Analysis of the Cutting Process of a Cylindrical Workpiece Clamped by a Three-Jaw Chuck

Abstract

A theoretical analysis has been carried out on the cutting dynamics of a solid cylindrical rotating workpiece clamped by a three-jaw chuck with balanced pressure at the jaws and subjected to a cutting operation. The net reaction balancing the cutting force is found to consist of infinite number of force components oscillating at frequencies 3ω, 6ω, 9ω ... etc., where ω is the angular speed of rotation of the workpiece, and a stationary force term 3F0 /2 where F0 is the static balancing force impressed on each jaw-line. The stationary force term tends to give a uniform depth of cut. However the harmonic force terms tend to spoil the uniformity in the depth of cut. Under resonant condition of the third harmonic force maximum depth of cut occurs in the mid positions between two jaws and minimum along the jaw-positions. Resonant vibration of the system takes place at angular spindle speeds ωr = ω0 /3P where P is an integer and ω0 = (K/M)1/2 is the angular natural frequency of vibration of the system.