Modeling the dynamic properties of conventional and high-damping boring bars

Robust Analysis of Stability in Internal Turning

“…Finite Element modeling and experimental modal testing on such a tooling system are presented in [10] in great detail.…”

“…In order to estimate the static compliance G, the model developed in [10] is adopted, as follows (2) where L 03 is the sum of the nominal bar overhang L=L 13 and the additional bar overhang L 01 which is necessary for describing the effect of imperfect cantilever constraint at node 1, see Figure 1c), in accordance with other authors [9][12]; η is a small correction of Euler-Bernoulli model due to shear effects considered by the Timoshenko beam theory; J is the moment of inertia, while E is the Young's modulus of the considered boring bar material; G u0t and H φ0t are the translational and rotational static compliances modeling the static tool-holder behavior at node 0. In the following, the static compliance G will be considered as a Gaussian random variable, with mean G best given by Eq.…”

“…c) Schematic representation of the tooling system. d) Adopted FE model [10] For estimating the damping coefficient ξ, the simple model tested in [10] was adopted…”

“…Under these hypotheses, (9) which is proportional to depth of cut a p , the classical result of chatter theory. For a curvilinear cutting edge including a significant nose radius r ε , under the hypothesis of a small feed to nose radius ratio and infinitesimal displacements, one obtains (10) where the "form factor" λ is given by (11) where (12) As a result, the theoretical regenerative radial cutting force coefficient k τ,th depends on depth of cut a p , nose radius r ε , main working cutting edge angle χ 1 and shearing normal cutting force coefficient k ns .…”

“…Main modal parameters as well as the regenerative radial force coefficient are considered as random variables. Their best guess values and probability density functions are calibrated by exploiting semi-analytical models based on the extensive experimental measurements presented in [10] and [11]. The model is finally experimentally validated, and main conclusions are drawn.…”