A generalized formulation for analyzing speeds and forces of the gear components of planetary automatic transmissions is proposed. The formulation is capable of analyzing any typical one-degree-of-freedom automatic transmission gear train containing any number of simple, compound or complex-compound planetary gear sets. It consists of three components: a kinematic analysis formulation, a gear ratio and kinematic configuration search algorithm, and a power flow analysis formulation. The kinematics module computes rotational speeds of gears and carriers. Given the type and number of planetary gear sets, the search module determines all possible kinematic configurations and gear tooth count combinations that result in a required set of gear ratios while eliminating all kinematic redundancies and unfavorable clutching sequences. The third component, the power-flow analysis formulation, performs a complete static force (power flow) analysis to determine all gear and bearing forces, and clutch and connection torque values. A five-speed transmission example is considered to highlight the capabilities of the proposed formulation.
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