Technical Configuration of Mechanic System

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 [1] 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 alarm 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-Rivaling. An excellent correspondence between the model and physical essence of the phenomenon.

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Many standard trendiest 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, Polyp-Air, Micro-Macro, Language. Ascribing air flow through cracks are available in [2], [3], 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. 1 Introduction An air pressure vessel (up to ATM) is composed of a metallic cylinder and a cover, and sealed with a rubber, square sectioned ring, as seen in Fig. L . Under a certain pressure difference (internal minus atmosphere pressure - p) and external sealing force, he 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 of the initial vertical dimension - ho).

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. Introduction and Targets Consider the axis-symmetric setup where the inner pressure is set to a constant value, which is different from the atmospheric pressure (fig. 1). The "Force" preventing from the piston to pop up and also causes the rubber seal (black) to be subjected to unsocial compression. Thus, the vertical length - originally ho - decreases to a controlled value h. Once deformed enough, the seal prevents leakage of air from the inside. Note that thanks to the upper airway the outer surface of the seal is subjected to the time measure. . 2. 1 Variables and their measuring methods p - with a computerized pressure gage installed as part of the cylinder.. Ho (free vertical dimension of the rubber sample) - with a micrometer h (current vertical dimension of a rubber sample) - using LIVED that track the displacement of the piston from its free force position. T (time)- by the computer clock. T (the temperature of the gasket or air) - with a thermocouple installed as a part of the cylinder. Only for additional data collecting proposes, not a controlled variable.

The main target is to investigate the pressure vs.. Time p(t) profile. The seal's function, is to preserve the pressure difference p=P-Pa between the two gasket sides. We'd like to observe how the magnitude of the initial pressure difference and the controlled deformation influence on the profile. The mechanism of air leakage through the seal is yet to be determined but when diffusion is neglected one can presume that the air flows through the rebuttal interface. Our initial assumption is that air flows through narrow cracks-like interracial passages.

The assumption about the diffusion arises from mineral notion about the characteristic time of gas diffusion through rubber in various applications, which is much larger than these experiments periods (about 1000 seconds). For example, based on [4], the pressure drop in 1000 seconds via diffusion in an UN-defected aircraft tire having similar pressure difference is 0. 06% at most. There is extensive work on air flow through material cracks. 2. 2. 2 Important Technical Aspects See details in fig. 2 for the following considerations. Deformation needs to be assured.

The force is actuated via a fine screw, enables measuring the vertical displacement with a LIVED and control he value to it with satisfying precision (10 microns). The purpose of the center ball is to transfer the pure vertical movement without rotational movement and torsion. Seal eccentricity: the experiment should be designed to assure closing force as uniform as possible, although it'll never be ideal, so it'll be wise to try centering the seal and avoid creating preferable air flow sites due to lack of symmetry in the compression field.

In the following setup "hand tolerance" is satisfying. Starting the "stopwatch" (time measure): practically, the seal is influenced by the way the pressure and deformation are reached. To overcome this problem, the experiment should be done in a way assuring results independent from the initialization. Experiment was stopped when pressure changes are very small. 2. 2 Course of Experiment Preliminary experiments showed a continuous air flow and pressure drop all along the experiment. The general p(t) profile exhibited "exponential decay" type of behavior.

We shall now briefly describe the experiment variables related issues such as the creation of p(t=O) and h , and the protocol of starting/stopping Force pa 2. 2. 3 The Experiment We measure p as a function of time, and determine owe p(t=O)= pop and h influence this profile. Observe fig. 2 for the actual setup. The first step is deforming the seal. Than, opening the main valve ( not in fig. 2), connected to the supply line, and building the pressure to a desired, stable value (waiting for stabilization is crucial). The secondary valve was then closed and p(t) was than monitored.

Figure 1 - Schematic section of the experiment setup. The compressed air is colored with blue. -2- Screw ones on the surface) move finely due to compression and each strand remain attached to its original Junctions. The Junctions are getting closer ND dense and so are the strands in the bulk of the rubber gasket, which were dense enough already to prevent air flow. However, the surface isn't a mosaic of Junctions but more of a blend of Junctions and loose strands - strands connected only to one junction. Had the surface was a lattice of Junctions, the contact mechanic would have been similar to metal-on-metal mechanics.

But this is not the case. Due to those loose strands, the surface only embedded with Junctions and between them - an entanglement of loose stands, rolled and smeared on the Junctions beneath them, preventing the creation f classic surface contact. In order to understand the air flow mechanism, let's observe hypothetically on a metal-on-metal sealing. Each metal plane has its own surface profile with peaks, valleys and defects where air can flow in and find its way out. The probability of perfect sealing - when one plan's peaks are pressed directly on the other plan's valleys - aspires to zero.

Practically, the metal-metal interface always consist paths that the air can use for its escaping. We refer to that situation as "use of built in paths". The reason behind the superiority of rebuttal sealing over the metal-metal one is he elasticity and compliance of the rubber. When pressed on the metal surface, the rubber's loose strands and even some of the Junctions and regular strands on the rubber surface fill the valleys of the metal. Since the strands are thin compared to the valley, they penetrate the "built in paths" and force (consider a thick bush in a flowing river).

This is the idea behind "labyrinth" seal -forcing the air to flow in a complicated path in order to reduce pressure leakage. The magnitude of a rubber monomer is about 5 LIVED sail Piston Secondary Valve Figure 2 - the actual setup 2. 3 Preliminary results and Conclusions (t) profile was recorded for different initial pressure differences and rubber deformations. The parameters range is: pop=l [ATM] to 5[ATM], to -0. 2. Preliminary results showed that p(t) graphs were different considerably one form the other for the same initial conditions.

It was concluded that the experiment is very sensitive to the rubber gaskets different surface profile over the different specimens. See fig. 4 for details. On the other hand, when repeating the experiment with the same gasket, as long as the experiment is not too long so the rubber won't behave differently due to service, we get similar graphs (fig. 3). Discussion 3. 1 Air Flow The proposed mechanically model of leakage is based on three phases. Phase I includes placing the rubber gasket and deforming it to the set value h. The process is described in figure 5. The polymer macrostructure is composed of strands and Junctions.

According to untangled mechanical models [5], the Junctions (at least, the experiment #2,#7 experiment #2 pressure[ATM] 4 3. 5 3 2. 5 2 Figure 3 - 4 experiments with ZEE%. The graphs are similar, with maximum of 0. 2[ATM] pressure difference. The difference is due to inability to reconstruct the same initial conditions and due to service effects. Oho 1 500 2000 time[sec] Figure 4 - pressure profiles in experiments #2, #7. pop?4. 1 EX-O. 148. -3- Aluminum Figure 5 - gasket compression process angstrom, and the strands are generally shorter than the average polymer length, each strand is formed maximum overall length about 5 micron.

See [6] for more information about strands length. However, this is not the end of the story. Recall that the rubber strands are rather flexible, given an energetic air Jet it might deform the strands, move them aside, and create a much more convenient path. Where it is practically impossible in metallic sealing, when rubber-metal is noninsured the air can create its own path and not use the "built in" paths by default. Of course, the strands are like springs - moving them aside require a transform of the air kinetic energy to potential spring energy.

So we stay with this trade-off: creating convenient path where the friction loss is minimal, or maybe use the built in paths with significant friction loss but save the energy of the path creation. The answer will be given by the minimum energy principle. The reasonable assumption is when the pressure p is great, the air is energetic and prefer create a convenient path. As long as p decreases, the path becomes more and more curvy. When p is too small, we cannot talk about paths anymore since the air kinetic energy isn't high enough. Alternately, the air molecules start percolate on their way out (still in the interface, not in the bulk).

Our model won't deal with that region. Only the regions with flow paths are in our interest. The latter discussion was proved qualitatively. An experiment assuring its results is in its design stages. Phase II of the experiment is the pressure buildup. We open the main valve, letting air to flow from the supply line to the cylinder. The supply line erasure is controlled and thus raising the pressure inside the cylinder. At this phase, air is pumped in and leaks out at the same time but the influx rate is much greater then the leakage rate.

When the level of pressure reaches the desired one, and stables, the secondary valve is closed and phase Ill is being executed. In phase Ill, the air flows out through the two planes described in phase I in a manner described above. 3. 2 Rubber Gasket Behavior cylinder, and that pressure acts on the already deformed gasket as it wants to expend it. Due to the normal forces, a friction force (FRR) avoiding the gasket from expending. Beneath is a figure showing the process form the rubber point of view using forces diagram on a vertical section.

Let's assume a standard friction model. After a certain level of pressure is achieved, the friction force FRR reaches its maximum static magnitude, which means that the rubber is entering the dynamic friction stage. While the pressure continue to increase, the rubber starts increasing its average radius, so the radii difference - outer against inner - and the height are decreasing due to incompressibility. Notice that h does not change - the piston is fixed - but the expansion decreases the ignited of the friction force even more. When maximum p is achieved, phase Ill starts.

The pressure begins to drop and the rubber enters the static fiction level again. The friction force continues its decrease until finally it changes its direction and grows back to the dynamical level. Afterwards, the rubber begins to decrease its radius -4- until the maximum-static-level friction force is enough to hold the rubber gasket in place. It is more than possible that before releasing the piston, the final average radius is different than the initial. There is also the possibility of small p and a strong enough friction force that succeed in keeping the gasket in place all over the experiment phases.

Important conclusion is that the volume which the air fills remains constant at the beginning and at the end of the experiment. That is, the contraction is happening at the middle of the experiment (if present). In order to check the validity of the previous speculative argument, a videotaped experiment was taken. There, one we can see how the rubber expends and contracts with the pressure (in [ATM] at the background), where the movement is in microscope (it was videotaped using a regular camera. The movement is absolutely seen to the naked eye).

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