TITLE: A HYDRAULIC SYSTEM WITH LINEAR ACTUATORS AND HYDROSTATIC AND NON-HYDROSTATIC MODES

CROSS-REFERNCE TO RELATED APPLICATIONS

[0001 ] This application claims the benefit of 35 USC 1 19 based on the priority of co-pending US Provisional Patent Application 62/381 ,361 filed August 30, 2016, entitled A HYDRAULIC SYSTEM WITH LINEAR ACTUATORS AND HYDROSTATIC AND NON-HYDROSTATIC MODES, which is incorporated herein in its entirety by reference.

FI ELD

[0002] The present subject matter of the teachings described herein relates generally to hydraulic power systems with linear hydraulic actuators.

BACKGROUND

[0003] US Patent No. 9, 151 ,018 (Knussman) discloses a hydraulic system that may have a pump with variable-displacement, a first linear actuator, and a second linear actuator coupled to the first linear actuator to operate in tandem. The first and second linear actuators may be connected to the pump in closed- loop manner, and each of the first and second linear actuators may have a first chamber and a second chamber separated by a piston. The hydraulic system may also have an accumulator in fluid communication with the second chamber of only the second linear actuator.

[0004] US Patent No. 9,051 ,944 (Wen) discloses a hydraulic unit adapted for connection to master and slave actuator system that includes three valves, the first configured for selective fluid passage between the cap ends, the second configured for selective fluid passage between the slave cap end and an accumulator, and the third fluidly coupled for selective fluid passage between each of a single open circuit pump and the accumulator, and the slave cap end. During actuator retraction, the valves permit pressurized fluid in the slave cap end to be delivered to accumulator for storage; during extension, the valves permit pressurized fluid from pump and accumulator to be delivered to the slave cap end. SUMMARY

[0005] This summary is intended to introduce the reader to the more detailed description that follows and not to limit or define any claimed or as yet unclaimed invention. One or more inventions may reside in any combination or sub-combination of the elements or process steps disclosed in any part of this document including its claims and figures.

[0006] A hydraulic system that utilizes two or more linear actuators may be configured so that it can operate in both a hydrostatic mode and a non-hydrostatic mode, and optionally may be switchable between the two modes. This may help provide a system that can be operated in a relatively energy efficient hydrostatic mode during some of its operation, and that can be switched to a more powerful non-hydrostatic mode when required/desired. This may help make the system more energy efficient than a similar system that is operable only in a non- hydrostatic mode. Using linear actuators may make the system suitable for lifting type operations, such as use on heavy equipment and the like. Optionally, the system may be switchable between modes on the fly, such that an operator need not stop using the system in order to change between modes. This may allow relatively uninterrupted use of the equipment utilizing the hydraulic system, while still allowing for energy savings in the hydrostatic mode when appropriate.

[0007] In accordance with one aspect of the teachings described herein, a hydraulic system may be switchable between a hydrostatic operating mode and a non-hydrostatic operating mode and may include a first linear actuator having a first rod end chamber, a first head end chamber and a first piston positioned therebetween. A second linear actuator may include a second rod end chamber fluidly connected in parallel with the first rod end chamber, a second head end chamber and a second piston positioned therebetween. The first and second pistons may be movable in unison between extended and retracted positions. A pump may be operable to pump fluid at a first flow rate and a second flow rate. The hydraulic system may be switchable between the hydrostatic mode and the non-hydrostatic mode. In the hydrostatic mode the pump may operate at the first flow rate and may be fluidly connected in a closed-loop manner between the first and second rod end chambers and the first head end chamber, the second head end chamber may be fluidly isolated from the first and second head end chambers and the pump, the pump may energize the first head end chamber to urge the first and second pistons toward the extended position with a first force, and the pump may recover energy from fluid driven from the first head end chamber to the first and second rod end chambers when the first and second pistons are urged toward the retracted position by the load. In the non-hydrostatic mode the pump may operate at the second flow rate, the second head end chamber ay be in fluid communication with the first head end chamber, the pump may be fluidly connected between the first and second rod end chambers and the first and second head end chambers, the pump can energize both the first head end chamber and the second head end chamber to urge the first and second pistons toward the extended position with a second force that is greater than the first force.

[0008] The sum of the piston areas of the first and second rod end chambers may be equal to the piston area of the first head end chamber.

[0009] A mode selection valve may be fluidly connected between the pump and the second head end chamber. The mode selection valve may be moveable between a first position in which the second head end chamber is fluidly isolated from the hydrostatic pump and the hydraulic system is in the hydrostatic mode, and a second position in which the second head end chamber is in fluid communication with the pump and is connected in parallel with the first head end chamber and the hydraulic system is in the non-hydrostatic mode.

[0010] When the mode selection valve is in the first position the second head end chamber may be fluidly connected to a fluid reservoir. When the second piston moves toward the extended position fluid may be supplied to the second head end chamber from the fluid reservoir, and when the second piston moves toward the retracted position fluid may be driven from the second head end chamber into the fluid reservoir. When the mode selection valve is in the second position the second head end chamber may be fluidly isolated from the reservoir.

[001 1 ] When moving between the first and second positions the mode selection valve may travel through at least a first transition position in which fluid communication is established between the second head end chamber, the pump and the fluid reservoir, whereby a leakage portion of the fluid can flow from the pump into the fluid reservoir without passing through the second head end chamber.

[0012] The second flow rate may be greater than the first flow rate and wherein the pump is operable at a third flow rate that is different than first and second flow rates while the mode selection valve is in the first transition position. The third flow rate may be greater than the first and second flow rates when the hydraulic system is changing from the hydrostatic mode to the non-hydrostatic mode, and may be greater than the first flow rate and less than the second flow rate when the hydraulic system is changing from the non-hydrostatic mode to the hydrostatic mode.

[0013] The hydraulic system may be switchable between the hydrostatic mode and the non-hydrostatic mode while the first and second pistons are translating and driving the load.

[0014] The pump may be changeable from the first flow rate to the second flow rate in a pump response time and the mode selection valve may be changeable from the first position to the second position in a valve response time that is equal to or greater than the pump response time.

[0015] The first and second pistons may translate at a piston speed and the piston speed ay be substantially the same when in both hydrostatic and non- hydrostatic modes.

[0016] The piston speed may remain substantially constant while the hydraulic system is transitioning between the hydrostatic mode and the non- hydrostatic mode.

[0017] A controller may be operable to control the pump and the mode selection valve. The controller may monitor a fluid pressure in the first head end chamber, and may be configured to automatically configure the hydraulic system in the hydrostatic mode when the fluid pressure is below a predetermined threshold value, and to change the hydraulic system to the non-hydrostatic mode when the fluid pressure exceeds the threshold value by changing at least one of the operation of the pump and the position of the mode selection valve.

[0018] The pump may be a bi-directional pump, and may be a variable displacement pump.

[0019] In accordance with another aspect of the teachings described herein, a method of operating a hydraulic system that is switchable between a hydrostatic operating mode and a non-hydrostatic operating mode and includes a first linear actuator comprising a first rod end chamber, a first head end chamber and a first piston positioned therebetween and a second linear actuator comprising a second head end chamber, a second rod end chamber fluidly connected in parallel with the first rod end chamber and a second piston positioned therebetween that is linked to and movable in unison with the first piston between extended and retracted positions, may include the steps of:

a) operating the system in the hydrostatic mode in which a pump is fluidly connected in a closed-loop manner between a first and second rod end chambers and a first head end chamber and the second head end chamber is fluidly isolated from the first and second head end chambers and the pump, wherein the pump can energize the first head end chamber to extend the first and second pistons and drive a load connected to the first piston with a first force; and b) converting the system to the non-hydrostatic mode by establishing fluid communication between the second head end chamber and the pump, whereby the pump is fluidly connected between the first and second rod end chambers and the first and second head end chambers and can simultaneously energize both the first and second head end chambers to extend the first and second pistons and drive the load connected to the first piston with a second force that is greater than the first force.

[0020] The method may include converting the system from the hydrostatic mode to the non-hydrostatic mode while first piston is extending.

[0021 ] The method may include operating the pump at a first flow rate when in the hydrostatic mode and operating the pump at a second fluid flow rate that is greater than the first fluid flow rate when in the non-hydrostatic mode whereby the first piston extends at a substantially constant piston translation speed in both the hydrostatic mode and the non-hydrostatic mode.

[0022] The method may include a mode selection valve fluidly connected to the pump. The second head end chamber may be in fluid communication with the pump when the mode selection valve is in a non-hydrostatic position. The second head end chamber may be fluidly isolated from the pump and may be in fluid communication with a fluid reservoir when the mode selection valve is a hydrostatic position.

[0023] The method may include simultaneously changing the pump from operating at the first fluid flow rate to operating at the second fluid flow rate and changing the mode selection valve from the hydrostatic position to the non- hydrostatic position.

[0024] The method may include operating the pump at a third fluid flow rate that is greater than the second fluid flow rate while the mode selection valve is in transition between the hydrostatic and non-hydrostatic positions.

[0025] The method may include transitioning from the hydrostatic mode to the non-hydrostatic mode while the first piston is extending and without changing the piston translation speed by temporarily positioning the mode selection valve in a transition position as the mode selection valve is moved between the hydrostatic and non-hydrostatic, in which the second head end chamber, pump and fluid reservoir are all in fluid communication with each other.

[0026] The method may include automatically controlling the operation of the mode selection valve and the pump using a controller.

[0027] The method may include sensing a fluid pressure in the first head end chamber while the system is operating in the hydrostatic mode, and automatically changing the system to the non-hydrostatic mode when the controller determines that the fluid pressure has exceed a pre-determined transition threshold pressure. [0028] The method may include returning the system to the hydrostatic mode when the fluid pressure in the head end chamber falls below the transition threshold pressure.

[0029] The method may include extracting energy from the system using the pump by retracting the first and second pistons using forces exerted by the load and routing fluid pushed out of the first head end chamber by the retraction of the first piston through the pump to drive the pump in a reverse direction. After passing through the pump to drive the pump in the reverse direction the fluid exiting the pump may be directed into the first and second rod end chambers. Fluid pushed out of the first head end chamber by retracting the first piston may be sufficient to fill both the first and second rod end chambers. Fluid pushed fluid pushed out of the second head end chamber by the retraction of the second piston bypasses the pump.

DRAWINGS

[0030] The drawings included herewith are for illustrating various examples of articles, methods, and apparatuses of the teaching of the present specification and are not intended to limit the scope of what is taught in any way.

[0031 ] In the drawings:

[0032] Figure 1 is a schematic representation of one example of a hydraulic system that is operable in a hydrostatic mode and a non-hydrostatic mode, in a hydrostatic configuration;

[0033] Figure 2 is the system of Figure 1 , in a non-hydrostatic configuration;

[0034] Figure 3 is the system of Figure 1 , in a transition configuration;

[0035] Figure 4 is a schematic representation of another example of a hydraulic system that is operable in a hydrostatic mode and a non-hydrostatic mode, in a hydrostatic configuration;

[0036] Figure 5 is the system of Figure 4, in a non-hydrostatic configuration;

[0037] Figure 6 is the system of Figure 4, in a transition configuration; [0038] Figure 7 is a flow chart illustrating one example of a method of operating a hydraulic system that is operable in a hydrostatic mode and a non- hydrostatic mode;

[0039] Figure 8 is a timing diagram illustrating the operation of some components of the hydraulic systems of Figures 1 to 6;

[0040] Figure 9 is a schematic representation of a hydraulic system used in a simulation;

[0041 ] Figure 10 is a plot showing orifice curves for a solenoid operated three-way valve, showing an underlapped transition;

[0042] Figure 1 1 is a plot showing Velocity response to a transition from hydrostatic model to high force mode at t=0 and back to hydrostatic mode at 500 ms, showing the effect of pump response time;

[0043] Figure 12 is a plot showing the effect of valve shift time and pump stroke time on the velocity error response as the system shifts from hydrostatic mode to high force mode and back;

[0044] Figure 13 is a plot showing RMS error with respect to pump response time, for selected valve response times;

[0045] Figure 14 is a plot showing RMS Error with respect to valve response time, for selected pump response times;

[0046] Figure 15 is a plot showing piston translation velocity during mode transition from hydrostatic mode to high force mode;

[0047] Figure 16 is a plot showing piston translation velocity during mode transition from high force mode to hydrostatic mode;

[0048] Figure 17 is a plot showing the RMS error in velocity following a step for the data shown in 1 1 and 12;

[0049] Figure 18 is a schematic representation of another example of a hydraulic system that is operable in a hydrostatic mode and a non-hydrostatic mode; [0050] Figure 19 is a schematic representation of an experimental apparatus based on the hydraulic system of Figure 18;

[0051 ] Figure 20 is a plot showing the experimental and modelled pressures for the hydraulic system of Figure 18 in hydrostatic (high efficiency) mode, with a 9.3 kN load;

[0052] Figure 21 is a plot showing the experimental and modelled pressures for the hydraulic system of Figure 18 in a non-hydrostatic mode, with a 9.3 kN load;

[0053] Figure 22 is a plot showing the experimental and modelled hydraulic power for the hydraulic system of Figure 18 in hydrostatic mode, with a 9.3 kN load;

[0054] Figure 23 is a plot showing the experimental and modelled hydraulic power for the hydraulic system of Figure 18 in a non-hydrostatic mode, with a 9.3 kN load;

[0055] Figure 24 is a plot showing the experimental and modelled hydraulic efficiency for the hydraulic system of Figure 18 in both the hydrostatic (HE) and non-hydrostatic (HF) modes, with a 9.3 N load;

[0056] Figure 25 is a plot showing modelled pump and load power as well as losses for a 10 kN external load with the hydraulic system of Figure 18 in a hydrostatic mode;

[0057] Figure 26 is an enlarged view of the plot of Figure 25 for smaller lifting velocities;

[0058] Figure 27 is a plot showing selected flows for the hydraulic system of Figure 18 in a hydrostatic mode and for a 10kN external load;

[0059] Figure 28 is a plot showing pressures for the hydraulic system of Figure 18 in a hydrostatic mode and for a 10kN external load;

[0060] Figure 29 is a plot showing the effect of increasing charge circuit relief valve maximum orifice area on the efficiency of the hydraulic system of Figure 18 in a hydrostatic mode; [0061 ] Figure 30 is a plot showing the effect of increasing charge circuit relief valve maximum orifice area the charge circuit pressure for the hydraulic system of Figure 18 in a hydrostatic mode;

[0062] Figure 31 is an efficiency map for full-scale system in hydrostatic mode;

[0063] Figure 32 is an efficiency map for full-scale system in non- hydrostatic mode.

[0064] Figure 33 is an efficient map for a comparable load-sensing system. The efficiency for negative velocities is less than zero as no energy recovery is possible;

[0065] Figure 34 is a schematic example of another example of a hydraulic system that is operable in a hydrostatic mode and a non-hydrostatic mode;

[0066] Figure 35 is an efficiency maps for the hydraulic system of Figure 34 in a non-hydrostatic mode with and without a Port B bypass solenoid valve, showing small increase in efficiency for positive velocities (extending) but large improvements for negative velocities (retracting);

[0067] Figure 36 is a plot showing the effect of cylinder area ratio imbalance on efficiency, for a force of 50 kN;

[0068] Figure 37 is a simplified schematic for linearized dynamic model;

[0069] Figure 38 is a plot showing experimental and model frequency response, normalized to unity DC gain, plotted for the model of Figure 37 in a non- hydrostatic mode for the parameters in Table 4 as well as β = 177 MPa and B _f = 6.54 kN/(m/s);

[0070] Figure 39 is a plot showing pole movement as mass is varied from 1 to 1000 kg, for the model of Figure 37 in non-hydrostatic mode. Hydrostatic mode is similar;

[0071 ] Figure 40 is a plot showing the effect of mass on system damping ratio for the model of Figure 37 in non-hydrostatic mode. Hydrostatic mode is similar [0072] Figure 41 is a plot showing the effect of pressure damping on system damping ratio for the model of Figure 37 in non-hydrostatic mode;

[0073] Figure 42 is a plot showing the effect of pressure damping on pole natural frequency for the model of Figure 37 in non-hydrostatic mode;

[0074] Figure 43 is a plot showing the experimental trace of load force (based on pressures) for a transition of the model of Figure 37 from a hydrostatic to a non-hydrostatic mode time zero; and

[0075] Figure 44 is a plot showing the effect of mass on damping ratio and pressure damping for the model of Figure 37.

DETAILED DESCRIPTION

[0076] Various apparatuses or processes will be described below to provide an example of an embodiment of each claimed invention. No embodiment described below limits any claimed invention and any claimed invention may cover processes or apparatuses that differ from those described below. The claimed inventions are not limited to apparatuses or processes having all of the features of any one apparatus or process described below or to features common to multiple or all of the apparatuses described below. It is possible that an apparatus or process described below is not an embodiment of any claimed invention. Any invention disclosed in an apparatus or process described below that is not claimed in this document may be the subject matter of another protective instrument, for example, a continuing patent application, and the applicants, inventors or owners do not intend to abandon, disclaim or dedicate to the public any such invention by its disclosure in this document.

[0077] Conventional, non-hydrostatic hydraulic systems using linear hydraulic cylinders typically have unequal fluid inlet and outlet flows, for example due to the differences in the chambers on opposing sides of the piston. When operating systems of this nature, the power of the system can generally be maximized (i.e. by supplying a desired flow of fluid) but it is generally not possible to operate the system in a closed loop and/or recover the fluid energy from the system (for example by using a hydrostatic pump) as one of the flows will require more flow, and therefore, the energy in the differential flow cannot be recovered.

[0078] Other types of known hydraulic systems using linear actuators are configured as hydrostatic systems where the fluid inlet and outlet flows are substantially balanced. However, such systems are often quite complicated and required exotic/ specialized components beyond the linear actuators, pump and valves. The geometry of these systems is often quite complicated and requires relative large volumes of space to provide performance that is comparable to a standard, non-balanced system. This can make the systems less suited for use in mobile applications, such as being vehicle mounted. In other versions, the maximum force of the system is less than those achievable using a similarly sized, unbalanced system to help achieve the desire of balancing the fluid flows.

[0079] Some hydrostatic hydraulic systems utilize rotary type actuators and can be configured in a hydrostatic mode while still providing acceptable force/torque. However, rotary hydraulic systems differ from hydraulic systems that utilize linear/ extending type actuators (i.e. pistons and cylinders) and serve different fluid power needs. As such, known rotatory hydrostatic systems have not be widely adopted in applications where linear actuators are used - such as to provide lifting/ pushing forces on heavy construction equipment, power diggers, dump trucks, cranes, industrial machines/ presses and the like.

[0080] Accordingly, there remains a need for a hydraulic system that utilizes linear actuators and that can optionally be operated in a hydrostatic mode to help recover energy and improve the energy efficiency of the system when appropriate, but can also be operated in a relatively higher force, non-hydrostatic mode to help provide increased lifting capacity when needed. Optionally, such a system may be convertible between the different operating modes without changing the system components, and optionally may be changed between operating modes while the system is in use (i.e. on the fly).

[0081 ] Optionally, the system may include any suitable controller, valve and the like so that the transition between hydrostatic and non-hydrostatic operating modes can be done relatively smoothly and optionally without substantially affecting the speed of the linear actuators while extending or retracting. This may help provide a system that is switchable between operating modes while still providing acceptably steady and/or consistent actuator movement. This may be useful if the system is used to lift heavy and/or loose loads (such as an excavator bucket that is full of gravel and/or soil), as sudden changes in the actuator speed may cause the load to shake/ shudder and may contributed to spilling and/or loss of control of the load. Rapid changes in speed and/or acceleration of the actuators may also increase the stresses exerted on the actuators and other system components. Optionally, the system may include a valve and controller mechanism such that the system can change relatively smoothly between the hydro-static and non-hydrostatic modes without incurring substantial jerks or interruptions in the movement of the actuators, and optionally, while maintaining a generally constant actuator speed. Synchronizing the operation of the valve and pump, and any other components that are used to change system operating modes, may help achieve a sufficiently smooth transition between operating modes.

[0082] Optionally, the system may be configured so that when it is in the non-hydrostatic mode its available force is equal to, or at least generally equal to, the lifting force that could be achieved using the same linear actuator in a standard, valve-controlled unbalanced flow system. In some configurations, the systems described herein may be able to achieve such lifting forces and may also be able to provide an actuator that has comparable, and optionally greater maximum actuator speed/velocity.

[0083] Optionally, the system may be formed from relatively standard linear actuator components. This may allow the system to be assembled from so called off-the-shelf components to suit a given application. For example, the actuators may be standard, unbalanced, two-port hydraulic actuators and the valves may be standard valves. This may help reduce the complexity and/or cost of the system.

This may also help make the system a modular-type system that can be assembled in various configurations to meet specific needs. It may also simplify service/ maintenance of the system, as individual components may be serviced by generally trained technicians (as opposed to requiring specialized component knowledge), and individual components may be swapped out or replaced using commonly available valves, pumps and the like (without the need to specially order or manufacture a custom replacement part). This may be useful in embodiments where the system is used outside a factory/ shop setting, such as if the system is used on an excavator or other portable piece of equipment. Providing a system that is relatively easily field-servicable using a stock of common replacement parts, possibly even shared between different hydraulic systems across multiple vehicles, may help reduce service time and costs.

[0084] In some embodiments, the system may include a relatively small number of components, and may be free, or at least generally free from flow limiting devices such as throttling valves, throttling orifices which can reduce the efficiency of the system. This may help reduce the energy input required to operate the system.

[0085] Optionally, the system may be arranged to occupy a relatively small physical volume, and preferably to occupy a volume that is not substantially larger than existing, non-hydrostatic linear actuator systems. This may allow the present system to be provided as a retrofit and/or addition to an existing hydraulic system without requiring substantially more space and/or requiring exotic mounting hardware. For example, some embodiments of the system described herein may be generally interchangeable with the current, single linear actuator systems used on the booms of cranes, excavators, power diggers, front end loaders and the like.

[0086] Systems of the type described herein may be useful in a variety of applications that utilize linear actuators and are utilized in a manner where energy is available for recovery. For example this may include energy recoverable when braking an inertial load or lowering a load against gravity, such as commonly done when using hydraulically powered excavators, backhoes and the like.

[0087] Optionally, the hydraulic system may include two linear actuators that are physically linked in some manner, such that both linear actuators move in unison with each other. The linear actuators may be arranged parallel to each other (i.e. such that they extend and retract in unison and in the same direction), opposite each other (such that extension of one actuator corresponds with retraction of the other) or arranged in any other physical configuration that allows for the linking of the actuator movements. One example of suitable actuators are hydraulic cylinders, that include a piston slidable within a housing.

[0088] Referring to Figures 1 to 3, there is provided a simplified schematic of one embodiment of a hydraulic system 100 includes two linear actuators 102 in the form of hydraulic cylinders 102a and 102b. Each cylinder 102 includes a respective piston 104a and 104b, having a piston head 106a and 106b that is slidably received in a corresponding housing 108a and 108b, and a piston rod 1 10a and 1 10b extending from the head. The free ends of the piston rods 1 10a and 1 10b are exposed, and in this embodiment are both connected to a common load 1 12 (for example the boom of an excavator). The pistons 104a and 104b are mechanically linked together such that both pistons 104a and 104b translate in unison with each other. This may be done using any suitable linkage, and in this example, piston rods 1 10a and 1 10b are mechanically linked by the load 1 12 and move simultaneously in the same direction. That is, both pistons 104a and 104b are extended (moving upwardly as shown in Figure 1 ) and retracted (moving downwardly as shown in Figure 1 ) in unison with each other. In this configuration, driving only one of the pistons 104 using pressurized fluid will result in the other one of the pistons translating within its housing, even if it is not separately energized or driven using pressurized fluid.

[0089] In this arrangement, both 102a and 102b define respective head end chambers 1 14a and 1 14b and rod end chambers 1 16a and 1 16b that can be selectably filled/energized with pressurized hydraulic fluid. Pressurizing one or both of the head end chambers 1 14a and 1 14b causes the pistons 104a and 104b to be extended and corresponds to the lifting action in the embodiment of Figures 1 -3. If only one of the head end chambers, such as head end chamber 1 14a is pressurized, piston 104a may be driven by the hydraulic fluid, and piston 104b may be pulled along with piston 104a due to the linking of the piston rods 1 10a and 1 10b (and vice versa if head end chamber 1 14b were pressurized while head end chamber 1 14a was not). If only one head end chamber 1 14 is pressurized, the maximum force that can be exerted by the system 100 on the load 1 12 may be a first force. If both head end chambers 1 14a and 1 14b are simultaneously pressurized, the maximum force that can be exerted by the system 100 on the load 1 12 may be a second force that is greater than the first force, and optionally may be double the first force.

[0090] Pressuring one or both of the rod end chambers 1 16a and 1 16b can cause the pistons 104a and 104b to retract (i.e. move downwardly as illustrated). If only one of the rod end chambers, such as rod end chamber 1 16a is pressurized, piston 104a may be driven by the hydraulic fluid, and piston 104b may be pulled along with piston 104a due to the linking of the piston rods 1 10a and 1 10b (and vice versa if rod end chamber 1 16b were pressurized while rod end chamber 1 16a was not).

[0091 ] Optionally, to help balance the fluid flows, for example when operating in a hydrostatic mode, the system 100 may be configured so that the piston area of the rod end chamber 1 16a is about 50% of the piston area of the head end chamber 1 14a, and that the piston area of the rod end chamber 1 16b is about 50% of the area of the head end chamber 1 14b. That is, the first piston 104a defines a rod end area facing the rod end chamber 1 16a (i.e. to be acted on by the pressurized fluid in the rod end chamber 1 16a) and an opposing head end area facing the head end chamber 1 14a (i.e. to be acted on by the pressurized fluid in the head end chamber 1 14a). The second piston 104b has an analogous rod end area facing the rod end chamber 1 16b and a head end area facing the head end chamber 1 14b. Optionally, sum of the first and second rod end areas may be equal to the head end area of the piston 104a or 104b.

[0092] In this configuration, the sum of the areas of the rod end chambers 1 16a and 1 16b is generally equal to the areas of either one of the head end chambers 1 14a or 1 14b. In such systems, a closed-loop circuit can be created when operating in hydrostatic mode, that includes the rod end chambers 1 16a and 1 16b, the pump 1 18 and one of the head end chamber 1 14a or 1 14b (head end chamber 1 14a is connected to the hydrostatic loop in the illustrated example). When the system 100 is in use in the hydrostatic mode, a volume of fluid may be pumped from the head end chamber 1 14a into both rod end chambers 1 16a and 1 16b, and vice versa, without requiring substantial make-up fluid and/or without requiring that excess fluid be dumped from the system in either the extending or retracting phases.

[0093] Optionally, a system may include more than two actuators, but may still be configured as a hydrostatic system in a similar way. For example, if the system includes any number of actuators, the actuators may be configured so that the sum of the rod end chamber areas of the actuators is generally equal to the area of one or more of the head end chambers that are to be included in the balanced, closed-loop flow circuit between the rod end chambers and the head end chambers. For example, if the system included three actuators, the piston area of each of the rod end chambers could be A/3 (where A is a total area). If one head end chamber were used in the hydrostatic circuit, its piston area could be A (i.e. the sum of the rod end chambers). If two head end chambers were to be used in the hydrostatic mode, each could have an area of A/2. Other combinations of chambers and areas are also possible.

[0094] A pump, optionally a hydrostatic pump, is fluidly connected in the system 100 and is operable to selectably provide pressurized fluid to the head end chambers and rod end chambers. The pump may be any suitable pump including a hydrostatic pump, i.e. any pump that is operable to drive pressurized fluid through the hydraulic circuit and can also be driven in reverse (i.e. in a motor-like mode) by a pressurized fluid flow to allow hydraulic power to be recovered from the hydraulic circuit and converted to mechanical and/or electrical power via the pump. In the illustrated embodiment, the system 100 includes a pump 1 18 that is a reversible, hydrostatic pump. The pump 1 18 can be driven in a first direction to pressurize the rod end chambers 1 16a and 1 16b, driven in the opposite direction to pressurize one or both of the head end chambers 1 14a and 1 14b (depending on the rest of the system configuration as described herein) a reverse direction.

[0095] Alternatively, instead of reversible pump, a uni-directional pump and a combination of flow control valves may be used to achieve a similar result. Using a reversible, hydrostatic pump may be preferable in some embodiments as it may reduce the complexity of the piping/valving required and/or may reduce the overall physical size of the system 100. Preferably, the same pump is used to energize the cylinders in the lifting phase, and to recover energy from the system when the cylinders are retracting under the load 1 12.

[0096] In some embodiments, such as if the system 100 were used to power the boom of an excavator or other such apparatus that lifts loads against the force of gravity, the weight of the load 1 12 (whether limited to the structure of the machine, or the structure of the machine plus an additional load such as bucket full of dirt) will tend to act on the cylinders 102a and 102b, and in the illustrated configuration may urge the pistons 104a and 104b toward their retracted positions. In such embodiments, the pistons 104a and 104b may be urged toward their retracted positions without having to pressurize either rod end chamber 1 16a or 1 16b, or optionally the rod end chambers 1 16a and 1 16b may be pressurized at a relatively lower pressure than would otherwise be used to retract the pistons 104a and 104b. In such circumstances, the forces exerted by the load 1 12 may effectively pump fluid out of the head end chambers 1 14a and 1 14b and through the fluid circuit that includes the pump 1 18. It is this fluid flow that can be utilized for energy recovery in hydrostatic mode.

[0097] Optionally, the pump may be a multi- or variable speed pump that is operable to provide at least two different output flow rates to the system 100. This may help provide different fluid flow rates based on the configuration or operating mode of the system. For example the flow rate required to operate the cylinders 102a and 102b at a given speed may be relatively lower when energizing only one of the head end chambers 1 14a or 1 14b, and may be relatively higher when energizing both of the head end chambers 1 14a and 1 14b in unison. Optionally, the pump may be operable to provide double the flow rate when pressurizing both head end chambers 1 14a and 1 14b, as compared to when pressurizing only one head end chamber, so that the actuator speed can remain substantially constant regardless of which of the chamber(s) 1 14a and 1 14b are being pressurized. This may help make the movements of a machine, such as the boom of an excavator, predictable and generally constant from a user standpoint, while still permitting different lifting forces to be exerted based on the configuration of the system 100. [0098] The pump output flow rates may be provided and adjusted using any suitable technique, including by having variable displacement, variable speed or both, such that pressurized fluid can be pumped through the system 100 at least two different flow rates, and optionally at different pressures.

[0099] Optionally, a mode selection valve may be positioned in the fluid path between the pump and at least one of the head end chambers (for example 1 14a and 1 14b) and is used to selectively connect or isolate the corresponding head end chamber from the pump and other head end chamber(s). This can allow the targeted head end chamber to be isolated when the system 100 is operating in a hydrostatic mode, and to be fluidly connected to the pump 1 18 to be pressurized when the system 100 is configured in the higher force, non- hydrostatic operating mode. For example, in the illustrated embodiment the system 100 includes a mode selection valve 120 that movable between a hydrostatic position (Figure 1 ), in which fluid connection between the pump 1 18 and the head end chamber 1 14b is interrupted, and a non-hydrostatic position (Figure 2) in which a fluid connection between the pump 1 18 and the head end chamber 1 14b is restored.

[00100] With the system in the hydrostatic mode (Figure 1 ) the head end chamber 1 14b is fluidly connected to a fluid reservoir, in the form of tank 126. In this embodiment, the tank 126 is a non-pressurized tank (i.e. is generally at atmospheric pressure). When the pistons 104a and 104b are extended by pressuring head end chamber 1 14a, the corresponding movement of piston 104b causes fluid to be drawn into the head end chamber 1 14b from the tank 126. When the pistons 104a and 104b are retracted (either by the load or by energizing the rod end chambers 1 16a and 1 16b, or both), fluid from the head end chamber 1 14b is returned to the tank 126.

[00101 ] With the system in the non-hydrostatic mode (Figure 2) the fluid flows are unbalanced. Therefore, additional make-up fluid may be introduced into the system 100 from any suitable source (such as via a check valve, accumulator and the like) when the pistons 104a and 104b are extended to provide an adequate flow of fluid to fill both head end chambers 1 14a and 1 14b. When the pistons 104a and 104b are retracted, excess fluid (i.e. fluid in excess of the total volume of the rod end chambers 1 16a and 1 16b) may be released from the system 100 in any suitable manner, such as via relief valve, check valve, accumulator and the like.

[00102] Optionally, the mode selection valve 120 may also be positionable in any other suitable positions. While illustrated as a single, two position valve, the mode selection valve may include more than one valve apparatus, may be a multi- position valve, may include a check valve and any other suitable mechanical members that can achieved the desired fluid path configurations.

[00103] The mode selection valve may be operated using any suitable mechanism and/or control system, including, for example, being manually operable and/or being controlled by a controller. The controller used may be any suitable controller, including, for example a computer, a PLC, a mechanical linkage, a pneumatic or hydraulic control/feedback circuit and the like.

[00104] In the illustrated embodiment, the system includes a controller 122 that is configured to the control the operation of the valve 120, by energizing a solenoid 124, to change the system 100 between hydrostatic and non-hydrostatic modes. In the illustrated embodiment, the system is in hydrostatic mode when the solenoid is not energized, and is changed to the non-hydrostatic mode when the solenoid 124 is triggered by the controller 122.

[00105] The controller 122 may be configured to automatically trigger the solenoid 124, thereby moving the valve 120, based on one or more input signals 128. The input signal(s) 128 may be based on system conditions such as pressure, piston position, load position, load weight and may automatically adjust the system 100 accordingly. For example, if the system is operating in hydrostatic mode and the system fluid pressure passes a pre-determined threshold (indicating that the load 1 12 may be too heavy to lift using a single cylinder 102), the controller 122 may automatically move the valve 120 to the non-hydrostatic position (Figure 2), thereby engaging the second head end chamber 1 14b and increasing the available lifting force of the system 100. When such additional lifting force is not required, the controller 122 may automatically shift the valve 120 and return the system to hydrostatic mode.

[00106] With an appropriately configured controller 122 and system components (such as valve 120 and pump 1 18), the system 100 may be smoothly switched between modes on the fly: spending time in the relatively more efficient hydrostatic mode when possible, and switching to high-force, non-hydrostatic mode when required.

[00107] In addition to controlling the position of the mode selection valve 120, the controller 122 (or a different, but linked controller) may also control other system components, such as the pump 1 18 and other valves. The controller 122 may control the overall behavior of the system 100 in any suitable manner, including by changing the mode selection valve 120 positions, varying the displacement of the pump 1 18, varying the shaft speed of the pump 1 18, varying a combination of both the displacement and the shaft speed and the like. Such changes may be made automatically based on the performance/ condition of the system, or may be manually selectable by a user, or both. For example, the system may be configured to automatically switch to hydrostatic, energy-recovery mode when the actuators are retracting while loaded, for example when lowering the boom of the excavator. The system may then stay in hydrostatic mode for normal boom raising and lowering operations, and may be switched to non- hydrostatic mode when the system (or the operator) determines that an increased lifting force is required for a particular lift/extension. The system may remain in high-power mode for as long as the increased lifting force is required/desired, and may then revert to hydrostatic mode when the higher lifting force is no longer required. In such systems, the hydrostatic mode may be the default/ standard operating mode, with the high-power, non-hydrostatic mode being utilized only on demand.

[00108] Preferably, the system 100 may be configured so that it can transition smoothly between operating modes, without causing material changes in the operating speed of the cylinders or otherwise causing jerky or unsteady movement of the cylinders. This may help reduce the chances of a mode change materially impacting the operation of the system 100, and may help facilitate on- the-fly mode changes without causing disruptions to the use of the system 100.

[00109] Generally, due to the effective doubling of the total head chamber area/volume in the non-hydrostatic mode (as compared to the hydrostatic mode) the flow rate of the pump 1 18 may be generally doubled to help maintain substantially constant/ steady state translation speed of the piston 104a and 104b when transitioning from the non-hydrostatic mode to the hydrostatic mode, and vice versa. However, there are also transient effects that can be compensated for during the transition between modes.

[001 10] In some embodiments, the transition from hydrostatic mode to high-force mode may occur when an external force is about to exceed the force capacity of a single cylinder 102a (i.e. when lifting a heavy load 1 12). Under this condition, head end chamber 1 14a may be at or near the maximum system pressure and/or a pre-set mode change threshold pressure, while head-end chamber 1 14b may be generally at tank pressure. This potentially large pressure imbalance may be at least partially equalized via providing a large flow of fluid through the mode selection valve 120 upon transitioning to high force mode. This may affect the pressures in both the chambers 1 14a and 1 14b and the required pump flow rate to maintain the desired, generally constant piston translation velocity. The time it takes the mode selection valve to transition between the positions of Figures 1 and 2 is understood to define a valve response time, and the time it takes the pump 1 18 to transition from pumping fluid at a first, steady state flow rate to a second, steady state flow rate is understood to define a pump response time.

[001 1 1 ] In addition, to help avoid cavitation while the mode selection valve 120 is in transition from the hydrostatic position (Figure 1 ) to the non- hydrostatic position (Figure 2) and 2, it may be desirable that the fluid communication between the head end chamber 1 14b and the pump is established before fluid communication between the head end chamber 1 14b and the tank 126 is completely blocked/interrupted . With the mode selection valve 120 is this temporary, transition position (Figure 3), there is fluid communication between the head end chamber 1 14b, pump 1 18 and tank 126 for a short period of time. To provide this configuration, the mode selection valve 120 can be configured to be positionable in the desirable transition position and may be, for example an underlapped valve, which may allow some leakage flow from supply to tank while the valve is in an intermediate, transition position. This leakage flow may be also be compensated for when supplying and/or releasing fluid from the system 100 during the mode change, as well as when operating the pump 1 18. When moving in the other direction (i.e. from the position of Figure 2 to the position of Figure 1 ), the mode selection valve 120 may move through the same, or at least an analogous temporary, transition position in which fluid communication between the head end chamber 1 14b and the tank 126 is re-established before fluid communication between the head end chamber 1 14b and the pump 1 18 is fully interrupted.

[001 12] Optionally, to help accommodate for some of the make-up and/or leakage flows, and optionally to help compensate for compressibility of the hydraulic fluid, the pump 1 18 output flows during the transition phase (i.e. while the valve is in the process of moving between the positions of Figures 1 and 2, or slightly before or after such a change) may be different than either of the steady state flow rates used in the hydrostatic or non-hydrostatic modes. For example, when the system is changed from the hydrostatic mode to the non- hydrostatic mode, the pump output flow rate may be dynamically adjusted, optionally via the controller 122, to help account for the varying flow conditions and dynamics. Optionally, the pump flow rate may be temporarily increased to a third flow rate that is greater than either of the steady state hydrostatic or non-hydrostatic flow rates to provide a temporary boost in the flow. When changing from non-hydrostatic to hydrostatic modes, the pump flow rate may temporarily be set at an intermediate flow rate that is between the steady state hydrostatic or non-hydrostatic flow rates, or optionally may be below the hydrostatic steady state flow rate. Optionally, the pump 1 18 may be configured to have a sufficiently fast pump response time such that these temporary flow rates may be utilized while the mode selection valve 120 is in transition, and optionally so that the pump 1 1 8 is returned to operating at the appropriate steady state flow rate by the time the mode selection valve 120 transition is complete.

[001 13] The relative operations of the pump 1 18 and mode selection valve 120 of one possible embodiment of the system 100, as the system transitions from hydrostatic mode to non-hydrostatic mode is illustrated in Figure 8. In this example, the pump flow rate, as a function of time, is illustrated by line 130 and the flow rate of fluid flowing between the tank 126 and head end chamber 1 14b is illustrated by line 132. The position of the valve 120 is illustrated in the middle portion of Figure 8, with the available percentage of flow area in communication with the tank 126 represented by line 134, and the percentage of flow area in communication with head end chamber 1 14b represented by line 136. The upper portion of Figure 8 illustrates the system pressure as recorded at the head end chamber 1 14a using line 138, and pressure at the head end chamber 1 14b represented by line 140.

[001 14] In some embodiments of the system 100, when the system 100 is operated in hydrostatic mode, with the pump 1 18 flow 130 is a first steady state flow rate (represented by line 142 in Figure 8) while lifting a load. The system pressure in the head end chamber 1 14a is monitored by the controller 122. As the forces exerted by the load 1 12 increases, the system pressure may reach a pre-determined transition pressure level 144 at a given time, represented by line 146. This may trigger the controller 122 to activate the mode selection valve 120 at the first time 146, to change the system 100 to non-hydrostatic mode, to help provide additional lifting force. The mode selection valve 120 can be actuated, and will reach its second position (the position of Figure 2) by second time 148.

[001 15] When illustrated in this manner, the lateral spacing between lines 146 and 148 can represent the valve transition time 150. During this transition, the flow area 1 34 in communication with the tank 126 is reduced from about 100% to about 0%, while the flow area 136 providing communication between the pump 1 18 and the head end chamber 1 14b increases from about 0% to about 1 00%, and during the transition time 1 50 the relevant flow areas 134 and 136 are both non-0% at the same time (representing the desired transition flows permitted by an underlapping valve).

[001 16] While the mode selection valve 120 is in transition, the pump flow rate 130 may be increased to account for the transition flow characteristics. Optionally, before the mode selection valve 120 reaches its non-hydrostatic position (Figure 2) at the second time 148, the pump flow rate 130 may temporarily reach a third, transition flow rate level (line 1 52), before settling into the second steady state flow level (line 154). In the illustrated example, the transition flow rate 152 is greater than the non-hydrostatic steady state flow rate 154, and the hydrostatic flow rate 142. In this example, the pump 1 18 has a relatively fast pump transition time (represented by distance 156) and responds quickly enough so that the pump flow rate 130 has returned to the non-hydrostatic steady state flow rate 1 54 when the mode selection valve 120 reaches its non-hydrostatic position at time 148.

[001 17] As the head end chamber 1 14b is pressurized, the lifting force required to lift the load 1 12 is shared between the head end chambers 1 14a and 1 14b, thereby reducing the pressure 138 in head end chamber 1 14a below the threshold pressure 144.

[001 18] The schematic diagrams provided in Figures 1 -3 are intended to illustrate the general arrangement of the components and the flow paths that contribute to the desired operation of the system 100. However, the schematics are somewhat simplified and do not show all of the specific components that may be present in a specific hydraulic system. For example, standard components such as relief valves, anti-cavitation valves, charging systems, cooling systems and the like are well understood by those skilled in the art, and have been excluded from the present schematics for clarity. Figures 4-6 are schematic representations of how the elements of the system 100 may be incorporated into a more realistic, real-word hydraulic circuit, and include various other hydraulic components such as an input/output shaft 160 connected to the pump 1 18, a charge pump 162, filter 164, optionally pump displacement controller 166 (which may by communicably linked to controller 122 and/or may be integral with the controller 122), charge relief valve 168, port relief valves 170 and make-up check valves 172. In these schematics, the elements of the system 100 operate in the same manner as described herein, when in the hydrostatic configuration (Figure 4), the high force, non-hydrostatic mode (Figure 5) or when in the temporary transition configuration (Figure 6).

[001 19] Referring to Figure 7, one example of a method 200 of operating a hydraulic system that is switchable between hydrostatic and non-hydrostatic modes (such as system 100) using a controller (such as controller 122) is illustrated. The method 200 may begin with engaging the controller at step 202 and optionally, reading a desired operator selected piston translation speed 204. The controller 122 may also sense the pressure in the head end chamber 1 14a at step 206.

[00120] At step 208, the controller 122 can query if the system is currently configured in hydrostatic mode, non-hydrostatic mode or is transitioning between modes.

[00121 ] If in hydrostatic mode at step 208, the controller 122 may then check if the pressure in head end chamber 1 14a is below a pre-determined transition pressure level at step 210. If not, the controller 122 may signal the pump 1 1 8 to continue operating at the hydraulic mode steady state flow rate at step 212, and repeat steps 202-208 on a pre-predetermined basis. If the pressure sensed in step 210 is greater than the pre-determined transition pressure level , the controller 122 may proceed to step 216 and begin changing the system 100 to hydrostatic mode.

[00122] At step 218 the controller 122 can trigger the mode selection valve 120 to change positions. While the valve 120 is in transition, the controller 122 may measure/sense the flow rate of fluid flowing to the tank 126 at step 220 (for example as a result of the leakage during the valve transition) and may determine suitable adjustments to the pump flow rate to compensate for any such tank flows.

[00123] The controller 122 may then measure the pressures in the head end chambers 1 14a and 1 14b in step 222, and optionally may determine suitable adjustments to the pump flow rate to help compensate for compressibility of the fluid under the sensed operating conditions.

[00124] At step 224, the controller 122 may determine the desired pump output level, for example based on the information obtained in steps 220 and 222, and may send a corresponding command signal to the pump 1 18 (or associated sub-controller) to adjust the pump flow rate. The method may then return to step 202, and may be repeated at any desired frequency.

[00125] If in non-hydrostatic mode at step 208, the controller 122 can check to determine if the system pressure is still at a level that justifies operating in non-hydrostatic mode at step 226. If so, the controller 122 can command the pump 1 18 to operate at the non-hydrostatic mode, steady state flow rate. If not, at step 230 the controller 122 may begin switching the system 100 to hydrostatic mode by triggering the valve at step 232. While the valve 120 is in transition, the controller 122 may measure/sense the flow rate of fluid flowing to the tank 126 at step 220 and may determine suitable adjustments to the pump flow rate to compensate for any such tank flows.

[00126] The controller 122 may then measure the pressures in the head end chambers 1 14a and 1 14b in step 222, and optionally may determine suitable adjustments to the pump flow rate to help compensate for compressibility of the fluid under the sensed operating conditions.

[00127] At step 224, the controller 122 may determine the desired pump out put level, for example based on the information obtained in steps 220 and 222, and may send a corresponding command signal to the pump 1 18 (or associated sub-controller) to adjust the pump flow rate. The method may then return to step 202, and may be repeated at any desired frequency.

[00128] If transitioning between modes at step 208, the controller 122 may measure/sense the flow rate of fluid flowing to the tank 126 at step 220 and may determine suitable adjustments to the pump flow rate to compensate for any such tank flows. [00129] The controller 122 may then measure the pressures in the head end chambers 1 14a and 1 14b in step 222, and optionally may determine suitable adjustments to the pump flow rate to help compensate for compressibility of the fluid under the sensed operating conditions.

[00130] At step 224, the controller 122 may determine the desired resultant pump flow rate level, for example based on the information obtained in steps 220 and 222, and may send a corresponding command signal to the pump 1 18 (or associated sub-controller) to adjust the pump flow rate. The method may then return to step 202, and may be repeated at any desired frequency.

[001 31 ] To help develop and/or evaluate the system 100, a dynamic model 1 100 of the system was constructed to help study the dynamics during mode switching events. The model layout was based on a schematic illustrated in Figure 9, which incorporates representations of the components of system 100, as well as other hydraulic components. Elements corresponding to features of the system 100 are labelled using like reference characters, indexed by 1000. The modelled system 1 100 includes a pump 1 1 18 and solenoid dynamics, static pressure and anti-cavitation valves, and cylinder models 1 1 02a and 1 102b, including compressible volumes 1 1 14a, 1 1 14b, 1 1 16a and 1 1 16b, and a mode selection valve 1 120.

[001 32] In this simulation, the two rod end chambers 1 1 16a and 1 1 16b are assumed to be connected without resistance. If a velocity dependent external load, Fext(x) is applied (which includes friction and inertial effects), the force balance is

[001 33] where P _A i and P _A2 are the pressures in the head end chambers 1 1 14a and 1 1 14b, P _B is the pressure in both rod end chambers 1 1 16a and 1 1 16b, and A _A and A _B are the piston areas of the head and rod end of each piston 1 104. The compressible volumes in the three chambers are assumed to not cavitate and to have constant bulk modulus β with volumes that vary with the piston stroke:

^V A

PB = ^T (X2A _B - Q _B ) [001 34] where Q _A i and Q _A2 are the flows into the head end chambers 1 1 14a and 1 1 14b of the cylinders, Q _B is the total flow out of the cylinder rod end chambers 1 1 16a and 1 1 16b, x is the piston translation extending velocity and the chamber volumes are given by V _A = V _A0 + xA _A

[001 35] where V _A o and V _B o are the cylinder dead volumes and x _max is the cylinder stroke.

[001 36] The three-way solenoid valve is assumed to have turbulent orifices, using an equation for the flows, Q, to avoid numerical instability around zero flow:

^CdA ^ _P ^AP if P > Pcr

-(f ³ "!) otherwise

[00137] where C _d is the discharge coefficient, A is the orifice area, ΔΡ is the pressure drop, v and p are the fluid kinematic viscosity and density, D is the orifice's hydraulic diameter, and P _CR is the transition pressure, related to the critical Reynolds Number, Re _cn by [00138] The above orifice equations are used to determine the flows through the valve between the two cylinders, Q _A \ _A2 = (ΡΛΙ - PA2, A _MA2 ) and from tank to the second cylinder, Q _TA 2 = f(Pr - PA2, A _T A2)-

[00139] The valve orifices are assumed to have linear orifice curves shown in Figure 10 which shows the orifice curves for the solenoid operated three-way valve, showing underlapped transition. Valve dynamics are approximated by a rate limiter that allows the valve to fully shift from one position to the other in time shift-

[00140] Relief valves and check valves are both assumed to respond infinitely fast with flow calculated using the same orifice model as in equation 7. The orifice area of each valve is assumed to increase linearly from the cracking pressure, P _ck , to the maximum orifice area, A _MAXL over the pressure override range, P _or :

[00141 ] The model was used to calculate flows for anticavitation valves Q _cvA d Q _cvB = f(Pr- PB), as well as relief valves = f{P _M - P _T ) and

[00142] Conservation of mass (assuming constant density) requires the following continuity equations:

[00143] where Q _s is the pump flow. Pump dynamics were simulated by a rate limiter which allows the pump to stroke from zero to maximum flow Q _smax in time Atstroke-

[00144] In order to test the above model, a simple load was implemented with viscous damping and inertia: x = - (Fext - B _f x) (1 3) m

[00145] where m is the mass of load and cylinder and B _f is the damping coefficient.

[00146] The above model was implemented in Matlab Simulink using solver ode23s.

[00147] When considering the control of a conventional hydrostatic system, one typically controls the pump flow, either by displacement control or shaft speed control. This is also the case for the systems 100 described herein, however the systems 100 may include the additional, optional aspect of wanting to provide a smooth transition between hydrostatic and high-force mode.

[00148] To help develop the controller 122, the inventors considered how a perfect pump controller would supply flow in order to maintain a constant piston transition velocity in the moments immed iately following a mode transition event. To facilitate this, one can sim plify the dynam ic model presented above. First, it was assumed that under normal operation, the check and relief valves on the head side of the system remain closed. Secondly, it was assumed that P _B the pressure in the rod end chambers 1 16a and 1 16b of both cylinders is low (i.e. at the cracking pressure for the anti-cavitation valve) and the anti-cavitation valve will maintain it at this level in order to make up flow after the transition to high-power mode. The system may then be simplified to the followin system of equations

Eqn 1 8 can be differentiated to obtain

PA A _A + P _A2 A _A = ( F _EXT (x) + P _CK 2A _B ) = 0 (1 9) [00149] It is noted that the right hand side is zero if the external load is only dependent on velocity, and if the controller maintains the velocity perfectly. Equations 2, 3, and 19 can be combined algebraically, with the resultant ideal pump flow of

[00150] where x _d is desired cylinder velocity and Q _sc is the command pump flow.

[00151 ] In reality, some mismatch between command pump flow and measured valve flow can be expected, as well as an error due to unmodeled dynamics, so a gain is applied in order to allow tuning of the response:

Qsc = 2 AA x<j - KQQTA2

[00152] Thus, it is believed that one can achieve velocity regulation through a mode transition if Q _TA2 is measured or estimated. Note that this equation also works prior to transition, when Q _T A2 = A _A x, requiring Q _sc = A _A x. It is also noted that if the pump dynamics (i.e. the pump transition time) are at least as fast as the dynamics of Q _T A2 (i.e. the valve transition time) to maintain generally ideal compensation. Counterintuitively, this may mean employing a slowly opening mode selection valve 120, such that its transition time is equal to or less than the transition time of the chosen pump 1 18, may help achieve smoother mode transitions.

[00153] The control law developed in equation 21 was simulated, with the full model schematic of Figure 9 to evaluate the system performance. Physical parameters for the simulation can be found in Table 1 . A simulation of the system was run in order to verify stability and study the interaction of pump and valve dynamics. A transition from hydrostatic to high force mode was commanded and the resultant velocity recorded. The root mean squared error was calculated as

ERMS = l/ ² ( x - xd )2dt (22) [00154] The pump response time and valve shift time were then varied with the error calculated for each case. The results are shown in Figures 1 1 -14. Fig. 1 1 shows the cylinder velocity response to mode shifts, first from hydrostatic mode to high force mode, then back. With a fast enough pump, the transitions can be made nearly seamlessly. That is, a user in a typical heavy machinery application would not observe a noticeable and/or material change in the translation speed of the pistons 104 when changing modes (in either direction).

Table 1 : Simulation Parameters

[00155] Figures 12-14 quantify the effect of the response speed of the pump and valve. This demonstrates that a fast pump response is critical to low mode transition error. It also demonstrates the somewhat unusual situation where a fast solenoid valve can cause increased error, if the pump cannot respond fast enough to keep up. [00156] An experimental test was also performed to help verify the stability of the control law developed above. Two standard cylinders were connected to a Vickers PVB5 variable displacement axial piston pump modified with direct displacement control. This pump has a fast displacement response, with a rise time between 15 and 35 ms. A Parker D3W solenoid valve was used to control the transition between hydrostatic and high-force modes, with a rated shift time of 25- 35 ms. The ideal control law in Eqn. 21 was implemented using a NIDAQ data acquisition and control system connected to a computer running Matlab Realtime Windows Target. The solenoid was also controlled by this system.

[00157] The system was instrumented with drag-type flow meters to measure Q _s and QTA2, and with pressure transducers on P _M , P _A 2 and P _B . The cylinder's velocity was estimated by measuring the cylinder outlet flow using a calibrated orifice. This orifice also simulated a load on the cylinder. Cavitation was avoided via an elevated tank pressure of 2.4 MPa.

[00158] Figures 15 and 16 show the results of transition events (with time set to zero when the controller initially commands the solenoid to shift). The controller gain was varied between 0.5 and 1 .0. With the gain set to 1 .0, the response was oscillatory and had a steady state error when reenergizing the solenoid. The best gain in this case is near 0.8, as demonstrated by the root mean squared error in the velocity, shown in Figure 17.

[00159] The amount of energy that may potentially be recovered by this system is dependent on the work cycle of the particular hydraulic circuit. One sample work cycle was used to provide one quantified example of the potential for energy recovery over a typical loading cycle. Other work cycles could be analyzed in an analogous manner. This analysis estimates the fractions of time that the system spends in each mode and the ideal energy that can be recovered in each.

[00160] The example work cycle selected was from a 40-ton hydraulic excavator loading a truck. An experienced operator was asked to load a series of trucks located on the same level as the excavator, at a swing angle of 90°. The soil was sandy loam. Repositioning via tracks and waiting for truck positioning were not considered part of the work cycle and these sections were removed from the data.

[00161 ] The excavator was instrumented with pressure transducers at each port of the boom, arm and bucket cylinders as well as the swing motor. The position of these three cylinders was measured via string potentiometer and the swing rotation was measured by ground speed radar units mounted on the upper structure. Actuator force or torque were calculated from pressures and the cylinder velocities were calculated from the derivative of position data.

[00162] The data set was then divided into portions, identifying which of the two modes would be active. If the cylinder force was greater than half the maximum force, the system was assigned high-force mode, and assigned to hydrostatic mode otherwise. The system was assumed to be able to recover all the available energy while in hydrostatic mode, while it can recover half the available energy when in high-force mode (due to approximately half of the flow being lost over the relief valve or entering the system at low pressure over the anticavitation valve). Note that this sample analysis assumed the recovery system is perfectly efficient, with no pump or line losses and no losses associated with charge pump or cooling losses. As such, this analysis may represent a best case scenario of the performance of the system for this sample work cycle.

[00163] The segmented data set was then analyzed to determine the maximum possible energy recovery available using P = Fv, where P is the actuator power, F and v are actuator force and velocity. If the actuator power is positive, the system is doing work and negative if there is energy to recover. The power was then integrated to obtain total energy.

[00164] Table 2 shows the breakdown of the total energy available for each function in this example. The swing circuit shows the highest fraction of energy recoverable (defined by the fraction of energy recoverable to work done), and many manufacturers have commercial examples available that apply hydrostatic systems, electrical swing drives or accumulator systems to recover this inertial energy. However, the maximum absolute value of energy recoverable is in the boom circuit, demonstrating that significant savings may be available if this energy can be recovered.

[00165] If one considers the boom work cycle for use with the example work cycle considered, the system will spend 52% of the cycle in hydrostatic mode and 48% in high-force mode. Although considerable time is spend in the less efficient high-force mode, there is still a potential to recover 5.1 MJ while in hydrostatic mode (84% of the total available), with an additional 0.5 MJ recoverable in high- force mode. This may result in a total energy recovery potential of 5.6 MJ, or 84% of the 6.1 MJ available in this example.

[00166] The above analysis does not consider losses such as leakage and flushing flows, or the efficiency of the energy recovery device on the shaft, but it does demonstrate that the two-mode system can still recover considerable energy even if it spends considerable time in the less efficient non-hydrostatic mode. This may be at least partially due to the fact that the potential for recoverable gravitational energy usually occurs at lower pressure, while the high pressure portions of the cycle correspond to digging, where the energy input is lost to irreversibly shearing the soil.

Table 2: Energy breakdown for an excavator truck-loading cycle.

NOMENCLATURE

A _A Head end piston area

AA I A2 max Maximum A1 -A2 orifice area

A _B Rod end piston area

AI Leakage area

Amax ck Check valve maximum orifice area

Amax rv Relief valve maximum orifice area

AjA2 max Maximum T-A2 orifice area

B _f Viscous damping coefficient

dXunderlap Valve underlap

C _d Discharge coefficient D Orifice hydraulic diameter

ERMS Root mean squared velocity error

Fext External load force

KQ Controller gain

m Load mass

PAI Cylinder 1 head end pressure

PA2 Cylinder 2 head end pressure

PB Cylinder 1 & 2 rod end pressure

Pck cv Check valve cracking pressure

Pck rv Relief valve cracking pressure

Por cv Check valve pressure override

Por rv Relief valve pressure override

PT Reservoir pressure

QA1 QA2 Flow into cylinder 1 & 2 head end

QA1A2 Flow through valve from Al to A2

QB Combined flow from cylinder head ends

QcvA QcvB Check valve flows

QrvA QrvB Relief valve flows

Qs Pump flow

Qsc Pump command flow

Qs max Maximum pump flow

QTA2 Flow from tank to A2

Re _cr Critical orifice Reynolds number

Δί ^' shift Valve shift time

Δ. stroke Pump stroke time

V _A VB Cylinder head end and rod end volumes

VAO BO Cylinder head and rod end dead volumes

X Cylinder position

Xd Desired cylinder velocity

Xmax Cylinder stroke

Xsp max Maximum valve spool displacement

β Bulk modulus

V Kinematic viscosity

P Fluid density

[00167] Referring to Figure 18, a schematic example of another hydraulic system 2100 includes two linear actuators 2102 in the form of hydraulic cylinders 2102a and 2102b that are configured as single-rod cylinders, each with a 2: 1 piston area ratio.

[00168] The hydraulic system 2100 is analogous to the hydraulic system 100, and like features are identified using like references characters indexed by 2000. In this example, Each cylinder 2102 includes a respective piston 2104a and 2104b, having a piston head 2106a and 2106b that is slidably received in a corresponding housing 2108a and 2108b, and a piston rod 21 10a and 21 10b extending from the head. The free ends of the piston rods 21 10a and 21 10b are exposed, and in this embodiment are both connected to a common load 21 12. The pistons 2104a and 2104b are mechanically linked together such that both pistons 2104a and 104b translate in unison with each other. This may be done using any suitable linkage, and in this example, piston rods 21 10a and 21 10b are mechanically linked by the load 21 12 and move simultaneously in the same direction. That is, both pistons 2104a and 2104b are extended (moving upwardly as shown in Figure 1 ) and retracted (moving downwardly as shown in Figure 1 ) in unison with each other. In this configuration, driving only one of the pistons 2104 using pressurized fluid will result in the other one of the pistons translating within its housing, even if it is not separately energized or driven using pressurized fluid.

In this arrangement, both 2102a and 2102b define respective head end chambers 21 14a and 21 14b and rod end chambers 21 16a and 21 16b that can be selectably filled/energized with pressurized hydraulic fluid.

[00169] In the illustrated embodiment, the system 2100 includes a pump 21 18 that is a reversible, hydrostatic pump. The pump 21 18 can be driven in a first direction to pressurize the rod end chambers 21 16a and 21 16b, driven in the opposite direction to pressurize one or both of the head end chambers 21 14a and 21 14b (depending on the rest of the system configuration as described herein) a reverse direction. The pump 21 18 may have any of the attributes or features described in relation to pump 1 18 herein. Like system 100, the hydraulic system 2100 can be operated in a hydrostatic, and relatively high efficiency mode, in which one of the hydrostatic pump's 21 18 ports are connected to one head-end chamber 21 14a and 21 14b and the other port is connected to both rod-end chambers 21 16a and 21 16b. The other head-end chamber 21 14a or 21 14b is connected to low pressure (in this case supplied by a charge circuit). The single head-end flow is approximately equal to the two rod-end flows, so the flows are generally balanced. This mode exhibits about half the maximum extending force of a conventional system with similarly sized cylinders, but may have about double the maximum extending velocity and may provide the ability to recover energy to the shaft when braking or lowering a load. [00170] The system 2100 can also include various other hydraulic components such as an input/output shaft 2160 connected to the pump 21 1 8, a charge pump 2162, a filter, an optional pump displacement controller (which may by communicably linked to controller 122 and/or may be integral with the controller 122), charge relief valve 2168, port relief valves 2170 and make-up check valves 2172. In these schematics, the elements of the system 21 00 operate in the same manner as described herein, when in the hydrostatic configuration , the high force, non-hydrostatic mode or when in the temporary transition configuration.

[00171 ] Like system 1 00, the hydraulic system 2100 includes a mode selection apparatus that can be used to change the system between its hydrostatic mode, in which fluid connection between the pump 21 18 and the head end chamber 21 14b is interrupted, and its non-hydrostatic position in which a fluid connection between the pump 21 18 and the head end chamber 21 14b is restored. While the system 1 00 includes a single valve 120 that can function as the mode selection apparatus, the hydraulic system 2100 includes a hydrostatic mode valve 2120a and a non-hydrostatic mode valve 2120b. Optionally, the valves 2120a and 2120b may be independently operable and may be provided with respective solenoids that can be controlled by the controller 2122 (or any other suitable controller).

[00172] The system 2100 was modelled, with the pump 21 18 assumed to be an ideal variable displacement pump with perfect displacement control in accordance with the follow:

[00173] where ω is the shaft angular speed (rad/s) and D is the pump's displacement (m ³ /rev). The pump's 21 18 internal and external leakage are assumed to be laminar:

where R _AB , R _AT , and fl _BT are the effective resistances of each leakage path. The charge pump 2162 is assumed to be an ideal fixed displacement pump:

Qc = ^ (26) where D _c is the pump displacement. Flows between the charge pump 2162 and tank are modelled as a relief valve, anti-cavitation valve and cooling orifice in parallel. Each orifice is modelled as a two-stage laminar-turbulent orifice, requiring parameters of discharge coefficient C _d , fluid density p, fluid viscosity v, and critical Reynolds number Re _cr . The relief valve and check valve orifice areas linearly increase from zero at the cracking pressure to a maximum area over the pressure override range. Therefore

QCT ⁼ Qor(A _RVCT , P _c — P _T )— Qor (A _CVCT , P _T — P _c ) + Q ₀ r(A _CT , P _c — P _T ) (27) where Q _or (A, AP) is the two-stage orifice equation, A _CT is the cooling orifice area, and the relief and check valve areas are given by

where P _cr is the cracking pressure, P _or is the pressure override range, and A _max is the maximum orifice area. The pump's 21 18 workport A relief and anticavitation check valves are modelled as above, again with linear orifice area:

QAC ⁼ Qor(A _RVAC , P _A — P ) — Qor (A _CVAC , P _c — P _A ) (29) where A _RVAC and A _CVAC are defined as in eq 28.

[00174] On workport B, an external relief valve was installed, which has a different opening characteristic. In this case

QBC ⁼ Qor(A _RVBC , P _B — P _c )— Qor(A _CVBC , P _B — P _c ) (30)

A _RVBC (AP) = (31 )

\ ^p rreeff J where K _RVB is an area-related coefficient, and a tanh function is used to smooth the infinite derivative near zero area, with the extent of the distortion controlled by P _REF . A _CVAC follows the linear area relationship in eq 28.

[00175] The cylinder(s) 2102 is modelled as an ideal cylinder with no leakage (cylinder leakage is lumped with the pump's R _AB although it is small relative to pump leakage). The flow into each head end is

where A _A is the piston head area and v is the cylinder's extending velocity. The combined flow from both rod end chambers is

Q _B = 2A _B v (33) where A _B is the rod end piston area of a single cylinder.

[00176] The forces acting on the cylinders 2012 are assumed to include an external force F, and viscous and Coulomb friction, given by

F _f = F _c tanh (^j + B _f v (34)

efJ

where F _c is the ideal Coulomb friction force, B _f is the viscous damping coefficient, and tanh is used instead of a sign function to avoid discontinuities around zero velocity. The velocity v _ref is used to control what is considered a "small" velocity around zero. The net force on the cylinder is then

Fnet = PAA _A + P _A2 A _A — P _B 2A _B — F— F _f (35) [00177] For numerical convenience and to allow for inversion of the orifice equation, the solenoid valves are assumed to be ideal turbulent orifices (i.e. no laminar region), only one of which may be open at a time. Therefore, in the hydrostatic, High Efficiency mode

P _{A 2} = P _c - l ^{QcA2 lQcA2} _? ^l (36)

^{AZ C} 2 (C _D A _C A2) ² '

Q _{A 1A2} = 0 (37) where A _CA2 is the HE valve's 2120a orifice area, while in High Force (non- hydrostatic) mode:

where A _A1A2 is the HF valve's 2120b area.

[00178] Assuming constant density, flow continuity equations give net flows at points B, A1 and C as

Qsnet = Q _B - Qs - QBC + QAB ^~ QBT (42) Q _Alnet = -Q _A1 - Q _AB - Q _A1C + Qs - QAIA2 - QAT (43)

Qcnet = Qc + QBC + QAIC ~ QcT ~ QcA2 (44)

[00179] The above equations may constitute a nonlinear system of equations that may be solved to determine the steady state operating point. This was achieved by using the Matlab "fsolve" function to numerically solve for values of P _A , P _B , P _c , and v that force the flow and force continuity equations 36, 42, 43, and 44 to zero. Although it is possible for this set of equations to result in more than one solution, the present simulation did not find any situations where this is case.

[00180] A performance metric used here is the hydraulic efficiency, defined as

where the load, main pump 21 18, and charge pump 2162 powers are

PWL = QAIPAI + QA ₂ A2 - QBPB (46)

Pw _s = Q _S P _AB - Q _S P _A { 1) Pw _s = Q _c P _c - Q _c P _T . (48) [00181 ] One possible deficiency in the above efficiency definition occurs when Pw _L < 0 but also (Pw _s + Pw _c ) < 0. This situation, where there both the load and pump are supplying energy to the hydraulic system, may result in an negative efficiency with little physical meaning, which goes to negative infinity as the load power approaches zero. Thus, a negative efficiency should be viewed as bad, but the magnitude is may not generally be useful for comparison.

[00182] Referring to Figure 19, as another part of the analysis of the hydraulic system 2100, a small scale experimental apparatus 2300 was constructed. The apparatus 2300 included a Hydogear model PY pump (not shown), which is a hydrostatic pump designed for use on lawn equipment, with a main pump maximum displacement of 21 .8 cc/rev and a 4.1 cc/rev charge pump. The apparatus 2300 also included a frame 2302, an arm 2304 movably coupled to the frame 2302 that can be loaded with weights 2308 (to simulate loads 1 12, 21 12) and a pair of cylinders 2306 to simulate the actuators 2102a and 2102b (with only one cylinder 2306 schematically shown in Figure 19). In this example, the distance 2310 was about 608mm, the distance 2312 was about 183mm and the distance 2314 was about 81 1 mm.

[00183] The pump in this experiment integrates workport check and relief valves as well as charge pump relief valve with experimentally determined parameters found in Table 3. A check valve was included to avoid cavitation at the charge pump outlet, but it is not believed that this valve ever opened during the experiments conducted. The pump was run by a 20 HP electric motor at 1750 rpm. This motor may be oversized for this application, which may help ensure a constant shaft speed.

[00184] In order to help facilitate adjustment of the workport B relief pressure, an external relief valve was installed, Hydraforce model RV08-22. The experimentally-determined parameters are found in Table 3. The solenoid valves used to control the modes were Parker model DSL102C for the HF valve and a Hydraforce SF20-22 for the HE valve. Note that while the HE valve (such as valve 2120a) may preferably be selected to be larger than the HF valve (such as valve 2120b) to help avoid the possibility of cavitation, it is recognized the valve used in the apparatus 2300 may be substantially oversized.

[00185] Solenoid valves were controlled over a J 1939 bus via Hydraforce EVDR 201 A valve drivers. The pump's swash plate position was controlled using a rotary hydraulic actuator with a separate power supply, operated by a servo valve controlled using an analog proportional closed loop controller.

[00186] A load was provided by the apparatus shown in Figure 19. This allows for a gravitational and inertial loading, by applying up to 247 kg of weight, which can apply up to 1 3.8 kN of force to the cylinders 2306. This apparatus 2300 was designed to mimic the nonlinear force characteristics of a front-end loader or other such piece of heavy equiment, in smaller scale.

[00187] The cylinders' 2306 position was measured using a MTI Instruments model LTC-300-200-SA laser displacement transducer, providing a calibrated analog output. Pressures were measured using STW model M01 -CAN J1939 pressure transmitters. Transmitters with a range of 25 MPa were used for P _A , P _AZ , and P _B , while P _c was measured using a range of 7 MPa. J 1939 signals were acquired using a Vector CANboard XL interfaces, while analog signals were acquired using a National Instruments PCIe-6251 interface. All data was logged at a 1 0 ms sample rate.

Table 3: Selected Steady State Model Parameters

[00188] It was noted by the inventors that it can be difficult to directly measure all of the flows involved in the system 21 00 and/or in the experiments conducted on the test apparatus 2300. As such, the inventors compared the measured pressures and velocities, and those powers that were available.

[00189] Figures 20 and 21 show the effect of cylinder velocity on pressures in HE (hydrostatic) and HF (non-hydrostatic) mode, with both model and experimental values. These data were recorded with the apparatus 2300 loaded with 204 kg of weights, which corresponds to approximately 9.3 kN force at the cylinders when the boom is horizontal. Figures 22 and 23 show the main pump, charge pump, and load hydraulic power (i.e. pressure times flow in each case). The load flows are calculated from load velocity and the pump nominal flow is calculated from swash plate angle. Therefore, the hydraulic system efficiency calculated from this data (shown in Figure 24), includes the effect of leakage (volumetric efficiency), but not mechanical frictional losses in the pump or load (mechanical efficiency).

[00190] This data shows generally good agreement between model and experiment, and it is believed that the unmeasured values will show similar agreement. One area where the model and experiment do show some disagreement was for medium-to-large positive velocities in HE (hydrostatic) mode. In this situation, the model predicts the use of check valve flow to prevent cavitation in the charge pump pressure. No pressures below atmospheric were measured during this test and nor were any signs of cavitation detected when the check valve was blocked. The discrepancy may be due to unmodelled leakage in the system and/or an unmodelled increase in charge pump volumetric efficiency under these situations. In any case, while this cavitation is important from a practical standpoint, the flows and the pressure differences are relatively small, and will therefore likely result in a relatively small change in the resulting efficiency analysis.

[00191 ] The experimental apparatus and results shown above are understood to generally validate the model, but do not show particularly good overall system performance in some circumstances, such as when operating at low velocities. This may be one factor that is used when designing a system (such as system 100 and/or 2100) or when selecting which system to use for a given application. For example, the inventors not that the High Force (non-hydrostatic) mode appears to show better efficiency than High Efficiency (hydrostatic) mode when lifting the load. This is believe to be largely due to the mismatch between the pump and load in the given experiment/ simulation. For example, in the data shown above, the pump was not operated at its maximum flow, which may mean that its volumetric efficiency suffered somewhat. This is shown in Figures 25 and 26, which are plots comparing the modelled power and losses in the system. The inventors note that the leakage losses are approximately constant with load velocity, which dominate the efficiency at low flows. Thus, the inventors believe that a better efficiency curve can be expected by either selecting a smaller pump with less leakage or using more flow by increasing the cylinder size (also increasing the maximum force) when implementing the systems 100, 2100 and the like.

[00192] Referring to Figure 25, the inventors also note that when lowering the load, one expects to recover much of the available power. However, in the present test case, much of the power appears to be lost to the charge pump circuit, especially at higher speeds. This is believed to be due to the fact that, when retracting the cylinders in HE (hydrostatic) mode, the flow from the head end of the second cylinder 2306 exits the system via the charge pump relief valve and cooling orifice. As shown in Figures 27 and 28, this may saturate the charge pump relief valve and the pressure may rises, which may then cause a power increase at the charge pump. This use is outside of the intended use of this charge circuit relief valve, which normally only has to handle the excess charge pump flow. If the charge circuit relief valve is enlarged to handle the anticipated flow, the situation appears to be improved. For example, as shown in Figures 29 and 30, if one doubles the valve's orifice area, it still saturates, but the efficiency is improved. If the area is doubled again, the valve no longer saturates and leakage becomes the generally more significant loss.

[00193] In addition to the small scale experimentation described above, a full-scale simulation study, intended to represent the boom lift circuit of the front- end loader of a backhoe tractor was also conducted.

[00194] Parameters used for this simulation can also be found in Table 3. These parameters are based on a John Deere 410G backhoe loader, cylinders dimensions according to ISO 6020-2, and an Eaton model 72400 closed circuit pump.

[00195] Efficiency maps for the system in both High Efficiency (hydrostatic) and High Force (non- hydrostatic) modes are shown in Figures 31 and 32. The inventors note that for this system, High Force (non-hydrostatic) mode is more efficient over most of its range of positive velocities (extending), meaning that High Efficiency (hydrostatic) mode would, in some embodiments of the system, be selected for use to recover energy while retracting and for operating high velocities that HF mode may not be able to achieve.

[00196] For comparison, the efficiency map for an ideal load-sensing system is shown in Figure 33. This assumes a pump with similar displacement and leakage characteristics connected to the same cylinders, with a load sense margin of 1 MPa. It also assumes no additional valve metering losses so the calculated efficiency is somewhat conservative. Both modes of the DCHA are more efficient that the load sensing system over the entire operating range except for very small extending velocities. Also note that this load sensing system may not be able to reach the relatively high velocities achievable by the DCHA in HE Mode.

[00197] Based on the experimental analysis conducted to date, the inventor believes that the efficiency of a system, such as system 100 or 2100, while lowering in High Force (non-hydrostatic) mode may be improved with the addition of an additional solenoid valve in the system. Referring to Figure 34, the system 2100 is shown with an additional valve 2180. In this example, when the system 2100 is in non-hydrostatic mode and when cylinder 2102a is retracted, approximately twice as much fluid exits the cylinders 2102a and 2102b as enters, with the excess flow venting to the charge system. Without this solenoid valve 2180, this occurs when P _B exceeds the workport relief valve setpoint pressure, which may cause at least some of the energy in a large volume of pressurized fluid to be lost. The inventors have discovered that with the addition of the solenoid valve 2180 arranged in parallel with the corresponding port relief valve 2170, at least a portion of this fluid can be vented at relatively low pressure, which may help reduce the energy loss, as shown in Figure 35. As this may help limit the maximum rod end pressure, the maximum negative force may be limited in High Force mode; however, there is no material difference in the maximum negative force between HE and HF mode, so HE mode can be used in this situation. An efficiency increase may also be achieved for a similar reason by bypassing the check valve in the circuit (such as valve 21 72) when extending, although the pressure drop is smaller, so the magnitude of this effect may be smaller.

[00198] Optionally, the actuators 1 02, 2102 and the like need not be configured such that the sum of the of the rod end pistons areas is exactly the same as one of the head-end piston areas. For example, the actuators may be selected such that the sum of the of the rod end pistons areas may be within about 10% of one of the head-end piston areas, or preferably maybe within about 5% and/or within about 2% or less of the one of the head-end piston areas. This may help facilitate the use of standard actuators, having generally standard, off- the-shelf configurations within the system 100 (or 2100 below, etc.), and may reduce the need to utilize actuators that are custom-machined to have the exact arrangements.

[00199] For example, when operating in the hydrostatic (High Efficiency) mode, ideally the flow out of the rod end chambers (e.g. 21 16a and 21 16b) would equal the flow into a single head end chamber, such as 21 14a (A _A / 2A _B ) = 1). In this case, there may be relatively little makeup flow required through either workport check or relief valves. However, in some embodiments of the system the actuators may not be perfectly balanced. For example, the ISO 6020-2 metric dimensions used for the present simulation specify a 64 mm bore and 45 mm rod diameter. This is the nearest mm to the ideal area ratio, but is not perfect. In this case, A _A / 2A _B ) = 1.02, meaning approximately 2% of the flow may be lost. Similarly, in inch sized cylinders, the closest ratio for a 2.5 inch bore is a 1 .75 inch rod, with A _A /(2A _B ) = 0.98. The effect on efficiency may be quantified using the steady state model. Figure 36 shows plots of the efficiency for a mid-range force of 50 kN, for a number of area ratios. This effect may be relatively small for commercially available cylinder sizes (on the order of 2% error).

[00200] One known issue with pump controlled systems is that, when the damping of a throttling valve is eliminated, the systems may sometimes become underdamped and/or oscillatory. This can impact the dynamic response of the system when in use. To analyze at least some of the dynamic responses of the hydraulic systems described herein, the inventors developed a simplified model, a schematic representation of which is shown in Figure 37. In this model 500, the behavior of both actuators 102a and 102 are represented by a single actuator 502 that is configured to drive a load 512, and system losses (such as solenoid valve pressure losses) were ignored. It was also assumed that the pump 518 has a pump swash plate having a response that is faster than the other system dynamics.

[00201 ] Compressible volumes at P _A1 and P _B were assumed to have constant bulk modulus (i.e. little to no cavitation or low-pressure effects). Hoses are assumed to contribute to these effective volumes, but pressure losses and wave propagation effects are ignored. The load 512 is modelled as a mass with viscous friction (neglecting Coulomb friction). The charge and tank pressures are assumed to be constant. The linear restrictions R _AB , R _AC , and R _BC represent internal and external laminar leakage, but also the linearized resistance of nonlinear workport check and relief valves (if open). Thus, the linearized model is understood to be valid for relatively small deviations around an operating point.

[00202] Based on these assumptions, the piston force balance is

m v = P _A A _A - P _B A _B — BfV— F (49) where A _A and A _B represents the effective piston areas (both cylinders for A _B and one cylinder for A _A in HE mode and both in HF mode). The compressible volumes are represented by B = -Q ^~ QB + QAB + vA _B (51 ) where V _A and V _B are the effective volumes, β is the bulk modulus, flows and velocities are as shown in Figure 20, and are given by

(52)

[00203] When transformed to the Laplace domain (with Laplace variable ^< ?), these equations can be written in matrix form as

AX = B (55) where

X= PA (56)

PB

ms -A _A A _B

1

A= A _A ^ + ^- (57)

l

-A _B -^ + ^-

[00204] For control purposes, we are interested in the transfer function v/Q _s , relating the commanded pump flow to load velocity. This can be solved algebraically to give fc! = ^ _B (^j + ^ j) (60) b ₀ =A _A R _AB R _A +A _B R _AB R _B (61) a ₃ = R _AB R _A R _B mf ^v (62) «2 = mR _A (R _AB + R _B ) + mR _B (R _AB + R _A ) + -

B _f R _AB R _A R _B - ^V f- ^V f (63) a _i = m(R _AB + R _A + R _B ) +—B _f R _AC (R _AB + R _B ) + - - ^V f B _f R _B {R _AB + R _A ) + R _AB R _A R _B (^-A ² + - ^V A ² _B ) (64) a ₀ = Bf {R _AB + R _A + R _B ) + A _A ² R _A (R _AB + R _c ) +... A ² _B R _B (R _AB + R _A ) - 2A _A A _B R _A R _B (65)

[00205] For the parameters shown in Table 4, this results in a system with three poles, two complex conjugate poles and a single pole located near the single zero. The response is dominated by the oscillatory complex conjugate poles.

Table 4: Base Dynamic Parameters

[00206] An experimental verification of this model was performed by the inventors. The system was excited by commanding a pump flow using a Maximal Length Sequence of length 8191 samples, sample rate 1 KHz, repeated 7 times. The response of the seven repetitions was averaged in the time domain before the frequency response of G{jw) was calculated using the Fourier method. This was performed in HF mode with the boom held approximately horizontal. The results are shown in Figure 38. Using the base parameters from Table 4, the model underestimates the damping of the system and there is also an error in the resonant frequency. This can be explained by experimental uncertainty in the system's bulk modulus and the neglection of Coulomb friction. If the bulk modulus is increased by 50% and the damping term increased to 6.54 kN/(m/s), generally better agreement may be achieved.

[00207] For a typical application for a hydraulic system of the type described herein, such as a loader or excavator, the load mass can vary considerably while the system is in use. This mass is a parameter that has an effect on the dynamic response and any variability of the mass can have an effect on performance of the system. This is demonstrated in Figure 39, which shows the pole movement as the load mass (e.g. load 512, or 1 12, 21 12, etc.) is varied. For relatively low masses, the system may, in some configurations, be underdamped while the damping ratio decreases quickly as the mass increases (damping ratio is shown in Figure 40). This may cause a different character for the system depending on load, which was also evident in the behavior of the experimental apparatus.

[00208] The experimental data and models described herein both demonstrate a common issue with pump-controlled systems. In the interest of efficiency, the throttling orifices can be removed and cylinder friction is reduced, which can leave the system with relatively little natural damping. This may result in systems with relatively highly oscillatory response. Adding mechanical damping to the highly efficient system may be undesirable in some implementations of the system, and an alternative source of damping may be desirable in some systems.

[00209] Optionally, the system could utilize the measured velocity at predetermined points in the fluid circuit to add a damping term to the pump controller (such as controller 122 or 2122). However this may have some drawbacks in some circumstances. For example, cylinder position sensors may not be commonly installed in the type of equipment that may utilize the system 100, 2100 in a retrofit capacity, and differentiating the signal may produce a relatively very noisy result. As another option, the inventor has developed and implemented a pressure-based term in the pump controller to help achieve some desired system damping. This may help facilitate a relatively a low-cost and relatively low-noise solution as compared to some alternative damping apparatus.

[00210] In this example, the pump flow is modified to include the pressure rate as

where Q _cmd is the uncompensated pump command and K is the pressure damping gain. This modifies the system A matrix to

while equations 38 through 44 can be modified by replacing each with + K. [0021 1 ] The effect of the pressure damping gain is shown in Figures 41 and 42. In these examples, the damping ratio of the conjugate poles may be increased, which may help reduce oscillations. The effects of this damping may be generally traded off against a slower dynamic response and a less stiff system. A system for a given application may be designed with a pre-determine, and acceptable combination of these features/values.

[00212] This was implemented experimentally on the test apparatus described herein. Figure 43 shows a transition from HE (hydrostatic) to HF (non- hydrostatic) mode with K = 2 x 10 ⁹ m ³ /s/Pa and an effective mass of 550 kg (it is noted that this plot shows cylinder force data). This transition creates a disturbance in the system, which may cause the base system to bounce for some time. The pressure damping system described herein may help reduce this bouncing. While it may not entirely eliminate the oscillations, perhaps due to only damping oscillations in P _A1 , while ignoring P _B , it may help provide a real and/or perceived improvement in the controllability of the system from the system user's perspective. As with the uncompensated system, a variable mass can affect the tuning of the pressure damping gain. As seen in Figure 44, the gain required to bring the damping ratio to unity varies by about an order of magnitude as the mass is varied from 100 to 1000 kg.

[00213] What has been described above has been intended to be illustrative of the invention and non-limiting and it will be understood by persons skilled in the art that other variants and modifications may be made without departing from the scope of the invention as defined in the claims appended hereto. The scope of the claims should not be limited by the preferred embodiments and examples, but should be given the broadest interpretation consistent with the description as a whole.