齿轮传动系统动态特性及双参数自适应稳定控制

Dongping Sheng, Fengxia Lu
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引用次数: 0

摘要

在考虑传动误差、时变啮合刚度、齿隙、轴承间隙和自适应双参数控制模块的基础上,提出了单级齿轮传动系统的非线性横扭耦合模型。推导了系统运动的非线性微分控制方程,并采用变步长龙格-库塔数值积分法求解。利用庞卡罗图的分岔图和参数稳定区域,系统地研究了系统的非线性动态特性和稳定性。首先,速度分岔图表明,在相同的阻尼比和间隙下,随着控制参数的增加[公式:见文],亚临界速度区域的混沌路径首先经历从危机到周期加倍,再到危机,但在超临界速度区域恢复周期运动的路径不受影响。此外,发现间隙也是影响混沌路径的关键参数。随着反冲的增加,无论[公式:见文]是什么,危机都成为亚临界区域走向混沌的唯一路径,但[公式:见文]的增加会改变从3t周期吸引子向2t周期吸引子回归周期运动的路径。其次,随着控制参数的增大[公式:见文],系统在不同的临界点、通过不同的路径开始进入混沌运动并退出混沌状态。此外,随着阻尼比的增大,不稳定区域会急剧缩小,危机之路也会受到抑制。第三,在双参数和速度全范围内建立的运动稳定区域分析提供了一个数学参考模型,并存储在控制模块中,控制模块可以利用该模型自动寻找最近的参数集,使运动在不稳定的工作状态下以最快的速度恢复稳定。最后,根据全局运动稳定性图,揭示了通过调整单个控制参数无法使系统运动稳定的禁区,在实际运行中,特别是在人工调节工况下,具有显著的指导价值。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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 Poincaré 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 [Formula: see text], 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 [Formula: see text] is, but the increase of [Formula: see text] 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 [Formula: see text], 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.
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