Static stiffness modeling and sensitivity analysis for geared system used for rotary feeding

The positioning accuracy of rotary feed system under load greatly depends on the static stiffness of mechanical transmission system. This paper proposes a unified static stiffness model of rotary feed system with geared transmission system. Taking the torsional stiffness of transmission shaft and mesh stiffness of gear pairs into account, the motion equations of the whole transmission system are presented. Based on the static equilibrium, a unified expression for the relationship between torsional angles of two adjacent elements is derived. Then a unified static stiffness model is presented. Furthermore, analytical expressions for sensitivity analysis of the static stiffness on the individual element's stiffness and design parameters are derived. The presented model is verified by a traditional model, and a good agreement is obtained. The influence of phase angle of meshing gear pairs on the resultant static stiffness is investigated. An example transmission system is employed to perform the sensitivity analysis and the results are analyzed. The proposed model provides an essential tool for the design of rotary feed system satisfying requirement of static stiffness.