Abstract
A nonlinear purely rotational dynamic model of a multistage closed-form planetary gear set formed by two simple planetary stages is proposed in this study. The model includes time-varying mesh stiffness, excitation fluctuation and gear backlash nonlinearities. The nonlinear differential equations of motion are solved numerically using variable step-size Runge-Kutta. In order to obtain function expression of optimization objective, the nonlinear differential equations of motion are solved analytically using harmonic balance method (HBM). Based on the analytical solution of dynamic equations, the optimization mathematical model which aims at minimizing the vibration displacement of the low-speed carrier and the total mass of the gear transmission system is established. The optimization toolbox in MATLAB program is adopted to obtain the optimal solution. A case is studied to demonstrate the effectiveness of the dynamic model and the optimization method. The results show that the dynamic properties of the closed-form planetary gear transmission system have been improved and the total mass of the gear set has been decreased significantly.
Highlights
Planetary gear sets have been widely used in engineering including automotive transmissions, aviation transmissions, and crane gearboxes as well as other marine and industrial power transmission systems
The results show that the dynamic properties of the closed-form planetary gear transmission system have been improved and the total mass of the gear set has been decreased significantly
Closed-form planetary trains are obtained from a number of single-stage differential planetary gear sets and one quasi-planetary stage whose central members are connected according to a given power flow configuration
Summary
Planetary gear sets have been widely used in engineering including automotive transmissions, aviation transmissions, and crane gearboxes as well as other marine and industrial power transmission systems. Planetary gear trains have many advantages over fixed-center counter-shaft gear systems. The flow of power via multiple-gear meshes increases the power density and helps to reduce the overall size of the transmission train. The ability of multistage planetary sets in providing multiple speed reduction ratios has been the main reason for their extensive use in automatic transmission applications. Closed-form planetary trains are obtained from a number of single-stage differential planetary gear sets and one quasi-planetary stage whose central members are connected according to a given power flow configuration. Output, and fixed member assignments are made to certain central members to achieve a given gear ratio
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