This study aims to analyze the chaotic dynamics and present a chaos controller for spur gear transmission systems with idler. The chaotic dynamics of the spur gear mechanism has already been investigated. However, the presence of idler gears affects the chaotic behavior and the route to chaos for the nonlinear model of spur gears. This is investigated through the derivation of dimensionless dynamics, defining a Poincare’ section, and extracting the bifurcation diagrams of the system for variations of several parameter models. A nonlinear time-varying dynamic model of a spur gear transmission system with idler is established where backlash, time-varying stiffness, static transmission error, and external excitation are included and a region for the occurrence of chaos is found. The chaotic vibration suppression of the system is done by detecting the unstable periodic orbits embedded in the strange attractors and developing control law by employing sliding mode and adaptive sliding mode control strategy. The controller transmits a chaotic trajectory into the detected unstable periodic orbits. Numerical simulations including phase plane portrait, time histories diagrams, Poincare’ sections, and bifurcation diagrams demonstrate the behavior of the system and confirm the performance of the proposed controller.

这项研究旨在分析混沌动力学，并提出一种带惰轮的正齿轮传动系统的混沌控制器。正齿轮机构的混沌动力学已经进行了研究。然而，对于正齿轮的非线性模型，惰轮的存在会影响其混沌行为和走向混沌的路径。通过无因次动力学的推导，定义Poincare的部分以及提取系统的分叉图来研究这几个参数模型的变化，对此进行了研究。建立了具有惰轮的正齿轮传动系统的非线性时变动力学模型，该模型包含了齿隙，时变刚度，静态传递误差和外部激励，并找到了发生混沌的区域。该系统的混沌振动抑制是通过检测嵌入在奇异吸引子中的不稳定周期轨道并采用滑模和自适应滑模控制策略制定控制律来完成的。控制器将混沌轨迹传输到检测到的不稳定周期轨道中。包括相平面肖像，时间历史图，庞加莱截面和分叉图在内的数值仿真演示了系统的行为并确认了所提出控制器的性能。