Nowadays machine engineers heavily depend on mathematical models for simulation, optimization and controller design. In either of these tasks reduced dimensional formulations are obligatory in order to achieve fast and accurate results. Usually, the structural mechanical systems of machine tools are of second order type. However, they become descriptor systems when extra constraints are imposed to the systems. This article discusses efficient techniques of Gramian based model order reduction for second order index-1 descriptor systems. The primary focus is on second order to second order reduction techniques for such systems, where the stability of the system can be preserved. The methods are applied to a structural FEM model of a micro-mechanical piezo-actuators based adaptive spindle support (ASS). Numerical results illustrate the efficiency of the techniques.