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Dynamic modeling of the electrical actuation system of the hypersonic aircraft considering the temperature effects

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Abstract

The electrical actuator is usually used in the navigation and control system of the hypersonic aircraft, and it can be described by a multi-body dynamical system, which contains brushless motor, gear pairs, ball screw, folk, rudder, etc. For such a complex multi-body system, it may contain clearance between the mating components, such as the gear pairs, the nut of the ball screw and the folk. Additionally, the discontinuous friction force is introduced due to the friction sheet between the folk and the rudder shaft. Since the working temperature of the electrical actuator for the hypersonic aircraft can be extremely high and time-varying, the stiffness, clearance and friction coefficient will also change during the maneuvering flight of the hypersonic aircraft. In this paper, the ordinary differential equations of each subsystem of the electrical actuation system for the hypersonic aircraft will be developed. The continuous and discontinuous interaction forces between the mating components will be derived. The temperature effects will be considered such that the stiffness, clearance and the friction coefficient of such an actuation system are in the function of the working temperature. The dynamic responses of such an electrical actuation system for different working temperatures will be compared based on the numerical simulations, which shows the evidence that the temperature can reduce the transmission ratio of such a system, as well as affecting the system flutter behavior, through changing the contact position of the adjacent meshing components.

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References

  1. Yoo CH, Lee YC, Lee SY (2004) A robust controller for an electro-mechanical fin actuator. In: Proceedings of the 2004 American control conference, vol. 5, pp. 4010–4015, IEEE

  2. Liu X, Wu Y, Deng Y, Xiao S (2014) A global sliding mode controller for missile electromechanical actuator servo system. Proc Inst Mech Eng, Part G: J Aerosp Eng 228(7):1095–1104

    Article  Google Scholar 

  3. Karpel M (1980) Design for active and passive flutter suppression and gust alleviation. Stanford University

    Google Scholar 

  4. Tian W, Yang Z, Zhao T (2019) Nonlinear aeroelastic characteristics of an all-movable fin with free-play and aerodynamic nonlinearities in hypersonic flow. Int J Non-Linear Mech 116:123–139

    Article  Google Scholar 

  5. Sebastian T (1995) Temperature effects on torque production and efficiency of PM motors using NdFeB magnets. IEEE Trans Ind Appl 31(2):353–357

    Article  MathSciNet  Google Scholar 

  6. Wang Y, Li H, Ren D (2016) Characteristics of BLDC motor drive system at high temperature. In: 2016 IEEE 8th International Power Electronics and Motion Control Conference. IEEE

  7. Garniwa I, Dipantara B, Nugroho MV, Sudiarto B, Noorfatima N (2019) Analysis of the effect of the motor temperature to brushless direct current motor performance on KARLING electric vehicle. J Phys: Conf Ser. https://doi.org/10.1088/1742-6596/1376/1/012024

    Article  Google Scholar 

  8. Choi J, Lee JH, Jung YG, Park H (2020) Enhanced efficiency of the brushless direct current motor by introducing air flow for cooling. Heat Mass Transf 56:1825–1831

    Article  Google Scholar 

  9. Kahraman A, Singh R (1991) Interactions between time-varying mesh stiffness and clearance non-linearities in a geared system. J Sound Vib 146(1):135–156

    Article  Google Scholar 

  10. Chen Q, Ma Y, Huang S, Zhai H (2014) Research on gears’ dynamic performance influenced by gear backlash based on fractal theory. Appl Surf Sci 313:325–332

    Article  Google Scholar 

  11. Liu Y, Jiao Y, Qi S, Yu G, Du M (2022) Study on the nonlinear dynamic behavior of rattling vibration in gear systems. Machines 10(12):1112

    Article  Google Scholar 

  12. Liu H, Yan P, Gao P (2020) Effects of temperature on the time-varying mesh stiffness, vibration response, and support force of a multi-stage planetary gear. J Vib Acoust 142(5):051110

    Article  Google Scholar 

  13. Gou X, Zhu L, Qi C (2017) Nonlinear dynamic model of a gear-rotor-bearing system considering the flash temperature. J Sound Vib 410:187–208

    Article  Google Scholar 

  14. Yang J, Li C, Xu M, Yang T, Zhang Y (2022) Nonlinear dynamic characteristics of ball screw feed system under thermal deformation. Nonlinear Dyn 107:1–23

    Article  Google Scholar 

  15. Luo B, Li W, Fu C, Li L, Zhang X (2020) Investigation of the thermal stiffness and thermal tooth profile modification of spur gears. J Braz Soc Mech Sci Eng 42:1–13

    Article  Google Scholar 

  16. Chen J, Li W, Xin G, Sheng L, Jiang S, Li M (2019) Nonlinear dynamic characteristics analysis and chaos control of a gear transmission system in a shearer under temperature effects. Proc Inst Mech Eng C J Mech Eng Sci 233(16):5691–5709

    Article  Google Scholar 

  17. Bowden FP, Hughes TP (1939) The friction of clean metals and the influence of adsorbed gases. The temperature coefficient of friction. Proc R Soc Lond Ser A Math Phys Sci 172(949):263–279

    Google Scholar 

  18. Schallamach AGVGV (1953) The velocity and temperature dependence of rubber friction. Proc Phys Soc Sect B 66(5):386–392

    Article  Google Scholar 

  19. Moufki A, Molinari A, Dudzinski D (1998) Modelling of orthogonal cutting with a temperature dependent friction law. J Mech Phys Solids 46(10):2103–2138

    Article  Google Scholar 

  20. De Wit CC, Olsson H, Astrom KJ, Lischinsky P (1995) A new model for control of systems with friction. IEEE Trans Autom Control 40(3):419–425

    Article  MathSciNet  Google Scholar 

  21. Li JW, Chen XB, An Q, Tu SD, Zhang WJ (2009) Friction models incorporating thermal effects in highly precision actuators. Rev Sci Instrum. https://doi.org/10.1063/1.3115208

    Article  Google Scholar 

  22. Liang K, Tu QZ, Shen XM, Fang ZH, Yang X, Zhang Y, Xiang HY (2022) An improved LuGre model for calculating static steering torque of rubber tracked chassis. Def Technol 18(5):797–810

    Article  Google Scholar 

  23. Jensen SC, Jenney GD, Dawson D (2000) Flight test experience with an electromechanical actuator on the F-18 systems research aircraft. In: 19th DASC. 19th Digital Avionics Systems Conference. Proceedings, Vol. 1, pp. 2E3–1, IEEE

  24. Shin WH, Lee SJ, Lee I, Bae JS (2007) Effects of actuator nonlinearity on aeroelastic characteristics of a control fin. J Fluids Struct 23(7):1093–1105

    Article  Google Scholar 

  25. Kim SH, Tahk MJ (2016) Modeling and experimental study on the dynamic stiffness of an electromechanical actuator. J Spacecr Rocket 53(4):708–719

    Article  Google Scholar 

  26. Lu J, Wu Z, Yang C (2021) High-fidelity fin-actuator system modeling and aeroelastic analysis considering friction effect. Appl Sci 11(7):3057

    Article  Google Scholar 

  27. Wan Q, Liu G, Zhou Y, Ma S, Tong R (2019) Numerical and experimental investigation on electromechanical aileron actuation system with joint clearance. J Mech Sci Technol 33:525–535

    Article  Google Scholar 

  28. Jian H, Xinhua Z, Zhaokai Z, Guan W, Jingwei W, Xueqin W (2017) The research of nonlinear factor characteristics and control method on large inertia electromechanical actuator servo mechanism. In: 2017 IEEE Transportation Electrification Conference and Expo, Asia–Pacific, IEEE

  29. Teppernegg T, Klünsner T, Kremsner C, Tritremmel C, Czettl C, Puchegger S, Ebner R (2016) High temperature mechanical properties of WC–Co hard metals. Int J Refract Metals Hard Mater 56:139–144

    Article  Google Scholar 

  30. Li W, Wang R, Li D, Fang D (2011) A model of temperature-dependent Young’s modulus for ultrahigh temperature ceramics. Phys Res Int 2011:1–3

    Article  Google Scholar 

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Funding

This work is partially supported by the 14th 5-years National Defense Pre-Research Foundation of China under Grant No. 50917060301, National Science Foundation of Chongqing under Grant No. cstc2021jcyj-msxmX0089, the Fundamental Research Funds for the Central Universities.

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Correspondence to Jianzhe Huang.

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Xiao, B., Huang, J., Tang, D. et al. Dynamic modeling of the electrical actuation system of the hypersonic aircraft considering the temperature effects. AS (2024). https://doi.org/10.1007/s42401-024-00274-5

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