Electrical discharge machining evaluation system and electrical discharge machining evaluation method

By designing a discharge processing evaluation system, using feature calculation, coefficient of variation calculation and divergence analysis modules to evaluate the discharge processing signals, the problem of large processing errors in traditional methods is solved, and more efficient and accurate discharge processing evaluation and adjustment is achieved.

CN119426734AActive Publication Date: 2025-02-14METAL INDS RES & DEV CENT
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Patent Information

Application Number
CN202310959005.6
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2023-08-01
Publication Date
2025-02-14
Estimated Expiration
2043-08-01

AI Technical Summary

Technical Problem

Traditional electric discharge processing methods rely on human eyes to observe or listen to sound to judge the processing conditions, which can easily lead to processing errors. Especially in long-term electric discharge processing, the error has a greater impact and lead to workpiece processing failure.

Method used

A discharge processing evaluation system is designed, including a storage device and a processor. Through the feature calculation module, the variation coefficient calculation module and the divergence analysis module, the characteristic parameters, the variation coefficient and divergence analysis results are calculated based on multiple sets of discharge signals to achieve the Evaluation of discharge processing results.

Benefits of technology

The system can effectively evaluate the results of discharge processing, reduce processing errors, and improve the success rate of workpiece processing. Especially in long-term discharge processing, it can provide immediate evaluation and adjustment and improve processing efficiency.

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Abstract

The invention provides an electrical discharge machining evaluation system and an electrical discharge machining evaluation method. An electrical discharge machining evaluation system includes a storage device and a processor. The storage device is used for storing a feature calculation module, a variable coefficient calculation module and a divergence analysis module. The processor is electrically connected with the storage device and is used for executing the characteristic calculation module, the variable coefficient calculation module and the divergence analysis module and receiving a plurality of groups of discharge signals from the electric discharge machine. The feature calculation module is used for calculating multiple sets of feature parameters according to the multiple sets of discharge signals. The variation coefficient calculation module is used for calculating a plurality of groups of variation coefficients according to the plurality of groups of characteristic parameters. The divergence analysis module is used for carrying out divergence calculation according to the plurality of groups of characteristic parameters so as to generate a divergence analysis result.
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Description

Technical Field

[0001] The invention relates to a workpiece machining evaluation mechanism, and in particular to an electrical discharge machining evaluation system and an electrical discharge machining evaluation method. Background Art

[0002] Generally speaking, conventional EDM requires the user to observe the machining conditions with the human eye or judge the machining results by listening to the sound, which is prone to machining errors. Furthermore, if the EDM time is long, the impact of the aforementioned machining errors will increase, and eventually lead to workpiece machining failure. Summary of the invention

[0003] According to an embodiment of the present invention, the electrical discharge machining evaluation system of the present invention includes a storage device and a processor. The storage device is used to store a feature calculation module, a coefficient of variation calculation module and a divergence analysis module. The processor is electrically connected to the storage device, and is used to execute the feature calculation module, the coefficient of variation calculation module and the divergence analysis module, and receive multiple sets of discharge signals from the electrical discharge machine. The feature calculation module is used to calculate multiple sets of feature parameters based on multiple sets of discharge signals, and the coefficient of variation calculation module is used to calculate multiple sets of coefficients of variation based on multiple sets of feature parameters. The divergence analysis module is used to perform divergence calculation based on multiple sets of feature parameters to generate divergence analysis results.

[0004] According to an embodiment of the present invention, the discharge machining evaluation method of the present invention includes the following steps: receiving multiple groups of discharge signals from an electric discharge machining machine; calculating multiple groups of characteristic parameters based on the multiple groups of discharge signals; calculating multiple groups of coefficients of variation based on the multiple groups of characteristic parameters; and performing divergence calculation based on the multiple groups of characteristic parameters to generate a divergence analysis result.

[0005] Based on the above, the electrical discharge machining evaluation system and the electrical discharge machining evaluation method of the present invention can effectively evaluate the electrical discharge machining results.

[0006] In order to make the above features and advantages of the present invention more clearly understood, embodiments are given below with reference to the accompanying drawings for detailed description. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] Figure 1 is a schematic diagram of an electrical discharge machining evaluation system according to an embodiment of the present invention;

[0008] Figure 2 is a flow chart of an electrical discharge machining evaluation method according to an embodiment of the present invention;

[0009] Figure 3 is a schematic diagram of multiple modules of an embodiment of the present invention;

[0010] Figure 4 is a schematic diagram of a workpiece according to an embodiment of the present invention;

[0011] Figure 5 is a schematic diagram of a discharge voltage and a discharge current according to an embodiment of the present invention;

[0012] Fig. 6A is a schematic diagram of parameter comparison of an embodiment of the present invention;

[0013] Figure 6B is a schematic diagram of parameter comparison of another embodiment of the present invention;

[0014] Figure 7 is a schematic diagram of a divergence analysis result according to another embodiment of the present invention.

[0015] Description of Reference Numerals

[0016] 100: EDM evaluation system;

[0017] 110: processor;

[0018] 120: storage device;

[0019] 201, 400: workpiece;

[0020] 202: electrical discharge machine;

[0021] 310: feature calculation module;

[0022] 320: parameter control module;

[0023] 330: coefficient of variation calculation module;

[0024] 340: divergence analysis module;

[0025] 350: evaluation module;

[0026] 401: first contact surface;

[0027] 402: second contact surface;

[0028] 501: discharge voltage signal;

[0029] 502: discharge current signal;

[0030] D1, D2, D3: direction;

[0031] S210~S240: steps. DETAILED DESCRIPTION

[0032] Reference will now be made in detail to exemplary embodiments of the present invention, examples of which are illustrated in the accompanying drawings. Whenever possible, the same reference numerals are used in the drawings and the description to refer to the same or like parts.

[0033] Figure 1FIG. 1 is a schematic diagram of an electrical discharge machining evaluation system according to an embodiment of the present invention. Figure 1 The EDM evaluation system 100 includes a processor 110 and a storage device 120. The processor 110 is electrically connected to the storage device 120. The storage device 120 can store algorithms and programs of multiple modules for the processor 110 to read and execute. The storage device 120 can also store relevant data, data and analysis results generated during the EDM evaluation process. In this embodiment, the processor 110 is electrically connected to the EDM machine 202, and the EDM machine 202 is used to perform EDM on the workpiece 201, wherein the workpiece 201 can be a metal material.

[0034] In this embodiment, the processor 110 may include, for example, a central processing unit (CPU), a graphics processing unit (GPU), or other programmable general-purpose or special-purpose microprocessors, digital signal processors (DSP), programmable controllers, application specific integrated circuits (ASIC), programmable logic devices (PLD), other similar processing devices, or a combination of these devices.

[0035] In this embodiment, the storage device 120 may be, for example, a dynamic random access memory (DRAM), a flash memory, or a non-volatile random access memory (NVRAM).

[0036] Figure 2 FIG. 1 is a flow chart of an electrical discharge machining evaluation method according to an embodiment of the present invention. Figure 1 as well as Figure 2, the EDM evaluation system 100 may execute the following steps S210 to S240. In the present embodiment, the user may operate the EDM machine 202 to perform EDM on the workpiece 201, wherein the user may set different sets of machining setting parameters for the EDM machine 202 to perform EDM on the workpiece 201 multiple times. In step S210, the processor 110 may receive multiple sets of discharge signals from the EDM machine 202. In the present embodiment, the multiple sets of discharge signals may include a discharge current signal and a discharge voltage signal, respectively, and the discharge current signal and the discharge voltage signal are high-frequency full-range signals, respectively. The EDM machine 202 may provide discharge signals to the processor 110 during multiple EDM processes.

[0037] In step S220, the processor 110 may calculate multiple sets of characteristic parameters according to the multiple sets of discharge signals. In this embodiment, the multiple sets of characteristic parameters may include average spark frequency (Average Speak Frequency, ASF), average discharge current pulse duration (Average Discharge Current Pulse Duration, ADCPD), average discharge peak current (Average Peak Discharge Current, APDC), average discharge energy (Average Discharge Energy, ADE), average ignition delay time (Average Ignition Delay Time, AIDT), average gap voltage (Average Gap Voltage, AGV) and open circuit ratio (Open Circuit Ratio, OCR).

[0038] The average spark frequency (ASF) can satisfy the following formula (1), where Nt is the total number of sparks in one operation period, and Tt is the time length of this operation period.

[0039]

[0040] The average discharge current pulse duration (ADCPD) may satisfy the following formula (2), where Δti is the duration length of the i-th spark, and i is a positive integer.

[0041]

[0042] The average discharge peak current (APDC) can satisfy the following formula (3), where Ii(max) is the maximum current value of the i-th spark.

[0043]

[0044] The average discharge energy (ADE) may satisfy the following formula (4), where Ei is the discharge energy of the i-th spark. Ei may satisfy the following formula (5), where Vt is the discharge voltage, and It is the discharge current.

[0045]

[0046]

[0047] The average ignition delay time (AIDT) may satisfy the following formula (6), where td,i is the open circuit voltage time of the i-th spark, and te,i is the ignition delay time of the i-th spark.

[0048]

[0049] The average gap voltage (AGV) may satisfy the following formula (7), where Vi(max) is the maximum gap voltage generated during the i-th spark generation period.

[0050]

[0051] The open circuit ratio (OCR) may satisfy the following formula (8), where Ot may be the total number of open circuits. An open circuit is defined as when the voltage peak Vi(max) ends and the discharge is about to begin, but the current peak Ii(max) does not rise.

[0052]

[0053] The processor 110 may execute the above formulas (1) to (8) to obtain the corresponding characteristic parameters. In step S230, the processor 110 may calculate multiple sets of coefficients of variation (CV) based on the multiple sets of characteristic parameters. In this embodiment, the coefficient of variation may be used as an evaluation indicator for evaluating the degree of dispersion of multiple discharge machining results corresponding to different machining setting parameters. The system or user may use the multiple sets of coefficients of variation to effectively evaluate whether specific machining setting parameters are suitable for the discharge machining of the workpiece 201. The coefficient of variation is defined as the value obtained by dividing the standard deviation (σ) of a set of data by the mean (μ) (CV = σ / μ). The coefficient of variation is a relative difference quantity and can be used to compare the dispersion of its data with another set of data.

[0054] In step S240, the processor 110 may perform a divergence calculation based on the multiple sets of characteristic parameters to generate a divergence analysis result. In this embodiment, the divergence analysis result may be used to provide a distribution relationship between different evaluation indicators of multiple EDM results corresponding to different machining setting parameters, so that the system or the user may effectively evaluate whether a specific machining setting parameter is suitable for the EDM of the workpiece 201. Therefore, the EDM evaluation system 100 and the EDM evaluation method of this embodiment may effectively provide a variety of evaluation indicators for the system or the user to effectively evaluate whether a specific machining setting parameter is suitable for the EDM of the workpiece 201. However, the specific implementation of the above steps will be illustrated by the following embodiments.

[0055] Figure 3 is a schematic diagram of multiple modules according to an embodiment of the present invention. Figure 4 is a schematic diagram of a workpiece according to an embodiment of the present invention. Figure 1 as well as Figure 3 The storage device 120 may, for example, store a feature calculation module 310, a parameter comparison module 320, a variation coefficient calculation module 330, a divergence analysis module 340, and an evaluation module 350. The processor 110 may execute the feature calculation module 310, the parameter comparison module 320, the variation coefficient calculation module 330, the divergence analysis module 340, and the evaluation module 350 to implement the electrical discharge machining evaluation method of the present invention.

[0056] For example, refer to Figure 4 , workpiece 201 can be realized as follows Figure 4 Workpiece 400 is shown. Figure 4 is a side perspective view of the workpiece 400. The opening surface of the workpiece 400 may be parallel to a plane (e.g., a horizontal plane) formed by the extension of the direction D1 and the direction D2. The electrode of the EDM machine 202 may enter the opening of the workpiece 400 along the direction D3 (e.g., a vertical direction) and perform EDM on the inside of the workpiece 400 to shape the internal structure of the workpiece 400. The direction D1, the direction D2, and the direction D3 may be perpendicular to each other. The EDM machine 202 may perform EDM on, for example, the first contact surface 401 and the second contact surface 402 inside the workpiece 400 according to a plurality of sets of EDM setting parameters, and the processor 110 may receive a plurality of sets of discharge signals from the EDM machine 202.

[0057] Matching reference Figure 5 , Figure 5 FIG. 1 is a schematic diagram of a discharge voltage and a discharge current according to an embodiment of the present invention. A set of discharge signals may include: Figure 5The discharge voltage signal 501 and the discharge current signal 502 are shown. In this regard, during the charging period T1, the discharge voltage signal 501 can be pulled up to generate a charging waveform (the discharge machining machine 202 charges the electrode), and during the discharge period T2, due to the spark generated between the electrode and the workpiece 400, the signal waveform of the discharge voltage signal 501 will be pulled down. In contrast, during the discharge period T2, the signal waveform of the discharge current signal 502 will be pulled up to generate a discharge waveform. However, Figure 5 This is only an exemplary embodiment, and the waveforms of the discharge voltage signal and the discharge current signal may be different for each discharge.

[0058] The characteristic calculation module 310 can obtain the duration of the spark △ti, the maximum current value of the spark Ii(max), the gap voltage value of the spark Vi(max), the open circuit voltage time td,i and the ignition delay time te,i, and other related parameters according to the discharge voltage signal 501 and the discharge current signal 502. Then, the processor 110 can perform operations such as the above formulas (1) to (8) according to the above-mentioned multiple parameters to obtain multiple sets of characteristic parameters.

[0059] Matching reference Fig. 6A as well as Figure 6B . Fig. 6A It is a schematic diagram of parameter comparison according to an embodiment of the present invention. Figure 6B is a schematic diagram of parameter comparison of another embodiment of the present invention. The parameter comparison module 320 can generate multiple sets of parameter comparison results based on the multiple sets of characteristic parameters, wherein each set of the multiple sets of parameter comparison results is a percentage distribution result corresponding to multiple different characteristic parameters of the same parameter type. For example, the EDM machine 202 can perform EDM on the workpiece 400 according to three different sets of machining setting parameters (e.g., parameter A, parameter B, and parameter C, wherein parameter A, parameter B, and parameter C are machine setting combinations such as voltage, current, and discharge time), and during the EDM process, the processor 110 can obtain three sets of parameter comparison results corresponding to the multiple characteristic parameters.

[0060] Fig. 6A as well as Figure 6B The percentage in is used to indicate the time proportion of different parameters in the EDM process. First of all, Fig. 6A as well as Figure 6B Each bar graph shown in FIG. 1 corresponds to a different characteristic parameter. Different characteristic parameters represent different percentages. Figure 6BFor example, assuming that feature 1 is the average spark frequency, the number of sparks measured by parameter B within a set time accounts for up to about 75%, and the total number of sparks is the sum of the number of sparks of parameters A, B and C within the set time. In other words, it can be said that parameter B has an excellent effect in the feature of average spark frequency. Or, assuming that feature 2 is average energy, the average energy measured by parameter C within a set time accounts for up to about 65%, and the basis of the proportion is the sum of the average energy of parameters A, B and C. In other words, the performance of parameters A, B and C in each feature can be comprehensively considered to select the most suitable parameter combination.

[0061] In this regard, Fig. 6A As shown, Fig. 6A The electrical discharge machining results of the first contact surface 401 of the workpiece 400 by the electrical discharge machining machine 202 based on three different sets of machining setting parameters are shown in FIG. Figure 6B As shown, Figure 6B The discharge machining results of the second contact surface 402 of the workpiece 400 by the discharge machining machine 202 based on three different sets of machining setting parameters are shown. Fig. 6A By comparing the percentages and according to different machining characteristics and calculation results, the user or system can observe that the difference in the influence of the relevant characteristic parameters generated by the EDM with different parameters on the first contact surface 401 (smaller working area) is small, but the user or system can still observe the more suitable parameters. Figure 6B The user or system can observe that the influence of the relevant characteristic parameters produced by the EDM with different parameters on the second contact surface 402 (larger working area) is quite different, and the user or system can observe the more suitable parameters more easily.

[0062] Regarding how to evaluate the optimal parameters, in this embodiment, the higher the average spark frequency, the better the processing efficiency. The average discharge current pulse duration is more consistent with the original setting of the machine, the better (the original setting of the machine will be affected by the processing environment, causing the actual processing performance to deviate from the original machine setting). The larger the average energy, the better the processing efficiency, but too large may cause damage to the workpiece. The smaller the ignition delay time, the better, but too small may cause a short circuit. The less the average gap voltage deviates from the original setting of the machine, the better. The smaller the open circuit ratio, the better.

[0063] For example, corresponding to the EDM result of the second contact surface 402 of the workpiece 400 (the calculation of the coefficient of variation and the divergence analysis of the EDM result of the first contact surface 401 can be analogized), the coefficient of variation calculation module 330 can calculate multiple sets of coefficients of variation based on the aforementioned multiple sets of characteristic parameters. The divergence analysis module 340 can perform divergence calculation based on the multiple sets of characteristic parameters to generate divergence analysis results. In this regard, the divergence analysis module 340 can perform KL (Kullback-Leibler) divergence calculation. Figure 7 , Figure 7 FIG. 3 is a schematic diagram of a divergence analysis result of another embodiment of the present invention. The divergence analysis module 340 may generate Figure 7 The divergence analysis results of . Figure 7 The horizontal axis of the divergence analysis result may correspond to the processing stability index, and the vertical axis may correspond to the processing efficiency index, but the present invention is not limited thereto. Figure 7 For example, it can be the result calculated by t-SNE (Manifold Learning model), where Figure 7 The distance between two adjacent points on the vertical and horizontal axes of the graph is expressed as the Euclidean distance ( Figure 7 The units of the vertical and horizontal axes are used to represent an interval of Euclidean distance. The vertical and horizontal axes of the divergence analysis results can also correspond to other indicators, not limited to Figure 7 As shown. In this regard, for example, the multiple EDM results corresponding to 6 different sets of machining setting parameters may have different distribution trends in the distribution relationship of machining efficiency and machining stability. For example, the multiple EDM results corresponding to the machining setting parameters of the first group (the darkest color) may have clear machining stability and machining efficiency, wherein the machining stability is medium, and the machining efficiency is generally poor. For example, the multiple EDM results corresponding to the machining setting parameters of the sixth group (the lightest color) may have clear machining stability, but have non-fixed machining efficiency, wherein the machining stability is medium, and the machining efficiency may be high or ordinary. In other words, relative to the machining setting parameters of the first group (the darkest color), the multiple EDM of this machining setting parameter (the lightest color) has a higher probability of achieving the EDM characteristics of higher machining efficiency.

[0064] The evaluation module 350 can be used to calculate the scoring parameters according to the divergence analysis results. In this regard, the evaluation module 350 includes a nonlinear machine learning model. After being trained, the evaluation module 350 can obtain the scoring parameters obtained in the divergence analysis results for different processing setting parameters, so that the user or the system can more easily dynamically adjust the processing setting parameters, and can intuitively assist the user or the system in making decisions, so that the EDM machine 202 can be efficiently operated to perform EDM on the workpiece 201.

[0065] Therefore, the EDM evaluation system 100 can establish the above-mentioned divergence analysis results through different machining setting parameters, and the EDM evaluation system 100 can obtain the real-time discharge signal during the actual machining process of the EDM machine 202 on the workpiece 201. In this regard, the real-time discharge signal can generate corresponding characteristic parameters and parameter comparison results after the calculation of the above-mentioned modules, and can be displayed in the divergence analysis result. The user or the system can immediately judge the current machining characteristics and actively or automatically adjust the machining setting parameters to achieve efficient and good EDM for the workpiece 201.

[0066] In summary, the EDM evaluation system and the EDM evaluation method of the present invention can collect multiple sets of discharge signals generated during multiple EDM processes, and perform signal analysis to generate divergence analysis results. In this way, the divergence analysis results can be used to evaluate whether the machining setting parameters used in multiple EDM processes are appropriate, so as to effectively assist users in making decisions.

[0067] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An electrical discharge machining evaluation system, characterized in that: include: A storage device, used to store a feature calculation module, a coefficient of variation calculation module and a divergence analysis module; as well as a processor, electrically connected to the storage device, and used to execute the feature calculation module, the variation coefficient calculation module and the divergence analysis module, and receive multiple sets of discharge signals from the electrical discharge machine, The characteristic calculation module is used to calculate multiple groups of characteristic parameters according to the multiple groups of discharge signals, and the variation coefficient calculation module is used to calculate multiple groups of variation coefficients according to the multiple groups of characteristic parameters. The divergence analysis module is used to perform divergence calculation according to the multiple sets of characteristic parameters to generate divergence analysis results.

2. The electrical discharge machining evaluation system according to claim 1, characterized in that: The plurality of groups of discharge signals respectively include a discharge current signal and a discharge voltage signal.

3. The electrical discharge machining evaluation system according to claim 2, characterized in that: The discharge current signal and the discharge voltage signal are respectively high-frequency global signals.

4. The electrical discharge machining evaluation system according to claim 2, characterized in that: During charging, the discharge voltage signal is pulled up to generate a charging waveform, and during discharging, the discharge voltage signal is pulled down.

5. The electrical discharge machining evaluation system according to claim 4, characterized in that: The plurality of groups of discharge signals also include discharge time respectively.

6. The electrical discharge machining evaluation system according to claim 1, characterized in that: The storage device further stores a parameter comparison module, and the processor executes the parameter comparison module. The parameter comparison module generates multiple groups of parameter comparison results according to the multiple groups of characteristic parameters, wherein each group of the multiple groups of parameter comparison results is a percentage distribution result corresponding to multiple different characteristic parameters of the same parameter type.

7. The electrical discharge machining evaluation system according to claim 1, characterized in that: The divergence analysis module is used to perform KL divergence calculation.

8. The electrical discharge machining evaluation system according to claim 1, characterized in that: The storage device further stores an evaluation module, and the processor executes the evaluation module. The evaluation module is used to calculate the scoring parameter according to the divergence analysis result.

9. The electrical discharge machining evaluation system according to claim 8, characterized in that: The evaluation module includes a non-linear machine learning model.

10. The electrical discharge machining evaluation system according to claim 1, characterized in that: The plurality of groups of characteristic parameters respectively include an average spark frequency, an average discharge current pulse duration, an average discharge peak current, an average discharge energy, an average ignition delay time, an average gap voltage and an open circuit ratio.

11. A method for evaluating electrical discharge machining, characterized in that: include: receiving a plurality of sets of discharge signals from an electrical discharge machine; Calculating multiple groups of characteristic parameters according to the multiple groups of discharge signals; Calculating multiple groups of coefficients of variation according to the multiple groups of characteristic parameters; as well as Divergence calculation is performed according to the multiple groups of characteristic parameters to generate a divergence analysis result.

12. The electrical discharge machining evaluation method according to claim 11, characterized in that: The plurality of groups of discharge signals respectively include a discharge current signal and a discharge voltage signal.

13. The electrical discharge machining evaluation method according to claim 12, characterized in that: The discharge current signal and the discharge voltage signal are respectively high-frequency global signals.

14. The electrical discharge machining evaluation method according to claim 12, characterized in that: During charging, the discharge voltage signal is pulled up to generate a charging waveform, and during discharging, the discharge voltage signal is pulled down.

15. The electrical discharge machining evaluation method according to claim 14, characterized in that: The plurality of groups of discharge signals also include discharge time respectively.

16. The electrical discharge machining evaluation method according to claim 11, characterized in that: Also includes: A plurality of groups of parameter comparison results are generated according to the plurality of groups of characteristic parameters, wherein each group of the plurality of groups of parameter comparison results is a percentage distribution result corresponding to a plurality of different characteristic parameters of the same parameter type.

17. The electrical discharge machining evaluation method according to claim 11, characterized in that: The divergence calculation is a KL divergence calculation.

18. The electrical discharge machining evaluation method according to claim 11, characterized in that: Also includes: The scoring parameters are calculated according to the divergence analysis results by an evaluation module.

19. The electrical discharge machining evaluation method according to claim 18, characterized in that: The evaluation module includes a non-linear machine learning model.

20. The electrical discharge machining evaluation method according to claim 11, characterized in that: The plurality of groups of characteristic parameters respectively include an average spark frequency, an average discharge current pulse duration, an average discharge peak current, an average discharge energy, an average ignition delay time, an average gap voltage and an open circuit ratio.

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