A design optimization of the mechanical gyroscope flywheel using flexible dynamics simulation

Abstract

Mechanical gyroscopes are actuators used for balancing and steering purposes due to their ability to generate torque, fast dynamic responses, high efficiency and control linearity. Analytical methods are available for their mechanical designs. Also optimization can be made thanks to simulations. In this study, the optima of the dimension and rotational speed, which are the basis for the design of a mechanical gyroscope, were determined by using the flexible body dynamic simulation and optimization method. The effects of the main structural parameters on the vibration frequency were also determined. The gyroscope has a flywheel and produces torque owing to its own weight. Classical (Newtonian) mechanics principles were followed. As a result, suitable gyroscope dimension and rotational velocity were determined. Thanks to the response function of the optimization, the relationships between the parameters were also determined. Initially, the disc thickness is 10 mm, the radius is 100 mm, the rotor diameter is 20 mm, and the length is 115 mm, while the optimum rotor length is 30 mm, the rotor radius is 30 mm, the disc radius is 265 mm, the thickness is 12 mm, and the operating speed is 400 rad/s. By using the optima, it has been ensured that the nutation, mass, energy consumption are minimized, the torque is maximized, thus it has a service life of more than one million cycle.

Keywords

• Balance
• Flexible dynamics
• Gyroscope
• Design
• Optimization

Esnek cisim dinamik simülasyonu kullanarak bir mekanik jiroskop volan tasarımının optimizasyonu

Öz

Mekanik jiroskoplar tork üretebilme yetenekleri, hızlı dinamik yanıtları, yüksek verimlilikleri ve kontrol doğrusallıkları sebebiyle dengeleme ve yönlendirme amaçlı olarak kullanılan eyleyicilerdendir. Mekanik tasarımları için analitik yöntemler mevcut olup bunun yanı sıra simülasyonlar sayesinde optimizasyon yapılabilmektedir. Bu çalışmada, esnek cisim dinamik simülasyonu ve optimizasyon yöntemi kullanılarak, bir mekanik jiroskopun tasarımına esas olan boyutların ve dönme hızının optimum değerleri tespit edilmiştir. Ana yapısal parametrelerin, titreşim frekansı üzerindeki etkileri de tespit edilmiştir. Jiroskop, bir volana sahip olup kendi ağırlığı sayesinde tork üretmektedir. Klasik (Newtonian) mekanik prensipleri takip edilmiştir. Neticede uygun jiroskop boyutları ve dönme hızı belirlenmiştir. Optimizasyonun verdiği cevap fonksiyonu sayesinde ayrıca parametreler arasındaki ilişkiler de tespit edilmiştir. Başlangıçta disk kalınlığı 10 mm, yarıçapı 100 mm, rotor çapı 20 mm, uzunluğu 115 mm iken optimum rotor uzunluğu 30mm, rotor yarıçapı 30 mm olup disk yarıçapın 265 mm, kalınlığı 12 mm ve işletme hızı 400 rad/s olmaktadır. Optimum değerler sayesinde nütasyonun, kütlenin, enerji sarfiyatının en az olması, torkun en fazla olması böylece bir milyon çevrim sayısının üzerinde ömre sahip olması temin edilmiştir.

Anahtar Kelimeler

• Denge
• Esnek dinamik
• Jiroskop
• Tasarım
• Optimizasyon

Kaynakça

1. F.A. Leve, B.J. Hamilton, and M.A. Peck, Spacecraft momentum control systems, Springer, Cham, Springer-Verlag GmbH, Heidelberg, 2015.
2. L. Arena, F. Piergentili, and F. Santoni, Design, manufacturing, and ground testing of a control-moment gyro for agile microsatellites. Journal of Aerospace Engineering, 30(5), 2017. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000754.
3. J. Gagne, et al., Gyrolock: Stabilizing the heart with control moment gyroscope (cmg)—from concept to first in vivo assessments. IEEE Transactions on Robotics, 28(4): p. 942-954, 2012. https://doi.org/10.1109/TRO.2012.2188162.
4. B. Thornton, et al., Zero-g class underwater robots: Unrestricted attitude control using control moment gyros. IEEE Journal of Oceanic Engineering, 32(3): p. 565-583, 2007. https://doi.org/10.1109/JOE.2007.899274.
5. Y. Zhu, et al., Adaptive control of a gyroscopically stabilized pendulum and its application to a single-wheel pendulum robot. Mechatronics, IEEE/ASME Transactions on, 20: p. 2095-2106, 2015. https://doi.org/10.1109/TMECH.2014.2363090.
6. D.R. Taur and J.S. Chern, Rolleron dynamics in missile applications, in 718-733. p. 718-733, 1999.
7. T. Xiu, et al., Structural engineering analysis for a control moment gyroscope framework. Journal of Physics: Conference Series, 2021 International Conference on Mechanical Engineering, Intelligent Manufacturing and Automation Technology (MEMAT 2021), Gulin, 1939(012119), 2021. https://doi.org/10.1088/1742-6596/1939/1/012119.
8. S. Zheng, et al., Power consumption reduction for magnetic bearing systems during torque output of control moment gyros. IEEE Transactions on Power Electronics, 32(7): p. 5752-5759, 2017. https://doi.org/10.1109/TPEL.2016.2608660.

9. J. Fang, S. Zheng, and B. Han, Amb vibration control for structural resonance of double-gimbal control moment gyro with high-speed magnetically suspended rotor. IEEE/ASME Transactions on Mechatronics, 18(1): p. 32-43, 2013. https://doi.org/10.1109/TMECH.2011.2161877.
10. B. Han, et al., Design, modeling, fabrication, and test of a large-scale single-gimbal magnetically suspended control moment gyro. IEEE Transactions on Industrial Electronics, 62(12): p. 7424-7435, 2015. https://doi.org/10.1109/TIE.2015.2459052.
11. F. Liu, et al., The optimization design with minimum power for variable speed control moment gyroscopes with integrated power and attitude control. Aerospace Science and Technology, 88: p. 287-297, 2019. https://doi.org/10.1016/j.ast.2019.03.028.
12. Y. Zhang, J. Tang, and X. Xu, Modal analysis and multidisciplinary optimization of disk-shaped rotor in mscmg. International Journal of Mechanical Sciences, 226: p. 107387, 2022. https://doi.org/10.1016/j.ijmecsci.2022.107387.
13. S. Pan, et al., Coupled dynamic modeling and analysis of the single gimbal control moment gyroscope driven by ultrasonic motor. IEEE Access, 8: p. 146233-146247, 2020. https://doi.org/10.1109/ACCESS.2020.3012694.
14. İ. Kacar, M.A. Eroğlu, and M.K. Yalçın, Design and development of an autonomous bicycle. Nigde Omer Halisdemir University Journal of Engineering Sciences, 10(1): p. 364-372, 2021. https://doi.org/10.28948/ngumuh.628580.
15. Ansys, Theory manual version 9.0. ANSYS Inc.: Canonsburg, PA, USA., 2004.
16. E. Bulut, et al., A new approach for battery thermal management system design based on grey relational analysis and latin hypercube sampling. Case Studies in Thermal Engineering, 28: p. 101452, 2021. https://doi.org/10.1016/j.csite.2021.101452.
17. D. Clifford, et al., Pragmatic soil survey design using flexible latin hypercube sampling. Computers & Geosciences, 67: p. 62-68, 2014. https://doi.org/10.1016/j.cageo.2014.03.005.
18. J. Roshanian and M. Ebrahimi, Latin hypercube sampling applied to reliability-based multidisciplinary design optimization of a launch vehicle. Aerospace Science and Technology, 28(1): p. 297-304, 2013. https://doi.org/10.1016/j.ast.2012.11.010.
19. M. Mieczkowski, P. Furmański, and P. Łapka, Optimization of a microchannel heat sink using entropy minimization and genetic aggregation algorithm. Applied Thermal Engineering, 191: p. 116840, 2021. https://doi.org/10.1016/j.applthermaleng.2021.116840.
20. S. Wang, et al., Optimization investigation on configuration parameters of spiral-wound heat exchanger using genetic aggregation response surface and multi-objective genetic algorithm. Applied Thermal Engineering, 119: p. 603-609, 2017. https://doi.org/10.1016/j.applthermaleng.2017.03.100.
21. K. Bot, A. Ruano, and M.G. Ruano, Forecasting electricity demand in households using moga-designed artificial neural networks. IFAC-PapersOnLine, 53(2): p. 8225-8230, 2020. https://doi.org/10.1016/j.ifacol.2020.12.1985.
22. L. Kumar, K. Kumar, and D. Chhabra, Experimental investigations of electrical discharge micro-drilling for mg-alloy and multi-response optimization using moga-ann. CIRP Journal of Manufacturing Science and Technology, 38: p. 774-786, 2022. https://doi.org/10.1016/j.cirpj.2022.06.014.
23. S. Selvakumar and R. Ravikumar, A novel approach for optimization to verify rsm model by using multi-objective genetic algorithm (moga). Materials Today: Proceedings, 5(5, Part 2): p. 11386-11394, 2018. https://doi.org/10.1016/j.matpr.2018.02.106.
24. C. Korkmaz and İ. Kacar, Hesaplamalı akışkanlar dinamiği simülasyonları için optimum ağ elemanı yapısının belirlenmesi, in Tarımsal mekanizasyon ve enerji üzerine güncel araştırmalar, O.G. Deniz Yılmaz, Önder Uysal, Mehmet Emin Gökduman, Ahmet Süslü, Editor. Akademisyen Yayinevi: Ankara, p. 109-125, 2021.
25. T. Xiu, et al., Structural engineering analysis for a control moment gyroscope framework. Journal of Physics: Conference Series, 1939: p. 012119, 2021. https://doi.org/10.1088/1742-6596/1939/1/012119.
26. A. Ahmed, et al., Design and analysis of gyro wheel for stabilization of a bicycle. International Journal for Scientific Research & Development, 4(04): p. 349-351, 2016.
27. Z. He, et al. Multi-physics coupling and thermal network analysis of mscmg. in 2022 China Automation Congress (CAC), pp. 4544-4548, 2022.
28. H. Heydari and A. Khorram, Effects of location and aspect ratio of a flexible disk on natural frequencies and critical speeds of a rotating shaft-disk system. International Journal of Mechanical Sciences, 152: p. 596-612, 2019. https://doi.org/https://doi.org/10.1016/j.ijmecsci.2019.01.022.
29. H. Goldstein, Classical mechanics, Addison-Wesley Publishing Company, 1980.
30. T. Kostyuchenko and N. Indygasheva, Computer-aided design system for control moment gyroscope. MATEC Web Conf., 158: p. 01021, 2018.
31. İ. Kacar, M.A. Eroğlu, and M.K. Yalçın, Design and development of an autonomous bicycle. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, 10(1): p. 364-372, 2021. https://doi.org/10.28948/ngumuh.628580.