Tooth Surface Modification and Anti-wear Design of Spline between Cylinder and Shaft of Piston Pumps

doi:10.3969/j.issn.1004-132X.2025.08.012

Abstract

Abstract:

During the operations of an axial piston pump， the changes in pressure inside the piston chamber might easily cause stress concentration when the contact of the spline pair between the cylinder and shaft of piston pumps， exacerbating the fretting wear of the tooth surfaces. In order to extend the service life of the splines， finite element method and Archard model were combined to study the wear resistance design of the spline pair between the cylinder and shaft of piston pumps. Firstly， a finite element contact model of the spline pair between the cylinder and shaft of piston pumps was developed using the finite element method. Secondly， a new method for modifying involute spline pairs was proposed， and compared with traditional tooth profile modification methods， the contact characteristics of spline pairs before and after modification were analyzed. Finally， the Archard model was used to predict and compare the fretting wear of the tooth surfaces before and after the modification of the spline pair. The results show that after appropriate modification of the spline tooth surfaces， the stress concentration phenomenon during contact is alleviated， and the maximum contact stress of the tooth surfaces is reduced. All four modification methods may reduce the fretting wear of the tooth surfaces at both ends of the spline， and the precise tooth surface modification method has a better modification effectiveness than the traditional tooth profile modification method. The results have certain guiding significance for the reliability and wear resistance design of piston pump spline operations.

Key words: axial piston pump, finite element method, tooth profile modification, contact characteristics, fretting wear

摘要：

轴向柱塞泵在运行过程中，其柱塞腔内压力的变化易使缸体和主轴花键碰撞时产生应力集中现象，加剧齿面的微动磨损。为了延长其花键的使用寿命，结合有限元法和Archard模型，对柱塞泵缸体和主轴花键抗磨损设计进行了研究。首先利用有限元法建立了轴向柱塞泵缸体-主轴花键碰撞有限元模型；然后提出一种新的渐开线花键副修形方法，对比传统的齿向修形方法，对花键副修形前后的接触特性进行分析；最后结合Archard模型对花键副修形前后的齿面微动磨损进行预测和对比。结果表明：对花键齿面进行适当的修形后，其接触时的应力集中现象有所缓解，齿面的最大接触应力有所减小；四种修形法都可以降低花键两端的齿面微动磨损，精准齿面修形法的修形效果比传统的齿向修形法好一些。研究结果对柱塞泵花键运行的可靠性和抗磨损设计有一定的指导意义。

关键词: 轴向柱塞泵, 有限元法, 齿向修形, 接触特性, 微动磨损

CLC Number:

TH322

Shaogan YE, Tianxing CHEN, Ding CHEN, Kefei MIAO, Shoujun ZHAO, Huixiang LIU. Tooth Surface Modification and Anti-wear Design of Spline between Cylinder and Shaft of Piston Pumps[J]. China Mechanical Engineering, 2025, 36(08): 1767-1773.

叶绍干, 陈天星, 陈鼎, 苗克非, 赵守军, 刘会祥. 柱塞泵缸体-主轴花键齿面修形及抗磨损研究[J]. 中国机械工程, 2025, 36(08): 1767-1773.

Figures/Tables 11

References 21

[1]	YE Shaogan， ZHANG Junhui， XU Bing， et al. Theoretical Investigation of the Contributions of the Excitation Forces to the Vibration of an Axial Piston Pump［J］. Mechanical Systems and Signal Processing， 2019， 129：201-217.
[2]	李英杰，赵广，吴学深，等. 航空花键-转子系统自激振动研究综述［J］. 航空学报， 2022， 43（8）：625532.
	LI Yingjie， ZHAO Guang， WU Xueshen， et al. Review of Research on Self-excited Vibration of Aviation Spline-rotor System［J］. Acta Aeronautica et Astronautica Sinica， 2022， 43（8）：625532.
[3]	CUFFARO V， CURÀ F， MURA A. Test Rig for Spline Couplings Working in Misaligned Conditions［J］. Journal of Tribology， 2014， 136（1）：011104.
[4]	CURÀ F， MURA A， ADAMO F. Fatigue Damage in Spline Couplings：Numerical Simulations and Experimental Validation［J］. Procedia Structural Integrity， 2017， 5：1326-1333.
[5]	肖立，徐颖强，陈智勇，等. 直升机浮动渐开线花键微动磨损影响因素分析［J］. 航空动力学报， 2021， 36（4）：751-766.
	XIAO Li， XU Yingqiang， CHEN Zhiyong， et al. Analysis of Influencing Factors of Fretting Wear with Helicopter Floating Involute Spline［J］. Journal of Aerospace Power， 2021， 36（4）：751-766.
[6]	肖立，徐颖强，陈智勇，等. 浮动渐开线花键微动损伤及磨损疲劳预测［J］. 西北工业大学学报， 2022， 40（3）：549-559.
	XIAO Li， XU Yingqiang， CHEN Zhiyong， et al. Prediction of Fretting Damage and Wear Fatigue of Floating Involute Spline Couplings［J］. Journal of Northwestern Polytechnical University， 2022， 40（3）：549-559.
[7]	陈壮，董庆兵，罗振涛，等. 花键微动磨损和损伤累积的耦合机制及寿命预测［J］. 机械工程学报， 2023， 59（3）：133-143.
	CHEN Zhuang， DONG Qingbing， LUO Zhentao， et al. Coupling Mechanism of Fretting Wear and Damage Accumulation of Spline Couplings and Service Life Prediction［J］. Journal of Mechanical Engineering， 2023， 59（3）：133-143.
[8]	XUE Xiangzhen， HUO Qixin， HONG Lin. Fretting Wear-fatigue Life Prediction for Aero-Engine's Involute Spline Couplings Based on Abaqus［J］. Journal of Aerospace Engineering， 2019， 32（6）：04019081.
[9]	薛向珍，霍启新，郑甲红，等. 基于齿向修形的航空渐开线花键副抗微动磨损研究［J］. 中国机械工程， 2019， 30（20）：2447-2455.
	XUE Xiangzhen， HUO Qixin， ZHENG Jiahong， et al. Investigation on Improving Fretting Wears of Aeroengine Involute Spline Couplings Based on Tooth Profile Modification［J］. China Mechanical Engineering， 2019， 30（20）：2447-2455.
[10]	XUE Xiangzhen， JIA Jipeng， HUO Qixin， et al. Experimental Investigation and Prediction Method of Fretting Wear in Rack-plane Spline Couplings［J］. Proceedings of the Institution of Mechanical Engineers， Part J：Journal of Engineering Tribology， 2021， 235（5）：1025-1037.
[11]	XUE Xiangzhen， LI Yifan， SUI Liqi， et al. Mechanism and Prediction Method of Fretting Damage in Involute Spline Couplings of Aero-engine［J］. Engineering Failure Analysis， 2023， 148：107200.
[12]	赵广，王梦茹，冯志飞，等. 航空鼓形花键设计及其不对中接触特性［J］. 航空动力学报， 2022， 37（4）：694-703.
	ZHAO Guang， WANG Mengru， FENG Zhifei， et al. Design Method and Its Misaligned Contact Characteristic of Aviation Crowned Spline［J］. Journal of Aerospace Power， 2022， 37（4）：694-703.
[13]	杨硕文，唐进元. 一种新的直齿轮复合修形设计方法［J］. 中南大学学报（自然科学版）， 2019， 50（5）：1082-1088.
	YANG Shuowen， TANG Jinyuan. A New Design Method for Compound Modification of Spur Gear［J］. Journal of Central South University （Science and Technology）， 2019， 50（5）：1082-1088.［14］胡娟娟，胡检发，谭援强，等. 渐开线花键副齿廓修形研究［J］. 机械强度， 2018， 40（1）：138-144.
	HU Juanjuan， HU Jianfa， TAN Yuanqiang， et al. Research on Profile Modification of Involute Spline Coupling［J］. Journal of Mechanical Strength， 2018， 40（1）：138-144.
[15]	扣田鑫. 摩擦离合器渐开线花键偏载及微动磨损研究［D］. 哈尔滨：哈尔滨工程大学， 2021.
	KOU Tianxin. Investigation on Eccentric Load and Fretting Wear of Involute Spline in Friction Clutch［D］. Harbin：Harbin Engineering University， 2021.
[16]	李永康. 渐开线斜齿圆柱齿轮齿向修形的研究［D］. 太原：太原理工大学， 2010.
	LI Yongkang. Research on Longitudinal Moducation of Involute Healical Gear［D］. Taiyuan：Taiyuan University of Technology， 2010.
[17]	FATOUREHCHI E， MOHAMMADPOUR M， KING P D， et al. Microgeometrical Tooth Profile Modification Influencing Efficiency of Planetary Hub Gears［J］. International Journal of Powertrains， 2018， 7（1/2/3）：162.
[18]	谭援强，胡检发，姜胜强，等. 基于有限元法渐开线花键副不对中载荷分布研究［J］. 机械传动， 2016， 40（9）：110-113.
	TAN Yuanqiang， HU Jianfa， JIANG Shengqiang， et al. Research of Misaligned Load Distribution of Involute Spline Pair Based on Finite Element Method［J］. Journal of Mechanical Transmission， 2016， 40（9）：110-113.
[19]	MADGE J J， LEEN S B， SHIPWAY P H. The Critical Role of Fretting Wear in the Analysis of Fretting Fatigue［J］. Wear， 2007， 263（1/2/3/4/5/6）：542-551.
[20]	薛向珍. 航空渐开线花键副微动磨损机理及磨损量预估方法研究［D］. 西安：西北工业大学， 2017.
	XUE Xiangzhen. Investigation on Maechanism and Prediction Method of Fretting Wear in Aero-engine Involute Spline Coupling［D］.. Xi'an：Northwestern Polytechnical University， 2017.
[21]	DING J， LEEN S B， WILLIAMS E J， et al. Finite Element Simulation of Fretting Wear-fatigue Interaction in Spline Couplings［J］. Tribology—Materials， Surfaces & Interfaces， 2008， 2（1）：10-24.

参数	外花键	内花键
齿数z	16	16
压力角α/（°）	30	30
齿顶圆直径D_a/mm	12.75	11.36
齿厚H/mm	1.31	1.29
泊松比υ	0.28	0.28
模数m/mm	0.75	0.75
齿槽宽E/mm	1.12	1.04
齿根圆直径D_f/mm	10.88	13.13
弹性模量E/GPa	211	211

参数	外花键	内花键
齿数z	16	16
压力角α/（°）	30	30
齿顶圆直径D_a/mm	12.75	11.36
齿厚H/mm	1.31	1.29
泊松比υ	0.28	0.28
模数m/mm	0.75	0.75
齿槽宽E/mm	1.12	1.04
齿根圆直径D_f/mm	10.88	13.13
弹性模量E/GPa	211	211

参数名称	参数值
轴承1沿Y向的刚度K_sh1_y /（N·m^-1）	2.8×10⁷
轴承1沿Z向的刚度K_sh1_z /（N·m^-1）	2.8×10⁷
轴承1沿Y向的阻尼C_sh1_y /（N·s·m^-1）	2.0×10³
轴承1沿Z向的阻尼C_sh1_z /（N·s·m^-1）	2.0×10³
轴承2沿Y向的刚度K_sh2_y /（N·m^-1）	3.2×10⁷
轴承2沿Z向的刚度K_sh2_z /（N·m^-1）	3.2×10⁷
轴承2沿Y向的阻尼C_sh2_y /（N·s·m^-1）	1.0×10³
轴承2沿Z向的阻尼C_sh2_z /（N·s·m^-1）	1.0×10³
轴承3沿Y向的刚度K_sh3_y /（N·m^-1）	2.0×10⁷
轴承3沿Z向的刚度K_sh3_z /（N·m^-1）	2.0×10⁷
轴承3沿Y向的阻尼C_sh3_y /（N·s·m^-1）	2.0×10³
轴承3沿Z向的阻尼C_sh3_z /（N·s·m^-1）	2.0×10³
缸体与配流盘间的刚度K_vp/（N·m^-1）	8.5×10⁸
缸体与配流盘间的阻尼C_vp/（N·s·m^-1）	1.0×10³

参数名称	参数值
轴承1沿Y向的刚度K_sh1_y /（N·m^-1）	2.8×10⁷
轴承1沿Z向的刚度K_sh1_z /（N·m^-1）	2.8×10⁷
轴承1沿Y向的阻尼C_sh1_y /（N·s·m^-1）	2.0×10³
轴承1沿Z向的阻尼C_sh1_z /（N·s·m^-1）	2.0×10³
轴承2沿Y向的刚度K_sh2_y /（N·m^-1）	3.2×10⁷
轴承2沿Z向的刚度K_sh2_z /（N·m^-1）	3.2×10⁷
轴承2沿Y向的阻尼C_sh2_y /（N·s·m^-1）	1.0×10³
轴承2沿Z向的阻尼C_sh2_z /（N·s·m^-1）	1.0×10³
轴承3沿Y向的刚度K_sh3_y /（N·m^-1）	2.0×10⁷
轴承3沿Z向的刚度K_sh3_z /（N·m^-1）	2.0×10⁷
轴承3沿Y向的阻尼C_sh3_y /（N·s·m^-1）	2.0×10³
轴承3沿Z向的阻尼C_sh3_z /（N·s·m^-1）	2.0×10³
缸体与配流盘间的刚度K_vp/（N·m^-1）	8.5×10⁸
缸体与配流盘间的阻尼C_vp/（N·s·m^-1）	1.0×10³

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