Various beam and shell models for long slender tools in the area of HSC milling

Abstract

AbstractHigh‐speed‐cutting) milling is an extensively used production process in tool‐making and mold‐making industries. For the purpose of a self‐balancing tool, a hollow shaft is used and filled partially with a fluid. This talk presents different beam and shell models for the investigation of nonlinear vibrations. Therefore, different theories are compared with respect to the influence of geometrical nonlinearities, spin‐softening as well as stress‐stiffening, and also shear deformation. Additionally, a stochastic Wedig–Dimentberg approach is presented for the simulation of a spatial distributed unbalance. Starting with the nonlinear kinematics for the tool‐deformation Hamilton's principle is evaluated for the variational formulation of each model. Regarding to the shear deformation, the theories of Euler–Bernoulli and Ehrenfest–Timoshenko (beam models) as well as Kirchhoff–Love and Mindlin–Reissner (shell models) are used. In the following up, the variational formulation is discretized under usage of a global Ritz approach on the one hand, and on the other hand with a local finite element (FE) discretization. Afterward, the governing system of differential equations is solved and discussed. Different results of rotating and nonrotating tools are presented, which show the available options of each theory and also their limits. In particular, results of the eigenfrequencies including their stochastic distribution, stationary deformation, stability behavior, and various time solutions are shown.