Abstract:Face-gear drives have great potential in the aviation and automotive industries. However, torsional vibrations are a key issue in face-gear pairs. This study focuses on modeling and analyses of the torsional vibrations in a face-gear pair. A torsional vibration model is given for a one-input, one-output face-gear drive with asymmetric time-varying mesh stiffness, backlash nonlinearity and static transmission errors. The torsional mesh stiffness of a face-gear pair is calculated from a loaded tooth contact analysis in a numerical example. The torsional vibration model is validated by comparing the responses with the dynamic responses predicted by Abaqus. The model is then used to analyze the dynamic behavior of a face-gear pair for the design conditions to investigate the effects of mesh stiffness, backlash, static transmission errors, and torque fluctuations on the dynamic characteristics of the face-gear pair and the nonlinear dynamic response. The results show that the model accurately predicts the face-gear pair torsional vibrations and can be used to study the mesh characteristics and the dynamic characteristics of face-gear pairs to guide the design of face-gear pairs.
[1] KISSLING U, BEERMANN S. Face gears:Geometry and strength[J]. Gear Technology, 2007(1/2):54-61. [2] BLOOMFIEID B. Designing face gears[J]. Machine Design, 1947, 19:129-134. [3] BILL R C. Advanced rotorcraft transmission program:NASA-TM-103276[R]. Washington, DC, USA:NASA, 1990. [4] HEATH G F, BOSSLER R B JR. Advanced rotorcraft transmission (ART) program:NASA-CR-191057[R]. Washington, DC, USA:NASA, 1993. [5] HEATH G F, FILLER R R, TAN J. Development of face gear technology for industrial and aerospace power transmission:NASA/CR-2002-211320[R]. Washington, DC, USA:NASA, 2002. [6] LEWICKI D G, HEATH G F, FILLER R R, et al. RDS-21 face-gear surface durability tests:NASA/TM-2007-214970[R]. Washington, DC, USA:NASA, 2007. [7] BINNEY D A, VINAYAK H, GMIRYA Y, et al. Face gear transmission development program at Sikorsky Aircraft[C]//Proceedings of ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Chicago, USA, 2003:307-313. [8] HEATH G F, SLAUGHTER S C, FISHER D J, et al. Helical face gear development under the enhanced rotorcraft drive system program:NASA/TM-2011-217125[R]. Washington, DC, USA:NASA, 2011. [9] CARUSO A, GORLA C. FACET:Face gears in aerospace transmissions[C]//Proceedings of the 25th European Rotorcraft Forum. Rome, Italy, 1999. [10] PENG X L, ZHANG L, FANG Z D. Manufacturing process for a face gear drive with local bearing contact and controllable unloaded meshing performance based on ease-off surface modification[J]. Journal of Mechanical Design, 2016, 138(4):043302. [11] WANG Y Z, HOU L W, LAN Z, et al. Precision milling method for face-gear by disk cutter[J]. The International Journal of Advanced Manufacturing Technology, 2017, 89(5-8):1545-1558. [12] LIN C, CAO X J, FAN Y, et al. Pitch deviation measurement and analysis of curve-face gear pair[J], Measurement, 2016, 81:95-101. [13] CHEN S Y, TANG J Y, CHEN W T, et al. Nonlinear dynamic characteristic of a face gear drive with effect of modification[J]. Meccanica, 2014, 49(5):1023-1037. [14] HU Z H, TANG J Y, CHEN S Y, et al. Effect of mesh stiffness on the dynamic response of face gear transmission system[J]. Journal of Mechanical Design, 2013, 135(7):071005. [15] HU Z H, TANG J Y, CHEN S Y, et al. Coupled translation-rotation vibration and dynamic analysis of face geared rotor system[J]. Journal of Sound and Vibration, 2015, 351:282-298. [16] 杨振, 王三民, 范叶森, 等. 正交面齿轮传动系统分岔特性[J]. 哈尔滨工业大学学报, 2011, 43(3):107-110. YANG Z, WANG S M, FAN Y S, et al. Bifurcation characteristics of face-gear transmission system[J]. Journal of Harbin Institute of Technology, 2011, 43(3):107-110. (in Chinese) [17] 林腾蛟, 冉雄涛. 正交面齿轮传动非线性振动特性分析[J]. 振动与冲击, 2012, 31(2):25-31. LIN T J, RAN X T. Nonlinear vibration characteristic analysis of face-gear drive[J]. Journal of Vibration and Shock, 2012, 31(2):25-31. (in Chinese) [18] 李晓贞, 朱如鹏, 李政民卿, 等. 非正交面齿轮传动系统的耦合振动分析[J]. 中南大学学报(自然科学版), 2013, 44(6):2274-2280. LI X Z, ZHU R P, LI Z M Q, et al. Analysis of coupled vibration of face gear drive with non-orthogonal intersection[J]. Journal of Central South University (Science and Technology), 2013, 44(6):2274-2280. (in Chinese) [19] 勒广虎, 朱如鹏, 鲍和云. 正交面齿轮传动系统的非线性振动特性[J]. 中南大学学报(自然科学版), 2010, 41(5):1807-1813. JIN G H, ZHU R P, BAO H Y. Nonlinear dynamical characteristics of face gear transmission system[J]. Journal of Central South University (Science and Technology), 2010, 41(5):1807-1813. (in Chinese) [20] TANG J Y, HU Z H, CHEN S Y, et al. Effects of directional rotation radius and transmission error on the dynamic characteristics of face gear transmission system[J]. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science, 2014, 228(7):1108-1118. [21] LITVIN F L, FUENTES A. Gear geometry and applied theory[M]. 2nd ed. New York, USA:Cambridge University Press, 2004. [22] KUANG J H, LIN A D. Theoretical aspects of torque responses in spur gearing due to mesh stiffness variation[J]. Mechanical Systems and Signal Processing, 2003, 17(2):255-271. [23] THEODOSSIADES S, NATSIAVAS S. Non-linear dynamics of gear-pair systems with periodic stiffness and backlash[J]. Journal of Sound and Vibration, 2000, 229(2):287-310. [24] HE S, GUNDA R, SINGH R. Effect of sliding friction on the dynamics of spur gear pair with realistic time-varying stiffness[J]. Journal of Sound and Vibration, 2007, 301(3-5):927-949. [25] PADMANABHAN C, BARLOW R C, ROOK T E, et al. Computational issues associated with gear rattle analysis[J]. Journal of Mechanical Design, 1995, 117(1):185-192. [26] BARTHOD M, HAYNE B, TÉBEC J L, et al. Experimental study of gear rattle excited by a multi-harmonic excitation[J]. Applied Acoustics, 2007, 68(9):1003-1025.