International Journal for Scientific Research & Development

IJSRD - International Journal for Scientific Research & Development| Vol. 8, Issue 8, 2020 | ISSN (online): 2321-0613

Design and Numerical Analysis of Bimetallic Strip Using Finite Element Method Deriya Ashish Rameshbhai UG Scholar Department of Mechanical Engineering Parul Institute of Engineering and Technology, Parul University, Vadodara 391760, India Abstract— The goal of this project was to design and materials. The length was chosen as 50mm so as to analyse a bi-metallic strip so that the free end of the strip achieve the necessary deflection. [1] would deflect when there is a 20°F change in temperature  By a Literature review we presume the deflection of relative to its reference temperature. The strip had to be not Bimetallic Strip smliar with properties as us, to achieve more than 2 inches long with one end fixed, and both metals deflection in range of 50-65 microns. had the same width, b. We were allowed to freely choose both materials as long as they were metallic. The deflection A. Market Survey could be controlled by changing their materials (which  The defrost thermostat used currently in all auto defrost changes the coefficient of thermal expansion and the elastic refrigerators, currently employ a snap action bimetallic modulus) and the height of the material. The first step was disc. to set the two deflection values equal to each other and find  Various manufactures of refrigerators use the bimetallic the force in the bi-metallic switch. The Deflection was then disc in thermostats as it provides instantaneous found out. Various other parameters like Radius of deflection and produces the necessary amount of force Curvature, Felicity, Stresses produced in the strip were also to lift the strip above it. calculated. These analytical figures were then compared  We took into consideration a defrost thermostat which with software analysis and the results were observed. uses a simply supported beam instead of disc. Keywords: Bimetallic Strip, FEA, Stresses On Beam, Ansys  Then cantilever type beam was chosen so as a Workbench, Cantilever Beam & Simply Supported Beam, replacement option for the disc type. Thermal Analysis, Brass & Steel Material  The disc type though satisfies various parameters, it has a general tendency to fail. I. INTRODUCTION  Thus, as an alternative cantilever type was chosen and  A bimetallic strip is used in a refrigerator thermostat to said report is presented. convert a temperature change into mechanical B. Objectives displacement of the strip. The bimetallic strip consists of two dissimilar metals strips of different metals which  To design a Bimetallic Strip for a Defrost Thermostat. expand and contract at various rates due to the heating  To analyze stresses developed in Bimetallic strip. of the strip, commonly steel and copper, or in special  Determine the various parameters of Bimetallic strip. cases steel and brass. The strips are combined together  To compare results with classical methods. throughout their length by riveting, brazing or welding. The various expansions force the flat strip to bend one II. DEFROSTING IN A REFRIGERATOR [3] side if heated, and in the opposite direction if cooled A. Cooling Cycle below its initial temperature.  The metal with the greater coefficient of thermal expansion is on the outward side of the curve when the strip is heated and on the inward side when cooled.

Fig. 1: Symmetric diagram of bimetallic strip  The aim of this project was to design and analyse a bimetallic strip for the thermostat that would achieve a Fig. 2: Circuit diagram of refrigerator cooling cycle. deflection when temperature would touch 100C. So as During cooling mode, the defrost timer disconnect a contact that it would stop the electrical contact and avoid to the compressor circuit so it’ll run. The circuit to the further heating of evaporator. defrost heater is now open. While and fan motors on and off  The constraints were that the strip had to be not greater to take care of an suitable temperature. than 3 mm thick and we were free to choose the

B. Defrost Cycle When a set colder temperature is touched, the defrost termination thermostat closes once again. This is OK since the defrost timer is not any longer supplying power to the defrost circuit, the heater doesn’t get energized. When the defrost timer again advances into the defrost mode, the limit thermostat will already be closed and can permit power to be supplied to the defrost heater to melt any frost that has created on the evaporator cooling coil again. D. Defrost Component Locations

Fig. 2: Circuit diagram of refrigerator defrost cycle. The defrost timer eventually switches into the defrost mode and it delivers power into the defrost heater to melt all frost that has accumulated on the evaporator cooling coil. The cold control contacts stay closed however since the defrost timer isn’t any further feeding power to that circuit, the compressor does not run.

Fig. 5: Location of defrost component(Thermostat) The most frost free refrigerators, the evaporator (cooling) coil is inner side of the freezer compartment covered by a panel. The freezer fan motor is typically within in the same general area. The defrost heater is located onto or woven right into the evaporator coil in the freezer. The defrost termination limit switch is normally located on the side of the evaporator coil or on one of the connecting tubing.

Fig. 3: Circuit diagram of refrigerator defrost cycle. Once the defrost termination thermostat (a.k.a. defrost limit switch) feels a set temperature, it opens the circuit to the defrost heaters, shutting them off. The timer remains within the defrost cycle until the timer advances back to the cooling mode. Since the limit switch is open, the heaters are not any longer on for the rest of the cycle. C. Cooling Cycle Fig. 6: Defrost limit thermostat. When the timer once again advances in return to the cooling The defrost timer may be in different places mode, the compressor will be start to move along with any including behind the kickplate at the front side of the air circulation fans. The defrost limit switch will be continue cabinet, inside the fridge compartment possibly in a control in the open condition till it’s retuned by cold temperatures. panel along with the thermostat or on older models, at the rear within the motor compartment by the compressor. E. The Defrost Heater

Fig. 7: Glass tube heater. Fig. 4.Circuit diagram of defrost cycle.

The defrost heater is a wire filament closed in in a design, evaporator fan motor is won’t begin moving after a quartz, glass, aluminium or any different material, tube sheat defrost cycle until the evaporator has had chance to begin which become hot when powered. It will either have cooling once more time. Whereas it’s the good design idea resistance (show continuity) or be good or it will have thus as to not blow the lukewarm defrost air throughout infinite resistance (no continuity) and be defective. How whole refrigerator, a failure in one a part of the defrost many resistance it has is not relevant as its resistance will system can ordinarily render the whole refrigerator not normally change except to being open when it fails. ineffective because of the shortage of air flow. F. The Defrost Termination Thermostat III. ANALYSIS & DESIGN The defrost termination thermostat is really a tiny little SPST electric switch and that’s motivated by temperature. As heat is added, one of the metals will expand faster than Depending on the temperature it is, it’ll either have none the other leading to a force equal in magnitude but opposite resistance (show continuity) and be good or it will have in direction acting on both metals. This means that the infinite resistance (no continuity) and be defective. At room change in length of each metal strip depends on the thermal temperature it will normally be open (which is normal and expansion as well as the deformation from axial loading. We not a sign of being defective) and only close when it gets also know that these deformations will be equal to one cold. How cold it has to be to close will depend on its another since the strips are permanently attached. We can special calibration but commonly near or below freezing solve for the force acting on these strips in terms of material point. and physical properties of the metals.

Fig. 9: Design model of bimetallic strip. Fig. 8: Defrost termination thermostat. The temperature Range at which the thermostat is A few latest model refrigerator and some older expected to perform is 320F to 400F. At 320 the bimetal is model refrigerator run power for the evaporator (freezer) fan supposed to connect the circuit and at 400F the strip should motor through the defrost heater part and also defrost limit break the circuit and thus stop the electric current flow and switch. If either of these any component should let down, switch off the heater. remaining open, the fan won’t move, it'll stop the spreading of cold air throughout whole refrigerator. During this system Young’s Modulus Length Width Thickness Sr. No Material Co-efficient of expansion (inch/inch oF) (psi) (inch) (inch) (inch) 1. Brass 14.93 x106 11 x10-6 ? 0.59 0.059 2. Steel 29 x106 6.1 x10-6 ? 0.59 0.059 Table 1: Material Property

IV. ANALYTICAL MODELING A. LINEAR BIMETALLIC BEAM[4] A bimetallic strip consists of the two dissimilar metals bonded along the length of the beam. Timoshenko (1925), he was the first man to study stresses in bimaterial beams. He used elementary beam concept to acquire an demonstration for the curvature of a bimetallic beam due to a uniform temperature change. The general expression for the radius of curvature of a cantilever beam of unit width heated from temperature T0 to T in absence of external forces (Timoshenko, 1953)

V. ANALYTICAL ANSWERS Solve For ℎ1 & ℎ2, 1) Radius of Curvature ℎ1 = 0.033 2 1 1 6(1+푝) (훼2−훼1)(푇−푇0) ℎ2 = 2( ⁄푡) − ℎ1 = 1 (Eq.1) 푅 푡[3(1+푝)2+(1+푝푞)(푝2+ )] 푝푞 ℎ2 = 0.026. 6(1 + 1)2 × (11 × 10−6 − 6.1 × 10−6) × (20) MOMENTS OF INERTIA (FROM PARALLEL-AXIS = THEOREM) 14.93 1 2 2 푏푡3 0.05[3(1 + 1) + (1 + 1 × ) × (1 + 14.93)] 푡 2 29 1× 퐼1 = +bt× (ℎ1 − ⁄ ) 29 12 2 −3 0.59×0.0293 2.325 × 10 = +0.59× 0.029(0.033 − 0.014)2 = 12 725.74 × 10−3 1 = 3.24 × 10−3 −6 푅 퐼1 = 7.375 × 10 R=308.56 µm bt3 I = + bt × (h − t⁄ )2 2) Deflection 2 12 2 2 2 3 2 3(1+푝 ) 0.59×0.029 2 d = 퐿 1 (훼2 − 훼1)(푇 − 푇0) = +0.59× 0.029(0.026 − 0.014) 푡(3(1+푝2)+(1+푝푞)(푝2+ ) 12 푝푞 I  3.662 10 6 (Eq.2) 2 Redesigning for Length, E1I1 + E2I2 = 216.306. 3(1+12) (From Table and values of I1& I ) (Eq.9) 0.0023 = 퐿2 × × (11 × 10−6 − 2 0.05[3(1+12)+(1+1×0.5148)] 7) Maximum Stresses 6.1 × 10−6) × 20 Maximum stress in Upper Layer Material 6 Mh1E1 2 −5 σ1 = (Substituting Moment and h1 & Eq.9) 0.0023 = 퐿 × −3 9.8 × 10 E1I1+E2I2 522.86 × 10 0.844 × 0.033 × 14.93 × 106 L = 1.58 𝑖푛푐ℎ = Thus, we will consider the length of 1.60 inch as 216.306 for the design of our current strip. σ1 = 1922.417 3) Flexivity Maximum Stress in lower layer 3 Mh2E2 K = × (훼 − 훼 ) (Eq.3) σ2 = (Substituting Moment and h2 & Eq. 9) 2 2 1 E1I1+E2I2 3 0.844 × 0.026 × 29 × 106 = × (11 × 10−6 − 6.1 × 10−6) = 2 216.306 −6 K = 7.35 × 10 σ2 = 2942.017 4) Force ∆푇(훼 −훼 )×푏×(퐸 푏ℎ × 퐸 푏ℎ ) A. Geometric Modelling and Analysis of Bimetallic Strip P= 1 2 1 1 2 2 (Eq.4) 퐸1푏ℎ1+퐸2푏ℎ2 [8] = Geometry of The bimetallic strip was modelled using the −6 −6 6 6 20 ×(11×10 −6.1×10 )(0.59)[(14.93×10 ×0.59×0.05)×(29×10 ×0.59×0.05)]ANSYS Workbench. ANSYS is a analysis tool for linear, 6 6 14.93×10 ×0.59×0.05+29×10 ×0.59×0.05 structural analysis, nonlinear, and dynamic studies. This 21.786 × 106 computer simulation product offer finite elements (FEA) to = 6 1.29 × 10 model behavior, and assist material models and equation 푃 = 16.88 푙푏푓 solvers for a wide range of mechanical design problems. 5) Moment (ℎ +ℎ ) ANSYS also consider coupled-physics and thermal analysis M = P × 1 2 (Eq.5) 2 capabilities involving piezoelectric, acoustics, thermo- 0.05+0.05 =16.88 × electric and thermal–structural analysis. 2 M =0.844 B. Model of the Strip 6) Neutral Axis The geometric model of the strip was prepared as per the dimensions taken in the study-

Fig. 10: Neutral axis. 푡 푌1퐴1 = (ℎ1 − ⁄2) × (푏푡) (Eq.6) 푡 푌2퐴2 = (ℎ1 − 푡 − ⁄2) × (푏푡) (Eq.7) Substituting Young’s modulus values and Eq.6 & Eq.7 in Eq..8 퐸1 × 푌1퐴1 + 퐸2 × 푌2퐴2 = 0 (Eq.8) 6 6 14.93 × 10 × (ℎ1 − 0.014)(0.59 × 0.029) + 29 × 10 × (ℎ1 − 0.029 − 0.014) × (0.59 × 0.029) = 0 Fig. 11: Solidworks model of the strip

Length – 1.6in (50mm) strip keeping the materials same, the deflection of strip Width - 0.59 in (25mm) reduces by a great extent. Thickness – 0.029 in each (1mm) C. Meshing Process Meshing is discretization process and it takes some time for process. It is the most essential part of an analysis and it can determined the efficiency and effectiveness of an analysis models. Hence, a lot of time is given to meshing of models.

Fig. 14: Deflection of strip. The Deflection produced in the strip is directly dependant on its length. In the above analysis , the length is varied 1.1 inch (26mm) the deflection observed is very less (0.00074 inch) than what we expect, and hence the analytically calculated length is correct, and the design Fig. 12: Meshing of the model. meets the condition necessary. The market survey resulted Statistics in getting us a strip currently used in thermostats. Amongst Nodes 62775 different types used we chose the simply supported as for Elements 14112 comparison and improvement purposes. Mesh Metric Orthogonal Quality A. Simply supported beam Min 1. Max 1.  An analysis is carried by fixing both the ends of the Average 1. bimetallic strip. Standard Deviation 0.  This results in analysis shows that the Def;ection produced along the height of strip in y axis is Table 2: Meshing Statistics comparatively very less Than what we have In ANSYS the orthogonal quality indicates the acceptability Dconsidered for design. of the mesh and it should always be of Quality 1. The  Thus, The observed results in analysis shows that if a analysis was carried as Steady state thermal and steady state cantilever is used the necessary deflection is achieved structural. The Initial Temperature of 250 F (-30 C) was set. and thus it is an improvement over the simply The Final Temperature of 410 F (50 C) was also entered. supported.  Another disadvantage being the cross curvature is also VI. RESULTS produced, Thus the strip is subjected to stresses not uniform.

Fig. 13: Deformation of the model. Fig. 15: Simply supported beam. The maximum deformation of 0.0023195 inches (0.060 mm) 60 microns was observed. This deformation is theoretically enough for breaking the contact points and achieving the purpose of stopping current flow to heater. The analysis further shows that as we vary the length and thickness of the

The maximum stress gives us the above mentioned results. 1) The stresses validated by calculations are present within the Given range. 2) Thus ,The software results have also been validated about the stresses developed. 3) The stresses produced are very well within the range as the maximum stress Produced on the surface which is analytically calculated. 4) Thus, the designed Bimetallic strip fulfills the necessary parameters and the design is safe.

VII. CONCLUSION

Fig. 16: Directional deformation 1) The Required deflection is achieved. 2) The Strip is very well within the stress limits. B. Von -Misses Stress Analysis[9] 3) Analytical calculations and software analysis have This theory suggest that the total strain energy can be provided answers in an acceptable close range. separated into two factor: the volumetric (hydrostatic) strain 4) By varying the mechanical properties of the material, energy and the shape (distortion or shear) strain energy. It is the deflection produced can be varied. declared that yield comes when the distortion component 5) The small temperature range avoids the presence of exceeds that at the yield point for a simple tensile test. The accountable thermal stresses. analytical method gives us the value of stresses produced on 6) Instantaneous deflection and re-curve of the strip has the surface of the body. These results matches closely within also been achieved. the range of stresses produced in the body through software analysis. Taking it one step further software analysis gives REFERENCES us the results of stresses produced along the length of the strip. [1] Capgo Bimetallic Strips.http://www.capgo.com/Resources/Temperature/B iMet/BiMetallic.html [2] Working of Refrigerator and refrigeration principle.www.learnengineering.org/2014/04/working- of-Refrigerator.html. [3] How does a Frost free refrigerator’s defrost works.www.appliance411.com/faq/howdefrostworks.sh tml [4] Design, fabrication and thermomechanical testing of a vertical bimorph sensor in the wafer plane.http://citeseerx.ist.psu.edu/viewdoc/download?doi =10.1.1.563.9816&rep=rep1&type=pdf [5] Kanthal Thermostatic Bimetal Handbook. [6] Design of a Bimetallic Thermal Switch. Fig. 17: Von-Misses stress analysis. [7] Stresses in Beams. C. Maximum Principal Stress [8] ANSYS workbench 16.0. [9] Difference between Von-misses stress and Maximum 1) Maximum Principal stress theory: Principal Stress. https://www.quora.com/What-is-the- According to this type of theory of failure will be come difference-between-von-Mises-Stress-and-Max- when the maximum principal stress in the system touching Principal-Stress the numeric value of the maximum strength at elastic limit in simplex tension.

Fig. 18: Maximum principal stress theory analysis.