Abstract
A force sensor utilizing a transformer concept with a ferrofluid core was developed. A ferrofluid reservoir was machined out of Teflon and the open top of the reservoir was sealed with a thin silicone membrane. Forces applied to the silicone membrane caused the membrane to deflect, resulting in the displacement of the ferrofluid in the reservoir through an external tube. The ferrofluid in the tube acted as the core of voltage transformer. The ferrofluid core was excited by an alternating current across a wire coil wound around the tube. A secondary coil was wound around the top portion of the tube which was vertically oriented. As the ferrofluid level in the tube rose in response to applied forces, the secondary coil became engaged by the magnetized ferrofluid, resulting in a voltage induced in the secondary coil that varied with the level of the ferrofluid. The sensor was characterized by the relationship between the forces applied to the membrane and the output voltage readings across the secondary coil in loading and unloading cycles. This relationship was found to be nonlinear and following a negative second-degree polynomial relationship. The sensor was tested at three primary frequencies of 60, 100 and 120 kHz. It was found that 13% of the 5 V A/C exciting voltage applied across the primary coil at 60 kHz was induced into the secondary coil when it was fully engaged by the magnetized ferrofluid. It was determined that the sensor generates the highest sensitivity of 68.3 mV/N over the effective range of 0.1–2.5 N at 60 kHz. The sensor was analyzed for error and the characteristic error was found to be comparable to existing inductive sensors. Sources of most significant of error were identified and proposals for improvements to future designs of this sensor type are provided.
Similar content being viewed by others
Abbreviations
- \( \varvec{\epsilon} \) :
-
Electromotive force (V)
- \( \varvec{\epsilon}_{1} \) :
-
Electromotive force across the primary coil (V)
- \( \varvec{\epsilon}_{2} \) :
-
Electromotive force across the secondary coil (V)
- \( \varvec{N}_{1} \) :
-
Number of wire turns in the primary coil
- \( \varvec{N}_{2} \) :
-
Number of wire turns in the secondary coil that are affected by the magnetic flux transferred by the ferrofluid core
- \( \varvec{\varPhi}_{\varvec{B}} \) :
-
Magnetic flux (Wb)
- \( \varvec{P} \) :
-
Force applied at the center of the membrane (N)
- \( \varvec{h} \) :
-
Linear vertical distance from the base of the secondary coil/end of the primary coil to the level of the ferrofluid (mm)
- \( \varvec{w} \) :
-
Deflection of the silicon membrane (mm)
- \( \varvec{\gamma} \) :
-
Constant representing the geometric and material property constants of the silicon membrane
- \( \varvec{R} \) :
-
Radius of the fixed edge of the silicon membrane (mm)
- \( \varvec{r} \) :
-
Internal radius of the tube through which the ferrofluid is displaced (mm)
- \( \varvec{\rho}_{\varvec{c}} \) :
-
Vertical linear coil density (turns/mm)
References
Al-Mai O, Ahmadi M, Albert J (2017) A compliant 3-axis fiber-optic force sensor for biomechanical measurement. IEEE Sens J 17(20):6549–6557
Boresi AP, Schmidt RJ (2003) Advanced mechanics of materials, 6th edn. Wiley, New York
Brookhuis RA, Sanders RG, Ma K, Lammerink TS, de Boer MJ, Krijnen GJ, Wiegerink RJ (2015) Miniature large range multi-axis force-torque sensor for biomechanical applications. J Micromech Microeng 25(2):025012
Cheng W, Dong Y, Feng G (2001) A multi-resolution wireless force sensing system based upon a passive SAW device. IEEE Trans Ultrason Ferroelectr Freq Control 48(5):1438–1441
Chitnis G, Ziaie B (2013) A ferrofluid-based wireless pressure sensor. J Micromech Microeng 23(12):125031
Cho C, Ryuh Y (2016) Fabrication of flexible tactile force sensor using conductive ink and silicon elastomer. Sens Actuators A 237:72–80
Coughlin T, Rashidi R (2020) A powerless iron oxide based magnetometer. Microsyst Technol 22:1–12
Curry EJ, Ke K, Chorsi MT, Wrobel KS, Miller AN, Patel A, Kim I, Feng J, Yue L, Wu Q, Kuo CL (2018) Biodegradable piezoelectric force sensor. Proc Natl Acad Sci 115(5):909–914
De Volder M, Reynaerts D (2009) Development of a hybrid ferrofluid seal technology for miniature pneumatic and hydraulic actuators. Sens Actuators A 152(2):234–240
DeGraff A, Rashidi R (2020) Ferrofluid transformer-based tilt sensor. Microsyst Technol 21:1–8
Felix M, Lizarraga A, Islas A, González A (2010) Analysis of a ferrofluid core LVDT displacement sensor. In: IECON 2010-36th annual conference on IEEE industrial electronics society. IEEE, pp. 1769–1772
Ferreira RR, Fukui H, Chow R, Vilfan A, Vermot J (2019) The cilium as a force sensor–myth versus reality. J Cell Sci 132(14):jcs213496
Gautschi G (2002) Piezoelectric sensors. In: Piezoelectric Sensorics. Springer, Berlin, pp 73–91
Harlow JH (2003) Electric power transformer engineering. CRC press, Boca Raton, FL, USA
Hashimoto M, Cabuz C, Minami K, Esashi M (1995) Silicon resonant angular rate sensor using electromagnetic excitation and capacitive detection. J Micromech Microeng 5(3):219
Homa D, Pickrell G (2014) Magnetic sensing with ferrofluid and fiber optic connectors. Sensors 14(3):3891–3896
Honda S, Zhu Q, Satoh S, Arie T, Akita S, Takei K (2019) Textile-based flexible tactile force sensor sheet. Adv Func Mater 29(9):1807957
Huang Y, Wang T, Deng C, Zhang X, Pang F, Bai X, Dong W, Wang L, Chen Z (2017) A highly sensitive intensity-modulated optical fiber magnetic field sensor based on the magnetic fluid and multimode interference. J Sens 2017:7. https://doi.org/10.1155/2017/9573061
Hussain D, Wen Y, Zhang H, Song J, Xie H (2018) Atomic force microscopy sidewall imaging with a quartz tuning fork force sensor. Sensors 18(1):100
Ikemoto Y, Suzuki S, Okamoto H, Murakami H, Asama H, Morishita S, Mishima T, Lin X, Itoh H (2009) Force sensor system for structural health monitoring using passive RFID tags. Sens Rev 29(2):127–136
Kaur S, Kaur D (2019) Analysis of effect of core material on the performance of single phase transformer using FEM. In: Muthusamy R (ed) IOP conference series: materials science and engineering, vol 561, no. 1, p. 012129). IOP Publishing, ICMSMT 2019, Coimbatore, India
Kim U, Lee DH, Yoon WJ, Hannaford B, Choi HR (2015) Force sensor integrated surgical forceps for minimally invasive robotic surgery. IEEE Trans Rob 31(5):1214–1224
Kim K, Park J, Suh JH, Kim M, Jeong Y, Park I (2017) 3D printing of multiaxial force sensors using carbon nanotube (CNT)/thermoplastic polyurethane (TPU) filaments. Sens Actuators A 263:493–500
Ko J, Bhullar S, Cho Y, Lee PC, Jun MB (2015) Design and fabrication of auxetic stretchable force sensor for hand rehabilitation. Smart Mater Struct 24(7):075027
Kou J, Zhang Y, Liu Y, Zhang K, Liu W, Zhai J (2017) Nano-force sensor based on a single tellurium microwire. Semicond Sci Technol 32(7):074001
Kulkarni SV, Khaparde SA (2004) Transformer engineering. Marcel Dekker, New York
Martinez L, Cecelja F, Rakowski R (2005) A novel magneto-optic ferrofluid material for sensor applications. Sens Actuators A 123:438–443
Mayer D (2015) An approach to measurement of permeability/permittivity tensor of ferrofluids. J Electr Eng 66(5):292–296
Medvegy T, Molnar A, Molnar G, Gugolya Z (2017) Analysis of a ferrofluid core differential transformer tilt measurement sensor. J Magn Magn Mater 428:189–193
Michelson T, Rudnick J, Baxter J, Rashidi R (2019) A novel ferrofluid-based valve-less pump. In: ASME 2019 international mechanical engineering congress and exposition. American Society of Mechanical Engineers Digital Collection
Mirzanejad H, Agheli M (2019) Soft force sensor made of magnetic powder blended with silicone rubber. Sens Actuators A 293:108–118
Nair S (2013) Industrial applications of ferrofluids. Chaos Complex Lett 7(1/2):99
Nazir TA, Hrycyk L, Moreau Q, Frak V, Cheylus A, Ott L, Lindemann O, Fischer MH, Paulignan Y, Delevoye-Turrell Y (2017) A simple technique to study embodied language processes: the grip force sensor. Behav Res Methods 49(1):61–73
Noh Y, Liu H, Sareh S, Chathuranga DS, Würdemann H, Rhode K, Althoefer K (2016) Image-based optical miniaturized three-axis force sensor for cardiac catheterization. IEEE Sens J 16(22):7924–7932
Olaru R, Arcire A, Petrescu C, Mihai MM (2017) Study of the magnetic force delivered by an actuator with nonlinear ferrofluid and permanent magnets. IEEJ Trans Electr Electron Eng 12(1):24–30
Perez-Castillejos R, Plaza JA, Esteve J, Losantos P, Acero MC, Cané C, Serra-Mestres F (2000) The use of ferrofluids in micromechanics. Sens Actuators A 84(1–2):176–180
Qian L, Li D (2014) Use of magnetic fluid in accelerometers. J Sens 2014:9. https://doi.org/10.1155/2014/375623
Răcuciu M, Creangă D, Călugăru G (2005) Synthesis and rheological properties of an aqueous ferrofluid. J Optoelectron Adv M 7:2859–2864
Raj K, Moskowitz B, Casciari R (1995) Advances in ferrofluid technology. J Magn Magn Mater 149(1–2):174–180
Ravaud R, Lemarquand G, Lemarquand V (2010) Mechanical properties of ferrofluid applications: centering effect and capacity of a seal. Tribol Int 43(1–2):76–82
Saari M, Xia B, Cox B, Krueger PS, Cohen AL, Richer E (2016) Fabrication and analysis of a composite 3D printed capacitive force sensor. 3D Print Additive Manuf 3(3):136–141
Sadeghi MM, Dowling K, Peterson RL, Najafi K (2013) High sensitivity, high density micro-hydraulic force sensor array utilizing stereo-lithography fabrication technique. In: 2013 IEEE 26th international conference on micro electro mechanical systems (MEMS). IEEE, pp. 673–676
Salpavaara T, Verho J, Lekkala J, Halttunen J (2009) Wireless insole sensor system for plantar force measurements during sport events. In: Proceedings of IMEKO XIX world congress on fundamental and applied metrology, pp 2118–2123
Scherer C, Figueiredo Neto AM (2005) Ferrofluids: properties and applications. Braz J Phys 35(3A):718–727
Song A, Wu J, Qin G, Huang W (2007) A novel self-decoupled four degree-of-freedom wrist force/torque sensor. Measurement 40(9–10):883–891
Toyama S, Tanaka Y, Shirogane S, Nakamura T, Umino T, Uehara R, Okamoto T, Igarashi H (2017) Development of wearable sheet-type shear force sensor and measurement system that is insusceptible to temperature and pressure. Sensors 17(8):1752
Volkova TI, Böhm V, Naletova VA, Kaufhold T, Becker F, Zeidis I, Zimmermann K (2017) A ferrofluid based artificial tactile sensor with magnetic field control. J Magn Magn Mater 431:277–280
Xiong L, Jiang G, Guo Y, Liu H (2018) A three-dimensional fiber Bragg grating force sensor for robot. IEEE Sens J 18(9):3632–3639
Yaniger SI (1991) Force sensing resistors: a review of the technology. In: Electro International. IEEE, pp 666-668
Yao J, Huang C, Li D (2015) Research on a novel ferrofluid inertial sensor with levitating nonmagnetic rod. IEEE Sens J 16(5):1130–1135
Yao J, Liu S, Li Z, Li D (2016) A novel ferrofluid inclinometer exploiting a hall element. IEEE Sens J 16(22):7986–7991
Zhang W, Lua KB, Senthil KA, Lim TT, Yeo KS, Zhou G (2016) Design and characterization of a novel T-shaped multi-axis piezoresistive force/moment sensor. IEEE Sens J 16(11):4198–4210
Zhang L, Guo S, Yu H, Song Y (2017a) Performance evaluation of a strain-gauge force sensor for a haptic robot-assisted catheter operating system. Microsyst Technol 23(10):5041–5050
Zhang Y, Rajamani R, Sezen S (2017b) Novel supercapacitor-based force sensor insensitive to parasitic noise. IEEE Sens Lett 1(6):1–4
Acknowledgements
We thank Trevor Michelson for his assistance in 3D printing the parts and initiating the test setup.
Funding
This research was supported by Alfred State Applied Learning Program.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
There is no conflict of interest.
Availability of data and material
Not applicable.
Code availability
Not applicable.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Martin, J., Rashidi, R. A differential transformer-based force sensor utilizing a magnetic fluid core. Microsyst Technol 27, 115–126 (2021). https://doi.org/10.1007/s00542-020-04923-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00542-020-04923-5