Dynamic Behavior and Double-Parameter Self-Adaptive Stability Control of a Gear Transmission System

This paper proposes a new nonlinear transverse-torsional coupled model for single-stage gear transmission system, by taking transmission error, time-varying meshing stiffness, backlash, bearing clearances and the self-adaptive double-parameter control module into account. The nonlinear differential governing equation of system motion is derived and solved by applying variable step-size Runge-Kutta numerical integration method. The system's nonlinear dynamic characteristics and stability are investigated systematically by a bifurcation diagram of the Poincare map and parameter stability region. Firstly, the velocity bifurcation diagrams have shown that, under the same damping ratio and backlash and with the increase of control parameter P-h1, the route to chaos in the subcritical velocity region is first experienced from crisis to periodic doubling, and to crisis again, but the route that reverts to periodic motion in the super-critical velocity region is not affected. Additionally, the backlash is found to be the key parameter to affect the route to chaos as well. With the increase of the backlash, the crisis becomes the unique route to chaos in sub-critical region no matter what the P-h1 is, but the increase of P-h1 could change the route that reverts to periodic motion from 3T-periodic attractor to 2T-periodic attractor. Secondly, with the increase of the control parameter P-h2, the system starts to enter the chaotic motion and exit the chaos state at different critical points and through different routes. Besides, the unstable region could shrink dramatically and the route to crisis is suppressed as well with the increase of damping ratio. Thirdly, the motion stability region analysis established in full range of double-parameter and velocity provides a mathematical reference model and is stored in control module, which could be utilized to make the control module seek a nearest parameter set automatically that could make the motion stable again in the quickest way under unstable working condition. Finally, according to global motion stability diagram, the forbidden zones that cannot make the system motion stable by adjusting single control parameter are revealed, which has remarkable guiding value during the practical operation especially under the manual adjusting working condition.