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The mechanics of bandsaw cutting

Mechanik des Bandsägens. Teil II: Simulation des Sägeverhaltens einer Bandsäge

Part II A Simulation of the Cutting Behavior of Bandsaws

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Abstract

A numerical model, developed in Part I of this paper, is used to investigate the effect of band saw variables on cutting accuracy. The effect of blade parameters upon tooth tip stiffness is examined and the response of a blade cutting through an idealized knot is considered in detail. In particular, the effect of side clearance is examined. Using a cutting force model based upon a Brownian function representation of the cutting forces, nondimensional variables are developed that govern the cutting accuracy predicted by the model. Finally, the question of choosing an optimum side clearance, to minimize fibre loss is considered.

Zusammenfassung

In Teil I dieser Arbeit wurden die Grundlagen eines Bandsägemodells entwickelt. Dieses Modell wird hier angewendet, um den Einfluß der Bandsägenparameter auf die Schnittgenauigkeit zu untersuchen. Ihr Einfluß auf die Steifheit der Sägezahnspitzen wird analysiert und die Reaktion des Sägeblattes beim Schneiden eines Modellastes wird ausführlich dargestellt. Insbesondere werden die Auswirkungen unterschiedlicher Größen des Freischnitts (Schrankgröße) auf das Sägverhalten untersucht. Ein Modell der Schneidekräfte wurde in Analogie zur Brown’schen Bewegungsfunktion entwickelt. Daraus wurden dimensionslose Variablen abgeleitet, welche die Schnittgenauigkeit steuern und voraussagen lassen. Schließlich wird die Frage diskutiert, wie ein optimaler Freischnitt zu bestimmen ist, der die Menge an, Sägemehl bzw. den Substanzverlust minimiert.

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Abbreviations

Dc :

depth of the cut

e:

component of the cutting force about the mean force

f:

frequency in cycles per second; force acting on a tooth

\(\bar f\) :

mean lateral cutting force

k:

stiffness

Keq :

equivalent tooth-tip stiffness

Ko, Qo :

effective tooth-tip stiffness

Ktt :

tooth-tip stiffness of a single tooth

m:

average cutting force at an instant in time

NT :

number of teeth in the cut

p:

planer allowance

p:

tooth pitch

{P}:

Load vector for Galerkin formulation

s:

side clearance

Sit :

cut path at the i-th increment into the cut for the t-th tooth

So :

standard deviation of blade deflection when no contact occurs

Se :

standard deviation of e

Sf :

standard deviation of the cutting forces

Sm :

standard deviation of m

ST :

standard deviation of blade deflection when contact occurs

T:

bandmill strain (axial preload)

\(\bar x\) :

mean tooth deflection for a cut

xT :

tooth-tip deflection

z:

a Gaussian random number; probability variable

Zo :

nondimensional clearance gap

α:

factor relating ST to σT

λ:

wave length; eigenvalue

μ:

mass per unit area

σB :

standard deviation of the between-board thickness; stress due to inplane bending

σc :

stress in center of the blade due to tensioning

σG :

gullet stress

σR :

roll tensioning stress at the edges of the blade

σW :

standard deviation of the within board thickness

σT :

standard deviation of the total board thickness; stress due to bandmill strain

σx :

axial stresses a stationary blade

ω:

frequency in radians per second

References

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  • Lehmann, B.F. 1995: The Cutting Behaviour of Hand Saws, Ph.D. Thesis, Department of Mechanical Engineering, University of British Columbia, Vancouver, British Columbia, Canada

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  • St. Laurent, A. 1971: Influence des noeuds sur les forces de coupe dans le sciage du bois, Canadian Journal of Forest Research, 1, 43–56

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  • Taylor, J.; Hutton, S.G. 1991: A Numerical Examination of Bandsaw Blade Tooth Stiffness, FORINTEK Canada Report, 17 pages

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Author information

Authors and Affiliations

  1. Thin Kerf Technologies Inc., 5454-192nd Street, V3S 8E9, Surrey, B. C.

    B. F. Lehmann

  2. Department of Mechanical Engineering, The University of British Columbia, V6T IZ4, Vancouver, B.C., Canada

    S. G. Hutton

Authors
  1. B. F. Lehmann
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  2. S. G. Hutton
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Additional information

The work reported in this paper was funded by the Science Council of British Columbia and MacMillan Bloedel Research

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Lehmann, B.F., Hutton, S.G. The mechanics of bandsaw cutting. Holz als Roh- und Werkstoff 55, 35–43 (1997). https://doi.org/10.1007/s001070050221

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  • DOI: https://doi.org/10.1007/s001070050221

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