On a Numerical Method for Simultaneous Prediction of Stability and Surface Location Error in Low Radial Immersion Milling

摘要

This brief proposes a numerical approach for simultaneous predictionnof stability lobe diagrams and surface location error innlow radial immersion milling based on the direct integrationnscheme and the precise time-integration method. First, the mathematicalnmodel of the milling dynamics considering the regenerativeneffect is presented in a state space form. With the cutter toothnpassing period being divided equally into a finite number of elements,nthe response of the system is formulated on the basis of thendirect integration scheme. Then, the four involved time-variantnitems, i.e., the time-periodic coefficient item, system state item,ntime delay item, and static force item in the integration terms ofnthe response, are discretized via linear approximations, respectively.nThe corresponding matrix exponential related functions arenall calculated by using the precise time-integration method. Afternthe state transition expression on one small time interval beingnconstructed, an explicit form for the discrete dynamic map of thensystem on one tooth passing period is established. Thereafter, thenmilling stability is predicted via Floquet theory and the surfacenlocation error is calculated from the fixed point of the dynamicnmap. The proposed method is verified by the benchmark theoreticalnand experimental results in published literature. The high efficiencynof the algorithm is also demonstrated.