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在研究轧钢机轧制过程中由打滑引起的自激振动时，考虑到实测中动滑动摩擦系数是随机的，以及万向联轴节具有间隙等因素，据此建立了具有随机系数和间隙的新广义Ｌｉéｎａｒｄ方程，并从理论上提出此方程算法。所得结论符合生产实际，可以用来诊断轧钢机产生设备事故的原因，同时对轧钢机设计与生产也有很大的实际意义，还可以推广到机床进给系统的爬行运动和转子轴承系统的研究。
In the study of the self-excited vibration caused by slippage during the rolling process of the rolling mill, taking into account the fact that the measured slippage coefficient of the slippage is random and the gap of the universal joint is random, the random coefficient and the gap The new generalized Liénard equation is proposed and the algorithm of this equation is proposed theoretically. The conclusion is in line with the actual production, which can be used to diagnose the cause of equipment accidents in rolling mills. It also has great practical significance for the design and production of rolling mills. It can also be extended to the study of creeping and rotor bearing systems of the machine tool feed system.