A time-frequency approach to ensuring stability of machining by turning

This paper reports a new approach to ensuring the stability of the turning process, which is based on the frequency-time characteristics of the technological machining system (TMS). The approach uses a mathematical model of the turning process as a single-mass system with one degree of freedom, taking into account negative feedback on the normal coordinate and positive feedback with a delay in cutting depth. A new criterion for the stability of the cutting process as a system with a delay in positive feedback is proposed, based on the analysis of frequency characteristics in the form of a Nyquist diagram. It is proved that such a system will be stable when the chart of its Nyquist diagram does not cover a point with coordinates [+1, 0] on the complex plane. The validity of the new criterion has been confirmed by comparing the simulation results in the time range with the location of the Nyquist diagram on the complex plane. Based on the new criterion of stability, an algorithm for automatic construction of a Stability Lobes Diagram (SLD) has been developed. The necessary a priori parameters of TMS, the ranges of frequency change, and the calculation step for constructing such a characteristic in the coordinates "cutting depth – spindle rotational speed" have been determined. The adequacy of the obtained results is confirmed by a full-scale experiment to assess the roughness of machined parts under cutting modes that fall into the area of stability and instability on the SLD chart. The full-scale experiment proved the possibility of a significant reduction in roughness according to the Rz parameter, from 43µm to 18µm, while increasing productivity by 1.28 times. The use of a stability lobes diagram is especially effective when programming CNC lathes where it is possible to select the spindle speed in a wide range