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1)Maxwell Model [Group: Mathematic Model]

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The simplest series combination of mechanical models is the Maxwell model. A given stress σ applied to the model produces a deformation ϵ₁ on the spring and a deformationϵ₂ on the dashpot. The stress-strain relation in the spring is

σ = M_Uϵ₁

where M_U is the elasticity constant of the spring. The subindex U denotes “unrelaxed”. Its meaning will become clear in the following discussion. The stress-strain relation in the dashpot is

σ = ηθ_tϵ₂ η > 0,

where η is the viscosity. Assuming that the total elongation of the system is ϵ = ϵ₁ + ϵ₂,the stress-strain relation of the Maxwell element is

θ_tσ/M_U + σ/η = θ_tϵ

(Carcione J.M., Wave fields in real media: wave propagation in anisotropic, anelastic, porous and electromagnetic media, second edition, pg.68)

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Viscoelastic materials have the properties of both viscosity and elasticity. A mathematical model for viscoelastic behavior therefore would include elements representing both. Typical models, either linear or nonlinear, include springs and dashpots. Spring is for elastic deformation and if can respond simultaneously to any applied load; whereas, dashpot reacts like viscous fluids, and moves at a rate proportional to the stress. 

A basic model for viscoelastic materials, called the Maxwell model, is represented by a dashpcd and a spring connected in series. Several extensions to the Maxwell model have been made. For example. Rabinovich used a nonlinear Maxwell's equation to predict the stress relaxation. Alfrey connected the springs and dashpots in parallel to generate a new model to describe the relaxation curve. These models have been successfully applied to predict the stress relaxation behavior at certain conditions. A generalized Maxwell model would result in a solution as 

Where σ_∞ , is the stress stabilized after a long lime, σ_i , depends on the applied strain lever and material propedies.  t  is time and  τ_i , is a material constant. This equation is often called the Prony series and is the most popular linear model for stress relaxation of polymeric malerials. 

As shown later. the SLR material studied in this work exhibits nearly linear behavior up to 25% strain which is in the range of interest in sealing application. As a consequence. the Prony series is adopted in this work.

(Experimental Mechanics on Emerging Energy Systems and Materials, Volume 5 , Tom Proulx, 2011)

2)Laser Beam Welding (LBW)
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Laser beam welding is a fusion welding process. Through the laser beam, the laser produces the energy necessary for welding. It is led to the focusing lens system by mirrors or optical fibers. The lens system then focuses the laser beam on the joint. Depending on the intensity generated there, different processes of beam–material interaction will take place. When the intensity is low, most of the radiation will be reflected by the workpiece, and only a very small part
will be absorbed by the metal in a thin layer (< 1μm) at the surface and transformed into heat. The energy input into the workpiece is achieved by heat conduction.With increasing intensity, the workpiece is locally heated by the laser radiation that is absorbed. When the melting temperature is reached, a molten puddle forms as the time of influence is increased. If the parameters are chosen so as to maintain a stationary state, the process is described as thermal conduction welding.
If, however, the intensity is further increased so that more energy is absorbed than can be dissipated by heat conduction, then the enormous energy density of the laser beam in the focus will cause the metal to vaporize. The pressure of the metal vapor that flows off creates a steam passage in the melt, the so-called keyhole. Typically, the diameter of such a capillary steam tube shows the magnitude of the beam diameter (0.1 to 1 mm). Characteristic threshold intensities for capillary formation lie in the range of 106W/cm2.
In laser beam penetration welding, the system of capillary steam tube and surrounding molten bath is led along the assembly line. The molten bath flows around the capillary on both sides, comes together behind it, and, when solidifying, forms a joint.
(Springer Handbook of Mechanical Engineering, Grote, Antonsson (Eds.),part B, p668-669)

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Laser beam welding (LBW) is a procees that melts and joins metals by heating them with a laser beam. The laser beam can be produced either by a solid-state laser or a gas laser. In either case, the laser beam can be focused and directed by optical means to achieve high power densities. In a solid-state laser, a single crystal is doped with small concentrations of transition elements or rare earth elements. For instance. in a YAG laser the crystal of yttrium-aluminum-garnet (YAG) is doped with neodymium. The electrons of the dopant element can be selectively excited to higher energy levels upon exposure to high-intensity flash lamps, as shown in Figure 1.29a. Lasing occurs when these excited electrons return to their normal energy state, as shown in Figure 1.29b. The power level of solid-state lasers has improved significantly, and continuous YAG; lasers of 3 or even 5 kW have been developed. 

In a CO2 laser, a gas mixture of CO2, N2, and He is continuously excited by electrodes connected to the power supply and lases continuously. Higher power can he achieved by a CO2 laser than a solid-state laser, for instance, 15 kW. Figure 1.30a shows LBW in the keyholing mode. Figure 1.30b shows a weld in a 13-mm-thick A633 steel made with a 15-kW CO2 laser at 200mm/s. 

Besides solid-state and gas lasers, semiconductor-based diode lasers have also been developed. Diode lasers of 2.5 kW power and 1 mm focus diameter have been demonstrated.While keyholing is not yet possible,conduction-mode (surface molting) welding has produced full-penetration welds with a depth-width ratio of 3:1 or better in 3-non-thick sheets. 

(Welding metallurgy,Sindo Kou,2003, pp. 30-31)

3)Ultrasonic Sensors [Group: Control Element]

[Old]Ultrasonic sensors radiate a short ultrasonic pulse in the 20kHz-500kHz range. The pulse bounces off a local object and the echo is detected, often by the transducer which lkaunched the pulse. Operation depends on the transmission of air and the sonic reflectivity of the target, which is a function of the orientation and material of its surfaces. Ultrasonic s is quite useful in sea water, which attenuates E and H fields but transmits sound well. Soft materials such as cloth and foam do not reflect well. (Capacitive Sensors, Baxter, p.68) 

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The accoustic waves emitted by the transmitter in the sensor hit the object and the reflected waves are sensed by the receiver to generate information about the presence of an object of any material. This is the ecomode of operation. In the opposed mode if the waves are not reflected the receiver does not get the signal due to blocking of the transmitted waves.

The main part in this type of sensor is the transducer element which can act both as the transmitter and the receiver. The transducer is covered by the resin block which protects it from dust and humidity. The absorber material behind the transducer performs the function of acoustic damping. The general protection is provided by the metallic housing. Information about the presence of the object is carried front the receiver through the leads and cable. Figure 2.20 shows the construction of an ultrasonic proximity sensor. 

(Mechatronics, G. Hegde,Ganesh S. Hegde,2010,p. 54)