Dynamic loads and interference between meshing pairs in multi-stage geared system

Abstract

Inside realistic multi-stage geared system the dynamic meshing tooth loads are in interference mutually between meshing pairs. This report deals with this multi-stage crosstalk theoretically by Receptance Operator Procedure (ROP) that has been developed by the author. ROP leads the original governing simultaneous linear differential equations with the time-variant meshing tooth stiffness into Fredholm type simultaneous integral equations and their solution, finally into the analytical expression of dynamic tooth force or vibration amplitude. To confirm the contribution factors in dynamic behavior two fundamental sets of the multiple stage system, namely 2 stage serial gearing and planetary gearing structures are taken up for numerical experiment on analytical ROP solution. Taking a meshing takt homogeneity into consideration, the vibration amplitudes and their interference inside the serial stage system and the parallel-serial combined branching and merging system have been investigated. The singularity in dynamic interferences caused by repeated eigen value is also discussed. In conclusion, torsional linear system-rule of the geared structure is categorized into zones according to the interference state as function of system-pattern, i.e., homogeneity of meshing period, interconnecting stiffness between meshing stages, meshing phase gap and contact ratio.

Keywords

• 2 stage gear system
• star type planetary gear system
• dynamic tooth load interference
• time variant meshing stiffness
• parametric excitation
• system-pattern
• system-rule
• repeated eigenvalue
• receptance operator procedure