Numerical analysis of vibrations of a moving blade in a narrow lubricated gap under parametric and follower load excitations

Abstract

Abstract A planar fluid–structure-interaction problem inspired by metal bandsawing is considered. The model consists of a blade that is moving through a narrow fully lubricated gap and subjected to axial parametric excitations and distributed follower loads. The blade is modelled as an unshearable beam. One-dimensional, incompressible Reynolds lubrication theory governs the accompanying quasi-hydrostatic fluid problem. A Hermitian finite element model is used to discretize the coupled variational problem in space. Linear modal analysis, numerical time-integration procedures of time-periodic boundary value problems and continuation techniques are utilized to estimate the effect of the fluid lubrication film on linear dynamics and in cases of self-excited vibrations and parametric excitation. The mechanical capacity of the fluid film is characterised by the dimensionless effective viscosity, which induces significant damping of the primary vibration modes; small internal damping of the bending blade is considered as well. The study highlights the theoretical and as-yet unexploited potential of a fully established lubrication film for cutting processes.