Hyper-third order full-discretization methods in milling stability prediction

• Simplified systematic derivation of full-discretization methods of hyper-third order is presented.
• Accuracy peaked at 4th order among the full-discretization methods of 1st to 5th order.
• The proposed methods are applicable to stability analysis of milling of higher degree of freedom.

Full-discretization methods beyond the third order is not yet explored except for this work in which the fourth and fifth order methods are presented. It is seen in earlier works that accuracy of milling stability analysis using the full-discretization method rises from the first order method to the second order method and continues to rise to the third order method. It is seen in this work that the rise in accuracy of the full-discretization method with order continues to the proposed fourth order method where it (accuracy) peaks before a decline to the proposed fifth order method.