Friction-Induced Effects on Band Saw Blade Lateral Dynamics: A PDE-Based Tribological Model

Abstract

The lateral dynamics of a band saw blade during cutting is investigated using a distributed-parameter model that combines mechanical and tribological effects. The active blade span between two lateral guides is represented as a tensioned continuous system governed by a damped wave equation, while cutting is introduced through a localized feed-speed-dependent force. Friction is modeled by an effective Coulomb-type term F_f=µF_N, with a constant representative normal contact force. The governing equation is solved using an explicit finite-difference scheme. Simulations without friction show bounded oscillatory motion dominated by the harmonic component of the cutting force, whereas feed speed has only a minor influence. For F_N=200 N, the maximum displacement increases from 0.213 mm at µ=0 to 1.036 mm at µ=0.6, corresponding to an approximately five-fold increase. The dependence on µis nearly linear, as expected from the adopted friction law. For a guide spacing of L=0.31 m, the predicted displacement well agrees with experimentally reported values for a comparable band-saw configuration. The results show that frictional conditions and guide spacing strongly influence lateral deflection and may therefore affect cutting accuracy. The model provides a transparent framework for parametric analysis, while machine-specific prediction requires experimentally calibrated contact parameters.