The effect of cross porting on derived displacement volume

Derived displacement volume (Vi) is very important for the calculation of volumetric and torque efficiency of positive displacement machines. A method for determining the derived displacement volume of a unit was introduced by Toet. This method is known to be more accurate than the current ISO 8426 standard, yet still has a speed dependent error. This paper reveals the main cause of the speed dependent error found in the method by Toet for the determination of derived displacement volume. An accurate pump model enabled the analysis of complex flow interactions inside a positive displacement machine. The analysis of the flows isolated the variations in derived displacement volumes to be dependent on the design of the valve plate. A case study of two valve plates with and without cross porting verified cross porting’s influence on derived displacement volume. Steady state measurement and the pump model simulations at low pressure differences show that the effective displacement volumes (Ve) at different rotational speeds follow nonlinear curves that all converge at Δp = 0. The main cause of the speed dependent error of derived displacement volume calculated using the method by Toet was discovered as the change in back flow volume due to cross porting.