Finite element modal analysis of moving bandsaw blades using incremental rod theory with consideration of the pre-stress distribution in the cross section

Abstract

Machining operations are susceptible to different kinds of adverse dynamic phenomena. This is especially true for the band sawing process with its slender endless-moving blade that may exhibit forced oscillations, self-excited vibrations, or even torsional flexural buckling under high load magnitudes. Current research primarily focuses on the cutting of metal slabs and is motivated by the need to improve the surface quality of the cut, to increase productiv- ity, to minimize scrap, and to reduce tool wear. In the present study, a mechanical model that accurately captures the dynamics of the moving blade under different working conditions is developed and verified by comparison against physical experiments. The bandsaw blade is modelled as an unshearable Kirchhoff rod with a thin rectangular cross-section. Linear modal and buckling analyses are performed with the incremental rod theory of second order that accounts for axial pre-tension and pre-twisting of the blade. This pre-twist is imposed by the tilting angle between the linear blade guides and the wheels of the drive system. A large pre-twist occurs when the wheel axes are deliberately not in parallel to the plane of the cut surface as is typical for horizontal bandsawing. Due to the Wagner effect, pre-tensioning and pre-twisting alter the effective torsional behaviour owing to the non-trivial uniaxial stress distribution over the width of the rectangular blade cross-section. The torsional rigidity of the rod must be modified accordingly. Forces in the cut are approximated by prescribed distributed loadings allowing for an estimation of how the load affects the modal spectrum of the blade; both follower and dead loadings are considered. The model may be extended in the future with respect to the tool-workpiece interaction in order to capture self-excited vibrations due to regenerative chatter. A non-material finite element model is implemented to compute actual numerical solutions and perform parameter studies. Numerical results are further compared with experimental measurement data for certain parameter configurations to empirically justify the simulation model.