The vibration of a rotor with variable mass as a one-mass system with two degrees of freedom is investigated. An analytical procedure for solving of the system of two coupled second-order differential equations with slow time variable parameters is developed. The trajectory of the rotor center for various initial conditions is obtained. The method developed in the paper is applied for determining the vibration of the work piece during turning operation. The analytically obtained results show the influence of mass variation, cutting parameters and cutting force on the dynamic properties of the work piece. A decrease in mass of the work piece increases the amplitude of vibration. The amplitude increase is faster if the cutting velocity is higher. The obtained results are compared with experimentally obtained ones. The correlation between vibration and surface roughness is determined.

研究了具有两个自由度的一质量系统作为可变质量转子的振动。提出了求解具有慢时变量参数的两个耦合二阶微分方程系统的解析程序。获得了各种初始条件下转子中心的轨迹。本文开发的方法适用于确定车削过程中工件的振动。分析获得的结果表明质量变化，切削参数和切削力对工件动力学性能的影响。工件质量的减小增加了振动的幅度。如果切割速度较高，则振幅增加更快。将获得的结果与实验获得的结果进行比较。