Preliminarily Experimental Study on Servo Control Strategy for Dry Electrical Discharge Machining

doi:10.21203/rs.3.rs-3128942/v1

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Preliminarily Experimental Study on Servo Control Strategy for Dry Electrical Discharge Machining

https://doi.org/10.21203/rs.3.rs-3128942/v1

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published 27 Oct, 2023

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In traditional liquid EDM, huge carbon emissions, and the process is not environmentally friendly. The emergence of electric discharge machining in gas (DEDM) has unfolded a new situation of sustainable development of EDM. However, the problems of poor discharge stability and low machining efficiency have restricted the application of DEDM. Considering that servo control is an important factor affecting the discharge state and machining performance, while related research is rarely reported up to now, we make an exploratively study on the servo control of DEDM to understand its feature and aim to improve the discharge stability and machining efficiency. The relative discharge ratio, machining efficiency, electrode wear and surface roughness with different control strategies were compared and analyzed using a self-built ball screw EDM servo system, and obtained a more effective improvement compared with traditional servo strategy in DEDM. It is found that PD control strategy improved the effective discharge ratio by 40.4% and machining efficiency by 136.55% compared with conventional control strategy. This work also analyzed the servo characteristics under different gas media (oxygen, nitrogen, argon) and putted forward servo optimization scheme, the experimental results verified the effectiveness of improving DEDM from servo strategy, which indirectly proved the matching characteristics of medium and servo in EDM.

EDM in gas (DEDM)

Servo strategies

Gas medium

Electric Discharge Machining in gas (DEDM) has been widely concerned in the field because of its advantages as low tool wear and environmentally friendly etc. It has always been considered as an alternative EDM method. Compared with conventional EDM in oil, the discharge gap in DEDM is very tiny, which makes it very sensitive to spindle servo control strategy. Therefore, a servo control system with strong stability and adaptability to different machining conditions is the basis of implementing the superiority of DEDM. However, most of the research on servo control strategy is based on conventional oil dielectric EDM in and the relevant research on DEDM is very few.

The control strategy of conventional EDM in oil can be generally divided into PID and its improving control method, adaptive control method and control method based on machine learning algorithm etc. ^[1]. Chang established the EDM gap control model based on PI control, and they searched for optimal setting parameters through genetic algorithm ^[2]. Andromeda designed differential evolution for optimization of PID gain in EDM control system ^[3]. Zhang designed a PID servo control system based on discharge current by using the micro-conductivity of wire-EDM medium ^[4]. All the above studies have confirmed the feasibility of establishing the conventional EDM gap control model based on PID algorithm, which has a guiding role in this study.

Researchers have also proposed adaptive control ^[5–6], fuzzy control and its optimal control technology ^[7–9], intelligence algorithm ^[10] etc. aiming to improve the processing efficiency by optimizing the machining process. Despite researchers have used fuzzy control, adaptive control and other control methods to adjust the servo reference voltage or servo speed and have achieved some achievements, however, due to the characteristics of small gap between two electrodes and unstable discharge feature in DEDM, the stability and fast response performance of the servo system are very demanding. Besides, information fuzzy processing in fuzzy control is closely related to knowledge base level, there is a lack of relevant data on DEDM, which may not conducive to control stability and sometimes may reduce control accuracy ^[11]. Meanwhile, adaptive control lacks universality and openness due to the coupling between optimization parameters, and there is a contradiction between parameter estimation methods and control accuracy ^[12]. The advantages of the above two methods have not been verified in DEDM. In this work, considering PID and its improved control strategy integrated the advantages of conventional PID and advanced algorithm like machine learning algorithm etc., it owns merits of simple principle, stable performance and fast response speed; therefore, it meets the internal requirements of DEDM, therefore, this method could be firstly used as a servo control strategy. In view of the description of machining stability, and efficiency are more general, and there is still a lack of basic research on PID control in DEDM, therefore, it is necessary to start with the characteristics of inter-electrode gap to carry out the process test of servo control in DEDM.

According to the preliminary basic experiments, the inter-electrode gap of DEDM under the experimental conditions (middle-fine gauge) is in the range of 10–20 µm. This means that DEDM discharge state is very sensitive to the variation of the inter-electrode gap. Improper spindle servo control could lead to repeated oscillations between open and short circuits; meanwhile, the proportion of short and open circuit in the processing process was more than 70% Therefore, short circuit and open circuit should be considered as the important factors affecting the efficiency of DEDM. By observing the discharge waveforms, we find that the positions of spark and arc discharge points mostly occur in the alternating range of open circuit and short circuit. According to this discharge features of DEDM, arc discharge in DEDM is regarded as effective discharge to improve the utilization ratio of power pulse. Thus, two kinds of servo strategies are adopted in this work. One is a modified servo control strategy; the strategy was determined based on the gap average voltage and short circuit ratio double servo criterion. In this strategy, a variable feeding speed was adopted to reduce the open duration as much as possible, and realized a slower feed speed near the effective discharge point to increase the transition time between the open and short circuit. Another servo strategy is classical PID control. Regard the servo feed system of DEDM as a typical feedback automatic control system, feed speed was adjusted in real time by PID control strategy, aim at the feed speed of spindle could match the clearance characteristics of DEDM better. In this work, basic study on modified and PID control was carried out, then further verify the effective of the servo adjustment through different gases experiments, which could lay a foundation for the improved strategy based on the intelligent optimization algorithm.

3.1 Establishment of inter-electrode gap model for DEDM

Mechanical drive mechanism in this work were ball screw nut. The rotation angle of the servo motor $\text{θ}\text{(}\text{s}\text{)}$ worked as the input and the linear displacement of the actuator ${\text{X}}_{\text{L}}\text{(s)}$ served as the output, then, the transfer function between them can be established as formula (1) [13].

$$G{\text{(}}s{\text{)=}}\frac{{{X_L}{\text{(}}s{\text{)}}}}{{\theta {\text{(}}s{\text{)}}}}{\text{=}}{i_s} \cdot \frac{{{K_L}}}{{{J_L}{s^{\text{2}}}{\text{+}}{B_L}s{\text{+}}{K_L}}}$$

where: i_s is the transmission ratio of the screw nut; K_L is torsional stiffness after conversion;J_L is the moment of inertia after conversion༛B_L is viscous damping coefficient after conversion.

Since it is difficult to measure the inter-electrode gap directly in the actual process, and the discharge gap is very tiny in DEDM, it is generally regarded as approximately proportional between the gap voltage and discharge gap on a very small stroke, therefore, the relationship between the gap voltage feedback signal$\text{ y}\text{(}\text{s}\text{)}$and the gap distance$\text{d}\text{(}\text{s}\text{)}\text{ }$can be expressed as:

$$y{\text{(}}s{\text{)=}}N \cdot d{\text{(}}s{\text{)}}$$

$$d{\text{(}}s{\text{)=}}D - {X_L}{\text{(}}s{\text{)}}$$

Where: N is proportional gain; D is initial inter-electrode gap distance.

Finally, we established the control model of DEDM inter-electrode gap as shown in Fig. 2.

Figure 2. Control model of discharge gap in DEDM.

3.2 PID control strategy simulation

The core of PID control strategy is to determine the appropriate PID parameters to ensure the stability of the system. In general, direct adjustment of PID parameters may cause unpredictable results, therefore for safety reasons, we first used a software to simulate the PID control system. In this section, we compared the effect of different PID parameters on the system, and analyzed the performance characteristics of different PID control strategies, so as to provide basis for the selection of subsequent values.

The proportional coefficient N of servo system feedback was determined. Figure 3 shows the fitted relationship between gap voltage and discharge gap of DEDM at 120V open circuit voltage.

Figure 3. Diagram of voltage and gap

According to the fitting line, determined the proportional gain N to be 4.128. It is noted, in this experimental condition, when the gap distance was more than 30µm, the gap voltage 120 V cannot breakdown compressed air to produce discharge, and the relationship of gap voltage and gap distance could not be obtained.

The spindle ball screw lead of DEDM in this work P_h was 10 mm. K_L, J_L and B_L were calculated according to literature ^[14] and the results are shown in Table 1.

Table 1

Simulation parameters summary
Simulation Parameters	Values
Proportional gain N	4.128
Initial inter-electrode gap D (µm)	180
The transmission ratio of the screw i_s (mm/rad)	1.592
The moment of inertia J_L (kg/m²)	1.377e-4
Torsional stiffness K_L(Nm/rad)	1.018e3
Viscous damping coefficient B_L	0.007

The simulation model of DEDM gap control based on a software was established by substituting parameters, and it as shown in Fig. 4. Based on this model, we conducted simulation on different control strategies.

The simulation results are shown in Fig.5. The main function of proportional control is to speed up the system regulation. We found that when K_p was small (as shown in Fig.5 a)), the oscillation of the control system was weak. With the increase of K_p value, the response speed of the system accelerated, and the system oscillation also increased, as shown in Fig. 5 b)，when K_p increased to 12.5, the oscillation amplitude of the system was close to the discharge gap value, which obviously does not meet the requirements. As shown in Fig.5, When K_p =5.8, the transition time was short and the gap oscillation value was within the range that the DEDM can maintain effective discharge. Therefore, the proportional coefficient K_p took 5.8 as its reference value.

The function of integral control is to eliminate the steady-state error of the system, and is generally used in the system with proportional control and differential control. We set K_d = 0, adjusted the integral coefficient K_i. The simulation results are shown in Fig. 6. The results show that the overshoot of the control system increased with the increasing of integral action. When K_i = 6, The spindle feed produced a negative clearance value, which must be avoided in practical machining. Therefore, on the premise of eliminating static difference, the influence of integral action should be reduced as much as possible. So, we set the reference value of K_i as 2.5.

Finally, we simulated the PD control strategy to analyze the regulating effect of differential control in DEDM. Fig.7 shows the simulation results of PD control strategies with different values. As can be seen from Fig. 7a), compared with P control, the system overshoot under PD control was significantly reduced. The simulation results also show that the increase of the differential coefficient contributed to the improvement of the system rapidity, but when the differential coefficient increased to 8, as shown in Fig.7b), the system produced serious oscillation. Therefore, we set the reference value of differential coefficient K_d as 3.

Figure 6. Simulations of different integral coefficients

A self-made experimental equipment is shown in Fig. 8. The tool electrode was a copper tubular electrode with external diameter of 3 mm and the inner hole was 1mm, the insulation medium was 0.4 MPa compressed air, and the processing polarity was positive.

Figure 8. DEDM machine tools

In order to fully explore the machining influence parameters, the tool electrode rotation was also included in the control group. The single processing time was 30 minutes, and the verification indexes included relative discharge ratio, material removal rate (MRR), tool electrode wear (TWR) and surface roughness (Ra).

4.1 Experiments of electrode without rotation

Aim to understand the basic DEDM performance of different control strategy, we carried out the machining experiment electrode without rotation. The experiment included conventional strategy, modified strategy, P control strategy, PI control strategy, PD control strategy and PID control strategy. The conventional control strategy was used as the control group for comparative analysis, the voltage threshold range was set of 4.5-1.5V.

Figure 9 shows the comparison of experimental results of DEDM with different control strategies. As can be seen from the Fig. 9a), compared with the conventional strategy, the modified strategy was better in controlling the short circuit ratio and reducing the open circuit ratio, the proportion of effective discharge ratio was increased by 32.6%, and the machining efficiency was increased by 21.5%. Compared with the four control strategies, it was found that although the proportional control strategy effectively reduced the open circuit ratio but aggravated the occurrence of short circuit state, so the machining efficiency was even lower than that of the conventional strategy. In PI, PD and PID control, the open circuit rate of PI control was low, while the short circuit rate remained high. Due to the introduction of early correction by differential control, the short circuit state of PD and PID control decreased. PID control had obvious improvement effect. Compared with the conventional strategy, the proportion of effective discharge state was increased by 79.2%, and the machining efficiency was improved by 88.3%. The electrode wear of all control strategies was very small, which is consistent with the machining characteristics of DEDM (Fig. 9c)).

Figure 9. Machining effect of different control strategies

Considering arc discharge was not suppressed in the modified strategy, its rationality needs to be proved by surface roughness. The conventional strategy, the modified strategy and the PID control strategy with the highest machining efficiency were compared in the experiment.

Figure 10. Comparison of workpiece surface topography (no rotation)

4.2 Experiments of electrode with rotation

Tool electrode rotation is an important factor affecting the performance of DEDM. The electrode speed was set at 800 rpm to obtain better experimental results, and the processing results of different control strategies with electrode rotation were compared and it is shown in Fig. 11. The effective discharge ratio and machining efficiency of the modified strategy were increased by 32.7% and 114%, respectively, compared with the conventional strategy, which indicates that the modified strategy can improve the performance of DEDM more obviously with the aid of tool electrode rotation. This is because the tool electrode rotation improves the chip ejection conditions in DEDM, which improved, to a certain extent, the adjustable margin in DEDM control and the pulse utilization rate.

Under the same electrode rotation condition, the control effects of PI, PD and PID were better reflected, and the effective discharge ratio of PI, PD and PID strategy was increased by 17.5%, 40.4% and 31.5%, respectively, compared with the conventional strategy. The processing efficiency increased by 63.3%, 136.5% and 93.3%, respectively. In addition, the comparison showed that the comprehensive control effect of PI and PID was not as good as that of PD. As shown in Fig. 11a), PI and PID control of the ratio of open circuit and short circuit ratio more than PD control, this is because compared with no rotation tool electrode, the tool electrode rotation of processing depth was deeper, and with the increase of processing depth, the possibility of worsening conditions inter-electrode increased.

Figure 11. Machining effect of different control strategies

Figure 11c) shows that the rotation of the tool electrode has little influence on the electrode wear under a given machining condition compared with Fig. 9c). We compared workpiece surface roughness of the conventional strategy, the modified strategy and the PD-controlled strategy with the highest processing efficiency and the results is shown in Fig. 12.

Fig. 12 shows the surface topography of the workpiece after processing and the corresponding surface roughness was 2.6756μm, 3.6316μm and 3.6488μm, respectively. Compared with Fig.10, for the conventional strategy, due to the joint action of the tool electrode rotation, the discharge state tends to improve, so the surface roughness of the workpiece is reduced. For the modified strategy, the arc made the surface roughness increase to some extent, but the surface did not deteriorate.

The results show that the PID servo control system can improve the discharge stability and machining efficiency, and does not lead to the deterioration of workpiece surface roughness.

4.3 Analysis of servo characteristics of different gas media

The previous verification experiment proves that the difference of servo control parameters will lead to the difference of discharge efficiency and stability. In this section, we further studied the servo control characteristics of different gas media. The difference of oxygen, nitrogen and argon in servo control was compared with compressed air as reference. Through the previous experiments, we found that the machining performance of conventional strategy, P control and PI control was not ideal. Therefore, the servo strategy selected in this section included modified strategy, PD control and PID control, the servo parameters used in the experiment were consistent with the previous section.

Figure13 shows the comparison of relative discharge ratios between oxygen medium and compressed air under different control strategies, and take PD control as an example, as shown in Fig. 14, to analyze the reasons. It can be seen that the short-circuit ratio of oxygen medium was much lower than that of compressed air, but the open circuit ratio was higher.

Figure 14. PD-controlled discharge waveform in oxygen

It can be seen from the PD controlled discharge waveforms in Fig. 14 that when several normal discharge waveforms appeared between poles, the discharge state transferred from spark discharge to open circuit state. There may be two reasons for this: first, the current feed speed was less than the removal speed of oxygen medium, and the gap increased due to effective discharge removal of materials cannot be compensated in time; second, due to the advance correction effect of differential control, when the deviation between gap voltage and target voltage was reduced, the controller adjusted the electrode back off. In the following experiments, we appropriately increased the upper limit of feed speed and servo regression length of the modified strategy. For PD and PID control, increased the proportional coefficient.

Figure 16. PD-controlled discharge waveform

Analysis of the reason, nitrogen and argon discharge gap is smaller than compressed air, so the current servo system is prone to overregulation in the face of a smaller adjustment range. Considering that the effective discharge of the two media generally occurs between the alternating state of open circuit and short circuit, on the premise of reducing the duration of open circuit state, the servo adjustment scheme of nitrogen and argon was determined: for modified strategy, reduced the upper limit of feed speed and deceased the length of servo backstep appropriately, to increase the possibility of effective discharge. For PD and PID control, reduced the proportional coefficient value and increase the differential coefficient value. After adjusting the servo parameters, the effective discharge ratio and discharge waveforms of three gases are shown in Fig. 17.

It can be seen from Fig. 17 that the effective discharge ratios of oxygen, nitrogen and argon were increased by 16.32%, 30.96% and 58.39%, respectively; more continuous effective discharge was achieved in oxygen, and the discharge waveforms in nitrogen and argon have also been improved. The experimental results verified the effectiveness of adjusting servo parameters.

The machining speed and surface roughness of different gases under different strategies were compared, and the results were shown in Fig.18. As can be seen from the Fig.18, oxygen processing speed is the highest, but due to the more intense discharge energy, the workpiece surface roughness was also the largest, suitable for rough machining process; for nitrogen and argon, even if the discharge state were improved by adjusting from the perspective of servo control, the processing speed were still very low because the chemical properties of the medium are more stable, and the dielectric less likely to form breakdown.

Figure 17. Comparison of effective discharge ratios and discharge waveforms after adjustment

In addition, we found the electrode wear and surface roughness of nitrogen and argon are relatively smaller than that of oxygen and compressed air. In compressed air medium, the machining speed, electrode loss and surface roughness after machining are relatively good, and the machining cost is low, in line with the concept of green manufacturing. Therefore, in order to promote the application of gas medium EDM, it is necessary to carry out in-depth research on the servo control of gas medium. EDM.

Figure 18. Comparison of machining performance after servo parameters adjustment

In this study, the servo control model of DEDM was simulated, experiment was carried out for different control strategies and gas media. conclusions are summarized as follows:

Compared with the conventional machining strategy, for no electrode rotation, the effective discharge ratio of modified and PID control strategies were improved by 36.2% and 79.2%; the machining efficiency of the modified and PID were improved by 21.5% and 88.3%. For the electrode rotation, the effective discharge ratio of the modified strategy, PD and PID control was increased by 32.7%, 40.4% and 31.5%, and machining efficiency increased by 114%, 136.55% and 93.3%, respectively.

Take the arc discharge is considered as effective discharge, the roughness of machined surface increases slightly.

The experiments of servo optimization scheme for different gases verified that the appropriate servo control is one of the effective methods to improve machining efficiency in DEDM.

Acknowledgements

This research was sponsored by the self-made equipment project construction funds of Harbin Institute of Technology.

Author contribution

All authors contributed to the study. Material preparation, structure of this work and manuscript refine were performed by Liqing Li. The servo strategies, the simulation analysis and the servo experiment of different gases were performed by Yunhang Wang, and academic literature collection and draft of the manuscript were conducted by Yitao Chen.

The authors declared no potential conﬂicts of interest with respect to the participation, publication, and competing interests.

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You are reading this latest preprint version

Preliminarily Experimental Study on Servo Control Strategy for Dry Electrical Discharge Machining

Status:

Journal Publication

Version 1

Abstract

Figures

1 Introduction

2 Proposal of servo control scheme for DEDM

3 PID control strategy model and simulation

3.1 Establishment of inter-electrode gap model for DEDM

3.2 PID control strategy simulation

4 Servo characteristics analysis and experiment

4.1 Experiments of electrode without rotation

4.2 Experiments of electrode with rotation

4.3 Analysis of servo characteristics of different gas media

5 Conclusions

Declarations

References

Status:

Journal Publication

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