Dynamic Behaviour of a Two-Stage Cycloidal Speed Reducer of a New Design Concept

Traditional cycloidal speed reducers (with two cycloid discs per one stage, mutually turned by an angle of 180 degrees) are well known for their remarkable dynamic stability. This paper analyses dynamic behaviour of a two-stage cycloidal speed reducer of a new concept, in which only one cycloid disc is used for each stage in order to further enhance its compactness. Lagrange's displacement equations have been used to develop independent dynamic models for both the first and the second stage (six degrees of displacement freedom for the first stage, and eight degrees of displacement freedom for the second stage). A normal force acting at the contact of the cycloid disc teeth and the corresponding ring gear roller has been taken as an excitation force. For the newly designed two-stage cycloidal speed reducer, systems of differential displacement equations of the first and second stage have been solved using the Matlab - Simulink software package. A comprehensive analysis of the obtained diagrams of elastic dynamic contact forces of the first and second stage has revealed a certain analogy. In terms of dynamics, the cycloid disc of the second stage behaves similarly to the cycloid disc of the first stage. Since these cycloid discs are mutually turned by an angle of 180 degrees, it can be concluded that from the aspect of the cycloid disc load, the two-stage cycloidal speed reducer of a new design concept exhibits good dynamic balance and stability.