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针对航空发动机中的摩擦振动问题,给出了对称黏滑运动摩擦力的分段表达式.利用谐波平衡方法推导了具有偶数次黏着的黏滑运动的级数形式解析解,并基于该解析解给出了参数平面内的黏滑边界线方程.黏滑运动响应仅包含奇次谐波成分,在奇次分数倍频处存在超谐次共振.当频率比小于0.4时,黏滑边界线呈现凸凹交替特征,局部极小值位于各阶超谐次共振频率处.黏性阻尼增大能够缩小无黏着运动的参数范围,但在各阶超谐共振频率附近,黏性阻尼增大会扩大无黏着运动的参数区域.
Aiming at the problem of friction and vibration in aeroengine, the piecewise expression of the friction of symmetrical stick-slip motions is given.The analytical solutions of series form of stick-slip motions with even number of sticking are deduced by harmonic equilibrium method. Based on the analysis Solution gives the stick-slip boundary line equation in the parametric plane. The stick-slip motion response contains only odd harmonic components and there is superharmonic resonance at the odd fractional frequency. When the frequency ratio is less than 0.4, The local minimum is located at the superharmonic resonance frequency of every order.The increase of viscous damping can reduce the parameter range of non-sticking motion, but the increase of viscous damping increases near the superharmonic resonance frequency of each order Parameter area for non-adhesive movement.