary motion under the k-th influencing factor; f _ck is the proportion of the k-th influencing factor of the c-th secondary motion; H _k is the entropy of the k-th influencing factor value.

According to the above formula, the correction value entropy weight β _k of each mapping weight influencing factor can be obtained:

In the formula: K is the total number of the cth secondary sports influencing factors;

Then the weight of the final mapping weight influencing factor is:

In the formula: is the weight of the kth influencing factor of the cth secondary movement, is the correction value entropy weight of the kth influencing factor of the cth secondary motion.

Let the evaluation matrix of the influence factors of the l-th expert on the c-th secondary motion mapping weight The coupling relationship will have an impact on the mapping weight, and the gray class set to which the evaluation influence degree belongs is recorded as X={x ₁ , x ₂ ,…, x _h }, and this influence degree is divided into four types, namely high, relatively high, Average and low, ie h=4, X={x ₁ , x ₂ , x ₃ , x ₄ }={high, higher, average, low}. Combined with IGST, you can find Weights belonging to class s s=1~4, the method adopted is the whitening weight function. Figures 5(a) and 5(b) are the function diagrams of four whitening weight functions. In the figure, P is the lower limit of the first category, G is the middle limit of the second category, Q is the middle limit of the third category, and Z is the fourth category upper limit, and let {P, G, Q, Z}={9, 7, 5, 2}, the calculation formulas of various whitening weight functions can be obtained from the figure.

① gray number Its calculation formula is:

In the formula: is the evaluation value of the kth influencing factor of the cth secondary motion mapping weight by the lth expert; for The weights belonging to the sth class.

② gray number Its calculation formula is:

③ gray number Its calculation formula is:

④ gray number Its calculation formula is:

get The weight of the sth gray class Finally, the gray statistics n _cs and the total gray statistics n _c of the judgment matrix can be obtained;

Based on the evaluation values of L experts for each secondary movement, for the c-th secondary movement, the mapping weight influencing factor k belongs to the s-th gray class evaluation weight is Thus, the gray evaluation matrix of the cth secondary motion can be obtained as:

After the gray evaluation matrix R ^(c) of the c-th secondary motion and the weight vector β ^(c) of the mapping weight influencing factors are determined, the comprehensive gray evaluation value of the c-th secondary motion can be obtained:

Z ^(c) = w ^(c) R ^(c) D ^T

In the formula: Z ^(c) is the comprehensive gray evaluation value of the cth two-level movement, D ^T is the value corresponding to the four-level evaluation method, D={P, G, Q, Z}={9, 7, 5, 2}, w ^(c) is the weight vector of the cth secondary motion influencing factor.

In the same way, the comprehensive gray evaluation value of other secondary motions under the main motion M _i can be obtained, then the mapping weight of each secondary motion is

In the formula The weight value of the _cth secondary motion under the main motion Mi.

Thus, the weight vector of the secondary motion layer mapping under the main motion M _i can be obtained as Map the positioning accuracy or repeated positioning accuracy of the main motion _Mi to the secondary motion motion layer according to the weight distribution:

In the formula: The positioning accuracy or repeatability matrix of the secondary motion layer under the main motion M _i , The positioning accuracy or repeat positioning accuracy value of the main motion M _i .

Then use the same mapping method to calculate the positioning accuracy or repeat positioning accuracy values of the secondary motion layers under other main motions, and finally integrate them into the positioning accuracy or repeat positioning accuracy matrix SP _SM of all secondary motion layers.

5) Map the positioning accuracy or repetitive positioning accuracy of the second-level motion layer to the meta-action unit layer, considering that there is a chain structure between the meta-action units. Now take a certain secondary motion M _ic as an example to perform precision mapping. The secondary motion includes m meta-action units, and the mathematical model of precision is established as follows:

Sensitivity refers to the ratio of the change in the design output of the system to the design input in a stable state of the mechanical system. Taking the secondary motion positioning accuracy or repetitive positioning accuracy P(M _ic ) as the design output, and the accuracy P(A _k ) of each element action unit as the design input, then the positioning accuracy or repetitive positioning accuracy of the secondary motion M _ic P(M _ic ) The sensitivity Z _pk to the precision P(A _k ) of the meta-action unit is:

Map the positioning accuracy or repetitive positioning accuracy of the second-level motor layer to the meta-action unit, and adopt a sensitivity-based allocation method according to the principle of equal action. The principle of equal action is to make the positioning accuracy or repeat positioning accuracy variation of the secondary motion and the accuracy variation of each element action unit satisfy the following relationship when performing precision allocation:

According to the principle of equal action, the secondary motion positioning accuracy or repeat positioning accuracy P(M _ic ) is related to the accuracy of each element action unit P(A _k ), P(A _k+1 ),...,P(A _k+m-1 ) should satisfy the following relationship:

(Z _Pk P(A _k )) ² ≈(Z _P(k+1) P(A _k+1 )) ² ≈…≈(Z _P(k+m-1) P(A _k+m-1 ) ) ²

(P(M _ic )) ² ＝(Z _Pk P(A _k )) ² +(Z _P(k+1) P(A _k+1 )) ² +…+(Z _P(k+m-1) P(A _k+m-1 )) ²

Therefore, when mapping the positioning accuracy or repetitive positioning accuracy of the secondary motion, the accuracy P(A _k ) of each element action unit must satisfy:

In the formula: P(A _k ) is the accuracy of the kth meta-action unit under the secondary motion M _ic ; P(M _ic ) refers to the precision value of the secondary motion M _ic , and m means that the secondary motion M _ic includes m meta-action unit; P ^k (M _ic ) is the positioning accuracy or repeatability component of the second-level motion M _ic for the k-th meta-action unit; ΔF ^k (M _ic ) is the k-th meta-action for the second-level motion M _ic The positioning error or repetitive positioning error component of the unit; Z _pk is the sensitivity of the secondary motion positioning accuracy or repetitive positioning accuracy to the motion accuracy of the meta-action unit; Z _k is the secondary motion positioning error or repetitive positioning error component and the motion error of the meta-action unit coefficient of variation;

The calculation of the equal sign in front of the formula is the actual value of the precision P(A _k ) of the meta-action unit, because the actual value cannot be accurately calculated, so the scaling method is adopted, and the value calculated according to the principle of equal action (the equal sign behind) is used as The final mapping value, thereby obtaining the precision value P(A _k ) of the meta-action unit.

Get the meta-action unit precision matrix under the second-level motion M _ic After that, the precision matrix of meta-action units under other secondary motions can be obtained in the same way. Integration is performed so that the overall meta-action unit layer precision matrix MP _MA can be obtained.

Further, it is necessary to control the precision value of each meta-action unit. Here, taking the gear rotation meta-action unit as an example, the precision control measures are as follows:

1. Because most of the parts of the gear rotation unit are mass-produced and high-precision with less ring size, the unit is assembled by group selection.

2. In the process of design, the outer circular contour 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 use the external circular contour of the gear shaft as the assembly reference.

3. When machining the gear shaft and gear, in order to ensure the accuracy of the two, it is necessary to allocate a reasonable machining allowance for the two.

4. Reasonably allocate the dimensional tolerances of each part. According to the design requirements, the process size chain of each part is established, and then the dimensional errors of the parts are reasonably distributed according to the process size chain, so as to ensure that the dimensional accuracy 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, rather than limiting the implementation of the present invention. Although the applicant has described the present invention in detail with reference to preferred embodiments, those skilled in the art can make other changes and changes in different forms on the basis of the above description. All the implementation manners cannot be exhaustively listed here. All obvious changes or changes derived from the technical solutions of the present invention are still within the protection scope of the present invention.

Claims (4)

1. A precision control method for CNC machine tools based on precision mapping, characterized in that: first obtain the design accuracy of the total function of the CNC machine tool, and then map the design precision value of the total function of the CNC machine tool down layer by layer until mapped to the meta-action unit In order to obtain the motion accuracy required by each element action unit, and finally perform precision control on the element action unit to meet the required motion accuracy, so as to realize the precision control of the CNC machine tool. 2. the CNC machine tool precision control method based on precision mapping according to claim 1, is characterized in that: element action unit precision influence factor comprises the dimensional accuracy of element action unit part, positional accuracy and assembly precision; In design process, from Starting from these three aspects, it is enough to give corresponding precision control measures for different meta-action units. 3. the numerical control machine tool accuracy control method based on accuracy mapping according to claim 1, is characterized in that, adopts the following steps to map the design accuracy value of total function to the element action unit: A. Structurally decompose the CNC machine tool according to the "function-movement-action" mode, and decompose it into five levels: total function layer, sub-function layer, main motion layer, secondary motion layer and meta-action unit layer, according to the structural decomposition The model establishes the precision waterfall mapping chain model of CNC machine tools; B. Extract the design accuracy value DP _TF of the general function layer of the CNC machine tool according to customer needs, and the precision mapping from the total function layer to the sub-function layer adopts the method of direct transfer, that is, the design accuracy value of each sub-function in the sub-function layer is equal to the total function Design precision value, thus obtain the design precision matrix of sub-functional layer as DP _F = (DP _TF , DP _TF ,..., DP _TF ) _t ; In the formula: t means that the CNC machine tool has t sub-functions; C. The accuracy mapping from the sub-function layer to the main motion layer first considers the accuracy requirements of each main motion relative to a certain sub-function F _x , and uses the characteristic root method to calculate the main motion weight vector under a certain sub-function F _x Then map the design accuracy value of the sub-function _Fx to the positioning accuracy or repeat positioning accuracy of the corresponding main motion layer according to the weight distribution which is Use the same method to obtain the positioning accuracy or repeat positioning accuracy of the main motion layer under other sub-functions considering the accuracy requirements, and then compare them. Each main motion layer is selected with high precision, so as to obtain the positioning accuracy of the main motion layer considering the accuracy requirements or repeat positioning accuracy matrix Then, considering the complexity of the structure of each main moving part, the weight vector of the main moving layer considering the complexity of the part structure is calculated by using the characteristic root method CRM as Then calculate according to the following formula to obtain the main motion layer positioning accuracy or repeat positioning accuracy matrix considering the complexity of the component structure Finally will and For comparison, each main motion layer selects the one with high precision requirements, so as to obtain the positioning accuracy or repeat positioning accuracy matrix SP _PM of the main motion layer; D. The precision mapping from the main motion layer to the secondary motion layer considers the complexity of each secondary motion structure, that is, the influence of the structural coupling between the secondary motions on the mapping process, and is calculated by fuzzy analytic hierarchy process and interval gray system theory The weight vector of secondary motion layer mapping under a certain main motion M _i is Then the positioning accuracy or repeat positioning accuracy of the main motion _Mi is determined by the following formula Mapping to obtain the positioning accuracy or repeat positioning accuracy of the corresponding secondary motion layer Then use the same mapping method to calculate the positioning accuracy or repeat positioning accuracy values of the secondary motion layers under other main motions, and finally integrate them into the positioning accuracy or repeat positioning accuracy matrix SP _SM of all secondary motion layers; E. The accuracy mapping from the second-level motion layer to the meta-action unit layer. Considering that there is a chain structure between the meta-action units, according to the accuracy of the second-level motion positioning accuracy or repeat positioning accuracy relative to the accuracy of each meta-action unit in the meta-action chain The sensitivity of each element action unit is calculated by the following formula; In the formula: P(A _k ) is the accuracy of the kth meta-action unit under the secondary motion M _ic ; P(M _ic ) refers to the precision value of the secondary motion M _ic , and m means that the secondary motion M _ic includes m meta-action unit; P ^k (M _ic ) is the positioning accuracy or repeatability component of the second-level motion M _ic for the k-th meta-action unit; ΔF ^k (M _ic ) is the k-th meta-action for the second-level motion M _ic The positioning error or repetitive positioning error component of the unit; Z _pk is the sensitivity of the secondary motion positioning accuracy or repetitive positioning accuracy to the motion accuracy of the meta-action unit; Z _k is the secondary motion positioning error or repetitive positioning error component and the motion error of the meta-action unit coefficient of variation; In this way, the precision matrix formed by the precision of all meta-action units under a certain level-2 motion M _ic can be obtained Finally, the meta-action unit precision matrix under all secondary motions After the integration, the precision matrix SP _MA formed by the precision of all meta-action units is obtained. 4. The precision control method for CNC machine tools based on precision mapping according to claim 1, characterized in that, the element action unit is divided into two categories, the movement element action unit and the rotation element action unit, wherein the precision value of the movement element action unit is The straightness of the movement of the unit actuator, the precision of the rotary element action unit is the rotation accuracy of the unit actuator.