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The mechanics of bandsaw cutting

Mechanik des Bandsägens. Teil I: Beschreibung der Wechselwirkungen zwchen Bandsäge und Werkstück

Part I: Modelling the Interactions Between a Bandsaw Blade and the Workpiece

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Abstract

This paper presents the development of a mathematical model designed to predict the effect of bandsaw variables upon cutting accuracy. New developments contained in the model are the explicit consideration of contact between the body of the bandsaw and the sawn surfaces of the wood and the representation of cutting forces in terms of Brownian motion functions. The model allows consideration of blade geometry, bandmill strain, tensioning stresses, blade speed, bandmill strain characteristics, blade speed, and side clearance.

Zusammenfassung

Ein Modell wird vorgestellt, das den Einfluß der Bandsägenparameter auf die Schnittgenauigkeit voraussagen kann. Die Neuentwicklung des Modells besteht zum einen darin, daß der direkte Kontakt zwischen Sägeblatt und Werkstück mit einbezogen wird, zum anderen, daß zur Darstellung der Schneidekräfte das mathematische Modell der Brown’schen Bewegungen herangezogen wird. Das Modell erlaubt Aussagen über folgende Parameter: Blattgeometrie, Sägespannung, Spannungsverformungen, Blattgeschwindigkeit, Spannungscharakteristik und Freischnitt.

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Abbreviations

b :

blade width

c :

blade speed

d :

tooth depth; difference between s and g

C :

knot cutting force coefficients

D :

plate bending stiffness=Eh3/12(1−ν2)

D c :

depth of the cut

e :

component of the cutting force about the mean force

E :

Young’s modulus

E mn(y):

shape functions of blade deflection

f :

frequency in cycles per second; force acting on a tooth

\(\bar f\) :

mean lateral cutting force

f c :

filter cutoff frequency

F :

lareral force on the blade

F L :

lateral cutting force

g :

clearance gap

[G] :

gyroscopic matrix

h :

plate thickness

k :

stiffness

[K] :

stiffness matrix

K eq :

equivalent tooth-tip stiffness

K o, Qo :

effective tooth-tip stiffnesses

K t :

bending stiffness of a tooth

K it :

tooth-tip stiffness of a single tooth

L :

span between the guides

m :

average cutting force at an instant in time

[M] :

mass matrix

N T :

number of teeth in the cut

p :

planer allowance

P :

tooth pitch

{P} :

Load vector for Galerkin formulation

q(x, y, t) :

lateral loading per unit area

r :

distance from the center of a knot

s :

side clearance

{S} :

Generalized coordinates for Galerkin formulation

S it :

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

S o :

standard deviation of blade deflection when no contact occurs

S e :

standard deviation of e

S f :

standard deviation of the cutting forces

S m :

standard deviation of m

S T :

standard deviation of blade deflection when contact occurs

t :

time

T :

bandmill strain (axial preload)

U, V :

sawn surfaces

w(x, y, t) :

lateral blade deflection

(x, y, z) :

coordinates on the blade

\(\bar x\) :

mean tooth deflection for a cut

x T :

tooth-tip deflection

z :

a Gaussian random number; probability variable

Z o :

nondimensional clearance gap

α:

factor relating S T to σ T

ε:

a small lever arm

κ:

strain system parameter

λ:

wave length; eigenvalue

μ:

mass per unit area

ν:

Poisson’s ratio

σ:

density

σ B :

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

σ c :

stress in center of the blade due to tensioning

σ G :

gullet stress

σ R :

roll tensioning stress at the edges of the blade

σ W :

standard deviation of the within-board thickness

σ T :

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

References

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Author information

Authors and Affiliations

  1. Thin Kerf Technologies Inc, 5454-192nd Street, V3S 8E5, Surrey, B. C.

    B. F. Lehmann

  2. Department of Mechanical Engineering, The University of British Columbia, V6T 1Z4, 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 54, 423–428 (1996). https://doi.org/10.1007/s001070050214

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  • DOI: https://doi.org/10.1007/s001070050214

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