A simple to apply, two-step observer design methodology is developed for a general class of systems with model uncertainty. This approach is applied to estimate bearing internal temperatures and the bearing preload of a machine tool spindle. The first step is the design of a model error compensator (MEC) to account for the model error associated with the bearing friction heat generation. The second step includes a conventional observer based on the nominal model that results from the implementation of the MEC. The sufficient condition for constructing an effective MEC loop for the target spindle system is derived. The effectiveness of the MEC loop is demonstrated experimentally by comparing several different conventional observer designs, with and without the MEC. A comparison of the measurements to the estimation results indicate in all cases tested the MEC improves the performance of the conventional observers. In addition, the results clearly show the distinctly different bearing outer ring/housing, rolling elements, and inner ring temperature behaviors. From the temperature estimation results, it is shown that previously published data on initial transient error associated with preload estimation is mainly due to the estimation error in the rolling element temperature. The proposed two-step observer methodology appears to be well suited for bearing temperature and preload monitoring problems.

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