Time-Domain Modeling of Varying Dynamic Characteristics in Thin-Wall Machining Using Perturbation and Reduced-Order Substructuring Methods

Abstract

The dynamic response of thin-walled parts becomes time and tool position dependent due to material removal along the toolpath. This article proposes a new reduced-order workpiece dynamic parameters update model using substructuring and perturbation methods. The removed volumes between discrete locations along the toolpath are defined as substructures of the initial global workpiece. The dynamically reduced-order initial workpiece structure and the removed substructures are obtained with model order reduction techniques. Equations of motion of the workpiece are updated in time-domain by rigidly coupling fictitious substructures having the negative mass and stiffness of the removed material. Instead of solving the generalized eigenvalue problem repeatedly along the toolpath, the mode shapes of the in-process workpiece are perturbed using the mass and stiffness of the removed substructures. Convergence of the perturbation is improved by integrating a vector sequence convergence accelerating algorithm. The corresponding updated mode frequencies are evaluated using Rayleigh Quotient with the perturbed mode shapes. The proposed reduced-order time-domain dynamics update model is verified in five-axis ball-end milling tests on a thin-walled twisted fan blade, and its predictions are also compared against the authors’ previously developed frequency-domain reduced-order model. It is shown that the newly introduced model is ∼4 times more computationally efficient than the frequency-domain model.