Modeling and Analysis of Theral Biorph Using COMSOL Rachita Shettar *, Dr B G Sheeparaatti 2 Basaveshwar Engineering college Bagalkot- 587102 *Corresponding author: D/o J.H Shettar, #156B Shivananda nagar, kalasapur road, Gadag 582101. rachita.shettar@gail.co Abstract: In this paper odeling and siulation results of a theral biorph is capable of producing increased displaceent for increasing teperatures are presented. Theral biorphs are popular actuation technology in MEMS (Micro-Electro-Mechanical Systes). Biorph actuators consist of two aterials with different coefficients of theral expansion. The ain objective of this work is to investigate the deforation in biorph actuator for varying teperatures. Deforation increases with increase in length of the actuator. Thus, teperature produces theral strain and therally induced deforation and this akes the icrostructure into a theral actuator. Keywords: Theral Biorph, icroactuator, theral actuator. 1. Introduction A biorph actuator consists of two thin-fil layers. Difference in the strains produced in the two layers causes a biorph to curl, there by leading to actuation [1]. Understanding about the actuation of theral biorph actuated probe and investigation of physical phenoena by heat transfer is achieved using finite eleent analysis ethods. Through virtual siulation, the author could predict deflections and teperature distribution [2]. The easureent of teperature and heat is widely practiced and can be achieved using any different principles. In this paper concentrated ainly on theral biorph sensors. Theral bietallic effect is a ethod used for sensing and actuation. This echanis allows the teperature variation in icrostructures to be exhibited as the transverse displaceent of the echanical beas. The theral biorph consists of two aterials joined along their longitudinal axis serving as a single echanical eleent. Often a theral bietallic actuator ay consist of ore than two layers of aterials [3]. Curved biorphs undergo cobined out-of-plane bending and twisting upon actuation. The analysis procedure outlined in this paper ay be extended to biorphs of arbitrary shape by treating the in-plane radius of curvature, R as a function of the distance along the biorph [3]. The large out-of-plane bending displaceent and force generated by this actuator at a low driving voltage and a low actuation teperature are quite unique characteristics [4]. The presented actuator can find applications where a large vertical displaceent is needed and it is fabricated to be sall in size, lightweight and low in cost [5]. Biaterial actuators consist of aterials with different coefficients of theral expansion and function siilarly to a bietallic therostat [6]. In this paper SiC as a new aterial for the botto layer of an electrotheral biorph actuator is proposed and tested [7]. The actuator, based on a piezocantilever, cobines the piezoelectric effect and the theral biorph principle [8]. The odel agrees with
experiental results within 15% for teperature distribution data and 10% for rotation angle versus voltage data for voltages less than 15 V. At higher voltages the experiental results deviate fro the results predicted by the odel [9]. Theral biorph is for the better understanding of relation between perforance and design paraeters [10]. 2. Methodology Principle of actuation is by increase in teperature heats the biorph, as aluinu expands ore bea bends and results in an angular displaceent. A theral biorph bea is coposed of two aterial fils, with different Coefficients of theral expansion CTE, bonded at an interface. Typically theral biorphs are ade of one aterial with a low CTE, such as a dielectric like Polysilicon, and another aterial with a high CTE, such as etal like aluinu. When the teperature of the biorph is raised, the high CTE aterial will expand ore than the low CTE aterial. Since both aterials are bonded together, stress develops in both aterial layers due to the bonded interface constraint.. The high CTE aterial exhibits a copressive stress because it is stretched below its equilibriu length, and the low CTE aterial exhibits a tensile stress because it is stretched past its equilibriu length. The stresses that developed upon an increase in teperature will cause the biorph to curl towards the Coefficient of theral expansion of aluinu with α 1 =23e - 6 [1/K] where, the Coefficient of theral expansion of Polysilicon is α 2 =2.33e -6 [1/K], low CTE aterial to iniize the internal energy stored by the stress. However theral expansion co-efficient for ost aterials are very sall hence aount of displaceent would be sall. The teperature at which the biorph aterials are deposited, assuing no residual stress is present fro processing conditions, both aterials will be at their equilibriu lengths and the biorph will be flat. The opposite effect happens when the teperature of a biorph is lowered. The high CTE aterial will contract ore than the low CTE aterial, and will develop tensile stress. The lower CTE aterial will be contracted to a length shorter than its equilibriu length and will develop copressive stress. When the teperature of a biorph is lowered, the biorph will bend towards the high CTE aterial to iniize the internal energy stored by the stress. The effects of an increase in teperature to the curl of a cantilevered biorph are shown in Fig 1. Figure 1 Theral bietallic bending (α 1 > α 2 ) Figure 2 Geoetry of theral biorphs actuator using cosol 4.2
3. COMSOL Ipleentation The proposed structures is odeled and siulated in COMSOL 4.2 siulation software. MEMS odule was used to design actuator. In Structural echanics physics the Joule heating and theral expansion is selected as physics in order to deterine deforations and teperature for varying tep and provide the fixed constraint on one of the edge of theral biorph. The polysilicon and aluinu aterials are used. In designing theral bietallic actuator consist of two etals used as the actuator aterial, the aterial properties of polysilicon are Young s odulus: 160[GPa], Density: 2320[kg/ 3 ], Poisson s ratio: 0.22, Coefficient of theral expansion (α1): 2.6*10-6 [1/K], Electrical conductivity: 5*10 4 [S/]. Siilarly aluinu is having Young s odulus 70e 9 [Pa], density 2700[kg/ 3 ] and Poisson s ratio 0.33, where Polysilicon is having Young s odulus 169e 9 [Pa], Density 2320[kg/ 3 ] and Poisson s ratio 0.22. Cosol siulations were prefored on the theral bietallic actuator to investigate the effect of variations in the teperature Vs deforations. Figure 4 Total displaceent is 31.381µ at T o =1000K and L=100µ (α1> α2). Figure 5 Teperature distribution of theral biorph (α2> α1) at T o =600K and L=250µ, resulting deforation is 29.861 µ. Figure 6 Teperature distribution of theral biorph (α1> α2) at T o =1000K and L=100 µ, resulting deforation is 31.38 µ. Figure 3 Total displaceent is 17.594µ at 1000K and L=100µ (α2> α1) In this work it is shown that by increasing the teperature fro 300K to 2500K the deflection also increases fro 0.1705µ to 54.93µ shown in Fig 3 and also in Fig 4. Initially in first
case aluinu block is plac botto and polysilicon block is plac top layer and observed that as two-layered aterials are tightly join the interface, the bea curve down towards the aluinu as shown in Fig 5. In second case aluinu block is plac top and polysilicon block is placed in botto layer and observed that the bea curves up towards the aluinu as shown in Fig 6. Hence the bea bends in downward direction as CTE of top bea is ore and when the CTE of botto bea is ore it bend in upward direction. 4. Theral Biorph The Biorph cantilever bea is ade of two layers of sae lengths. Coposite bea with two layers, ade of aterials 1 and 2, having the sae length (L) but different coefficients of theral expansion (CTE) (α 1 > α 2 ) shown in Fig 1. The layer on top is ade of aluinu, where as the layer on botto is ade of Polysilicon. The width of both layers is 20µ. In geoetry length of the both segent is equal to 100µ as shown in Fig 2. The subscript refers to the aterial layer. Likewise, Young s odulus, width, and thickness of the two layers are denoted E i, w i, and t i (i=1 or 2). T is Unifor rise in teperature, the length of two sections changes equally. Because the two-layered aterials are tightly join interface, the bea ust curve towards the layer ade of the aterial with lower CTE value. A transverse bea bending is therefore produced. The below equation is analyzed in order to calculate the displaceent of a bietallic bea. Initially values of radius of curvature for unifor change in teperature are deterined. Radius of Curvature decreases with increase in T. 1 6w1 w2e1e 2t1t 2( t1+ t2)( α1 α2) T = 2 2 2 2 2 r ( w E t ) + ( w E t ) + 2w w E E t t (2t + 3t t + 2t 1 1 1 2 2 2 1 2 1 2 1 2 1 1 2 Let bea curves under unifor change in teperature of T, assue the shape of the section for an arc with length of the arc being L. The radius of curvature of the arc r can be calculated using this forula. Where w 1 =20µ, w 2 =30µ, t 1 =1µ, t 2 =2µ, E 1 =70Gpa, E 2 =169Gpa, α 1 =23*10-6 [1/K], α 2 =2.33*10-6 [1/K], let L=100µ, Where α is Co-efficient of theral expansion. The arc is a section of a circle with radius of curvature being denoted r, spanning an arc angle ɵ. The value of ɵ is deterined using values of length of the bea and deterined radius of curvature as given in following equation ɵ = L /r Once the radius of curvature is found, the vertical displaceent of the free end of the bea can be deterined by trigonoetry. The vertical displaceent at the free end of the cantilever is given in equation d = r - r cos ɵ If the overall bending angle is sall, the agnitude of vertical displaceent can be estiated by replacing cos ɵ with the first two ters in its Taylor series expansion given in equation below. d = r r (1-1/2 ɵ 2 + O (ɵ 4 ) = ½ r ɵ 2 2 2 )
5. Result and discussion The siulation results obtained in this work corresponds to their analytical odels validating the confority of the analysis using above expressions. Coparisons between Siulated and analytical values for displaceent with L=100 µ shown in table 1and corresponding graph is shown in Fig 7. Now for a varying length L=100µ, 150µ, 200µ, 250µ deforations are deterined and it is found to be increasing with increase in length of a bea shown in table 2 and corresponding graph representing teperature Vs displaceent between the lengths L is varied fro 100µ to 250µ shown in Fig 8, here one can say as length of biorph increases deforation also increases. Figure 7 Plot showing Coparison of analytical and siulated results of Theral Biorph actuator, at L=100µ. Table 1 Coparison of siulated and analytical displaceent with L=100 µ. Teperature difference (K) T Displaceent (µ) Siulated Analytical* 50 1.2445 1.5819 100 2.4891 3.0432 200 4.978 6.0800 500 12.4484 15.10385 1000 24.891 29.519 Table 2 Coparison of siulated displaceent for varying length L=100 µ, 150 µ, 200 µ, 250 µ. Teperat ure difference (K) T Siulat L=100µ Siulat L=150µ Siulat L=200µ Siulat L=250µ 50 1.2445 2.345 3.565 4.866 100 2.4891 4.6904 7.1297 9.732 200 4.978 9.3804 14.259 19.463 500 12.4484 23.4514 35.657 48.657 1000 24.891 46.901 71.303 97.32 Figure 8 Plot showing increase in deforations for varying length 6. Conclusion In this work coupled ultiphysics siulation and study of the theral behavior of a theral biorph is carried out using COMSOL 4.2. The siulation and analytical results are also copared. Their operating principle is based on differential theral expansion induced by Joule heating and theral expansion. Theral biorphs and other theral actuators have been used in any applications, like icro grippers, icro-optical irrors etc. In ost cases open
loop control is used due to difficulties in fabricating positioning sensors together with actuator. 7. References 1. Sagnik Pal and Huikai Xie, Analysis and Siulation of Curved Biorph Microactuators ISBN 978-1-4398-3402-2 Vol 2,2010 2. Younghnk Cho, Beojoon Ki, Seokkwan Hong, Jeongjin Kang, Fabrication and Characterization of therally actuated biorph Probe for Living Cell Measureents with Experiental and Nuerical Analysis Vol 20 No 3, pp 297-309,2006. 3. Chang Liu, Foundations of MEMS, Pearson International Edition, 2006. 4. J. Wei, T. Chu Duc, G.K. Lau and P.M. Sarro Novel Electrotheral Biorph Actuator for Large out-of-plane displaceent and force ieee January 13-17, pp 46-49, 2008. 5. Won-Kyu Jeung, Seog-Moon Choi and Yong-Jun Ki, Large Displaceent Polyer Biorph Actuator for Out-of- Plane Motion Journal Vol. 1, No. 2, pp. 263~267, 2006. 6. Leslie M. Phinney, Michael S. Baker and Justin R. Serrano, Theral Microactuators pp 416-434. 7. M. Aarts, J. Wei, P.M. Sarro, Silicon- Polyer Electro-theral biorph actuators with SiC botto-layer for large out-of-plane otion and iproved power efficiency pp 253-256, March 5-8, 2012. 8. Micky Rakotondrabe, eber, IEEE and Ioan Alexandru Ivan, eber, IEEE, Developent and dynaic odeling of a new hybrid theropiezoelectric icro-actuator IEEE Transaction on Robotics 26, 6 (2010) 1077-1085. 9. Shane T. Todd, Student Meber, IEEE, and Huikai Xie, Senior Meber, IEEE, An Electrotheroechanical Luped Eleent odel of an Electrotheral Biorph Actuator pp 213-225,Vol. 17, No.1, FEBRUARY 2008. 10. Wuyong Peng, Optiization Studies Of Theral Biorph Cantilevers, Electrostatic Torsion Actuators and Variable Capacitors May 2004.