Sensor placement optimization for thermal error compensation on machine tools

One of the most significant factors affecting the accuracy of machine tools is thermal error. Thermal error compensation can potentially be an effective way to reduce thermal errors. However, lack of accuracy and robustness of thermal error modeling prevents thermal error compensation from achieving greater success. This thesis proposes a novel methodology for improving the accuracy of thermal error modeling through optimizing temperature sensor placement. It addresses the question: Given a limited number of temperature sensors, where should they be placed on a spatially distributed machine tool structure so that the temperature data from those sensors will give the best estimation of the thermal errors?; A thermal deformation modal analysis method is proposed to analyze the transient temperature fields and thermal deformations of a machine tool structure. Natural time constants and temperature field mode shapes can be computed from transient heat transfer finite element models through eigen-analysis. Thermal deformation and thermal error mode shapes can be computed from thermoelastic finite element models.; A modal frequency domain method of inverse heat transfer analysis is also proposed. From temperature measurement data from multiple sensors mounted on a machine tool structure, transient thermal loads of multiple heat sources can be estimated simultaneously. With mode truncation and frequency truncation, both efficiency and stability of the method can be improved.; The temperature sensor placement optimization problem is formulated as a two-level optimization model. The first level is a sensor location optimization problem and is formulated as a discrete programming model. The second level is a thermal error model parameter optimization problem and is formulated as a nonlinear programming model. The minimax goal programming approach is applied to formulate the objective function. A hybrid genetic algorithm combining the advantages of both the cyclic local search algorithm and the genetic algorithm is developed. The methodology is applied to a machining center column assembly. Experimental results prove that the optimized sensor location set improves the accuracy and robustness of thermal error modeling.