A theoretical and experimental study of spindle imbalance induced forced vibration and its effect on surface generation in diamond turning

In diamond turning, spindle error motions exhibit dynamic characteristics under spindle imbalance, which significantly deteriorate form accuracy and surface roughness. However, in the spindle error motion community dynamic characteristics of spindle imbalance induced forced vibration have not attracted much attention, involving unbalanced magnetic forces induced forced spindle vibration, unbalanced air bearing pressure induced forced spindle vibration, and spindle whirling and spindle tilting under bearing hydrodynamics along with inertial effect. In this study, a theoretical and experimental investigation has been conducted to discuss dynamic characteristics of spindle imbalance induced forced vibration and its effect on surface generation in diamond turning. Firstly, an analysis model of magnetic forces for a spindle motor was built up to study dynamic characteristics of unbalanced magnetic forces induced forced spindle vibration. Secondly, a mathematical model of Reynolds equations for air bearings was established with a five-DOF dynamic model for spindle motion to discuss dynamic characteristics of unbalanced air bearing pressure induced forced spindle vibration, spindle whirling and spindle tilting. Finally, it has been verified by two kinds of designed face-turning tests for comparison carried out in diamond turning. The theoretical and experimental results revealed that bearing hydrodynamics coupled with inertial effect would jointly induce synchronous quasi-elliptical spindle whirling/tilting, accordingly producing a quasi-elliptical concave/convex surface in diamond turning, whose cyclic frequency is 2 rev.−1. Under spindle imbalance, unbalanced magnetic forces induced forced spindle vibration with the fundamental cyclic frequency of 2p rev.−1 (the spindle motor pole number) would occur as well as unbalanced air bearing pressure induced forced spindle vibration with the cyclic frequency of α rev.−1 (the air bearing orifice number) further to produce the corresponding straight radial patterns at the machined surface. This research work gives a deep insight into dynamic characteristics of spindle imbalance induced forced vibration and its effect on surface generation in diamond turning. [Display omitted] •Theoretical modelling is built up for spindle imbalance induced forced vibration.•Unbalanced magnetic forces induced spindle vibration yields straight radial patterns.•Air bearing pressure induced spindle vibration yields straight radial patterns.•