Search Results
An iterative method for the multipliers of periodic delay-differential equations and the analysis of a PDE milling model
2009, Rott, Oliver, Jarlebring, Elisa
Locally convergent iterative schemes have turned out to be very useful in the analysis of the characteristic roots of delay-differential equations (DDEs) with constant coefficients. In this work we present a locally convergent iterative scheme for the characteristic multipliers of periodic-coefficient DDEs. The method is an adaption of an iterative method called residual inverse iteration. The possibility to use this method stems from an observation that the characteristic matrix can be expressed with the fundamental solution of a differential equation. We apply the method to a coupled milling model containing a partial and an ordinary differential equation. The conclusion of the numerical results is that the stability diagram of the coupled model differs significantly from the combined stability diagrams for each subsystem
A milling model with thermal effects including the dynamics of machine and work piece
2008, Rott, Oliver, Rasper, Patrick, Hömberg, Dietmar, Uhlmann, Eckart
This paper deals with the development of a new mathematical model that characterizes the structure-process interaction for a complex milling system. The structure is divided into a work piece and a machine part, which are represented by different models. While the machine dynamics is characterized by a standard multi-body system, the work piece is described as a linear thermo-elastic continuum. The coupling of both parts is carried out by an empirical process model permitting an estimate of heat and coupling forces occurring during milling. This work reports the derivation of the governing equations emphasizing the coupling and summarizes the numerical algorithms being applied to solve the coupled equation system. The results of numerical simulations that show the dynamics of the complex thermo-mechanical system are presented at the end.
On a thermomechanical milling model
2008, Chełminski, Krzysztof, Höberg, Dietmar, Rott, Oliver
This paper deals with a new mathematical model to characterize the interaction between machine and workpiece in a milling process. The model consists of a harmonic oscillator equation for the dynamics of the cutter and a linear thermoelastic workpiece model. The coupling through the cutting force adds delay terms and further nonlinear effects. After a short derivation of the governing equations it is shown that the complete system admits a unique weak solution. A numerical solution strategy is outlined and complemented by numerical simulations of stable and unstable cutting conditions.
A comparison of analytical cutting force models
2006, Rott, Oliver, Hömberg, Dietmar, Mense, Carsten
The modeling of dynamic processes in milling and the determination of stable cutting conditions have become increasingly important for the optimization of manufacturing processes. Analytic approaches and time domain simulations based on simplified dynamic systems are used to identify chatter-free machining conditions. Stresses applied to the system are generally estimated by cutting force models. The goal of this paper is to compare the influence of the cutting force models on the stability limits. Numerical simulations of a simplified, generic milling machine model are therefore performed, while varying the cutting force approach. In order to distinguish stable from unstable cutting conditions a numerical stability criterion is used. The resulting stability charts are then investigated and analyzed to show the effect of the different cutting force models.