二自由度扭转干摩擦系统的频域响应计算方法

针对一类作扭转振动的干摩擦系统,基于库仑阻尼模型和谐波平衡思想给出了其频域响应的求解方法,考虑了干摩擦界面上可能出现的周期内全滑移运动及阻滞-滑移运动.首先,建立了扭转干摩擦系统的二自由度集中质量模型,并进行了无量纲化.其次,建立了以谐波平衡思想处理该动力学模型的方法,并给出了系统的接触面作周期内全滑移运动及阻滞-滑移运动的判定条件.最后,对于这两种接触运动状态,分别给出了其摩擦力的处理方法和谐波展开形式,从而建立了扭转干摩擦系统的频域求解方法.以此方法计算了系统在一组不同的正压力下的响应,其结果与数值积分法所得的结果取得了相当的一致.此半解析方法较数值积分方法更能揭示扭转干摩擦系统的工作机理,并可以大幅提高计算时间,其推导和求解过程可用于类似的非线性系统.

Frequency domain solution of 2-DOF torsional dry friction system

The forced vibration response of a two degree of freedom (DOF) torsional system with Coulomb friction was studied,with a full consideration of the pure-slip and stick-slip contact motions.First,the 2-DOF lumped parameter model of such nonlinear system was presented and derived into a non-dimensional form.Second,the harmonic balance approach was used to establish a general frame of solving the response under different contact motion.Accordingly,the critical condition as well as the harmonic expands of friction force of the pure-slip and stick-slip contact motions were presented.Finally,the procedure of dealing with frequency domain solution was proposed.Based on this method,a group of results were obtained under different normal pressures,and were validated by the numerical integration method with a very good agreement.The proposed semi-analytical method provides more clear insights of the torsional dry friction system and therefore has advantage in computational cost.