Abstract
Capacitive and optical-based pressure sensors are considered for wide application in industries and R&D labs due to their superior performance. In general, these sensors use a diaphragm as a sensing element that needs to be designed accurately to achieve the desired level of accuracy for a higher operating range of the sensor. To design such a diaphragm, the conventional strain-based model cannot be used efficiently as the strain gradient starts dominating to introduce non-linear deformation with respect to the applied load when the diaphragm thickness reduces or the operating range increases beyond a certain value. Thus, there is a need to establish a comprehensive understanding and accurate modeling method to establish the underlying mechanism of the strain gradient. In view of this, a finite element analysis is carried out with moving-mesh to investigate the effect of the strain gradient phenomenon extensively in this paper. For the investigation, a few parameters are studied such as strain, strain gradient, bending rigidity, and deflection. It shows that the strain gradient spreads radially on the diaphragm and its zone of influence depends on the thickness as well as the applied pressure. This increases the bending rigidity significantly and the diaphragm deflection becomes non-linear as compared to the classical theory of bending. For validation of the present model, the bending rigidity and the deflection behavior are also compared with an earlier developed mathematical model as well as experimental results, and the same is discussed in this paper. The present work is useful for an accurate design and optimization of a diaphragm or a flexure for small size or/and higher operating range of pressure sensors and actuators.
Similar content being viewed by others
References
AkgÖz B, Civalek Ö (2012) Investigation of size effects on static response of single-walled carbon nanotubes based on strain gradient elasticity. Int J Comput Methods. https://doi.org/10.1142/S0219876212400324
Akgöz B, Civalek Ö (2014) Longitudinal vibration analysis for microbars based on strain gradient elasticity theory. Jvc/journal Vib Control. https://doi.org/10.1177/1077546312463752
Akgöz B, Civalek Ö (2015) A novel microstructure-dependent shear deformable beam model. Int J Mech Sci. https://doi.org/10.1016/j.ijmecsci.2015.05.003
Akgöz B, Civalek Ö (2016) Bending analysis of embedded carbon nanotubes resting on an elastic foundation using strain gradient theory. Acta Astronaut. https://doi.org/10.1016/j.actaastro.2015.10.021
Bao MH (2000) Chapter 2 Basic mechanics of beam and diaphragm structures. Handbook sensors actuators. Elsevier, Amsterdam. https://doi.org/10.1016/S1386-2766(00)80016-X
Catling DC (1998) High-sensitivity silicon capacitive sensors for measuring medium-vacuum gas pressures. Sens Actuators A Phys 64:157–164. https://doi.org/10.1016/S0924-4247(98)80009-5
Chen L, Mehregany M (2008) A silicon carbide capacitive pressure sensor for in-cylinder pressure measurement. Sensors Actuators A Phys. https://doi.org/10.1016/j.sna.2007.09.015
Eswaran P, Malarvizhi S (2013) MEMS capacitive pressure sensors: a review on recent development and prospective. Int J Eng Technol 5:2734–2746
Gabrielson TB (1993) Mechanical-thermal noise in micromachined acoustic and vibration sensors. IEEE Trans Electron Devices. https://doi.org/10.1109/16.210197
Ghildiyal S, Ranjan P, Mishra S, Balasubramaniam R, John J (2019) Fabry-Perot interferometer-based absolute pressure sensor with stainless steel diaphragm. IEEE Sens J. https://doi.org/10.1109/JSEN.2019.2909097
He Z, Chen W, Liang B, Liu C, Yang L, Lu D et al (2018) Capacitive pressure sensor with high sensitivity and fast response to dynamic interaction based on graphene and porous nylon networks. ACS Appl Mater Interfaces. https://doi.org/10.1021/acsami.8b01050
Hu J, Duan W, Fan S, Xiao H (2022) A triangular wavy substrate-integrated wearable and flexible piezoelectric sensor for a linear pressure measurement and application in human health monitoring. Measurement 190:110724. https://doi.org/10.1016/J.MEASUREMENT.2022.110724
Jena S, Pandey C, Gupta A (2021) Mathematical modeling of different diaphragm geometries in MEMS pressure sensor. Mater Today Proc. https://doi.org/10.1016/j.matpr.2020.11.249
Jiang J, Zhang T, Wang S, Liu K, Li C, Zhao Z et al (2017) Noncontact ultrasonic detection in low-pressure carbon dioxide medium using high sensitivity fiber-optic Fabry-Perot sensor system. J Light Technol. https://doi.org/10.1109/JLT.2017.2765693
Jiranusornkul N, Kraduangdej S, Niltawach N, Pimpin A, Srituravanich W (2020) Development of a paper-based pressure sensor fabricated by an inkjet-printed water mask method. Microsyst Technol 26:2117–2121. https://doi.org/10.1007/s00542-020-04771-3
Kim Y, Neikirk DP (1995) Micromachined Fabry-Perot cavity pressure transducer. IEEE Photonics Technol Lett 7:1471–1473. https://doi.org/10.1109/68.477286
Lam DCC, Yang F, Chong ACM, Wang J, Tong P (2003) Experiments and theory in strain gradient elasticity. J Mech Phys Solids. https://doi.org/10.1016/S0022-5096(03)00053-X
Lampron O, Therriault D, Lévesque M (2021) An efficient and robust monolithic approach to phase-field quasi-static brittle fracture using a modified Newton method. Comput Methods Appl Mech Eng. https://doi.org/10.1016/j.cma.2021.114091
Landau LD, Lifshitz EM (1986) Theory of elasticity, Third Edition: (Course of Theoretical Physics), Pergamon Press, Oxford
Lee YS, Wise KD (1982) A batch-fabricated silicon capacitive pressure transducer with low temperature sensitivity. IEEE Trans Electron Devices. https://doi.org/10.1109/T-ED.1982.20656
Lei KF, Lee KF, Lee MY (2012) Development of a flexible PDMS capacitive pressure sensor for plantar pressure measurement. Microelectron Eng. https://doi.org/10.1016/j.mee.2012.06.005
Li G, Li D, Cheng Y, Sun W, Han X, Wang C (2018) Design of pressure-sensing diaphragm for MEMS capacitance diaphragm gauge considering size effect. AIP Adv. https://doi.org/10.1063/1.5021374
Li J, Jia P, Fang G, Wang J, Qian J, Ren Q et al (2022) Batch-producible all-silica fiber-optic Fabry-Perot pressure sensor for high-temperature applications up to 800 °C. Sens Actuators A Phys 334:113363. https://doi.org/10.1016/J.SNA.2022.113363
Lou L, Zhang S, Lim L, Park WT, Feng H, Kwong DL et al (2011) Characteristics of NEMS piezoresistive silicon nanowires pressure sensors with various diaphragm layers. Procedia Eng. https://doi.org/10.1016/j.proeng.2011.12.354
Ma J, Jin W, Ho HL, Dai JY (2012) High-sensitivity fiber-tip pressure sensor with graphene diaphragm. Opt Lett. https://doi.org/10.1364/ol.37.002493
Öchsner A (2021) Euler-Bernoulli beam theory. Class Beam Theor Struct Mech. https://doi.org/10.1007/978-3-030-76035-9_2
Perić B, Simonović A, Ivanov T, Stupar S, Vorkapić M, Peković O et al (2018) Design and testing characteristics of thin stainless steel diaphragms. Procedia Struct Integr. https://doi.org/10.1016/j.prostr.2018.12.141
Sanli H, Alptekin E, Canakci M (2022) Using low viscosity micro-emulsification fuels composed of waste frying oil-diesel fuel-higher bio-alcohols in a turbocharged-CRDI diesel engine. Fuel 308:121966. https://doi.org/10.1016/J.FUEL.2021.121966
Thai HT, Vo TP, Nguyen TK, Kim SE (2017) A review of continuum mechanics models for size-dependent analysis of beams and plates. Compos Struct. https://doi.org/10.1016/j.compstruct.2017.06.040
Van Hieu D, Chan DQ, Phi BG (2022) Analysis of nonlinear vibration and instability of electrostatic functionally graded micro-actuator based on nonlocal strain gradient theory considering thickness effect. Microsyst Technol. https://doi.org/10.1007/s00542-022-05321-9
Wan S, Bi H, Zhou Y, Xie X, Su S, Yin K et al (2017) Graphene oxide as high-performance dielectric materials for capacitive pressure sensors. Carbon N Y. https://doi.org/10.1016/j.carbon.2016.12.023
Wang H, Tao J, Jin K, Wang X, Dong Y (2022) Multifunctional pressure/temperature/bending sensor made of carbon fibre-multiwall carbon nanotubes for artificial electronic application. Compos Part A Appl Sci Manuf 154:106796. https://doi.org/10.1016/J.COMPOSITESA.2021.106796
Wilson SA, Jourdain RPJ, Zhang Q, Dorey RA, Bowen CR, Willander M et al (2007) New materials for micro-scale sensors and actuators. An engineering review. Mater Sci Eng R Rep. https://doi.org/10.1016/j.mser.2007.03.001
Xu M, Feng Y, Han X, Ke X, Li G, Zeng Y et al (2021) Design and fabrication of an absolute pressure MEMS capacitance vacuum sensor based on silicon bonding technology. Vacuum. https://doi.org/10.1016/j.vacuum.2021.110065
Yin J, Liu T, Jiang J, Liu K, Wang S, Qin Z et al (2014) Batch-producible fiber-optic fabry-pérot sensor for simultaneous pressure and temperature sensing. IEEE Photonics Technol Lett. https://doi.org/10.1109/LPT.2014.2347055
Young DJ, Du J, Zorman CA, Ko WH (2004) High-temperature single-crystal 3C-SiC capacitive pressure sensor. IEEE Sens J. https://doi.org/10.1109/JSEN.2004.830301
Zhou MX, Huang QA, Qin M, Zhou W (2005) A novel capacitive pressure sensor based on sandwich structures. J Microelectromech Syst. https://doi.org/10.1109/JMEMS.2005.859100
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Ranjan, P. Modeling and analysis of the effect of strain gradient to design diaphragm for pressure sensing application through finite element analysis. Microsyst Technol (2024). https://doi.org/10.1007/s00542-024-05643-w
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00542-024-05643-w