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Parker PVplus axial piston pump with variable displacement has been designed and optimized for demanding use in heavy duty industrial and marine applications. With pressure ratings of up to 420 bar and high-speed ratings this open circuit, swashplate principle axial piston pump provides high productivity and power density to its users. Beside its robustness and exceptionally long service life, PVplus is also characterized by a very high conversion flexibility. As a standard every PVplus comes with an integrated pre-compression volume which ensures low ripple operation and reduced noise emissions. A wide range of displacements and control options allows for a wide range of applications.

The fundamental goal of the topology optimization method is to obtain the best structural performance by properly placing material within a prescribed design domain [21]. This method originates from the field of solid mechanics by the end of the 1980s and then spreads to a range of different disciplines such as acoustics [22], photonics [23], electromagnetism [24], heat condition [25], and fluid flow [26], etc. Nowadays topology optimization is available in all major finite element analysis packages and even in many computer-aided design packages. Some researchers have made use of this method to reduce the structural vibration and noise of the axial piston pumps [27]. In this paper, the topology optimization is conducted on the suction duct to obtain the minimum pressure loss.

where J(·) is the objective function, γ is the optimization design variable, R is the vector of governing equations written in residual form, and gi is a set of inequality constraints.

where u is the fluid velocity and η is the fluid viscosity. Ω is the initial design domain as shown in Figure 7(b). α is the impermeability of a porous medium whose value depends on the optimization design variable γ by an interpolation function:

andq is a real and positive parameter used to adjust the convexity of the interpolation function. γ is the optimization design variable, and it is the artificial density of the design domain. During the iteration process, γ varies between 0 and 1, where 0 represents the solid domain and 1 is the fluid domain.

The process of the whole topology optimization is shown in Figure 7, and the flow-chart of computation for topology optimization is shown in Figure 8. The steps to run the optimization require first to define an initial material distribution. Then the CFD computation is conducted to get the flow characteristics and calculate the dissipated energy under the initial guess. Next, we calculate the sensitivities by the adjoint method. The sensitivity information is used to compute the next design material distribution, i.e., update the design variables by the optimizer. But before that, the step of sensitivity filtering is needed to suppress the problems like chessboard, mesh dependency, and grey transition [31]. The optimizer chosen in this optimization is the widely used method of moving asymptotes (MMA). If the updated design variables are not converged, the above process needs to be conducted again. The material distribution of the process of the iterations is shown in Figure 7(c).

After the design variables converge, the final volume is still coarse and needs post-processing. To smoothen the boundary, the NURBS spline is used to fit it in 3D CAD software. The optimized suction duct after fitting is shown in Figure(d).

Figure 9 shows the contrast of the pressure distribution between the original and optimized suction duct, which demonstrates that the optimized suction duct has less pressure loss. During the suction phase of the piston pump, the two main factors accounting for the pressure loss are the frictional pressure loss and the local pressure loss.

The pressure loss in the suction duct gives rise to the cavitation phenomenon and the generated bubbles will be sucked into the piston chambers in the suction phase. Therefore, the piston pump cannot deliver enough fluid in the discharge phase, leading to a decrease of the volumetric efficiency and the speed limit.

Additionally, as shown in Figures 10 and 11, the velocity on the outlet port of the original suction duct is not well-distributed compared to the optimized one. In the low speed region shown in Figure 10, the piston chambers of the piston pump are not able to suck enough fluid. As a result, the pressure in the piston chambers drops off, which may also cause cavitation.

Corresponding to the experimental data, three different inlet pressures, 0.1 MPa, 0.07 MPa, and 0.05 MPa, are set in the CFD model to simulate the cavitation intensity and the speed limit. Figure 12 shows the comparisons of the gas volume fraction in the piston chamber with the original and optimized suction duct. The cavitation region with the optimized suction duct is smaller than the original one under all three inlet pressures. The results indicate that the optimized suction duct can effectively reduce the cavitation intensity under different inlet pressures. Consequently, the optimized suction duct increases the delivery flow rate at a relatively high rotational speed as shown in Figure 13. And the speed limit of the axial piston pump is improved with it. The simulation results prove the effectiveness of the topology optimization method on increasing the speed limit of the axial piston pumps.

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