Regenerative Structural Fatigue Testing with Digital Displacement Pump/Motors ^†

Abstract

Historically, a large fraction of fatigue testing of both components and structures has been performed using hydraulic actuators. These are typically driven by servo-valves, which are in themselves very inefficient. But, as most tests involve elastically stressing mechanical components, a lot of stored energy could be recovered. Unfortunately, servo-valves are not regenerative—simply metering out fluid in order to relax the system prior to the start of the next cycle. There is much to be gained with a more intelligently controlled system. The FastBlade facility in Scotland uses a new type of regenerative test hydraulics. Digital displacement pump/motors (DDPMs), originated by Artemis Intelligent Power, now Danfoss Scotland, are used to load and unload the test structure directly via hydraulic rams. The DDPMs are driven by induction motors supplied by three-phase frequency converters, each with a very loose speed correction target, such that they can speed up or slow down according to the instantaneous torque exerted by the load. The rotating assembly of the induction motor and DDPM is designed to have sufficient inertia so as to function as a kinetic energy storage flywheel. The loading energy is then cyclically transferred between the rotating inertia of the motor/DDPM and the spring energy in the test structure. The electric motor provides sufficient energy to maintain the target average cyclical shaft speed of the DDPM whilst the bulk of the system energy oscillates between the two storage mechanisms. Initial tests (at low load) suggest that this technique requires only 30% of the energy previously needed. FastBlade is a unique facility built by the University of Edinburgh and Babcock, with support from the UK EPSRC, conceived as a means of testing and certifying turbine blades for marine current turbines. However, this approach can be used in any cyclical application where elastic energy is stored.

1. Introduction

There are many facilities that conduct fatigue testing of large structures, a large proportion of which use hydraulic systems to load and unload the assembly under test. Some of these structures, such as wind turbine blades, are in the fortunate position that the cyclic loading can be performed at a resonant frequency and, therefore, with very little energy input. Stiffer structures, particularly those containing highly hysteretic materials, such as polymers, cannot make use of this approach, as the internal heating, which would result from high-frequency load cycling, would cause failure for reasons unrelated to those seen in normal operation. This work contains considerations related to high-efficiency, full-scale testing of stiff structures and extends the scope of work initially presented at the Twelfth Workshop on Digital Fluid Power (DFP24) [1].

1.1. The Importance of the Work in Exploiting the Tidal Energy Potential

Tidal energy is a resource that has been successfully harvested for decades. Since the first large-scale commercial project was commissioned near Saint-Malo in France in the 1960s, tidal stream turbine projects have become more widespread [2,3]. Relative to renewable resources, such as wind or solar energy, which have already been exploited on a significantly larger scale, tidal energy has the great advantage of being highly predictable. Recent years witnessed substantial growth in the investment in tidal energy-related technologies, both in the UK and worldwide [4,5,6]. The tidal energy potential in the UK is estimated to reach 50 TWh per year, constituting half of the total European resource [7]. Moreover, it is predicted that tidal energy can account for the supply of 100 GW of electric energy to grids worldwide by 2050 [8].

However, the technology associated with tidal energy is at a significantly less mature level than the corresponding infrastructure in the wind energy sector. One of the most critical aspects of any tidal energy turbine is the design of its blades. Full-scale fatigue testing is one of the proven ways to validate the design of a structure before it is commissioned for a lifetime of deployment, and it has been applied to test aircraft wings [9], bridge members [10,11], and wind turbine blades [12,13,14].

Fatigue tests of wind turbine blades can be run efficiently by exciting the blades at a frequency close to their natural frequency [12,13,14], typically around 3 Hz. The actuation at the blade’s resonant frequency drastically reduces the amount of energy required to run the test. Due to the similarities between wind and tidal energy sectors, some of the test standards can be directly transferred to the tidal domain. However, since the density of water is around 800 times that of air, tidal turbine blades need to be much shorter and stiffer, meaning that excitation at their natural frequency (typically 18–20 Hz) is not feasible [15] and would not produce reliable fatigue test results. The requirements for the tidal turbine tests are specified in the standard IEC TS 62600-3:2020 [16]. Of particular interest are the static test at maximum design load and the fatigue test with service loads representing the period of intended operation. In most cases, the static test does not require a substantial energy input. In contrast, fatigue testing without an energy recovery system is costly since it has to apply a power equivalent to that which the blade will produce during its operational life.

FastBlade has been created to mitigate this issue by incorporating synthetic resonance, described in Section 3, which makes it possible to recover energy while operating at a frequency significantly lower than the resonant frequency of a specimen [17]. A variety of different parameters are measured during operation to provide precious insights into the operation of the facility’s loading system.

1.2. The Structure of a Fatigue Test

Section 5 describes in detail FastBlade’s energy recovery system, which allows it to perform the IEC TS 62600-3:2020 standard [16] test sequence in an efficient way. The test described in this work, which showcases the operation of the hydraulic system at FastBlade, was performed on a decommissioned 500 kW tidal stream turbine blade previously installed by the European Marine Energy Centre (EMEC). The blade length is 5.25 m, and the NACA 63-4XX aerofoil series defines the blade cross-section. The blade is made from composite materials and has a total mass of 1588.59 kg (15,584.07 N) [17].

The FastBlade system can work either using a single actuator or a series of actuators, delivering more complex load profiles. Moreover, FastBlade demonstrated its ability to perform fatigue tests under different loads and frequencies. The load distributions used in a test should be chosen to best represent the real deployment conditions using real data, such as water velocity profiles close to the seabed collected using acoustic velocity sensors [18].

1.3. Existing Solutions to Full-Scale Fatigue Testing

The standard solution to this problem is to use a hydraulic loading system, which is controlled by a servo- or proportional valve. This creates a very energy-intensive system. During the loading phase, some hydraulic power is lost in the control valve, which must always have a pressure drop across it to maintain authority over the loading actuator’s motion. Nevertheless, when the strain energy in the structure is released, the entirety of it is converted into heat. For large, stiff, structures, which must be tested for many millions of cycles, this represents a vast amount of wasted energy. If a load-sensing pump control is used, then some improvement is possible, seeing as the pressure drop across the valve is kept relatively constant, as shown by Scopesi [19] and Manring [20].

The structural testing application is not the only one dealing with this problem of poor hydraulic efficiency. Virtually all hydraulic systems are similarly affected. One solution that has been widely promoted for the off-road machine market is that of direct actuator control in a circuit typified by the simplified schematic in Figure 1.

Generally, two different approaches have been considered to drive this circuit. The first is to use a fixed, positive-displacement pump/motor driven by an electric servomotor, where the flow rate is proportional to motor speed and where flow direction can be reversed by changing the direction of rotation of the motor. The second is to couple a variable pump/motor to a fixed-speed electric motor. Here, flow reversal is achieved by moving the stroking mechanism of the pump/motor over the centre so that the intake line becomes the output and vice versa.

The servo-motor approach has three disadvantages, the first being that a separate motor and high-power electronic controller are required for each loading actuator. The second and more concerning one is that there will be times during the cycle when the pump/motor is at high pressure and very low, or zero, shaft speed. In these conditions, all of the bearing films have no hydrodynamic separation to bear the very intense loads within the hydraulic machines. It is also worth noting that despite the motor being at zero velocity, there will be some level of leakage in the hydraulic machine, which means that the actuator is still moving even when the motor is not. The third disadvantage is that control bandwidth is limited by the combined inertia of the electric motor’s rotor and the spinning components inside the pump/motor.

The second approach, using conventional variable stroke hydraulic machines, can benefit from the fixed-speed electric motor’s ability to drive multiple machines. However, these machines have different challenges as a result of their variable geometry mechanism. The first is that with mechanical commutation of the cylinders, the compressibility energy in the high-pressure oil cannot be properly recovered over a broad range of strokes and pressures. This, coupled with the inherently low efficiency of the pumping mechanisms at the lower end of the stroke range, makes the achievable efficiency much less than might be expected. The physical inertia of the stroking mechanism and the consequent force required to have authority over its position require the stroking control to be performed by a separate hydraulic circuit, one which also has significant parasitic losses.

2. The Digital Displacement Pump/Motor

The digital displacement pump or DDP was initially conceived at the University of Edinburgh and then subsequently developed by Artemis Intelligent Power Ltd., now Danfoss Scotland [21]. Its core mechanism could be any positive displacement machine with individual working chambers of varying volume. The DDP cross-section presented in Figure 2 highlights the basic elements of the pump.

The Artemis machines have almost universally been built around a radial format, with banks of cylinders along a common crankshaft, very much following the architecture of radial aero engines. In terms of a high-pressure fluid machine, this format provides many advantages. The high-speed, highly loaded, sliding interface between the piston and eccentric shaft—the single highest loss source in the mechanism—is at its minimum diameter, i.e., slightly larger than the shaft’s end. This keeps the sliding velocity to a minimum and, therefore, also its associated piston bearing losses. In comparison, axial format machines need much larger diameter bearings (for equivalent displacement).

The commutation is performed by valves located on the periphery of the machine. As the pressure drops through the valves that are typically the second-highest loss source, it is helpful to locate the valves around the outside, where there is space to create sufficient flow area with, consequently, an acceptably low-pressure drop. The machine’s power can be increased by either proportionally scaling the components or by adding additional banks of cylinders. In practical terms, adding banks in pairs has the advantage of allowing the piston forces on each bank’s eccentric to counteract the adjacent one, which minimises shaft deflection, bearing loading, and consequent friction loss.

What made the DDP significantly different from legacy machines is that the commutation of flow into and out of the cylinders is managed by electromagnetically actuated poppet valves. The pump/motor variant, or DDPM, has two electrically controlled valves in order to allow bi-directional control of fluid flow, as described by Rampen [22]. By sequencing the opening and closing of the active low- and high-pressure valves (LPVs, HPVs), three different operating cycles can be achieved. A pumping cycle can be created by opening the LPV during the expansion phase of the cylinder and then closing it by the Bottom Dead Centre, BDC. The subsequent contraction phase of the cylinder is used to automatically open the HPV and expel the HP liquid into the HP manifold, from where it can perform useful work on an actuator. As the piston goes over centre at the TDC, the HPV will naturally close, allowing the LPV to reopen and continue the cycle. The pumping cycle is, in itself, very efficient. Part of this is due to the radial mechanism, as outlined above, but a considerable loss component is avoided by allowing the valves to choose their own opening time. This means that the compressibility energy in the oil is expanded in a controlled and regenerative way, rather than dissipated across the mechanical commutator, as it would be in a conventional axial piston machine.

An idle cycle can be created by preventing the LPV from closing at the BDC. The contracting volume then exhausts the fluid back through the LPV without raising significant pressure in the chamber. Thus, the HPV remains closed and sealed. The idle cycle incurs some parasitic loss—breathing loss in the LPV and shear losses in the moving components, but these are very low in comparison with the full power rating of the machine—typically in the range of 0.5%. There is no pressure-related leakage or loading of bearings, as would be the case in conventional machines.

The final cycle, that of motoring, is not generally possible with asymmetric poppet valve commutation. It is achieved in the DDPM by having both the LPV and HPV electromagnetically actuated. Starting at the exhaust portion of the cycle, the piston moves upward towards the TDC with the LPV open. Before the TDC is reached, the LPV is commanded to be closed, and the remaining stroke of the piston is used to raise the cylinder pressure to equal that of the high-pressure manifold. The HPV actuator is turned on to pull the valve open once the pressure equalises. The motoring stroke then follows with the high-pressure fluid, pushing the piston towards the BDC. Before the BDC is reached, the HPV actuator coil is turned off, and a spring closes the HPV at the desired point in the expansion stroke. The remaining piston movement is used to decompress the cylinder’s volume, such that the internal pressure reaches that of the low-pressure manifold. The LPV can then be reopened—usually, this is accomplished automatically by the force of a spring. Details of this cycle are described in [22].

The DDPM is controlled by a micro-controller, which has two inputs. The first is a shaft encoder, which allows it to keep track of the position of the eccentrics in the machine. The second is a demand signal, which can be either analogue or digital. The outputs of the controller consist of solenoid actuation signals, one or two per cylinder. The controller can additionally manage external switching solenoids, which can combine and isolate the different output services of the DDPM.

As the control occurs in discrete events—the opening and closing of valves in synchrony with the piston movements followed by the subsequent movement of a piston, which either adds or subtracts fluid from the HP manifold—there is a necessary delay in response. This is on the order of half a shaft revolution, or approximately 25 ms when the machine is running at 1500 RPM. In practice, this allows a control bandwidth of approximately 20 Hz.

Part of the challenge of controlling the DDPM is that fluid is delivered in quanta, which can be half a cylinder’s volume in error of demand. This is a result of the controller’s sigma–delta algorithm, which accumulates the error between the demanded and the provided displacement. A cylinder, either pumped or motored, is only triggered when the demand reaches the 50% threshold. This displacement error can cause significant pressure spikes in a stiff system. The introduction of compliance, local to the DDPM, in the high-pressure output can make these pressure variations acceptable. This is an exact analogue of the capacitor used to smooth the output of an electronic pulse-mode power supply.

The bulk modulus of oil is around 1.6 GPa, or two-thirds that of water. In the FastBlade DDPM, the cylinder displacement is 8 cc, which means that a displacement error of 4 cc should not exceed the specified level of pressure ripple. For example, by providing a 6-litre volume of oil in the high-pressure circuit, the pressure ripple would be limited to 10 bar. The penalty for introducing too much compliance is that the system, in becoming less stiff, loses frequency response. For this reason, compliance sizing is important for proper system function.

3. Synthesised Natural Frequency

The fundamental concept of the FastBlade actuation system was that it should mimic natural frequency oscillation—with minimal energy input—as is used for testing large floppy structures. Seeing as the test structures themselves would oscillate at too high a frequency, another means of storing the strain energy had to be found. This was achieved by cycling the strain energy between the test structure and a flywheel on the DDPM’s driveshaft. The loading energy was transferred from the flywheel to the blade structure through hydraulic ram actuators during the loading phase and then back again as it was unloaded. Losses were made up by the electric motor driving the DDPM. The electric motor needed only to provide a continuous but low amplitude positive torque in order to allow for sustained cycling.

The key enabler for this was a variable frequency drive, which could be set to allow large deviations in the output speed without strongly attempting to limit its variation. The controller also needed to ensure that sufficient torque was provided during each cycle such that the average speed was maintained. Danfoss VLT drives should be able to be programmed to provide these characteristics (though, in the current setup, the VLT stops providing power when shaft speed exceeds the target set point, which makes for an intermittent delivery).

The electric motors, 75 kW six-pole induction machines, were oversized as a means of providing sufficient flywheel inertia to store the cyclical energy within the operational speed range of the DDPM. It should be noted that the speed range was also limited by the maximum acceleration of the flywheel.

There is one fundamental difference between natural and synthesised oscillation. Whereas natural frequency oscillation is always described as a sine function, the synthesised one is not. In fact, because the frequency response of the DDPMs is much higher than the test frequency and because positive displacement pumps always have a flow limit, it can make sense to use a test cycle that approximates a triangle wave. In this situation, most of the cycle has the DDPMs running flat out in either pumping or motoring modes. The transition at the ends of each phase can be carefully composed to give a smooth direction change, possibly with the introduction of reduced flow as the change nears and as the next phase begins.

4. Driveline Implementation at FastBlade

The large structural fatigue testing facility built in Rosyth, Scotland consists of a large steel loading frame fabrication. It has a 12 m loading bed, along which actuators can be placed to load the test specimen (typically, but not necessarily, a turbine blade). The root of the specimen can be anchored to a large faceplate on the strong wall. This has an array of holes to permit the attachment of a wide range of blades or other test specimens.

The loading comes from actuators spaced along the loading bed. As all of the actuators are fed with the same supply pressure, the number and spacing of the actuators effectively determine the load distribution along the structure. Figure 3 illustrates the main components of the loading system, whilst the photo in Figure 4 shows the actual implementation, as photographed from deck level.

The hydraulic actuators are themselves driven from a common high-pressure manifold. The hydraulic circuit has various levels of over-pressure protection and isolating valves but is essentially connected straight from the combined outputs of four Artemis/Danfoss DDPMs, which can source or sink the actuator energy. The undercroft level, with its machines, is shown in the photo in Figure 5. When pumping, they convey power to the actuators and thereby store strain energy in the specimen. When motoring, they largely convert that strain energy into flywheel energy. There is one further important component in the circuit, a compliance, the hydraulic equivalent of a capacitor, to absorb and average the small pulsation error between the flow demanded and achieved. FastBlade has a 4-litre high-pressure filter body in line for this purpose. A simplified schematic of the hydraulic loading system is shown in Figure 6.

5. Results from FastBlade

The test facility was commissioned with a 5.25 m turbine blade on the test. As it is relatively short, the amount of strain energy stored is modest relative to the capacity of FastBlade’s jacking system. As such, only one of the four DDPMs and a single jacking ram were employed for these initial tests. The tests were conducted at 1.0 Hz using a pure sinewave loading function. Figure 7 shows two curves that represent the energy stored at each end of the loading system. The red trace follows the shaft speed of the DDPM and electric motor, showing a relatively constant 1 Hz frequency component as the energy oscillates in and out of the flywheel. The trace is not purely sinusoidal, and the vertical asymmetry is largely due to the fact that the Danfoss VLT frequency converter stops providing power above the target speed of 2000 RPM.

The blue trace, almost 180 degrees out of phase with the shaft speed, shows the load exerted on the specimen blade, representing the strain energy stored. The two traces might be expected to be exactly 180 degrees out of phase, but because the frequency converter torque input shuts off when the shaft speed is above 2000 RPM, there is a lag in the order of 100 ms in the shaft response.

To demonstrate the regenerative capability of the system, a test was conducted where the DDPM was run up to the target speed and cycled a few times to establish an equilibrium condition. The drive motor to the DDPM was then electrically disconnected, with the driveline spinning, such that no electrical torque was exerted on the DDPM, as shown in Figure 8.

The drive signal to the DDPM continued as before, with the amplitude of the loading decreasing cycle by cycle. Figure 8a shows the load trace continuing for 25 cycles beyond the motor switch off. Figure 8b shows the corresponding rotation speed of the DDPM in two different loading conditions, the first where cyclic loading of the specimen continues, and the second where the DDPM valve actuation is stopped. Finally, Figure 8c displays the energy transferred during each cycle, which can be seen above at 3 kJ at the start of the test, decreasing to 1 kJ after 25 loading cycles.

In order to gauge the parasitic loss–and therefore the maintenance power required to keep the system operational–a trace of the freewheeling system, still providing cyclic loading of the jack, can be compared to the natural run-down of the motor/DDPM with all cylinders in idle mode, as shown in Figure 8b.

If the load was a properly resonant one, with damping proportional to velocity, we would expect to see the amplitude reducing exponentially with every cycle, such as would be described mathematically by a logarithmic decrement. But, in this case, the damping is not really related to the jack velocity; it is a loss consisting of various components, only a small proportion of which relate to jack velocity. The standing losses on the rotating DDPM shaft are dominated by bearing and breathing losses across the DDPM’s valves, both of which are determined by DDPM shaft speed rather than jack velocity. The trace in Figure 8b of the freewheeling run down is very similar in shape and amplitude to the one where the un-driven and slowing motor continues to cycle the loading jack, suggesting that these rotational losses are of a similar magnitude, at 4.5 kJ per cycle, to the energy exchanged in the specimen loading system.

The average motor power required to maintain the 2000 RPM shaft speed is 6 kW, which, over a 1 s cycle, amounts to 6 kJ. During that second, a loading energy of 2.2 kJ is cycled to and from the flywheel. By contrast, the energy cycled to the loading jack is approximately 3.1 kJ.

Whilst the parasitic power may appear high for this test, the relatively limited loading demand of the 5.25m test blade must be kept in mind. The DDPM is working at a small fraction of its maximum (hydraulic) power of 134 kW, and thus is actually capable of around 30 kJ per loading cycle (based on averaging a 50% mean pressure and 50% pumping, 50% motoring) and, as previously explained, the parasitic loss is not affected much by anything other than shaft speed. With a system running at peak capacity, the parasitic loss would be in the range of 16% of the energy being cycled back and forth.

6. Analysis

The data necessary to analyse the system’s performance are logged using chosen data acquisition (DAQ) modules manufactured by National Instruments, compatible with analogue sensor outputs. All sensor data are read at 250 Hz, with the exception of the power supplied to the motors, which are logged at 2500 Hz. In this work, all data are brought to a common frequency of 250 Hz, corresponding to a timestep of 4 ms between consecutive measurements. A summary of the most important parameter measurements considered in this work, together with the associated sensors, is presented in

Table 1. Physical quantities used in the analysis and the corresponding sensors used.

Measured Quantity	Sensor Type	Manufacturer	Comments
Actuator load	Pancake load cell	Applied Measurements Ltd. (Aldermaston, UK)	Load range: 0 kN to 500 kN; sensing accuracy: 0.05%.
Actuator displacement	Absolute, non-contact position sensor	MTS (Lüdenscheid, Germany)	Maximum stroke length: 1 m; sensing accuracy: ±0.02%; analogue current output.
Shaft speed	Rotational autoencoder	Not specified	Sensing accuracy: ±1 RPM. The sensor is integrated inside the Danfoss’ DDPM.
Power supplied to inverter	Calculated from current and voltage measurements	Danfoss (Nordborg, Denmark)	Calculated internally. Estimated accuracy: ±5%; estimated read-out delay: 0.5 s.
Oil pressure at the actuators	Pressure transmitter	WIKA (Klingenberg, Germany)	Pressure range: 0 bar to 400 bar; accuracy: ±0.5% of full scale; analogue output.

.

The motor energy input is measured power from the Danfoss VLT output during the actual loading phase, whilst energy is flowing into the specimen (the remaining parasitic loss is provided by the VLT during the other half of the cycle). Flywheel energy input due to speed variation and work performed at the actuator are also evaluated using the parameters outlined in Table 1. The DDPM losses are from characterisation tests conducted at Danfoss, which will be described more fully below. Pipe, valve, and actuator losses are apportioned from the total using the unpowered rundown experiment, where the active cycling system took 71% of the time required by the idle one to pass through the same flywheel speed range. The energy from the flywheel is taken from its speed at the beginning and end of the loading phase. It should be noted that these data points do not correspond to the maximum and minimum flywheel cyclic speeds. This is because the maximum speed of the flywheel oscillation is approximately 132 degrees ahead of the minimum strain condition of the specimen.

6.1. Quantifying the Key Efficiency Parameters from Experimental Data

Using various techniques to separate the losses within the actuation system, it is possible to quantify them individually. This process is useful, as it provides guidance for improving energy efficiency further.

6.1.1. Modelling System’s Electric Energy, Kinetic Energy, and Work Performed

Electric power supplied to the motors by the inverters is measured directly by the VLT units. This information is used to estimate the amount of electric energy, $\mathrm{E}\mathrm{E}$, consumed in the loading and unloading portions of the cycle by integrating the power trace, $\mathrm{P}\left(\mathrm{t}\right)$, over a suitable time interval marked by ${\mathrm{t}}_0$ and ${\mathrm{t}}_1$ as follows:

$$\mathrm{E}\mathrm{E}={\int }_{{\mathrm{t}}_0}^{{\mathrm{t}}_1}\mathrm{P}\left(\mathrm{t}\right)\mathrm{d}\mathrm{t}$$

(1)

The variation of the energy delivered and stored in the loading and unloading parts of the cycle respectively is evaluated based on its kinetic energy, $\mathrm{K}\mathrm{E}$, as follows:

$$\mathrm{K}\mathrm{E}={\displaystyle \frac{1}{2}}\mathrm{I}{\mathsf{\omega }}^2$$

(2)

where $\mathsf{\omega }$ is the rotational speed and $\mathrm{I}$ is the moment of inertia of the flywheel, which is estimated at 4.25 $\mathrm{k}\mathrm{g}{\mathrm{m}}^2$ for the motor and the DDPM combined. The work performed on the specimen, ${\mathrm{W}}_{\mathrm{o}\mathrm{u}\mathrm{t}}$, is evaluated on a per-cycle basis considering the upward stroke as follows:

$${\mathrm{W}}_{\mathrm{o}\mathrm{u}\mathrm{t}}={\int }_{{\mathrm{s}}_0}^{{\mathrm{s}}_1}\mathrm{F}\left(\mathrm{s}\right)\mathrm{d}\mathrm{s}$$

(3)

where ${\mathrm{s}}_0$ and ${\mathrm{s}}_1$ are the lower and highest actuator displacement in a cycle and $\mathrm{F}\left(\mathrm{s}\right)$ is the respective loading trace.

6.1.2. Modelling DDPM Losses

The characteristic power loss of a digital displacement machine can be found through four runs on a test rig, each performed over the range of operating speeds. The DDPM is driven by a variable-speed drive with an HBM torque transducer in the driveline. The output flow of the DDPM is measured by a positive displacement flow meter. The first run is with the machine at full output but at the lowest possible output pressure. The power loss this represents is that of breathing loss through the valves and manifolds, shear loss across the various sliding interfaces, and churning loss in the crankcase. The second test is a repeat of the first but with the machine at maximum operating pressure, in this case, 300 bar. This test effectively adds leakage, compressibility, and loaded bearing losses to those recorded in the first test. The third test is also a repetition, but this time at a third of maximum operating pressure, i.e., 100 bar. This test is needed to establish the form of the loss curves, seeing as the effects of pressure on loss are not linear. The three curves which result from these test runs allow the loss in output due to compressibility effects, internal leakage, and pressure-related bearing losses to be characterised, as shown in Figure 9.

These polynomial curves can be fitted with parameters, allowing the entire operating range of speeds and pressures to be condensed into a simple model. A fourth test can be conducted, whereby the machine is run across the speed range at idle. The model can then be enlarged to incorporate flow-related losses simply by apportioning the percentage of machine capacity at idle vs. that where pumping occurred.

To estimate power loss at a given operating speed, the corresponding power loss should be estimated for HP, MP, LP, and idle conditions (${\mathrm{P}}_{\mathrm{H}\mathrm{P}}$, ${\mathrm{P}}_{\mathrm{M}\mathrm{P}}$, ${\mathrm{P}}_{\mathrm{L}\mathrm{P}}$, and ${\mathrm{P}}_{\mathrm{i}\mathrm{d}\mathrm{l}\mathrm{e}}$, respectively) using the curves given in Figure 9. Subsequently, the loss can be calculated for the DDPM operating at full output displacement, i.e., between the maximum test pressure of 300 bar, pmax, and the mid-test pressure of 100 bar, pmid, as given in the following equations:

$$\mathrm{c}\mathrm{o}\mathrm{e}\mathrm{f}{\mathrm{f}}_{\mathrm{A}}={\displaystyle \frac{\left({\mathrm{P}}_{\mathrm{L}\mathrm{P}}-{\mathrm{P}}_{\mathrm{M}\mathrm{P}}\right)·\mathrm{p}\mathrm{m}\mathrm{i}\mathrm{d}-\left({\mathrm{P}}_{\mathrm{H}\mathrm{P}}-{\mathrm{P}}_{\mathrm{M}\mathrm{P}}\right)·\mathrm{p}\mathrm{h}\mathrm{i}\mathrm{g}\mathrm{h}}{\mathrm{p}\mathrm{m}\mathrm{i}\mathrm{d}·\mathrm{p}\mathrm{h}\mathrm{i}\mathrm{g}\mathrm{h}·(\mathrm{p}\mathrm{h}\mathrm{i}\mathrm{g}\mathrm{h}-\mathrm{p}\mathrm{m}\mathrm{i}\mathrm{d})}}$$

(4)

$$\mathrm{c}\mathrm{o}\mathrm{e}\mathrm{f}{\mathrm{f}}_{\mathrm{B}}={\displaystyle \frac{\left({\mathrm{P}}_{\mathrm{H}\mathrm{P}}-{\mathrm{P}}_{\mathrm{M}\mathrm{P}}\right)·\mathrm{p}\mathrm{h}\mathrm{i}\mathrm{g}{\mathrm{h}}^2-\left({\mathrm{P}}_{\mathrm{L}\mathrm{P}}-{\mathrm{P}}_{\mathrm{H}\mathrm{P}}\right)·\mathrm{p}\mathrm{m}\mathrm{i}\mathrm{d}}{\mathrm{p}\mathrm{h}\mathrm{i}\mathrm{g}{\mathrm{h}}^2·\mathrm{p}\mathrm{m}\mathrm{i}\mathrm{d}-\mathrm{p}\mathrm{h}\mathrm{i}\mathrm{g}\mathrm{h}}}$$

(5)

$${\mathrm{P}}_{\mathrm{p}\mathrm{u}\mathrm{m}\mathrm{p}\mathrm{i}\mathrm{n}\mathrm{g}}=\mathrm{c}\mathrm{o}\mathrm{e}\mathrm{f}{\mathrm{f}}_{\mathrm{A}}·{\mathrm{p}}_{\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{p}}^2+\mathrm{c}\mathrm{o}\mathrm{e}\mathrm{f}{\mathrm{f}}_{\mathrm{B}}{·\mathrm{p}}_{\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{p}}+{\mathrm{P}}_{\mathrm{M}\mathrm{P}}$$

(6)

where ${\mathrm{P}}_{\mathrm{p}\mathrm{u}\mathrm{m}\mathrm{p}\mathrm{i}\mathrm{n}\mathrm{g}}$ is the loss associated with the maximum output displacement and ${\mathrm{p}}_{\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{p}}$ is the system pressure at each time step. Subsequently, the value obtained can be used to calculate the pressure loss for smaller flow demand values. For example, if the flow demand is 25% of the maximum, the loss would be

$${\displaystyle \frac{{\mathrm{P}}_{\mathrm{p}\mathrm{u}\mathrm{m}\mathrm{p}\mathrm{i}\mathrm{n}\mathrm{g}}}{4}}+{\displaystyle \frac{3·{\mathrm{P}}_{\mathrm{i}\mathrm{d}\mathrm{l}\mathrm{e}}}{4}}$$

(7)

When the DDPM output losses are calculated for each 4 ms interval and summed, the DDPM-related loss corresponds to 1.6 kJ, or 27% of the total.

6.1.3. Modelling and Differentiating Other System Losses

The electric motor was decoupled from the DDPM and allowed to coast down unpowered from an initial 2000 RPM. Its initial deceleration rate was estimated at 33 RPM per second, which represents a loss of 2.8 kJ of kinetic energy per second, i.e., 2.8 kW of parasitic power loss. This is composed of bearing, windage, and fan losses, of which the fan deserves particular attention. The six-pole motor is effectively being driven at double its 50 Hz speed by the VLT, so the fan will be drawing eight times the intended amount of power, according to fan laws as follows:

$$\mathrm{P}\propto {\mathrm{v}}^3$$

(8)

where $\mathrm{P}$ and $\mathrm{v}$ are the fan’s power and speed, respectively. It was also noted that the bearings were becoming very hot in operation, and there was some speculation as to the quality of these components. In any case, it should be noted that 46% of the total system loss is attributable to the electric motor. Replacing the shaft-mounted fan with an external, thermostatically controlled, cooling airflow could reduce this power significantly.

The flow emerging (during the loading phase) from the DDPM has to pass through approximately 8.5 m of a 1″ (25.4 mm) hose or pipe, a bend, and a manifold before emerging at the actuator. A loss calculation has been made for the sequence of the pipe and minor loss components. Therefore, the expression for the total loss, ${\mathrm{p}}_{\mathrm{l} \mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$, can be given by

$${\mathrm{p}}_{\mathrm{l} \mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}={\mathrm{p}}_{\mathrm{l} \mathrm{h}\mathrm{o}\mathrm{s}\mathrm{e}\mathrm{s}}+{\mathrm{p}}_{\mathrm{l} \mathrm{p}\mathrm{i}\mathrm{p}\mathrm{e}\mathrm{s}}+{\mathrm{p}}_{\mathrm{l} \mathrm{m}\mathrm{a}\mathrm{n}\mathrm{i}\mathrm{f}\mathrm{o}\mathrm{l}\mathrm{d}}+{\mathrm{p}}_{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{o}\mathrm{r} \mathrm{l}\mathrm{o}\mathrm{s}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{o}\mathrm{n}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{s}}$$

(9)

The losses in the pipes, hoses, and manifold, ${\mathrm{p}}_{\mathrm{l} \mathrm{p}\mathrm{i}\mathrm{p}\mathrm{e}\mathrm{s}}$, ${\mathrm{p}}_{\mathrm{l} \mathrm{h}\mathrm{o}\mathrm{s}\mathrm{e}\mathrm{s}}$, and ${\mathrm{p}}_{\mathrm{l} \mathrm{m}\mathrm{a}\mathrm{n}\mathrm{i}\mathrm{f}\mathrm{o}\mathrm{l}\mathrm{d}}$, are evaluated for each member using

$${\mathrm{p}}_{\mathrm{l}}=\mathrm{f}·{\displaystyle \frac{\mathrm{L}}{\mathrm{D}}}·\mathsf{\rho }·{\displaystyle \frac{{\mathrm{v}}^2}{2}}$$

(10)

where $\mathrm{f}$ is the corresponding friction factor, $\mathrm{L}$ and $\mathrm{D}$ are the length and diameter of the member, and $\mathsf{\rho }$ and $\mathrm{v}$ are the density and velocity of the fluid, respectively. The total pressure loss due to the minor loss components is evaluated using

$${\mathrm{p}}_{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{o}\mathrm{r} \mathrm{l}\mathrm{o}\mathrm{s}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{o}\mathrm{n}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{s}}={\mathrm{K}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}·\mathsf{\rho }·{\displaystyle \frac{{\mathrm{v}}^2}{2}}$$

(11)

where ${\mathrm{K}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$ is the sum of all loss coefficients due to the geometry of the pipework. This has been applied to the data at each time interval in order to calculate actual energy consumption through the cycle by multiplying the gross pressure loss with the volumetric flow rate, yielding a result in Watts. It is a small fraction of the total—around 4%.

The actuator loss has been calculated at each time step by finding the force difference between that applied by the pressurised oil inside the actuator versus the force measured by the load cell in line with it. The pressure exerted on the piston has been sampled by a pressure transducer at the actuator base, ${\mathrm{p}}_{\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{r}}$, resulting in the force

$${\mathrm{F}}_{\mathrm{o}\mathrm{i}\mathrm{l}}={\mathrm{p}}_{\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{r}}·\mathrm{A}$$

(12)

where $\mathrm{A}$ is the effective cylinder area. Again, this loss is a relatively small value, being 6% of the total.

The sum of the plumbing and actuator losses can be corroborated by comparing it to the data shown graphically in Figure 8b, seeing as, during the coast-down experiments, the difference between the active cycling and idling curves effectively reveals the loss of the sum of these two components. These two results are within 10% of one another, which is acceptable, given the general precision of these measurements.

There is a further loss introduced by a flow control valve located at the base of the actuator (Sun valve model FDCBHAN; fully adjustable pressure compensated flow control valve with reverse flow check; capacity: 12 gpm). The purpose of the valve was to allow some of the oil to be returned to the tank via a cooler, such that heat could be removed from the system to protect the actuator seals. This valve was set to its minimum flow level, ${\mathrm{Q}}_{\mathrm{m}\mathrm{i}\mathrm{n}}$, equal to 0.8 litres/min during the test run. Its loss, ${\mathrm{P}}_{\mathrm{c}\mathrm{o}\mathrm{o}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g}}$, is a product of displaced fluid volume and the instantaneous measured pressure as follows:

$${\mathrm{P}}_{\mathrm{c}\mathrm{o}\mathrm{o}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g}}={\mathrm{Q}}_{\mathrm{m}\mathrm{i}\mathrm{n}}·{\mathrm{p}}_{\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{p}}$$

(13)

${\mathrm{P}}_{\mathrm{c}\mathrm{o}\mathrm{o}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g}}$ was summed through both phases of the cycle and represented approximately 17% of the loss total. This could be largely negated through the use of an in-line heat exchanger located at the actuator base rather than by leaking away the working fluid at pressure.

6.2. Whole System Energy Flows During Loading and Unloading Phases

All of the losses and energy flows described in Section 6.1 can be assembled to model the entire system. The Sankey diagram in Figure 10 shows the energy flows of the loading phase, with the losses shown at the top of the diagram. The contribution of the slowing flywheel can be seen to supplement the VLT energy to help deflect the specimen blade.

The energy balance of the unloading phase (Figure 11) of the cycle is similar to that of the loading one. Essentially, the same amount of energy is exchanged between the flywheel and the test specimen, but the direction is reversed. The motor is driven with a relatively small amount of energy from the VLT during the unloading, again with very poor efficiency due to the extreme part load. The losses of the DDPM, hydraulic circuit, and actuator are assumed to be the same as in the loading portion. The motor loss is also assumed to be the same as that during the loading phase, though with the knowledge that this will not be quite correct as, during unloading, the motor is producing half of the energy that it does during the loading phase. It is difficult to split the motor losses into two separate phases, given the dominating effect of the standing parasitic effects discussed earlier, so the simple expedient of apportioning half to each one is used.

Whilst the energy balances of the two phases of the cycle show a relatively large loss fraction relative to productive work, this is only due to the specimen size and the consequent restriction on testing load relative to the capacity of the testing system. The DDPM is operating at an average of 4 kW, when its actual peak hydraulic power is 134 kW, roughly 33 times higher. Many of the losses will remain relatively constant as power levels grow. The motor efficiency will also move from the very low 55% value up to 95% at full power (assuming fan losses are corrected).

6.3. Comparison with a Conventional Proportional Valve Controlled System

If a notional conventional system is compared to the regenerative DDPM, then the energy savings can be evaluated, even under this very modest loading condition. In this case, a fixed-speed induction motor drives a variable axial pump at a continuous pressure and flow, which supplies an accumulator. A proportional valve, which must have at least 20% pressure authority over the maximum load pressure (in both cases, this is 128 bar), supplies oil to the actuator.

During the loading phase, a significant amount of pressure energy is lost over the valve due to the reduced load of the test specimen at small deflections. During the unloading phase, all of the strain energy stored in the specimen is throttled through the proportional valve, producing heat in the oil. Whilst the DDPM system required 6 kJ to complete a test cycle, the conventional system will be something like 20 kJ, as shown in Figure 12. These numbers also take into account the relatively low efficiency (around 55%) of the induction motor at a small fraction of full load since constant windage and bearing losses must all be borne by a relatively small throughput power. This is based on a typical swash-plate pump efficiency graph, showing efficiency as a function of both pressure and displacement fraction, as might be found in both the commercial and academic literature [23]. The pump loss during the test cycle is calculated at 4 ms intervals in the same manner as the DDPM losses were.

7. Conclusions

The FastBlade facility has shown its ability to regeneratively fatigue test marine current turbine blades using a synthesised natural frequency, where much of the loading energy is cycled between the driveline flywheel inertia and the strained specimen.

The system has been demonstrated to work at a 1 Hz cyclical frequency, with the potential to increase both the frequency and amplitude of testing.

A comparison of cyclical energy consumption has been made with a conventional variable pump and proportional valve, demonstrating that the DDPM system can achieve the same test cycle with approximately 30% of the input energy.

Further improvements in the FastBlade actuation system can be made by reducing motor losses by changing the forced-air cooling system and removing heat from the actuator without needing to leak off oil. It is anticipated that this would reduce the loss per cycle by approximately 2 kJ, a 33% reduction.

Following the series of tests on the tidal turbine blade described in this work, larger structures are expected to be tested at FastBlade. By examining longer and heavier blades in future runs, which require larger displacements at higher loads, it will be possible to examine the performance of the set up while operating closer to the system’s design capacity. Further studies will verify how the increased stiffness of the specimen affects the energy recovery properties, as well as how the system losses are impacted by the increased flow rate in the system.

The FastBlade hydraulic system can be utilised in other cyclical loading situations in order to save energy through regeneration. Whilst the obvious applications involve fatigue testing, there may well be repeating motions in manufacturing and construction where the same energy-saving results will be beneficial to operating expenses (OPEX) and, if internal combustion engine driven, emissions.

8. Patent

Displacement of an object with hydraulic actuators, US-11137330-B2 2021-10-05. Inventors: Rampen, William Hugh Salvin; Caldwell, Niall, and McCurry, Peter.