目的 研究钢-聚酰胺短齿变位齿轮在实际工况下的最小膜厚与最大压力分布特性,提出一种通过改变齿廓形状的短齿变位齿轮结构,以避免齿顶干涉、节省安装空间并提升弹流润滑性能。方法 基于无限长线接触弹流润滑理论,建立钢-聚酰胺齿轮副的短齿变位齿轮弹流润滑数值模型,并对最小油膜厚度的数值解进行了有效性验证。对钢-聚酰胺标准齿轮进行等温瞬态弹流润滑分析,研究不同转速、载荷及压力角对最小膜厚和最大压力的影响规律。进一步分析了4种不同传动方式对齿轮副弹流润滑特性的影响规律。针对短齿正变位齿轮,选取单齿啮入点、节点及单齿啮出点3个典型位置,分析膜厚与压力的瞬态分布特征。最后比较短齿变位齿轮、短齿齿轮和标准齿轮最大压力和最小膜厚沿啮合线的变化规律。结果 数值解与经验解的相对误差为1.87%~5.09%,验证了模型的准确性。在不同传动形式中,正传动齿轮的最小膜厚最大、最大压力最小。短齿变位齿轮的最小膜厚随转速升高而增大,随载荷增加而减小,随压力角增大而增大,最大压力变化趋势相反。综合对比表明,短齿变位齿轮的整体最小膜厚最大、最大压力最小,润滑性能最优。结论 在考虑避免齿顶干涉及空间受限的情况下,正变位、高转速、低载荷条件下的钢-聚酰胺短齿齿轮副表现出更优的弹流润滑性能,有助于改善其承载能力与运行稳定性。
Abstract
This paper investigates the transient elastohydrodynamic lubrication (EHL) characteristics of steel- polyamide involute short-tooth profile-shifted gears. A novel gear structure combining tooth shortening with positive profile modification is proposed to eliminate tip interference, enhance load-carrying capacity, and improve lubrication stability. A transient EHL numerical model is developed considering the real tooth geometry and time-varying meshing conditions. The model couples the generalized Reynolds equation and the elastic deformation equation, and employs the finite difference method combined with a multigrid iterative algorithm to achieve efficient convergence and accurately capture the transient pressure and film thickness distribution within the contact zone. Validation against the Dowson-Higginson empirical formula shows that the relative error of the minimum film thickness remains between 1.87% and 5.89%, confirming the model's accuracy and numerical stability.
An isothermal transient EHL analysis is carried out for the steel-polyamide standard gear pair to study the influence of rotational speed, applied load, and pressure angle on the minimum film thickness and the maximum pressure. Furthermore, the lubrication characteristics are comparatively analyzed under four different transmission configurations: positive drive, negative drive, standard gear drive, and equivariant profile shifted gear drive. For the short-tooth positive profile-shifted gear, transient analyses are conducted at three key meshing positions: the approach point, pitch point, and recess point. The results indicate that at the pitch point, where single-tooth contact occurs, the Hertzian half-width increases significantly, leading to the highest peak pressure. Although the short-tooth design reduces the nominal contact length, it increases the gradient between the inlet and outlet clearances, thereby forming a stronger wedge-shaped hydrodynamic effect that enhances oil film generation and raises the overall film thickness. The positive profile modification further enlarges the equivalent radius of curvature, enhances lubricant entrainment at the inlet, and reduces local stress concentration, leading to a smoother pressure transition and more stable lubrication film formation. The parametric analysis reveals that as the rotational speed increases, the oil film thickness increases while the maximum pressure decreases; as the load increases, the film thickness decreases and the pressure rises; and with an increasing pressure angle, the oil film exhibits improved stability and uniformity. Comparative investigations among the standard gear, short-tooth gear, and short-tooth profile-shifted gear show that the short-tooth positive profile-shifted gear exhibits the largest minimum film thickness and the lowest maximum pressure throughout the meshing cycle, indicating the best overall lubrication performance among all configurations. The study demonstrates that the coupling of tooth shortening and positive profile modification fundamentally alters the inlet geometric convergence ratio and the combined curvature radius, thereby strengthening the hydrodynamic wedge effect and promoting more effective oil film formation. This coupled mechanism mitigates the adverse influence of reduced contact length and ensures stable lubrication performance even under transient loading conditions.
In conclusion, the research elucidates the mechanism by which the interaction between short-tooth geometry and positive profile modification enhances the EHL behavior of steel-polyamide gear pairs. The developed transient numerical model provides a reliable theoretical and computational foundation for the design and optimization of non-standard polymer-metal gears. The findings offer valuable insights for the application of steel-polyamide short-tooth profile-shifted gears in high-speed, lightweight, and space-constrained transmission systems, where efficient lubrication and wear resistance are critical.
关键词
聚合物 /
钢-聚酰胺 /
短齿变位齿轮 /
瞬态弹流润滑 /
承载能力
Key words
polymer /
steel-polyamide /
short-tooth profile shifted gear /
transient elastohydrodynamic lubrication /
load- carrying capacity
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参考文献
[1] KUMAR A, PAREY A, KANKAR P K.Effect of Teeth Modifications and Gear-Paired Materials on Vibration and Acoustic Characteristics of Polymer Gears[J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2023, 45(12): 642.
[2] MYSHKIN N K, KOVALEV A.Polymer Mechanics and Tribology[J]. Industrial Lubrication and Tribology, 2018, 70(4): 764-772.
[3] KURDI A, CHANG L.Recent Advances in High Performance Polymers-Tribological Aspects[J]. Lubricants, 2018, 7(1): 2.
[4] GUPTA P, TOKSHA B, PATEL B, et al.Recent Developments and Research Avenues for Polymers in Electric Vehicles[J]. The Chemical Record, 2022, 22(11): e202200186.
[5] KAYSSER W, ESSLINGER J, ABETZ V, et al.Research with Neutron and Synchrotron Radiation on Aerospace and Automotive Materials and Components[J]. Advanced Engineering Materials, 2011, 13(8): 637-657.
[6] FERNANDES C M C G, ROCHA D M P, MARTINS R C, et al. Hybrid Polymer Gear Concepts to Improve Thermal Behavior[J]. Journal of Tribology, 2019, 141(3): 032201.
[7] MERTENS A J, SENTHILVELAN S.Durability of Polymer Gear-Paired with Steel Gear Manufactured by Wire Cut Electric Discharge Machining and Hobbing[J]. International Journal of Precision Engineering and Manufacturing, 2016, 17(2): 181-188.
[8] ALHARBI K A M. Wear and Mechanical Contact Behavior of Polymer Gears[J]. Journal of Tribology, 2019, 141: 011101.
[9] SINGH A K, SIDDHARTHA, SINGH P K. Polymer Spur Gears Behaviors under Different Loading Conditions: A Review[J]. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2018, 232(2): 210-228.
[10] ZIEGLTRUM A, MAIER E, LOHNER T, et al.A Numerical Study on Thermal Elastohydrodynamic Lubrication of Coated Polymers[J]. Tribology Letters, 2020, 68(2): 71.
[11] REITSCHUSTER S, MAIER E, LOHNER T, et al.Friction and Temperature Behavior of Lubricated Thermoplastic Polymer Contacts[J]. Lubricants, 2020, 8(6): 67.
[12] DEARN K D, HOSKINS T J, PETROV D G, et al.Applications of Dry Film Lubricants for Polymer Gears[J]. Wear, 2013, 298: 99-108.
[13] 周家傲, 刘晓玲, 李群, 等. 钢-聚合物直齿轮副的弹流润滑分析[J]. 机械传动, 2024, 48(7): 114-120.
ZHOU J A, LIU X L, LI Q, et al.Analysis of Elastohydrodynamic Lubrication for Steel-Polymer Spur Gear Pairs[J]. Journal of Mechanical Transmission, 2024, 48(7): 114-120.
[14] 王杰斌. 金属-聚合物齿轮副的动态接触分析[D]. 岳阳: 湖南理工学院, 2024: 9-15.
WANG J B.Dynamic Contact Analysis of Metal Gears Meshing with Polymer Gear Pair[D]. Yueyang: Hunan Institute of Science and Technology, 2024: 9-15.
[15] JIAN G X, WANG Y Q, ZHANG P, et al.Thermal Elastohydrodynamic Lubrication of Modified Gear System Considering Vibration[J]. Journal of Central South University, 2020, 27(11): 3350-3363.
[16] JIAN G X, WANG Y Q, ZHANG P, et al.Analysis of Lubrication Performance for Internal Meshing Gear Pair Considering Vibration[J]. Journal of Central South University, 2021, 28(1): 126-139.
[17] XIAO Z L, ZHOU C J, LI Z D, et al.Thermo-Mechanical Characteristics of High-Speed and Heavy-Load Modified Gears with Elasto-Hydrodynamic Contacts[J]. Tribology International, 2019, 131: 406-414.
[18] DAI L, PU W, WANG J X.Mixed EHL Analysis of Planetary Drives with Small Teeth Number Difference Considering Real Tooth Geometry[J]. Lubrication Science, 2018, 30(6): 317-330.
[19] 戴翎, 蒲伟, 田兴, 等. 混合润滑下短齿啮合对行星齿轮接触疲劳的影响[J]. 摩擦学学报, 2018, 38(2): 121-128.
DAI L, PU W, TIAN X, et al.Effect of Short Teeth on Contact Fatigue in Planetary Gears under Mixed Lubrication[J]. Tribology, 2018, 38(2): 121-128.
[20] YANG P R, WEN S Z.A Generalized Reynolds Equation for Non-Newtonian Thermal Elastohydrodynamic Lubrication[J]. Journal of Tribology, 1990, 112(4): 631-636.
[21] ROELANDS C J A, WINER W O, WRIGHT W A. Correlational Aspects of the Viscosity-Temperature-Pressure Relationship of Lubricating Oils[J]. Journal of Lubrication Technology, 1971, 93(1): 209-210.
[22] DOWSON D, HIGGINSON G R.Elasto-Hydrodynamic Lubrication[M]. Oxford: Pergamon Press, 1977: 362-366.
[23] 菅光霄, 王优强, 罗恒, 等. 齿轮动力学与弹性流体动力润滑耦合研究[J]. 机械传动, 2020, 44(2): 22-27.
JIAN G X, WANG Y Q, LUO H, et al.Study on the Coupling of Gear Dynamics and Elastohydrodynamic Lubrication[J]. Journal of Mechanical Transmission, 2020, 44(2): 22-27.
[24] VENNER C H.Multilevel Solution of the EHL Line and Point Contact Problems[D]. Enschede: University of Twente, 2014.
[25] BRANDT A, LUBRECHT A A.Multilevel Matrix Multiplication and Fast Solution of Integral Equations[J]. Journal of Computational Physics, 1990, 90(2): 348-370.
[26] 张翔, 刘晓玲, 孙文东, 等. 计入表面吸附膜的热弹流润滑体系建模及分析[J]. 表面技术, 2022, 51(3): 57-65.
ZHANG X, LIU X L, SUN W D, et al.Modeling and Analysis of Thermal EHL System Considering Adsorption Film on Surfaces[J]. Surface Technology, 2022, 51(3): 57-65.
[27] 杨沛然. 流体润滑数值分析[M]. 北京: 国防工业出版社, 1998: 1-391.
YANG P R.Numerical Analysis of Fluid Lubrication[M]. Beijing: National Defense Industry Press, 1998: 1-391.
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