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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.
Aiming at a kind of dry friction system with torsional vibration, the method of solving frequency domain response is given based on coulomb damping model and harmonic balance theory. The whole slip cycle and retardation - Slip motion.Firstly, a two-degree-of-freedom mass model for torsional dry friction system was established and dimensionless.Secondly, a method to deal with the dynamic model with harmonic balance was established and a systematic Contact surface for the whole slip movement and retardation-slip movement of the judgment conditions.Finally, the two contact movement state, respectively, its friction force processing and harmonic expansion form, thus establishing a torsion In this method, the response of the system under a set of different positive pressures is calculated, and the result is in good agreement with that obtained by the numerical integration method. Compared with the numerical integration method, the semi-analytical method Can reveal the working mechanism of torsion dry friction system, and can greatly improve the calculation time, and its derivation and solving process can be used for similar non-linear system.