No abstract

This paper proposes a strategy of optimizing temperature sensor placement for thermal error compensation based on dynamic characteristics of temperature field and thermal deformation of a machine tool structure. A simple example of one-dimensional thermal expansion is given to signify the importance of sensor placement to the accuracy and robustness of thermal error modeling. Time and frequency domain analyses of optimal sensor placement are carried out for the simple one-dimensional thermal expansion and then extended to more complex two and three-dimensional thermal expansions. To apply the strategy to a machine tool, a new method of analyzing machine tool thermal errors called thermal deformation chain analysis is proposed to predetermine the sensor locations on a machine tool structure. The method is very effective in identifying thermal error contributors and their significance, and has been proven to be efficient in choosing sensor locations on a turning center.

Thermal loads of internal and external sources cause thermal deformations of a machine tool structure and affect its accuracy. Software-based real-time error compensation method is an effective way to reduce the thermal errors. However, lack of knowledge of thermal loads impedes greater success. In this paper, a method of inverse heat transfer analysis is developed that, using temperature measurement data from multiple sensors mounted on a machine tool structure, the transient thermal loads of multiple heat sources can be estimated simultaneously. The method uses modal method and is carried out in frequency domain. The temperature measurement data are first transformed into frequency spectra through DFT. The modal method of inverse frequency response analysis is then used to obtain the thermal load spectra. Finally the thermal loads are recovered from their spectra through IDFT. The estimated thermal loads play crucial roles in estimating transient temperature fields and transient thermal errors of a machine tool structure. The issues of mode truncations and frequency truncations, and their effects on the efficiency and stability of the method are also discussed with simulation results. Finally, experimental results on a machining center column are presented.