Three-dimensional stability lobe diagram construction in milling process with considering multiple modes

Abstract In the milling process, chatter has a significant impact on tool abrasion, machining surface quality and productivity. Stability lobe diagram (SLD) is one of the earliest methods used for offline chatter prediction. Traditionally, a two-dimensional SLD constructed by only selecting the most flexible mode and can seek the limit of axial depth of cut at a corresponding spindle speed. However, the SLD constructed only with the most flexible mode is not accurate enough when two or more important flexible modes existed with nearly the same modal stiffness, moreover, when the whole number of full vibration cycles between passages of two teeth is relatively small the SLD will fail to predict in some certain spindle speed ranges. This paper develops a three-dimensional SLD of the spindle speed, axial and radial depth of cut with considering multiple modes to solve the inaccurate prediction problem mentioned above. In consideration of the fact that accurate calibration milling force coefficients is essential for construction of SLD, a calibration procedure is presented to obtain more accurate milling force coefficients based on the average force method. In addition, as the basic input parameters for establishing the SLD, four modal parameters are identified via impact test. Then, a two-dimensional SLD is established in frequency domain by using the zero-order approximation method (ZOA) with two important flexible modes existed with nearly the same modal stiffness. Finally, a three-dimensional SLD can be constructed by scanning at different radial depths of cut and taking the lowest envelop of the two modes SLD. The validity, accuracy and basic principles of the above method are verified by a series of experiments.