| Compound planetary gear transmission system has been widely appled in vehicle and aircraft with the advantages of larger torque-to-weight ratio and more transmission ratios. However, the structure of compound planetary gear transmission system is more complex and there are more factors affecting its dynamic characteristics so its noise and vibration levels are higher. Making an intensive study on its dynamic characteristics, analyzing its vibration mechanics and taking structural dynamic modification are the fundamental measures to reduce the vibration and noise and improve its reliability and transmission efficiency. But the researches are still in the initial stage and mainly focus on its internal characteristics at present. The dynamic characteristics, internal characteristics and eigensensitivity and load sharing characteristics of compound planetary gear transmission system are made systematic study in this thesis.According to the processing mode to lumped mass kinematic pattern, gear dynamic model can be classified into purely torsional model and translational-rotational coupling model. Firstly, a purely torsional nonlinear dynamic model of compound planetary gear transmission system is built. The model includes gear time-varying mesh stiffnesses, backlash as well as comprehensive mesh errors nonlinearities. It also includes all possible power flow configurations, any number of planet sets in any spacing arrangement and any planet mesh phasing configurations. By introducing relative displacements between components as the new generalized coordinates, uniform nonlinear differential equations of compound planetary gear transmission system are constricted in terms of matrices and system nondimensional dynamic differential equations are derived.Solution principle of ariable step size Gill numerical integration method is analyzed to solve the nonlinear differential equations effectively. Typical qualitative research methods of chaos are discussed. Then based on compound planetary gear transmission system purely torsional analytic model, by changing system nondimensional excitation frequency, monocycle anharmonic response, multiply periodic subharmonic response, quasi-peridic response and chaotic response are obtained utilizing ariable step size Gill method and system responses basic rules are generalized. By means of time histories, phase-plane diagram, Poincare maps and power spectrum, system kinestate is identified and various responses are compared and analyzed in detail. Bifurcation diagram is plotted in order to investigate the route to chaos under the condition of changing the mesh damping ratio.The purely torsional dynamic model cannot be used to analyze and calculate system dynamic characteristics when the ratio of gear mesh stiffness and support stiffness is less than 10. For more accurately reflecting the actual situation, a translational-rotational coupling nonlinear dynamic model is proposed. In the model, each component has one torsional degree of freedom and two translation degree of freedom. So there are 6N+12 degrees of freedom, in which N means the number of planet sets. Many nonlinear factors also have been taken into account, such as time-varying mesh stiffness, mesh errors and gyroscopic effects, etc. Furthermore, system nondimensional nonlinear dynamic differential equations are derived by choosing appropriate coordinate transformation. And it established the foundation for internal characteristics and load sharing characteristics analysis.System natural frequency and modal shapes are obtained by solving eigenvalue problem and system internal characteristics laws are generalized. Eignsensitivities to design parameters are analyzed and their relational expressions which are proportional to modal strain/kinetic energies are derived. Then the vibration modes are solved employing numerical method to research the trend of internal characteristics with the key parameters by changing a single parameter. The key parameters include mass, moment of inertia, support stiffness, torsional stiffness and relative position of two kinds of planet. System internal characteristics are also studied under the condition that planet sets are inhomogeneous distribution on planet carrier.There is a higher requirement to system coaxality and symmetry because of the complex structure of compound planetary gear transmission system. As it is impossible that components’ assembly variations and manufacturing errors are eliminated entirely, loads cannot be shared averagely among planets actually. System manufacturing and alignment errors are analyzed, whose concrete expressions are given and the translational-rotational coupling dynamic model built is modified. The load sharing coefficient of each pinion is calculated. And the influences of design parameters to load sharing characteristics are studied. Parameters under consideration include number of planet set, support stiffness of sun pinion, relative position of two kinds of planet and operating speed of planet carrier.Through the present researeh, the nonlinear dynamic characteristics of compound planetary gear transmission system are revealed and the influence laws of design parameters on inherent characteristics and load sharing characteristics are obtained, which provide theoretical foundation for achieving its dynamic design. |
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