Axial pumps with cam-driven commutation units — so-called PWK pumps — emerged as a result of a research project conducted in the Department of Hydraulics and Pneumatics at the Gdansk University of Technology. As for all axial hydraulic piston pumps, several cylinder chambers are positioned around the rotating shaft of an axial pump with cam-driven commutation units — called PWK pumps. The rotation of the shaft and the attached swash plate leads to movement of the pistons that alternately decreases and increases the fluid volume of the chambers. A window — which is part of the control sleeve or commutating bushing — connects the chamber between the pistons with the low-pressure and highpressure intake and outtake channels.

Figure 1. Variable displacement pump with four chambers (visible).
The axial piston pumps with constant displacement show a very good performance with a working pressure of up to 55 MPa, an overall efficiency of 94%, and good power density. In constant displacement pumps, the pistons always travel the same distance inside the cylinder chamber, resulting in a constant amount of output fluid.

To control the fluid amount, variable displacement pumps are used. Usually, the piston displacement of these pumps is controlled with a complicated hydraulic servomechanism. Theoretical analysis shows that the displacement of the PWK pump can be controlled by a low-energy actuator. This is the major advantage of the new developed pumps because it reduces the pump’s cost and dimension significantly, thereby simplifying the entire process chain.

Figure 2. CAD models of a pump with two chambers (left) and seven chambers (right). The left model is a symmetric half model. All movable parts are shown in red.
To steer the displacement of the pump, and thereby the amount of fluid that is put through, the angular position of the control cam in relation to the pump’s shaft has to be controlled. As both parts are rotating fast, a special planetary gearbox that ensures precise control over the displacement in the operating range was developed. This can be driven by a stepping motor.

First prototypes of the variable displacement PWK pumps have been built and tested, and showed good performance. Unfortunately, harmful pressure peaks that could lead to pump damage were observed. With the help of a compensation chamber, these peaks could be significantly reduced. To find the optimal layout of the pump and the compensation chamber, experiments and numerical simulation were used.

Pressure Peaks

First tests of the control mechanism for the variable displacement pump confirmed the feasibility of the concept. However, harmful pressure peaks in the cylinder chambers were observed when the cylinder chamber is disconnected from the inlet and the outlet channel. The pressure reaches very high values — 20 MPa above the average pressure in the chamber — for a short time.

These peaks are influenced by many different factors. The most important ones are the displacement adjustment, the rotational speed, and leakage. When the displacement of the pump is decreased, the pressure peaks increase. This is due to the higher velocity of the pistons at the moment when the chamber is disconnected from the intake and outtake channels. A higher rotational speed of the shaft also leads to higher pressure peak values; mainly, because it reduces the effect of leakage. Oil leakage reduces the amount of fluid to be compressed and thereby decreases pressure peak value. For pumps with high rotation numbers, the piston movement is fast, shortening the time during which the fluid is compressed and reducing the influence of leakage. This increases the pressure peak values.

Figure 3. Abaqus model of the wall of the compensation chamber with boundary conditions.
The compressibility of the hydraulic oil is directly connected to the occurring leakage and thereby also plays an important role in the investigation of pressure peaks. Leakage is influenced significantly by the pressure of the fluid. The small gaps in the pump through which small amounts of fluid can leave the pump cycle get considerably larger during pressure increase. This aggravates the leakage, which in turn, influences the pressure, resulting in a very complicated feedback.

Pressure Peak Compensation

The pressure peaks of up to 20 MPa could damage the pump and produce a lot of noise. To get a more robust pump, these pressure peaks need to be compensated. The peaks occur when the cylinder chamber is disconnected from the intake and outtake channels and the fluid is compressed. To shorten the period of disconnection from the channels and to give the fluid more room, an additional compensation chamber with an elastic wall was introduced. The cylinder chamber connects to the compensation chamber when it is disconnected from the pump’s main channels.

In the phase of compression, the compensation chamber is connected to the fluid volume in the cylinder; the surplus fluid can flow into the compensation chamber, which results in a reduction of the pressure peaks. When the pistons move back, increasing the volume of the cylinder chamber, the compensation chamber again connects to the cylinder and the fluid can flow back. As the different cylinder chambers (in most cases seven, nine, or 11 cylinder chambers are used) compress in an alternating cycle, one compensation chamber can be used for all cylinders.

First experimental tests showed that the introduction of the compensation chamber reduced the pressure peak value by 50% without decreasing the efficiency of the pump. The main objective of the interdisciplinary numerical simulation is to find the optimal layout of the compensation chamber. Differences in shape, elasticity, and volume, and their effect on the pressure peak values, are to be investigated. Computational fluid dynamics (CFD) models of the pump and FEA models of the elastic compensation chamber are developed.

Coupled CFD and FEA Simulation

A CFD model of the PWK pump, including the compensation chamber, was developed. For most simulations, a symmetric half-model of a pump with two cylinder chambers and the compensation chamber was used to keep the model relatively small and simple. A full model of a pump with seven cylinder chambers was also developed. The CAD geometry that was used to generate the models is depicted in Figure 2. Fluent (version 12.1) was used for the CFD simulations. The movement of the pistons and the commutating bushing (connecting the cylinder chamber with the intake and outtake channels, as well as the compensation chamber) was modeled with user-defined functions.

The wall of the compensation chamber is subject to pressure exerted by the hydraulic oil. To catch the deformation of the elastic wall, an Abaqus/Explicit (version 6.11) model — only consisting of the wall of the compensation chamber — was created. Abaqus/Explicit simulates the deformation of the elastic wall using the fluid pressure calculated with Fluent as a boundary condition. Fluent receives the deformation of the wall and updates the fluid domain mesh. This is a classic example of fluidstructure interaction. To pass the quantities between Abaqus/Explicit and Fluent, Fraunhofer SCAI’s code-coupling tool MpCCI was used.

Simulation Models

This description of the simulation models will only refer to the symmetric half-model with two cylinder chambers. The mesh in Fluent consists of hexahedral elements. The increasing and decreasing of the cylinder chamber volume is realized by the dynamic layering method. The motion of the pistons and the bridge connecting the cylinder chamber to intake and outtake channels, and the compensation chamber, are implemented with user-defined functions.

Figure 4. Solid Abaqus model showing U displacement contours with a maximum value of 1e-04.
The hydraulic oil is assumed to be slightly compressible — the density is defined with a user-defined function. The transient problem is solved using the Spalart-Allmaras turbulence model and a coupled solver for pressure and velocity. Two cycles of the pump (depending on the configuration) take 0.08 s. A time step of 1e-05 s or 5e-05 s is used. The high pressure in the outtake channel is 10 MPa and the low pressure is set to 0.2 MPa.

The geometry of the Abaqus/Explicit model can be seen in Figure 3. It consists of linear quadrilateral shell elements of type S4. Boundary conditions are employed to keep the top and bottom fixed. The left and right sides of the chamber wall are also fixed with the help of boundary conditions. The wall of the compensation chamber is slightly larger than the chamber itself, which can be seen in Figure 4. The overlapping parts on the left and right are kept in a fixed position due to pump design. The thickness of the elastic wall is 1.5 mm.

The Young’s modulus of the isotropic elastic material is 2.1e11 Pa, and the Poisson ratio is 0.3. The density is 7850 kg/m3. The problem is solved with a geometric nonlinear solver in Abaqus/ Explicit. The time increment in Abaqus/Explicit is fixed and the same as in Fluent. In MpCCI, the quantities “relative wall force” and “nPosition” (the nodal position of the deformed wall) are selected for coupling. Relative wall force values (for the wall of the compensation chamber) are transferred from Fluent to Abaqus. Using the wall forces, Abaqus/Explicit calculates the deformation of the wall, which is then transferred back to the Fluent model. Fluent updates the mesh and performs the next time step. The coupling time step equals the time step from Fluent and Abaqus/Explicit.

Under-relaxation is used in MpCCI to stabilize the coupled simulations. Both quantities — the relative wall force and the displacements of the coordinates — are under-relaxed with a value of 0.8. The under-relaxed displacement is then added to the old coordinates to get the new position of the nodes. Additionally, in Abaqus/Explicit, the applied load is ramped linearly over the time step.

To get a better understanding of the structural problem, a solid model consisting of C3D8 hexahedron elements was also built and simulated using Abaqus/Explicit (see Figure 4).

Simulation Results

The simulation results showed the necessity of a coupled simulation for this application. The simulation, including the fluid-structure interaction at the elastic wall, agrees significantly better with the experimental findings than the standalone CFD simulation.

For an easy comparison of simulation results and experimental data during the simulation, the pressure at three discrete points of the pump is monitored: one point located in the center of the upper chamber, one in the lower chamber, and the last point in the center of the compensation chamber. The pressure at these points is monitored during the simulations and can be compared for different pump parameters or simulation variations.

The pressure contours of the fluid on the moving geometry can also be visualized to get a general idea of the working pump and the quality of the simulation, but the slight differences between the standalone CFD solution and the fluid-structure interaction (FSI) solution cannot be perceived visually on these contour plots. The big negative pressure peaks that were observed for all simulations (CFD standalone and FSI) are probably due to cavitation occurring at the small passages between the different chambers. The oil reaches high velocities when flowing from a cylinder chamber to the compensation chamber. Highvelocity narrow passages and high pressure both point towards cavitation.

The negative pressure peaks are much less pronounced in the FSI solution. Furthermore, the pressure in the compensation chamber shows a different behavior in the two cases. The values during the “high-pressure phase” are higher for the FSI solution. Also, a qualitative difference can be observed when investigating how the pressure rises or falls in the compensation chamber.

The FSI simulations showed a very good agreement with the experiments that were conducted. The CFD model on its own is not capable of catching the pressure behavior — especially in the compensation chamber — in a satisfactory way. The elastic behavior of the wall cannot be integrated into a CFD model without coupling with a structural mechanics solver like Abaqus/Explicit.

Summary and Outlook

The FSI simulation for the simplified symmetric PWK pump model with two chambers produced results that coincide with experimental data in a very satisfactory way. Several configurations and settings for the simple pump model can now be checked with the help of numerical fluid-structure interaction simulation with the aim of finding an optimal configuration.

Simultaneously, the full model of the pump should be investigated with a FSI simulation. This model is quite complex — for seven chambers, the motion of the pistons and the motion of the bridges has to be defined — and therefore will only be simulated for relevant cases that were identified using the symmetric half models. Furthermore, the cavitation that supposedly occurs could be integrated into the CFD model in the future. This might reduce the negative pressure peaks further and lead to a more physical behavior of the fluid.

Another interesting aspect of the pump development is the leakage of hydraulic oil through small gaps. To capture such a phenomenon in a CFD simulation is a challenging task, but would clearly lead to more realistic simulations.

This article was written by Bettina Landvogt of Fraunhofer SCAI in Germany; Leszek Osiecki of Gdansk University of Technology in Poland; Tomasz Zawistowski of Space Research Center of the Polish Academy of Sciences in Poland; and Bartek Zylinski of Bandak Engineering in Norway. For more information on the software used in this work, visit Dassault Systèmes SIMULIA at .