Control-Oriented Modeling of Thermal Deformation of Machine Tools Based on Inverse Solution of Time-Variant Thermal Loads with Delayed Response

With the new emerging technologies of high performance machining and the increasing demand for improved machining accuracy in recent years, the problem of thermal deformation of machine tool structures is becoming more critical than ever. The major problem in implementing real-time control systems is the difficulty of measuring the relative thermal displacement between the tool and the workpiece during machining. Therefore, the design of a generic multi-axis control system requires the development of control-based models to estimate the transient thermal load and the thermal deformation of the structure in real-time. To satisfy the stringent accuracy and stability requirements of the control system, a new inverse heat conduction problem IHCP solver is developed. This solution is capable of including the inertia effect and the delay in the thermal response, in order to accommodate situations where the measured points cannot be located near the heat source, which may be buried into the structure. Experimental validation of these models showed their inherent stability even when the temperature measurements are contaminated with random errors. The excellent computational efficiency of the integrated system, which is well suited for real-time control applications involving multi-dimensional structures, was achieved by incorporating an inverse numerical Laplace transformation procedure. 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.

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