Abstract:

The actions of nonlinear spring force and nonlinear frictional force on dynamic characteristics of NC table were emphatically studied by means of theoretical analysis and experimental verification. NC table was subjected to several kinds of forces such as axial forces, transverse forces, torques, frictional forces and cutting forces etc. Values of every kind of spring stiffness were intimately related to the support types of ball screw. Stiffness values varied with displacement and moving direction of NC table and shown nonlinear regulations such as soft spring property or hard spring property. The varying regulation of frictional force obeyed Streibeck curve. The conclusions are drown,that the effect of nonlinear spring can be described by Duffing equation, the effect of nonlinear frictional force can be described by van der Pol equation, and their coupling effect can be described by Lienard equation. The jump phenomenon caused by soft or hard spring property and the self-excited vibration and creep phenomenon caused by nonlinear frictional force make the stable zone of systemic responses complex.The jump phenomenon takes place under condition that the exciting frequency is close to the natural frequency and the creep phenomenon takes place under condition that the NC table moves at lower speed and in poor lubrication. The existence of limited cycles shows that nonlinear factors are stable factors to limit the unstable phenomenon expend infinitely. 

Key words: NC table, nonlinear dynamic characteristics, soft spring property, hard spring property, jump phenomenon, self-excited vibration, limited cycle

摘要：

通过理论分析和试验验证，着重研究了非线性弹簧力和非线性摩擦力对数控工作台动态特性的作用。数控工作台受滚珠丝杠轴向力、横向力、扭矩、摩擦力和切削力等多种载荷的作用，滚珠丝杠各类刚度的大小与滚珠丝杠的支承方式密切相关；各类刚度随着工作台位移和运动方向的变化而变化，呈现出软弹簧特性或硬弹簧特性等非线性规律；摩擦力变化规律服从Streibeck曲线。指出非线性弹簧力作用可以用有阻尼的Duffing方程描述，非线性摩擦力作用可以用van der Pol方程描述，非线性弹簧力和非线性摩擦力的耦合作用可以用Lienard方程描述。软硬弹簧特性引起的跳跃现象和非线性摩擦力自激振动引起的爬行现象使系统响应的稳定区域复杂化；跳跃现象主要发生在激励频率与固有频率接近的情况下,而爬行现象主要发生在低速润滑条件不良的情况下。极限环的存在表明非线性因素是限制失稳状态无限发展的稳定因素。

关键词: 数控工作台；非线性动态特性；软弹簧；硬弹簧；跳跃现象；自激振动；极限环