齿轮齿条动态啮合及传动分析的SPH数值算法研究

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振动与冲击 ›› 2021, Vol. 40 ›› Issue (16) : 39-44.

论文

唐宇峰1,2，胡光忠1，曹修全1，阳明君1,2

作者信息 +

An SPH algorithm for gear rack dynamic meshing and transmission analysis

TANG Yufeng1,2，HU Guangzhong1，CAO Xiuquan1，YANG Mingjun1,2

Author information +

文章历史 +

摘要

针对现有光滑粒子流体动力学(smoothed particle hydrodynamics，SPH)方法在对齿轮齿条等具有复杂边界的机构进行动态啮合及传动过程分析的不足，基于齿轮齿条啮合及传动特点进行了改进。通过改进其相互作用力，提出了一种适用于复杂边界动态啮合及传动分析的SPH计算方法，并编程实现了相应的SPH程序。采用该SPH算法对一个简化的齿轮齿条啮合及传动算例进行了分析，得到了不同时刻齿轮齿条位置、速度变化及应力分布等信息，揭示了齿轮齿条机构发生齿面点蚀及齿根破坏的力学原理，并与有限元方法对比验证了方法的可行性。该研究提出的SPH方法可广泛应用于齿轮、齿条、轴承等具有复杂动态接触边界的机构的强度评价和优化分析，为该领域的数值分析提供了一种新的思路，同时也推动了SPH在该领域内的进一步发展。

Abstract

This paper aims at the shortcomings of the existing smoothed particle hydrodynamics(SPH) methods in the dynamic meshing and transmission process analysis of gear rack and other mechanisms with complex boundaries, and improves the gear rack meshing and transmission characteristics.First, by improving its interaction force, an SPH calculation method for dynamic meshing and transmission analysis of complex boundaries was proposed, and the corresponding SPH program was programmed.Secondly, a simplified gear rack meshing and transmission example was analyzed by using the SPH algorithm, and the information of gear rack position, velocity change, and stress distribution at different times were obtained.The mechanical principle of tooth surface pitting and root failure of gear rack mechanism was revealed, and the feasibility of the method was verified by comparison with a finite element method to verify the feasibility of the method.The proposed SPH method in this paper can be widely used for strength evaluation and optimization analysis of mechanisms with complex dynamic contact boundaries such as gear, rack, and bearing.It provides a new idea for numerical analysis in this field and also promotes further development of SPH in this field.

导出引用

唐宇峰，胡光忠，曹修全，阳明君. 齿轮齿条动态啮合及传动分析的SPH数值算法研究[J]. 振动与冲击, 2021, 40(16): 39-44

TANG Yufeng，HU Guangzhong，CAO Xiuquan，YANG Mingjun. An SPH algorithm for gear rack dynamic meshing and transmission analysis[J]. Journal of Vibration and Shock, 2021, 40(16): 39-44

参考文献

［1］HWANG S C, LEE J H, LEE D H, et al.Contact stress analysis for a pair of mating gears［J］.Mathematical and Computer Modeling, 2013,57(1/2): 40-49.

［2］贾海涛,王峰,方宗德.圆柱斜齿轮齿面接触动应力计算与分析研究［J］.振动与冲击,2014,33(22):168-171.
JIA Haitao, WANG Feng, FANG Zongde.Calculation and comparative analysis of helical gear tooth contact dynamic stress［J］.Journal of Vibration and Shock, 2014,33(22): 168-171.

［3］闫晓青,郑卫力,张银婷,等.大模数重载齿条中的缺陷应力场数值模拟［J］.水运工程, 2020(2): 157-163.
YAN Xiaoqing, ZHENG Weili, ZHANG Yinting, et al.Numerical simulation of stress fields of defects in large modulus and heavy load rack［J］.Port & Waterway Engineering, 2020(2): 157-163.

［4］强洪夫,张国星,王广,等.SPH方法在宽速域岩石侵彻问题中的应用［J］.高压物理学报, 2019,33(5): 174-182.
QIANG Hongfu, ZHANG Guoxing, WANG Guang, et al.Application of SPH method of problem of rock penetration within the wide-ranged velocity［J］.Chinese Journal of High Pressure Physics, 2019,33(5): 174-182.

［5］陈佩佩,白冰.非饱和岩土介质渗流问题的光滑粒子法模拟［J］.岩石力学与工程学报, 2016,35(10): 2124-2130.
CHEN Peipei, BAI Bing.Simulation of seepage problems in unsaturated soil using the smoothed particle hydrodynamics (SPH) method［J］.Chinese Journal of Rock Mechanics and Engineering, 2016,35(10): 2124-2130.

［6］王维国,陈育民,刘汉龙,等.基于SPH-FEM耦合法的土体爆炸效应数值研究［J］.岩土力学, 2013,34(7): 2104-2110.
WANG Weiguo, CHEN Yumin, LIU Hanlong, et al.Numerical simulation of explosion in soil based on a coupled SPH-FEM algorithm［J］.Rock and Soil Mechanics, 2013,34(7): 2104-2110.

［7］骆钊,汪淳.改进的SPH边界处理方法与土体大变形模拟［J］.计算力学学报, 2018,35(3): 364-371.
LUO Zhao, WANG Chun.Improved SPH boundary conditions and simulation for large deformation of soil［J］.Chinese Journal of Computational Mechanics, 2018,35(3): 364-371.

［8］FRISSANE H, TADDEI L, LEBAAL N, et al.SPH modeling of high velocity impact into ballistic gelatin.Development of an axis-symmetrical formulation［J］.Mechanics of Advanced Materials and Structures, 2019,26(22): 1881-1888.

［9］BECKER M, SEIDL M, MEHL M, et al.Numerical and experimental investigation of SPH, SPG, and FEM for high-velocity impact applications［C］//12th European LS-DYNA Conference 2019.Koblenz: DYNAmore GmbH, 2019.

［10］热合买提江•依明江,买买提明•艾尼.SPH分析中的齿轮建模方法研究［J］.新疆大学学报(自然科学版), 2008,25(1): 122-126.
Rahmatjan Imin, Mamtimin Geni.Study on the gear modeling in SPH analysis［J］.Journal of Xinjiang University (Natural Science Edition), 2008,25(1): 122-126.

［11］IMIN R, GENI M.Stress analysis of gear meshing impact based on SPH method［J］.Mathematical Problems in Engineering, 2014,2014: 328216.

［12］热合买提江•依明,买买提明•艾尼.两齿轮正确啮合和相互耦合接触的SPH计算方法研究［J］.振动与冲击, 2015,34(12): 65-69.
Rahmatjan Imin, Mamtimin Geni.SPH algorithm for proper meshing and coupling contact of gears［J］.Journal of Vibration and Shock, 2015,34(12): 65-69.

［13］KELLER M C, BRAUN S, WIETH L, et al.Smoothed particle hydrodynamics simulation of oil-jet gear interaction［J］.Journal of Tribology, 2019,141(7): 071703.

［14］LIU G R, LIU M B.Smoothed particle hydrodynamics: a meshless particle method［M］.Singapore: World Scientific Publishing, 2003.

［15］唐宇峰.尾矿库稳定性及失稳式溃坝的光滑粒子流体动力学(SPH)数值模拟研究［D］.成都：西南交通大学, 2016.

［16］MONAGHAN J J.An introduction to SPH［J］.Computer Physics Communications, 1989,48: 89-96.