Design and Testing of a Multi-Cylinder Piezopump for Hydraulic Actuation

Abstract

Hydraulic actuation systems are widely used in industries such as aerospace, the marine industry, off-highway vehicles, and manufacturing. There has been a shift from the hydraulic distribution of power from a centralized supply to electrical power distribution, to reduce the maintenance requirements and weight and improve the efficiency. However, hydraulic actuators have many advantages, such as power density, durability, and controllability, so the ability to convert electrical to hydraulic power locally to drive an actuator is important. Traditional hydraulic pumps are inefficient and unsuitable for low-power applications, making piezopumps a promising alternative for the conversion of electrical to hydraulic power in the sub-100 W range. Currently, the use of piezopumps is limited by their maximum power (typically a few watts or less) and low flows. This paper details the design, simulation, and testing of a multi-cylinder piezopump designed to push the envelope of the power output. The simulation results demonstrate that pumps with two or three cylinders show increasing benefits in terms of hydraulic and electrical performance due to the reduced flow and current ripple compared to a single-cylinder pump. The experimental results from a two-cylinder pump confirm this, and the effect of the phase relationship between the drive signals is investigated in detail. The experimental pump has fast-acting disc-style reed non-return valves, allowing piezostack drive frequencies of up to 1.4 kHz to be used. Custom power electronics tailored to the pump are developed. These features are critical in demonstrating the potential for multi-cylinder piezopumps to play an important role as a future actuation solution.

1. Introduction

There is an ongoing, rapid increase in the number of actuators in use today. Whether due to the automating of previously manual tasks or the drive towards smarter and more efficient machines (such as morphing wings), this growth in actuation has led to an increase in the variety and style of actuators needed. One specific niche within this wide space is the piezoelectro-hydrostatic actuator. This is a low-power hydraulic actuator (typically less than 100 W) that has the traditional benefits of hydraulics, such as durability and robustness, and is able to switch to a free running mode in the event of failure. Furthermore, the number of moving mechanical parts is very low, and it can be driven by an electrical power supply instead of a hydraulic one Figure 1.

This is of particular appeal in aerospace, where there is a significant weight saving available if the hydraulic ring main can be removed [1]. There are existing solutions for medium- and high-power actuators but not in the low-power range defined above [2]. In a previous paper, the initial design, simulation, and testing of a single-cylinder piezopump, which formed the drive unit of a piezoelectro-hydrostatic actuator, was reported, with a measured power output of 20 W [3].

In a piezopump, a piezoelectric stack is used to oscillate a piston (or diaphragm) in a fluid-filled cylinder at a high frequency (typically greater than 100 Hz), and a pair of non-return valves, either active [4,5] or passive [6,7], is used to rectify the flow of the fluid displaced from the cylinder. Figure 2 shows the four stages of a piezopump’s operating cycle.

Stage one is the compression stage, where the piezoelectric stack extends and compresses the fluid in the cylinder. When the pressure in the cylinder is equal to that at the pump outlet, the next stage, delivery, begins. The outlet valve opens and any further extension of the piezostack is used to push the fluid out of the cylinder. Once the stack has reached the end of its stroke, it begins retracting and the expansion stage begins. As the stack retracts, the pressure in the cylinder drops towards the pressure at the inlet valve. Once these pressures are equal, the final stage, intake, begins as the inlet valve opens, allowing fluid to flow into the cylinder. As shown in Figure 1, this low-pressure fluid may come from an accumulator on the pump inlet. This accommodates volume changes in the closed hydraulic actuation system (e.g., due to the unequal area actuator shown or thermal expansion) and also raises the net pressure of the circuit above the atmospheric pressure to avoid cavitation at the inlet.

The pump in [3] is believed to have the highest measured output power of any piezopump described in peer-reviewed publications to date, although there are unverified reports of higher power from industrially developed pumps [8]. It used a Physik Instrumente ring stack capable of $80$ μm free displacement and a $9600$ kN blocking force [9]. The $20$ W delivered could potentially be increased further by optimising the valve charactersitics, stack pre-loading, and bias pressure.

It would be theoretically possible to increase the design power output further by increasing the size of the piezostack used in the pump. However, there are practical limits on the thermal performance, cost, and manufacturability of such a stack to consider. A more practical route is the use of more than one cylinder, each operated by an individual stack. This would also mean that any improvements in the single-cylinder device would be directly transferrable to the multi-cylinder piezopump (MPP).

It is possible to connect the multiple cylinders in either a parallel or series arrangement depending on whether an increase in flow or pressure is desired Figure 3 or to reconfigure between them using valves.

Early work by Ullmann [10] looked at the effect of different connections between two pump cylinders joined with diffuser nozzles. It was expected that the series connection would double the pressure difference and the parallel connection would double the flow rate, as shown in Figure 3. However, it was found that with the diffuser nozzles, the series connection also gave a flow increase. In all instances, the pumping elements were operated in-phase after this was found to be advantageous for the series-connected pump. No explanation was given as to why this result was expected to be generalised across all architectures. It is also unclear whether the results were tied specifically to the use of diffuser nozzles in place of valves or whether they apply to MPPs in general.

Alongside the connection of the cylinders, the phasing between the cylinders is a design variable that is not relevant to single-cylinder pumps. These two variables, the output connection and phasing, have therefore formed the subject of most MPP research. The phase is a continuous variable but, at its extremes, the pistons in a two-cylinder pump move together (in-phase) or in opposite directions (anti-phase), with stages 1 and 3 occurring simultaneously in the two cylinders. Figure 4 depicts this in a parallel-connected pump.

Kan et al. [11] also looked at series-connected MPPs but with valves in place of the diffuser nozzles. They found that as the number of series-connected cylinders increased, the maximum pressure occurred at increasing operating frequencies, starting at 130 Hz for one cylinder and reaching 300 Hz for four. A correlation between the flow rate and number of cylinders was also observed, with the flow increasing from 2 mL/min with one cylinder to 7.5 mL/min with four. This is likely to be due to the valve pressure losses being a smaller proportion of the total pump output. The output pressure scaled linearly with the cylinder number to a maximum of 50 kPa or 0.5 bar.

Li et al. [12] used two cylinders to drive a hydraulic actuator and experimentally investigated the difference in performance with parallel and series connections and in-phase and anti-phase setups. They found that, in all cases, driving the two cylinders in anti-phase gave better performance than in-phase, but the size of the hydraulic actuator dictated whether a series or parallel connection was preferable to achieve the desired force and velocity. This is expected, with a parallel connection generally giving large flows but at lower pressures, which are more suited to larger actuator piston areas. Whilst unsurprising, these conclusions highlight the potential capabilities of a pump that can be reconfigured to achieve a wider operating envelope. The parallel configuration could be used for rapid advancement and the series connection utilised for higher force movements. There are several applications where the need for a high velocity and high force do not coincide that could make use of such a device. It was estimated from the actuator’s force and displacement that the serial-connected pump was able to produce 53 bar and the parallel-connected pump 1.65 L/min.

Zhang et al. [13] investigated pumps of a similar size and form as those of Ullman [10] but with check valves and five serially connected cylinders in place of the two of Ullman.

The term serial–parallel hybrid was used to refer to the design, which utilised differing combinations of in-phase and anti-phase cylinders. They found that the maximum pressure and efficiency were achieved with all cylinders being anti-phase, with the following cylinder and maximum flow with two adjacent in-phase cylinders. The authors hypothesised that having some cylinders in-phase is similar to having a larger cylinder, and having differently sized cylinders within a single pump modifies the optimum operating frequency. This coupling with the frequency gave rise to a $7\%$ increase in the output flow.

Özkayar et al. [14] focused specifically on the effect that multiple cylinders have on the performance due to the strength of the pressure pulsation that they impart. The focus on pressure ripple was driven by a desire to use piezopumps in Organ-on-Chip (OoC) testing, which requires a ripple of less than 3 Pa for a maximum pressure of 1.5 bar and flow of 50 μL/min. In the simulation, the effect of increasing the number of cylinders from 1 to 99 was investigated, with the cylinders’ phase being equally spaced across 360°. They found a significant reduction in flow ripple when an appropriate number of cylinders was used and a significant diminish in the benefit above five cylinders. They were able to validate their findings regarding pump ripple for three cylinders and found that there was a significant increase in both the pressure and flow output when moving from two to three cylinders but not a corresponding increase from one to two cylinders. No explanation for this was given in the paper, but it is believed that this is due to the lower ripple resulting in more available stroke from the piezoactuator for the same mean pressure.

Aside from their impact on downstream systems, pressure and flow pulsations can have a detrimental effect on pump performance. One of the characteristics of a piezostack is that, at the maximum force, there is no movement, and, at the maximum extension, there is no ability to generate force. This means that an increase in pressure at the pump outlet will reduce the flow output. In most hydraulic circuits, there is a correlation between the instantaneous pressure and flow due to the restrictions from pipes, valves, and other components. Therefore, achieving a lower peak pressure for the same mean pressure, or a reduction in ripple, will increase the flow output.

Zhang et al. [15] looked at the effect of pressure pulsation on the performance of piezopumps. Instead of using multiple cylinders with varying phases to minimise the pulsations, they placed quarter-wave tubes on a side branch of the inlet and outlet. These were designed to operate as a bandstop filter, with the pressure waves from the tube cancelling out the pressure wave leaving the pump. Compared to an identical pump without the quarter-wave tubes, there was around a three-fold increase in flow rate for the same load. This highlights the ability of MPPs to exceed the performance of large individual pumps by minimising the pressure and flow ripple. The advantages of an MPP over the quarter-wave solution are the packaging, the capability to operate over a range of frequencies, and the potential for higher power.

Recent work in magnetostrictive-actuated pumps is directly applicable to the development of piezopumps. Like piezoelectric materials, magnetostrictive materials can produce actuators with no moving parts as they deform when subjected to a magnetic field, instead of the voltage that deforms piezoelectric materials. The principle of the magnetostrictive-actuated pump is identical to that presented for piezopumps in Figure 2. Paralleling the development of piezopumps, efforts were made to increase the flow by using larger actuators [16,17] but they struggled to achieve the improvements expected or package the actuator, respectively. Regarding the developments in smart-material-driven electro-hydrostatic actuators (SMEHAs), Zhang et al. [18] conclude that a better development path is to operate multiple cylinders in parallel to increase the flow rate, as can be found in the piezopump literature.

The magnetostrictive-actuated pump developed by Zhang et al. used a rotary valve driven by a servo motor in place of the passive valves in Figure 2. This valve connects the ports of the four pumps to the cylinder sequentially, with a phase shift between each cylinder of 90°. This phase shift is fixed by the geometry of the valve. However, the servomotor allows the timing of the valve opening and cylinder position to be modified. The maximum flow was found with a phase of 340° at the optimal driving frequency of 250 Hz, meaning that the valve opens and closes slightly ahead of the bottom-dead-centre and top-dead-centre, respectively. This gave a flow of 4.1 L/min, but no pressure or load data were provided to convert this into power. As the phasing between the cylinders could not be modified, there was no insight provided regarding how this may affect the performance.

There is another system aspect that is also affected by ripple and is not considered in any of the literature reviewed but is crucial to the success of MPPs, namely the power electronics. There is a lack of consideration of power electronics across the piezopump literature in general, which is surprising given that the performance of the power electronics is often a limiting factor in experimental tests [19]. As piezostacks are a largely capacitive load, there is significantly more power cycling between the power electronics and stack than the mechanical power at the actuator. In the best case, the PICA P025 stack used in [3] could produce $505$ W of mechanical power on average for an electrical throughput of 2.8 kW, based on its capacitance of $1.2$ μF and a driving voltage of 1000 V at 1 kHz. In a single-cylinder pump, this excess electrical power must be drawn from the power supply and then returned to it at each cycle, generally requiring large capacitors within the power electronics.

This paper discusses the results of simulated and experimental testing of the effect of the phase shift between the cylinders on the integrated system’s hydraulic and electric performance. It is organised into five sections. The first covers the simulation of MPPs to quantify the scale and form of improvements. The second is an overview of the physical construction of the MPP and the design compromises and choices made in building the pump. The third is an overview of the high-speed power electronics used to drive the MPP, including the allowances necessary to support a wide testing space. The fourth section details the experimental setup and sensing requirements of the multi-cylinder pump and power electronics. Finally, the experimental results are given and compared to both the measured performance of a single pumping cylinder and the simple simulation results given above, before the article is concluded.

2. Modelling of a Multi-Cylinder Pump

A simple model can be used to show that a multi-cylinder pump can deliver more flow than a single-cylinder pump of the same total capacity. This is due to reduced flow ripple. In a single-cylinder pump, the piezostack delivers the flow against high pressure peaks, which reduces its displacement and hence the average flow delivered.

If $x_f$ is the free (i.e., zero load) extension of the stack caused by an applied voltage, F is the stack compressive force, and x is the actual stack extension under a combined electrical input and mechanical loading, the relationship between them is given by

$$x=x_f-{\displaystyle \frac{F}{k_s}}$$

(1)

where $k_s$ is the stiffness of the stack. The free displacement is proportional to the voltage, and if this is a sinusoid of frequency $\omega$ (offset to be unidirectional), we can write the stack displacement during the delivery stroke at time t as

$$x=X_f(sin\omega t+1)-{\displaystyle \frac{P_{c}A}{k_s}}$$

(2)

where $X_f$ is the peak free displacement, A is the piston area, and $P_c$ is the cylinder pressure. For a pump with n cylinders and equally spaced phasing of the drive signal, we can write Equation (2) for cylinder i as

$$x_i=X_f(sin(\omega t+{\displaystyle \frac{2\pi i}{n}})+1)-{\displaystyle \frac{P_{c}A}{k_s}}$$

(3)

Neglecting compressibility, the delivered flow from each cylinder is

$$\begin{array}{ccc}\hfill Q_i& =A{\displaystyle \frac{d{x}_i}{dt}}\hfill & \hfill when{\displaystyle \frac{d{x}_i}{dt}}\ge 0\\ \hfill Q_i& =0\hfill & \hfill when{\displaystyle \frac{d{x}_i}{dt}}<0\end{array}$$

(4)

and the total flow delivered by the pump is

$$Q_O=\sum _{i=1}^n{Q}_i$$

(5)

Assuming ideal non-return valves and a zero pump outlet pressure, the individual cylinder pressures are also zero, and Equation (3) to Equation (5) give the pump flow shown in Figure 5. This is for a 3-cylinder pump sized to give a peak cylinder flow $A{X}_f\omega$ of 0.8 L/min.

To perform useful work, the pump must operate against a non-zero outlet pressure. A common load is a restrictor characterised as a sharp-edged orifice where the pressure is proportional to the square of the flow:

$$P_O=k{Q}_O^2$$

(6)

Thus, with the flow varying in the manner shown in Figure 5, the outlet pressure can be characterised by a mean value and a ripple, and the ripple amplitude would be expected to reduce as the number of cylinders increases.

During the delivery stroke, the stack displacement given by Equation (3) will be zero, while the cylinder pressure is lower than the outlet pressure, i.e., the delivery non-return valve remains shut, so the cylinder pressure builds up according to

$$P_{ci}={\displaystyle \frac{X_f{k}_s}{A}}(sin(\omega t+{\displaystyle \frac{2\pi i}{n}})+1)when{P}_{ci}<P_O$$

(7)

At other times, when the ideal non-return valve opens, the cylinder pressure equals the outlet pressure and Equation (3) becomes

$$x_i=X_f(sin(\omega t+{\displaystyle \frac{2\pi i}{n}})+1)-{\displaystyle \frac{P_{O}A}{k_s}}$$

(8)

The combination of Equation (4) to Equation (8) allows the influence of the number of cylinders in the pump on the average flow output to be investigated, as differences in flow ripple and hence pressure ripple affect the ability of stacks to extend (Equation (8)) and hence displace fluid. Figure 6 shows the result for pumps with 1 to 5 cylinders, which are sized to give the same average flow at zero pressure, and all develop a maximum pressure (at zero flow) of 50 bar. There is a clear increase in flow with the number of cylinders up to three cylinders, particularly at higher average outlet pressures. There is still a ripple reduction from three to five cylinders but the ripple is so small with three cylinders that this does not cause an appreciable difference in the delivered flow.

A simple way to represent the piezostack electrically is as a capacitor with a parallel resistor. The capacitor’s value can be taken from the manufacturer’s specifications, with the resistor’s value calculated to disspiate power equal to the expected mechanical power output. Figure 7 shows the result of using this simple model for a three-cylinder pump using a 1.2 μF capacitance value, 505 W power dissipation, and stacks driven with a zero to 1 kV sine wave at 1 kHz.

The combined electrical power requirement is constant, compared to the high swings between input (positive) and returned (negative) power for the individual stacks. This makes the piezopump as a whole a significantly easier electrical load to drive. It also significantly reduces the size of the passive components needed in the power supply stage of the power electronics and, therefore, both the cost and volume.

3. Multi-Cylinder Piezopump

The design of a high-power single-cylinder piezopump was introduced in [20]. Here, a two-cylinder pump is created by using two of these units together. The design makes use of a PICA P025.50H ring stack from PI [9], capable of delivering a blocking force of 9.6 kN and maximum extension of $80$ μm. Its full specifications can be found in

Table 1. PICA P025.50H ring stack parameters.

Parameter	Value	Unit
Cross-sectional area	2.89	cm2
Outer diameter	25	mm
Inner diameter	16	mm
Length	66	mm
Maximum voltage	1000	V
Free displacement	80	μm
Blocking force	9.6	kN
Capacitance	1.2	μF
Natural frequency	17	kHz

.

This drives a piston of 26.7 mm diameter, forming the heart of each cylinder. A labelled cross-section is shown in Figure 8, with the components listed in

Table 2. Bill of materials.

	Item	Material
1	Piezostack	PIC151
2	Piston	Stainless Steel 440C
3	Piston clamp	Stainless Steel 440C
4	Belville washer spacer	Copper BS B32
5	Inlet reed valve	Stainless Steel 440C
6	Valve screw	Stainless Steel 440C
7	Belville washer	Carbon Steel 51CrV4

.

The choice of a ring stack offers several advantages. Firstly, the inlet flow can be passed through the stack cavity, allowing the inlet valve to be housed within the piston, making for a more compact cylinder (see Figure 8). Additionally, the piston rod passing through the center and tensioned to the rear using Belville washers is a convenient way to pre-load the stack. The Belville washers provide a high pre-load stack stress of approximately 15 MPa, as appropriate for dynamic piezostack operation, and offer a more compact solution than coil springs.

The ring stack’s design also maximises the surface area for heat transfer, critical in managing the susceptibility of the piezoceramic material to de-poling at the Curie temperature. The selected stack’s recommended maximum operating temperature is 85 °C [9], and self-heating is usually a key performance constraint for the dynamic operation of large stacks.

The flow generated by the piston is rectified by a pair of bespoke 0.2 mm disc-style reed valves. A cross-section of the full pump can be seen in Figure 9, showing the position of these valves. Figure 10 shows the valve disc itself.

4. Power Electronics

A bespoke power electronic converter was developed to drive the piezostacks at the high frequencies and voltages required. The electronics were designed to produce a sinusoidal voltage between 0 and $1$ kV at frequencies ranging from $500$ Hz to $1.4$ kHz. The power supply was envisaged from a High-Voltage Direct Current (HVDC) bus. For testing, this was emulated by a 450 V lab power supply unit (PSU). High efficiency and high power density were achieved through a switched mode topology, utilising 1200 V SiC MOSFETs. The driver consisted of two stages. Firstly, an asynchronous boost converter increased the voltage from the lab power supply by a ratio of 2.25:1. Then, a PWM-controlled half-bridge generated the sinusoidal output waveform by tracking a referenced signal provided by a controller implemented in the Simulink Real-Time environment. This is shown schematically in Figure 11.

The electronics were designed to be able to operate across a very wide range and follow arbitrary signals. This meant that in the case of user error or extreme edge cases, there could be stability issues. Therefore, a resistor was included at the output of the boost converter, but it is not expected to be needed outside the laboratory environment. Given the prototype construction, there was significant free space within the electronics enclosures, so the boost converter and one wave generator were housed in the same enclosure. The assembled units can be seen in Figure 12; the large passive components of the boost converter are visible in the upper unit but the same PCB is used for both, with some components not populated in the lower unit.

5. Experimental Set-Up

The test circuit replicated the configuration used in [3], with the addition of a second parallel pumping cylinder. A schematic representation is presented in Figure 13, and the corresponding components are listed in

Table 3. Components of the experimental test rig.

1	Pumping cylinder
2	Chamber pressure and temperature sensor
3	Dynamic pressure sensor
4	Filling valve
5	Load pressure sensor
6	Moog D633-303B servo valve (load)
7	Flow meter
8	Senior metal bellows accumulator 10cc

. A photo of the test rig can be found in Figure 14, an assembled single-cylinder unit is shown in Figure 15, and the two cylinders connected together are shown in Figure 16.

The pressure and temperature in the cylinder chamber are measured using an EFE PCM127 sensor, which combines a PT1000 temperature probe with a thin film pressure transducer. This is connected to the cylinder via a small drilling so that the volume of the cylinder is not increased unduly. The pressure difference across the Moog D633 load valve is measured using Parker PTDVB250 sensors on either side of the valve. A summary of the sensors and their accuracy is given in

Table 4. List of sensors and their reported accuracy.

Sensor	Model	Accuracy
Chamber pressure sensor	EFE PCM127	±0.25 bar
Chamber temperature sensor	EFE PCM127	±0.02%
Dynamic pressure sensor	PCB Piezotronics 112A21	≤1%
Load pressure sensor	Parker PTDVB250	±0.5 bar
Flow meter	Max Machinery P214 flow meter	±0.2%
Current meters	Micsig CP2100B	±4%
Voltage probes	pico TA057	±2%

.

Both mean and instantaneous flow rates were measured to explore the high-frequency behaviour of the pump. The mean flow was measured by a Max Machinery P214 Piston flow meter with a maximum bandwidth of $100$ Hz; this is an order of magnitude smaller than the pump’s intended operating frequency. To capture the higher-frequency flow dynamics, the three-transducer method [21] was utilised, employing a PCB Piezotronics 112A21 dynamic pressure sensor. These measurements were combined using two complementary filters, calibrated to cross over at $50$ Hz, ensuring accuracy in both data sets. The design of these filters followed the approach outlined in [22].

To confirm the effect of phasing on the pump performance, the two pump units were tested at 72°, 108°, 144°, and 180° out of phase. To protect the electronics, a peak voltage of $700$ V was used in place of the stack’s maximum voltage of 1000 V. This also gave a correspondingly lower current. At each phase shift, the load on the pump was varied by modulating the Moog D633 valve from fully open to fully closed in 18 geometrically spaced steps.

In addition to the hydraulic sensors listed in Table 3, the voltage and current at the output of each stage in Figure 11 were logged using a pair of National Instruments (NI) PCI cards. Most of the hydraulic sensors were sampled at $10$ kHz using a NI PCI6229 card via a Simulink Real-Time control program. This controller also provided the commands for the Moog load valve and the references for the wave generators. The electrical signals and dynamic pressure sensors were logged at $50$ kHz using a PCI6251 card with the MATLAB 2017b Data Acquisition Toolbox. It was necessary to separate out the data logging due to the wide range of different time constants within the system, with the bulk hydraulic system dynamics being around $100$ Hz and the flow and current ripples being harmonics of the pump drive frequency, which was $1250$ Hz for the tests presented here. The data sets were synchronised with a trigger signal. Each test ran for $3sec$ to eliminate start-up transients, and the reported data represent the mean of the last second or 1250 cycles.

6. Experimental Results

As discussed above, all tests were conducted at $700$ V, which is markedly lower than the voltage used in [3]. Therefore, the hydraulic output is also lower for a single cylinder as the voltage reduction leads to a corresponding reduction in piston movement (Figure 17).

Figure 17 is constructed from 18 experiments, with the load valve opening varied across them. The data set from one of these experiments can be seen in Figure 18.

When two cylinders are operated in tandem, there is a doubling of the output flow if they are operated in anti-phase, with the expected drop off in output as they move towards being in-phase. This is most notable between 144° and 72°; see Figure 19.

In the same way as for the single-cylinder characteristics, the pressure–flow characteristics for each different phase shift are derived from 18 experiments. Figure 20 shows the instantaneous pressure difference and flow in one of these experiments (for 180° phase shift).

The pressure difference at the load is near-constant due to the filtering effect of the fluid impedance and hose compliance between the pump and pressure sensor and also the bandwidth of the Parker PTDVB250 sensors. However, the pressure ripple at the pump outlet is captured by the PCB Piezotronics 112A21 sensors, with Figure 21 showing around a three-fold reduction in ripple when the cylinders are anti-phase.

The ability of multiple cylinders to be more effective and generate lower ripple is demonstrated in these data; however, this effect is not as strong as expected. Looking at the cylinder pressures from the two pumping cylinders gives a potential explanation for this; see Figure 22.

Cylinder 1 only achieves around $65\%$ of the pressure of cylinder 2, suggesting that, even though they are nominally identical, they are not in practice. Multi-layer piezoelectric actuators, such as those used in the pumping cylinders, consist of stacked piezoelectric elements enclosed between electrodes. Existing research highlights that delamination during processing, attributed to causes such as insufficient adhesion between the electrodes and piezoelectric layers, may result in crack propagation [2]. This gives a possible explanation for the difference in the performance of the two pumping cylinders.

To investigate the potential presence of defects or the onset of fatigue damage in the two piezostack actuators, a non-destructive testing method was employed. Specifically, the impedance spectroscopy (IS) method, validated in prior research [23,24], was utilised. If the stacks are performing as expected, they should both conform to the manufacturer’s specifications and exhibit the same behaviour as one another.

Impedance spectroscopy was conducted using a Newtons4th Ltd. PSM3750 Frequency Response Analyzer. Each cylinder received a sinusoidal AC signal of $0.1$ V at 100 frequency points spanning from $100$ Hz to $1$ MHz. This is a reasonably coarse grid of frequencies for the full identification of stack behaviour but sufficient to confirm a defect’s presence.

Figure 23 compares the impedance of the stacks, highlighting the likely presence of a defect in Stack 1.

The shift in the resonant peak between the two cylinders is visible and amounts to $1.5$ kHz, with the damaged stack having a lower peak and a higher frequency. It was found that the pre-load also affected the exact location of the resonant peak, but the frequency shift was observed at all different pre-load conditions.

The hydraulic power output of the pump shows a clear improvement in power as the pumping cylinders move towards being anti-phase; see Figure 24.

There is an anomaly at around 10 bar load pressure, where the 144° results show a steep improvement not seen in the other data sets. It is hypothesised that, given the difference in each cylinder’s response, the addition of outputs may be improved when not in perfect anti-phase. Whilst it is believed the scale of the difference between the two piezostacks’ performance is due to damage to one of the stacks, the tolerance in the stack performance is also quite large, with the maximum displacement having tolerance of up to $30\%$ [9]. This means that the possibility of small movements away from anti-phase, leading to improved performance, is likely to be true in general.

Although the piezopump is not functioning at its maximum efficacy, the test results still enable the behaviour of the power electronics when driving a multi-cylinder pump to be investigated. Looking at the electrical input during the phase tests, there is a clear reduction in current ripple measured at the power supply; see Figure 25.

This reduction in current ripple has a knock-on effect on the stability of the voltage from the boost converter, as shown in Figure 26, with a five-fold reduction in the voltage ripple in the condition plotted.

Unlike with the hydraulic power results, there seems to be a consistent improvement as the stack drive signals move towards anti-phase. The power factor of the pump also shows a steady increase as the cylinders move towards anti-phase, with a three-times increase between 72° and 180°; see Figure 27.

Comparing the current drawn by the single-cylinder and two-cylinder pumps, it can be seen that whilst the maximum flow doubled, only 1.6 times the power was used. This, again, demonstrates the ability of multiple cylinders to improve the performance.

7. Conclusions

To increase the power from piezopumps, it is necessary to increase the number of cylinders within each pump as there is a practical limit on the size of a single stack. It was posited that this would also be beneficial for pump performance, above that expected with a simple increase in capacity. Using a simple simulation, it was shown that having multiple parallel-connected cylinders operating with equally spaced phasing should give an increased flow output due to reduced ripple. A corresponding improvement in electrical power quality was also postulated due to the large current swings for each stack alone being cancelled out in the pump as a whole. In this work, bespoke power electronics have been co-designed along with the mechanical and hydraulic features of the novel pump.

These hydraulic and electrical improvements were demonstrated experimentally using a two-cylinder pump. A significant advantage in terms of hydraulic flow and power output was demonstrated. However, differences in the behaviour of the two piezostacks were identified, causing some deviation in performance from that expected. This highlights that adjusting the phasing of the stacks in light of the actual performance is preferable to relying on the theoretical optimum. Likewise, a reduction in the power supply current ripple and an increase in the power factor are observed. All results are presented for 700 V peak drive voltages, well below the 1 kV maximum stack voltage.

This work has demonstrated the potential for a piezopump to deliver a suitable flow and pressure to drive a hydraulic actuator in the tens of watts power range. In terms of piezopumps, this is a high power output, and the significant advantages of a multi-cylinder design are clearly demonstrated for the first time at this power level. Hydraulic pumps of a traditional rotary design are not available or suitable at this small scale.

Future pump development building on this research will include the testing of a three-cylinder pump and further refining the power electronics by optimisation for a reduced operating range to ensure load stability.