Position error adjustment method for RV reducers based on state space model

Addressing the issue of positional errors in key load-bearing components such as crankshaft, cycloidal wheel, and pin gear housing during machining and manufacturing, which reduce the transmission accuracy and smoothness of RV reducers, this paper proposes methods for adjusting positional errors and allocating positional tolerances. Firstly, using the BX40E reducer as a study object, an error transmission chain is constructed to illustrate the error transmission path of RV reducers. Secondly, a state-space model for the error transmission process is established. Then, combining optimal control theory and considering factors such as transmission accuracy, adjustment labor costs, and measurement uncertainty, optimal adjustment amounts for each assembly step and the final error state are provided. Subsequently, a genetic algorithm was employed to allocate positional tolerances for critical components to minimize the overall manufacturing cost. Simulation results demonstrate that the transmission error decreases by approximately 40% when the precision weight Q ranges from 0 to 5, and by about 15% when Q ranges from 5 to 10. The proposed method proves effective in enhancing the transmission accuracy and stability of the RV reducer, but it is recommended to select different precision weights based on actual accuracy requirements to minimize costs.