This paper presents a generalised model of stability that aims to take into account effects such as the feed magnitude and direction, the geometry of the mill cutter, the machining position and the multi-frequency nature of the force. The model has been applied to the study of the stability of peripheral milling with cylindrical helical milling cutters and to conventional milling. The proposed algorithms are capable of predicting both traditional (Hopf) and double period (flip) instabilities.
The application to peripheral milling with helical milling cutters has shown that the helix has an influence on the stability of the milling process through the variation of the double period zones. Due to the effect of the helix, the dual period instability zones are closed islands separated by horizontal lines corresponding to cutting depths equal to multiples of the pitch of the helical cutter. The traditional chatter (Hopf) is not influenced by the helix. The existence of these zones has been experimentally validated.
The model has also been applied to conventional planning by studying the effect of the magnitude and direction of the feed on stability. For this purpose, an exponential force model is considered, which allows the variations of the specific shear force with the feed rate to be taken into account. The model has been linearized by means of a Taylor/McLaurin series expansion allowing advance-dependent stability diagrams to be obtained. The predictions obtained with this technique have been compared with simulations performed in the time domain, and an adjusted correlation is presented. Only in cases where the average directional coefficients are very low and the harmonics of these directional coefficients dominate, does the quality of these predictions decrease.
Finally, a new method has been proposed to characterise the dynamic stability of the universal milling machines. The proposal is based on the combination of four tests: measurement of dynamic stiffness throughout the workspace, simulation of the stability of standardised tests, experimental correlation using shear tests and modal analysis. The methodology is based on previous work, but its novelty lies in placing the stability simulation at the centre of the characterisation.