Static and dynamic analysis of a large linear motion guide rail grinding machine

Rail grinding machines for linear motion guides combine a feed stroke of more than 10 m with a micrometre-level straightness requirement, for which the machine structure matters as much as the grinding process. This paper presents a structural finite element analysis of such a machine with a 12 m bed, in which the supporting feet are modelled by the load-dependent contact stiffness of the metal-concrete interface and the guides by equivalent stiffness and damping. Static analysis shows that the bed deflection is governed by the arrangement of the supports as well as their number, and that the travel of the heavy table produces a straightness error of about 9 µm at the grinding point. Modal analysis yields 10 natural frequencies between 42.9 and 108.6 Hz, dominated by bending of the spindle columns and bed torsion. Harmonic responses at the spindle housings agree with impact-test measurements for the dominant modes at 58.8 and 76.7 Hz. Transient analysis shows that the feed acceleration excites the modes at 46.1 and 87.0 Hz and displaces the side grinding spindles by about 1.2 µm in the Z direction. The validated model gives design guidelines for the support arrangement, spindle speeds and feed acceleration profile.