Least squares approximated stability boundaries of milling process

• Simply structured approximate polynomial representation of state terms is derived.
• The structure of the polynomial is systematic allowing fast check of accuracy.
• Reduced computation time of stability lobes from monodromy needing less number of calculations.
• Reduction in computation time improves with rise in order of approximation.

First and second order least squares methods are used in generating simple approximation polynomials for the state term of the model for regenerative chatter in the milling process. The least squares approximation of delayed state term and periodic term of the model does not go beyond first order. The resulting discrete maps are demonstrated to have same convergence rate as the discrete maps in other works that are based on the interpolation theory. The presented discrete maps are illustrated to be beneficial in terms of computational time (CT) savings that derive from reduction in the number of calculation needed for generation system monodromy matrix. This benefit is so much that computational time of second order least squares-based discrete map is noticeably shorter than that of first order interpolation-based discrete map. It is expected from analysis then verified numerically that savings in CT due to use of least squares theory relative to use of interpolation theory of same order rises with rise in order of approximation. The experimentally determined model parameters used for numerical calculations are extracted from literature.