# Experimental investigation of the pulse duration on the efficiency and electrode wear of electrohydraulic forming process

Yann Ledoux

► To cite this version:

Yann Ledoux. Experimental investigation of the pulse duration on the efficiency and electrode wear of electrohydraulic forming process. Manufacturing Review, 2023, 10, pp.380 - 398. 10.1051/mfre-view/2023016. hal-05347537

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RESEARCH ARTICLE

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# Experimental investigation of the pulse duration on the efficiency and electrode wear of electrohydraulic forming process

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Yann Ledoux*

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Univ. Bordeaux, I2M, UMR 5295, 33400 Talence, France

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Received: 3 July 2023 / Accepted: 24 October 2023

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**Abstract.** Electrohydraulic Forming (EHF) is a high velocity sheet metal forming technique using high-energy electrical discharges in a water chamber to shape complex parts. Despite its potential benefits, the EHF process is not well understood, and further research is needed to comprehend the underlying physical mechanisms and optimize the process parameters. One of the critical factors is the control of energy discharge within the forming chamber in terms of arc duration. The proposed study aimed to analyze its impact on the characteristics of electrohydraulic forming focusing on the efficiency of the operation and electrode wear. As a result, the height of the formed parts was compared and used to evaluate the efficiency of the operation. The electrode wear was estimated by a phenomenological model. By comprehending the relationships between these factors and operational efficiency, a tradeoff was established to enhance the EHF process, taking into account electrode wear, thereby expanding its industrial applications.

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**Keywords:** Electrohydraulic forming / pulse duration / electrode erosion / process efficiency

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## 1 Introduction

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Electrohydraulic forming (EHF) is a sheet metal forming process that uses high-energy electrical discharges between electrodes placed in a water chamber. The generation of arcs produces pressure waves that exert force on the metal, enabling the production of complex-shaped parts with significant cost and time savings. This process is particularly advantageous for the automotive, aerospace, and construction industries, as it enables the production of complex-shaped parts while minimizing costs and production time. With high deformation rates ($10^2$ to $10^4$ s$^{-1}$), it becomes feasible to shape high-performance alloys (Dual Phase, titanium alloys) (e.g., in [1–3]), that are difficult to form using traditional methods. Additionally, the high deformation speeds reduce spring backs and result in good geometric precision in the produced parts.

However, despite its potential advantages, electrohydraulic forming remains a process that requires extensive research to better understand the complex and interconnected physical mechanisms. Key aspects requiring further investigations include pressure wave generation and propagation in water, water-electrode interaction, and heat transfer phenomena.

From a technological standpoint, the ability to control the quality of the formed parts is a critical factor that currently limits the widespread adoption of electrohydraulic forming in various industries (reported in [4] or in [5]).

Among these process parameters, few studies focus on controlling the energy discharge within the forming chamber. Technical solutions exist to facilitate arc generation (e.g., using a bridge wire between electrodes or several electrodes...), but none address how to control the energy deposition within the forming chamber in terms of arc duration and shape of the power signal. However, depending on the characteristics of the electrical circuit (i.e., circuit configuration and choice of component values), the energy deposition can be significantly modified leading to directly impact the process characteristics.

The proposed study aims to analyze the impact of arc duration and shape on the characteristics of electrohydraulic forming, in order to investigate the influence of the electrical discharge on forming performance. Controlling the characteristics of the electrical discharge (power level, duration) can affect the efficiency of the forming operation and the level of stress endured by electrical components, particularly the electrodes and their wear. This aspect is critical in industrial applications, as it will be necessary to adjust the electrode shape and gap between pulses of energy.

In this study, electrohydraulic forming tests were conducted to investigate the impact of pulse duration on the efficiency of the operation and electrode wear. The

<footnote>* e-mail: yann.ledoux@u-bordeaux.fr</footnote>
<table><caption>**Table 1.** Comparison of HVF processes (form [6]).</caption><thead><tr><th rowspan="2"></th><th colspan="3">Explosive forming</th><th rowspan="2">Electromagnetic forming</th><th colspan="2">Electrohydraulic forming</th></tr><tr><th>Standoff</th><th>Contact</th><th>Confined</th><th>Bridge wire</th><th>Spark discharge</th></tr></thead><tbody><tr><td>Size limits</td><td>6 m diam.</td><td>6 m diam.</td><td>1.5 m diam</td><td>0.3 m diam.</td><td>1.2 m diam.</td><td>1.2 m diam.</td></tr><tr><td>Shape complexity</td><td>Moderately</td><td>Simple</td><td>Complex</td><td>Complex</td><td>Complex</td><td>Complex</td></tr><tr><td>Advantages</td><td>Large parts</td><td>High pressures</td><td>Reduced operations for complex shapes</td><td>Controllability & repeatability</td><td>Controllability & repeatability</td><td>Controllability & repeatability</td></tr><tr><td>Capital cost</td><td>Low</td><td>Low</td><td>Low</td><td>Moderate to high</td><td>Moderate</td><td>Moderate</td></tr><tr><td>Tooling cost</td><td>Low</td><td>Low</td><td>Moderate</td><td>Moderate to high</td><td>Low</td><td>Low</td></tr><tr><td>Production rate</td><td>0.4–4 pts/hr</td><td>0.4–4 pts/hr</td><td>2–12 pts/hr</td><td>To 1000 pts/hr</td><td>4–12 pts/hr</td><td>To 50 pts/hr</td></tr><tr><td>Leadtime</td><td>Short</td><td>Short</td><td>Short</td><td>Moderate to long</td><td>Moderate to long</td><td>Moderate</td></tr><tr><td>Facility</td><td>Remote</td><td>In-plant or remote</td><td>In-plant or remote</td><td>In-plant</td><td>In-plant</td><td>In-plant</td></tr></tbody></table>

experimental setup included typical tooling capable of producing hemispherical deep-drawn components. Measurement devices were used to quantify the stored electrical energy and the characteristics of the energy pulse (current and voltage at the electrodes) during each discharge. To vary the pulse duration while maintaining the same energy level, the RLC electrical circuit was utilized. This circuit was adjusted to provide pulse durations ranging from 60 µs to several milliseconds. By analyzing the height of the component achieved after each test, the influence of pulse duration on the forming process could be quantified. Additionally, electrode wear was estimated using a phenomenological model sourced from the literature. Through these experimental procedures, valuable insights were gained regarding the relationship between pulse duration and the efficiency of the electrohydraulic forming operation, as well as the extent of electrode wear. The results obtained from this analysis will contribute to a deeper understanding of how different pulse durations affected the overall performance and durability of the electrohydraulic forming process. Ultimately, this knowledge will aid in optimizing process parameters of electrohydraulic forming in practical industrial applications.

## 2 Bibliographic review

### 2.1 High velocity forming processes (HVF)

Samei, in [6], stated that automotive industries first ventured into developing new metal forming technology not only to reduce costs and increase manufacturing productivity but also to be able to shape thinner sheets and thus decrease the weight of vehicles.

In this regard High Energy Rate Forming (HERF) technologies such as explosive forming, electromagnetic forming, and electrohydraulic forming came into focus. Recently, there has been a commercial interest in adopting the electrohydraulic technique for the production of smaller parts requiring very high die contact pressures but little overall sheet expansion as reported in [7]. These authors have demonstrated that since the 1960s, the EHF process has been employed as a specialized high-speed

forming method for shaping sheet metal components. The research works in High Velocity Forming (HVF) were extensively studied between about 1955 to 1970 (e.g., technological and scientific synthesis proposed by [8]). Despite the potential benefits of these forming processes in various sectors, including transportation, automotive parts, medical tools, joining, packaging, and forming different machinery parts, there has been a lack of research activity over the past 40 yr. Some studies can be noticed dedicated to setting up of complex numerical simulations or to studying the formability of low ductility material like aluminum alloys, nickel alloys, magnesium alloys, stainless steels, advanced high-strength steels (AHSS), high-strength steels (HSS) titanium, Inconel 718 like in [9] or more recently in [10].

HVF refers to a set of techniques which are used for metal forming with high strain rate. In HVF process the strain rate ranges from $10^2$ to $10^4$ s$^{-1}$ [11] and the forming duration can be microseconds to nanosecond scale. In these techniques a high kinetic energy is exerted to the work piece by accelerating it to a highly velocity until it fills the cavity of the die or to undergo the process of plastic deformation without die. Three kinds of high velocity forming techniques can be listed i, Explosive forming technique; ii, Electromagnetic forming technique and iii, Electrohydraulic forming technique. A comparison can be found in Table 1, proposed by [6] derived from book of [8]. In the explosive forming technique, it is assessed characteristics based on the proximity of the explosives to the workpiece – either in direct contact (Contact) or at a specified distance (Standoff). A latter scenario corresponds to a hollow workpiece where the explosives are positioned internally (Confined). In the electrohydraulic forming process, there are two defined variants: one involves using a bridge wire made of either aluminum or copper to guide the discharge. In this method, the wire is fused during the process, creating a plasma channel. The second variant utilizes a direct spark discharge.

From this comparison it is clearly visible that there is a remarkable difference in the sheet size limits, production rate and facility between electrohydraulic forming, electromagnetic forming and explosive forming. By
electrohydraulic forming the limitation is up to 1.2 m diameter whereas by explosive forming it is possible to form a part up to 6 m diameter.

## 2.2 Electrohydraulic forming process (EHF)

Electrohydraulic forming (EHF) is a process using electrical energy to generate mechanical energy for forming metallic parts. The process involves charging a bank of capacitors to a high voltage, which is then discharged across a gap between two electrodes. During the high-voltage discharge, a plasma channel forms between the electrode tips, generating a high-pressure and high-temperature environment within the liquid-filled chamber. Usually water, or salty water, is used as a medium of transforming the shock wave. [12] found that when the electric energy was discharged through the liquid, it produced heat, which almost instantaneously vaporized the surrounding fluid and a vapor bubble of high pressure and temperature were formed. This vapor bubble gave rise to a pressure shock wave within the liquid. After a brief expansion, the bubble underwent a collapse once the pressure inside the bubble dropped below the ambient pressure, resulting in the generation of a second pressure pulse similar to the first. The application of the high-voltage discharge for impulse loading had been observed to exhibit as direct shock waves, hydraulic flows, quasi-static pressure of gas bubbles, reflected shock waves, cavitation and secondary shock waves, etc. [9]. The resulting shockwave in the liquid impacted the sheet metal blank placed on a die, causing it to deform and take the shape of the die. Control over the deformation could be achieved by either applying external restraint in the form of a die or adjusting the amount of released energy. There were many advantages of this EHF process. It could be cited the ability to form hollow shapes with much ease and at less cost compared to other forming techniques. Even if the high voltage was required, this process was more tractable and flexible to be used in the press shops compared to other high energy rates forming techniques (explosive technique). It was well adapted for producing small to intermediate-sized parts that didn't have excessive energy requirements and fewer manufacturing equipment were needed compared to conventional stamping technology.

The behavior of the electrohydraulic forming (EHF) technique was directly related to the characteristics of the electric circuit. The circuit itself consisted of several components, including an electric source, rectifier, voltage amplifier, resistor, inductor, capacitor, connecting cable, relay, switches, and electrodes. Typically, an RLC (Resistor, Inductor, and Capacitor) circuit was employed and played a crucial role in shaping the discharge characteristics during the EHF process. The resistor helped to control the flow of the current, the inductor stored energy in the form of a magnetic field, and the capacitor stored electrical energy. Together, these elements regulated the discharge duration, damping, and energy deposition within the system. By employing the RLC circuit in parallel, specific discharge characteristics can be achieved, allowing for fine-tuning of the forming process and directly impacting the efficiency of the operation.

Watkins, in [13], reported that it was more efficient to achieve a given deformation with only one discharge of appropriate energy than by multiple discharges, each of smaller energy. He demonstrated that the level of deformation achievable before fracture was reduced when all the energy was applied in a single discharge, regardless of the number of discharges. This suggested that the deformation extent was primarily influenced by the total energy rather than the number of discharges. Similar conclusions were given in [14] where it was shown that the pressure of the first shock wave was higher than the second shock wave and it decreased sequentially. In [15], the authors identified that for circuit voltage ranging from 20 to 30 KV and energy stored into the capacitor's bank between 6.64 kJ and 14.94 kJ, the spark gap should range between 17 and 22 mm. Through different experimental trials, the authors showed that voltage, energy, spark gap, and volume chamber had a direct influence on the resulting shock wave pressure.

According to [13], if both the energy and discharge durations were kept constant, increasing the voltage had little effect on the deformation produced on the forming part. An increase in deformation could be obtained by reducing the time of discharge and as a consequence, the inductance of the circuit should be kept as low as possible. [16] has detailed the influence of energy level on the evolution of underwater shock waves measured in case of an under-damped RLC circuit. Three regimes of behavior were identified based on the level of energy stored in the capacitor bank. This observation was emphasized by the authors and analyzed in relation to plasma behavior. The work of [17] focused on studying the influence of EHF process parameters on the formed part's height from both numerical and experimental approaches. The authors tested the discharge energy level, the gap between electrodes and the distance between electrodes and the workpiece. It was also examined the impact of a bridge wire between electrodes which facilitated the discharge phenomenon but required a significant setup time. As a conclusion on their results, higher discharge energy led to a greater formed part height; increasing the standoff distance resulted in less deformation; the electrode gap parameter had an optimal value for a specific test condition, and deviating from this point decreased the dome height.

The volume and the shape of the chamber were both responsible for creating a heterogeneous pressure field on the work sheet. In this case, it might be interesting to design both the chamber and electrodes that could generate a uniformly distributed pressure front on the work piece [7]. This salient point had already been discussed in the work of [13] where complex shapes of tools were tested and optimized.

Other approaches were tested to improve EHF efficiency and can be classified as a hybridization of processes. It could be cited the works of [2] where the authors showed the improvement of EHF operation in case of applying an initial quasi-static pressure before the electric pulse. This operational evolution led to designing a classical hydraulic forming operation added to the EHF process. A same kind of sequence process was proposed by [18]. In [19], the hybridization was based on magnetic forming followed by EHF processes. Another original
approach was proposed by [20], where the authors used an energetic material instead of a bridge wire that was activated during the electrical discharge of EHF. As a result, a lower level of electrical energy was then required to form the part.

## 2.3 Main technical limitations and objectives of this study

Each of the rapid forming techniques had limitations. Regarding explosive forming, despite the advantages in forming large-sized parts, the constraints associated with the use of explosives hindered its industrial application. Magnetic forming required a magnetic material for shaping, and limitations arise from the fatigue of the coil elements subjected to significant and repetitive mechanical loads.

EHF, despite constraints related to chamber filling time and arc initiation control, offered the advantage of being simpler in tooling implementation. Moreover, non-magnetic materials could be used, expanding the range of applications. Among the limitations, high voltage and current usage required proximity between capacitor banks and forming tools to minimize energy losses due to cable lengths. The repeatability of arc generation also introduced significant process variability. Additionally, electrode wear was an important technical limitation to address. It required the use of materials with good electrical conductivity and abrasion resistance. As the electrical arc resistance was related to the electrode distance, it was important to monitor the electrode gap during electrical pulses. Various scientific articles specifically addressed these issues. It can be cited as an example [21,22]. Furthermore, controlling pressure waves was crucial to enhance process efficiency [13]. Recent studies aimed to increase the number of electrodes in tooling and explore different chamber shapes and process sequences like in [10,23,24] to improve the efficiency of pressure wave actions on the workpiece. The influence of pulse duration was also emphasized in the literature by [13]. According to these authors, it was preferable to have short discharge durations (on the order of tens of nanoseconds) with power levels in the range of several MW. This improvement in energetic efficiency came at the expense of electrode erosion. It was shown in [25], that the EHF efficiency and reliability (i.e., energy and pressure) were influenced by the equivalent resistance of the discharge channel. This value was related to the distance between electrodes and their shape and orientation compared to the part to be formed. All these parameters impacted the energy discharge characteristics and by this turn, the peak pressure of generated shock wave and its propagation to a sheet blank.

The control of the EHF process relied on numerous complex physical phenomena with rapid dynamics. Controlling the discharge was a major challenge, requiring precise identification of all the characteristics of the electrical components in the RLC circuit, including electrical arc resistance. The latter was directly controlled by electrode spacing and shape. Additionally, electrode wear appeared to be a critical aspect of the process, necessitating frequent verification and adjustments, making process implementation complex.

# 3 Material and method

## 3.1 Electrical circuit and tooling

In this study, it was proposed to test the influence of arc duration on the forming operation. To achieve this, different values of resistance, inductance, and capacitance, as well as variations in the electrical configuration, were implemented to create RLC setups with underdamped or overdamped responses, thereby modifying the characteristics of the electrical discharge and arc durations.

To do this, a modular electrical setup was designed. It consisted of different inductors, resistors, and capacitors that could be connected in various ways (in series or parallel) and allowed modification of the RLC circuit behavior, transitioning from an underdamped response to an overdamped response (as shown in the electrical circuit design in Fig. 3). Depending on the configuration, the duration of the energy pulse was modified while maintaining the same energy level.

The mechanical parts of the forming tool are detailed in Figures 1 and 3 (referred to as the mechanical device). This tool was used to maintain the electrode spacing, ensuring water chamber sealing, and withstand the pressure rise during the forming operation. The blank was used to close the water chamber. An inlet was used to fill the chamber with water, and vents were used to remove air from the chamber during the filling phase. Figure 1 lists the main dimensions and characteristics. We used an open die with a diameter of 50 mm and a die radius of 6 mm. The hydraulic part of the tooling (water chamber) corresponded to a cylindrical shape with a diameter of 60 mm and a height of 40 mm. The electrodes were positioned at 30 mm away from the blank (before forming). They passed through the water chamber via two PTFE inserts to ensure their electrical isolation from the tooling. The central part of the electrodes was a cylinder with a diameter of 8 mm made of AISI 316. Blanks with a diameter of 80 mm were cut from a sheet of aluminum alloy 2017A with a thickness of 0.8 mm. For each blank forming, a single electrical discharge was performed, and the formed part was then disassembled and measured. An illustration of the measurement device and formed part is shown in Figure 1, allowing the total height of the part to be quantified. Regarding the boundary condition of the blank, the water chamber and the die were clamped together through 8 screws and no sliding was observed between the part and the tool.

Regarding the electrical part (shown in Fig. 3), two distinct phases of circuit operation were identified. The first phase involved charging the capacitor banks. To do this, switch SW1 was closed, and switch SW2 was open. A high-voltage DC power supply was used for this charging phase. Once the required voltage level in the capacitor bank was reached, switch SW1 was opened. The second phase of the operation then became possible. This involved closing switch SW2 and discharging all the stored energy in the water chamber through the plasma channel. Two main elements were used to measure the discharge phenomenon. The first element was the voltage measurement between the two electrodes of the device. The probe

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<figure><img src="image_2.png" /><figcaption>Fig. 1. Details of the mechanical device. A) view of the experimental tool; B and C) technical drawing of the tooling components.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 2. Illustration of the few formed parts and height measurements through digital height gage.</figcaption></figure>

used was a Tektronix P6015 High Voltage Probe (P6015). The current evolution was measured using a clamp meter (Tektronix A621 Current Probe). A digital oscilloscope (Tektronix TPS 2024) was used to capture and store the different electric signals throughout the energy pulse discharge.

Figure 3 shows a configuration with a single stage of the RLC circuit connected in series (referred to as the 2nd loop). This was this part of the electric circuit that we have modified to change the signature of the electrical discharge (duration and signal amplitude).

## 3.2 Description of the experimental tests

Different electric components were available to change the electric circuit configuration. Specifically, there were four different capacitors (204 µF) and four inductances (63.63 µH, 70 µH, 11.4 µH, 10.92 µH). To simulate the behavior of the electric circuit, the numerical software Tina was used. The equivalent resistance values of the circuit and of the plasma channel were experimentally quantified by experiments (in short circuit or assuming discharge). The resistance of the arc was estimated to be equal to 200

mΩ. Figure 4 presents some simulation results for both the classical one-stage and three stage electric circuits. It could be noticed the influence of the inductance value of the electric discharge amplitude and duration. In the case of the one-stage circuit, the maximum power amplitude reached 15 MW for 0.3 ms, whereas it decreased to 625 kW for 1.7 ms in the three-stage circuit.

## 3.3 Experimental results 411

To define the influence of the arc duration on the efficiency of the operation, a series of different experimental tests were conducted. All combinations are summarized in Table 2. These configurations were defined to significantly change the shape of the electrical signal and the duration of the energy pulse. Each experiment type was repeated 4 times. After each experiment, the blank was removed from the tool and the high of the part was measured by the mean of digital height gage (Mitutoyo QM Height Gage with Air-Suspension 24” / 600 mm). An illustration of the typical measurement was available in Figure 2. The provided values correspond to the mean of the height measured from the four experiments. A good level of

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<figure><img src="image_4.png" /><figcaption>Fig. 3. Schematic drawing of the electrohydraulic forming process.</figcaption></figure>

<table><caption>Fig. 4. Configuration of electric circuit characteristics and computed pulse discharges.</caption><thead><tr><th># stage</th><th>Electrical circuit</th><th>Pulse discharge power</th></tr></thead><tbody><tr><td>1</td><td></td><td></td></tr><tr><td>2</td><td></td><td></td></tr><tr><td>3</td><td></td><td></td></tr><tr><td>4</td><td></td><td></td></tr></tbody></table>
<table><caption>**Table 2.** Different circuit configurations and key measured and calculated characteristics.</caption><thead><tr><th rowspan="2">Exp. type</th><th rowspan="2">Circuit configuration</th><th rowspan="2">Voltage (kV)</th><th rowspan="2">Stored energy (J)</th><th rowspan="2">Arc duration (ms)</th><th colspan="2">Part apex</th><th rowspan="2">Calculated erosion (µg)</th></tr><tr><th>Mean (mm)</th><th>Std dev. (mm)</th></tr></thead><tbody><tr><td>1</td><td>2 stages<br>(70 µH + 63 µH)</td><td>4</td><td>3293</td><td>1.73</td><td>6.68</td><td>0.36</td><td>3032</td></tr><tr><td>2</td><td>3 stages<br>(70 µH + 63.63 µH + 11.4uH)</td><td>3.27</td><td>3265</td><td>2.33</td><td>6.07</td><td>0.37</td><td>355</td></tr><tr><td>3</td><td>4 stages<br>(70 µH + 63.63 µH + 11.4 µH + 10.9uH)</td><td>2.84</td><td>3283</td><td>2.51</td><td>5.8</td><td>0.4</td><td>259</td></tr><tr><td>4</td><td>1 stages<br>(70 µH)</td><td>5.68</td><td>3280</td><td>1.52</td><td>7.4</td><td>0.41</td><td>4207</td></tr><tr><td>5</td><td>2 stages<br>(10.9 µH + 464µH)</td><td>4</td><td>3297</td><td>1.96</td><td>7.1</td><td>0.37</td><td>4908</td></tr><tr><td>6</td><td>3 stages<br>(10.9 µH + 70 µH + 63.63 µH)</td><td>3.27</td><td>3272</td><td>1.97</td><td>6</td><td>0.40</td><td>3152</td></tr><tr><td>7</td><td>1stage<br>(5.21 µH)</td><td>5.67</td><td>3280</td><td>0.67</td><td>12.47</td><td>0.38</td><td>7419</td></tr><tr><td>8</td><td>2 stages<br>(10.9 µH + 11.4 µH)</td><td>4.02</td><td>3297</td><td>0.90</td><td>11.00</td><td>0.36</td><td>7923</td></tr></tbody></table>

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /><figcaption>**Fig. 5.** Experimental power evolution over time, case of the 1-stage configuration with $L = 5.21$ µH.</figcaption></figure>

repeatability was observed across the experiments, with a standard deviation close to 0.4 mm. In all trials, the spark gap remained constant at 10 mm and only one pulse was applied in every aluminum blank. In order to enable a fair comparison between experiments with different electric circuit configurations, the same energy level was stored in the capacitor bank (equal to 2622 J). To achieve this, the load voltage was adjusted, and the values are provided in the third column of Tab. 2. Throughout the energy discharge process, the electric signal was captured using various probes, allowing for the quantification of arc duration and arc power as a function of time.

Figure 5 represents a power measurement over time during the energy pulse. This graph corresponds to the measured signal obtained for a single-stage configuration with an inductance of 5.21 µH and a capacitance of 204 µF (experiment 7 in Table 2). It can be observed that for this shot, the maximum power amplitude was 8 MW, and the discharge signal consisted of 5 oscillations (with the last one

being of low amplitude). The duration of the pulse corresponded to 0.67 ms. The current evolution during the discharge was ranging from 7800 A to -9000 A.

Based on all the measurements available in Table 2, it can be noted that the arc duration is a highly influential parameter on the apex value of the formed piece. Thus, Figure 7 shows the apex evolution as a function of the pulse duration. The apex variation in mm over time appears to follow a downward linear trend in red dashed line on the graph; The fitted equation is estimated within the range of tested arc durations by equation (1).

$$Apex = 2.2 \times 10^6 \cdot T_{arc\_duration}^2 - 10500 \cdot T_{arc\_duration} + 18 \text{ with } R^2 = 0.97 \text{ Where } Apex \text{ is defined in mm.} \quad (1)$$

This equation provides a good fit ($R^2 = 0.97$) within the range of tested arc durations. These measurements confirm the findings highlighted in the work of [13],

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<figure><img src="image_7.png" /><figcaption>Fig. 6. Estimation of electrode erosion as a function of energy pulse current per second (from [26]).</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 7. Evolution of the part Apex function of the Arc duration; estimation of the spark erosion.</figcaption></figure>

<figure><img src="image_9.png" /></figure>

where the authors recommend, without any quantification, a shorter arc duration to ensure better operational efficiency.

## 3.4 Estimation of the electrode erosion

Given the energy levels involved in the electrohydraulic forming process, the electrodes endure high current and voltage densities, resulting in surface degradation. This erosion constitutes the primary factor limiting the lifespan of the electrodes, necessitating adjustments to their distance and rectification of their shapes. There are several factors that influence this erosion, such as the electrode material, surface conditions, current intensity, operating pressure, electrode cooling and the nature of the surrounding fluid. These factors are interdependent and challenging to model. As per existing literature, it is feasible to develop phenomenological models through experiments in order to estimate electrode wear, relying on the discharge kinetics of the energy pulse. Figure 6, taken from Turner's work [26] or by [27,28], provides an estimation of wear as a function of the arc intensity. The equations for estimating the erosion rate are then derived

and presented in equation (1). The computed coefficients were found to be consistent with those suggested in more recent studies, as seen in [29].

$$ 
\begin{array}{l}
\text{For } i(t) < 3500\,\text{A, } E_{\text{rate}} = \int_{0}^{r_{\text{arc}}} 3.6 \cdot i(t)^{1.44} dt \\
\text{for } i(t) \ge 3500\,\text{A, } E_{\text{rate}} = \int_{0}^{t_{\text{arc}}} 41 \cdot i(t)^{1.53} dt
\end{array}
\qquad (2) $$

where $i(t)$ is the effective current as a function of time.

From equation (2), the erosion rates (referred to as $E_{\text{rate}}$) of the electrodes were computed according to the recorded pulse current intensity over the time of arc pulse for each experiment. Their respective values are given in the last column of Table 2.

All these values have been plotted in Figure 7 and it can be observed a wild range of erosion rate, from 259 µm (Exp.3) to 7923 µm (Exp.8). Over this range, it can also be observed that electrode erosion follows a linear decrease trend with respect to arc duration. An empirical equation was then estimated (Eq. (2)).

$$ Erosion = -4 \times 10^6 \cdot T_{\text{arc\_duration}} + 10900 \qquad (3) $$

with $R^2 = 0.87$ Where Erosion is estimated in µm

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## 3.5 Discussion

Based on the obtained results, it can be seen that the arc duration has a significant influence on the electrohydraulic forming process. In the presented cases, this duration was controlled by modifications to the electrical circuit (parallel connection of one or more RLC circuits). With the same amount of energy stored in the capacitors, doubling the height of the formed part (from 6 mm to 12 mm) was achievable by adjusting the arc duration. A shorter discharge time led to greater part height, thereby improving the efficiency of the operation. These trends were in accordance with recommendations in the literature that identify arc duration as the primary parameter for enhancing operational efficiency [13], albeit without quantifying it. However, this gain in efficiency comes with significant consequences for electrode erosion values. According to the reported values in Table 2, the erosion values of the electrodes are multiplied by 30 (increasing from 259 µm to 7923 µm), thereby limiting the electrode lifespan.

Finding a compromise between operational efficiency and electrode erosion would be interesting. Based on the obtained curves, it is possible to select a height target and deduce the corresponding erosion rate. For example, with an arc duration of 1ms, the height would be approximately 10 mm and the erosion rate would be estimated to 6800 µm.

Apart from energy efficiency and erosion considerations, there are additional motivations for constraining the arc duration. Prolonging discharge times in the electrical circuits helps attenuate the peaks in current and voltage that need to be managed. Technologically, constraining these values allows for the utilization of lengthier power cables and facilitates the integration of impulse generators (limiting the electric stresses of the components and leading to extend the life duration). More to this, this could also pave the way for new forming units (e.g., put on robots).

To mitigate erosion phenomena, employing multiple pairs of electrodes within the water chamber can curtail the maximum current intensity, subsequently reducing the erosion on each pair of electrodes as suggested by [23]. This approach can lead to a more even distribution of pressure waves in space, even with all electrodes effectively synchronized to form an electric arc. However, addressing this aspect may not be straightforward.

## 4 Conclusion

This original work aims to experimentally study the influence of the energy pulse This original work aimed to experimentally study the influence of energy pulse duration in electro-hydroforming operations. For this purpose, a specific tooling system was developed, including a modular power electrical component. To vary the arc duration, different RLC-type configurations were implemented to modify the discharge regime, ranging from underdamped systems (rapid discharge below 0.6 ms) to overdamped systems (slow discharge above 1ms). It was demonstrated that the arc duration directly affected the efficiency of the forming operation, with observed height variations ranging

from 6 mm to 12 mm. This increase in efficiency also impacted electrode erosion, which represented a significant technological limitation in this type of tooling. Using an empirical model, erosion values were estimated based on measured discharge current values. The variation in part height and erosion values with respect to pulse duration was plotted, and the results obtained aligned with trends identified in the literature. A decreasing linear influence with a steep slope for erosion and a quadratic decrease in height with duration were obtained. This allowed for a search for a compromise between amplitude loss and erosion values. Beyond the experimental findings, this study contributed to enhancing the understanding of electrohydraulic forming process and provided valuable insights for optimizing process parameters. Moreover, this study opened the way, particularly through the possible trade-off between electrode wear and process efficiency (thereby limiting pulse voltage and current), for future research to explore and propose other potential applications of electrohydraulic forming.

## Conflict of interest

The authors declare that they have no known competing or financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## References

1. M. Ahmed, D.R. Kumar, M. Nabi, Enhancement of formability of AA5052 alloy sheets by electrohydraulic forming process, J. Mater. Eng. Perf. 26 (2017) 439–452 580 581

2. A.J. Gillard, S.F. Golovaschenko, A.V. Mamutov, Effect of quasi-static prestrain on the formability of dual phase steels in electrohydraulic forming, J. Manuf. Process 15–2 (2013) 201–2018 582 583

3. A. Jenab, D.E. Green, A.T. Alpas, S.F. Golovashchenko, Experimental and numerical analyses of formability improvement of AA5182-O sheet during electro-hydraulic forming, J. Mater. Process. Technol. 255 (2018) 914–926 587 588 589

4. Pulse-Pressure Forming (PPF) of Lightweight Materials, 2012, DOE Vehicle Technologies Program (Project 60184/ Agreement 22422) 591 592

5. High velocity forming of steel sheets and tubes for applications in the automotive industry – HI-VEL Report EUR 24994 En(2011) 594 595

6. J. Samei, Multi-scale characterization of hyperplasticity and failure in dual phase steels subject to electrohydraulic forming, Electronic theses and dissertations, University of Windsor, Paper 4929, (2013) 597 598

7. V.J. Vohnout, G. Fenton, G.S. Daehn, Pressure heterogeneity in small displacement electrohydraulic forming processes, 4th International Conference on High Speed Forming, 2010, http://dx.doi.org/10.17877/DE290R-13049 600 601

8. M.C. Noland, H.M. Gadberry, J.B. Loser, E.C. Sneegas, High-velocity metalworking, A Survey, United States, 1967 605 606

9. S.F. Golovashchenko, J. Alain, A.V. Mamutov, B. Gillard, Formability of dual phase steels in electrohydraulic forming, J. Mater. Process. Technol. 213 (2013) 1191–1212 607 608
610 10. G. Avrillaud, G. Mazars, E. Cantergiani, F. Beguet, J.-P. Cuq-Lelandais, J. Deroy, Examples of how increased formability through high strain rates can be used in electro-hydraulic forming and electromagnetic forming industrial applications, J. Manuf. Mater. Process. 5 (2021)

Q1

615 11. A. Taylan, A.E. Tekkaya, Sheet metal forming: processes and applications, 2012, ISBN-10: 1615038442, Page 228

617 12. W.M. Heigl, P. Robert, R.P. Radtke, R.H. Stokes, A. David, D.A. Glowka, A low-frequency downhole sparker for borehole seismic applications, Vol. 38, No. 08, 2013

620 13. M.T. Watkins, The shaping of metals, 9 (1968) 447–474

Q2

621 14. A.V. Pavlenko, A.N. Grigor, V.N. Afanas. I.V. Glazyrin, V.B. Bychkov, Pressure waves generated by a nanosecond electric explosion of a tungsten wire in water, Tech. Phys. Lett. 34 (2007) 129–132

625 15. J.S. José, I. Perez, M. Knyazyev, Ya. Zhovnovatyuk, Pressure fields repeatability at electrohydraulic pulse loading in discharge chamber with single electrode pair, 5th International Conference on High Speed Forming, 2012

629 16. W. Yuan, R. Han, P. Li, Y. Cao, C. Li, Y. Zhang, Evolution of underwater shock wave in far-field regime of electrical wire explosion system over wide range of electric pulse energy, Exp. Therm. Fluid Sci. 149 (2023) 111022

633 17. M. Zohoor, S.M. Mousavi, Experimental analysis and smoothed particle hydrodynamics modeling of electrohydraulic forming of sheet metal parts, J. Manuf. Process. 35 (2018) 16–28

637 18. X. Lu, H. Jin, Combined process of hydroforming and electro hydraulic precision reshaping for aluminium alloy, Proceedings of the 17th International Conference on Metal Forming METAL FORMING 2018 September 16–19, 2018, Loisir Hotel Toyohashi, Toyohashi, Japan

642 19. M. Linnemann, V. Psyk, E. Djakow, R. Springer, W. Homberg, D. Landgrebe, High-speed incremental forming – new technologies for flexible production of sheet metal parts, 6th International Conference on Accuracy in Forming Technology, Saxony Conference on Advanced Metal Forming Processes in the Automotive Industry, 2019

646 20. H. Yu, X. Xie, Q. Zheng, A novel method of processing sheet metals: electric-pulse triggered energetic materials forming, J. Mater. Process. Tech. 295 (2021) 117192

648 21. J.J.F. Bonnen, S.F. Golovashchenko, S.A. Dawson, A.V. Mamutov, Electrode erosion observed in electrohydraulic discharges used in pulsed sheet metal forming, J. Mater. Eng. Perf. 22 (2013) 3946–3958

651 22. A.M. Loske, F.E. Prieto, The influence of electrode shape on the performance of electrohydraulic lithotripters, J. Stone Dis. 5 (1993) 228–239

655 23. S.F. Golovashchenko, Electrohydraulic forming process with electrodes that advance within a fluid chamber towards a workpiece, 2014, U. S. Patent 8, 844,331B2

660 24. J.J.F. Bonnen, S. Fedorovich, S. Golovashchenko, D. Rochester, Electrode assembly for electro hydraulic forming process, 2014, US Patent, US 8,667,824 B2

664 25. I. Perez, M.K. Knyazyev, J. Jose, Experimental investigation of electric discharge parameters in correlation with peak pressure at industrial electrohydraulic forming, SN Appl. Sci. 1 (2019) Article number: 1299

668 26. H.W. Turner, C. Turner, Contact wear by arc erosion. Electrical Times, 1966, p. 363–365, 4 fig., 10 mars 1966

671 27. W. Bussiere, Electric fuses operation, a review: 2. Arcing period, international symposium on electrical arc and thermal plasmas in Africa (ISAPA), IOP Conf. Ser.: Mater. Sci. Eng. 29 (2012) 012002

674 28. A.L. Donaldson, M.O. Hagler, M. Kristiansen, G. Jackson, L. Hatfield, Electrode erosion phenomena in a high-energy pulsed discharge, IEEE Trans. Plasma Sci. PS-12 (1984) 28–381st

678 29. N. Garaboldi, J. Mantilla, Electrical wear in high-voltage circuit breakers using SF6 alternative gases, 2021, May 22, 2021 Industry Topics, Summer 2021 Industry Topics

682 683 Cite this article as: Yann Ledoux, Experimental investigation of the pulse duration on the efficiency and electrode wear of electrohydraulic forming process, Manufacturing Rev. Vol, No (2023)
Author Queries

Q1 Please provide page range for reference 10. **Q1. the pages for this article are from 1 to 17.**

Q2 Please provide journal title for reference 13.

Q2. the complete reference is
"M. T. Watkins (1968) The shaping of metals, Contemporary Physics, 9:5, 447-474,
DOI: 10.1080/00107516808205817"