Active Time Delay Control For Cutting Vibration

Cutting is one of the most widely used material removal processes in the modernmanufacture industry. Vibration inevitably exists in the machine operation and is one of theimportant factors those limit the productivity and quality. How to reduce and control thecutting vibrations is an interesting topic which deserves more attention.In this effort, a delay differential equation is set up to describe the dynamics of turningprocesses based on classic cutting theory. It is pretty difficult to solve all the characteristicroots for retard equation of cutting processes due to the root quantity is limitless. Frequencydomain method is adopted in this paper to work out the stable region of feedback controlwith single time delay. Based on the stable region, numerical simulation is carried out todemonstrate the viability of the presented control method. The disadvantages are alsoelaborated in the paper. A multiple time-delay controller is developed based on discreteoptimal control method for turning vibration control which may overcome the weakness ofsingle time delay feedback control. The time domain simulations indicate the designedcontroller can suppress the cutting vibration efficiently and improve the stability of thecutting processes. The effect of the time lag on the control performance and control forceare also discussed. The control robustness is illustrated against the measuring error of timedelay.For the milling processes, we set a two-degree-of-freedoms system with time delayand periodic time-varying coefficients. Semi-discretization method is used to study thefeasibility of time-delay state feedback control. In order to avoid the trouble caused bytime-varying coefficients, we average them over one period which results the periodicdifferential delay equations (DDE) into DDEs with constant coefficients. An activecontroller with double time delays is presented according to the DDEs with constantcoefficient. The effects of the time delays on the control performance are discussed. Inaddition, we find the controller become invalid in the case of the milling processes loss ofthe stability through a period-doubling bifurcation. This problem can be solved in somedegree when the minimum control object is fixed on a constant instead of varying with thespindle speed as shown in the stability lobe diagram.