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清华大学学报(自然科学版)  2024, Vol. 64 Issue (1): 33-43    DOI: 10.16511/j.cnki.qhdxxb.2023.21.020
  车辆与交通 本期目录 | 过刊浏览 | 高级检索 |
王钦1, 贺迪1, 桂良进1, 胡智宇2, 彭金3, 范子杰1
1. 清华大学 车辆与运载学院, 汽车安全与节能国家重点实验室, 北京 100084;
2. 陕西汉德车桥有限公司, 西安 710201;
3. 汉德车桥(株洲)齿轮有限公司, 株洲 412000
Calculation method of hypoid gear meshing efficiency of drive axles with considering system deformation
WANG Qin1, HE Di1, GUI Liangjin1, HU Zhiyu2, PENG Jin3, FAN Zijie1
1. State Key Laboratory of Automotive Safety and Energy, School of Vehicle and Mobility, Tsinghua University, Beijing 100084, China;
2. Shaanxi Hande Axle Co., Ltd., Xi'an 710201, China;
3. Hande Axle(Zhuzhou) Gear Co., Ltd., Zhuzhou 412000, China
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摘要 准双曲面齿轮是驱动桥系统的关键零部件之一,常在高速重载工况下工作。由于系统变形大且齿面啮合状态复杂,重载工况下会引起齿面载荷的显著偏载。因此,考虑系统变形对准双曲面齿轮啮合性能的影响具有重要意义。该文针对复杂工况下的驱动桥准双曲面齿轮,提出了考虑系统变形的齿轮啮合效率计算方法。首先,将驱动桥系统简化为多支撑轴系耦合模型,计算不同载荷工况下系统变形引起的齿轮啮合错位量。然后,基于齿轮机床加工参数计算实际齿面,并采用齿轮摩擦加载接触分析(frictional loaded tooth contact analysis,FLTCA)方法求解得到实际运行工况下齿面载荷分布与啮合效率。最后,通过驱动桥台架试验对比不同工况下齿轮副齿面载荷分布和啮合效率。试验结果表明:系统变形对准双曲面齿轮齿面载荷分布具有不可忽略的影响。同时,该试验验证了驱动桥准双曲面齿轮啮合效率计算方法的有效性。
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关键词 驱动桥准双曲面齿轮接触分析啮合效率混合润滑系统变形    
Abstract:[Objective] The face-hobbing hypoid gear is a crucial component of drive axles owing to its continuous indexing processing capabilities. However, in practical engineering applications, gear pairs rarely operate under ideal conditions. Instead, they frequently experience heavy-load and high-speed conditions. These conditions result in substantial system deformation and a complex meshing state of the tooth surface. Under heavy-load conditions, considerable skewing of the load on the tooth surface can occur, greatly affecting the performance of the gear pair and drive axles. Currently, the system deformation factor under actual working conditions is not sufficiently considered, making it challenging to address the aforementioned issue. Consequently, this paper proposes the analysis of the tooth surface load distribution by employing a semi-analytic loaded tooth contact analysis method to accurately predict the tooth surface load distribution. Based on a load distribution analysis, a highly accurate calculation method for gear meshing efficiency is proposed.[Methods] This paper proposes a calculation method for gear meshing efficiency under mixed-lubrication conditions for hypoid gears in drive axles operating under complex working conditions. First, a multi-support shaft system modeling method is employed to analyze the drive axles system. This method can calculate the forces acting on various components, such as gears and bearings, as well as the gear misalignment caused by system deformation under various load conditions. Second, by simulating the spatial motion process of the actual gear machining machine, the coordinates of the tool cutting point are transformed to the coordinate system of the gear blank via coordinate transformation. This process results in the correspondence of the tooth profile with the actual machining parameters. The time-varying friction coefficient distribution of the tooth surface under different working conditions is derived by combining the point contact mixed-lubrication friction coefficient model of the tooth surface with its relative motion relationship. Then, taking into account the tooth surface deformation equilibrium equation, tooth surface torque equilibrium equation, and tooth surface contact pressure equilibrium equation, a gear frictional loaded tooth contact analysis method is established. This method accurately calculates the tooth surface load distribution and mesh efficiency of gears under different working conditions through an iterative solution. Finally, the calculation results of the tooth surface load distribution under various working conditions are compared with the experimental results obtained from a loading experiment conducted on the entire drive axles. The meshing efficiency of the gear pair under various working conditions is determined by conducting a system no-load efficiency experiment and loading efficiency experiment and comparing the results with those obtained by calculations.[Results] In the gear no-load experiment, the contact patterns of the gear tooth surface were compared under forward and reverse working conditions. The experimental results were found to be in good agreement with theoretical calculations, verifying the accuracy of the tooth surface calculation method and no-load tooth contact analysis. Subsequently, a loading experiment was conducted on the drive axles system, indicating that the system deformation had a considerable impact on the load distribution of the hypoid gear tooth surface. For instance, in the experiment drive axles, under heavy-load conditions, system deformation caused the tooth surface load on the driving side of the gear pair to shift toward the outside, while the tooth surface loaded on the driven side shifts toward the inside. The meshing efficiency experiment results revealed that system deformation considerably impacted the gear meshing efficiency under heavy-load and high-speed working conditions. In addition, the vehicle speed had a considerable impact on the meshing efficiency, with an increase in speed from 10 to 80 km/h, resulting in a 1% improvement in meshing efficiency.[Conclusions] By comprehensively considering gear meshing misalignment caused by system deformation and the mixed-lubrication state of the tooth surface, the tooth surface load distribution and meshing efficiency can be accurately calculated under loaded conditions. Therefore, the proposed process enhances the accuracy of calculating the drive axles system efficiency while providing a solid foundation for gear optimization research.
Key wordsdrive axles    hypoid gear    contact analysis    meshing efficiency    mixed lubrication    system deformation
收稿日期: 2023-02-08      出版日期: 2023-11-30
通讯作者: 范子杰,教授,     E-mail:
作者简介: 王钦(1994—),男,博士研究生。
王钦, 贺迪, 桂良进, 胡智宇, 彭金, 范子杰. 考虑系统变形的驱动桥准双曲面齿轮啮合效率计算方法[J]. 清华大学学报(自然科学版), 2024, 64(1): 33-43.
WANG Qin, HE Di, GUI Liangjin, HU Zhiyu, PENG Jin, FAN Zijie. Calculation method of hypoid gear meshing efficiency of drive axles with considering system deformation. Journal of Tsinghua University(Science and Technology), 2024, 64(1): 33-43.
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[1] 杜进辅. 摆线齿准双曲面齿轮齿面啮合性能分析及设计技术研究[D]. 西安:西北工业大学, 2015. DU J F. Tooth contact pattern analysis and design technology research of cycloid hypoid gears[D]. Xi'an:Northwestern Polytechnical University, 2015. (in Chinese)
[2] TALBOT D, KAHRAMAN A, LI S, et al. Development and validation of an automotive axle power loss model[J]. Tribology Transactions, 2016, 59(4):707-719.
[3] XU H, KAHRAMAN A. Prediction of friction-related power losses of hypoid gear pairs[J]. Proceedings of the Institution of Mechanical Engineers, Part K:Journal of Multi-Body Dynamics, 2007, 221(3):387-400.
[4] KOLIVAND M, LI S, KAHRAMAN A. Prediction of mechanical gear mesh efficiency of hypoid gear pairs[J]. Mechanism and Machine Theory, 2010, 45(11):1568-1582.
[5] SIMON V V. Improvements in the mixed elastohy- drodynamic lubrication and in the efficiency of hypoid gears[J]. Proceedings of the Institution of Mechanical Engineers, Part J:Journal of Engineering Tribology, 2020, 234(6):795-810.
[6] DING H, LI H P, CHEN S Y, et al. Energy loss and mechanical efficiency forecasting model for aero-engine bevel gear power transmission[J]. International Journal of Mechanical Sciences, 2022, 231:107569.
[7] 谷建功, 方宗德, 苏进展, 等. 混合弹流润滑下弧齿锥齿轮传动啮合效率计算方法[J]. 农业机械学报, 2010, 41(5):188-192. GU J G, FANG Z D, SU J Z, et al. Calculation of meshing efficiency for spiral bevel gears under the condition of mixed elastohydrodynamic lubrication[J]. Transactions of the Chinese Society for Agricultural Machinery, 2010, 41(5):188-192. (in Chinese)
[8] 曹伟, 蒲伟, 王家序, 等. 弧齿锥齿轮摩擦系数与啮合效率研究[J]. 摩擦学学报, 2018, 38(3):247-255. CAO W, PU W, WANG J X, et al. Friction coefficient and mesh efficiency in spiral bevel gears[J]. Tribology, 2018, 38(3):247-255. (in Chinese)
[9] 蒋进科, 方宗德, 刘钊. Ease-off拓扑修形准双曲面齿轮齿面多目标优化设计方法[J]. 西安交通大学学报, 2019, 53(6):44-53. JIANG J K, FANG Z D, LIU Z. Design of multi-objective tooth optimization for hypoid gear with ease-off topological modification[J]. Journal of Xi'an Jiaotong University, 2019, 53(6):44-53. (in Chinese)
[10] 魏冰阳, 王振, 杨建军, 等. Ease-off拓扑修形齿面拟Hertz接触与摩擦特性分析[J]. 机械工程学报, 2021, 57(1):61-67. WEI B Y, WANG Z, YANG J J, et al. Analysis on quasi Hertzian contact and friction characteristics of tooth surface modified by ease-off topology[J]. Journal of Mechanical Engineering, 2021, 57(1):61-67. (in Chinese)
[11] 唐效贵, 王斌, 李佩鸿, 等. 基于复杂润滑状态的直齿锥齿轮啮合效率分析[J]. 机械传动, 2017, 41(7):33-41. TANG X G, WANG B, LI P H, et al. Analysis of meshing efficiency of straigh bevel gear based on integrated lubrication[J]. Journal of Mechanical Transmission, 2017, 41(7):33-41. (in Chinese)
[12] KAKAVAS I, OLVER A V, DINI D. Hypoid gear vehicle axle efficiency[J]. Tribology International, 2016, 101:314-323.
[13] 王旺平. 微型汽车传动系统效率建模及试验研究[D]. 武汉:武汉理工大学, 2015. WANG W P. Efficiency modeling and experimental research of mini-car transmission system[D]. Wuhan:Wuhan University of Technology, 2015. (in Chinese)
[14] ZHOU C, WANG Q, DING W Q, et al. Numerical simulation of drive axles considering the nonlinear couplings between gears and bearings[J]. Proceedings of the Institution of Mechanical Engineers, Part D:Journal of Automobile Engineering, 2019, 233(4):851-861.
[15] 田程, 周驰, 桂良进, 等. 考虑轴承刚度耦合性和非线性的多支撑轴系有限元分析方法[J]. 机械工程学报, 2015, 51(17):90-95. TIAN C, ZHOU C, GUI L J, et al. Method of finite element analysis for multi-support shaft system based on the coupling and nonlinearity of bearing stiffness[J]. Journal of Mechanical Engineering, 2015, 51(17):90-95. (in Chinese)
[16] 田程, 周驰, 丁炜琦, 等. 轴系的热膨胀对于锥齿轮错位量的影响[J]. 清华大学学报(自然科学版), 2016, 56(6):565-571. TIAN C, ZHOU C, DING W Q, et al. Influence of the thermal expansion of a shaft on the misalignment of bevel gears[J]. Journal of Tsinghua University (Science and Technology), 2016, 56(6):565-571. (in Chinese)
[17] DING H, TANG J Y, ZHONG J, et al. A hybrid modification approach of machine-tool setting considering high tooth contact performance in spiral bevel and hypoid gears[J]. Journal of Manufacturing Systems, 2016, 41:228-238.
[18] WANG Q, ZHOU C, GUI L J, et al. Optimization of the loaded contact pattern of spiral bevel and hypoid gears based on a kriging model[J]. Mechanism and Machine Theory, 2018, 122:432-449.
[19] 田程, 丁炜琦, 桂良进, 等. 基于回归分析的准双曲面齿轮齿面误差修正[J]. 清华大学学报(自然科学版), 2017, 57(2):141-146. TIAN C, DING W Q, GUI L J, et al. Flank error correction of hypoid gears based on regression analyses[J]. Journal of Tsinghua University (Science and Technology), 2017, 57(2):141-146. (in Chinese)
[20] CASTRO J, SEABRA J. Coefficient of friction in mixed film lubrication:Gears versus twin-discs[J]. Proceedings of the Institution of Mechanical Engineers, Part J:Journal of Engineering Tribology, 2007, 221(3):399-411.
[21] HAMROCK B J, SCHMID S R, JACOBSON B O. Fundamentals of fluid film lubrication[M]. New York:Marcel Dekker, 2004.
[22] XU H. Development of a generalized mechanical efficiency prediction methodology for gear pairs[D]. Columbus:The Ohio State University, 2005.
[23] 王琪, 周驰, 桂良进, 等. 准双曲面齿轮LTCA弯曲变形约束方法[J]. 航空动力学报, 2017, 32(11):2800-2807. WANG Q, ZHOU C, GUI L J, et al. Constraint method of calculating tooth bending deformation of hypoid gears in LTCA[J]. Journal of Aerospace Power, 2017, 32(11):2800- 2807. (in Chinese)
[24] WILCOX L E, CHIMNER T D, NOWELL G C. Improved finite element model for calculating stresses in bevel and hypoid gear teeth[R]. Alexandria:AGMA, 1997.
[25] HAMMAMI M, MARTINS R, ABBES M S, et al. Axle gear oils:Friction behaviour under mixed and boundary lubrication regimes[J]. Tribology International, 2017, 116:47-57.
[26] WANG C, WANG S R, WANG G Q. A method for calculating gear meshing efficiency by measured data from gear test machine[J]. Measurement, 2018, 119:97-101.
[27] Bearings SKF. The SKF Model for Calculating the Frictional Moment[J/OL]. (2012-12-15)[2023-02-07]. The-SKF-model-for-calculating-the-frictional-moment_tcm_12-299767.
[1] 王琪, 周驰, 桂良进, 范子杰. 螺旋锥齿轮齿面加载性能多目标优化[J]. 清华大学学报(自然科学版), 2018, 58(6): 529-538.
[2] 田程, 丁炜琦, 桂良进, 范子杰. 基于回归分析的准双曲面齿轮齿面误差修正[J]. 清华大学学报(自然科学版), 2017, 57(2): 141-146.
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