Design of a non circular gear Mechanism with Twice Unequal Amplitude Transmission Ratio

This study proposes a new non–circular gear transmission mechanism with an involute–cycloid composite tooth profile to realize the twice unequal amplitude transmission (In a complete rotation cycle of gear transmission, instantaneous transmission ratio has twice fluctuations obvious with unequal amplitude) of non–circular gears. The twice unequal amplitude transmission ratio curve was designed based on Fourier and polynomial functions, the change law of the Fourier coefficient on the instantaneous transmission ratio(In non-circular gear transmission, the transmission ratio changes with time, and the transmission ratio of non-circular gear should be instantaneous transmission ratio) was analyzed, and the pressure angle and contact ratio of the involute–cycloid composite tooth profile was calculated. The involute–cycloid composite tooth profile non–circular gear was machined by WEDM technology, while its meshing experiment was performed using high-speed camera technology. The results demonstrate that the instantaneous transmission ratio curve value obtained via the high-speed camera experiment was consistent with the simulation value of virtual software. Furthermore, the involute–cycloid composite tooth profile was applied in the seedling pickup mechanism of non–circular gear planetary gear train. The possibility of the application of the involute–cycloid composite tooth profile in the seedling pickup mechanism was verified by comparing the consistency of the theoretical and simulated seedling picking trajectory.

Dynamic Modeling and Analysis of Nonlinear Compound Planetary System

In the vehicle composite planetary gear transmission system, nonlinear excitations such as time-varying meshing stiffness, backlash and comprehensive error would lead to large vibration and noise, uneven load distribution, unstable operation and other problems. To address these issues, this work focuses on compound planetary gears and develops the bending-torsion coupling nonlinear dynamic model of the system based on the Lagrange equation. There are internal and external multi-source excitations applied to the system. This model is used to study the bending-torsion coupling meshing deformation relationship of each meshing pair along with the translational and torsional directions. The natural frequencies and vibration modal characteristics of the system are extracted from the model, and the influence of rotational inertia and meshing stiffness on the inherent characteristics of the system are studied. The coupling vibration characteristics of the system under operating condition are analyzed in terms of the inherent characteristics and time–frequency characteristics of the system. The simulation results exhibit that the planetary gear system has three modes. The change in natural frequency trajectory has two phenomena: modal transition and trajectory intersection. The main frequencies include engine rotating frequency, meshing frequency and its double frequency, and the rotation frequency and harmonic frequency of the engine have a great influence on the vibration response of the system. Finally, the virtual prototype of the composite planetary system is used to verify the accuracy of the established model from speed, inherent characteristics, meshing force and frequency composition.