Programming piston displacements for constant flow rate piston pumps with trigonometric transition functions

An analytical method for programming piston displacements for constant flow rate piston pumps is presented. A total of two trigonometric transition functions are introduced to express the piston velocities during the transition processes, which can guarantee both constant flow rates and the continuity of piston accelerations. A kind of displacement function of pistons, for two-piston pumps, and two other kinds, for three-piston pumps, are presented, and the physical meaning of their parameters is also discussed. The results show that, with the given transition functions, cam profiles can be designed analytically with parameterized forms, and the maximum accelerations of the pistons are determined by the width of the transition domain and the rotational velocities of the cams, which will affect contact forces between cams and followers.