Vibration of bandsaws
Thesis DisciplineMechanical Engineering
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
The aim of this thesis was to investigate the vibrational characteristics of wide band bandsaws. Firstly, the vibration of bandsaw structures was considered. A computer program was developed to predict the natural frequencies and mode shapes of three dimensional structures, consisting of beams, springs, viscous dampers, concentrated masses, and gyroscopic rotors. The method used was the dynamic stiffness method. Some of the vibrational characteristics of the bandsaw structure were then established from experimental results and results obtained from the computer program. The gyroscopic effects on the bandsaw structure due to rotating pulleys were also examined. Secondly, the dynamic stiffness method was used to solve the moving beam problem. The moving beam had been used previously to model the bandsaw blade. The dynamic stiffness method allowed complex problems to be analysed in a systematic manner. A moving beam proved to be too crude a representation of a wide bandsaw blade at the level of detail being investigated. Therefore, attempts were made to model the dynamic behaviour of wide bandsaw blades with moving plates. A general approach to the solution of the moving plate problem is presented in this thesis, it uses the extended Galerkin method to discretise the partial differential equation of motion and the boundary conditions into a quadratic eigenvalue problem. The solutions for this problem were obtained by using a linearisation technique. The effects of in-plane stresses on bandsaw blades are considered in this thesis. Three cases are examined; a linearly distributed stress across the width of the blade due to wheel-tilting and/or backcrowning, a parabolic distributed stress across the width of the blade due to prestressing, and stresses induced by tangential cutting forces. Parametric instabilities due to fluctuating tension, and due to periodic tangential cutting forces were investigated. The harmonic balance method was used on the discretised form of the moving plate equation to obtain the required instability regions. Finally, the dynamic instability of a moving plate due to a nonconservative component of the tangential cutting force was considered. The method of solving this nonconservative problem was the same as that used to solve the conservative case.