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The finite element method (FEM) is a numerical method for solving problems of engineering and mathematical physics. It is also referred to as finite element analysis (FEA). Typical problem areas of interest include structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential.
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Jan Albrecht, Rainer Dudek, Jilrgen Auersperg, Remi Pantou, Sven Rzepka Fraunhofer ENAS, Micro Materials Center, Technologie-Campus 3, 09126 Chemnitz, Germany [email protected]; +49-371-4500-
Abstract The determination of the mechanical and thermo mechanical behaviour of a UHF-RFID-based smart system embedded in a transmission belt has been the goal of the work reported in this paper. The complex bending and thermal loads occurring during fabrication and service are taken into account by finite element simulations using ABAQUS standard™. In order to achieve quantitatively correct results, dynamic mechanical analyses using DMA Q800, DMA 2000+ as well as thermo-mechanical analyses using TMA Q have been performed to characterize the behaviour of the different materials. The results of the finite element analyses match the experimental observations very well. Therefore, recommendations for design optimization could be deduced that prevent early and fatigue failures of the smart system inside the transmission belt.
provide the functionality, the embedded smart system must reliably withstand all mechanical and thermal loads that occur during fabrication and operation of the belt. During fabricating, temperatures in excess of 180°C and high pressures are applied. In consequence, a substantial material shrinkage occurs during these vulcanization processes so that large thermo-mechanical stresses are induced into the smart system as well as at its interfaces to the rubber composite material of the belt. During operation, frequent cyclic bending as well as tension and various pulse loads of high magnitudes occur. They cause frictional self-heating of the belt with the consequence of thermal expansion. The smart system must endure all the thermal and mechanical stresses caused by this complex cyclic dynamic load situation. These loadings also applied to the implemented tag which can be reduced by positioning the tag close to the neutral fibre of the belt, which means close to the embedded cords.
RFID-tag
components FR4 substrate
To model the behaviour close to reality, appropriate material parameters have to be determined by experimental tests and transferred into material laws. The behaviour of belts under bending loads has been investigated for instance in [4]. The base material of the tag is FR4, a glass-reinforced epoxy laminate with an orthotropic material behaviour. The material properties could be used from former investigations. The embedded die within the tag is assumed as bulk silicon. All other components of the smart system like the antenna and the electronic components beside the die are neglected. The ethylene-propylene-diene (EPDM) material (elastomer) of the belt can be described by hyperelastic material laws, which means that the material is nearly incompressible under pressure and exhibits large strains under tension. The behaviour is markedly nonlinear. To describe this behaviour, various material laws with different ranges of validity exist like NeoHook, Mooney Rivlin, Odgen, Arruda-Boyce etc. (Fehler! Verweisquelle konnte nicht gefunden werden.) [5-8].
model applied strain range Neo-Hookean upto 30 % Mooney-Rivlin < 100 % (2nd + 3rd order) < 200 % (5th + 9th order) Ogden upto 700 % Yeoh <300% Polynomial <300%
In this work, the 2nd order Mooney-Rivlin model has been used. It combines a sufficiently large strain range with only three parameters to be determined. As shown in [10], the hyperelastic material model is based on the strain energy potential U
U =u(II,!2,J) (I)
which is a function of I) and 12 as first and second
invariant of the deviatoric stretch matrix, respectively, and J as the volume change, while the strain (stretch) A is defined by: A, = (^1) + &" (^) (2)
In case of the Mooney-Rivlin relation, (1) is defmed by:
u=c1o(II -3)+Co1(12 -3)+_1 (Je/-1)
(^2) (3) D where D1, C)o and CO) are material parameters. The last
term of equation (3) describes the compressibility of the material. It becomes zero when the material is fully incompressible. Then, C10 and CoI are the only
parameters left to be determined by the tensile tests.
The specimens for the dynamic mechanical analysis (DMA) were 20.0 mm x 9.5 mm x 2.3 mm in size. The tests applied the tensile load with a frequency of 1 Hz and within a temperature range from -50°C to 150 °C. The thermo-mechanical analyses (TMA) for obtaining the CTE used specimens of 6.0 mm x 9.5 mm x 2.3 mm in size. The parameters of the Mooney Rivlin equation describing the hyperelastic material behaviour utilized specimens with two and three layers of the EPDM and fiber material in the tensile tests along the longitudinal and transversal directions, respectively. FE simulation of the tensile tests and OptiSlang parameter identification was employed to calibrate the Mooney-Rivlin parameters according to equation (3). Beside the classical analytical equation, these FE models consider the pressure of the clamp during the fixing process in addition.
em bedded tag
The thermally induced stress is evaluated by cooling down the belt from its stress free state at 180 °C to 20 °C. During the vulcanization process the change of the temperature is slow, therefore the temperature field inside the belt is assumed as homogenous. The length of the belt is constraint during the vulcanisation process. The bending process of the belt with the axial preload has been modelled by superimposing the two following steps. The first one is the bending around the pulley and the second one is the impinging of the axial load. Any thermal heating due to mechanical loads was neglected.
thermal thermal + mechanical 511 [MPa] 100 o
500 533 [MPa] 100 o
00
y� (^) ,
However, the interface toughness between the FR4 tag material and the EPDM material is not well understood. Between the tag and the EPDM material shear stresses between 16 MPa and -26 MPa occur at the edges of the tag (see Fig. 10). The sharp edges also increase the risk of crack initiation into the rubber material. This can be reduced by rounding theses edges. Within this investigation, the thermal-mechanical load due to the heat of the tag up to the vulcanisation temperature has not been investigated.
been detected inside the tag. However, the interface behaviour between the tag and the surrounding rubber material is not well understood yet and requires further investigation. In particular, delamination processes at the interface are not debarred although they may not be too critical due to the surrounding pressure.
Acknowledgments Part of this work has been supported by the German government within the project 'smartFIT' (FKZ: KF2427003KM3). Financial support from BMWi is gratefully acknowledged. The authors thank Dr. Kaulfersch for his helpful advices and Mrs. KreyJ3ig for help at the material testing. They are also grateful to Mr. Tchouangte and Mr. Scheele from OPTIBELT for providing samples for the material characterization and Mr. Bilker for the legwork. References I. Yang, Li, Rida, A., Li, J.: "Antenna advancement techniques and integration of RFID electronics on organic substrates for UHF RFID applications in automotive sensing and vehicle security", Vehicular Technology Conference, IEEE 66th, pp. 2040-2041, 2007
RFID Technology and Applications Conference, [EEE, pp. 97-[02, 2014
Electronic Components and Technology Conference, pp. 867-870, 2005
, Master Thesis, University of Toronto, Department of Mechanical and Industrial Engineering, pp. 92, 2010
, Journal of Mechanics and Physics of Solids, Vol. 41, No. 2, pp. 389-412, 1993
, Philosophical Transactions of the Royal
Society of London. Series A, Mathematical and Physical Sciences, Vol. 241, pp. 379-397, 1948
, PhD Thesis, University of Twente, Netherlands, pp. 1-162, 2012
Journal of Applied Science, Vol. 83, pp. 2474-2484, 2002