Machine tool fault risk sorting method fusing fuzzy-optimal worst-multi-criterion optimization compromise

Abstract

The invention discloses a machine tool fault risk sorting method fusing fuzzy-optimal worst-multi-criterion optimization compromise, and the method comprises the following specific steps: 1, carrying out the analysis according to the structural characteristics of a machine tool through focusing on a numerical control gear milling machine main shaft system, and reducing the interference of non-key factors; step 2, fault data acquisition: historical fault records of a target machine tool are collected; and step 3, formulating an evaluation standard based on intuitionistic reminding fuzziness. And 4, weighting and defuzzifying expert evaluation according to an intuitionistic trapezoidal fuzzy formula, integrating the frequency O and the maintenance cost M of the fault to form a comprehensive evaluation matrix, and performing defuzzification operation. And 5, determining an index weight based on a BWM method. And step 6, realizing fault mode sorting based on a VIKOR method. According to the method, evaluation indexes are considered more perfectly, and the analysis adaptability to the machine tool field is better; subjective deviation is reduced, and accuracy is improved; risk calculation is more scientific, and simplification and mechanization of a traditional method are avoided.

Description

TECHNICAL FIELD

[0001] The present technology belongs to the technical field of numerical control machine tool reliability analysis, and particularly relates to a machine tool fault risk ranking method fusing trapezoidal fuzzy numbers, best worst method (BWM) and multi-criteria optimization and compromise solution method (VIKOR), which is suitable for fault risk ranking of key subsystems (such as spindle system and feeding system) of numerical control machine tools, and can provide technical support for machine tool design optimization, maintenance strategy formulation and reliability improvement. BACKGROUND

[0002] Reliability is a core indicator for measuring the performance of numerical control machine tools. As a national strategic equipment, numerical control machine tools are the "industrial mother machine" in manufacturing industry, and their reliability level directly restricts the processing quality and production efficiency. Under complex working conditions, the key subsystems and key components of numerical control machine tools are prone to multiple potential faults, which may cause equipment downtime and production plan delay, or even safety accidents and significant economic losses. Therefore, systematically identifying potential fault modes of machine tools, accurately evaluating fault risks and formulating preventive measures have become key problems to be solved in the field of machine tools.

[0003] Fault risk ranking is one of the most widely used structured methods in machine tool reliability analysis. Traditional methods such as failure mode, effects and criticality analysis (FMECA) originated in the United States in the 1960s and were initially used for preventive quality control in the fields of aerospace, automobiles and ships. By systematically evaluating potential faults and their consequences in product design or production processes, high-risk problems can be prioritized and solved. However, after being introduced into the field of machine tools, although this method has achieved certain results in the preliminary identification of fault risks, it still has significant limitations:

[0004] 1. Single evaluation index, difficult to cover machine tool complexity: Traditional FMECA relies only on three discrete indexes of severity (S, severity of fault consequences), occurrence (O, frequency of fault occurrence) and detectability (D, difficulty of fault detection), without considering key factors in the operation and maintenance process of numerical control machine tools (such as maintenance cost), which cannot fully reflect the actual economic impact of faults on enterprises;

[0005] 2. Large subjective bias, insufficient evaluation accuracy: The evaluation of S, O and D relies on the subjective experience of experts, and the cognitive differences of different evaluators can easily lead to fuzzification of evaluation results and increase of uncertainty;

[0006] 3. Simple risk calculation, lack of scientificity in ranking: Traditional methods determine the priority of faults through risk priority number (RPN=S×O×D), without considering the weight differences of each index, which can easily be influenced by a single index (such as high S value) and cannot objectively reflect the actual risk level of faults;

[0007] 4. Poor adaptability, unable to meet the needs of the machine tool field: Although the 2019 FMEA manual update action priority (AP number) replaces the traditional method of RPN calculation, it is not designed for machine tool-specific risk factors and is still not suitable for machine tool reliability failure risk ranking analysis. SUMMARY

[0008] The present application aims to overcome the shortcomings of traditional failure risk ranking methods (such as FMECA) in machine tool reliability analysis, specifically addressing the following core problems: 1. Insufficient evaluation index dimension: traditional methods only cover S, O, D, without including maintenance cost (M), which cannot reflect the economic impact of failure, leading to incomplete risk assessment; 2. Subjective evaluation uncertainty: experts' evaluation of each index relies on fuzzy language (such as "more serious" and "difficult to detect"), lacking standardized quantitative means, which is prone to bias; 3. Unscientific index weight and ranking: traditional methods do not consider the weight difference between S, O, D, and M, and RPN calculation is easily dominated by a single index, which cannot objectively reflect the actual risk level of failure.

[0009] The present application proposes a machine tool failure risk ranking method based on trapezoidal fuzzy numbers and BWM-VIKOR, which realizes accurate ranking of machine tool failure risk through the combination strategy of "expanded index system + fuzzy information quantification + scientific weighting + multi-attribute ranking", with the specific steps as follows:

[0010] Step 1: Focus on key subsystems (such as the spindle system of a numerical control gear milling machine) based on machine tool structural characteristics to reduce interference from non-critical factors.

[0011] Step 2: Failure data collection: Collect historical failure records of the target machine tool, including failure modes (such as circular toothed belt damage, spindle overheating), failure causes (such as insufficient pre-tightening force, poor lubrication), failure frequency (O), and maintenance cost (M);

[0012] Step 3: Develop evaluation criteria based on intuitionistic fuzzy, invite 3 or more machine tool experts, and conduct fuzzy language evaluation of "severity (S)" and "detectability (D)" of each failure mode based on pre-set criteria. Evaluation parameters such as .

[0013] Step 4: Weighted processing and defuzzification of expert evaluation according to intuitionistic trapezoidal fuzzy formula, combine failure frequency O and maintenance cost M, and perform defuzzification operation.

[0014] Assuming there are experts in the team to evaluate risk factors, each expert's weight is , then the weighted evaluation value of each failure is :

[0015]

[0016] wherein: — the element of the kth expert evaluation matrix in the ith row and jth column;

[0017] — the element of the comprehensive evaluation matrix in the ith row and jth column;

[0018] The de-fuzzification operation is performed on the elements of the comprehensive evaluation matrix:

[0019]

[0020] wherein: — the element of the de-fuzzified evaluation matrix;

[0021] — the vertices of the fuzzy number element in the ith row and jth column of the comprehensive evaluation matrix.

[0022] Step 5: Determine the index weight based on the BWM method. First, the experts specify the "best criterion" and "worst criterion" from the expanded index system (S, O, D, M); and compare each other with the best and worst indicators one by one to construct the comparison vector , .

[0023] Best-to-Others (BO): describe the importance of the best criterion relative to all other criteria with a 1-9 scale (1 means equal importance, 9 means extreme importance), that is .

[0024] Others-to-Worst (OW): describe the importance of all criteria relative to the worst criterion with the same scale, that is .

[0025]

[0026]

[0027]

[0028]

[0029] wherein, — error, in general, the smaller the error, the better;

[0030] the jth element of the vector the jth element of the vector

[0031] weight of the jth criterion

[0032] weight of the best and worst criteria

[0033] After the model is solved, the consistency ratio needs to be checked, usually requiring CR < 0.1 to ensure the result is reliable.

[0034] Step 6: Sort the failure modes based on the VIKOR method.

[0035] The evaluation matrix is normalized to eliminate the influence of dimension. The maximum group benefit , the minimum individual regret and the comprehensive evaluation value of the failure modes are calculated by the VIKOR method, and the results are sorted according to .

[0036] The main theory of the VIKOR method is as follows:

[0037] Let there be m failures and n criteria forming . Normalize the data to eliminate the influence of dimension, and use different processing methods for benefit-type criteria (the larger the better) and cost-type criteria (the smaller the better), as shown in equations (7) and (8) respectively:

[0038]

[0039]

[0040] Where: — dimensionless value after normalization processing

[0041] — value of the ith scheme under the jth criterion

[0042] — minimum value and maximum value of the jth evaluation index respectively

[0043] Determine the positive ideal solution and the negative ideal solution of the matrix, as shown in equations (9) and (10).

[0044] ​​​

[0045]

[0046] Computing group utility and individual regret Take the ideal solution as an example, such as formula (11) (12):

[0047]

[0048]

[0049] Finally, the interest rate of each is calculated , and the ranking result can be obtained according to the size of each fault.

[0050]

[0051] In the formula: v is used to balance the group utility and individual regret, usually v=0.5.

[0052] Compared with the prior art, the present technology has many advantages:

[0053] (1) The evaluation index is more perfect. The traditional method (such as classic FMECA) relies on S-O-D three-dimensional index, only focuses on technical hazards, and does not consider the particularity of machine tool industry. Machine tool failure not only affects technical safety, but also is associated with economic cost, and the traditional system is easy to underestimate the failure with low technical risk but high economic loss due to the lack of maintenance cost (M). The present technology adds M to form a four-dimensional framework of S-O-D-M, which fully reflects the influence of technology, efficiency and cost, and the index can be expanded to add personalized index as needed, improving the evaluation pertinence.

[0054] (2) The analysis of machine tool field is better adapted. The traditional FMECA originated from the aerospace field in the 1960s, and due to the lack of consideration of the complex characteristics of machine tools, it is not well adapted in the field of machine tools: first, it is easy to miss the key risk or redundant calculation for "non-differential analysis" of each subsystem, and the present technology focuses on key subsystems to reduce interference from non-key factors; Second, the sorting logic is not adapted to the characteristics of high maintenance cost and strong fault chain of machine tools, and even the AP method in 2019 has not improved, while the present technology can provide accurate support for maintenance strategy through BWM weighting (adapted to the experience of machine tool industry) and VIKOR sorting, which is more practical than the traditional generalized sorting.

[0055] ​(3) Reduced subjective bias and improved accuracy. In traditional FMECA, experts evaluate indicators based on fuzzy language without standardized quantitative means, resulting in large subjective bias - both due to expert cognitive differences leading to scattered results and due to language ambiguity exacerbating uncertainty. This technology directly uses machine tool operation and maintenance data such as frequency and maintenance cost for some indicators, fundamentally avoiding errors in subjective evaluation. Moreover, for indicators that are difficult to quantify directly, a standardized system is established using "intuition trapezoidal fuzzy numbers": first, define clear standards to achieve precise mapping of fuzzy language and numerical intervals; then invite multiple experts to evaluate and reduce individual bias by weighted fusion of opinions; finally, de-fuzzify to get accurate numerical values, upgrading evaluation from qualitative to quantitative and fundamentally solving the problem of subjective bias.

[0056] (4) Risk calculation is more scientific, avoiding the simplification and mechanization of traditional methods. The risk calculation of traditional methods has two major defects: first, it assumes that all indicators are equally important, relying on RPN multiplication to determine priority without considering the actual impact of indicators on machine tool failure; second, the sorting logic is single, only relying on RPN numerical sorting without balancing overall risk and extreme risk. This technology upgrades risk calculation with "scientific weighting + multi-attribute sorting": the weighting step uses the BWM method to derive the relative importance of indicators, making the weights fit the needs of the machine tool industry; the sorting step uses the VIKOR method to achieve the "overall risk low + no extreme short board" goal, accurately distinguishing risk differences and avoiding the simplification of traditional "RPN-only theory", making the sorting more consistent with the risk logic of machine tool actual operation. BRIEF DESCRIPTION OF DRAWINGS

[0057] Figure 1 Figure 1 is a schematic diagram of a machine tool fault risk sorting method based on trapezoidal fuzzy numbers and BWM-VIKOR.

[0058] Figure 2 Figure 2 is a comparative diagram of the results of the method of the present invention and traditional analysis. DETAILED DESCRIPTION

[0059] The following takes a certain company's numerical control gear milling machine spindle system as the research object to explain the implementation process of the technology in detail and verify the effectiveness and feasibility of the technology:

[0060] First, according to the user's recorded fault information, perform fault analysis, the results of which are shown in Table 1.

[0061] Table 1 Machine tool fault mode information

[0062]

[0063] Develop relevant intuition trapezoidal fuzzy evaluation standards, such as Tables 2 and 3.

[0064] Table 2 Severity level division

[0065]

[0066] Table 3 Detectability rating scale

[0067]

[0068] The expert team evaluated the failure modes. Three experts were invited to evaluate the severity S and the detectability D according to the fuzzy language (Table 4). The expert evaluation was weighted and de-fuzzified according to formula (3) and formula (4), and the frequency O and the maintenance cost M of the failure were aggregated to form a comprehensive evaluation matrix (Table 5).

[0069] Table 4 Expert decision evaluation table

[0070]

[0071] Table 5 Comprehensive decision table

[0072]

[0073] According to the expert suggestions and relevant research materials, comprehensive consideration was given. The severity S was determined as the optimal criterion, the detectability D was determined as the worst criterion, and the other indexes were compared one by one with the optimal and worst indexes to construct a comparison vector

[0074]

[0075] After optimal and worst analysis, the weight of each index was obtained, and the weight distribution result is shown in Table 6. The consistency check CR=0.0178, indicating that the result is reasonable.

[0076] Table 6 Risk index weight table

[0077]

[0078] The maximum group benefit of the failure mode was calculated by the VIKOR method , the minimum individual regret and the comprehensive evaluation value , and the results were sorted according to , and the results are shown in Table 7.

[0079] Table 7 Failure mode Si, Ri, Qi table

[0080]

[0081] ​​Therefore, in the main failure modes of the gear milling machine spindle system, the risk of F1 circular tooth profile belt damage has the highest priority and should be focused on in maintenance or improvement. It is recommended to replace the tooth profile belt regularly and optimize its selection and design. The risk of F11 spindle encoder loosening has the lowest priority and only needs to be checked and reinforced regularly in daily maintenance.

[0082] In addition, the proposed method is compared with the traditional analysis results, as shown in Figure 2 The overall ranking trend is consistent, but the ranking of some failure modes has changed significantly, indicating that the defect of the traditional method being easily affected by a single risk factor has been effectively improved in this method. At the same time, the introduction of maintenance cost into the risk factor system further improves the rationality and practicality of the results. After discussing the analysis results with enterprise and user-related technical personnel, the feasibility and effectiveness of the method in practical application are verified. In summary, the proposed method can more accurately identify the potential risks of machine tool failure modes and provide a basis for developing targeted improvement strategies.

Claims

1. A machine tool failure risk ranking method that combines the fuzzy-optimal-worst-multiple criteria optimization compromise, realizes the accurate ranking of machine tool failure risk through the combination strategy of "expanding index system + fuzzy information quantification + scientific weighting + multi-attribute ranking"; characterized in that, The specific steps are as follows: Step 1: According to the structure characteristics of machine tool, focus on the spindle system of numerical control gear milling machine for analysis, reduce the interference of non-key factors; Step 2: Fault data collection: collect the historical fault records of the target machine tool, including fault mode, fault reason, fault frequency O, maintenance cost M; The fault mode includes circular tooth profile belt damage and spindle heating, and the fault reason includes insufficient pre-tightening force and poor lubrication; Step 3: Develop fuzzy evaluation criteria based on intuitive reminders, invite 3 or more machine tool field experts, and evaluate the "severity S" and "detectability D" of each failure mode according to the preset criteria; evaluation parameters such as ; Step 4: The expert evaluation is weighted and de-fuzzed according to the intuition trapezoidal fuzzy formula, the frequency O and the maintenance cost M of the fault are combined, and the comprehensive evaluation matrix is obtained and de-fuzzed; Step 5: Determine the index weight based on the BWM method; first, the experts specify the "best criterion" and the "worst criterion" from the expanded index system (S, O, D, M); and compare each other index with the best and worst index one by one to construct a comparison vector , ; Step 6: Realize fault mode sorting based on VIKOR method; The evaluation matrix is normalized to eliminate the dimension effect; the maximum group utility of the failure mode is calculated by the VIKOR method , the minimum individual regret , and the comprehensive evaluation value , and the results are sorted according to .

2. A fuzzy-optimistic-pessimistic-multiple criteria optimization compromise fused machine tool failure risk ranking method according to claim 1, characterized in that, In step 4, there are members of the team. Several experts conducted risk factor evaluations, with each expert having a weight of [weight missing]. Then the weighted evaluation value of each fault for: In the formula: - the element of the i-th row and j-th column of the k-th expert evaluation matrix; - the element of the synthetic evaluation matrix in the i-th row and j-th column; The elements of the comprehensive evaluation matrix are de-fuzzed: In the formula: — the deblurred evaluation matrix element; - Evaluate each vertex of the fuzzy number elements of the matrix i rows and j columns.

3. A fuzzy-optimistic-pessimistic-multiple criteria optimization compromise fused machine tool failure risk ranking method according to claim 1, characterized in that, In step 5, the best-other vector BO: describes the importance of the best criterion relative to all other criteria on a 1-9 scale, i.e. ; 1 represents equal importance, and 9 represents extreme importance; Other - Worst Vector OW: Describes the importance of all criteria relative to the worst criterion on the same scale; i.e. ; wherein - an error, which in general it is desirable to be as small as possible; - the jth element of - the jth element of denotes the jth element of - weight of the jth indicator; , - weights of the best and worst criteria; After solving the model, the consistency ratio needs to be checked, and generally CR<0.1 is required to ensure the result is reliable.

4. A fuzzy-optimistic-pessimistic-multiple criteria optimization compromise fused machine tool failure risk ranking method according to claim 1, characterized in that, The VIKOR method in step 6 is as follows: With m faults, n criteria form ; data normalization, eliminate the dimensional effect, the benefit type criteria and cost type criteria using different processing methods, respectively, as formula (7) and formula (8): wherein: — a dimensionless value after normalization; - the value of the ith scheme under the jth criterion; - the minimum and maximum values of the jth evaluation criterion, respectively Determining positive and negative ideal solutions of a matrix As in equations (9), (10);​ Computing group utility and individual regret The positive ideal solution is as formula (11), (12): Finally, the benefit ratio of each benefit is calculated and the ranking result is obtained according to the size of each failure ​ In the formula: v is used to weigh the group utility and individual regret, and v=0.5 is taken.

Images