Research on Optimization of Height Difference of a Precision Horizontal Machining Center

This work proposes a methodology to determine the height difference of the guideways of machine tools where two guideways are not placed on the same horizontal plane. Firstly, a rigid-flexible coupling system consisting of a moving rigid mass and an elastic overhanging beam is presented as an equivalent mechanical model of a column and a spindle box. Then, the relationship between the deviation of a reference point and the height difference or the spindle box's stroke is modeled. Next, the natural frequency and mode shape function of the overhanging beam, and the frequency response functions of the coupling system, are derived. The results indicate that there always exists an optimal height difference minimizing the relative deflection over the stroke of the moving part, and the optimal value depends on the loads in two directions and the stroke of the moving part. Similarly, there is also an optimal choice maximizing the first-order resonant frequency of the coupling system; however, the optimal solutions for both static and dynamic cases are not the same. This work provides beneficial instruction for choosing the height difference of machine tools with two guideways on a bed that are not on the same plane.