Challenges for multi-quadrant hydraulic piston machines

In search of more efficient hydraulic systems, new system architectures are explored. These system architectures are often electrically driven and include energy recuperation. This requires hydraulic machines to function both as pumps, converting mechanical power into hydraulic power, and as motors, converting hydraulic power back into mechanical power. However, the availability of machines that can operate in all desired modes is limited. This indicates that operation in multiple modes comes with performance penalties. This paper highlights the challenges for multi-quadrant operation of hydraulic piston pump/motors, with a particular focus on commutation, i.e., the transition between high-and low-pressure level for each chamber. Various commutation strategies for piston machines are examined. Furthermore, other important aspects for pump/motor operation such as hydrostatic compensation ratios, design of inlet channels, low-speed capability, and flow control through speed or displacement control are discussed. The article shows that the design of multi-quadrant machines is challenging, and this has to be considered when choosing the system architecture.


Introduction
Traditional mobile fluid power systems tend to be very inefficient, with reports of typical system efficiency values of around 21 % [1].However, standard fluid power components such as pumps and cylinders often have peak efficiencies above 90 % [2], and thus this system inefficiency is not an inherent characteristic of the fluid power domain; rather, it originates from the design and usage of the systems, where energy efficiency is often not a top priority.But in recent years there is a trend towards more energy efficient solutions due to environmental concerns and increased energy cost.Electrification of mobile machinery is a substantial part of this trend.Researchers have presented many different solutions for increased energy efficiency, which amongst others target to recover energy, to reduce throttling losses, and to operate machines in operating conditions with high efficiency [3].
Conventional hydraulic systems in machines such as excavators typically have one or more main pump(s).Valves are used to distribute the flow to the actuators.No energy recuperation takes place.In contrast to that, many of the new solutions include electric energy recuperation, meaning that the hydraulic machines must be able to transform mechanical power into hydraulic and vice versa (i.e., be able to work both as a pump and a motor).Furthermore, there is a tendency to go from conventional valve-control towards pump-control, where the pump/ motor flow is used to control the actuator.This means that the hydraulic pump/motor must be able to handle flow in two directions, as well as reversed pressure sides.It also means that the damping that traditional valve-control have provided is removed, meaning that active damping in the pump control might be needed.This puts new demands on the dynamic performance of the machines.Moreover, capability to run at higher speeds than before is desired since that means that the electric machines can be downsized (challenges regarding this have been summarised by Chao et al. [4] and will not be discussed in this paper).
It is clear that the system architecture, and the type of control, affect the requirements for the pump/motor heavily.Compromises in the pump/motor design are required to allow operation in different conditions, and reduced efficiency and increased noise might come as a consequence.However, publications focusing on the system level do typically not consider performance changes of the pump/motor caused by a new system architecture.This is despite the fact that manufacturers offer different machines for the use in different operating conditions.
Research in hydraulic machines usually focuses on pump operation, and less often, on motor operation.When operation in multiple modes (often referred to as quadrants) is discussed, it is typically only for specific machine designs.However, with the development of new system architectures requiring new hydraulic pump/motors, general discussions on how to design hydraulic pump/motors to be operated in multiple quadrants, and what performance to expect, are required.
This paper contributes to this discussion by summarising challenges for the design of hydraulic piston machines which operate in multiple quadrants.The focus is on the additional challenges due to operating in multiple quadrants, and thus challenges which are covered by designing a pump for just one quadrant are not discussed.The paper gives insight into the compromises that need to be taken to enable multi-quadrant operation of hydraulic piston pump/motors, thus enabling more informed trade-offs for defining system architectures.Furthermore, to the authors' knowledge, this is the first publication to systematically discuss and evaluate the potential of various commutation techniques to be used in multiple quadrants.
This paper is structured as following: Section 2 defines different operation modes of hydraulic pump/motors.Section 3 presents conventional valve-controlled systems, as well as pump-controlled systems, and systems using a common pressure-rail.The potential and drawbacks of each system are presented, and the requirements that each system causes for the hydraulic pump/motor are discussed.Section 4 contains a summary of commercially available hydraulic pump/motors from some leading manufacturers.Section 5 introduces the commutation of hydraulic pump/motors, which is one of the main challenges for multiquadrant operation.Poor commutation can cause losses and noise, and even lead to machine failure.On the example of axial piston machines, various conventional and unconventional commutation features are discussed, and their suitability for the different operating quadrants is systematically explored.Section 6 discusses other aspects for the design of multi-quadrant piston machines, such as the design of inlet and outlet channels, the design of the hydrostatic bearing between valve plate and cylinder barrel, and low speed operation.Section 7 discusses speed control in comparison to displacement control.Section 8 presents this paper's conclusions.

Modes of operation
In fluid power systems, where high pressure levels are desired, positive displacement machines are used (not rotodynamic machines such as centrifugal pumps).The term machine can refer to both a pump and a motor, and that will be used as the general term from here on.A pump transforms mechanical power to hydraulic and a motor does the opposite.Most positive displacement machines can principally do both even though they typically are optimised for one or the other.
A conventional hydraulic machine has two working ports and the flow through an ideal positive displacement machine is independent of the pressure level (if compression effects are neglected).From a functional perspective, a two-port hydraulic machine has four operating modes (often referred to as quadrants) -the flow can go in one or the other direction, and the pressure difference between the ports can either be positive or negative.This is illustrated in Fig. 1.When the pressure increases with the flow direction over the machine, the machine works as a pump.When the pressure decreases, it works as a motor.
The terms closed-circuit and open-circuit are often used to describe hydraulic machines.A closed-circuit machine is a machine that can have both ports pressurised.An open circuit machine is made to work with high pressure on just one side, meaning that it is limited to operation in two of the quadrants shown in Fig. 1.In circuit diagrams it is typically shown what modes of operation the hydraulic machines are supposed to be able to run in.Symbols for common combinations are shown in Fig. 2.
In conventional mobile hydraulic systems, where combustion engines have been used as prime movers, displacement control has been used to control the pump flow when needed.In applications where the flow direction should vary, the pump has been of so-called over-centre type, meaning that its displacement setting can change sign.However, when machinery is electrified, the relevance of using the speed and the rotational direction to control the flow increases.When adding the direction of the speed as a degree of freedom, the number of operational modes increases to eight.This is illustrated in Fig. 3.The functionality is, however, not extended.To have a machine that can perform in all eight modes is therefore probably not very relevant.The question is rather which degree of freedom should be used to control the flow direction.To use the speed to control the flow is of high interest since a fixed displacement pump can then be used.Fixed displacement pumps are in general more efficient and less expensive than variable pumps.However, a problem with speed control is that the machine should be able to run at very low speeds as well as to withstand frequent start-stop conditions, which they generally not have been designed for.

Importance of drive cycle
It is to be noted that the relative importance of the different operation modes depends on the system architecture and the used drive cycle.In some cases, the hydraulic machine rarely operates in certain quadrants.In that case, the machine's design may target to just "survive" (i.e., maintain an appropriate minimum pressure level and not exceed a maximum pressure level) in some quadrants.High noise and low efficiency in those quadrants may then be accepted in order to achieve better performance in those quadrants that dominate the drive cycle.

Pump efficiency vs. motor efficiency
Separate equations are applicable for calculating the efficiencies in pump operation and in motor operation.The most important international standard for measuring steady state performance of hydraulic machines is ISO 4409:2019 [5], and it refers to the efficiency definitions in ISO 4391:1983 [6].
However, please note that both of ISO 4409:2019 [5] and its predecessor, ISO 4409:2007 [7], have been criticised due to inconsistencies Fig. 1.Modes of operation from a functional perspective.in the efficiency definitions.The change of the fluid's internal energy during commutation is not considered by the standards, which can lead to experimental results of hydro-mechanical efficiencies above 100 % for motors [8].Contributions to the discussion on improved efficiency definitions were made by Achten et al. [9], Li and Barkei [10], and Schänzle and Pelz [11].This will not be further discussed in this paper, but it is important to bear in mind when comparing how machines perform in different modes of operation.

System architectures
As stated above, the requirements on the hydraulic machine are heavily dependent on the system architecture.How different architectures affect the requirements on the hydraulic machines is summarised here.

Valve-controlled systems
Conventional, valve-controlled, fluid power systems principally utilize one hydraulic pump that powers multiple actuators.Valves are used to control the flow distribution to the different actuators.Since the pump pressure must be matched to the load that requires the highest pressure, large throttling losses are typically present when several actuators are operated simultaneously.Furthermore, conventional systems cannot recuperate energy.These two aspects generally make conventional fluid power systems very inefficient.
Since energy recuperation is not applicable, motor operation is not relevant.Moreover, the direction of flow over the pump is not changed.This means that the pump only needs to be optimised for one of the quadrants of operation.In systems powered by diesel engines, the operational speed is also well defined, and it does not vary to a great extent.Displacement control is often used to control the flow when needed.However, the operational pressure can vary a lot.
In the case of rotational actuators (i.e., motors), the requirements are more spread.Frequent start/stop is a common use case and the speed range as well as the direction often varies a lot.There are low-speed motors that perform well down to fractions of rpm [12], typically of radial piston design.Then there are axial piston motors that can run up to around 10'000 rpm [13].As a rule up thumb, the smaller the displacement, the higher the maximum speed.However, these motors usually do not need to work in pump operation to a great extent since energy recovery features are limited.
A non-conventional approach to make valve-controlled systems more efficient is to place hydraulic motors in series with the loads and control the motors so that good pressure matching is achieved [14].
There are also examples where hydraulic motors have been implemented in the return line of certain functions to allow energy recuperation, e.g., during lowering [15,16].In such systems, both the pump and the motor are operated in just one quadrant.

Pump-controlled systems
A class of systems that is gaining prominence with the electrification are so-called pump-controlled systems.In such systems, at least one hydraulic machine is used to control each actuator, and its flow is used to control the actuator.Traditionally, this principle has been used in hydrostatic transmissions for vehicle propulsion.By using pumpcontrolled systems also for other functions, losses due to simultaneous operation of multiple actuators can be eliminated and energy recuperation can be allowed.The system efficiency will therefore most often be improved significantly.Ketelsen et al. published an overview in 2019 of what had been done until that point on pump-controlled systems [17].From that review it is clear that systems relying on closed-circuit machines are dominating, and it has persisted in this manner.However, there are examples of solutions based on open-circuit machines.Fig. 4 shows examples of generalised pump-controlled systems of closed and open circuit type respectively.
Work done on open-circuit based pump-controlled systems is, in fact, quite limited.Nevertheless, an early example of an open circuit-based system was presented by Heybroek and Palmberg [18].Ivantysyn and Weber also presented a simulation study on an open-circuit system [19].A more recent example is from Qu et al., who tried it in a skid-steer loader with a hydraulic gear pump integrated in an electric machine [20,21].
An argument for using open-circuit-based pump-controlled systems is that open-circuit machines can be used (why this is beneficial is clarified in Section 5, where commutation issues are discussed).The filtering solution is typically also more straight forward, and maintenance is likely easier since air-bleeding likely is less problematic.However, a disadvantage is that the flow direction must change if the pressure difference of the load changes sign.A smooth switch between certain modes of operation can therefore be difficult to achieve [22].
Closed circuits usually offer better mode-switching performance, even though they also can suffer from issues related to that.It should also be stated that there are system architectures that rely on both closed and open circuit machines, as illustrated in Fig. 5, and they also take advantages (and disadvantages) from both approaches [23].
In most pump-controlled systems, valves are used to compensate for the unequal flow rate of single rod cylinders.It is, however, possible to solve this by using an asymmetric pump with three ports [24][25][26][27].A limitation of this method is that the flow rate ratio of the three ports of T. Heeger et al. the asymmetric pump needs to be dedicated to the area ratio of the single rod cylinder.

Common pressure-rails
Another class of systems with the potential of being very energy efficient is based on so-called common pressure-rails.The number of pressure rails is two or more, and each pressure rail typically has a predefined pressure level.Accumulators are generally used to keep the pressures within defined boundaries.An arbitrary number of actuators can be connected to the pressure rails, and this is illustrated in the simplified circuit shown in Fig. 6, where the actuator control described below is also included.
Controlling a motor in a common pressure-rail system is somewhat straightforward since the torque can be controlled by means of the displacement setting (this is often referred to as secondary control).Linear actuation is more problematic since cylinders do not have a continuously variable active area.There are different approaches to controlling the cylinders.One way is to use multi-chamber cylinders in combination with a set of on/off-valves.This provides a discrete number of available forces.The number of available forces increases with the number of chambers and pressure rails.This is often referred to as a kind of digital hydraulics and quite a lot of work has been done on such systems in academia [28].However, the discrete nature of such systems can make them jerky.Smoother control can be achieved by combining on/ off-valves with proportional valves [29,30].Another approach is to use hydraulic transformers.Hydraulic transformers are machines that can transform one flow and pressure level into another, and ideally keeping the product of flow and pressure constant.A hydraulic transformer can principally be based on rotary machines (e.g., two interconnected hydraulic machines).They can also be based on fastswitching valves and utilise the inertial effects of the fluid [31].There is currently no commercially available hydraulic transformer, but there is ongoing work.A key player is the company Innas BV, which has been working on a three-port transformer since the 1990s [32].
The supply unit in a common pressure-rail system only has to work at very well-defined operating conditions.It often only has to work in one quadrant, the pressure levels are constant and set by the pressure rails, it can be of fixed displacement type, and it can run at a defined speed.The problem lies in the control of the actuators (i.e., the transformer or the control of the valves).

Commercial products
From the above, it can be seen that it primarily is the pumpcontrolled systems that place new demanding requirements on the hydraulic machines.In many studies about such systems, it is assumed that hydraulic machines perform well in all four quadrants and are able to run at low speed rates are available.However, the availability of such machines seems to be limited.A very brief overview of what some major suppliers have to offer follows here.
Bucher Hydraulics has developed their AX series, which is a fixed displacement axial piston machine based on the floating cup principle [33].The machine is available in one-quadrant, two-quadrant (opencircuit), and four-quadrant versions.The floating cup principle is known for high overall efficiency and good low-speed performance.
Another hydraulic machine that can work in four quadrants is Danfoss' Digital Displacement Pump/Motor.It is, however, currently only available as a pump [34], but the four-quadrant pump/motor version will come and Danfoss has presented several studies on it [35][36][37].Unlike the Bucher AX, it offers four quadrants by means of changing the displacement.The rotational direction is fixed, and it is not built for lowspeed operation.
Bosch Rexroth offers a series of variable-speed drives, in which internal gear pumps or axial piston pumps of the swashplate type are used [38].Depending on the use case, they offer different pump types.The internal gear pumps are only supposed to work in two quadrants, whereas some of the piston pumps can work in four quadrants.These are based on the A4 and A10 series.Bosch Rexroth also offers external gear motors of multi-quadrant type.For example, their AZMF series is available in one-, two-or four-quadrant versions [39].Furthermore, Rexroth's product portfolio also contains radial piston motors that are marketed as four-quadrant machines [40].
Parker also has a wide range of pump types for their electrified solutions, including external and internal gear pumps, vane pumps, swashplate and bent-axis piston pumps [41].
It is worth mentioning that all the machines presented above (excluding the Bucher AX) have a specified minimum operating speed ranging from around 50 to 500 rpm.

Commutation challenges in multi-mode operation of hydraulic machines
The limited number of available four-quadrant machines and the fact that some suppliers offer the same machine with different quadrant options indicate that there are challenges with making multi-quadrant machines.The core problem lies in the commutation, which is when a displacement chamber (e.g., formed by a piston and a cylinder) moves from low to high pressure and vice versa.

Importance of commutation in positive displacement machines
In piston machines, each piston commonly changes from a highpressure to a low-pressure port and vice versa once per revolution.These changes are referred to as commutation, and how they take place is crucial for machine performance, especially for efficiency and noise.An Fig. 6.Simplified circuit of how a common pressure-rail system can be used for different types of actuators.The figure shows a system with two pressure rails that are powering a four-chamber cylinder controlled by on/off-valves, a twochamber cylinder controlled by a transformer, and a displacementcontrolled motor.
ideal commutation would provide instant opening between the displacement chamber and the port exactly when the chamber reaches the port's pressure.An earlier or later opening causes a pressure mismatch when the chamber and the port are connected.Typically, valve plate (also known as port plate) design plays a crucial role in the timing of the commutation and therefore in providing an efficient and silent machine.
When there is a pressure mismatch between a displacement chamber and the port that it is connected to, fluid is filled into a displacement chamber (or leaves the chamber) until the chamber pressure is equal to the port pressure.The greater the pressure mismatch between the chamber and the port, and the higher the flow needed to equalise the pressures, the greater the throttling losses from commutation are.In some operating conditions, commutation losses can account for up to 50 % of the total losses in a pump [42].
The flow required to equalise the port's and the chamber's pressure is also known as compressible flow.Fig. 7 illustrates the commutation behaviour of a zero-lapped valve plate, i.e., a valve plate design without commutation features.The sharp peaks of the flow are so-called compressible flow pulsations and illustrate the necessity of commutation features, which aim to provide a better pressure match between the chamber and the port once the chamber is connected to the port.
Noise in hydraulic machines is a complex topic.Several characteristics contribute to noise creation, e.g., flow pulsations in the discharge port and inlet port, piston forces, bending moments and driving shaft torque [44,45].These contributors cause fluid-borne and structureborne noise, which both turn into air-borne (and thus potentially audible) noise eventually.There is no generally valid trade-off between the different contributors, as how much noise emission is caused by which factor is strongly dependent on the system the machine is used in.However, minimising individual contributors such as the flow ripple or cylinder pressure rate can have positive effects on the other contributors as well [44].
It is challenging to make a design that performs well for all operating conditions.The ideal design depends on the application system and its drive cycle (i.e., pressure-and flow levels as well as modes of operation).Which quadrants the machine works in affects which commutation features are feasible, and how well they will perform.

Classification and performance of commutation features
Amongst others, Johansson [46] and Heeger [47] described different commutation features.Fig. 8 visualises conventional and unconventional commutation features, and they are described and discussed in Sections 5.3-5.5.Typically, the discussion will focus on precompression, but the same principles are viable for de-compression as well if not otherwise stated.
Kärnell and Ericson [49] categorised commutation features as: Furthermore, one can distinguish between whether a common commutation feature is used for all chambers, or if each chamber has individual commutation features.
If one common commutation feature is used for all chambers, the frequency that this feature is used in is the product of shaft speed and the number of pistons.The commutation feature is only active for a small part of the piston stroke.
The use of individual commutation features for each chamber means that each commutation feature is used once per shaft revolution.This gives the possibility of using the commutation feature for a longer part of the stroke (or even the whole piston stroke).Note that there are two commutations per revolution.Some commutation features are used in pairs, and each of the features is active during one of the commutations (e.g., check valves).Other solutions such as shuttles are active for both commutations, and thus used twice per revolution.
The difference between individual and common commutation features can for example be shown for the commutation using check valves.Check valves can be used in combination with a valve plate, with the check valve opening a connection between chamber and port once the chamber has reached the port pressure.In that case, the same check valve is used for all chambers.In contrast to that, so-called wobble plate pumps also use check valves, however, here, each chamber has its own check valves.Fig. 7.In zero-lapped valve plates, the high-and low-pressure sides are separated by the bridge angles at bottom dead centre (BDC) and top dead centre (TDC), which cover exactly the swept angle over one of the openings from a displacement chamber φ chamber .As zero-lapped valve plates do not possess any commutation features, the displacement chamber's pressure equalisation during commutation causes compressible flow pulsations [43].How different commutation features perform in different modes of operation is described in Section 5.3-5.5.Table 1 summarises the discussion of the individual commutation features.

Mechanically forced commutation
This section presents some features of mechanically forced commutation.They can be used individually or in combination with other commutation features.

Pre-(de-) compression angle
Pre-and de-compression angles as sketched in Fig. 8a are simple, mechanically forced commutation features.The idea of these commutation features shall be explained on the example of the pre-compression angle in a pump: To increase the pressure level of a chamber coming from the low-pressure side, the opening to the high-pressure side (i.e., the delivery port) is delayed.That means, that after passing the bottom dead centre, the chamber volume is decreased, and thus the fluid in this chamber is pre-compressed.If the pressure level of the delivery port is known, the pre-compression angle can be chosen so that the pressure mismatch is minimal once the connection between chamber and delivery port is opened.
The optimal location of pre-and de-compression depends on the mode that the machine operates in, i.e., the direction of speed, the direction of the swashplate angle, and the location of the high-pressure side [50].Fig. 9 visualises that a reversed speed direction does not affect the ideal location of pre-and de-compression (or, to be precise, pre-and de-compression switch locations), whereas reversed pressure sides or reversed swashplate angle require pre-and de-compression in a new location.
As fixed pre-(or de-) compression angles only provide good performance for fixed pressure levels and displacement settings, they are not of interest in applications with varying pressure levels.However, besides giving insights into the location or part of the stroke commutation features should act, they can be relevant for use in common pressure-rails as described by Van Malsen et al. [51].

Pressure relief grooves
Pressure relief grooves, also known as silencing grooves, as sketched in Fig. 8b reduce the aforementioned limitation of fixed pre-(or de-) compression angles.By allowing a small amount of flow between the port and the chamber during pre-(de-) compression, a more gradual pressure build-up takes place and the pressure match of the chamber and the port under varying operating conditions is improved drastically, at the expense of losses [45,52].Their manufacturing is simple, and they are the most common commutation feature.
Heeger and Ericson [53] investigated how reversed speed direction and reversed pressure sides affect the ideal pressure relief groove design.yes yes yes 1 Reversed speed and reversed setting ratio do not change the direction of flow in machines with check valves for each chamber. 2 Assuming actively controlled valves for both ports.
Fig. 9. Desired locations of pre-and de-compression zones in different operating modes.
Using model-based optimisation, ideal groove design for the operation in different numbers of quadrants was developed.Fig. 10 shows the qualitative design for one-, two-and four-quadrant operation.The principal design for operation in just one pump quadrant is very similar to the design for two quadrants with operation in an additional motor quadrant with reversed speed direction.In the above-mentioned exemplary simulation study [53], the Pareto fronts of ideal designs for one-or two-quadrant operations showed commutation losses of 1.2 to 2.1 %, and the average of the peak-to-peak flow pulsations was 10.8 to 35.6 % of the average of the delivered flow of the considered operating points.Similarly, Mommers et al. [42] quantified the commutation loss in a floating cup with pressure relief grooves as 1.54 % in an exemplary operating point.
When operating in four quadrants with additionally reversed pressure sides, the ideal groove design changes significantly.The change in pressure sides requires two additional grooves [53].However, in order to avoid cavitation which can lead to severe damage [54,55], each of the grooves needs to be shorter and wider, which results in increased losses and flow pulsations.In [53], the Pareto front of ideal designs for fourquadrant operations showed commutation losses of 2.9 to 3.0 %, and in average, the peak-to-peak flow pulsations were 17.5 to 33 % of the delivered flow.
In the simulation study by Heeger and Ericson [53] reversed pressure side operation came with a reduction of the efficiency by 1.8 percentages for designs solely targeting efficiency, and an increase of average peak-to-peak flow pulsations by 6.7 % of the average delivered flow (which equalled an increase of flow pulsations by 62 %) for designs solely targeting low noise.The Pareto fronts are shown in [53].Mommers et al. [42] tested different valve plate designs.Their experimental results showed an average difference of efficiency of around 0.75 percentages between a valve plate designed to minimise commutation losses in one quadrant, and a valve plate designed for operation in four quadrants.
As shown in Fig. 9, a reversed direction of the swashplate angle has a similar effect on ideal groove design as reversed pressure sides and thus similar effect on performance.

Pre-compression (-expansion) filter volume
Pre-compression (or -expansion) filter volumes (sometimes referred to as ripple chambers), sketched in Fig. 8c, take a small amount of highpressure fluid to pressurise the chamber during commutation, similarly to pressure relief grooves.However, this high-pressure fluid is not provided directly from the port, but through an auxiliary volume between the port and the dead centre.This volume is discharged in the previously described process, and recharged when the chamber is in contact with the port [46].Machines with filter volumes are available on the market [56].
The same principle also works for the de-compression process.Then the volume is called pre-expansion filter volume.Besides noise reduction, pre-expansion filter volumes have shown the ability to reduce cavitation [57].
Filter volumes and pressure relief grooves can be combined for enhanced performance [58].Filter volumes require more space and are more costly than pressure relief grooves, but they provide better performance and less sensitivity to changes in operating conditions [46].
Filter volumes need to be loaded with the corresponding pressure level of the target port and are thus placed at the entrance of this port.Desired filter volume positions for the different operating modes are shown in Fig. 11.
Fig. 11 visualises that in motor operation, the filter volume for the high-pressure port is not located in the pre-compression zone, but on the other side of the dead centre axis or very close to the dead centre.The same applies for the filter volume for the low-pressure port, which is not located in the de-compression zone.This leads to reduced performance of this feature [50].
One could attempt to combine multiple volumes to achieve multimode operation: • For two-quadrant pump/motor operation (independent of if motor operation is achieved by reversed speed, reversed setting ratio, or reversed pressure sides), there will be cross-flow between the two volumes around the same dead centre, as they need to be located quite close to each other.This will reduce the filter volumes capability of matching the target port's pressure, but in principle, the functionality should still be available.• For two-quadrant pump/pump operation, additional volumes are required if commutation takes place in different locations (refer to Fig. 11).The volumes do affect each other not negatively.• For four-quadrant operation, it needs to be considered which four quadrants are chosen.If the direction of speed is fixed, then the volumes for reversed pressure side and reversed swashplate angle Fig. 10.Qualitative valve plate designs [53].
Fig. 11.Desired location of pre-and de-compression filter volumes in different operating modes.The figure can be extended for reversed setting angles, and appropriate locations for the filter volumes for pre-and de-compression can be derived with help of Fig. 9.
operation are in the same location, so no disadvantages to twoquadrant operation are expected.However, if the direction of speed is variable, then the different pump quadrants require filter volumes on opposite sides of the dead centres.This will make it even more challenging to provide a good pressure match and to provide connection of the volume to the correct port in motor mode.

Cross angle
A cross angle is applicable to variable swashplate machines.It can be beneficial to use it in combination with other commutation features such as pre-compression angle, pressure relief groove, or pre-compression filter volume [50,59].
The cross angle is illustrated in Fig. 8d.It is essentially a secondary swashplate angle.It gives an additional incline of the swashplate, in the direction perpendicular to the swashplate angle.Due to the cross angle, the dead centres' location on the swashplate plane varies with the swashplate angle [46,50].For smaller swashplate angles, the dead centre location is thereby moved away from the traditional dead centre locations, thus increasing the axial length of the pre-compression stroke.For larger swashplate angles, the dead centres move closer to the traditional dead centre locations, thus reducing the axial length of the pre-compression stroke.Assuming a constant target pressure, this is advantageous as the pre-compression stroke length is adjusted to the chamber volume and the dead volume at each swashplate angle, thus providing a constant effective pre-compression.
Rambaks and Schmitz [60] investigated and summarised the effect of cross-angle on the flow ripple, the torque ripple, the bearing forces and the required actuator forces.
An interesting feature of the cross angle is that when going overcentre, the dead centre axis moves in a way that pre-and decompression take place in the correct locations according to Fig. 9. Thus, cross angles are functional for reversed speed direction and reversed swashplate angle direction.However, fixed cross angles do not work for reversed pressure sides [46,50].

Pressure-dependent commutation
This section discusses pressure-dependent commutation utilising check valves (see Sections 5.4.1 and 5.4.2) or the shuttle technique (see Section 5.4.3).

Check valves in valve plates
Using check valves in combination with pre-and de-compression angles, as sketched in Fig. 8e, is a method of pressure-dependent commutation.Here, in the case of pre-compression, the port opening is delayed, so that the chamber pressure can reach the highest operating pressure.When the port's pressure is reached, a check valve opens a flow path from the chamber to the port [61].With this method an almost ideal commutation can be achieved, with simulation results showing commutation losses of only 0.35 % [42].
Grahl [62] presented test results for this commutation technique.For low pressures, the sound pressure level was significantly reduced.However, for higher pressures, the sound pressure level was increased contrary to the theoretical expectation.
Generally, the high frequency at which check valves in a pump operate leads to two concerns: the frequency response of the valve may limit the switching performance, and the large number of switches leads to a limited lifetime and noise [45].Furthermore, Harrison [45] pointed out that in case of an unboosted pump, the maximum pressure difference for the check valve in the de-compression phase is 1 bar, and raised the concern that the check valves opening time may be insufficient.
To reduce the aforementioned issues, Harrison [45] suggested two heavily damped check valves operating in parallel.Due to the heavy damping, the check valves would not fully close for each cylinder, but it would be a "self-tuning" variable restrictor, which reacts to the delivery port's pressure.To provide the correct amount of damping for these valves is challenging, and in Harrison's study, the check valves needed around 5 to 6 s to react to operating point changes, leading to very noisy behaviour during these transients.
Pettersson [61] discussed the use of vortex diodes.Their advantage is that they do not require any moving parts, and wear is less critical.Their disadvantage is that they cannot fully seal in the direction that check valves block.However, in Pettersson's study, the dynamic behaviour during the formation of the vortex was insufficient to provide positive effects on the commutation.Fig. 12 shows the required locations of check valves for each mode.It can be seen that reversed speed operation and reversed swashplate angle operation are possible, maybe on the expense of the installation of additional check valves.Reversed pressure side operation is not possible with the shown technique, as simply combining the required check valves would lead to the installation of check valves with opposite orientations.

Check valves for each chamber
One of the first piston pumps -Ctesibius' force pumpused this commutation technique [63].The basic principle is that a piston moves in a cylinder, which is connected to two check valves -one for the inlet and one for the outlet (see Fig. 8f).When the cylinder volume increases, the pressure in the chamber is reduced to below the inlet's pressure level, meaning that the check valve opens to the inlet.When the piston changes direction and the chamber volume starts to decrease, the pressure is increased which in turn causes the inlet check valve to close.Then, the pressure increases further until it reaches the level of the outlet and the check valve for the outlet opens.This principle is commonly used in hand pumps such as the ones found in hydraulic jacks, but it is also used in pumps with rotational input.The pistons' translating motions are then achieved by either crankshafts (see e.g., triplex pumps/ Fig. 12. Desired location of check valves in different operating modes.The figure can be extended for reversed setting angles, and appropriate locations for the check valves for pre-and de-compression can be derived with help of Fig. 9.The check valves are oriented to allow flow to the high-pressure port during pre-compression, and flow from the low-pressure port during de-compression. ram pumps) or rotating swashplates (see wobble plate pumps).The frequency response of the check valve is, however, a limiting factor for the speed of the pump, and pumps based on check valves are typically not built for high-speed applications.But, they are known to be quiet since the commutation is close to ideal, independently on the outlet pressure.However, they function only in one pumping quadrant.The highpressure side cannot move the machine since the flow is blocked by the check valve.If the high-pressure side is changed, all check valves will open, and the flow will simply go through the machine without creating any torque on the drive shaft.Changing the rotational direction (or, when applicable, over-centre operation of the swashplate) does not affect the flow direction, as the check valves respond solely to the piston's translational movement, irrespective of its cause.

Shuttle technique
The idea to use fluid from a neighbouring chamber for precompression during commutation has been presented many decades ago, with a mechanism which was intended to provide a variable opening between neighbouring chambers.It was designed with compensation for operating pressure and speed [64], but it was judged to be costly, prone to leakage, and unreliable [45].
In later decades, the idea of transferring fluid between neighbouring chambers was picked up in a different way, leading to the development of the so-called shuttle technique.The shuttle technique, as illustrated in Fig. 8f, is a pressure-dependent commutation feature that attempts to provide ideal pre-(and de-) compression for varying pressure levels.Shuttles are located in-between adjacent chambers, and allow for small amounts of fluid to be moved between them.For this technique to work, the valve plate design incorporates delayed port openings, to ensure that the pressure in the chamber has reached the port pressure before connecting to it.Furthermore, it is very important to have the correct shuttle position when commutation starts.Mommers and Achten [48] solved the shuttle positioning by using the pressure difference created by the channel connecting a chamber to a port.Fig. 13a shows the functionality of the shuttle technique as described by Mommers and Achten [48].While adjacent chambers are both connected to the same port, the pressure drop caused by the restriction between chamber and port positions the shuttle into one of the seats.During commutation from low pressure to high pressure, the shuttle stays in this seat until the chamber is pre-compressed to the highpressure port's level.Then, the shuttle starts moving and maintains the pressure level by increasing the chamber's volume.Analogously, the shuttle decreases the volume at the commutation from high-pressure to low-pressure and thus avoids pressure undershoots (and cavitation).Achten et al. [65] have reported an efficiency increase of several percentages on a commercial pump by implementing the shuttle technology.
Fig. 13b shows the behaviour for operation with reversed speed, i.e., in motor mode.In this situation, pre-compression takes place before the top dead centre, and de-compression takes place after the bottom dead centre (see also Fig. 9).The shuttles are correctly positioned, and the technique is thus suitable for reversed speed operation.This has also been described by Mommers and Achten [48].
Fig. 13c shows the behaviour for reversed pressure sides.Here, two issues occur: Firstly, the pre-and de-compression should take place in different locations (see Fig. 9).Secondly, the orientation of the pressure drop positions the shuttle into the wrong seat for commutation, e.g., before the commutation from low-pressure to high-pressure, the shuttle is in the "upper" seat.If one were to add a pre-compression angle in the required position, the pre-compression would be disturbed by this shuttle, as it will hinder the chamber to be pre-compressed to a higher pressure level than the low-pressure port.Thus, the shown shuttle technique is not suitable for operation with reversed pressure sides.
Fig. 13d shows the behaviour for reversed swashplate angles.The same issues as for reversed pressure sides occur.Thus, the shown shuttle technique is not suitable for operation with reversed swashplate angles.

Actively controlled commutation
Actively controlled commutation attempts to overcome the limitations of mechanically forced and pressure-dependent commutation features.It aims to improve the mechanisms shown in Sections 5.3 and 5.4 by adding active control to them.
In 1997, Harrison summarised some attempts at variable pre-and decompression angles [45].However, he noted that neither of the concepts has been commercialised, with cost and the complexity of compensating for pressure, flow, and speed characteristics as primary reasons.This section will discuss recent approaches for valve plate rotation (Section 5.5.1), for active control of valve plate restriction during commutation (Section 5.5.2), and for active control of individual valves for each chamber (Section 5.5.3).

Valve plate rotation
Valve plate rotation, as sketched in Fig. 8h, is an interesting concept, as it has been considered both a method of noise reduction for small valve plate rotation angles [62,66] and a method of variable displacement for large valve plate rotation angles [67,68].It has also been investigated for combining variable displacement and noise reduction by using a double pump, in which two valve plates affect the commutation [43].Depending on the control method for valve plate rotation, different classifications are possible.However, active control seems most promising.
Valve plate rotation is a crucial concept for the design of 3-port hydraulic transformers, which can reduce hydraulic system losses (see Section 3.3).In the 3-port hydraulic transformer, the valve plate rotation angle controls the distribution of the flow between a low-pressure rail, a high-pressure rail, and the load [32].The commutation behaviour of these valve plates has been discussed by Achten and Fu [69], who stated that the relationship between load pressure and control angle is advantageous to achieve low compressible flow pulsations despite having fixed porting angles.However, in a 3-port design, the pistons do not complete a full stroke while in contact to the same port, which increases kinematic flow pulsations.
When rotating a valve plate, the timing of the commutation is changed.This affects the pressure build-up.The larger the distance of the valve land to the dead centres, the larger the pressure build-up during pre-compression for the same pre-compression angle [43].Grahl [62] presented test results for the modified pressure build-up for valve plate rotation angles between 0 • and 6 • , and showed the potential for reduced sound pressure emission.
In principle, valve plate rotation can take place in either direction, and thus it can move the commutation to either side of the dead centre.This means, for each operating mode, a good valve plate position can be achieved.However, Edge and Liu [70] already noted that the possibility to operate in more modes comes with increased complexity.
Edge and Liu [70] have tested valve plate rotation in combination with pressure relief grooves.
Grahl [62] and Edge and Liu [70] have suggested control mechanisms for pump operation in one quadrant.However, the control of valve plate rotation is challenging.The relationship between operating condition and optimal valve plate position is non-linear [43], and the pre-and de-compression cannot be controlled independently of one another [43,71].Therefore, the ideal valve plate position for precompression might cause cavitation during de-compression [70].Furthermore, design features that minimise the valve plate friction are required, but Achten et al. [32] presented a solution for this.

Actively controlled valves in valve plate
Nafz et al. [72] and Tvaružek et al. [73] suggested valves which provide a variable restriction from (near) the dead centres to each port.With this variable restriction, the timing of the commutation can be influenced.The method can be considered similar to an "actively controlled pressure relief groove".The restriction area is chosen for each operating condition, thus requiring active control.Nafz et al. [72] found ideal settings by simulation of each operating condition, and Tvaružek et al. [73] point out the potential to optimise the timing for different objectives (efficiency, noise/vibration, moments for swash-angle control, and cavitation).
Both above-mentioned works [72,73] have only been applied to pump operation.However, as commutation takes place in the same locations, the principle is also viable for reversed speed operation.
When commutation should take place on the other side of the dead centre, it is possible to add another channel, and to activate or deactivate the restriction on the desired location of commutation.

Actively controlled valves for each chamber
The best-known example of the use of actively controlled valves for commutation is probably the so-called Digital Displacement machine from Danfoss (already mentioned in Section 4) [34].It uses one or more electronically controlled valves for each piston.There are several possible valve configurations and control methods, and the valve setup can be partly passive, as illustrated in Fig. 14a.A great advantage of this type of commutation is that it enables variable displacement since pistons can be disabled individually.Another advantage is that pistons can be isolated from each other.They can thereby function as several small hydraulic machines, and losses due to simultaneous operation of actuators can thus be eliminated.As for pumps that use check valves for each chamber, Digital Displacement machines tend to be based on machine types where the pistons do not rotate with the drive shaft, since that means that the valves do not have to rotate.If both valves are actively controlled, as shown in Fig. 14b, four-quadrant operation is possible.
The Digital Displacement technique has been developed since the late 1980's, when the first patent was filed [74].Much work related to it has been conducted by the company Artemis Intelligent Power, which was acquired by Danfoss some years ago [75].There has been much focus on control, but also valve design since the valves should be very fast and have low pressure drops.Work has also been carried out in academia, primarily at the University of Edinburgh (from where Artemis Intelligent Power originates) [76,77], Purdue University [78][79][80], and Aalborg University [81][82][83][84].
The simplest design is partly passive, and commutation-wise it is identical to using check valves, as described in Section 5.4.2.The difference is basically that the valve connecting to the low-pressure side can be actively kept open, thereby preventing the piston to deliver flow to the high-pressure port.This setup only works in one quadrant.To allow operation in more quadrants, the valve setup must be changed.By using two on/off valves (one for each port) four-quadrant operation can be achieved since that means full freedom in when the cylinder should be connected to each port.With fast-switching valves, close to ideal commutation can principally be achieved if the shaft angle, and pressure levels are known.However, the higher the rotational speed, the higher the requirements on the valve response.Roemer et al. concluded that the valve switching time should be at most 5 % of the revolution time if satisfactory performance should be obtained [85].This typically means that the valves should switch within a few milliseconds.How the response and size of the valve affects the performance has also been exemplified by Merrill et al. [86].

Additional design considerations for multi-quadrant machines
It is not only the commutation design that makes a pump different from a motor.Other important aspects are the machine's channel design, the design of the hydrostatic bearing in the interface between valve plate and cylinder barrel, and the machine's low-speed capability.

Design of inlet and outlet channels
Self-suction capability is an important performance parameter of a pump, and can limit its high-speed capabilities [87].Assuming atmospheric pressure in the tank and no relevant differences of the gravimetric potential of tank and pump, the maximum pressure difference to fill the pump's suction chambers is approximately 1 bar.To avoid large pressure drops in the line between the tank and the pump, a large line diameter is desired.However, there is a conflict between this Fig.14.Examples of valve configurations for a Digital Displacement machine.requirement and the desired inlet area of the pump itself, which can be seen from Eq. 1, derived by Manring [52].The equation describes the maximum pump speed that can be achieved without causing cavitation.
In this equation, ω is the rotational speed of the cylinder barrel, p i is the inlet pressure, p cav is the cavitation pressure, ρ is the fluid's density, r is the piston pitch radius, A p is the area of a single piston, A k is the kidney area, A i is the inlet area, N is the number of pistons, and α is the swashplate angle.
The equation shows that an increased inlet area will reduce the maximum speed.It can also be seen that boosting the inlet pressure is an easy way of increasing the machine's maximum speed capability, which should not come as a big surprise.
Another aspect to consider is that large channel areas increase the load on the channel walls.Therefore, inlet channels with large areas usually cannot be charged with high pressures.
When designing a machine to operate with reversed pressure sides, both channels can be low-pressure inlet channels resp.high-pressure outlet channels.This is typically solved by using the same design for inlet and outlet channel, and by boosting the low-pressure side.

Contact between valve plate and cylinder barrel
In axial piston machines of swash-plate type, there are three main lubrication interfaces: between cylinder barrel and valve plate, between cylinder barrel and piston, and between slipper and swash plate.The fluid films in each of these interfaces represent very complex tribological pairs, and each of the interfaces is crucial for a well-functioning machine.In these interfaces, the fluid's pressure field interacts with the solid bodies causes elastic deformation, which in turn affects the pressure field.Furthermore, the fluid film shear stress causes viscous friction and thus heat generation.The temperature change affects the fluid's viscosity as well as the solid bodies geometry.Therefore, the fluid films are characterised by thermo-elastohydrodynamic lubrication, and it requires advanced numerical models for computing the aforementioned effects [88].However, for the purpose of this paper simplified qualitative considerations are made.

Compensation ratio for contact between valve plate and cylinder barrel
Besides separating the inlet from the outlet and providing an efficient and quiet commutation, the valve plate must also provide an axial bearing for the cylinder barrel in axial piston machines [89] as sketched in Fig. 15.In axial piston machines, this bearing constitutes the lubrication zone with the largest contact surface, and its force balance is crucial for minimising volumetric losses and energy dissipation [90].Wegner et al. [89] and Zhao et al. [90] summarised many different methods to calculate this force balance based on the chosen assumptions and simplifications.
The core idea of the force balance is to compare the forces loading and relieving the contact between the valve plate and cylinder barrel in the socalled compensation ratio ζ as defined in Eq. 2. In its simplest form, the calculation of compensation ratios only considers hydrostatic forces.The pressurised chambers create an axial force pressing the cylinder barrel against the valve plate, which are counteracted (compensated) by pressure-dependent forces in the hydrostatic bearing [91].This leads to the definition of the compensation ratio ζ as the ratio between loading forces F load and compensating hydrostatic forces F comp , see Eq. 2.
For compensation ratios larger than 100 %, the cylinder barrel lifts off the valve plate, thus leading to undesired leakage from the highpressure port.To ensure sufficient sealing between the ports, compensation ratios need to be smaller than 100 %.However, non-compensated forces must be taken through solid contact between valve plate and cylinder barrel.The combination of the two requirements leads to compensation ratios just below 100 % [52,89,91].However, the calculation methods for the compensation ratio differ in literature, and the correct numerical target for the compensation ratio depends on the used calculation method [89].Furthermore, Ernst and Vacca [92] claimed that the hydrodynamic forces in pumps are drastically underestimated, and Vacca and Franzoni [93] stated that the hydrodynamic forces typically balance 10 to 20 % of the load forces.An important difference between pump and motor operation is the required compensation ratio.Pumps are traditionally hydrostatically underbalanced, as hydrodynamic effects also add a lift force.However, in motor operation, the breakaway torque from standstill is a critical performance parameter [94].For a reduced breakaway torque, higher compensation ratios very close to 100 % are advantageous.
Ivantysynova and Baker [95] have investigated the lubrication gap between cylinder barrel (also known as cylinder block) and valve plate for swashplate machines.They used the Reynolds equation and considered elastic deformation of the cylinder block (however, they neglect deformation of the valve plate).The effect of friction between the piston and cylinder bore was also considered.Ivantysynova and Baker [95] ran simulations for the same machine set-up in pump and in motor mode.The resulting lubrication gap heights were the same for both modes when the machine's operating pressure is low.However, when operating pressures were high, the minimum film thickness was decreased in motor mode.This could imply that motor designs require increased compensation ratios to avoid lack of lubrication.
In contrast to the simulation results in Ivantysynova and Baker [95], Innas BV [96] published measurement results for different machines at pump and motor operation at very low speeds.The results showed decreased friction and increased leakage at motor operation, implying that gap heights were higher.The reason given for this is the direction of movement of the pistons during the high-pressure stroke.The highpressure stroke's friction forces between piston and cylinder barrel are larger than those during the low-pressure stroke.In pump operation, the friction forces between pistons and cylinder barrel push the cylinder barrel against the valve plate, whereas in motor operation, they pull the cylinder barrel off the valve plate.
Ivantysyn and Ivantysynova [91] have made similar considerations for the effect of friction between cylinder barrel and piston on the pressing force between a piston and its slipper.
A good compromise for the design of the axial bearing in the interface between valve plate and cylinder barrel for pump and motor operation could be facilitated by a redesign of the hydrostatic bearing as Fig. 15.Contact between valve plate and cylinder barrel [89].The pressurised pistons create a load force pressing the cylinder barrel against the valve plate.The hydrostatic forces in the axial bearing are also known as compensation forces.
presented by Achten et al. [97] and summarised in Section 6.3.

Low-speed capability
Pump manufacturers usually specify that their pumps should be operated above a certain minimum speed.However, speed-controlled systems typically require hydraulic machines to run at very low speeds, and even with frequent zero-crossings [98].This provides multiple challenges for the design of the hydraulic machines.
In swashplate pumps, the interfaces between slipper and swashplate, and between valve plate and cylinder barrel are loaded by large forces from the pressurised chambers.To reduce the force in the contacts, hydrostatic bearings as described in Section 6.2.1 are designed to compensate for most of the load force.However, the design of these pumps typically also relies on a hydrodynamic pressure to build up in the interfaces between slipper and swashplate, and between valve plate and cylinder barrel, and hydrodynamic bearings need relatively high velocities to function [97].
operation at load holding states is very challenging due to the combination of low speeds and high pressures (i.e., high forces).Also, the low flow rates limit the cooling capacity, thus reducing viscosity.In this state, strong wear occurs due to the lack of lubrication.As a consequence, electro-hydraulic flight actuators are currently only used as back-up devices due to their short lifetime [98].Furthermore, at low speeds, stick-slip becomes a challenge for the control of electrohydraulic actuators [97].The control also needs to consider that pumps require a minimum speed to deliver flow due to leakage, and if very low speeds are to be controlled, it needs to be considered that the torque loss varies with the driveshaft angle [99].
Low-speed performance is also of interest for traditional axial piston motors, as the breakaway torque determines a motor's ability to initiate movement of a specified load from standstill conditions [94].

Attempts to improve low-speed performance
Ivantysyn et al. [100] focused on the interface between slipper and swashplate, and showed reductions in friction losses at very low speeds by introducing new surface structures on the slippers of traditional swashplate machines.
Achten et al. [97] focused on the interface between cylinder barrel and valve plate.They separated the conventional sealing land into three concentric rings and added pockets in the middle ring.Each pocket was connected to the corresponding chamber through a small groove.When the gap between cylinder barrel and valve plate is small, this small groove ensures that the pocket has a similar pressure level as the corresponding chamber.However, when the gap between cylinder barrel and valve plate is large, the leakage over the seal lands dominates, and the pressure in the pocket is in-between the chamber pressure and the pressure of the drain port.That means, at low gap heights, a large hydrostatic force acts to lift the barrel off the valve plate, whereas at larger gap heights (e.g., introduced by hydrodynamic bearing effects), the hydrostatic force is reduced, and thus excessive leakage is avoided.Furthermore, tipping loads on the barrel are counteracted.

Speed control vs. displacement control
Earlier in this paper, the following question was posed: should displacement control or speed control be used to control the flow?Section 6.3 clarified that low-speed operation poses challenges for most positive displacement machines.When using displacement control, low speed operation can be avoided, and it is therefore advantageous from that perspective.However, displacement control comes with parasitic losses during idling, both related to friction and to the controller itself, which often requires a bypass flow to achieve sufficient damping [101].
Section 5 revealed significant differences between speed and displacement control in terms of commutation.If pressure relief grooves are used to facilitate the commutation performance, which most often is the case, it can be seen that they work for reversed speeds but not for reversed displacement setting.This means that speed control is advantageous in this aspect.From Table 1, it can additionally be seen that most other commutation features also work with reversed speed, but fewer work with a reversed swashplate angle.
Another important aspect for control, not yet discussed here, is the dynamic behavior.Typical variable swashplate pumps can go from zero to full displacement in 70 to 500 ms (depending on the pressure level, pump size, and controller type), and they can destroke in around 30 to 100 ms [56,102].According to Manring and Mehta, the bandwidth of the displacement control is usually limited to around 25 Hz [103].However, they conclude that "the frequency response of the pump is primarily limited by how fast the moving actuator can be filled and emptied by the three-way valve".This means that higher bandwidths can principally be achieved if needed.Furthermore, it should be noted that the Digital Displacement machines are based on a different technique that is considerably faster than conventional techniques.
The response of a speed-controlled pump is principally limited by the torque that can be applied by the drive unit.The inertia that should be accelerated is crucial.If the speed should be able to go from zero to full speed in 100 ms, the required torque for the acceleration is very significant in comparison to the required torque for steady-state operation at high pressure levels.
Efficiency is also a relevant consideration.The peak efficiency of a fixed hydraulic machine is typically higher than that of a variable displacement machine (mainly due to losses related to the displacement controller).This characteristic gives an advantage to speed control.However, even if displacement control is used to change flow direction, the flow control can be combined with speed control.It is then possible to optimise the operating points of the hydraulic and electric machines.The overall efficiency for a drive cycle can therefore be similar or even better when variable displacement is used [104].This especially applies if the cycle often requires low flow rates at high pressure levels.The dynamic response can also be improved when displacement control and speed control are combined [105].

Conclusions and future directions
There are differences in how a hydraulic pump and a hydraulic motor should be designed.A machine that can work as both pump and motor is a compromise, and a deeper understanding on those compromises is needed.
This especially applies to the commutation, which is related to efficiency and noise.Most commutation features have issues with handling reversed pressure sides.This means that system architectures based on open-circuit machines are preferable.Avoiding reversed pressure sides also offers advantages in terms of channel sizing and hence self-suction capability and losses.Therefore, system designers should make an active choice on whether to accept the compromises of designing the system so that the hydraulic machine does not need to operate with reversed pressure sides, or whether to accept the compromises that come with four-quadrant operation of the hydraulic machine.More research is needed to better evaluate the trade-offs.
When it comes to comparing speed control to displacement control, it has been observed that commutation generally is better if speed control is used to alter the flow direction.However, that means that low-speed operation is desired, which is problematic for most conventional machines.Improvements on the tribological interfaces are required, and recent research on the interfaces between slipper and swashplate as well as between cylinder barrel and valve plate has been summarised.Further research in this direction is expected.
In general, more development efforts for commutation features to operate in four quadrants are necessary.To be able to achieve ideal commutation in all modes of operation, the connection to both ports should be actively controlled individually.This is theoretically possible with valves actively controlling each commutation, a principle as in the Digital Displacement machine.However, in practise, this is not trivial, and therefore more research is needed to better understand its noise and vibration behaviour, and to prove its durability.Furthermore, as active control comes with increased cost and complexity, there is room for more solutions.
Research on improved commutation is ongoing, e.g., on the shuttle technique, or on Digital Displacement machines which use active valve control.The shuttle technique provides close to ideal commutation, but currently only performs well in two quadrants with reversed speeds.Future research might be able to expand its application range to reversed pressure sides.
With the increased interest in multi-quadrant machines, there is a need for further development and inventions.To overcome the limitations of conventional machines, new solutions that might incur higher cost and complexity are expected.However, considering the demand for improved efficiency and lower noise levels in fluid power applications, the market is expected to adopt innovative solutions, even at increased cost.

Fig. 2 .
Fig. 2. Symbols for common machine types.The column indicates the number of quadrant that the machine can work in.

Fig. 3 .Fig. 4 .
Fig. 3. Modes of operation.The four different functional modes (presented in Fig. 1) are colour coded as shown.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 5 .
Fig. 5.A pump-controlled system based on a closed and an open circuit machine.

Fig. 8 .
Fig. 8.Some commutation features in hydraulic machines, sketched for the pump case.

Fig. 13 .
Fig. 13.Shuttle technique in different operating modes.Reversed speed operation is feasible, reversed pressure side and reversed swashplate angle operation are not feasible.

Table 1
Summary of performance of commutation features in different operating modes.