REAL-TIME ADAPTIVE MODELING APPROACH TO COMPENSATE THE THERMAL DEFORMATION OF NONLINEAR MACHINE TOOL STRUCTURES

ABSTRACT Machine tool structures cannot be fully optimized at the design stage to cover the wide range of operating conditions. Therefore, reliable control systems emerge as the logical solution to compensate for thermal errors. Due to the difficulty of measuring the relative thermal displacement δ between the tool and the workpiece during machining, δ has to be accurately estimated in real-time. A new concept of adaptive modeling is introduced to develop control-based dynamic models to predict and compensate for thermal deformation of nonlinear complex machine tool structures. A key element of this approach is to replace the changes in the contact pressures along the joint by fictitious contact heat sources FCHS. This allows us to track the system nonlinearity through temperature measurements and real-time inverse heat conduction IHCP solution. The proposed approach dealt successfully with a number of challenges; namely, the non-uniqueness of the problem, and the lack of sufficient conditions to identify each of such unusual FCHS separately. The results showed that the models are capable of satisfying the accuracy, stability and computational efficiency requirements, even when the temperature measurement signal is contaminated with random noise. The results also showed that the thermal deformation transfer function behaves as low-pass filters, and as such it attenuates the high frequency noise associated with temperature measurement error. KEYWORDS Nonlinear structures, machine tools, thermal deformation, control, compensation, inverse heat conduction INTRODUCTION Management of thermal effects associated with high cutting speeds and federates is a focal point for a number of emerging technologies; namely, high speed and high precision machining. The problem of thermal deformation of machine tool structures is becoming, therefore, more critical than ever. Control systems based on inductive and deductive approaches were developed over the years to circumvent the difficulty of measuring the relative thermal displacement vector δ(t) between the tool and the workpiece during machining. In the inductive approach, indirect displacement or temperature measurements In response to the problems associated with both the empirical and numerical approaches, the authors of this paper have recently introduced the theory of generalized modelling and proposed integrating it into a new control syste