№3 2019


Mathematical modeling of piezoelectric step-engine work


1A.V. Azin, 2S.A. Kuznetsov, 1S.A. Ponomarev, 1S.V. Ponomarev, 1S.V. Rikkonen


1Tomsk State University
Tomsk, Russian Federation
2JSC Academician M. F. Reshetnev Information Satellite Systems
Zheleznogorsk, Krasnoyarsk region, Russian Federation


In the article the results of new piezoelectric step-engine research are presented. The original construct of piezoelectric step-engine is contained in special engineering lever called grab device that can organize back and forward rod’s motion with only one piezo element activity. To choose the effective process of piezoelectric step-engine work the mathematical model was created. This mathematical model describes inner piezoelectric step-engine process like a non-linear vibrational system. The mathematical model identifies speed of piezoelectric step-engine elements over the vibration period with different frequency, load level and voltage. The prototype of piezoelectric step-engine was produced. Experimental issues were conducted. Piezoelectric step-engine’s technical specifications are positioning accuracy over 10–6 meter, speed of movement over 10 mm per minute with weight of load to 1 kg and voltage to 100 Volt. On the results of experimental research it is defined that mathematical model enables to model working process of piezoelectric stepengine with an error not more than 10 %. This research verifies viability of proposed construction and provides the way to increase output power of piezoelectric step-engine.


piezoelectric motor, step-engine, sawtooth driving signal, mathematical model, PZT stack


[1] Ozawa S. Design concept of large deployable reflector for next generation L-band SAR satellite // The 2nd International Scientific Conference Advanced Lightweight Structures and Reflector Antennas Proceedings, Tbilisi, 2014, pp. 43–51.

[2] Nakamura K., Nakamura N. Concept Design of 15m class Light Weight Deployable Antenna Reflector for L-band SAR Application // 3rd AIAA Spacecraft Structures Conference, AIAA SciTech Forum, San Diego, 2016. doi: 10.2514/6.2016-0701.

[3] Zheng F., Chen M. New Conceptual Structure Design for Affordable Space Large Deployable Antenna // IEEE Transactions on Antennas and Propagation, 2015, vol. 63, no. 4, pp. 1351–1358. doi: 10.1109/TAP.2015.2404345

[4] Ponomarev S. V. Transformiruemye reflektory antenn kosmicheskikh apparatov [Transformable reflectors of spacecraft antennas] // Tomsk State University Bulletin. Mathematics and mechanics, 2011, no. 4 (16), pp. 110–119. (In Russian)

[5] Peng Y., Gu X., Wang J., Yu H. A review of long range piezoelectric motors using frequency leveraged method // Sensors and Actuators, 2015, vol. 235, pp. 240–255. doi: 10.1016/j.sna.2015.10.015

[6] Wang L., Chen W., Liu J., Deng J., Liu Y. A review of recent studies on non-resonant piezoelectric actuators // Mechanical Systems and Signal Processing, 2019, vol. 133, no. 106254. doi: 10.1016/j.ymssp.2019.106254

[7] Azin A., Rikkonen S., Ponomarev S., Kuznetsov S. Alignment of distributed oscillation systems in piezo motors // IOP Conf. Series: Journal of Physics, 2019, vol. 1145, no. 012007. doi: 10.1088/1742-6596/1145/1/012007

[8] Azin A., Rikkonen S., Ponomarev S., Kuznetsov S. Design issues of the piezo motor for the spacecraft reflector control system // MATEC Web of Conferences, 2018, vol. 158, no. 01005. doi: 10.1051/matecconf/201815801005

[9] Azin A., Rikkonen S., Ponomarev S., Orlov S. Linejnyj reversivnyj vibrodvigatel' [Linear reversible vibration motor]. Patent RU 2187888, 2019, bulletin no. 10.

[10] Azin A., Rikkonen S., Ponomarev S., Kuznetsov S., Maritsky N. Designing a precision motor for the spacecraft reflector control system // AIP Conference Proceedings, 2019, vol. 2103, no. 020001. doi: 10.1063/1.5099865

[11] Panich A. E. P'ezokeramicheskie aktyuatory [Piezoceramic actuators]. Rostov-on-Don, Southern Federal University, 2008, 159 p. (In Russian)

[12] Bobtsov A. A., Boykov V. I., Bystrov S. V., Grigoriev V. V., Karev P. V. Ispolnitel'nye ustroystva i sistemy dlya mikroperemeshcheniy [Actuators and systems for micromotion]. St. Petersburg, ITMO University, 2017, 134 p. (In Russian)

[13] Multilayer piezoelectric actuators. Available at: (accessed: 23.09.2019)

For citing this article

Azin A.V., Kuznetsov S.A., Ponomarev S.A., Ponomarev S.V., Rikkonen S.V. Mathematical modeling of piezoelectric step-engine work // Spacecrafts & Technologies, 2019, vol. 3, no. 3, pp. 164-170. doi: 10.26732/2618-7957-2019-3-164-170

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