Optimal Design of a Damped Arbor for Heavy-Duty Machining of Giant Parts

Aiming to suppress chatter vibration during machining of huge mechanical parts, dies, and molds, a design method for a damped arbor imbedded with a mass damper was devised. First, an analysis method coupled with Rayleigh’s method was developed and used to calculate the stiffness of an arbor with a tapered hollow space for installing the mass damper inside. In the formulation of the vibrating system with two degrees of freedom, the displacement ratio is introduced for accurate calculation of the counter force of the damper mass. Then, the shape and size of the hollow space was optimized in order to maximize the negative real part of the compliance of the arbor. The proposed design method can increase the dynamic stiffness of the damped arbor with a hollow with the minimum reduction in its static stiffness. Furthermore, it is found that once the damper is optimized for the maximum length of an arbor in a certain design range, it can be applied to a shorter arbor without deterioration of dynamic stiffness. Finally, chatter noise and machined surface roughness measured experimentally proved that a damped arbor prototyped by the proposed design method has much higher cutting performance than a conventional one.