Analytical prediction of stability lobes in ball end milling

The paper presents an analytical method to predict stability lobes in ball end milling. Analytical expressions are based on the dynamics of bull end milling with regeneration in the uncut chip thickness, tune varying directional factors nod the interaction with the machine tool structure. The cutting force coefficients are derived from orthogonal cutting data base using oblique transformation method. The influence of cutting coefficients on the stability is investigated. A computationally efficient, an equivalent average cutting force coefficient method is developed for bail end-milling. The prediction of stability lobes Sor bail end milling is reduced rb the solution of a simple quadratic equation. The analytical results agree well with the experiments and the computationally expensive and complex numerical time domain simulations.