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Parametric excitations of a traveling beam and the washboarding problem in bandsawing Dalziel, Michael


This thesis is investigates the effect of primary cutting parameters and simple bandsaw blade geometry on the occurrence and severity of Type I washboarding in bandsaws. The mechanisms causing Type I washboarding are not currently well understood. To achieve a better understanding of the problem, both an analytical approach dealing with parametric axial excitations of a traveling beam, and an experimental approach are undertaken and the results of both studies are compared. The effect of in plane axial blade loading on a simple traveling beam model is examined. The governing differential equations of motion contain parametric stiffness terms that require the use of a perturbation method for an approximate solution. The perturbation method used in this work is the method of multiple scales. In one blade model, the effect of axial tension fluctuations at the tooth passing frequency due to fluctuations in the total axial cutting load is studied. In the second model, the effect of low frequency axial tension fluctuations in combination with a lateral excitation at the tooth passing frequency is studied. The second model gives response characteristics very similar to those seen in experimental cutting tests including a response at the tooth passing frequency and a response below the tooth passing frequency by an amount equal to the low frequency axial tension fluctuation. Cutting test data is examined to determine the pertinent response characteristics during Type I washboarding. It is found that two main components of response lead to Type I washboarding; a response at the tooth passing frequency and one at a frequency slightly lower than the tooth passing frequency. The behavior of these two responses with changes in primary cutting parameters is very similar to what is predicted by the second traveling beam model

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