A multi-level and multi-dimensional comprehensive evaluation method for precision retention of a numerical control machine tool

Abstract

This invention discloses a multi-level, multi-dimensional comprehensive evaluation method for the overall precision retention of CNC machine tools, relating to the field of CNC machine tool performance evaluation technology. The method first constructs an evaluation system of "target layer—criteria layer—indicator layer" based on the type and requirements of the machine tool. The target layer is the comprehensive score for the overall precision retention of the CNC machine tool; the criteria layer covers geometric accuracy, positional accuracy, and machining accuracy; and the indicator layer consists of key indicators with high importance selected from various precision indicators under each precision set. During the calculation process, fuzzy mathematics is used to process the evaluation values ​​of each indicator, and the Lagrange multiplier method is used to integrate the subjective weights of the analytic hierarchy process (AHP) with the objective weights of the proportional weighting method to solve for the optimal combination of weights. Finally, through layer-by-layer weighted summation, a comprehensive evaluation score for the overall precision retention of the machine tool is obtained. This invention overcomes the limitations of single weighting and achieves a scientific and comprehensive quantitative evaluation of the overall precision retention capability of CNC machine tools.

Description

Technical Field

[0001] This invention relates to the field of CNC machine tool performance evaluation technology, specifically a multi-level, multi-dimensional comprehensive evaluation method for the overall accuracy retention of CNC machine tools. Background Technology

[0002] With the development of high-end manufacturing and the continuous improvement of precision requirements for parts processing, CNC machine tools, as core equipment in the manufacturing industry, have seen their precision retention become a key indicator for measuring their reliability and core competitiveness. Machine tool precision retention is a dynamic and complex attribute involving multiple coupled factors, and it lacks intuitive observability. Therefore, constructing a scientific and effective evaluation method for machine tool precision retention has become a crucial basis for measuring the precision retention capabilities of various machine tools. Currently, there is limited research on comprehensive evaluation methods for CNC machine tool precision retention; most studies focus on a single precision aspect of the machine tool, failing to provide a comprehensive evaluation of the overall precision retention capability of the CNC machine tool.

[0003] This invention proposes a multi-level, multi-dimensional comprehensive evaluation method for the overall precision retention of CNC machine tools. The method divides the precision evaluation system into three levels: target level, criterion level, and indicator level. Precision degradation rate, precision retention, precision fluctuation, machining precision consistency, and precision deviation are used as evaluation indicators. Targeted evaluation indicators are selected from these indicators to conduct multi-dimensional evaluations of each precision indicator item in the indicator level. In particular, this method abandons the limitations of single weighting and innovatively integrates the subjective judgment advantages of the analytic hierarchy process (AHP) with the data objectivity of the weighted method using the Lagrange multiplier method. This allows for the determination of the optimal combination weights for each evaluation indicator, thereby obtaining scores for each item in the indicator level. Finally, by weighting and summing the scores at each level, a percentage score for the overall precision retention evaluation is obtained. Summary of the Invention

[0004] To address the shortcomings of existing methods, this invention proposes a multi-level, multi-dimensional comprehensive evaluation method for the overall accuracy retention of CNC machine tools. The specific steps are as follows:

[0005] Step 1: Based on the type of machine tool and actual needs, construct a machine tool accuracy maintenance evaluation system consisting of "target layer - criterion layer - indicator layer". The target layer is the comprehensive score for the overall accuracy maintenance of the CNC machine tool; the criterion layer covers accuracy sets such as geometric accuracy, positional accuracy, and machining accuracy; the indicator layer consists of key indicators with high importance selected from the accuracy indicators under each accuracy set.

[0006] Step 2: Regularly collect machine tool accuracy data using relevant precision testing equipment. After processing the raw data, use accuracy degradation rate, accuracy retention, and accuracy fluctuation as evaluation indicators to conduct multi-dimensional evaluation of each accuracy indicator under the machine tool's geometric accuracy and positional accuracy. Use machining accuracy consistency and accuracy deviation to conduct multi-dimensional evaluation of each accuracy indicator under the product machining accuracy. Use fuzzy mathematics to score the data and combine it with the Lagrange multiplier method to determine the comprehensive weight of each evaluation indicator, and obtain the comprehensive evaluation value of each accuracy indicator at the indicator layer.

[0007] Step 3: Determine the weights of each accuracy indicator item in the indicator layer, the weights of each item in the criterion layer, and the evaluation values, and calculate the comprehensive evaluation score of the overall accuracy retention of the CNC machine tool.

[0008] The invention will be further described below:

[0009] In step 1, a multi-level and multi-dimensional comprehensive evaluation system for maintaining the overall machine tool accuracy is constructed from the target layer, criterion layer, and indicator layer. The accuracy of the entire machine is divided into major categories based on accuracy sets such as geometric accuracy, positional accuracy, and machining accuracy, which constitute the elements of the criterion layer. Furthermore, each accuracy set can be divided into various specific accuracy indicators, and after screening, each accuracy indicator constitutes the elements of the indicator layer.

[0010] In step 2, machine tool accuracy data is collected periodically using relevant accuracy testing equipment, and the average accuracy value from multiple samples is taken as the final data for that sampling. The final data is then functionalized using the least squares method to construct a precision degradation function model. The accuracy indicators of machine tool geometry and position accuracy are evaluated in multiple dimensions using accuracy degradation rate (ARDR), accuracy retention (ARD), and accuracy fluctuation (AFD) as evaluation indicators. The accuracy indicators of product machining accuracy are evaluated in multiple dimensions using machining accuracy consistency (ACD) and accuracy deviation (AD).

[0011] The specific calculation formulas for each evaluation indicator are as follows:

[0012] (1) Accuracy degradation rate (ARDR) is a quantitative parameter characterizing the rate at which machine tool accuracy degrades over service time. It describes the dynamic process of accuracy evolving from an initial high-precision state to a low-precision state. Its calculation formula is as follows:

[0013]

[0014] In the formula, ARDR is the machine tool speed at t i The rate of degradation of time precision.

[0015] (2) Accuracy Retention (ARD) is a relative quantitative indicator that characterizes the ability of a machine tool to maintain its core accuracy indicators in their initial state during its service life. It is used to comprehensively evaluate the long-term stable retention level of machine tool accuracy and is one of the core parameters of the accuracy retention evaluation system. Its calculation method is as follows:

[0016] Calculate a certain accuracy index δ over time t n The mean change in the corresponding error within is:

[0017]

[0018] To represent a certain precision index The ability to maintain the initial state, while considering the guaranteed range of the accuracy index δ, is derived from statistical distance discrimination theory. The machine tool accuracy index δ within t... n The precision retention of time is:

[0019]

[0020]

[0021] In the formula, ρ is a conditional function; For time t n The mean change in error within the range; The failure accuracy corresponding to the accuracy index of CNC machine tools; This refers to the initial factory precision corresponding to the precision specifications of CNC machine tools.

[0022] (3) Accuracy fluctuation (AFD) is an important indicator characterizing the random fluctuation of accuracy during the machine tool degradation process, reflecting the long-term stability of the system. Its calculation formula is:

[0023]

[0024] (4) ACD (Accuracy in Difference) is an important technical indicator for evaluating the manufacturing quality of products. It reflects the degree to which the key precision of mass-produced parts approximates its mathematical expectation (or design ideal value) in a statistical sense. Its calculation formula is as follows:

[0025]

[0026] In the formula, m is the number of samples, and T is the absolute value of the difference between the upper and lower limits of the accuracy index tolerance. For accurate measured values, This represents the average precision.

[0027] (5) Precision deviation (AD) is a quantitative indicator that measures the degree of coincidence between the measured mean value of machining accuracy and the target value of tolerance center. It reflects the level of systematic error in the machining process. Its calculation formula is as follows:

[0028]

[0029] In the formula, M is the center value of the tolerance zone.

[0030] In step 2, fuzzy mathematics is used to process the calculation results of each evaluation index to obtain the corresponding evaluation value; the subjective and objective weights of each evaluation index are determined by the analytic hierarchy process-weighting method, and the optimal combination weights are obtained by the Lagrange multiplier method.

[0031] (1) Using fuzzy mathematics, the evaluation values ​​of each evaluation index are output by comparing and calculating with the set ideal limit and extreme limit; the positive evaluation method is used for the accuracy retention and processing accuracy consistency as positive indicators, and the negative evaluation method is used for the accuracy degradation rate, accuracy fluctuation and accuracy deviation as negative indicators.

[0032]

[0033]

[0034] (2) The subjective weights of each indicator are determined using the analytic hierarchy process. The specific steps are as follows:

[0035] (a) Construct a judgment matrix to compare the importance of accuracy degradation rate (ARDR), accuracy retention rate (ARD), and accuracy fluctuation rate (AFD) indicators pairwise (using the 1-9 scale) to determine the subjective weights of the three indicators. Let the index set be ;

[0036]

[0037] A judgment matrix is ​​constructed to compare the importance of machining accuracy consistency (ACD) and accuracy deviation (AD) pairwise (using the 1-9 scale) to determine the subjective weights of the two indicators. Let the index set be ;

[0038]

[0039] (b) Calculate the largest eigenvalue λ of the matrix. max And its corresponding eigenvector α, and perform a consistency check.

[0040]

[0041] In the above formula, CI is the consistency index; n is the order of the discriminant matrix; CR is the consistency ratio; RI is the random consistency index. If CR < 0.1, the discriminant matrix is ​​considered to have satisfactory consistency and the weight allocation is reasonable. If CR ≥ 0.1, the consistency of the discriminant matrix does not meet the requirements and the elements of the discriminant matrix need to be adjusted until CR < 0.1.

[0042] (3) The objective weights of each evaluation index are calculated using the weighting method. and The specific calculation method is as follows:

[0043] Accuracy Degradation Rate (ARDR) Objective Weights:

[0044]

[0045] Accuracy Retention (ARD) Objective Weighting:

[0046]

[0047] Accuracy Fluctuation (AFD) Objective Weights:

[0048]

[0049] Objective weighting of machining accuracy consistency (ACD):

[0050]

[0051] Accuracy Deviation (AD) Objective Weighting:

[0052]

[0053] In the formula, This is an evaluation value for the rate of accuracy degradation. This is the value for accuracy retention evaluation. This is the accuracy fluctuation evaluation value. This is the evaluation value for consistency in machining accuracy. This is the accuracy deviation evaluation value.

[0054] (4) The analytic hierarchy process (AHP) and weighting method are used to determine the subjective and objective weights of each evaluation index. Based on the principle of minimum relative information entropy, the optimization objective is to minimize the deviation between the combined weights and the subjective and objective weights. The Lagrange multiplier method is introduced to derive and solve the combined weights. The specific content is as follows:

[0055] Let the combined weight vector be... ,

[0056] Construct the objective function:

[0057]

[0058] In the formula, Subjective weighting, For objective weighting.

[0059] Introduce normalization constraints:

[0060]

[0061] The analytical solution derived using the Lagrange multiplier method is:

[0062]

[0063] Ultimately, the comprehensive evaluation value of this accuracy index is

[0064]

[0065] In step 3, after calculating and obtaining the evaluation values ​​of each indicator layer, the weight of each element at each layer is determined by the analytic hierarchy process (AHP). Then, combined with the evaluation values ​​of each element, the scores are weighted and summarized layer by layer according to the hierarchical relationship to finally obtain the comprehensive evaluation score of the machine tool's overall precision retention. The specific steps are as follows:

[0066] (1) The weights of each precision index in the index layer are determined using the analytic hierarchy process (AHP), and combined with the evaluation values ​​of each precision index item,

[0067] The evaluation values ​​for each precision set in the criterion layer are determined, and the formulas for calculating the evaluation values ​​for each precision set in the criterion layer are as follows:

[0068]

[0069] In the formula These are the evaluation values ​​for each accuracy indicator item. The weights for each accuracy indicator item.

[0070] (2) The weights of each accuracy set in the criterion layer are determined using the analytic hierarchy process (AHP). Combined with the evaluation values ​​of each accuracy set, a comprehensive evaluation of the target layer (overall accuracy retention of the CNC machine tool) is obtained. The formula for calculating the comprehensive evaluation of overall machine accuracy retention is as follows:

[0071]

[0072] In the formula, The evaluation values ​​for each set of indicators, Weights are assigned to each precision set. Attached Figure Description

[0073] Figure 1 A flowchart illustrating the comprehensive evaluation method for the accuracy retention of CNC machine tools. Detailed Implementation

[0074] The following will be combined with the appendix Figure 1 Taking a certain type of vertical machining center as an example, this paper details a multi-level, multi-dimensional comprehensive evaluation method for the overall accuracy retention of CNC machine tools. Specifically, it includes the following steps:

[0075] Step 1: Based on the characteristics of this machine tool model and the customer's requirements for key precision indicators, construct a machine precision maintenance evaluation system consisting of "target layer—criteria layer—indicator layer." Among these,

[0076] The target layer (A) is the overall score (S) for maintaining the accuracy of the entire machine;

[0077] The criteria layer includes geometric accuracy (B1), positional accuracy (B2), and machining accuracy (B3).

[0078] The geometric accuracy corresponds to the following index layer accuracy: X-axis straightness (C11), Y-axis straightness (C12), and X / Y-axis perpendicularity (C13).

[0079] The positional accuracy corresponds to the following index layer accuracy: X-axis positioning accuracy (C21) and X-axis repeatability positioning accuracy (C22).

[0080] The precision of the corresponding index layer for machining accuracy is surface roughness (C31) and specimen roundness (C32).

[0081] The relevant thresholds for each accuracy index are shown in Table 1 below:

[0082]

[0083] Step 2: During normal use of the machine tool, a standardized accuracy test is conducted on the machine tool over a period of 200 days using relevant accuracy testing equipment, with a total of 10 samplings (t1 to t). 10 ).

[0084] The full-cycle measured sampling data are shown in Table 2 below:

[0085]

[0086] The evaluation indexes for each accuracy index item are calculated using formulas 1 to 7.

[0087] The calculation results are shown in Table 3 below:

[0088]

[0089] Using formulas 8-9 and fuzzy mathematics, the evaluation values ​​of each evaluation index are output. Precision retention and processing precision consistency are positive indicators and are evaluated using a positive evaluation method, while precision degradation rate, precision fluctuation, and precision deviation are negative indicators and are evaluated using a negative evaluation method.

[0090] The multidimensional evaluation results of each accuracy index are summarized in Table 4 below:

[0091]

[0092] The subjective weights of each indicator are determined using the analytic hierarchy process (AHP), and consistency is verified using Formula 10. The specific calculation steps are as follows:

[0093] (1) Taking C11 as an example, the weights of the three-dimensional (ARDR, ARD, AFD) evaluation indicators are derived:

[0094] (a) Subjective weights in AHP ( ): Judgment Matrix Passed the consistency test.

[0095] .

[0096] (b) Weighting of objective weights ( ) .

[0097] (c) Lagrange portfolio weights ( ): .

[0098] (d)

[0099] (2) Taking C31 as an example, the weights of the two-dimensional (ACD, AD) evaluation index are derived:

[0100] (a) Subjective weights in AHP ( ): Judgment Matrix , It passed the consistency test. .

[0101] (b) Weighting of objective weights ( ): .

[0102] (c) Lagrange portfolio weights ( ): .

[0103] (d) C31 Final Overall Score:

[0104] Step 3: After calculating and obtaining the evaluation values ​​of each indicator layer, the weight of each element in each layer is determined by the analytic hierarchy process. Then, combined with the evaluation values ​​of each element, the scores are weighted and summarized layer by layer according to the hierarchical relationship to finally obtain the comprehensive evaluation score of the machine tool's overall precision maintenance.

[0105] The scores and weights of each layer of the machine tool are shown in Table 5 below:

[0106]

[0107] Target layer overall system score calculation:

[0108] .

Claims

1. A multi-level, multi-dimensional comprehensive evaluation method for the overall accuracy retention of CNC machine tools, characterized in that: The method includes the following steps: Step 1: Based on the type of machine tool and actual needs, construct a machine tool accuracy maintenance evaluation system consisting of "target layer - criterion layer - indicator layer". The target layer is the comprehensive score of the overall accuracy maintenance of the CNC machine tool; the criterion layer covers the accuracy sets of geometric accuracy, positional accuracy and machining accuracy; the indicator layer consists of key indicators with high importance after screening of the accuracy indicators under each accuracy set. Step 2: Regularly collect machine tool accuracy data using relevant accuracy testing equipment. After processing the raw data, use accuracy degradation rate, accuracy retention, and accuracy fluctuation as evaluation indicators to conduct multi-dimensional evaluation of each accuracy indicator under the machine tool's geometric accuracy and positional accuracy. Use machining accuracy consistency and accuracy deviation to conduct multi-dimensional evaluation of each accuracy indicator under the product machining accuracy. Use fuzzy mathematics to score the data and combine it with the Lagrange multiplier method to determine the comprehensive weight of each evaluation indicator, and obtain the comprehensive evaluation value of each accuracy indicator at the indicator layer. Step 3: Determine the weights of each accuracy indicator item in the indicator layer, the weights of each item in the criterion layer, and the evaluation values, and calculate the comprehensive evaluation score of the overall accuracy retention of the CNC machine tool.

2. The multi-level, multi-dimensional comprehensive evaluation method for the overall accuracy retention of CNC machine tools according to claim 1, characterized in that, In step 2: fuzzy mathematics is used to calculate the evaluation values ​​of each evaluation indicator; the analytic hierarchy process (AHP) with weighting is used to determine the subjective and objective weights of each evaluation indicator; based on the principle of minimum relative information entropy, minimizing the deviation between the combined weight and the subjective and objective weights is taken as the optimization objective; the Lagrange multiplier method is introduced to derive and solve for the combined weights, as detailed below: Let the combined weight vector be... , Construct the objective function: ； in, Subjective weighting, For objective weighting; Introduce normalization constraints: ； The analytical solution derived using the Lagrange multiplier method is: ； Ultimately, the comprehensive evaluation value of this accuracy index is ; In the formula, These are the evaluation values ​​for each evaluation indicator.

3. The multi-level, multi-dimensional comprehensive evaluation method for the overall accuracy retention of CNC machine tools according to claim 1, characterized in that, Step 3 includes: The weights of each precision index under each precision set in the criterion layer are determined using the analytic hierarchy process (AHP). Combined with the comprehensive evaluation value of each precision index item, the evaluation value of each precision set in the criterion layer is determined. The scoring formula for each precision set in the criterion layer is as follows: ； In the formula, These are the evaluation values ​​for each accuracy indicator item. Weights for each accuracy indicator item; The Analytic Hierarchy Process (AHP) is used to determine the weights of each accuracy set in the criterion layer, namely geometric accuracy, positional accuracy, and machining accuracy. Combining the evaluation values ​​of each accuracy set, a comprehensive evaluation of the overall accuracy retention of the CNC machine tool in the target layer is obtained. The formula for calculating the comprehensive accuracy retention evaluation is as follows: ； In the formula, For each precision set evaluation value, Weights are assigned to each precision set.

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