Comprehensive performance evaluation method for CNC machine tools based on improved pull-off grade method

Abstract

A comprehensive performance evaluation method for the CNC machine tools based on an improved pull-off method belongs to the technical field of performance evaluation of CNC machine tools. A linear proportional method is used to standardize the performance index data of machine tool. The entropy weight method and mean variance method are used to determine the two objective weights of each level of indicator. Based on the principle of vector A comprehensive evaluation of three-level index is obtained from the linear weighted evaluation function. Finally, a similar method was used to calculate the comprehensive evaluation of a large system layer by layer. The present invention is used for the comprehensive performance evaluation of various CNC machine tools and also for a lateral comparison of specific performance of different machine tools, providing a scientific and possible evaluation method and process for the comprehensive performance evaluation of machine tools.

Claims

1. A comprehensive performance evaluation for CNC machine tools based on improved pull-off grade method, wherein the steps are as follows: (I) establishment of a key performance index system for CNC machine tools the key performance indicators of CNC machine tools are summarized as four aspects: accuracy, efficiency, reliability, and energy consumption; effect of different factors on the comprehensive performance of CNC machine tools is quite different; types of indicators are divided, and subordinate relationships are analyzed; multilevel indicator sets are established, and an evaluation system is built step by step; the key performance indicators of CNC machine tools, the following classification is made: a first level: accuracy, efficiency, reliability, and energy consumption of CNC machine tools; a second level: three sublevel indicators of geometric error, thermal error, and composite motion error, and specific indicators of an other three first-level indicators; when a machine tool works in a usual manner, an error forms and sizes in different axial directions and planes are different; therefore, a supplementary classification is as follows; a third level: the second level of accuracy indicators are reflected in the errors of different axes and planes, including X-axis geometric error, perpendicularity error, X-feed axis thermal error, and X-Y plane roundness error; a form and size of deviation of relative ideal position of the machine tool moving parts along different axes are different; therefore, the three-level index of geometric error can be classified as follows: a fourth level: three movement errors and rotation angle errors of each axis and a perpendicularity error among the three axes; an affiliation relationship between the evaluation indicators at all levels is determined; according to a general process of multilevel comprehensive evaluation, the key performance index system of CNC machine tools with four-level structure is finally determined; (II) obtaining raw data for evaluation indicators the machine tool performance data are obtained using a laser interferometer, ball bar apparatus, and other devices; n performance indexes of m CNC machine tools are evaluated, and the original data matrix of mn order evaluation index is constructed; (III) evaluation index pretreatment first, all the indicators are unified into a maximal type, and linear proportional method m.sub.j, which can make a difference of evaluation values larger, a stability optimal, and retain an information about data variation to the maximum, is selected as a dimensionless method: $\begin{array}{cc}{x}_{\mathrm{ij}}^{*}=\frac{x_{\mathrm{ij}}}{x_j^{}}& \left(1\right)\end{array}$ where x.sub.j is taken as a minimum value of j-th evaluation index in a sample to be evaluated; (IV) order relationship analysis method to determine subjective weight {circle around (1)} determine the order relationship first, select the index with a highest importance of evaluation target in the original evaluation index set as x.sub.1 and then continue to screen in the remaining m1 indicators; based on this principle, an order relationship of evaluation indicator set is finally determined:
x.sub.1>x.sub.2> . . . >x.sub.m(2) {circle around (2)} evaluate an importance degree of adjacent indicators let a rational judgment of a ratio of importance degree between the adjacent evaluation indicators x.sub.k-1 and x.sub.k be $\begin{array}{cc}{r}_k=\frac{w_{k-1}}{w_k},k=m,m-1,\mathrm{.Math.},2& \left(3\right)\end{array}$ where values of r.sub.k are taken as 1.0, 1.2, 1.4, 1.6, and 1.8, respectively representing that an index x.sub.k-1 is equally important, slightly important, obviously important, strongly important, and extremely important than x.sub.k; {circle around (3)} weight coefficient calculation according to the evaluation of degree of importance, a subjective weighting coefficient of the index is obtained using the following formula: $\begin{array}{cc}{w}_m={\left(1+\underset{k=2}{\overset{m}{.Math.}}\underset{i=k}{\overset{m}{.Math.}}{r}_i\right)}^{-1}& \left(4\right)\end{array}$ (V) entropy method to determine an objective weight coefficient {circle around (1)} normalize a standardized data $\begin{array}{cc}{p}_{\mathrm{ij}}=\frac{x_{\mathrm{ij}}}{\underset{i=1}{\stackrel{n}{.Math.}}{x}_{\mathrm{ij}}}& \left(5\right)\end{array}$ {circle around (2)} calculate the entropy of each evaluation index $\begin{array}{cc}{e}_j=-k\underset{i=1}{\overset{n}{.Math.}}{p}_{\mathrm{ij}}\ln \left(p_{\mathrm{ij}}\right)\mathrm{where}k=\frac{1}{\ln n}>0,e_j>0;& \left(6\right)\end{array}$ {circle around (3)} determine a normalized weight coefficients $\begin{array}{cc}{w}_j=\frac{g_j}{\underset{j=1}{\stackrel{m}{.Math.}}{g}_j},j=1,2,\mathrm{.Math.},m& \left(7\right)\end{array}$ where a difference coefficient of each evaluation index g.sub.j=1e.sub.j; (VI) indicate variance method to determine the objective weight coefficient {circle around (1)} calculate the indication of each evaluation index $\begin{array}{cc}{\stackrel{}{x}}_j=\frac{1}{n}\underset{i=1}{\overset{n}{.Math.}}{x}_{\mathrm{ij}},j=1,2,\mathrm{.Math.},m& \left(8\right)\end{array}$ {circle around (2)} calculate the indication variance of each evaluation index $\begin{array}{cc}{s}_j^2=\frac{1}{n}\underset{i=1}{\overset{n}{.Math.}}{\left(x_{\mathrm{ij}}-{\stackrel{}{x}}_j\right)}^2,j=1,2,\mathrm{.Math.},m& \left(9\right)\end{array}$ {circle around (3)} determine the normalized weight coefficient $\begin{array}{cc}{w}_j=\frac{s_j}{\underset{k=1}{\overset{m}{.Math.}}{s}_k},j=1,2,\mathrm{.Math.},m& \left(10\right)\end{array}$ (VII) comprehensive integration empowerment based on Pearson correlation coefficient a connotation of this method is to analyze a correlation between several subjective and objective weighting methods, and to obtain the quantitative correlation degree between a single weight vector and other weight vectors, and to measure the relative importance of each weighting method, highlighting the role of stable and reliable weight vectors; for any two weight vectors X={x.sub.1, x.sub.2, . . . , x.sub.n}, Y={y.sub.1, y.sub.2, . . . , y.sub.n}, the correlation coefficients P (X, Y) are defined as follows: $\begin{array}{cc}P\left(X,Y\right)=\frac{\underset{i}{.Math.}\left(x_i-{\stackrel{\_}{x}}_j\right)\left(y_i-{\stackrel{}{y}}_j\right)}{\sqrt{\underset{i}{.Math.}{\left(x-{\stackrel{\_}{x}}_i\right)}^2}\sqrt{\underset{i}{.Math.}{\left(y_i-\stackrel{}{y_i}\right)}^2}}& \left(11\right)\end{array}$ where x.sub.i and y.sub.i are an average values of X and Y, respectively, P(X, Y)=[1, 1]; when P (X, Y)=1, two variables have complete linear correlation; when P (X, Y)=0, the two variables are linearly independent; to facilitate subsequent calculations, adjust the value interval of P(X, Y) and define the correlation between the two variables:
(X,Y)=[P(X,Y)+1](12) furthermore, a total correlation between a certain weight vector W.sub.k and the remaining weight vectors can be given as $\begin{array}{cc}{}_k=\underset{i=1,ik}{\overset{l}{.Math.}}\left(W_i,W_k\right),k=1,2,\mathrm{.Math.},l& \left(13\right)\end{array}$ an importance of weighting vector is measured by the total correlation degree, and the weighting coefficients of comprehensive integration are determined $\begin{array}{cc}{}_k=\frac{\underset{i=1,ik}{\overset{l}{.Math.}}\left(W_i,W_k\right)}{\underset{k=1}{\overset{l}{.Math.}}\underset{i=1,ik}{\overset{l}{.Math.}}\left(W_i,W_k\right)}& \left(14\right)\end{array}$ (VIII) determine a final weight coefficient based on the improved pull-off grade method first, each evaluation index is weighted to distinguish the degree of importance
x.sub.ij*.sup.(2,t,q)=w.sub.j.sup.(2,t,q)x.sub.ij.sup.(2,t,q)(15) where w.sub.j.sup.(2,t,q) is a comprehensive integrated weighting factor that characterizes the importance of indicator; an indication of x.sub.ij.sup.(2,t,q) is a standard observation of an index of the j-th subordinate to the second hierarchical subsystem s.sub.q.sup.(2,t) belonging to an i-th large system, where i=1, 2, . . . , n; j=1, 2, . . . , m.sub.tq; t=1, 2, . . . , n.sub.1; q=1, 2, . . . , m.sub.t; then, the weighted index matrix is obtained; $\begin{array}{cc}{A}^{\left(2,t,q\right)}=\left[\begin{array}{ccc}{x}_{11}^{*\left(2,t,q\right)}& \mathrm{.Math.}& x_{1m_{\mathrm{tq}}}^{*\left(2,t,q\right)}\\ \mathrm{.Math.}& & \mathrm{.Math.}\\ x_{n1}^{*\left(2,t,q\right)}& \mathrm{.Math.}& x_{{\mathrm{nm}}_{\mathrm{tq}}}^{*\left(2,t,q\right)}\end{array}\right]& \left(16\right)\end{array}$ a corresponding positive definite matrix is
H.sup.(2,t,q)=(A.sup.(2,t,q)).sup.TA.sup.(2,t,q)(17) constructing a comprehensive evaluation function of subsystems by linear weighted synthesis $\begin{array}{cc}{y}_i^{\left(2,t,q\right)}=\underset{j=1}{\overset{m_{\mathrm{tq}}}{.Math.}}{b}_j^{\left(2,t,q\right)}{x}_{\mathrm{ij}}^{*\left(2,t,q\right)},i=1,2,\mathrm{.Math.},n& \left(18\right)\end{array}$ a basic idea of determining the weight coefficient vector b.sup.(2,t,q) is to evaluate the difference between different evaluation objects and the evaluation target to a greatest extent and convert it into a mathematical language, even though a linear comprehensive evaluation function y.sub.i.sup.(2,t,q) has a maximum degree of dispersion for the comprehensive evaluation values of n evaluation objects; if b.sup.(2,t,q) is an eigenvector corresponding to a largest of all a basic eigenvalues of positive definite matrix H.sup.(2,t,q), then the evaluation value has a highest degree of discreteness; after normalizing the eigenvector, the index weight coefficient vector is obtained; using formula (18), the comprehensive evaluation values of all subsystems s.sub.q.sup.(2, t) of the evaluation object are obtained; (IX) hierarchical evaluation of multilevel indicators for the three-level index of Y-axis geometric error, Z-axis geometric error, secondary indicators such as thermal error, specific performance indicators of the first-level indicators such as efficiency and reliability, repeat steps (I) to (VIII); for the four third-level indicators U.sub.111-U.sub.114 under the geometric error, repeat steps (I) to (VIII) to obtain the comprehensive evaluation value of geometric error of different machine tools; it should be pointed out that a magnitude of data is consistent when the evaluation value of secondary index is calculated according to the evaluation value of three-level index; therefore, a standardization process is no longer performed; for the three sublevel indicators U.sub.11-U.sub.13 under an accuracy, repeat steps (I) to (VIII) to obtain the comprehensive evaluation value of the accuracy of different machine tools.

Description

DRAWINGS

(1) FIG. 1 shows a tree diagram of the key performance indicator system of CNC machine tools.

(2) FIG. 2 shows a flow chart for the comprehensive evaluation of performance of CNC machine tools based on the improved pull-off method.

DETAILED DESCRIPTION

(3) To make the technical solutions and advantageous effects of the present invention more clear, it will be described in detail below in conjunction with a static comprehensive evaluation model and with reference to the accompanying drawings. The present embodiment is carried out on the premise of a technical solution of the present invention, and detailed implementation manners and specific operation procedures are given. However, the scope of protection of the present invention is not limited to the following embodiments.

(4) (1) Establishing a Key Performance Indicator System for CNC Machine Tools

(5) The CNC machine tool performance index system is shown in FIG. 1. The system can be decomposed into four levels of subsystems, namely, large systems: machine performance (S); first-level subsystem: accuracy (S1.sup.(1)), efficiency (S2.sup.(1)), reliability (S3.sup.(1), and energy consumption (S4.sup.(1)); second-level subsystem: geometric error (S1.sup.(2,1)), thermal error (S2.sup.(2,1)), and composite motion error (S3.sup.(2,1); third-level subsystem: X-axis geometric error (S1.sup.(3,1,1), Y-axis geometric error (S2.sup.(3,1,1), Z-axis geometric error (S3.sup.(3,1,1), and verticality error (S4.sup.(3,1,1)).

(6) (2) Acquisition of Raw Data for Evaluation Indicators

(7) Take the historical data of the performance test part of four different types of CNC machine tools of Shenyang Machine Tool Group as an example to demonstrate the evaluation process. The raw data of indicators are shown in Table 1.

(8) TABLE-US-00001 TABLE 1 CNC machine performance indicators raw data No. 1 No. 2 No. 3 No. 4 Machine Machine Machine Machine index Unit Tool Tool Tool Tool U.sub.1111 0.011 0.022 0.008 0.014 U.sub.1112 0.009 0.026 0.019 0.012 U.sub.1113 mm 0.029 0.017 0.018 0.019 U.sub.1114 0.000012 0.000015 0.000019 0.000023 U.sub.1115 0.000009 0.000013 0.000018 0.000023 U.sub.1116 0.000006 0.000017 0.000012 0.000007 U.sub.1121 0.015 0.013 0.021 0.029 U.sub.1122 0.023 0.028 0.027 0.026 U.sub.1123 mm 0.017 0.031 0.013 0.021 U.sub.1124 0.000021 0.000007 0.000016 0.000025 U.sub.1125 0.000015 0.000016 0.000015 0.000014 U.sub.1126 0.000014 0.000021 0.000019 0.000017 U.sub.1131 0.015 0.015 0.028 0.041 U.sub.1132 0.019 0.016 0.013 0.01 U.sub.1133 mm 0.008 0.011 0.024 0.037 U.sub.1134 0.000018 0.000023 0.00002 0.000017 U.sub.1135 0.000022 0.000014 0.000009 0.000004 U.sub.1136 0.000031 0.000024 0.000017 0.00001 U.sub.1141 0.018 0.015 0.019 0.023 U.sub.1142 mm 0.031 0.011 0.023 0.035 U.sub.1143 0.014 0.018 0.026 0.034 U.sub.121 0.064 0.051 0.092 0.133 U.sub.122 mm 0.033 0.043 0.031 0.019 U.sub.123 0.059 0.068 0.046 0.024 U.sub.124 0.074 0.056 0.077 0.098 U.sub.131 mm 0.029 0.026 0.022 0.018 U.sub.132 0.025 0.019 0.031 0.043 U.sub.133 0.018 0.027 0.024 0.036 U.sub.21 rpm 12000 8000 12000 10000 U.sub.22 30 24 28 32 U.sub.23 m/min 32 28 30 36 U.sub.24 34 29 32 38 U.sub.31 1055 1124 1029 934 U.sub.32 h 1327 1437 1376 1315 U.sub.33 18 17 24 31 U.sub.41 Kw 7.4 10.3 6.1 5.7 U.sub.42 0.57 0.85 0.42 0.3

(9) (3) Pretreatment of Evaluation Indicators

(10) According to the linear proportional method m.sub.j, the original matrix composed of all the underlying index data of the four CNC machine tools shown in Table 1 are standardized to obtain a standard observation matrix.

(11) (4) Order Relationship Analysis Method to Determine Subjective Weight

(12) Considering the order relationship analysis of the key performance index system of CNC machine tools shown in FIG. 1, it is necessary to design an expert score table. The consultants are professors of research in CNC machine tools at Dalian University of Technology. They have rich experience in CNC machine tools research and practice, and the reliability of scoring results is high.

(13) The basic principle of order relationship analysis method can be stated as follows: The first step is to sort the relative importance degree of evaluation indicators and then evaluate the importance of adjacent indicators and assign them. Based on this design score sheet, a score table of the six four-level indicators under the X-axis geometric error U.sub.111 in the evaluation index system is shown in Table 2. The design methods of other levels of indicator score tables are similar and not described here.

(14) Take the four-level indicator importance score of X-axis geometric error as an example. The three experts who participated in the scoring provided the same ranking results for the importance of the six four-level indicators, namely, U.sub.1111>U.sub.1112>U.sub.1113>U.sub.1114>U.sub.1115>U.sub.1116; however, the importance degree was different. The assignment vector (i.e., the vector formed by the ratio of importance of each indicator in the table) is [1.4, 1.0, 1.2, 1.0, 1.0], [1.5, 1.0, 1.3, 1.0, 1.0], and [1.3, 1.0, 1.4, 1.0, 1.0], combining three assignment vectors into a 35 matrix and averaging each column element to obtain the final assignment vector as [1.4, 1.0, 1.3, 1.0, 1.0]. Then, using the weight calculation principle of order relationship analysis method, the subjective weight vector U.sub.1=[0.2452, 0.1752, 0.1752, 0.1348, 0.1348, 0.1348] of the four-level index of X-axis geometric error is obtained.

(15) TABLE-US-00002 TABLE 2 X-axis geometric error subordinate four-level indicator importance score U.sub.1111~U.sub.1116importance U.sub.1111~U.sub.1116importance degree ranking degree assignment most important indicator for the X-axis geometric error R1 second most important the importance of R1 indicator for the X-axis versus R2 geometric error R2 third most important the importance of R2 indicator for the X-axis versus R3 geometric error R3 fourth most important the importance of R3 indicator for the X-axis geometric error R4 fifth most important the importance of R4 indicator for the X-axis versus R5 geometric error R5

(16) For the four primary indicators of comprehensive performance of the machine tool, the ranking results provided by the three experts are the same. All are U.sub.1>U.sub.3>U.sub.2>U.sub.4, and the assignment vectors are [1.5, 1.5, 1.4], [1.7, 1.6, 1.4], and [1.6, 1.4, 1.4]. The average of the columns of composite matrix is calculated to obtain the final assignment vector [1.6, 1.5, 1.4], and the subjective weight vector of the first-order index is U.sub.12=[0.4275, 0.1781, 0.2672, 0.1272].

(17) The process of determining the subjective weights of other score tables is similar and is not described here. Only the subjective weight vector calculation results of each level of indicators are shown in Table 3:

(18) The system S.sub.1.sup.(3,1,1) in Table 3 represents the No. 1 third-level indicator subordinate to the No. 1 second-level indicator of the No. 1 first-level indicator, representing the X-axis geometric error three-level subsystem; similarly, S.sub.1.sup.(2,1) represents the geometric error secondary subsystem, and so on.

(19) TABLE-US-00003 TABLE 3 Summary Table of Subjective Weight Coefficients of Indicators at Different Levels number of ordered relationship analysis method to determine system indicators subjective weight coefficients S.sub.1.sup.(3,1,1) 6 0.2452 0.1752 0.1752 0.1348 0.1348 0.1348 S.sub.2.sup.(3,1,1) 6 0.2452 0.1752 0.1752 0.1348 0.1348 0.1348 S.sub.3.sup.(3,1,1) 6 0.2452 0.1752 0.1752 0.1348 0.1348 0.1348 S.sub.4.sup.(3,1,1) 3 S.sub.1.sup.(2,1) 4 0.2692 0.2692 0.2692 0.1924 S.sub.2.sup.(2,1) 4 0.2174 0.2174 0.2174 0.3478 S.sub.3.sup.(2,1) 3 0.4594 0.2703 0.2703 S.sub.1.sup.(1) 3 0.4828 0.3017 0.2155 S.sub.2.sup.(1) 4 0.3616 0.2128 0.2128 0.2128 S.sub.3.sup.(1) 3 0.2428 0.4659 0.2913 S.sub.4.sup.(1) 2 0.5833 0.4167 S 4 0.4257 0.1781 0.2672 0.1272

(20) (5) Entropy Weight Method and Mean Variance Method to Determine Objective Weight

(21) According to the above two objective weighting methods, the objective weight vector of each level of indicators can be obtained. For example, the objective weight vector of the six indicators of subsystem S.sub.1.sup.(3,1,1) based on the entropy weight method is [0.1808, 0.2055, 0.1024, 0.1224, 0.1786, 0.2102]; the three index weight vectors of subsystem S1.sup.(1) are [0.6737, 0.0231, 0.3032].

(22) (6) Comprehensive Integration Empowerment Based on Pearson Correlation Coefficient

(23) According to the subjective weight vector of each level index shown in Table 3, combined with the two objective weight vectors calculated using the objective data, the optimal weight vector is obtained using the integrated weighting method based on vector Pearson coefficient. The results are shown in Table 4. Each evaluation index is multiplied by the corresponding comprehensive weight (i.e., the index weighting process is performed) to obtain the weighting matrix A.

(24) TABLE-US-00004 TABLE 4 List of comprehensive weights of indicators at all levels number of Comprehensive integration weighting to determine system indicators the weight coefficient (first weighting) S.sub.1.sup.(3,1,1) 6 0.1970 0.1923 0.1300 0.1308 0.1651 0.1849 S.sub.2.sup.(3,1,1) 6 0.2382 0.0869 0.2191 0.2741 0.0602 0.1216 S.sub.3.sup.(3,1,1) 6 0.2043 0.1320 0.2172 0.0770 0.2000 0.1695 S.sub.4.sup.(3,1,1) 3 0.2152 0.4266 0.3582 S.sub.1.sup.(2,1) 4 0.2127 0.2058 0.0556 0.5259 S.sub.2.sup.(2,1) 4 0.2843 0.2327 0.3074 0.1756 S.sub.3.sup.(2,1) 3 0.2643 0.3986 0.3371 S.sub.1.sup.(1) 3 0.5204 0.1367 0.3429 S.sub.2.sup.(1) 4 0.4024 0.2121 0.1878 0.1977 S.sub.3.sup.(1) 3 0.2140 0.1502 0.6358 S.sub.4.sup.(1) 2 0.3971 0.6029 S 4 0.1215 0.1902 0.2842 0.4041

(25) (7) Determining the Index Weight Coefficient Based on the Improved Pull-Off Method

(26) According to the relevant principle of the pull-off method, the positive definite matrix corresponding to the weighted index matrix is given first, and then the eigenvector corresponding to the largest eigenvalue is the final weight of the index. The results are shown in Table 5.

(27) TABLE-US-00005 TABLE 5 List of final weights of indicators at all levels system number of indicators Improved pull-off method to determine weight (second weight) S.sub.1.sup.(3,1,1) 6 0.2036 0.1981 0.1224 0.1216 0.1615 0.1929 S.sub.2.sup.(3,1,1) 6 0.2516 0.0730 0.2294 0.2864 0.0500 0.1097 S.sub.3.sup.(3,1,1) 6 0.2090 0.1189 0.2323 0.0645 0.2102 0.1651 S.sub.4.sup.(3,1,1) 3 0.1983 0.4317 0.3700 S.sub.1.sup.(2,1) 4 0.1325 0.1552 0.0388 0.6735 S.sub.2.sup.(2,1) 4 0.2988 0.2297 0.3057 0.1658 S.sub.3.sup.(2,1) 3 0.2425 0.4172 0.3402 S.sub.1.sup.(1) 3 0.3233 0.1575 0.5191 S.sub.2.sup.(1) 4 0.4363 0.2063 0.1724 0.1851 S.sub.3.sup.(1) 3 0.1960 0.1279 0.6761 S.sub.4.sup.(1) 2 0.3801 0.6199 S 4 0.0256 0.1270 0.3169 0.5305

(28) (8) Calculation of Comprehensive Evaluation Values

(29) Using the final weight coefficient and weighted data shown in Table 5, the evaluation values of indicators at each level are calculated step by step, and the evaluation values of the first-level indicators of CNC machine tools and the comprehensive performance evaluation values are finally obtained. The evaluation results are shown in Table 6.

(30) TABLE-US-00006 TABLE 6 Summary of the comprehensive evaluation results of four CNC machine tools comprehensive energy evaluation machine number precision effectiveness reliability consumption value sort 1 0.1220 0.3979 0.6768 0.6903 0.2189 3 2 0.1274 0.2883 0.6955 0.5247 0.1825 4 3 0.1168 0.3894 0.5932 0.7753 0.2294 2 4 0.0972 0.3674 0.4910 0.8339 0.2322 1

(31) Table 6 clearly shows the first-level performance index of the machine tool and the evaluation value of comprehensive performance, fully reflecting the performance of each machine tool. The order of comprehensive performance of the four machine tools is: No. 4>No. 3>No. 1>No. 2. Although the accuracy of No. 2 machine is the best, its comprehensive performance is the worst. The comprehensive performance of No. 4 machine is the best; however, the accuracy performance is the worst. It is observed that although the comprehensive performance of machine tool is superior, whether there is a defect in one aspect cannot be ruled out, and the performance of machine tool can be improved from the first-level performance index. For example, the accuracy of No. 4 machine can be comprehensively tested, and targeted compensation measures can be taken.

(32) The hierarchical comprehensive evaluation based on the improved pull-off method can distinguish the advantages and disadvantages of multiple machine tools; it can also compare the performance of different machine tools at various levels to achieve comprehensive and multilevel comparative analysis.

(33) It should be noted that the above specific application of the present invention is only intended to exemplify the principles and flow of this invention and does not constitute a limitation of this invention. Therefore, any modifications and equivalent substitutions made without departing from the idea and scope of this invention shall be included in the scope of protection of the present invention.