A new type of two-dimensional (2D) piston pump with a stacked cone roller set was introduced to eliminate the influence of the gap between the guiding rail and the cone roller. First, the structure and working principle of the 2D piston pump were studied; then, a corresponding mathematical model which considered the oil viscosity and oil churning loss caused by the rotation of the guiding rail in the enclosed chamber was established to examine the volumetric and mechanical efficiency of the 2D piston pump. The effects of different speeds, load pressures, and rolling friction coefficients between the guiding rail and the cone rollers on the efficiency were considered. During the test, when the speed was 6000 r/min and the load pressure was 6 MPa and 8 MPa, the volumetric efficiency reached 98.3% and 96.8%, respectively, basically consistent with the theoretical analysis. Because the temperature rise of the tested pump caused the oil viscosity and the eccentricity of the piston and piston rings increased the leakage, the test result was slightly lower than that of the theoretical analysis. When the speed was 1000 r/min and the load pressure was 5 MPa, the mechanical efficiency was 69.3%, and the mechanical efficiency model was consistent with the test results. However, with the increase in speed and load pressure, the difference between the test results and theoretical analysis results increased because the supporting force of the cone roller on the guiding rail increased, increasing the rolling frictional losses.

Since the clearance between the guide rail and the roller reduces the efficiency of the 2D pump, this paper proposes a novel 2D piston pump with stacked taper roller sets to eliminate the effect of the clearance. The structure of the 2D pump is introduced, and the mathematical model of the torque and the mechanical efficiency of the bilateral force on the guide rail are established and analyzed. The model takes into account the change in the oil viscosity, the spatial angle and the oil churning loss. A test rig was built to test the mechanical efficiency under different operating conditions. The unilateral and bilateral force models of the guide rail were compared, which proved that the bilateral force model of the guide rail can predict the mechanical efficiency more accurately than the unilateral force model. In the case of high load pressure, there was a clearance between the test results and the model calculation results. It is speculated that the main reason for this is that the greater oil pressure causes the size of the contact area between the two taper rollers and between the taper roller and the guide rail to become larger. The resulting rolling friction coefficient becomes larger, which affects the mechanical efficiency.