Force frequency effect in square quartz crystals

Document Type : Research Article


1 زنجان-مهندسی- گروه مهندسی مکانیک

2 Department of Mechanical Engineering University of Tehran


In this investigation, the force-frequency effect in a square AT-Cut quartz resonator is studied. Based on the force-frequency effect, by insertion of diametrical forces, the natural frequency of thickness shear vibration mode in AT-Cut quartz resonators is changed. This criterion is of importance in designing quartz resonators and force sensors. In this paper, the frequency change of a square AT-Cut quartz crystal subjected to a pair of opposing forces on different points of its edge is studied experimentally. Also, the force-frequency effect in the square crystal is modeled by a previously developed mathematical-finite element model. The accuracy of the model is verified by the experimental results. Then, the model is applied for evaluating the force-frequency effect in the AT-Cut crystal, and the frequency shifts in different loading configurations are obtained. The new loading configurations are produced by moving the loading points along the edges, and by rotating the edges of the crystal around its thickness axis. Also, the distributed loading tests are performed on the crystal. Based on this, the loading configurations with maximum and minimum frequency shifts are obtained. Moreover, the design of quartz crystal force sensors having high sensitivity and also the crystal oscillator with high-frequency stability are discussed.


Main Subjects

[1] H. Daneshpajooh, M. Mohammadi, M. Hamedi, K. Uchino, Off-Center Force Effect on Quartz Resonator Sensors, Analyzed with Nonlinear Finite Element Method, Sensor Letters, 16(11) (2018) 884-887.
[2] S. Pisupati, D. Kundukoori, N. Mekala, S. Kaluvan, H. Zhang, Design of resonance based DC current sensor using BAW quartz resonators, Sensors and Actuators A: Physical, 271 (2018) 104-110.
[3] M.S. Patel, B.K. Sinha, A dual-mode thickness-shear quartz pressure sensor for high pressure applications, IEEE Sensors Journal, 18(12) (2018) 4893-4901.
[4] J. Ratajski, Force-frequency coefficient of singly rotated vibrating quartz crystals, IBM Journal of Research and Development, 12(1) (1968) 92-99.
[5] A. Ballato, E. EerNisse, T. Lukaszek, Force-frequency effect in doubly rotated quartz resonators, Sandia Labs., Albuquerque, NM (USA), 1977.
[6] M. Valdois, B.K. Sinha, J.-J. Boy, Experimental verification of stress compensation in the SBTC-cut, IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 36(6) (1989) 643-651.
[7] Z. Wang, Y. Dong, H. Zhu, G. Feng, Effect of transverse force on the performance of quartz resonator force sensors, ieee transactions on ultrasonics, ferroelectrics, and frequency control, 51(4) (2004) 470-476.
[8] Z. Wang, H. Zhu, Y. Dong, G. Feng, Off-centre load-insensitive digital quartz resonator force sensor, IEE Proceedings-Science, Measurement and Technology, 148(5) (2001) 215-220.
[9] C. Gehin, C. Barthod, Y. Teisseyre, Design and characterisation of a new force resonant sensor, Sensors and Actuators A: Physical, 84(1-2) (2000) 65-69.
[10] F. Chen, W. Tian, Y. Wei, Highly sensitive resonant sensor using quartz resonator cluster for inclination measurement, Review of Scientific Instruments, 91(5) (2020) 055005.
[11] Y. Murozaki, S. Sakuma, F. Arai, Improvement of the measurement range and temperature characteristics of a load sensor using a quartz crystal resonator with all crystal layer components, Sensors, 17(5) (2017) 1067.
[12] Y. Murozaki, F. Arai, Wide-range Load Sensor Using Vacuum Sealed Quartz Crystal Resonator for Simultaneous Biosignals Measurement on Bed, in:  2020 IEEE International Conference on Robotics and Automation (ICRA), IEEE, 2020, pp. 1015-1020.
[13] F. Arai, Y. Murozaki, S. Sakuma, Wide-range load sensor using quartz resonator, in, Google Patents, 2019.
[14] F. Chen, J. Gao, W. Tian, Force-frequency characteristics of multi-electrode quartz crystal resonator cluster, Sensors and Actuators A: Physical, 269 (2018) 427-434.
[15] W. Tian, Q. Zhao, S. Feng, B. Ma, Finite Element Analysis Of thin Quartz Wafer Stress Distribution In The Radial Force, in:  5th International Conference on Civil Engineering and Transportation, Atlantis Press, 2015.
[16] N. Goel, S. Tadigadapa, In-Situ Measurement of Stress in Thin Films using Micromachined Quartz Bulk Acoustic Wave Resonators, in:  2019 20th International Conference on Solid-State Sensors, Actuators and Microsystems & Eurosensors XXXIII (TRANSDUCERS & EUROSENSORS XXXIII), IEEE, 2019, pp. 1878-1881.
[17] M. Mohammadi, H. Daneshpajooh, M. Hamedi, E ect of anisotropy and piezoelectricity on the force-frequency coe cient of AT-cut quartz crystals, Scientia Iranica, 23(5) (2016) 2203-2210.
[18] M.M. Mohammadi, M. Hamedi, H. DaneshPajooh, High frequency vibrations of quartz crystals subject to initial thermo-mechanical bias, Scientia Iranica, 24(2) (2017) 684-697.
[19] M.M. Mohammadi, M. Hamedi, Experimental and numerical investigation of force-frequency effect in crystal resonators, Journal of Vibroengineering, 18(6) (2016) 3709-3718.
[20] R.D. Mindlin, J. Yang, An introduction to the mathematical theory of vibrations of elastic plates, World Scientific, 2006.
[21] P. Lee, Y. Wang, X. Markenscoff, High− frequency vibrations of crystal plates under initial stresses, The Journal of the Acoustical Society of America, 57(1) (1975) 95-105.
[22] M.S. Patel, Nonlinear behavior in quartz resonators and its stability, Rutgers University-Graduate School-New Brunswick, 2008.