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

Abstract

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 43 µm to 18 µm, 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.

Assignment of the cutting mode when boring holes on CNC machine

“…Approbation of the obtained results was carried out using a special program that allows you to calculate the response of the machining system in both time and frequency domains. When simulating in the time domain, a complete mathematical model of the system was used, taking into account positive feedback through the function of a delay argument, and when assessing stability according to the criterion [10], an open-loop system model was used (see Fig. 6).…”

“…Therefore, such a cutting mode is unacceptable and can lead to significant vibrations and even accidents. The graph of the Nyquist diagram for this mode of operation covers a point with coordinates [+1,0], which, according to the new stability criterion [10], leads to the loss of stability of the system with positive feedback through the function of the delay argument (Fig. 8, b).…”

“…The program uses an algorithm for searching for data arrays, the maximum depth of cut and spindle speed, which form a stability diagram of the machining system. The algorithm is based on a new criterion for the stability of systems with positive feedback loop through the function of the delay argument [10]. This is how the cutting process is presented, taking into account the machining along the trace, which is the main reason for the occurrence of regenerative oscillations in the machining system.…”

“…For further manipulations in order to determine the stability of MS in accordance with the new stability criterion proposed in [10], it is necessary to obtain the transfer function of a closed system (Fig. 6).…”

“…+ To construct a system stability diagram, the program [10] uses a new criterion for the stability of systems with positive feedback through the function of the delay argument. A system is stable if the graph of its Nyquist diagram does not cover the point with coordinates [+1,0] in the complex plane.…”