NURBS Method for Cycloidal Steel Ball Reducer Profile Design

The profile design of cycloid disk in cycloidal steel ball reducer is the core of reducer design, which directly affects the performance of reducer. The cycloidal ball reducer is driven by a certain number of steel balls in a tooth profile composed of a pair of intermeshing internal and external cycloidal lines. The performance of the reducer can be optimized by adjusting the design equation of the cycloidal disc type line. However, in the process of design and optimization, the requirement of freedom and controllability of cycloid is getting higher and higher. The traditional design method of cycloidal profile based on cycloid parameter equation can no longer meet the requirements of design. The NURBS method can accurately represent the free curve and the conic quadratic curve. The cycloidal profile is actually a complex curve composed of a certain number of arcs. In this paper, the NURBS curve is applied to the design of cycloid disk of reducer, and the cycloidal profile based on NURBS is deeply studied. By sampling the known cycloidal profile, the sample point, the inverse control point, the weight factor, the node vector and the sample point are obtained, and the analysis verifies that the error between the fitted NURBS curve and the original curve is within the feasible range. Taking the BR85us-10G-6 reducer as an example, the fitting curve of the inner cycloid disk profile is obtained by using cubic NURBS curve, which can improve the flexibility and local adjustment of the cycloidal disc profile design.