A N AIR - POLYMER ANALOGY FOR MODELING AIR
FLOW THROUGH RUBBER - METAL INTERFACE –
T ECHNICAL NOTE
GILAD PAGI , ELI ALTUS
T ECH NICAL R EPORT ETR-2007-02
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An air-polymer analogy for modeling air flow through rubber-metal interface – Technical note
GILAD PAGI, ELI ALTUS
Faculty of Mechanical engineering
Technion – Israel Institute of Technology
Abstract: - This note compliments the technical part of the paper with the title, which will be presented in the WSEAS FMA’07 conference. This note presents the mechanical design of the system in question and more experimental findings which support the assumption of the novel model constructed there. Moreover, this note contains first conclusions and preliminary discussions.
A system composed of a metallic cylinder filled with pressured air (up to 5 atm), and a rubber, square sectioned ring, as a seal was investigated theoretically and experimentally. Under a certain pressure difference (internal minus atmosphere pressure - p) and external sealing force, the rubber seal is compressed (h) and should prevent air leakage. However, experiments show a continuous, nonlinear decrease in p(t) as a function of time. A few classical (macro) thermodynamic models for predicting p(t), via considering air flow through cracks, have been suggested before, based on  but they have failed to describe the profile in question due to the coupled constitutive properties of rubber and a construction that allow the creation of micro-scale "tunnels" in the rubber-lid interface, through which the air can pass. A novel heuristic model, which assumes a symmetry preserving analogy between the micro-scale air tunnels and the rubber polymer strands is proposed. Thus, polymer equations based on statistical thermodynamics are applied on the air streamlines. Using this model, there are four unset parameters whose values are being determined by the experimental profiles, similar to the semi-phenomenological rubber model of Mooney-Rivlin. An excellent correspondence between the model and the experimental data is achieved, which suggests that the model captures the physical essence of the phenomenon. Many standard trendlines have been tried and failed to describe p(t) accurately, including 3rd order polynomial which has also four parameters. Key-Words: - Sealing, Pressure drop, Air leakage, Air-Polymer analogy, Polym-Air, Micro-Macro, Langevin. describing air flow through cracks are available in
, , but those have to be adjusted to describe air
flow through rubber-metal interface.
In the following note we will describe the
experiment set mechanical design and the final
system configuration itself. Moreover, we will
mention some results regarding the experiment.
An air pressure vessel (up to 5atm) is composed
of a metallic cylinder and a cover, and sealed with a
rubber, square sectioned ring, as seen in Fig.1.
Under a certain pressure difference (internal minus
atmosphere pressure - p) and external sealing force,
the rubber seal is compressed (h) and should prevent
air leakage. However, experiments show a
continuous, nonlinear decrease in p as a function of
time for small values of h (up to 20% of the initial
vertical dimension – h0).
A few classical (macro) thermodynamic models
for predicting p(t), by describing air flow through
cracks (of heat regenerator for example) , have been
previously suggested () but they have failed to
accurately describe the profile in the following
specific setup due to the coupled constitutive
property of rubber and a construction that allows the
creation of micro-scale "tunnels" in the rubber-lid
interface, through which the air can pass. A few
more mathematical and physical models of
2 Experiment Setup
2.1 Introduction and...
References: matrix regenerators, International Journal of
Heat and Mass Transfer, No.48, 2005, pp
cracks, International Journal of Pressure Vessels
and Piping, No.82, 2005, pp
No.26, 2003, pp. 1069-1079, 2003.
 B. Erman, J.E. Mark, Structures and Properties
of Rubberlike Networks, Oxford, 1997
Polymer Networks, Macromolecules, No. 36,
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