延迟反馈控制齿轮传动系统的动力学特性分析

Analysis of Dynamic Characteristics of Gear Transmission System Controlled by Delayed Feedback

齿轮传动系统在高速重载过程中容易出现混沌运动,由此产生异常振动与噪声,严重影响齿轮传动过程的平稳性与安全性。因此,使用延迟反馈控制(DFC)方法,通过DFC-RD、DFC-RV两种控制途径,对单级三自由度齿轮传动系统进行振动控制。建立含延迟反馈控制的齿轮传动动力学模型,并通过数值法对系统求解,获得无控制时齿轮啮合副的动力学特性及冲击状态。然后通过施加DFC-RD、DFC-RV两种控制方式,在控制参数取不同值时得到齿轮传动系统的I/P分岔特性的转迁过程。根据两种途径的控制效果可以得到,在DFC-RD下,较小的时滞量就可将系统从高周期轨道控制至低周期轨道,但对系统冲击状态没有很好的控制效果。在DFC-RV下,则需要相对大一些的时滞量来达到预期目标,这种方式的优点在于合适的时滞τ2会使齿轮传动系统从齿面冲击状态向无冲击状态转变。

The gear transmission system is prone to chaotic motion in the process of high-speed and heavy load,resulting in abnormal vibration and noise,which seriously affects the stability and safety of the gear transmission process.Therefore,delayed feedback control is used(DFC)method,the vibration of single-stage three degree of freedom gear transmission system is controlled by DFC-RD and DFC-RV.The gear transmission dynamic model with delayed feedback control is established,and the system is solved by numerical method to obtain the dynamic characteristics and impact state of gear meshing pair without control.Then,by applying DFC-RD and DFC-RV control methods,when the control parameters are not taken at the same value,the transition process of I/P bifurcation characteristics of gear transmission system is obtained.According to the control effects of the two approaches,under DFC-RD,the system can be controlled from high period orbit to low period orbit with small time delay,but it has no good control effect on the impact state of the system.Under DFC-RV,a relatively large amount of time delay is required to achieve the expected goal.The advantage of this method is that the appropriate time delay will change the gear transmission system from the tooth surface impact state to the no impact state.