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UBC Theses and Dissertations

Flutter instability speed of guided splined disks, with applications to sawing Mohammadpanah, Ahmad


In this thesis the vibration characteristics of guided splined saws are studied, both analytically and experimentally. Significant insights into the complex dynamic behavior of guided splined saws are presented by analytical investigation of the dynamic behaviour of spinning splined disks and then by conducting idling and cutting experimental tests of guided splined saws. Cutting tests are conducted at different speeds, at critical, supercritical, and post flutter speeds of a guided splined saw. The cutting results are compared to determine the stable operation speeds for guided splined saws. For the analytical studies, the governing linear equations are derived for the transverse motion of a constant speed spinning splined disk. The disk is subjected to lateral constraints and loads. Rigid body translational and tilting degrees of freedom are included in the analysis of total motion of the spinning disk. Also considered in the analyses are applied conservative in-plane edge loads at the outer and inner boundaries. The numerical solution of these equations is used to investigate the effect of the loads and constraints on the natural frequencies, critical speeds, and stability of the spinning disk. The sensitivity of the eigenvalues of the splined spinning disk to the in-plane edge loads is analyzed by taking the derivative of the spinning disk’s eigenvalues with respect to the applied loads. This analysis contains an evaluation of the energy transfer from the applied loads to the disk vibrations and is used to examine the role of critical system components in the development of instability. Experimental results are presented that support the validity of the analysis. The experimental results indicate that flutter instability occurs at speeds when a backward travelling wave of a mode meets a reflected wave of a different mode. The maximum stable operating speed of the rotating splined disk is defined as the initiation of flutter. Flutter instability speeds of splined saws of various sizes were computed and verified experimentally. Then flutter speed charts of splined saws were developed which provides primary practical guide lines for sawmills to choose optimum blade diameter, eye size, blade thickness, and a stable rotation speed.

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