Dynamic modeling of a standard internal tool holder

The interface between the boring bar and the clamp housing has a significant influence on the dynamic properties of the bar. The dynamic rigidity of an internal turning bar is usually low and decreases with the increase of the bar length to diameter (L/D) ratio, leading to the occurrence of vibrations, which can result in rough machined surfaces and reduced tool life. This paper presents a mathematical model of the boring bar as a three-span Euler–Bernoulli beam with free-pinned-pinned-free (F-P-P-F) constraints, and investigates its dynamic characteristics and frequency response. The bar’s characteristic equation is expressed succinctly in terms of Krylov–Duncan functions, and the first natural frequencies and mode shapes of the multi-span boring bar are obtained by numerical calculation. The results demonstrate that the constraints and the overhang have significant impact on the dynamic characteristics of the boring bar. The results of this analysis and numerical simulation are compared with direct measurements obtained through an actual internal turning of a hardened steel specimen. The analytical model developed here can be valuable in guiding costly experiments for determining dynamical properties of boring bars with varying overhangs.