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Parametric vibrations of traveling plates and the mechanics of washboarding in bandsaws

University of British Columbia

This thesis presents a study on the high frequency dynamic behavior of traveling plates subjected to in-plane stresses. The effects of damping, parametric and modulated excitations on the vibration characteristics of the plates are considered. The application of this work to the explanation of the mechanisms responsible for washboarding in bandsaws is presented. A high frequency mode of a traveling plate is defined using the envelope of its mode shapes. Modal analysis of a traveling plate is conducted theoretically and experimentally. The effects of the traveling speed, the in-plane stresses and the plate geometry on the natural frequencies are examined. The self-excited vibration of a smooth band subjected to lateral regenerative forces is studied and the instability regions are determined. In order to model the tooth profiles and the moving lateral cutting forces applied at the teeth of a bandsaw blade, a finite element model is built and three moving plate elements are developed. The stability of the blade is investigated based on this model. The analytical results based on the smooth band model and the finite element model are consistent with the experimental results from modal testing. The vibration responses and stability of a damped spring-mass system and a damped smooth band subjected to both parametric and modulated excitations are investigated. The maximum magnification factor corresponds to the excitation at the lowest exciting frequency due to the effect of regenerative forces. The instability regions of this system are reduced by increasing damping or decreasing regenerative forces. A kinematic model of washboarding is built based on the loci of teeth so that a washboarding pattern can be simulated and the washboarding mode can be determined by decoding the pattern. Two types of washboarding patterns are observed in the cutting tests. Type I washboarding is explained as the result caused by the modulated and forced vibration due to the displacement excitations from the guides. Type II washboarding is caused by the self-excited vibration due to the regenerative cutting forces.

Thesis/Dissertation

application/pdf

2009-10-08

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http://hdl.handle.net/2429/13767

Mechanical Engineering

University of British Columbia

UBCV

DSpace