Closed-form equations for statically analyzing shaft-gear systems

Shaft-gear systems are integral parts of industry. To analyze these systems using an existing classical method, one should first write the static equilibrium and compatibility equations and then solve these equations simultaneously, which is tedious for complex problems. This study proposes a novel method for analyzing shaft-gear systems. The systems are modeled as parallel or series arrangements using torsional springs. By introducing a concept of torque propagation, relationships of the stiffness/flexibility, torque, and twist angle are derived, resulting in closed-form equations with the unknown torques or the twist angles that can be directly found without concurrently solving the static equilibrium and compatibility equations. Illustrative examples are presented to validate and address the efficiency of the proposed method to quickly analyze the shaft-gear systems, even for a combination of parallel and series ones. The results are exact and portend that the technique requires cost-efficiency of computations compared to the existing method, especially when the systems are hybrid, or the number of unknowns is high. Also, a concise computer program can be provided by the proposed equations.