Chatter suppression with productivity improvement by scheduling a C³ continuous feedrate to match spindle speed variation

Available spindle speed variation (SSV) methods, which are used to suppress regenerative chatter through disrupting the phase relationship between the inner and outer modulation on the machined surface, are usually performed in conjunction with the periodically varying feeds per tooth from the originally given constant feedrate. This article presents a new feedrate scheduling algorithm to match the SSV so that feed per tooth can be maximized during the whole machining. Concretely, a sinusoidal profile of feedrate is scheduled to match the designed SSV, meanwhile, the C³ continuous condition is guaranteed within all kinematic constraints. The feedrate is scheduled as two parts, i.e. a jerk continuous acceleration profile with the constant feedrate and a continuous sinusoidal profile above the constant feedrate. The continuity of the junction between these two parts is achieved through scheduling a gradually varying sinusoidal profile. To guarantee the kinematic constraints, the derivatives of the sinusoidal amplitude variation are obtained by the properties of trigonometric functions. As a result, a constant feed per tooth, which actually corresponds to the maximum of the periodically varying feeds per tooth associated with all existing SSV methods, is obtained, while the speed still periodically varies. It proves that the proposed scheduling algorithm can improve the machining efficiency since the feed per tooth is kept at the maximum level in most machining periods, and this is a great advancement over all existing SSV methods. Experiments confirm that chatter can be well suppressed with the significantly reduced machining time by using the proposed method.