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|Title: ||Tension variations in pliable material in production machinery|
|Authors: ||Whitworth, David P.D.|
|Issue Date: ||1979|
|Publisher: ||© D.P.D. Whitworth|
|Abstract: ||Many production machines are used in which flexible material is processed. In these machines, cyclic tension variations can
be induced in the material by interaction with the machine components.
At resonance, these variations can be large and may result in
breakage or distortion of the material. It is important to determine
these resonant frequencies, and their dependence on the machine
parameters, to help avoid these problems at the machine design stage.
A mathematical model of such machines has been developed.
Materials with linear elastic and linear visco-elastic tensile
properties have been considered. The effects of friction between
material and guide rollers have been included. A numerical method
has been used to solve the resulting differential equations. This
method gives accurate results even when adhesion between the material
and some machine components is lost.
By assuming the tension perturbations proportionately small,
an approximate linear model was derived. It was found to give resonant
frequencies close to those predicted by the non-linear model, but
gave less accurate estimates of the amplitudes at resonance.
For the linear model orthogonality relations for the eigenvectors
were derived. Using these relations expressions were obtained which
are first order approximations to the amplitudes of oscillation at
resonance. The amplitudes are related to the angles of wrap round
the rollers and, in the visco-elastic case, to the loss factor of
the material. In addition, the expressions
determine how the amplitudes
are related to the position of the corresponding span in the system. Expressions were also found using perturbation theory. They give
the local variation of the resonant frequencies with respect to
the span lengths and moments of inertia of components of the
system. These relations are used to carry out an analysis of
certain types of system.
Experimental work has been carried out, using a closed loop
of material, to test the predictions of the mathematical model.
A variety of materials was used with several different systems
of rollers. In general, the results show that the resonant
frequencies detected corresponded closely with those predicted,
but the amplitudes tended to be over-estimated. Finally a programme
of work was carried out on a production machine, and the results
compared with model predictions.|
|Description: ||A Doctoral Thesis. Submitted in partial fulfillment of the requirements for the award of Doctor of Philosophy of Loughborough University.|
|Appears in Collections:||PhD Theses (Mechanical, Electrical and Manufacturing Engineering)|
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