Experimental analysis of parabolic bimetallic shell

Despite the fact that electronics has become predominant in many areas of technology, thermostatic bimetals are still employed in a wide and continually growing range of applications. Bimetal components both simple and complex are at the heart of numerous measuring instruments, regulation systems and safety devices. In heating and sanitary equipment, in electrical engineering systems and domestic appliances, in automobiles and television sets, and wherever a device must react to changes in temperature.
Thermostatic bimetals can be readily adapted to meet the constraints imposed by the construction of devices into which they are incorporated. This leads to a diversity of forms which can be divided into three major categories. Straight strips are the commonest form of bimetals, being the simplest and cheapest. When the available space is limited, a U shape can be employed. Spiral and helical bimetals convert temperature changes into a rotational movement or torque when the displacement is impeded. A spiral shape enables a large length of bimetal to be incorporated into a small volume, producing high sensitivity, limited only by strength considerations beyond a certain length. Bimetallic shallow shells reverse suddenly at a critical temperature which depends on the grade of bimetal employed and the geometry. They are used in numerous regulation devices and protection systems.

Thin and shallow bimetallic shells with suitable material and geometric properties have the characteristic of snapping-through into a new equilibrium position at a certain temperature. The result of such a fast snap-through of a bimetallic shell, acting as a switching element in a thermal switch, is the instantaneous shutdown of electric power and the machine. The snap-through of the bimetallic shell is a dynamic occurrence that lasts a very short time and as such prevents the damaging sparking and melting of electric contacts and extends the life time of the thermal switch.

Bimetallic shallow shells shown in Fig. 1 display a range of interesting features that can be tested in various experiments, ranging from very simple ones to very sophisticated ones that can be done only with hi-tech equipment.

Step 1: Physical and technical backgroung

Experimental analysis of parabolic bimetallic shell
Experimental analysis of parabolic bimetallic shell

Thermo-bimetal shallow shells are widely used as thermostats, for instance, to automatically switch off the electric current in kettles, irons, water boilers and other appliances. Their function is to regulate temperature by switching off electrical power at predetermined temperatures. There is a large product range of thermostatic controls, each designed to work with a particular heating element design, providing an integrated heating and control system.
A thermo-bimetal shallow shell determines the temperature at which each thermostatic control operates. These shells are constructed from a laminated composite of metals with different thermal expansion coefficients. They deform with changes in temperature. At least one bimetallic shallow shell is used in each device; however, there are some controls that use three of them. The bimetallic shallow shell performs a snap action at defined temperatures and produces enough force to open or close electrical contacts. The temperature at which a bimetallic shallow shell "snaps through" on heating is called the "break temperature" and the temperature at which it "snaps back" on cooling is called "remake temperature".

Bimetallic shallow shells have been developed by purely empirical means. A great deal of experimentation has been carried out over the past decade to improve performance, and the improvements have been remarkable.

It has been said that "Bimetallic shallow shells lend themselves poorly to calculation. They are designed empirically, based largely on experience. More than any other form of bimetal, they require starting materials whose physical and mechanical properties are precise and uniform, with small thickness variations, and excellent surface quality and flatness".

The parabolic bimetallic shallow shells, with a diameter of up to thirty millimetres, consist of two metal layers, for instance, one of invar (passive layer) and the other of steel (active layer), being cold-welded together. In 1897 Guillaume discovered the original "Invar" property, i.e. a ferromagnetic face centred cubic FeNi alloy containing about 35% wt. Ni that has a thermal expansion close to zero at room temperature. In Fig. 2 we can see the cross section of the bimetallic shallow shell, the invar layer is visible and shiny. The steel layer is located next to it.

Fig. 2. Microstructure of bimetal shallow shell specification Kanthal 94S bimetal strip, specification through its thickness, arrow shows rolling direction

At low temperatures, bimetallic shallow shells have a concave shape which then snaps to a convex shape at high temperatures. During this process, the shell can exert a force great enough to activate a switch or make an electrical contact mechanically. As is common in discontinuous phase changes, shallow shells show considerable hysteresis behaviour (Fig. 3). With adequate materials and correct shaping, the lower and upper snap temperatures, Tls and Tus, respectively, can be adjusted within a wide range.

Step 2: From technical use to playful application 1/2

Experimental analysis of parabolic bimetallic shell
Experimental analysis of parabolic bimetallic shell
Experimental analysis of parabolic bimetallic shell
Experimental analysis of parabolic bimetallic shell

One of the features of a bimetallic shallow shell is that it can reach temperatures of up to 40C when rubbed between your dry fingers. This temperature is sufficient to click the shell into its other configuration - unstable at normal room temperature, in which it can remain temporarily until it cools down. If the bimetallic shallow shell is then placed concave-side down on a hard, cool surface quickly enough, it will snap back into the stable configuration and jump up about 60 cm (1 cm). A repetition of the experiment with the same disc results in a noticeable variation in height, and there can be even greater divergences between different bimetallic shallow shells. If placed on the surface convex-side down, the disc jumps as much as about 30 cm into the air. This phenomenon will be discussed later.

From the measurement of the jump height h and the mass m (= 1.207 g 0.003 g), you can calculate the potential energy E (= m·g·h = 0.001235kg·10ms-2·0.60m = 7.4·10-3 J). The initial jumping speed can be calculated with

v = Sqrt(2gh) = Sqrt(2 x 10ms-2 x 0.60m) = 3.5 ms-1 .

Air resistance can be disregarded because of the low speed, as can rotational energy due to rotations. An additional experiment shows that there is even more energy in the disc. If some small metal sheets only a few square millimetres in size and with a thickness of 0.3 to 0.4 mm are put under the centre of the clicked disc, the disc jumps up to 85 cm high! By using this trick, the disc can be accelerated along the whole distance of the bent disc. For this reason, the original discs had a notch of about 0.3 mm in the centre of the disc (figure 4). The question arises of what happens to the energy which does not contribute to the jump without the metal sheets. We can only guess that the energy is dissipated due to the juddering and therefore inelastic collision upon the impact of the centre of the disc on the surface.

The initial acceleration, which can be estimated from the force F = 35 N (5 N), necessary to bend the disc is extremely great. To determine this force, the disc is laid flat on a plane surface, and then the centre of the disc is loaded with weights until it bends (figure 5). The assumption of a uniform acceleration results in:

a = F/m = 35.823N / 1.207 10-3 = 29688 ms-2

To get an idea of the dimension, compare this with the acceleration of a bullet, which is only a hundred times greater. The plastic popper has an acceleration of thirty times less!

With an adequate digital camera, the hotplate already mentioned and a thermometer, you can measure quantitatively the bending of the disc against the temperature. The disc in the photo was laid flat on the hotplate and photographed directly from the side. In figure 6, two situations are shown. In the lower part, you can see the disc cooling from high temperatures before reaching the lower snap point. At the top, the disc is shown heating up from low temperatures after the snap state. From pictures like this, the shape of the disc can be determined with an accuracy of at least 0.1 mm (figure 7). The distance the disc is accelerated without metal sheets under the centre is about s = 0.70 mm (figure 7). This will be analysed more precisely later. With the following calculation, the time for the initial jump process can be roughly estimated.

t = Sqrt( 2 a / s ) = Sqrt( 2 0.0007 / 29688 ) = 2.172 10-4 s = 217 μs

Step 3: From technical use to playful application 2/2

Experimental analysis of parabolic bimetallic shell
Experimental analysis of parabolic bimetallic shell
Experimental analysis of parabolic bimetallic shell
Experimental analysis of parabolic bimetallic shell
Experimental analysis of parabolic bimetallic shell

In our experiments we decided to document the initial part of the jump with an adequate high-speed video camera. In Fig. 9, the separate phases of the jump, taken with a camera with 16000 frames per second (fps), are shown. The resolution of the camera is very limited at this speed. The difference between each picture is 62 μs. The start of the jump takes place relatively slowly. In the picture at 250 μs, levitation of the disc is very constricted but clearly visible above the surface. In the picture at 312 μs, the disc already has contact with the surface. Then the disc is shown above the surface and jumps up with a speed of 3.6 m/s, as can be derived very accurately from the video. This is consistent with the value of 3.5 m/s calculated at the beginning of jump height. Together with the measurements concerning the shape of the disc, some reflections and estimations can be made.

The upper part of Fig. 10 shows the shape of the bimetallic shallow shell shortly before start. The centre of mass (red point) can be located at a distance of about 0.30 mm (0.05 mm) from the surface, which can only be estimated due to the irregular form of the bimetallic shallow shell. At the beginning of the snap process, the centre of the bimetallic shallow shell moves downwards, which takes about 250 μs. Within this time, the bimetallic shallow shell falls down only by

0.5 10ms-2 (0.25 10-3 s)2 = 0.312 μm

due to gravitation. Therefore, the edge of the bimetallic shallow shell must move upwards because the centre of mass remains at almost constant height. The phase at 250 μs shown in Fig. 9, where the bimetallic shallow shell levitates above the surface, demonstrates this clearly. The centre of the bimetallic shallow shell moves further downwards until it touches the surface at about 270 μs (10 μs). It is only now that acceleration of the bimetallic shallow shell begins, continuing until the bimetallic shallow shell is bent completely. At about 330 μs (10 μs), the bimetallic shallow shell lifts off the surface. The centre of mass can now be located more precisely at about 0.50 mm (0.05 mm) above the surface because the centre of mass of a thin spherical cap is found at exactly half of the height.? ? ? ? ?
Due to the simplifications made here, congruence can only be expected within a certain order of magnitude.

Fig. 9 also shows that the bimetallic shallow shell jumps up if it has been placed on the surface the 'wrong way', this means convex-side down. In this case, the edge of the disc accelerates downwards, touches the surface and consequently the bimetallic shallow shell jumps upwards. This effect is even stronger if the bimetallic shallow shell is put on a ring with a diameter of about 25mm, such as on the neck of an open bottle.

Experimental analysis of parabolic bimetallic shell
Experimental analysis of parabolic bimetallic shell - Step #3(256x28) 1 KB

Step 4: Conslusion

The work presents some relevant technical information on spherical bimetallic shallow shells and investigates the physical phenomenon of snap-through. It is shown how, through simple measurements and calculations, we can determine the initial speed, the acceleration and the lower and upper snap temperature. From high speed camera shots it was established that the bimetallic shallow shell jumps up with a speed of 3.6 m/s. A comparison of this to simple calculation where the initial speed of jump is calculated from the jump height and is 3.5 m/s, shows a calculation error of 2.8%. We can conclude that investigations with a high speed camera offer an even deeper insight into the phenomenon of snap-through in spherical bimetallic shallow shells.

 
 

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