针对销轴位置度误差引起的齿轮位置偏移问题，分析了行星轮系内外啮合副啮合误差、时变啮合刚度及齿侧间隙，将误差作用下的激励引入到行星齿轮系统动力学模型，研究了销轴位置度误差相位对内外齿轮副动态响应及行星轮系均载特性的影响规律及作用机理，结果表明，位置度误差下齿侧间隙的减小以及负的啮合误差会导致啮合力激增，降低系统均载性能。研究结果可为人字行星齿轮系统低噪声设计加工和装配提供理论参考。
For the offset of gear position caused by the position error of pin shaft, the meshing error, time-varying meshing stiffness and gear backlash of the internal and external meshing pairs in planetary gear train are analyzed, then each excitation under the position error is introduced into the system dynamic model. The influence law and mechanism of pin position error phase on the dynamic response of internal and external gear pairs and the load sharing characteristics of star gear system are studied. The results show that the reduction of gear backlash and negative meshing error under position error will lead to the surge of meshing force and reduce the load sharing performance of the system. The research results can provide a theoretical reference for the low-noise design, machining and assembly of the herringbone star gear system.
2024,46(17): 84-90 收稿日期：2023-10-20
DOI：10.3404/j.issn.1672-7649.2024.17.014
分类号：TH132.425
作者简介：国枫(1997-),男,硕士研究生,研究方向为轮机工程
参考文献：
[1] 秦大同, 谢里阳. 现代机械设计手册[M]. 北京: 化学工业出版社, 2011.
[2] MO S, ZHANG Y, WU Q, et al. Research on natural characteristics of double-helical star gearing system for GTF aero-engine[J]. Mechanism and Machine Theory, 2016, 106: 166-189.
[3] 任菲. 考虑制造误差的人字齿行星传动系统动力学特性及动态均载研究[D]. 重庆: 重庆大学, 2015.
[4] 王宇航, 佟占胜, 吴秀英, 等. 行星齿轮传动的均载机构及选择[J]. 重型机械, 2010(s2): 158-162.
[5] MUCCHI E, DALPIAZ G, RIVOLA A. Elastodynamic analysis of a gear pump. Part II: Meshing phenomena and simulation results[J]. Mechanical Systems and Signal Processing, 2010, 24(7): 2180-2197.
[6] FERNÁNDEZ A, IGLESIAS M, DE-JUAN A, et al. Gear transmission dynamic: Effects of tooth profile deviations and support flexibility[J]. Applied Acoustics, 2014, 77: 138-149.
[7] CHEN Z, ZHOU Z, ZHAI W, et al. Improved analytical calculation model of spur gear mesh excitations with tooth profile deviations - science direct[J]. Mechanism and Machine Theory, 2020, 149.
[8] YUAN B, LIU G, LIU L. Quasi-static characteristics and vibration responses analysis of helical geared rotor system with random cumulative pitch deviations[J]. Applied Sciences, 2020, 10(12): 4403.
[9] LUO T, QIN P, HUANG J. Effects of helix deviation on load distributions and bending stresses of continuous engaged helical gear drives[J]. Advances in Mechanical Engineering, 2015, 7(6).
[10] ZHANG T, WANG J, WU Y, et al. Effect of Machining Errors on the Gear Engagement Using Contact Finite Element Method[C]// ASME Turbo Expo 2015: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2015.
[11] CHANG L, CA O X, HE Z, et al. Load-related dynamic behaviors of a helical gear pair with tooth flank errors[J]. Journal of Mechanical Science and Technology, 2018, 32(4): 1473-1487.
[12] WOJNAR G, JUZEK M. The impact of non-parallelism of toothed gear shafts axes and method of gear fixing on gearbox components vibrations[J]. Acta Mechanica et Automatica, 2018, 12(2): 165-171.
[13] PARK Y J, LEE G H, OH J S, et al. Effects of non-torque loads and carrier pinhole position errors on planet load sharing of wind turbine gearbox[J]. International Journal of Precision Engineering and Manufacturing-Green Technology, 2019.
[14] INALPOLAT M, KAHRAMAN A. A dynamic model to predict modulation sidebands of a planetary gear set having manufacturing errors[J]. Journal of Sound and Vibration, 2010, 329(4): 371-393.
[15] BIELECKI A, BARSZCZ T, WÓJCIK M. Modelling of a chaotic load of wind turbines drivetrain[J]. Mechanical Systems and Signal Processing, 2015, 54: 491-505.
[16] MOHAMMED O. D, RANTATALO M, AIDANPÄÄ J. O. Dynamic modelling of a one-stage spur gear system and vibration-based tooth crack detection analysis[J]. Mechanical Systems and Signal Processing, 2015, 54: 293-305.
[17] SAXENA A, CHOUKSEY M, PAREY A. Effect of mesh stiffness of healthy and cracked gear tooth on modal and frequency response characteristic of geared rotor system[J]. Mechanism and Machine Theory, 2017, 107: 261-273.
[18] 卢剑伟, 曾凡灵, 杨汉生, 等. 随机装配侧隙对齿轮系统动力学特性的影响分析[J]. 机械工程学报, 2010, 46(21): 82-86.
[19] 唐进元, 陈海锋, 王祁波. 考虑间隙与摩擦时的齿轮传动动力学键合图建模研究[J]. 机械工程学报, 2011, 47(9): 53-59.
[20] 王成, 高常青, 崔焕勇. 基于啮合特性的人字齿轮动力学建模与分析[J]. 中南大学学报, 2012, 43(8): 3019-3024.
[21] LIGATA H, KAHRAMAN A, SINGH A. A closed-form planet load sharing formulation for planetary gear sets using a translational analogy[J]. Journal of Mechanical Design, 2009, 131(2).
[22] KIM J G, PARK Y J, LEE G H, et al. An experimental study on the effect of carrier pinhole position errors on planet gear load sharing[J]. International Journal of Precision Engineering and Manufacturing, 2016, 17(10): 1305-1312.
[23] MO S, ZHANG T, JIN G, et al. Influence mechanism of multi-coupling error on the load sharing characteristics of herringbone gear planetary transmission system[J]. Proceedings of the Institution of Mechanical Engineers, 2019, 233(4): 792-816.
[24] HU S, FANG Z, XU Y, et al. Meshing impact analysis of planetary transmission system considering the influence of multiple errors and its effect on the load sharing and dynamic load factor characteristics of the system[J]. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 1464419320986285.
[25] 朱增宝, 朱如鹏, 李应生, 等. 安装误差对封闭差动人字齿轮传动系统动态均载特性的影响[J]. 机械工程学报, 2012, 48(3): 16-24.
[26] 莫帅, 张以都, 吴琼, 等. GTF发动机星形传动系统多分流均载机理研究[J]. 航空动力学报, 2016, 31(3): 763-768.
