非对称渐开线齿轮传动特性及应用基础研究
|
摘要
齿轮是动力机械装备的主要传动零件之一。非对称齿轮是一种为了提高轮齿的抗弯曲强度而提出的新型齿轮。该齿轮具有承载能力大、体积小、重量轻、使用寿命长等优点,开展非对称齿轮的研究,对航天、航空等场合下重载、高速齿轮的应用具有重要的理论指导和现实意义。本文采用理论分析、数值模拟和实验测试相结合的方法,以非对称渐开线齿轮为对象,研究齿面摩擦下单、双模数非对称齿轮的传动性能,探索提高非对称齿轮传动性能的新方法、新理论和新技术,主要研究工作如下：
1.阐述了非对称渐开线斜(圆锥)齿轮齿廓曲面的生成原理,推导出单、双模数非对称渐开线齿条刀具的参数方程
根据非对称齿轮的结构特点,阐述了非对称渐开线斜(圆锥)齿轮齿廓曲面的生成原理,为进一步推广非对称齿轮奠定了理论基础；为了加快单、双模数非对称齿轮的研究和应用,结合单、双模数非对称齿轮的特点,推导出单、双模数非对称渐开线齿条刀具的参数方程。
2.建立齿面摩擦下非对称渐开线齿轮齿面接触应力和齿根弯曲应力的数学模型
在考虑齿面摩擦影响的情况下,通过建立轮齿受力的数学模型,推导出单、双模数非对称渐开线齿轮齿面接触应力和齿根弯曲应力的数学模型,为提高齿面接触强度和齿根弯曲强度提供了理论依据。
3.建立齿面摩擦下非对称渐开线齿轮支座反力的数学模型
通过对轮齿受力进行分析,在引入齿间载荷分配因数的情况下,建立齿面摩擦作用下单、双模数非对称渐开线齿轮支座反力的数学模型,给出了表征齿轮支座反力波动程度的评价指标,为提高齿轮传动平稳性提供了理论参考。
4.建立非对称渐开线齿轮齿廓滑动系数的数学模型
利用啮合齿廓接触点的公法线矢量和接触点相对运动速度方向的法曲率,推导出空间啮合状态下,单、双模数非对称渐开线齿轮齿廓滑动系数的矢量计算公式；以及单、双模数非对称渐开线直齿圆柱齿轮齿廓滑动系数的简化计算公式；为揭示齿轮摩擦、磨损的机理提供了理论依据。
5.实现了非对称渐开线齿轮啮合效率的预测
在引入轮齿啮合点齿廓曲率半径的条件下,通过对轮齿的单、双齿啮合情况进行受力分析,建立任意齿间载荷分配因系数下单、双模数非对称渐开线齿轮啮合效率的数学模型,并对各种条件下齿轮啮合效率进行了预测,为非对称渐开线齿轮传动效率的确定,提供了一种快速、便捷的方法。
6.非对称渐开线齿轮传动系统的测试及实验设计
设计了非对称渐开线齿轮传动系统的测试平台,进行了齿轮传动装置噪声和振动加速度的测试,分析了对称齿轮和非对称齿轮在不同啮合状态下的动态性能。
研究表明,在非对称渐开线齿轮齿面接触应力和齿根弯曲应力的计算中不可忽视齿面摩擦的影响；非对称渐开线齿轮在轮齿强度、齿廓滑动系数、啮合效率、振动、噪声等方面的性能指标均优于对称渐开线齿轮；相对于单模数对称渐开线齿轮,双模数非对称渐开线齿轮不仅可节省材料、减轻重量、提高齿面接触强度和齿根弯曲强度,而且由于齿廓滑动系数值较小,齿面磨损也较轻。与对称渐开线齿轮相比,非对称渐开线齿轮齿面接触应力可降低28.86%,齿根弯曲应力可降低6.37%。在考虑齿面摩擦的情况下,非对称渐开线齿轮齿面接触应力将增大7.51%,齿根弯曲应力将增大7.12%。与单模数对称渐开线齿轮相比,双模数非对称渐开线齿轮齿面接触应力可降低34.74%。对于单模数非对称齿轮,增大压力角,齿顶滑动系数可降低17.42%,齿根滑动系数可降低40.28%。对于双模数非对称齿轮,增大压力角,齿顶滑动系数可降低21.81%,齿根滑动系数可降低34.75%。对称渐开线齿轮的啮合效率为97.73%,而同等条件下非对称渐开线齿轮的啮合效率为98.24%。对称渐开线齿轮的噪声为83.685.0 dB,而非对称渐开线齿轮噪声72.6—73.7 dB。对称渐开线齿轮的振动加速度峰—峰值为4.49 G—-4.29 G,而非对称渐开线齿轮的振动加速度峰—峰值为1.02G—-1.08 G。研究表明,采用非对称齿轮能显著提高齿轮的传动性能,对于高速、重载、大功率齿轮传动场合具有非常重要的意义。
本文的研究得到了国家自然科学基金资助(No.51075192)。
Gear is one of the driving parts of power machinery and equipment. In order to improve the bending strength at the tooth root of gear, a kind of new gear,namely, asymmetric gear was put forward. The advantages of this kind of gear have larger carrying capacity, smaller volume, lighter weight and longer life. The study of asymmetric gear has important theoretical direction and realized significance to the application of the heavy load and high-speed gear for aerospace. The methods of theory analysis combined numerical simulation and experimental test are used in the paper. The asymmetric involute gear was used as object, the transmission performance of the single & double moduli asymmetric involute gear is researched under the friction force between teeth.The new technique, the new theory,and the new methods, of improving the transmission performance are explored. The main works are as follows:
1. The generated principles of the tooth profile curved surface of asymmetric involute gear are stated, the parametric equation of single & double moduli asymmetric involute rack tools is deduced
According to the structural features of asymmetric involute gear, the generated principles of the tooth profile curved surface of asymmetric involute gear are stated, this will establish the theory basis for popularizing the asymmetric involute gear. To accelerate the study and application of single & double moduli asymmetric involute gear, the parametric equation of single & double moduli asymmetric involute rack tools are deduced according to the characteristic of single & double moduli asymmetric involute gear.
2. The mathematic models on tooth face contact stress and tooth root bending stress of asymmetric involute gear are established under friction force between teeth
The mathematic models on tooth face contact stress and tooth root bending stress of asymmetric involute gear with double pressure angles are deduced by through fully analyzing the forces exerted on the driving gear of asymmetric spur gear drive under the action of sliding friction. Simulation results provide a theoretical basis to improve the tooth face contact strength and tooth root bending strength of asymmetric involute gear with double pressure angles.
3. The mathematic models of gear supports of asymmetric gear driving system are established under the sliding friction force
The author of the paper deduced the calculation equation of the gear supports reaction, under the action of the sliding friction between teeth, through fully analyzing the forces exerted on the driving gear of reducing-speed asymmetric spur gear drive system with double pressure angles in the single & double gears meshing range. And presented the index of gear supports reaction fluctuation in the condition of the random interteeth load.Simulation results provide the theoretical references for improving the transmission smoothness of the asymmetric gear with double pressure angles.
4. Establish the mathematical model of the sliding coefficient of asymmetric involute gear tooth profile
The vector calculation formula of tooth profile sliding coefficient of single & double moduli asymmetric involute gear was deduced by using the normal curvature of meshing point relative velocity direction and the common normal line vector of meshing point on the contac tooth profile under the spatial meshing state.And the simplified formula of tooth profile sliding coefficient of single & double moudli asymmetric involute spur gear was also deduced. Simulation results provide the theoretical references for revealing the working principle of friction and wear of the asymmetric gear with double pressure angles.
5. Prediction of meshing efficiency on asymmetric gear with double pressure angles
The author of the paper deduced the calculation equation of the gear mesh efficiency in the condition of the random interteeth load, under the action of the sliding friction between teeth, making use of the radii of teeth outline curvature at the mating points, through fully analyzing the forces exerted on the gears'teeth of single or double moduli asymmetric involute spur gear drive system with double pressure angles in the single & double gears meshing range.And, calculation of the mating efficiency was carried out by changing the sliding interteeth friction, pressure angle, modulus and gear's rotating speed ratio on the diving & driven gears of single or double moduli asymmetric spur gear drive system with double pressure angles. And provides a fast, convenient way in order to determine the transmission efficiency of asymmetric spur gear drive system with double pressure angles.
6. Testing and experimental design of the asymmetric involute gear drive system with double pressure angles.
The test platform of the asymmetric involute gear driving system with double pressure angles was designed, the noise and vibration acceleration of gear driving equipment was tested,and the dynamic performance of both unsymmetric gear and symmetric gear are analyzed under different meshing states in this paper.
The results show that the effect of the sliding friction between teeth can not be neglected in the tooth root bending stress calculation and tooth face contact stress calculation of asymmetric involute gear with double pressure angles. The performance index of noise and vibration, meshing efficient, tooth profile sliding coefficient,and gear strength,of asymmetric involute gear are superior to symmetric involute gear. Compared to single modulus symmetrical involute gear,dual modulus asymmetric involute gear can not only save material, reduce weight, improve tooth surface contact strength and root bending strength, and because of the smaller sliding coefficient of tooth profile, tooth wear lighter.
Compared with the symmetric involute gear, asymmetric involute gear tooth face contact stress can be reduced 28.86%, tooth root bending stress can be reduced 6.37%. Considering the tooth surface friction, asymmetric involute gear tooth surface contact stress will increase to 7.51%, the tooth root bending stress will increase to 7.12%.The tooth face contact stress of double moduli asymmetric involute gear can reduce to 34.74% comparing with single modulus symmetric involute gear. Tooth profile Sliding coefficient of tooth addendum can reduce to 17.42%, Sliding coefficient of tooth root can reduce to 40.28% by increasing the pressure angle for single modulus asymmetric involute gear. Tooth profile sliding coefficient of tooth addendum can reduce to 21.81%, Sliding coefficient of tooth root can reduce to 34.75% by increasing the pressure angle for double moduli asymmetric involute gear.The meshing efficiency of symmetric involute gear is 97.73%, but the meshing efficient of symmetric involute gear is 98.24% under the same conditions.The noise of symmetric involute gear is from 83.6 to 85.0 dB, but the noise of asymmetric involute gear is from 72.6 to 73.7 dB, The vibration acceleration peak-peak of symmetric involute gear is from 4.49 G to -4.29G, while on the asymmetric involute gear is from 1.02 G to -1.08 G. The results show that the asymmetric gear can significantly improve the transmission performance of the gear, has very important significance for the high-speed, overload, high-power gear working environment.
The dissertation is supported by National Natural Science Foundation (No.51075192).
1.阐述了非对称渐开线斜(圆锥)齿轮齿廓曲面的生成原理,推导出单、双模数非对称渐开线齿条刀具的参数方程
根据非对称齿轮的结构特点,阐述了非对称渐开线斜(圆锥)齿轮齿廓曲面的生成原理,为进一步推广非对称齿轮奠定了理论基础；为了加快单、双模数非对称齿轮的研究和应用,结合单、双模数非对称齿轮的特点,推导出单、双模数非对称渐开线齿条刀具的参数方程。
2.建立齿面摩擦下非对称渐开线齿轮齿面接触应力和齿根弯曲应力的数学模型
在考虑齿面摩擦影响的情况下,通过建立轮齿受力的数学模型,推导出单、双模数非对称渐开线齿轮齿面接触应力和齿根弯曲应力的数学模型,为提高齿面接触强度和齿根弯曲强度提供了理论依据。
3.建立齿面摩擦下非对称渐开线齿轮支座反力的数学模型
通过对轮齿受力进行分析,在引入齿间载荷分配因数的情况下,建立齿面摩擦作用下单、双模数非对称渐开线齿轮支座反力的数学模型,给出了表征齿轮支座反力波动程度的评价指标,为提高齿轮传动平稳性提供了理论参考。
4.建立非对称渐开线齿轮齿廓滑动系数的数学模型
利用啮合齿廓接触点的公法线矢量和接触点相对运动速度方向的法曲率,推导出空间啮合状态下,单、双模数非对称渐开线齿轮齿廓滑动系数的矢量计算公式；以及单、双模数非对称渐开线直齿圆柱齿轮齿廓滑动系数的简化计算公式；为揭示齿轮摩擦、磨损的机理提供了理论依据。
5.实现了非对称渐开线齿轮啮合效率的预测
在引入轮齿啮合点齿廓曲率半径的条件下,通过对轮齿的单、双齿啮合情况进行受力分析,建立任意齿间载荷分配因系数下单、双模数非对称渐开线齿轮啮合效率的数学模型,并对各种条件下齿轮啮合效率进行了预测,为非对称渐开线齿轮传动效率的确定,提供了一种快速、便捷的方法。
6.非对称渐开线齿轮传动系统的测试及实验设计
设计了非对称渐开线齿轮传动系统的测试平台,进行了齿轮传动装置噪声和振动加速度的测试,分析了对称齿轮和非对称齿轮在不同啮合状态下的动态性能。
研究表明,在非对称渐开线齿轮齿面接触应力和齿根弯曲应力的计算中不可忽视齿面摩擦的影响；非对称渐开线齿轮在轮齿强度、齿廓滑动系数、啮合效率、振动、噪声等方面的性能指标均优于对称渐开线齿轮；相对于单模数对称渐开线齿轮,双模数非对称渐开线齿轮不仅可节省材料、减轻重量、提高齿面接触强度和齿根弯曲强度,而且由于齿廓滑动系数值较小,齿面磨损也较轻。与对称渐开线齿轮相比,非对称渐开线齿轮齿面接触应力可降低28.86%,齿根弯曲应力可降低6.37%。在考虑齿面摩擦的情况下,非对称渐开线齿轮齿面接触应力将增大7.51%,齿根弯曲应力将增大7.12%。与单模数对称渐开线齿轮相比,双模数非对称渐开线齿轮齿面接触应力可降低34.74%。对于单模数非对称齿轮,增大压力角,齿顶滑动系数可降低17.42%,齿根滑动系数可降低40.28%。对于双模数非对称齿轮,增大压力角,齿顶滑动系数可降低21.81%,齿根滑动系数可降低34.75%。对称渐开线齿轮的啮合效率为97.73%,而同等条件下非对称渐开线齿轮的啮合效率为98.24%。对称渐开线齿轮的噪声为83.685.0 dB,而非对称渐开线齿轮噪声72.6—73.7 dB。对称渐开线齿轮的振动加速度峰—峰值为4.49 G—-4.29 G,而非对称渐开线齿轮的振动加速度峰—峰值为1.02G—-1.08 G。研究表明,采用非对称齿轮能显著提高齿轮的传动性能,对于高速、重载、大功率齿轮传动场合具有非常重要的意义。
本文的研究得到了国家自然科学基金资助(No.51075192)。
Gear is one of the driving parts of power machinery and equipment. In order to improve the bending strength at the tooth root of gear, a kind of new gear,namely, asymmetric gear was put forward. The advantages of this kind of gear have larger carrying capacity, smaller volume, lighter weight and longer life. The study of asymmetric gear has important theoretical direction and realized significance to the application of the heavy load and high-speed gear for aerospace. The methods of theory analysis combined numerical simulation and experimental test are used in the paper. The asymmetric involute gear was used as object, the transmission performance of the single & double moduli asymmetric involute gear is researched under the friction force between teeth.The new technique, the new theory,and the new methods, of improving the transmission performance are explored. The main works are as follows:
1. The generated principles of the tooth profile curved surface of asymmetric involute gear are stated, the parametric equation of single & double moduli asymmetric involute rack tools is deduced
According to the structural features of asymmetric involute gear, the generated principles of the tooth profile curved surface of asymmetric involute gear are stated, this will establish the theory basis for popularizing the asymmetric involute gear. To accelerate the study and application of single & double moduli asymmetric involute gear, the parametric equation of single & double moduli asymmetric involute rack tools are deduced according to the characteristic of single & double moduli asymmetric involute gear.
2. The mathematic models on tooth face contact stress and tooth root bending stress of asymmetric involute gear are established under friction force between teeth
The mathematic models on tooth face contact stress and tooth root bending stress of asymmetric involute gear with double pressure angles are deduced by through fully analyzing the forces exerted on the driving gear of asymmetric spur gear drive under the action of sliding friction. Simulation results provide a theoretical basis to improve the tooth face contact strength and tooth root bending strength of asymmetric involute gear with double pressure angles.
3. The mathematic models of gear supports of asymmetric gear driving system are established under the sliding friction force
The author of the paper deduced the calculation equation of the gear supports reaction, under the action of the sliding friction between teeth, through fully analyzing the forces exerted on the driving gear of reducing-speed asymmetric spur gear drive system with double pressure angles in the single & double gears meshing range. And presented the index of gear supports reaction fluctuation in the condition of the random interteeth load.Simulation results provide the theoretical references for improving the transmission smoothness of the asymmetric gear with double pressure angles.
4. Establish the mathematical model of the sliding coefficient of asymmetric involute gear tooth profile
The vector calculation formula of tooth profile sliding coefficient of single & double moduli asymmetric involute gear was deduced by using the normal curvature of meshing point relative velocity direction and the common normal line vector of meshing point on the contac tooth profile under the spatial meshing state.And the simplified formula of tooth profile sliding coefficient of single & double moudli asymmetric involute spur gear was also deduced. Simulation results provide the theoretical references for revealing the working principle of friction and wear of the asymmetric gear with double pressure angles.
5. Prediction of meshing efficiency on asymmetric gear with double pressure angles
The author of the paper deduced the calculation equation of the gear mesh efficiency in the condition of the random interteeth load, under the action of the sliding friction between teeth, making use of the radii of teeth outline curvature at the mating points, through fully analyzing the forces exerted on the gears'teeth of single or double moduli asymmetric involute spur gear drive system with double pressure angles in the single & double gears meshing range.And, calculation of the mating efficiency was carried out by changing the sliding interteeth friction, pressure angle, modulus and gear's rotating speed ratio on the diving & driven gears of single or double moduli asymmetric spur gear drive system with double pressure angles. And provides a fast, convenient way in order to determine the transmission efficiency of asymmetric spur gear drive system with double pressure angles.
6. Testing and experimental design of the asymmetric involute gear drive system with double pressure angles.
The test platform of the asymmetric involute gear driving system with double pressure angles was designed, the noise and vibration acceleration of gear driving equipment was tested,and the dynamic performance of both unsymmetric gear and symmetric gear are analyzed under different meshing states in this paper.
The results show that the effect of the sliding friction between teeth can not be neglected in the tooth root bending stress calculation and tooth face contact stress calculation of asymmetric involute gear with double pressure angles. The performance index of noise and vibration, meshing efficient, tooth profile sliding coefficient,and gear strength,of asymmetric involute gear are superior to symmetric involute gear. Compared to single modulus symmetrical involute gear,dual modulus asymmetric involute gear can not only save material, reduce weight, improve tooth surface contact strength and root bending strength, and because of the smaller sliding coefficient of tooth profile, tooth wear lighter.
Compared with the symmetric involute gear, asymmetric involute gear tooth face contact stress can be reduced 28.86%, tooth root bending stress can be reduced 6.37%. Considering the tooth surface friction, asymmetric involute gear tooth surface contact stress will increase to 7.51%, the tooth root bending stress will increase to 7.12%.The tooth face contact stress of double moduli asymmetric involute gear can reduce to 34.74% comparing with single modulus symmetric involute gear. Tooth profile Sliding coefficient of tooth addendum can reduce to 17.42%, Sliding coefficient of tooth root can reduce to 40.28% by increasing the pressure angle for single modulus asymmetric involute gear. Tooth profile sliding coefficient of tooth addendum can reduce to 21.81%, Sliding coefficient of tooth root can reduce to 34.75% by increasing the pressure angle for double moduli asymmetric involute gear.The meshing efficiency of symmetric involute gear is 97.73%, but the meshing efficient of symmetric involute gear is 98.24% under the same conditions.The noise of symmetric involute gear is from 83.6 to 85.0 dB, but the noise of asymmetric involute gear is from 72.6 to 73.7 dB, The vibration acceleration peak-peak of symmetric involute gear is from 4.49 G to -4.29G, while on the asymmetric involute gear is from 1.02 G to -1.08 G. The results show that the asymmetric gear can significantly improve the transmission performance of the gear, has very important significance for the high-speed, overload, high-power gear working environment.
The dissertation is supported by National Natural Science Foundation (No.51075192).
引文
[1]Dabnichki P,Crocombe A.Finite element modelling of local contact conditions in gear teeth[J]. Journal of Strain Analysis for Engineering Design,1999,34 (2):129-142.
[2]Li C H, Chiou H S, Hung C,et al.Integration of finite element analysis and optimum design on gear systems[J]. Finite Elements in Analysis and Design,2002,38(3):179-192
[3]周彦伟,方宗德,邓效忠.航空弧齿锥齿轮齿面接触应力计算与优化[J].航空动力报,2002,17(3)：373-376.
[4]高创宽,周谋,亓秀梅.齿面摩擦力对齿轮接触应力的影响[J].机械强度,2003,25(6)：642-645.
[5]杨生华.齿轮接触有限元分析[J].计算力学学报,2003,20(2)：189-193.
[6]邓效忠,方宗德,魏冰阳.接触路径对弧齿锥齿轮接触应力和弯曲应力的影响[J].中国机械工程,2003,14(22)：1895-1898.
[7]Tseng Rui-Tang, Tsay Chung-Biau.Contact characteristics of cylindrical gears with Curvilinear shaped teeth[J]. Mechanism and Machine Theory,2004,39:905-919.
[8]龙慧,张光辉,罗文军.旋转齿轮瞬时接触应力和温度的分析模拟[J].机械工程学报,2004,40(8)：24-29.
[9]李秀莲,董晓英,曹清林.基于摩擦的斜齿轮齿面接触疲劳强度计算[J].农业机械学报,2005,36(4)：123-124.
[10]阎树田,梁继斌,沙成梅,等.精确模型下斜齿轮接触应力的有限元分析[J].兰州理工大学学报,2006,32(3)：47-49.
[11]屈文涛,沈允文,徐建宁.基于ANSYS的双圆弧齿轮接触应力有限元分析[J].农业机械学报,2006,37(10)：139-141.
[12]Sraml M., Flasker J. Computational approach to contact fatigue damage initiation analysis of gear teeth flanks [J].International Journal of Advanced Manufacturing Technology, 2007,31(11-12):1066-1075.
[13]Li Shuting. Finite element analyses for contact strength and bending strength of a pair of spur gears with machining errors, assembly errors and tooth modifications[J]. Mechanism and Machine Theory,2007,42:88-114.
[14]Hedlund J,Lehtovaara A.Modeling of helical gear contact with tooth deflection[J]. Tribology International,2007,40:613-619.
[15]Pasta A, Mariotti G V. Finite element method analysis of a spur gear with a corrected Profile. Journal of Strain Analysis for Engineering Design,2007,42 (5):281-292.
[16]陈赛克,王毅.基于精确模型的齿轮接触疲劳寿命有限元分析[J].机械传动,2007,31(2)：81-82.
[17]张金良,方宗德,曹雪梅,等.弧齿锥齿轮齿面接触应力分析[J].机械科学与技术,2007,26(10)：1268-1272.
[18]谢最伟,吴新跃,陈艳锋.人字齿轮齿面应力的接触元分析[J].机械设计,2007,24 (10)：25-28.
[19]姚齐水,李常义,潘存云.渐开线环形齿球齿轮副接触点共轭曲率半径及接触强度计算研究[J].机械科学与技术,2007,26(1)：96-100.
[20]张慧.啮合误差状态下渐开线圆柱齿轮接触应力有限元分析[J]_中国制造业信息化,2008,37(7)：72-74,-75.
[21]张宏文,吴杰.传动齿轮接触应力的有限元分析[J].石河子大学学报(自然科学版),2008,26(2)：238-240.
[22]胡爱萍,刘善淑,陈权.标准直齿圆柱齿轮传动接触强度计算的研究[J].机械设计,2008,25(11)：45-48.
[23]Jabbour Toni, Asmar Ghazi.Stress calculation for plastic helical gears under a real Transverse contact ratio[J]. Mechanism and Machine Theory,2009,44:2236-2247.
[24]Hassan A R. Contact stress analysis of spur gear teeth pair[J]. World Academy of Science, Engineering and Technology,2009,58:611-616.
[25]徐辅仁.对水面舰艇纵向轴系游动端支座间隙设计的深化研究[J].船舶力学,1999,3(4)：61-64.
[26]徐辅仁,范小钢,徐增豪,等.计入船体变形及齿间摩擦的齿面接触疲劳强度[J].船舶力学,2006,10(2)：104-110.
[27]李秀莲.计入摩擦的船用斜齿轮齿面接触疲劳强度计算[J].机械设计与研究,2009,25(3)：52-55.
[28]李秀莲.基于船体变形及齿间摩擦的斜齿轮齿根弯曲疲劳强度计算[J].兵工学报,2008,29(8)：1019-1024.
[29]李秀莲.船用高速齿轮齿根弯曲疲劳强度的计算[J].热能动力工程,2009,24(3)：373-377.
[30]李秀莲.基于遗传算法的船用斜齿轮传动模糊可靠优化的研究[J].舰船科学技术,2009,31(2)：76-79.
[31]陈奇,赵韩,黄康,等.分形理论在齿轮接触应力分析中的应用研究[J].中国机械工程,2010,21(9)：1014-1017,1057.
[32]黄海,厉海祥,罗齐汉.点线啮合齿轮接触强度计算的研究[J].机械制造,2010,48(55)5：10-12.
[33]杨凡,孙首群,于建华,等.齿轮啮合过程中接触应力的精确分析[J].机械传动,2010,34(7)：56-59.
[34]武志斐,王铁,张瑞亮.18Cr2Ni4WA齿轮接触疲劳特性试验研究[J].兵工学报,2010,31(5)：598-602.
[35]Von Eiff H, Hirschmann K H, Lechner G. Influence of gear tooth geometry on tooth stress of external and internal gears[J]. Journal of Mechanical Design,1990,112(4):575-583.
[36]Bibel G D, Reddy S K, Savage M, et al. Effects of rim thickness on spur gear bending stress[J]. Journal of Mechanical Design,1994,116(4):1157-1162.
[37]Filiz I F,Eyercioglu O. Evaluation of gear tooth stresses by fininte element method[J]. Journal of Engineering for Industry,1995,117 (2):232-239.
[38]许洪斌,张光辉,加藤正名.分阶式双渐开线齿轮弯曲应力的有限元研究[J].机械工程学 报,2000,36(6)：12-15.
[39]许洪斌,张光辉,加藤正名.分阶式双渐开线齿轮的光弹试验与弯曲强度试验研究[J].机械工程学报,2000,36(8)：39-42.
[40]Litvin F L, Fuentes A, Fan Q, et al. Computerized design, simulation of meshing, and contact and stress analysis of face-milled formate generated spiral bevel gears[J]. Mechanism and Machine Theory,2002,37:441-359.
[41]李秀莲.齿间摩擦力作用下的圆锥齿轮齿根弯曲疲劳强度的计算[J].机床与液压,2004,(1)：102-103.
[42]李秀莲,雷良育,曹清林,等.齿间摩擦对斜齿轮齿根弯曲应力的影响[J].农业机械学报,2005,36(1)：121-122,133.
[43]唐进元,周长江,吴运新.齿轮弯曲强度有限元分析精确建模的探讨[J].机械科学与技术,2004,23(10)：1146-1150.
[44]罗齐汉,李成刚,厉海祥,等.齿轮弯曲强度有限元精确分析方法研究[J].机械科学与技术,2007,26(9)：1212-1215.
[45]唐进元,刘艳萍.齿轮弯曲强度与沉切量关系研究[J].制造技术与机床,2007,(11)：31-35.
[46]李盛鹏,方宗德,张金良,等.弧齿锥齿轮齿根弯曲应力分析[J].航空动力学报,2007,22(5)：843-847.
[47]周长江,钟志华,唐进元.基于齿轮误差与柔度的弯曲强度计算力点研究[J].湖南大学学报,2007,34(7)：35-38.
[48]郭辉,赵宁,方宗德,等.基于接触有限元的面齿轮传动弯曲强度研究[J].航空动力学报,2008,23(8)：1438-1442.
[49]许浩,方宗德,曹雪梅.弧齿锥齿轮弯曲应力计算[J].机械传动,2008,32(6)：60-63.
[50]黄丽娟,朱如鹏.基于ANSYS的斜齿面齿轮传动的弯曲应力分析[J].机械传动,2009,33(3)：91-93.
[51]李东波,张艳冬,尤绍君.基于ANSYS的正交面齿轮参数化模型的弯曲应力分析[J].辽宁工：业大学学报(自然科学版),2009,29(4)：249-251.
[52]邓洪超,康一坡.基于总成的重型汽车变速箱齿轮弯曲应力分析[J].机械设计,2009,26(4)：71-75.
[53]杨小安,张伟社,高勇,等.基于BP网络的齿轮弯曲疲劳强度极限的确定[J].机械传动,2009,33(3)：94-96.
[54]赵韩,陈奇,黄康.基于精确建模的微线段齿轮弯曲强度理论分析[J].组合机床与自动化加工技术,2010,(7)：62-64.
[55]肖义成.车辆传动系统齿轮弯曲疲劳探讨[J].湖北工业大学学报,2010,25(5)：26-28.
[56]林财和.齿轮磨损量与滑动系数优化设计的探讨[J].武汉工业大学学报,1992,14(2)：67-71.
[57]杨建中.齿轮传动相关滑动率分析和提高磨损承载能力的措施[J].机械传动,1996,20(2)：31-34.
[58]柴畅.传动比对齿轮传动应力、相对滑动和磨损的影响[J].安徽工学院学报,1996,15(1)：71-75.
[59]阎树田,胡赤兵,邬再新,等.齿轮齿廓滑动磨损的数值计算方法[J].机械设计与制造工程,2001,30(4)：9-10.
[60]章易程,李蔚,聂昌平.渐开线内齿轮副相对滑动率的研究[J].机械传动,2001,25(2)：25-27.
[61]章易程,李蔚,陈昭莲,等.渐开线外齿轮副相对滑动率的研究[J].机械设计,2001,(7)：27-29.
[62]贲霖,徐辅仁.直齿渐开线齿轮齿面磨损模拟计算[J].航空精密制造技术,2003,39(5)：29-32.
[63]赵亚平,魏文军,董学朱,等.点接触齿面滑动率计算方法及其对交错轴渐开线斜齿轮传动的应用[J].中国机械工程(增刊),2006,17：40-43.
[64]杜雪松,林腾蛟,李润方,等. AGMA按均衡滑动率原则选择齿轮变位系数的原理[J].重庆大学学报(自然科学版),2007,30(8)：6-9.
[65]徐学忠,宋天麟.直线共轭齿廓齿轮副的滑动系数研究[J].淮阴师范学院学报(自然科学版),2007,6(3)：225-228.
[66]Luo Shanming, Wu Yue, Wang Jian. The generation principle and mathematical models of a novel cosine gear drive[J]. Mechanism and Machine Theory,2008,43:1543-1556.
[67]Wang Jian, Luo Shanming, CHEN Iifeng, et al. Analysis of transmission characteristics of cosine gear drive[J]. Chinese Journal of Mechanical Engineering,2008,21 (3):94-99.
[68]Wang Jian, Luo Shanming, Zhu Shimin. Initiative design of tooth profiles with small sliding coefficients[J]. Applied Mechanics and Materials,2009,16-19:811-815.
[69]Wang Jian, Luo Shanming, Wu Yue. A method for the preliminary geometric design of gear tooth profiles with small sliding coefficients[J]. Journal of mechanical design,2010, 132(5):054501-1-054501-8.
[70]Antal T A. A new algorithm for helical gear design with addendum modification[J]. Mechanika, 2009,77 (3):53-57.
[71]Antal T A, Antal A.Determination of the geometrical dimensions of the helical gears with addendum modifications based on the specific sliding equalization model[J]. Advanced Techniques in Computing Sciences and Software Engineering,2010,85-90.
[72]Weiss T, Hirt M, Efficiency Improvements for High Speed Gears[A]. International Conference on Gears[C]. Munich, Germany:VDI,2002:1161-1174.
[73]Anderson N E, Loewenthal S H. Efficiency of nonstandard and high contact ratio involute spur gears[A]. Fourth International Power Transmission and Gearing Conference[C]. Cambridge, Massachusetts, Britain,1984.
[74]刘福林,姜弘,朱均.干摩擦条件下聚甲醛塑料动力齿轮传动啮合效率的分析研究与计算[J].摩擦学学报,1995,15(3)：263-270.
[75]姚建初,陈义保,周济,等.齿轮传动啮合效率计算方法的研究[J].机械工程学,2001,37(11)：18-21，27.
[76]徐辅仁.关于仪器渐开线齿轮副效率计算的研究[J].仪器仪表学报,2001,22(5)：446-450.
[77]王三民,沈允文,孙智民.基于动态损失功率的行星齿轮传动效率计算[J].机械传动,2001, 25(2)：4-5,8.
[78]姚九成.按平均滑动速度法计算平动齿轮机构的啮合效率[J].机械设计,2002,(10)：61-62.
[79]Michlin Y, Myunster V. Determination of power losses in gear transmissions with rolling and sliding friction incorporated[J]. Mechanism and Machine Theory,2002,37 (2):167-174.
[80]Heingartner P, Mba D. Determining power losses in the helical gear mesh:case study [A]. Proceedings of DETC'03 [C]. Chicago, USA:ASME 2003 Design Engineering Technical Conferences and Computers and Information in Engineering Conference,2003
[81]牟柳晨,殷国富,余力.速比法在行星齿轮传动效率计算中的应用[J].中国制造业信息化,2004,33(6)：88-91.
[82]崔丽,秦大同,石万凯.行星齿轮传动啮合效率分析[J].重庆大学学报(自然科学版),2006,29(3)：11-14,44.
[83]Changenet C, Velex P. A Model for the Prediction of Churning Losses in Geared Transmissions—Preliminary Results[J]. Journal of Mechanical Design,2007,129:128-133.
[84]Xu H, Kahraman A, Anderson N E,et al.Prediction of mechanical efficiency of parallel-axis gear pairs[J]. Journal of Mechanical Design,2007,129:58-68.
[85]Xu H, Kahraman A. Prediction of friction-related power losses of hypoid gear pairs[J]. Proc IMechE (part K:J Multi-body Dynamics),2007,221:387-400.
[86]Al-Shibl K, Simmons K, Eastwick C N. Modelling windage power loss from an enclosed spur gear[J]. Proceedings of the Institution of Mechanical Engineers, part A:Journal of Power and Energy,2007,331-341.
[87]陈立锋,吴晓铃,秦大同.基于图论的风力发电机组齿轮传动系统效率分析[J].机械传动,2008,32(6)：18-20.
[88]Koffel G, Ville F, Changenet C, et al. Investigations on the power losses and thermal effects in gear transmissions[J]. Proc. IMechE (part J:J Engineering Tribology),2009,223:469-479.
[89]Li Sheng, Vaidyanathan A, Harlanto J, et al. Influence of design parameters on mechanical power losses of helical gear pairs[J]. Journal of Advanced Mechanical Design, Systems, and Manufacturing,2009,3 (2):146-158.
[90]Seetharaman S, Kahraman A. Load-Independent Spin Power Losses of a Spur Gear Pair:Model Formulation[J]. Journal of Tribology,2009,131:022201-1-022201-11.
[91]Seetharaman S, Kahraman A, Moorhead M D, et al. Oil churning power losses of a gear pair experiments and model validation [J]. Journal of Tribology,2009,131:022202-1-022202-10.
[92]王成,方宗德,贾海涛.斜齿轮滑动摩擦功率损失的计算[J].燕山大学学报,2009,33(2)：99-103.
[93]周春国,王付岗,刘宏昭,等.基于虚拟样机的行星齿轮机构效率仿真分析[J].机械传动,2009,33(4)：65-68.
[94]Kolivand M, Li S, Kahraman A. Prediction of mechanical gear mesh efficiency of hypoid gear pairs[J]. Mechanism and Machine Theory,2010,45:1568-1582.
[95]Li Sheng, Kahraman A. Prediction of spur gear mechanical power losses using a transient elastohydrodynamic lubrication model[J]. Tribology Transactions,2010,53:554-563.
[96]Magalhaes Luis, Martins Ramiro, Locateli Cristiano, et al. Influence of tooth profile and oil formulation on gear power loss[J]. Tribology International,2010,43:1861-1871.
[97]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.
[98]许翔,杨定富,索文超,刘刚.基于时变载荷的齿轮摩擦功率损失计算研究[J].工程设计学报,2010,17(3)：224-228.
[99]李润方,王建军.齿轮系统动力学[M].北京：科学山版社,1997.
[100]林腾蛟,李润方,陶泽光.齿轮传动三维间隙非线性冲击——动力接触特性数值仿真[J].机械工程学报,2000,36(6)：55-58.
[101]Velex P, Sainsot P. An analytical study of tooth friction excitations in errorless spur and helical gears[J]. Mechanism and Machine Theory,2002,37:641-658.
[102]张锁怀,沈允文,丘大谋.齿轮耦合的转子轴承系统的不平衡响应[J]_机械工程学报,2002,38(6)：51-55.
[103]李华,沈允文,孙智民.基于A一算符方法的齿轮系统的分岔与混沌[J].机械工程学报,2002,38(6)：11-15.
[104]孙智民,季林红,沈允文.2K-H行星齿轮传动非线性动力学[J].清华大学学报(自然科学版),2003,43(5)：636-639.
[105]王三民,沈允文,董海军.含间隙和时变啮合刚度的弧齿锥齿轮传动系统非线性振动特性研究[J].机械工程学报,2003,39(2)：28-32.
[106]董海军,沈允文,刘梦军,等.齿轮系统Rattling动力学行为研究[J].机械工程学报,2004,40(1)：136-141.
[107]杨宏斌,高建平,邓效忠,等.弧齿锥齿轮和准双曲面齿轮非线性动力学研究[J]_航空动力学报,2004,19(1)：54-56.
[108]王志,谢华锟,王贵成.锥齿轮测量新方法的误差分析[J].中国机械工程,2005,16(7)：623-626.
[109]王志,王贵成,谢华锟.锥齿轮测量的误差分离法[J].农业机械学报,2005,36(9)：128-130,134.
[110]王志,谢华锟,王贵成.齿轮传动系统仿真[J].农业机械学报,2005,36(12)：110-113.
[111]郜志英,沈允文,董海军,等.齿轮系统倍周期分岔和混沌层次结构的研究[J].机械工程学报,2005,41(4)：44-48.
[112]Yang Jianming, Zhang Ce. Elasto-dynamics of internal gear planetary transmissions[J]. Mechanism and Machine Theory,2005,40:1107-1125.
[113]刘晓宁,沈允文,王三民.3自由度齿轮系统的混沌控制[J].机械工程学报,2006,42(12)：52-58.
[114]钱直睿,黄晓燕,李明哲,等.多轴齿轮传动系统的动力学仿真分析[J].中国机械工程,2006,17(3)：241-244.
[115]Parker R G, Ambarisha V K. Nonlinear dynamics of planetary gears using analytical and finite element models[J]. Journal of Sound and Vibration,2007,302:577-595.
[116]Velex P, Ajmi M. Dynamic tooth loads and quasi-static transmission errors in helical gears-Approximate dynamic factor formulae[J]. Mechanism and Machine Theory,2007,42: 1512-1526.
[117]Song He, Gunda R, Sinqh R. Inclusion of sliding friction in contact dynamics model for helical gears[J]. Journal of Mechanical design,2007,129(1):48-57.
[118]邓效忠,杨建军,魏冰阳,等.超声激励下弧齿锥齿轮研齿系统动态研磨力分析[J].中国机械工程,2007,18(19)：2359-2361.
[119]王立华,黄亚宇,李润方,等.弧齿锥齿轮传动系统的非线性振动特性研究[J].中国机械工程,2007,18(3)：260-264.
[120]邵忍平,黄欣娜,张延超,等.弹性支撑条件下齿轮体的动力特性与啮合齿的动力响应[J].航空学报,2007,28(3)：757-762.
[121]杨振,王三民,范叶森.转矩分流式齿轮传动系统的非线性动力学特性[J].机械工程学报,2008,44(7)：52-57.
[122]Wang Jun, Lim T C. Effect of tooth mesh stiffness asymmetric nonlinearity for drive and coast sides on hypoid gear dynamics[J]. Journal of Sound and Vibration,2009,319:885-903.
[123]陈思雨,唐进元.间隙对含摩擦和时变刚度的齿轮系统动力学响应的影响[J].机械工程学报,2009,45(8)：119-124.
[124]朱才朝,陆波,宋朝省,等.大功率船用齿轮箱系统耦合非线性动态特性研究[J].机械工程学报,2009,45(9)：31-35.
[125]彭国民,余波,马小英.动力总成NVH分析中齿轮啮合特性研究[J].振动工程学报,2010,23(6)：681-686.
[126]石照耀,康焱,林家春.基于齿轮副整体误差的齿轮动力学模型及其动态特性[J1.机械工程学报,2010,46(17)：55-61.
[127]崔亚辉,刘占生,叶建槐,等.内外激励作用下含侧隙的齿轮传动系统的分岔和混沌[J].机械工程学报,2010,46(11)：129-136.
[128]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.
[129]Chang-Jian Cai-Wan. Nonlinear analysis for gear pair system supported by long journal bearings under nonlinear suspension[J]. Mechanism and Machine Theory,2010,45:569-583.
[130]Guo Yichao, Parker Robert G. Purely rotational model and vibration modes of compound planetary gears[J]. Mechanism and Machine Theory,2010,45:365-377.
[131]Li Yinong, Li Guiyan, Zheng Ling. Influence of asymmetric mesh stiffness on dynamics of spiral bevel gear transmission system[J]. Mathematical Problems in Engineering,2010:1-13.
[132]Huang Kuo Jao, Su Hsin Wei. Approaches to parametric element constructions and dynamic analyses of spur/helical gears including modifications and undercutting[J]. Finite Elements in Analysis and Design,2010,46:1106-1113.
[133]Faggioni M, Samani F S, Bertacchi G, et al. Dynamic optimization of spur gears[J]. Mechanism and Machine Theory,2011,46:544-557.
[134]Yoerkie C A, Chory A G. Acoustic vibration characteristics of high contact ratio planetary gears[J]. The Journal of American Helicopter Society,1984,40:19-32.
[135]Bolotovskii I A. Involute gears with asymmetric teeth[J]. Soviet Engineering Research Vestnik Mashinostroeniya,1984,4(4):9-10.
[136]孙庆华.非对称渐开线外啮合齿轮泵的计算和分析[J].机械传动,1984,(8)2：24-27.
[137]鲁明山.非对称渐开线齿形的圆柱齿轮[J].北京航空学院科学研究报告,1985：47-51.
[138]Kapelevich A L. Cutting dimensions for spur gears with asymmetric teeth[J]. Mashinov-edenie, 1986,6:109-110.
[139]Kapelevich A L. Synthesis of unsymmetric involute gearing (in Russian) [J]. Mashino-stroenie,1987, (1):62-67. Translated to English in Soviet Machine Science. Allerton Press Inc.,1987, (1):55-59.
[140]Vulgakov E B, Kapelevich A L, Non-symmetrical gear transmissions:possible developments (in Russian) [J]. Vestnik Mashinostroeniya,1987,66(4):14-16. Translated to English in Soviet Engineering Research,1987,6(4):2-3.
[141]张延淼.非对称齿形齿轮滚刀的设计[J].工具技术,1988,8：15-18.
[142]吴继泽,王统.齿根过渡曲线与齿根应力[M].北京：国防工业出版社,1989.
[143]褚世华.一种新型非对称齿形的齿轮泵[J].化工矿山技术,1994,23(6)：37-39.
[144]DiFrancesco G, Marini S. Structural analysis of asymmetrical teeth:reduction of size and weight[J]. Gear Technology,1997,14(5):47-51.
[145]Difrancesco G, Marini S.Structural analysis of teeth with asymmetrical profiles[J]. Gear Technology,1997,14(4):16-22.
[146]刘元伟,杨丽珍.非对称齿齿轮泵非对称齿轮电化学机加工机床设计[J].大连铁道学院学报,1998,19(3)：42-44.
[147]Kapelevich A L. Geometry and design of involute spur gears with asymmetric teeth[J]. Mechanism and Machine Theory,2000,35 (1):117-130.
[148]杨奇顺.新型内外啮合多齿轮泵的理论研究[J].煤矿机械,2000,12：8-10.
[149]徐克圣,刘元伟,李丽.非对称齿形加工的计算机仿真[J].大连铁道学院学报,2000,12(4)：13-7.
[150]徐克圣.非对称齿轮齿根过渡曲线与齿根应力[J].大连铁道学院学报,2002,23(1)：31-33.
[151]陈天旗,高鹏,刘元伟.非对称齿齿轮泵非对称齿轮公法线的测量[J].大连铁道学院学报,2000,21(2)：25-27.
[152]Litvin F L, Lian Q, Kapelevich A L. Asymmetric modified spur gear drives:reduction of noise, localization of contact, simulation of meshing and stress analysis[J]. Computer methods in applied mechanics and engineering,2000,188:363-390.
[153]Litvin F L, Fuentes A, Howkins M. Design, generation and TCA of new type of asymmetric face-gear drive with modified geometry[J]. Computer methods in applied mechanics and engineering,2001,190:5837-5865.
[154]黄志军.双压力角齿轮在汽车变速箱中应用及加工分析[J].现代制造工程,2002,(11)：36-37.
[155]Deng G, Nakanishi T, Inoue K. Bending load capacity enhancement using an asymmetric tooth profile (1st report, influences of pressure angle on tooth root stress and bending stiffness) [J]. JSME International Journal, series C,2003,46(3):1171-1177.
[156]吴忠.双压力角非对称齿廓渐开线齿轮的传动设计及承载能力研究[D].北京：北京科技大学,2003.
[157]吴忠.非对称齿廓渐开线齿轮齿形的仿真设计分析[J].包头钢铁学院学报,2004,23(2)：155-158.
[158]吴忠.菲对称渐开线齿轮齿根弯曲应力的计算分析[J].包头钢铁学院学报,2004,23(1)：61-64.
[159]吴忠,逢晓红.双压力角非对称齿廓齿轮接触应力的计算研究[J]_包钢科技,2010,36(5)：37-41.
[160]樊智宏.渐开线齿形双压力角的实现[J].现代制造工程,2004,(10)：57-58.
[161]娄依志,王小群,李威.非对称渐开线圆柱齿轮的动力学特性[J].北京科技大学学报,2005,27(3)：334-337.
[162]李梅,王小群,李威.非对称渐开线直齿轮设计计算CAD系统的开发[J].仪器仪表用户,2005,12(6)：34-35.
[163]张玉梅.双压力角非对称齿轮啮合特性及应力分析研究[D].南京：南京航空航天大学,2005.
[164]Yang S C. Mathematical model of a helical gear with asymmetric involute teeth and its analysis[J]. Int J Adv Manuf Technol,2005,26:448-456.
[165]Yang S C. Study on an internal gear with asymmetric involute teeth[J]. Mechanism and Machine Theory,2007,42:977-994.
[166]Karpat F, Cavdar K, Fatih F C. Computer aided analysis of involute spur gears with asymmetric teeth[J]. VDI Berichte,2005,190(4):145-163.
[167]Cavdar K, Karpat F, Fatih F C. Computer aided analysis of bending strength of involute spur gears with asymmetric profile[J]. Journal of Mechanical Design,2005,127 (3):477-484.
[168]Karpat F, Ekwaro-Osire S, Cavdar K, et al. Dynamic analysis of Involute spur gears with asymmetric teeth[J]. International Journal of Mechanical Sciences,2008,50:1598-1610.
[169]Karpat F, Ekwaro-Osire S, Khandaker M P H. Probabilistic analysis of MEMS asymmetric gear tooth[J]. Journal of Mechanical Design,2008,130:042306-1-042306-6.
[170]Karpat F, Ekwaro-Osire S. Wear of involute spur gears with asymmetric teeth under dynamic loading[A].2006 ASME International Mechanical Engineering Congress and Exposition[C]. Chicago, USA,2006.1-9.
[171]Karpat F, Ekwaro-Osire S. Dynamic analysis of high-contact-ratio spur gear with asymmetric teeth[A].2008 ASME international mechanical engineering congress and exposition[C]. Boston, USA,2008.1-7.
[172]谭伟明,安军,陈就,等.非对称齿形渐开线非圆齿轮的齿廓曲线数学模型[J].佛山科学技术学院学报(自然科学版),2006,20(2)：22-26.
[173]周明.采用非对称齿形减小齿轮泵的异常噪声[J].机床与液压,2006(9)：168-169.
[174]徐晓东.非对称渐开线齿轮的啮合特性及应力分析研究[D].南京：南京航空航天大学, 2006.
[175]Francesco G D, Marini S. Asymmetric Teeth:Bending Stress Calculation[J]. Gear Technology, March/April 2007,52-55.
[176]Novikov A S, Paikin A G, Dorofeyev V L, et al. Application of gears with asymmetric teeth in turboprop engine gearbox [A]. ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE2007) [C]. Las Vegas, USA:Pennsylvania State University Press,2007.327-334.
[177]王小群,孙萍,李威.非对称渐开线圆柱齿轮建模与扭转振动仿真[J].北京科技大学学报,2007,29(12)：1264-1267.
[178]王成兵.外啮合非对称齿轮泵的设计与分析[D].北京：北京科技大学,2007.
[179]李威,王成兵.外啮合非对称齿轮泵工作原理及流量分析[J].起重运输机械,2008,(4)：53-56.
[180]刘延军.非对称齿轮滚刀设计及弹流润滑分析[D].北京：北京科技大学,2007.
[181]李威,刘延军,邱丽芳.新型非对称齿轮滚刀设计理论与方法[J].北京科技大学学报,2007,29(8)：837-840.
[182]闫占磊.双压力角非对称齿廓齿轮弯曲应力的理论分析及实验研究[D].北京：北京科技大学,2007.
[183]肖望强,李威,韩建友,等.双压力角非对称齿轮传动接触分析[J].北京科技大学学报,2006,28(12)：1167-1173.
[184]肖望强,李威,韩建友.双压力角非对称齿廓齿轮的啮合机理分析[J].农业机械学报,2008,39(5)：169-173.
[185]肖望强,李威,韩建友.非对称齿廓渐开线齿轮传动的热分析[J].农业机械学报,2006,37(12)：164-167.
[186]肖望强,李威,韩建友,等.非对称齿廓齿轮弯曲疲劳强度理论分析与试验[J].机械工程学报,2008,44(10)：44-50.
[187]肖望强.高性能双压力角非对称齿轮传动啮合机理及承载能力研究[D].北京：北京科技大学,2008.
[188]肖望强,李威,韩建友,等.双压力角非对称齿廓渐开线齿轮的振动分析[J].中国机械工：程,2006,17(6)：645-649.
[189]Kumar V S, Muni D V, Muthuveerappan G. Optimization of asymmetric spur gear drives to improve the bending load capacity[J]. Mechanism and Machine Theory,2008,43:829-858.
[190]Dhorje M, Ekwaro-osire S, Khandaker M P H, et al. A weibull failure theory for contact loading in gears with asymmetric teeth[A].2008 ASME International Mechanical Engineering Congress and Exposition 2008[C]. Boston, USA,2008.1-6.
[191]张占东.非对称直齿圆锥齿轮的啮合特性与应力分析研究[D].太原：太原理工大学,2008.
[192]宋波.双压力角非对称渐开线直齿轮的应力分析及齿廓曲线的优化[D].太原：太原理工大学,2008.
[193]李华川.基于动载荷的双压力角非对称齿轮稳态弹流润滑分析[J].煤矿机械,2008,29(7)：76-79.
[194]郝瑞贤,李威,李元宗.非对称齿廓在渐开线塑料齿轮中的应用[J].工程塑料应用,2008,36(1)：45-47.
[195]郝瑞贤,李威,李元宗.非对称塑料齿轮副侧隙的分析与计算[J].太原理工大学学报,2008,39(2)：161-163.
[196]郝瑞贤,李威,李元宗.非对称塑料齿轮接触应力的解析法计算[J].机械设计与研究,2008,24(6)：56-59.
[197]郝瑞贤,李威,李元宗.非对称塑料齿轮弯曲应力的解析法计算[J].机械设计与研究,2009,25(1)：61-64.
[198]Costopoulos T, Spitas V. Reduction of gear fillet stresses by using one-sided involute asymmetric teeth[J]. Mechanism and Machine Theory,2009,44:1524-1534.
[199]Moya J L, Machado A S, Becerra A M, et al. Determining the lewis factor for plastic spur gears with asymmetric teeth[A]. Proceedings of the ASME 2009 International Mechanical Engineering Congress & Exposition[C]. Lake Buena Vista, America,2009.1-9.
[200]Brown F W, Davidson S R, Hanes D B, et al. Analysis and testing of gears with Asymmetric involute tooth form and optimized fillet form for potential application in helicopter main drives[A]. AGMA Technical Paper[C]. Alexandria, America:American Gear Manufacturers Association,2010.3-15.
[201]Pedersen N L. Improving bending stress in spur gears using asymmetric gears and shape optimization[J]. Mechanism and Machine Theory,2010,45:1707-1720.
[202]钱学毅,吴双.基于弹流润滑理论的非对称齿轮胶合强度多目标优化[J].工程设计学报,2010,17(6)：426-431.
[203]刘贵敏.非对称渐开线齿轮传动系统动力学仿真分析与研究[D].天津：天津工业大学,2010.
[204]Alipiev O. Geometric design of involute spur gear drives with symmetric and asymmetric teeth using the Realized Potential Method[J]. Mechanism and Machine Theory,2011,46:10-32.
[205]Kapelevich A. Direct design of asymmetric gears:approach and application[A]. Proceedings of MPT 2009[C]. Sendai,Japan:JSME International Conference on Motion and Power Transmissions,2009.
[206]Sandor R N, Mircea L. Manufacture of gears with asymmetric teeth on CNC machine tools[J]. Annals of the Oradea University (Fascicle of Management and Technological Engineering),2010.
[207]Chira F, Banica M, Butnar L, et al. Optimising the gears with asymmetric involute teeth by modification the generation gear rack angles[A]. Mod Tech International Conference- New face of TMCR[C].2009:127-128.
[208]黄锡恺,郑文纬.机械原理[M].北京：高等教育出版社,1995.
[209]沈伟,徐辅仁.齿间摩擦对齿轮轮齿表面疲劳强度的影响[J].机床与液压,2001,29(6)：70-73.
[210]刘鸿文.材料力学[M].北京：机械工业出版社,1997.
[211]濮良贵,纪名刚,陈国定,等.机械设计[M].北京：高等教育出版社,2007.
[212]XV Furen. Effective measures for restraining the vibration of the supports of the involute gearing[J]. Journal university of shanghai for science and technology,2000,22(4):320-328.
[213]吴序堂.齿轮啮合原理[M].西安：西安交通大学出版社,2009.
[214]王三民,沈允文,董海军.含摩擦和间隙直齿轮副的混沌与分叉研究[J].机械工程学报,2002,38(9)：8-11.
[215]陈建玲.改善齿轮噪声的措施.机械传动,2004,28(1)：61-63.
[2]Li C H, Chiou H S, Hung C,et al.Integration of finite element analysis and optimum design on gear systems[J]. Finite Elements in Analysis and Design,2002,38(3):179-192
[3]周彦伟,方宗德,邓效忠.航空弧齿锥齿轮齿面接触应力计算与优化[J].航空动力报,2002,17(3)：373-376.
[4]高创宽,周谋,亓秀梅.齿面摩擦力对齿轮接触应力的影响[J].机械强度,2003,25(6)：642-645.
[5]杨生华.齿轮接触有限元分析[J].计算力学学报,2003,20(2)：189-193.
[6]邓效忠,方宗德,魏冰阳.接触路径对弧齿锥齿轮接触应力和弯曲应力的影响[J].中国机械工程,2003,14(22)：1895-1898.
[7]Tseng Rui-Tang, Tsay Chung-Biau.Contact characteristics of cylindrical gears with Curvilinear shaped teeth[J]. Mechanism and Machine Theory,2004,39:905-919.
[8]龙慧,张光辉,罗文军.旋转齿轮瞬时接触应力和温度的分析模拟[J].机械工程学报,2004,40(8)：24-29.
[9]李秀莲,董晓英,曹清林.基于摩擦的斜齿轮齿面接触疲劳强度计算[J].农业机械学报,2005,36(4)：123-124.
[10]阎树田,梁继斌,沙成梅,等.精确模型下斜齿轮接触应力的有限元分析[J].兰州理工大学学报,2006,32(3)：47-49.
[11]屈文涛,沈允文,徐建宁.基于ANSYS的双圆弧齿轮接触应力有限元分析[J].农业机械学报,2006,37(10)：139-141.
[12]Sraml M., Flasker J. Computational approach to contact fatigue damage initiation analysis of gear teeth flanks [J].International Journal of Advanced Manufacturing Technology, 2007,31(11-12):1066-1075.
[13]Li Shuting. Finite element analyses for contact strength and bending strength of a pair of spur gears with machining errors, assembly errors and tooth modifications[J]. Mechanism and Machine Theory,2007,42:88-114.
[14]Hedlund J,Lehtovaara A.Modeling of helical gear contact with tooth deflection[J]. Tribology International,2007,40:613-619.
[15]Pasta A, Mariotti G V. Finite element method analysis of a spur gear with a corrected Profile. Journal of Strain Analysis for Engineering Design,2007,42 (5):281-292.
[16]陈赛克,王毅.基于精确模型的齿轮接触疲劳寿命有限元分析[J].机械传动,2007,31(2)：81-82.
[17]张金良,方宗德,曹雪梅,等.弧齿锥齿轮齿面接触应力分析[J].机械科学与技术,2007,26(10)：1268-1272.
[18]谢最伟,吴新跃,陈艳锋.人字齿轮齿面应力的接触元分析[J].机械设计,2007,24 (10)：25-28.
[19]姚齐水,李常义,潘存云.渐开线环形齿球齿轮副接触点共轭曲率半径及接触强度计算研究[J].机械科学与技术,2007,26(1)：96-100.
[20]张慧.啮合误差状态下渐开线圆柱齿轮接触应力有限元分析[J]_中国制造业信息化,2008,37(7)：72-74,-75.
[21]张宏文,吴杰.传动齿轮接触应力的有限元分析[J].石河子大学学报(自然科学版),2008,26(2)：238-240.
[22]胡爱萍,刘善淑,陈权.标准直齿圆柱齿轮传动接触强度计算的研究[J].机械设计,2008,25(11)：45-48.
[23]Jabbour Toni, Asmar Ghazi.Stress calculation for plastic helical gears under a real Transverse contact ratio[J]. Mechanism and Machine Theory,2009,44:2236-2247.
[24]Hassan A R. Contact stress analysis of spur gear teeth pair[J]. World Academy of Science, Engineering and Technology,2009,58:611-616.
[25]徐辅仁.对水面舰艇纵向轴系游动端支座间隙设计的深化研究[J].船舶力学,1999,3(4)：61-64.
[26]徐辅仁,范小钢,徐增豪,等.计入船体变形及齿间摩擦的齿面接触疲劳强度[J].船舶力学,2006,10(2)：104-110.
[27]李秀莲.计入摩擦的船用斜齿轮齿面接触疲劳强度计算[J].机械设计与研究,2009,25(3)：52-55.
[28]李秀莲.基于船体变形及齿间摩擦的斜齿轮齿根弯曲疲劳强度计算[J].兵工学报,2008,29(8)：1019-1024.
[29]李秀莲.船用高速齿轮齿根弯曲疲劳强度的计算[J].热能动力工程,2009,24(3)：373-377.
[30]李秀莲.基于遗传算法的船用斜齿轮传动模糊可靠优化的研究[J].舰船科学技术,2009,31(2)：76-79.
[31]陈奇,赵韩,黄康,等.分形理论在齿轮接触应力分析中的应用研究[J].中国机械工程,2010,21(9)：1014-1017,1057.
[32]黄海,厉海祥,罗齐汉.点线啮合齿轮接触强度计算的研究[J].机械制造,2010,48(55)5：10-12.
[33]杨凡,孙首群,于建华,等.齿轮啮合过程中接触应力的精确分析[J].机械传动,2010,34(7)：56-59.
[34]武志斐,王铁,张瑞亮.18Cr2Ni4WA齿轮接触疲劳特性试验研究[J].兵工学报,2010,31(5)：598-602.
[35]Von Eiff H, Hirschmann K H, Lechner G. Influence of gear tooth geometry on tooth stress of external and internal gears[J]. Journal of Mechanical Design,1990,112(4):575-583.
[36]Bibel G D, Reddy S K, Savage M, et al. Effects of rim thickness on spur gear bending stress[J]. Journal of Mechanical Design,1994,116(4):1157-1162.
[37]Filiz I F,Eyercioglu O. Evaluation of gear tooth stresses by fininte element method[J]. Journal of Engineering for Industry,1995,117 (2):232-239.
[38]许洪斌,张光辉,加藤正名.分阶式双渐开线齿轮弯曲应力的有限元研究[J].机械工程学 报,2000,36(6)：12-15.
[39]许洪斌,张光辉,加藤正名.分阶式双渐开线齿轮的光弹试验与弯曲强度试验研究[J].机械工程学报,2000,36(8)：39-42.
[40]Litvin F L, Fuentes A, Fan Q, et al. Computerized design, simulation of meshing, and contact and stress analysis of face-milled formate generated spiral bevel gears[J]. Mechanism and Machine Theory,2002,37:441-359.
[41]李秀莲.齿间摩擦力作用下的圆锥齿轮齿根弯曲疲劳强度的计算[J].机床与液压,2004,(1)：102-103.
[42]李秀莲,雷良育,曹清林,等.齿间摩擦对斜齿轮齿根弯曲应力的影响[J].农业机械学报,2005,36(1)：121-122,133.
[43]唐进元,周长江,吴运新.齿轮弯曲强度有限元分析精确建模的探讨[J].机械科学与技术,2004,23(10)：1146-1150.
[44]罗齐汉,李成刚,厉海祥,等.齿轮弯曲强度有限元精确分析方法研究[J].机械科学与技术,2007,26(9)：1212-1215.
[45]唐进元,刘艳萍.齿轮弯曲强度与沉切量关系研究[J].制造技术与机床,2007,(11)：31-35.
[46]李盛鹏,方宗德,张金良,等.弧齿锥齿轮齿根弯曲应力分析[J].航空动力学报,2007,22(5)：843-847.
[47]周长江,钟志华,唐进元.基于齿轮误差与柔度的弯曲强度计算力点研究[J].湖南大学学报,2007,34(7)：35-38.
[48]郭辉,赵宁,方宗德,等.基于接触有限元的面齿轮传动弯曲强度研究[J].航空动力学报,2008,23(8)：1438-1442.
[49]许浩,方宗德,曹雪梅.弧齿锥齿轮弯曲应力计算[J].机械传动,2008,32(6)：60-63.
[50]黄丽娟,朱如鹏.基于ANSYS的斜齿面齿轮传动的弯曲应力分析[J].机械传动,2009,33(3)：91-93.
[51]李东波,张艳冬,尤绍君.基于ANSYS的正交面齿轮参数化模型的弯曲应力分析[J].辽宁工：业大学学报(自然科学版),2009,29(4)：249-251.
[52]邓洪超,康一坡.基于总成的重型汽车变速箱齿轮弯曲应力分析[J].机械设计,2009,26(4)：71-75.
[53]杨小安,张伟社,高勇,等.基于BP网络的齿轮弯曲疲劳强度极限的确定[J].机械传动,2009,33(3)：94-96.
[54]赵韩,陈奇,黄康.基于精确建模的微线段齿轮弯曲强度理论分析[J].组合机床与自动化加工技术,2010,(7)：62-64.
[55]肖义成.车辆传动系统齿轮弯曲疲劳探讨[J].湖北工业大学学报,2010,25(5)：26-28.
[56]林财和.齿轮磨损量与滑动系数优化设计的探讨[J].武汉工业大学学报,1992,14(2)：67-71.
[57]杨建中.齿轮传动相关滑动率分析和提高磨损承载能力的措施[J].机械传动,1996,20(2)：31-34.
[58]柴畅.传动比对齿轮传动应力、相对滑动和磨损的影响[J].安徽工学院学报,1996,15(1)：71-75.
[59]阎树田,胡赤兵,邬再新,等.齿轮齿廓滑动磨损的数值计算方法[J].机械设计与制造工程,2001,30(4)：9-10.
[60]章易程,李蔚,聂昌平.渐开线内齿轮副相对滑动率的研究[J].机械传动,2001,25(2)：25-27.
[61]章易程,李蔚,陈昭莲,等.渐开线外齿轮副相对滑动率的研究[J].机械设计,2001,(7)：27-29.
[62]贲霖,徐辅仁.直齿渐开线齿轮齿面磨损模拟计算[J].航空精密制造技术,2003,39(5)：29-32.
[63]赵亚平,魏文军,董学朱,等.点接触齿面滑动率计算方法及其对交错轴渐开线斜齿轮传动的应用[J].中国机械工程(增刊),2006,17：40-43.
[64]杜雪松,林腾蛟,李润方,等. AGMA按均衡滑动率原则选择齿轮变位系数的原理[J].重庆大学学报(自然科学版),2007,30(8)：6-9.
[65]徐学忠,宋天麟.直线共轭齿廓齿轮副的滑动系数研究[J].淮阴师范学院学报(自然科学版),2007,6(3)：225-228.
[66]Luo Shanming, Wu Yue, Wang Jian. The generation principle and mathematical models of a novel cosine gear drive[J]. Mechanism and Machine Theory,2008,43:1543-1556.
[67]Wang Jian, Luo Shanming, CHEN Iifeng, et al. Analysis of transmission characteristics of cosine gear drive[J]. Chinese Journal of Mechanical Engineering,2008,21 (3):94-99.
[68]Wang Jian, Luo Shanming, Zhu Shimin. Initiative design of tooth profiles with small sliding coefficients[J]. Applied Mechanics and Materials,2009,16-19:811-815.
[69]Wang Jian, Luo Shanming, Wu Yue. A method for the preliminary geometric design of gear tooth profiles with small sliding coefficients[J]. Journal of mechanical design,2010, 132(5):054501-1-054501-8.
[70]Antal T A. A new algorithm for helical gear design with addendum modification[J]. Mechanika, 2009,77 (3):53-57.
[71]Antal T A, Antal A.Determination of the geometrical dimensions of the helical gears with addendum modifications based on the specific sliding equalization model[J]. Advanced Techniques in Computing Sciences and Software Engineering,2010,85-90.
[72]Weiss T, Hirt M, Efficiency Improvements for High Speed Gears[A]. International Conference on Gears[C]. Munich, Germany:VDI,2002:1161-1174.
[73]Anderson N E, Loewenthal S H. Efficiency of nonstandard and high contact ratio involute spur gears[A]. Fourth International Power Transmission and Gearing Conference[C]. Cambridge, Massachusetts, Britain,1984.
[74]刘福林,姜弘,朱均.干摩擦条件下聚甲醛塑料动力齿轮传动啮合效率的分析研究与计算[J].摩擦学学报,1995,15(3)：263-270.
[75]姚建初,陈义保,周济,等.齿轮传动啮合效率计算方法的研究[J].机械工程学,2001,37(11)：18-21，27.
[76]徐辅仁.关于仪器渐开线齿轮副效率计算的研究[J].仪器仪表学报,2001,22(5)：446-450.
[77]王三民,沈允文,孙智民.基于动态损失功率的行星齿轮传动效率计算[J].机械传动,2001, 25(2)：4-5,8.
[78]姚九成.按平均滑动速度法计算平动齿轮机构的啮合效率[J].机械设计,2002,(10)：61-62.
[79]Michlin Y, Myunster V. Determination of power losses in gear transmissions with rolling and sliding friction incorporated[J]. Mechanism and Machine Theory,2002,37 (2):167-174.
[80]Heingartner P, Mba D. Determining power losses in the helical gear mesh:case study [A]. Proceedings of DETC'03 [C]. Chicago, USA:ASME 2003 Design Engineering Technical Conferences and Computers and Information in Engineering Conference,2003
[81]牟柳晨,殷国富,余力.速比法在行星齿轮传动效率计算中的应用[J].中国制造业信息化,2004,33(6)：88-91.
[82]崔丽,秦大同,石万凯.行星齿轮传动啮合效率分析[J].重庆大学学报(自然科学版),2006,29(3)：11-14,44.
[83]Changenet C, Velex P. A Model for the Prediction of Churning Losses in Geared Transmissions—Preliminary Results[J]. Journal of Mechanical Design,2007,129:128-133.
[84]Xu H, Kahraman A, Anderson N E,et al.Prediction of mechanical efficiency of parallel-axis gear pairs[J]. Journal of Mechanical Design,2007,129:58-68.
[85]Xu H, Kahraman A. Prediction of friction-related power losses of hypoid gear pairs[J]. Proc IMechE (part K:J Multi-body Dynamics),2007,221:387-400.
[86]Al-Shibl K, Simmons K, Eastwick C N. Modelling windage power loss from an enclosed spur gear[J]. Proceedings of the Institution of Mechanical Engineers, part A:Journal of Power and Energy,2007,331-341.
[87]陈立锋,吴晓铃,秦大同.基于图论的风力发电机组齿轮传动系统效率分析[J].机械传动,2008,32(6)：18-20.
[88]Koffel G, Ville F, Changenet C, et al. Investigations on the power losses and thermal effects in gear transmissions[J]. Proc. IMechE (part J:J Engineering Tribology),2009,223:469-479.
[89]Li Sheng, Vaidyanathan A, Harlanto J, et al. Influence of design parameters on mechanical power losses of helical gear pairs[J]. Journal of Advanced Mechanical Design, Systems, and Manufacturing,2009,3 (2):146-158.
[90]Seetharaman S, Kahraman A. Load-Independent Spin Power Losses of a Spur Gear Pair:Model Formulation[J]. Journal of Tribology,2009,131:022201-1-022201-11.
[91]Seetharaman S, Kahraman A, Moorhead M D, et al. Oil churning power losses of a gear pair experiments and model validation [J]. Journal of Tribology,2009,131:022202-1-022202-10.
[92]王成,方宗德,贾海涛.斜齿轮滑动摩擦功率损失的计算[J].燕山大学学报,2009,33(2)：99-103.
[93]周春国,王付岗,刘宏昭,等.基于虚拟样机的行星齿轮机构效率仿真分析[J].机械传动,2009,33(4)：65-68.
[94]Kolivand M, Li S, Kahraman A. Prediction of mechanical gear mesh efficiency of hypoid gear pairs[J]. Mechanism and Machine Theory,2010,45:1568-1582.
[95]Li Sheng, Kahraman A. Prediction of spur gear mechanical power losses using a transient elastohydrodynamic lubrication model[J]. Tribology Transactions,2010,53:554-563.
[96]Magalhaes Luis, Martins Ramiro, Locateli Cristiano, et al. Influence of tooth profile and oil formulation on gear power loss[J]. Tribology International,2010,43:1861-1871.
[97]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.
[98]许翔,杨定富,索文超,刘刚.基于时变载荷的齿轮摩擦功率损失计算研究[J].工程设计学报,2010,17(3)：224-228.
[99]李润方,王建军.齿轮系统动力学[M].北京：科学山版社,1997.
[100]林腾蛟,李润方,陶泽光.齿轮传动三维间隙非线性冲击——动力接触特性数值仿真[J].机械工程学报,2000,36(6)：55-58.
[101]Velex P, Sainsot P. An analytical study of tooth friction excitations in errorless spur and helical gears[J]. Mechanism and Machine Theory,2002,37:641-658.
[102]张锁怀,沈允文,丘大谋.齿轮耦合的转子轴承系统的不平衡响应[J]_机械工程学报,2002,38(6)：51-55.
[103]李华,沈允文,孙智民.基于A一算符方法的齿轮系统的分岔与混沌[J].机械工程学报,2002,38(6)：11-15.
[104]孙智民,季林红,沈允文.2K-H行星齿轮传动非线性动力学[J].清华大学学报(自然科学版),2003,43(5)：636-639.
[105]王三民,沈允文,董海军.含间隙和时变啮合刚度的弧齿锥齿轮传动系统非线性振动特性研究[J].机械工程学报,2003,39(2)：28-32.
[106]董海军,沈允文,刘梦军,等.齿轮系统Rattling动力学行为研究[J].机械工程学报,2004,40(1)：136-141.
[107]杨宏斌,高建平,邓效忠,等.弧齿锥齿轮和准双曲面齿轮非线性动力学研究[J]_航空动力学报,2004,19(1)：54-56.
[108]王志,谢华锟,王贵成.锥齿轮测量新方法的误差分析[J].中国机械工程,2005,16(7)：623-626.
[109]王志,王贵成,谢华锟.锥齿轮测量的误差分离法[J].农业机械学报,2005,36(9)：128-130,134.
[110]王志,谢华锟,王贵成.齿轮传动系统仿真[J].农业机械学报,2005,36(12)：110-113.
[111]郜志英,沈允文,董海军,等.齿轮系统倍周期分岔和混沌层次结构的研究[J].机械工程学报,2005,41(4)：44-48.
[112]Yang Jianming, Zhang Ce. Elasto-dynamics of internal gear planetary transmissions[J]. Mechanism and Machine Theory,2005,40:1107-1125.
[113]刘晓宁,沈允文,王三民.3自由度齿轮系统的混沌控制[J].机械工程学报,2006,42(12)：52-58.
[114]钱直睿,黄晓燕,李明哲,等.多轴齿轮传动系统的动力学仿真分析[J].中国机械工程,2006,17(3)：241-244.
[115]Parker R G, Ambarisha V K. Nonlinear dynamics of planetary gears using analytical and finite element models[J]. Journal of Sound and Vibration,2007,302:577-595.
[116]Velex P, Ajmi M. Dynamic tooth loads and quasi-static transmission errors in helical gears-Approximate dynamic factor formulae[J]. Mechanism and Machine Theory,2007,42: 1512-1526.
[117]Song He, Gunda R, Sinqh R. Inclusion of sliding friction in contact dynamics model for helical gears[J]. Journal of Mechanical design,2007,129(1):48-57.
[118]邓效忠,杨建军,魏冰阳,等.超声激励下弧齿锥齿轮研齿系统动态研磨力分析[J].中国机械工程,2007,18(19)：2359-2361.
[119]王立华,黄亚宇,李润方,等.弧齿锥齿轮传动系统的非线性振动特性研究[J].中国机械工程,2007,18(3)：260-264.
[120]邵忍平,黄欣娜,张延超,等.弹性支撑条件下齿轮体的动力特性与啮合齿的动力响应[J].航空学报,2007,28(3)：757-762.
[121]杨振,王三民,范叶森.转矩分流式齿轮传动系统的非线性动力学特性[J].机械工程学报,2008,44(7)：52-57.
[122]Wang Jun, Lim T C. Effect of tooth mesh stiffness asymmetric nonlinearity for drive and coast sides on hypoid gear dynamics[J]. Journal of Sound and Vibration,2009,319:885-903.
[123]陈思雨,唐进元.间隙对含摩擦和时变刚度的齿轮系统动力学响应的影响[J].机械工程学报,2009,45(8)：119-124.
[124]朱才朝,陆波,宋朝省,等.大功率船用齿轮箱系统耦合非线性动态特性研究[J].机械工程学报,2009,45(9)：31-35.
[125]彭国民,余波,马小英.动力总成NVH分析中齿轮啮合特性研究[J].振动工程学报,2010,23(6)：681-686.
[126]石照耀,康焱,林家春.基于齿轮副整体误差的齿轮动力学模型及其动态特性[J1.机械工程学报,2010,46(17)：55-61.
[127]崔亚辉,刘占生,叶建槐,等.内外激励作用下含侧隙的齿轮传动系统的分岔和混沌[J].机械工程学报,2010,46(11)：129-136.
[128]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.
[129]Chang-Jian Cai-Wan. Nonlinear analysis for gear pair system supported by long journal bearings under nonlinear suspension[J]. Mechanism and Machine Theory,2010,45:569-583.
[130]Guo Yichao, Parker Robert G. Purely rotational model and vibration modes of compound planetary gears[J]. Mechanism and Machine Theory,2010,45:365-377.
[131]Li Yinong, Li Guiyan, Zheng Ling. Influence of asymmetric mesh stiffness on dynamics of spiral bevel gear transmission system[J]. Mathematical Problems in Engineering,2010:1-13.
[132]Huang Kuo Jao, Su Hsin Wei. Approaches to parametric element constructions and dynamic analyses of spur/helical gears including modifications and undercutting[J]. Finite Elements in Analysis and Design,2010,46:1106-1113.
[133]Faggioni M, Samani F S, Bertacchi G, et al. Dynamic optimization of spur gears[J]. Mechanism and Machine Theory,2011,46:544-557.
[134]Yoerkie C A, Chory A G. Acoustic vibration characteristics of high contact ratio planetary gears[J]. The Journal of American Helicopter Society,1984,40:19-32.
[135]Bolotovskii I A. Involute gears with asymmetric teeth[J]. Soviet Engineering Research Vestnik Mashinostroeniya,1984,4(4):9-10.
[136]孙庆华.非对称渐开线外啮合齿轮泵的计算和分析[J].机械传动,1984,(8)2：24-27.
[137]鲁明山.非对称渐开线齿形的圆柱齿轮[J].北京航空学院科学研究报告,1985：47-51.
[138]Kapelevich A L. Cutting dimensions for spur gears with asymmetric teeth[J]. Mashinov-edenie, 1986,6:109-110.
[139]Kapelevich A L. Synthesis of unsymmetric involute gearing (in Russian) [J]. Mashino-stroenie,1987, (1):62-67. Translated to English in Soviet Machine Science. Allerton Press Inc.,1987, (1):55-59.
[140]Vulgakov E B, Kapelevich A L, Non-symmetrical gear transmissions:possible developments (in Russian) [J]. Vestnik Mashinostroeniya,1987,66(4):14-16. Translated to English in Soviet Engineering Research,1987,6(4):2-3.
[141]张延淼.非对称齿形齿轮滚刀的设计[J].工具技术,1988,8：15-18.
[142]吴继泽,王统.齿根过渡曲线与齿根应力[M].北京：国防工业出版社,1989.
[143]褚世华.一种新型非对称齿形的齿轮泵[J].化工矿山技术,1994,23(6)：37-39.
[144]DiFrancesco G, Marini S. Structural analysis of asymmetrical teeth:reduction of size and weight[J]. Gear Technology,1997,14(5):47-51.
[145]Difrancesco G, Marini S.Structural analysis of teeth with asymmetrical profiles[J]. Gear Technology,1997,14(4):16-22.
[146]刘元伟,杨丽珍.非对称齿齿轮泵非对称齿轮电化学机加工机床设计[J].大连铁道学院学报,1998,19(3)：42-44.
[147]Kapelevich A L. Geometry and design of involute spur gears with asymmetric teeth[J]. Mechanism and Machine Theory,2000,35 (1):117-130.
[148]杨奇顺.新型内外啮合多齿轮泵的理论研究[J].煤矿机械,2000,12：8-10.
[149]徐克圣,刘元伟,李丽.非对称齿形加工的计算机仿真[J].大连铁道学院学报,2000,12(4)：13-7.
[150]徐克圣.非对称齿轮齿根过渡曲线与齿根应力[J].大连铁道学院学报,2002,23(1)：31-33.
[151]陈天旗,高鹏,刘元伟.非对称齿齿轮泵非对称齿轮公法线的测量[J].大连铁道学院学报,2000,21(2)：25-27.
[152]Litvin F L, Lian Q, Kapelevich A L. Asymmetric modified spur gear drives:reduction of noise, localization of contact, simulation of meshing and stress analysis[J]. Computer methods in applied mechanics and engineering,2000,188:363-390.
[153]Litvin F L, Fuentes A, Howkins M. Design, generation and TCA of new type of asymmetric face-gear drive with modified geometry[J]. Computer methods in applied mechanics and engineering,2001,190:5837-5865.
[154]黄志军.双压力角齿轮在汽车变速箱中应用及加工分析[J].现代制造工程,2002,(11)：36-37.
[155]Deng G, Nakanishi T, Inoue K. Bending load capacity enhancement using an asymmetric tooth profile (1st report, influences of pressure angle on tooth root stress and bending stiffness) [J]. JSME International Journal, series C,2003,46(3):1171-1177.
[156]吴忠.双压力角非对称齿廓渐开线齿轮的传动设计及承载能力研究[D].北京：北京科技大学,2003.
[157]吴忠.非对称齿廓渐开线齿轮齿形的仿真设计分析[J].包头钢铁学院学报,2004,23(2)：155-158.
[158]吴忠.菲对称渐开线齿轮齿根弯曲应力的计算分析[J].包头钢铁学院学报,2004,23(1)：61-64.
[159]吴忠,逢晓红.双压力角非对称齿廓齿轮接触应力的计算研究[J]_包钢科技,2010,36(5)：37-41.
[160]樊智宏.渐开线齿形双压力角的实现[J].现代制造工程,2004,(10)：57-58.
[161]娄依志,王小群,李威.非对称渐开线圆柱齿轮的动力学特性[J].北京科技大学学报,2005,27(3)：334-337.
[162]李梅,王小群,李威.非对称渐开线直齿轮设计计算CAD系统的开发[J].仪器仪表用户,2005,12(6)：34-35.
[163]张玉梅.双压力角非对称齿轮啮合特性及应力分析研究[D].南京：南京航空航天大学,2005.
[164]Yang S C. Mathematical model of a helical gear with asymmetric involute teeth and its analysis[J]. Int J Adv Manuf Technol,2005,26:448-456.
[165]Yang S C. Study on an internal gear with asymmetric involute teeth[J]. Mechanism and Machine Theory,2007,42:977-994.
[166]Karpat F, Cavdar K, Fatih F C. Computer aided analysis of involute spur gears with asymmetric teeth[J]. VDI Berichte,2005,190(4):145-163.
[167]Cavdar K, Karpat F, Fatih F C. Computer aided analysis of bending strength of involute spur gears with asymmetric profile[J]. Journal of Mechanical Design,2005,127 (3):477-484.
[168]Karpat F, Ekwaro-Osire S, Cavdar K, et al. Dynamic analysis of Involute spur gears with asymmetric teeth[J]. International Journal of Mechanical Sciences,2008,50:1598-1610.
[169]Karpat F, Ekwaro-Osire S, Khandaker M P H. Probabilistic analysis of MEMS asymmetric gear tooth[J]. Journal of Mechanical Design,2008,130:042306-1-042306-6.
[170]Karpat F, Ekwaro-Osire S. Wear of involute spur gears with asymmetric teeth under dynamic loading[A].2006 ASME International Mechanical Engineering Congress and Exposition[C]. Chicago, USA,2006.1-9.
[171]Karpat F, Ekwaro-Osire S. Dynamic analysis of high-contact-ratio spur gear with asymmetric teeth[A].2008 ASME international mechanical engineering congress and exposition[C]. Boston, USA,2008.1-7.
[172]谭伟明,安军,陈就,等.非对称齿形渐开线非圆齿轮的齿廓曲线数学模型[J].佛山科学技术学院学报(自然科学版),2006,20(2)：22-26.
[173]周明.采用非对称齿形减小齿轮泵的异常噪声[J].机床与液压,2006(9)：168-169.
[174]徐晓东.非对称渐开线齿轮的啮合特性及应力分析研究[D].南京：南京航空航天大学, 2006.
[175]Francesco G D, Marini S. Asymmetric Teeth:Bending Stress Calculation[J]. Gear Technology, March/April 2007,52-55.
[176]Novikov A S, Paikin A G, Dorofeyev V L, et al. Application of gears with asymmetric teeth in turboprop engine gearbox [A]. ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE2007) [C]. Las Vegas, USA:Pennsylvania State University Press,2007.327-334.
[177]王小群,孙萍,李威.非对称渐开线圆柱齿轮建模与扭转振动仿真[J].北京科技大学学报,2007,29(12)：1264-1267.
[178]王成兵.外啮合非对称齿轮泵的设计与分析[D].北京：北京科技大学,2007.
[179]李威,王成兵.外啮合非对称齿轮泵工作原理及流量分析[J].起重运输机械,2008,(4)：53-56.
[180]刘延军.非对称齿轮滚刀设计及弹流润滑分析[D].北京：北京科技大学,2007.
[181]李威,刘延军,邱丽芳.新型非对称齿轮滚刀设计理论与方法[J].北京科技大学学报,2007,29(8)：837-840.
[182]闫占磊.双压力角非对称齿廓齿轮弯曲应力的理论分析及实验研究[D].北京：北京科技大学,2007.
[183]肖望强,李威,韩建友,等.双压力角非对称齿轮传动接触分析[J].北京科技大学学报,2006,28(12)：1167-1173.
[184]肖望强,李威,韩建友.双压力角非对称齿廓齿轮的啮合机理分析[J].农业机械学报,2008,39(5)：169-173.
[185]肖望强,李威,韩建友.非对称齿廓渐开线齿轮传动的热分析[J].农业机械学报,2006,37(12)：164-167.
[186]肖望强,李威,韩建友,等.非对称齿廓齿轮弯曲疲劳强度理论分析与试验[J].机械工程学报,2008,44(10)：44-50.
[187]肖望强.高性能双压力角非对称齿轮传动啮合机理及承载能力研究[D].北京：北京科技大学,2008.
[188]肖望强,李威,韩建友,等.双压力角非对称齿廓渐开线齿轮的振动分析[J].中国机械工：程,2006,17(6)：645-649.
[189]Kumar V S, Muni D V, Muthuveerappan G. Optimization of asymmetric spur gear drives to improve the bending load capacity[J]. Mechanism and Machine Theory,2008,43:829-858.
[190]Dhorje M, Ekwaro-osire S, Khandaker M P H, et al. A weibull failure theory for contact loading in gears with asymmetric teeth[A].2008 ASME International Mechanical Engineering Congress and Exposition 2008[C]. Boston, USA,2008.1-6.
[191]张占东.非对称直齿圆锥齿轮的啮合特性与应力分析研究[D].太原：太原理工大学,2008.
[192]宋波.双压力角非对称渐开线直齿轮的应力分析及齿廓曲线的优化[D].太原：太原理工大学,2008.
[193]李华川.基于动载荷的双压力角非对称齿轮稳态弹流润滑分析[J].煤矿机械,2008,29(7)：76-79.
[194]郝瑞贤,李威,李元宗.非对称齿廓在渐开线塑料齿轮中的应用[J].工程塑料应用,2008,36(1)：45-47.
[195]郝瑞贤,李威,李元宗.非对称塑料齿轮副侧隙的分析与计算[J].太原理工大学学报,2008,39(2)：161-163.
[196]郝瑞贤,李威,李元宗.非对称塑料齿轮接触应力的解析法计算[J].机械设计与研究,2008,24(6)：56-59.
[197]郝瑞贤,李威,李元宗.非对称塑料齿轮弯曲应力的解析法计算[J].机械设计与研究,2009,25(1)：61-64.
[198]Costopoulos T, Spitas V. Reduction of gear fillet stresses by using one-sided involute asymmetric teeth[J]. Mechanism and Machine Theory,2009,44:1524-1534.
[199]Moya J L, Machado A S, Becerra A M, et al. Determining the lewis factor for plastic spur gears with asymmetric teeth[A]. Proceedings of the ASME 2009 International Mechanical Engineering Congress & Exposition[C]. Lake Buena Vista, America,2009.1-9.
[200]Brown F W, Davidson S R, Hanes D B, et al. Analysis and testing of gears with Asymmetric involute tooth form and optimized fillet form for potential application in helicopter main drives[A]. AGMA Technical Paper[C]. Alexandria, America:American Gear Manufacturers Association,2010.3-15.
[201]Pedersen N L. Improving bending stress in spur gears using asymmetric gears and shape optimization[J]. Mechanism and Machine Theory,2010,45:1707-1720.
[202]钱学毅,吴双.基于弹流润滑理论的非对称齿轮胶合强度多目标优化[J].工程设计学报,2010,17(6)：426-431.
[203]刘贵敏.非对称渐开线齿轮传动系统动力学仿真分析与研究[D].天津：天津工业大学,2010.
[204]Alipiev O. Geometric design of involute spur gear drives with symmetric and asymmetric teeth using the Realized Potential Method[J]. Mechanism and Machine Theory,2011,46:10-32.
[205]Kapelevich A. Direct design of asymmetric gears:approach and application[A]. Proceedings of MPT 2009[C]. Sendai,Japan:JSME International Conference on Motion and Power Transmissions,2009.
[206]Sandor R N, Mircea L. Manufacture of gears with asymmetric teeth on CNC machine tools[J]. Annals of the Oradea University (Fascicle of Management and Technological Engineering),2010.
[207]Chira F, Banica M, Butnar L, et al. Optimising the gears with asymmetric involute teeth by modification the generation gear rack angles[A]. Mod Tech International Conference- New face of TMCR[C].2009:127-128.
[208]黄锡恺,郑文纬.机械原理[M].北京：高等教育出版社,1995.
[209]沈伟,徐辅仁.齿间摩擦对齿轮轮齿表面疲劳强度的影响[J].机床与液压,2001,29(6)：70-73.
[210]刘鸿文.材料力学[M].北京：机械工业出版社,1997.
[211]濮良贵,纪名刚,陈国定,等.机械设计[M].北京：高等教育出版社,2007.
[212]XV Furen. Effective measures for restraining the vibration of the supports of the involute gearing[J]. Journal university of shanghai for science and technology,2000,22(4):320-328.
[213]吴序堂.齿轮啮合原理[M].西安：西安交通大学出版社,2009.
[214]王三民,沈允文,董海军.含摩擦和间隙直齿轮副的混沌与分叉研究[J].机械工程学报,2002,38(9)：8-11.
[215]陈建玲.改善齿轮噪声的措施.机械传动,2004,28(1)：61-63.