A. G. Ulsoy Assistant Professor, Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, Mich. 48109 Assoc. Mem. ASME CD. Mote, Jr. Professor, Department of Mechanical Engineering, University of California, Berkeley, Calif. 94720 Mem. ASME Vibration of Wide Band Saw Blades The vibration and stability of wide band saw blades is investigated using an axially moving plate model which includes the effect of in-plane stresses upon stiffness. The equation of motion is developed from Hamilton's principle, and approximate solutions are obtained using both the classical Ritz and finite element-Ritz methods. Experimental results from a large-scale band saw are presented and show good agreement with the results of the approximate analyses. Analytical results are presented which show the contributions of axial velocity, the wheel support system, blade damping, transverse forces, and in-plane stresses to band vibration and stability. The implications of these results for optimizing the band saw design are also indicated. 1 Introduction The band saw vibration problem belongs to a class of problems referred to as axially moving material vibrations [1] that encompasses many diverse technologies, such as moving fibers and threadlines, transmission belts and chains, pipes transporting fluids, magnetic and paper tapes, and, of course, band saws. It is usual in these problems for the material vibration to be detrimental to design function. In band saws, and particularly in large band saws, vibration results in wastage of raw material, reduced tool life, and poorer dimensional accuracy and surface quality in the product. For all intents and purposes band vibration only degrades the process, sometimes catastrophically, but nearly always significantly. A review of the research on band saw vibration, published in 1978, summarized the state of our understanding [2], The earliest work focused on two problems. First, the inclusion of the transport velocity in the vibration analysis of strings and beams in axial motion was completed, and, second, the dependence of the band tension upon the system used to support the band wheels was clarified [3, 4]. The material frequencies of transverse motion are always reduced with increasing transport velocity at a rate depending upon this wheel support system. Parametrically excited transverse vibration occurs when the tension variation frequently is twice any natural frequency, and especially the lowest few natural frequencies, as expected from classical theory [5,6], The edge buckling load decreases significantly with increasing axial velocity in pure torsional and in coupled transverse-torsional motion [7, 8, 9]. The results of vibration experiments on a narrow bladed table band saw showed excellent agreement with exact and approximate natural frequency analyses of an axially moving beam at low to moderate axial velocities [10]. The dynamics of large scale, wide band saws, similar to those in saw mill applications, are not represented by the Contributed by the Production Engineering Division and presented at the Winter Annual Meeting, Washington, D.C., November 15-20, 1981, of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS. Manuscript received at ASME Headquarters, June 18,1981. Paper No. 81-WA/PROD-15. Fig. 1 Band coordinates and geometry models analyzed through 1978. Large bands are axially moving plates with membrane stresses dependent upon edge loading, thermal effects, and purposely induced initial stresses. Their motion is constrained by moveable hydrodynamic pressure guides (bearings) as shown in Fig. 1. The adequacy of their design for processing is closely tied to the contributions of the membrane stresses to band vibration, though this relationship has yet to be addressed. The coupled transverse and torsional vibration of large- scale band saw blades, including the effects of typical in-plane stresses, is analyzed in this paper. Hamilton's principle is used to develop the equation of motion. Two direct variational methods, the classical Ritz and the finite element-Ritz, are used to formulate approximate solutions. The analytically determined natural frequencies compare favorably with those determined experimentally. The results confirm the sensitivity of the band vibration spectrum to the presence of membrane stresses. Journal of Engineering for Industry FEBRUARY 1982, Vol. 104/71 Copyright © 1982 by ASME Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/ on 11/17/2014 Terms of Use: http://asme.org/terms