Research on the mass unbalance response of an inner planetary gear reducer
A new inner planetary gear reducer with three axes is introduced. Three constructions and fixing techniques of the planetary gears are also introduced and compared with each other. Considering the meshing stiffness and damping of the gear pairs and the stiffness of the bearings, the dynamic governing equations of an inner planetary gear reducer with three axes are established based on the lumped mass method and corresponding deformation conditions. According to the different constructions of the reducer, the natural frequency and the mass unbalance response is investigated in frequency field. It is found that the natural frequency of the reducer with different numbers of inner planetary gears has almost the same frequency value. Mass unbalance force can not only result in bending vibrations, but also result in twisting vibrations. When the reducer has three inner planetary gears, the amplitude of the dynamic response is smallest.
On Modelling of a Three-Ring Reducer for Elasto-dynamic Analysis
The governing equations for elasto dynamic analysis of three ring reducers are derived with consideration of many factors including the elasticity of input and support shaft, the elasticity of bearings in the planetary and driven shaft, the elasticity of meshing gears and errors of the eccentric cranks in indexing and eccentricity. The eigenfrequency of a three ring reducer is also calculated.
Deflections and Moments Due to a Concentrated Load on a Rack-Shaped Cantilever Plate with Finite Width for Gears
In helical gear design, deflections and moments of rack-shaped cantilever with finite width, must be taken into consideration. This paper contains numerical solutions for deflections and moments of rack-shaped cantilever with finite width. These solutions are obtained with applying calculus of finite differences to the basic differential equation. For a finite rack-shaped cantilever, deflections and moments are closely related to its pressure angle and profile of its section. The numerical solutions showed good agreement with the experimental results of rack shaped cantilever simulating a gear tooth.