Effects of splined shaft bending rigidity on cylinder tilt behaviour for high-speed electro-hydrostatic actuator pumps

High-speed axial piston pumps are hydraulic power supplies for electro-hydrostatic actuators (EHAs). The efficiency of a pump directly affects the operating performance of an EHA, and an understanding of the physical phenomena occurring in the cylinder/valve plate interface is essential to investigate energy dissipation. The effects of the splined shaft bending rigidity on the cylinder tilt behaviour in an EHA pump need to be considered, because the deflection and radial expansion of a steel shaft rotating at a high speed cannot be ignored. This paper proposes a new mathematical model to predict the cylinder tilt behaviour by establishing a quantitative relationship between the splined shaft deflection, the cylinder tilt angle, and the tilt azimuth angle. The moments exerted by the splined shaft are included in the equilibrium equation of the cylinder. The effects of solid and hollow splined shafts equipped in an EHA pump prototype are compared at variable speeds of 5000–10,000 r/min. With a weight saving of 29.7%, the hollow shaft is experimentally found to have almost no influence on the volumetric efficiency, but to reduce the mechanical efficiency by 0.6–2.4%. The results agree with the trivial differences of the simulated central gap heights of the interface between the two shafts and the enlargement of the simulated tilt angles by the hollow shaft. The findings could guide designs of the cylinder/valve plate interface and the splined shaft to improve both the efficiency and power density of an EHA pump.