Kinematics and geometrical admissibility conditions of balanced vane pumps with twin lip vanes

The present work is devoted to analyze the kinematics of twin lip vanes adopted in balanced vane pumps. The work provides the analytical description of the vane motion according to its geometrical parameters and the cam ring profile. Attention is given to the duality of the solution, an intrinsic property of twin lip vanes that may be considered as followers with two symmetrical half-circular tips. Based on the linkage kinematics, the analytical dissertation is further deepened to define the geometrical admissibility of the vane design and its mathematical domain. In order to evaluate the proposed approach, an extended parametric study is performed on the basis of the Buckingham theorem, detailing how the twin lip configuration affects the machine kinematics. Additional calculations are proposed to determine the vane design configurations that satisfy the fundamental law of cam design and to highlight how this requirement dramatically reduces the subset of available choices in presence of cam ring with a precompression profile. Finally, design guidelines are proposed in order to overcome these drawbacks and expand the admissibility domain.