Gaurav, Kumar
(2015)
Stability Analysis of Machining Processes.
Masters thesis, Indian Institute of Technology Hyderabad.
Abstract
In this work, we do a parametric stability analysis of the turning and milling process. We observe that the governing equation for these processes is a delay differential motion, and therefore use the quasi polynomial and the spectral tau method for DDEs to analyze their stability. In quasi polynomial method, we convert the quasi polynomial into an approximate polynomial expression using Taylor series expansion. The roots of the polynomial expression are then used to determine the stability of the system. Next we discuss the spectral tau method based on the Galerkin series approximation to study the stability of DDEs. Here we first obtain an equivalent PDE representation of the DDE, and then use spectral approximation techniques to obtain a finite dimensional ODE approximation of the DDE. The boundary condition is incorporated using the
tau method, where the last row of the system ODE is replaced with the boundary condition. We then use these methods to obtain the stability diagrams for the single and multi-degree of freedom turning and milling process and compare them with literature. The numerical examples clearly demonstrate that these methods can be used to determine the stable zones of operation, therefore can be used to demarcate the regions of parametric space for which the machining process will be stable.
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