渐开线少齿差行星传动线面共轭啮合理论研究
|
摘要
渐开线少齿差行星传动具有单级减速比大、传动平稳、结构紧凑、中心距可分、制造加工技术成熟、啮合副为凸凹接触、轮齿的接触应力小、承载能力高等优点,因而得到了广泛的应用。开展渐开线少齿差行星传动基础理论的研究,创新其啮合的原理,对于降低啮合副滑动率、提高传动性能等具有重要的理论意义和工程实用价值。
本文的主要内容包括:
①根据齿轮啮合相关原理,提出了渐开线线面共轭的概念,推导了渐开线少齿差线面共轭啮合副齿廓接触线方程、啮合方程等;论证了渐开线线面共轭啮合副啮合过程为点接触,其端面投影仍为渐开线共轭啮合副,具有渐开线齿轮传动中心距可分等优点。
②提出了管状啮合齿面(啮合管)的概念,建立了渐开线管状啮合齿面方程,讨论了啮合管与共轭曲面的啮合传动特性。
③由啮合副滑动率的定义,给出运用啮合副齿廓共轭曲线方程推导啮合副滑动率的通用方法;推导了渐开线少齿差行星传动传统啮合副和线面共轭啮合副的滑动率计算公式;与渐开线传统啮合副相比,线面啮合副最大滑动系数降低了近100倍;讨论了齿廓参数对渐开线面啮合副滑动率的影响。
④根据渐开线线面共轭啮合理论,给出了基于线面共轭的渐开线少齿差行星传动的设计方法及设计实例,讨论了基于PROE的渐开线线面共轭啮合副参数化设计方法。
⑤建立了渐开线少齿差行星传动传统啮合副及线面啮合副接触有限元分析模型,利用ANSYS求解器进行求解,并对结果进行了对比分析,进一步揭示渐开线线面啮合副的接触特性。
Involute planetary transmission with small tooth difference is widely used in mechnical engineering for its advantages such as high transmission ratio, compact structure, detachable central distance, developed processing technology, convexo-concave mating surface, low contact press, high bearing capacity etc. This thesis will mainly study the curve-surface conjugate meshing theory of the involut planetary transimission with small tooth differenc. It is of important theoretic significance and practical value for reducing the slippage of meshing pair and improving the characteristics of transmission, etc.
Major contents of the thesis as follows:
①The involute curve-surface conjugate theory was proposed according to the gear geometry theory interrelated; the tooth profile contact lines’equations and meshing equations of the involute curve-surface conjugate meshing pair with small tooth difference were deducted; It was demonstrated that the meshing process of the involute curve-surface conjugate pair was point-contact and can keep the advantages of the conventional involute pair such as the detachability of the center distance etc.for its end plane projection was still conventional involute pair.
②A new tubular tooth profile surface named meshing tube was proposed to substitute the involue tooth surface of the planetary gear; the involute tubular tooth profile equation was established; And the meshing characteristic between the meshing tube and the conjugate surface were disscussed.
③Based on the definition of the slip ratio between the meshing pair, a new method that the slip ratio could be resolved by the conjugate equation was proposed; Both the tranditial involute conjugate and the curve-surface conjugate meshing pair’s slip ratio equation were deducted; Conpared with the trandital involute meshign pair, the maximal slip ratio of the curve-surface meshing pair has been almost 100 times reduced. Further more, the effect from the value difference of tooth profile parameter to the slip ratio is disscused.
④According to the result of theoretical research, the design methodology of the involute curve-surface conjugate planetary transimission with small tooth difference was put forward and an example was followed; The parameterization modelling method based on PROE was carried out.
⑤Both the tranditial involute surface-surface conjugate and the curve-surface conjugate meshing pair’s finite elements contact models were built; The analysis result of the contact pair rosolved in ANSYS was compared.
本文的主要内容包括:
①根据齿轮啮合相关原理,提出了渐开线线面共轭的概念,推导了渐开线少齿差线面共轭啮合副齿廓接触线方程、啮合方程等;论证了渐开线线面共轭啮合副啮合过程为点接触,其端面投影仍为渐开线共轭啮合副,具有渐开线齿轮传动中心距可分等优点。
②提出了管状啮合齿面(啮合管)的概念,建立了渐开线管状啮合齿面方程,讨论了啮合管与共轭曲面的啮合传动特性。
③由啮合副滑动率的定义,给出运用啮合副齿廓共轭曲线方程推导啮合副滑动率的通用方法;推导了渐开线少齿差行星传动传统啮合副和线面共轭啮合副的滑动率计算公式;与渐开线传统啮合副相比,线面啮合副最大滑动系数降低了近100倍;讨论了齿廓参数对渐开线面啮合副滑动率的影响。
④根据渐开线线面共轭啮合理论,给出了基于线面共轭的渐开线少齿差行星传动的设计方法及设计实例,讨论了基于PROE的渐开线线面共轭啮合副参数化设计方法。
⑤建立了渐开线少齿差行星传动传统啮合副及线面啮合副接触有限元分析模型,利用ANSYS求解器进行求解,并对结果进行了对比分析,进一步揭示渐开线线面啮合副的接触特性。
Involute planetary transmission with small tooth difference is widely used in mechnical engineering for its advantages such as high transmission ratio, compact structure, detachable central distance, developed processing technology, convexo-concave mating surface, low contact press, high bearing capacity etc. This thesis will mainly study the curve-surface conjugate meshing theory of the involut planetary transimission with small tooth differenc. It is of important theoretic significance and practical value for reducing the slippage of meshing pair and improving the characteristics of transmission, etc.
Major contents of the thesis as follows:
①The involute curve-surface conjugate theory was proposed according to the gear geometry theory interrelated; the tooth profile contact lines’equations and meshing equations of the involute curve-surface conjugate meshing pair with small tooth difference were deducted; It was demonstrated that the meshing process of the involute curve-surface conjugate pair was point-contact and can keep the advantages of the conventional involute pair such as the detachability of the center distance etc.for its end plane projection was still conventional involute pair.
②A new tubular tooth profile surface named meshing tube was proposed to substitute the involue tooth surface of the planetary gear; the involute tubular tooth profile equation was established; And the meshing characteristic between the meshing tube and the conjugate surface were disscussed.
③Based on the definition of the slip ratio between the meshing pair, a new method that the slip ratio could be resolved by the conjugate equation was proposed; Both the tranditial involute conjugate and the curve-surface conjugate meshing pair’s slip ratio equation were deducted; Conpared with the trandital involute meshign pair, the maximal slip ratio of the curve-surface meshing pair has been almost 100 times reduced. Further more, the effect from the value difference of tooth profile parameter to the slip ratio is disscused.
④According to the result of theoretical research, the design methodology of the involute curve-surface conjugate planetary transimission with small tooth difference was put forward and an example was followed; The parameterization modelling method based on PROE was carried out.
⑤Both the tranditial involute surface-surface conjugate and the curve-surface conjugate meshing pair’s finite elements contact models were built; The analysis result of the contact pair rosolved in ANSYS was compared.
引文
[1]何卫东,李欣,李力行.高承载能力高传动效率新型针摆行星传动研究[J].中国机械工程, 2005,(07): 565-569.
[2] S.K.Malhotra, M.A.Parameswaran. Analysis of a cycloid speed reducer. Mech. Mach. Theory, 1983, 18(6): 491~499.
[3]关天民,雷蕾,施晓春.摆线针轮行星传动减速器可靠性评价体系的研究[J].机械工程学报, 2001,(12): 54-58.
[4]程彦春,庄家友,张树杰.摆线行星传动新结构的探讨[J].东北大学学报(自然科学版) , 1990,(04): 401-405.
[5] D.C.H.Yang, J.G.Blanche. Design and application guideline cycloid drives with machining tolerances. Mech. Mach. Theory, 1990, 25(5): 487~501.
[6] Li Lixing, etc. The computer aided design of cycloid drive. Chinese Journal of Mechanical Engineering, 1990,3(2): 221~231
[7]李力行等.摆线针轮行星传动的齿形修正及受力分析[J].机械工程学报, 1986, 22(1): 40～49.
[8]李充宁,孙爽.摆线针轮行星传动的运动平稳性分析[J].机械设计与制造, 2000, 3:48～49.
[9]李充宁,刘继岩等. 2K-V型行星传动中摆线轮啮合的传动精度研究[J].机械工程学报,2001,37(4):61～65.
[10]李充宁,摆线针齿行星传动轮齿的相对运动及滑动系数[J].机械传动, 1998, 22(3):19～21.
[11]李立行等,大型摆线针轮行星传动的合理结构和齿形[J].机械工程学报, 1999, 24(3): 28～33.
[12]舒小龙,李平.渐开线少齿差传动的最小啮合角[J].机械设计与研究, 2000,16 (04): 47- 49+8.
[13]张春林等.渐开线少齿差行星传动的变位系数的选择[J].北京理工大学学报, 1998,18(05): 563-566.
[14]万朝燕等.渐开线少齿差行星传动啮合点的确定方法[J].大连铁道学院学报, 1997,18(02): 47-50.
[15]杨锡和,石辉.少齿差内啮合齿轮的强度计算[J].雷达与对抗, 2003, (02): 58-59+62.
[16]叶志刚等. K-H-V型渐开少齿差行星传动的建模设计与CAD技术[J].机械设计与研究, 2000,(03): 47-49+8.
[17]李红保,黄凯.少齿差内啮合传动多齿啮合的研究[J].辽宁工业大学学报(自然科学版), 2008, 28(04): 250-252+256.
[18]何韶君,罗跃纲.渐开线少齿差行星传动的弹流润滑分析[J].煤矿机械, 2007, 28(04): 92- 94.
[19]丁志等.基于UG的渐开线变位齿轮传动系统的设计[J].机械, 2004, 31(S1): 101-102+104.
[20]陶桂宝,李泽群等. NN型渐开线少齿差行星传动齿轮副的设计[J].现代制造工程, 2007, (08): 116-118+18.
[21]张文照,王光华.渐开线少齿差内啮合同时接触齿数研究及实际重合度的一种计算方法[J].上海化工学院学报, 1980, (01): 93-102.
[22]杨静等.圆弧少齿差传动齿轮弯曲应力的分析及实验研究[J].机械设计与研究, 2001, 17(03): 45-46+75-8.
[23]神会存等.圆弧少齿差传动齿轮啮合作用力分析[J].山东科技大学学报(自然科学版), 2000, 19(03): 73-76.
[24]董师予,张黎明等.圆弧针齿行星传动中替代参数对传动性能的影响[J].机械设计与研究, 1987,(05): 1-9.
[25]李充宁,周有强等.圆弧齿行星减速器的效率计算[J].机械传动, 1993,(04): 21-23+62.
[26]张广军等.圆弧针齿行星传动动力学的计算机仿真[J].机械设计, 1995, (07): 16-18+ 22+44-45.
[27]王正为等.双内圆弧针齿少齿差传动及其效率[J].山东矿业学院学报. 1993, 12(01): 1-5.
[28]尹华杰.活齿少齿差传动力学模型和强度分析[J].郑州工学院学报, 1990,(03): 30-39.
[29]左洪福,周有强等.活齿传动啮合副的滑动情况研究[J].南京航空学院学报, 1992, 24(02): 135-142.
[30]陈兵奎等.空间凸轮活齿行星传动[J].机械工程学报, 2004,40(01): 29-32.
[31]陈兵奎等.摆线凸轮活齿传动原理及齿形理论[J].机械传动, 2003,(03): 14-16+67.
[32]曾强等.空间凸轮活齿传动的接触有限元分析[J].机械, 2004, 31(S1): 12-14.
[33]彭程.少齿差摆动活齿传动的模糊可靠性优化设计[J].现代机械, 2006,(01): 20-21+24.
[34]李明山等.活齿少齿差行星齿轮传动的功率流分析[J].组合机床与自动化加工技术, 1991,(02): 17-20+50.
[35] M.Neagoe etc,“On a New Cycloidal Planetary Gear used to Fit Mechatronic Systems of RES”, TOKYO INSTITUTE OF TECHNOLOGY, Volume 45, Issue 11-12, pp. 1931-1939, July 2004.
[36] John Argyris, etc,“Determination of envelope to family of planar parametric curves and envelope singularities”, Computer methods in applied mechanics and engineering, Volume 175, Issues 1-2, Pages 175-187, June 1999.
[37] Alberto Demenego, etc,“Design and simulation of meshing of a cycloidal pump”, Mechanism and Machine Theory, Volume 37, Issue 3, Pages 311-332, March 2002.
[38]谷丽瑶,黄恺等.共轭啮合原理实现斜齿圆锥齿轮的三维实体造型[J].辽宁工业大学学报(自然科学版), 2008, 28(04): 246-249.
[39]狄玉涛,陈明等.弧齿线圆柱齿轮齿面形成原理及啮合性能分析[J].研究探讨, 2006,(09): 50-52.
[40]刘健.机械制造中曲面的共轭原理[J].大连工学院学刊, 1959.
[41]李高敬.螺旋齿轮啮合原理及其应用[J].精密制造与自动化, 1979,(04): 34-47
[42]刘杰华.用空间啮合原理精确设计非渐开线齿轮滚刀刃形的研究[J].工具技术. 1988,(01): 22-27.
[43]郭燕利等.平面二次包络环面蜗轮副研究综述与展望[J].机械, 2000, 27:209～210
[44]重庆大学蜗轮传动科研组.平面二次包络弧面蜗杆传动的研究与应用[J].重庆大学学报, 1978,(04): 1-18.
[45]酒井高男,牧充.交错轴齿轮传动中第二次作用的研究[J].国际齿轮装置与传动会议论文选.机械工业出版社, 1977.
[46]南开大学数学系齿轮研究小组.齿轮啮合理论的数学基础(一) [J].数学的实践与认识, 1976, 1:52~62.
[47]南开大学数学系齿轮研究小组.齿轮啮合理论的数学基础(二) [J].数学的实践与认识, 1976, 2:41~58.
[48]南开大学数学系齿轮研究小组.齿轮啮合理论的数学基础(三) [J].应用数学学报, 1976, 1(1):84~88.
[49]吴大任,骆家舜著.齿轮啮合理论[M].北京:科学出版社, 1985.
[50]陈兵奎.二次包络摆线行星传动装置[P].中国, ZL200610054263.6[P], 2006.4.30.
[51]房婷婷.摆线包络行星传动啮合理论研究[D]. 2007.
[52]陈兵奎.锥形摆线轮行星传动装置[P].中国, ZL20063117879.0, 2005.02.16.
[53]陈兵奎,王淑妍,李朝阳.双圆盘摆线轮行星传动装置[P].中国, 200510057463.2, 2005.12.23.
[54]贺敬良,吴序堂等.交错轴渐开线锥形齿轮副啮合原理研究[J].机械工程学报, 2004, 40(04): 81-84.
[55]毛世民,吴序堂等.点接触内啮合直齿锥齿轮全成形加工原理[J].制造技术与机床, 1991,(10): 14-17.
[56]毋荣亮.圆弧齿线双圆弧齿轮的基本啮合原理[J].太原工业大学学报, 1997, 28(03): 73-78+111.
[57]陶昇元等.诺维可夫齿轮的啮合原理与计算[J].合肥工业大学学报, 1959.
[58]段德荣.圆弧齿轮啮合原理的误差[J].机械传动, 1996, (03): 8-12+55.
[59] Y. Chen, G. Xing, X. Peng,“The Space Curve Mesh Equation and its kinematics Experiment”, Proceedings of 12th IFToMM World Congress, Besan?on France, 2007, 6: 18-21.
[60] Y. Chen, X. Peng, G. Xing,“Dynamics Modeling and Experiment on Micro-Elastic-Meshing- Wheel Mechanism”, Proceeding of ITIC’2006, Hangzhou China, 2006,11(56):7.
[61] Yang-zhi Chen, Xiang Xiao-yong, Luo Liang;“A Corrected Equation of Space Curve Meshing”; Mech. Mach. Theory, 2009, 44 (7): 1348-1359.
[62] CHEN Yang-zhi, LUO Liang, HU Qiang“Contact Ratio of Space-Curve Meshing-Wheel Transmission Mechanism”; Journal of Mechanical Design, 2009, 131 (7): 074501-5.
[63] Y. Chen, X. Liu, D.G..Chetwynd, P. Huang,“Investigation of a novel elastic–mechanical wheel transmission under light conditions”, Mech. Mech. Theory, 2008, 43: 1462-1477.
[64] Yang-zhi Chen, Qiang Hu, Lei-hou Sun,“The Design Criterion of the Space-Curve Meshing- Wheel Mechanism Based on Elastic Deformation of the Tine”, Journal of Mechanical Design, 2010, 132 (5): 054502 -6.
[65] CHEN Yang-zhi, LUO Liang, HU Qiang,“The Parameters of SCMW mechanism for helix–shaped driving tine”, Chinese Journal of Mechanical Engineering, 2009.
[66]黄小平等.齿轮纯滚动啮合的原理与实现[J].机械传动, 2001, 25(03): 5-8.
[67]杨兰春.渐开线内齿轮副的设计与计算[M].北京:机械工业出版社, 1995.1.
[68]李瑰贤著.空间几何建模及工程应用[M].北京:高等教育出版社, 2007.
[69]章易程,李蔚聂等.渐开线内齿轮副相对滑动率的研究[J].机械传动, 2001, 25(02): 25-27+ 40.
[70]章易程,李蔚聂等.渐开线外齿轮副相对滑动率的研究[J].机械设计, 2001,(07): 27-29.
[71]赵亚平等.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, 2006, 17(S2): 40-43.
[72]饶振刚.行星传动机构设计[M].北京:国防工业出版社, 1994.6.
[73]刘晖.基于参数化的齿轮传动接触有限元分析[D].大连交通大学, 2004.11.
[74]李润方等.接触问题数值方法[M].重庆大学出版社, 1992,(03): 11-14.
[75]关天明,张东升,蕾蕾. FA新型摆线针轮行星传动受力分析方法与齿面接触状态有限元分析[J].机械设计, 2005, 22(3):31-43.
[2] S.K.Malhotra, M.A.Parameswaran. Analysis of a cycloid speed reducer. Mech. Mach. Theory, 1983, 18(6): 491~499.
[3]关天民,雷蕾,施晓春.摆线针轮行星传动减速器可靠性评价体系的研究[J].机械工程学报, 2001,(12): 54-58.
[4]程彦春,庄家友,张树杰.摆线行星传动新结构的探讨[J].东北大学学报(自然科学版) , 1990,(04): 401-405.
[5] D.C.H.Yang, J.G.Blanche. Design and application guideline cycloid drives with machining tolerances. Mech. Mach. Theory, 1990, 25(5): 487~501.
[6] Li Lixing, etc. The computer aided design of cycloid drive. Chinese Journal of Mechanical Engineering, 1990,3(2): 221~231
[7]李力行等.摆线针轮行星传动的齿形修正及受力分析[J].机械工程学报, 1986, 22(1): 40～49.
[8]李充宁,孙爽.摆线针轮行星传动的运动平稳性分析[J].机械设计与制造, 2000, 3:48～49.
[9]李充宁,刘继岩等. 2K-V型行星传动中摆线轮啮合的传动精度研究[J].机械工程学报,2001,37(4):61～65.
[10]李充宁,摆线针齿行星传动轮齿的相对运动及滑动系数[J].机械传动, 1998, 22(3):19～21.
[11]李立行等,大型摆线针轮行星传动的合理结构和齿形[J].机械工程学报, 1999, 24(3): 28～33.
[12]舒小龙,李平.渐开线少齿差传动的最小啮合角[J].机械设计与研究, 2000,16 (04): 47- 49+8.
[13]张春林等.渐开线少齿差行星传动的变位系数的选择[J].北京理工大学学报, 1998,18(05): 563-566.
[14]万朝燕等.渐开线少齿差行星传动啮合点的确定方法[J].大连铁道学院学报, 1997,18(02): 47-50.
[15]杨锡和,石辉.少齿差内啮合齿轮的强度计算[J].雷达与对抗, 2003, (02): 58-59+62.
[16]叶志刚等. K-H-V型渐开少齿差行星传动的建模设计与CAD技术[J].机械设计与研究, 2000,(03): 47-49+8.
[17]李红保,黄凯.少齿差内啮合传动多齿啮合的研究[J].辽宁工业大学学报(自然科学版), 2008, 28(04): 250-252+256.
[18]何韶君,罗跃纲.渐开线少齿差行星传动的弹流润滑分析[J].煤矿机械, 2007, 28(04): 92- 94.
[19]丁志等.基于UG的渐开线变位齿轮传动系统的设计[J].机械, 2004, 31(S1): 101-102+104.
[20]陶桂宝,李泽群等. NN型渐开线少齿差行星传动齿轮副的设计[J].现代制造工程, 2007, (08): 116-118+18.
[21]张文照,王光华.渐开线少齿差内啮合同时接触齿数研究及实际重合度的一种计算方法[J].上海化工学院学报, 1980, (01): 93-102.
[22]杨静等.圆弧少齿差传动齿轮弯曲应力的分析及实验研究[J].机械设计与研究, 2001, 17(03): 45-46+75-8.
[23]神会存等.圆弧少齿差传动齿轮啮合作用力分析[J].山东科技大学学报(自然科学版), 2000, 19(03): 73-76.
[24]董师予,张黎明等.圆弧针齿行星传动中替代参数对传动性能的影响[J].机械设计与研究, 1987,(05): 1-9.
[25]李充宁,周有强等.圆弧齿行星减速器的效率计算[J].机械传动, 1993,(04): 21-23+62.
[26]张广军等.圆弧针齿行星传动动力学的计算机仿真[J].机械设计, 1995, (07): 16-18+ 22+44-45.
[27]王正为等.双内圆弧针齿少齿差传动及其效率[J].山东矿业学院学报. 1993, 12(01): 1-5.
[28]尹华杰.活齿少齿差传动力学模型和强度分析[J].郑州工学院学报, 1990,(03): 30-39.
[29]左洪福,周有强等.活齿传动啮合副的滑动情况研究[J].南京航空学院学报, 1992, 24(02): 135-142.
[30]陈兵奎等.空间凸轮活齿行星传动[J].机械工程学报, 2004,40(01): 29-32.
[31]陈兵奎等.摆线凸轮活齿传动原理及齿形理论[J].机械传动, 2003,(03): 14-16+67.
[32]曾强等.空间凸轮活齿传动的接触有限元分析[J].机械, 2004, 31(S1): 12-14.
[33]彭程.少齿差摆动活齿传动的模糊可靠性优化设计[J].现代机械, 2006,(01): 20-21+24.
[34]李明山等.活齿少齿差行星齿轮传动的功率流分析[J].组合机床与自动化加工技术, 1991,(02): 17-20+50.
[35] M.Neagoe etc,“On a New Cycloidal Planetary Gear used to Fit Mechatronic Systems of RES”, TOKYO INSTITUTE OF TECHNOLOGY, Volume 45, Issue 11-12, pp. 1931-1939, July 2004.
[36] John Argyris, etc,“Determination of envelope to family of planar parametric curves and envelope singularities”, Computer methods in applied mechanics and engineering, Volume 175, Issues 1-2, Pages 175-187, June 1999.
[37] Alberto Demenego, etc,“Design and simulation of meshing of a cycloidal pump”, Mechanism and Machine Theory, Volume 37, Issue 3, Pages 311-332, March 2002.
[38]谷丽瑶,黄恺等.共轭啮合原理实现斜齿圆锥齿轮的三维实体造型[J].辽宁工业大学学报(自然科学版), 2008, 28(04): 246-249.
[39]狄玉涛,陈明等.弧齿线圆柱齿轮齿面形成原理及啮合性能分析[J].研究探讨, 2006,(09): 50-52.
[40]刘健.机械制造中曲面的共轭原理[J].大连工学院学刊, 1959.
[41]李高敬.螺旋齿轮啮合原理及其应用[J].精密制造与自动化, 1979,(04): 34-47
[42]刘杰华.用空间啮合原理精确设计非渐开线齿轮滚刀刃形的研究[J].工具技术. 1988,(01): 22-27.
[43]郭燕利等.平面二次包络环面蜗轮副研究综述与展望[J].机械, 2000, 27:209～210
[44]重庆大学蜗轮传动科研组.平面二次包络弧面蜗杆传动的研究与应用[J].重庆大学学报, 1978,(04): 1-18.
[45]酒井高男,牧充.交错轴齿轮传动中第二次作用的研究[J].国际齿轮装置与传动会议论文选.机械工业出版社, 1977.
[46]南开大学数学系齿轮研究小组.齿轮啮合理论的数学基础(一) [J].数学的实践与认识, 1976, 1:52~62.
[47]南开大学数学系齿轮研究小组.齿轮啮合理论的数学基础(二) [J].数学的实践与认识, 1976, 2:41~58.
[48]南开大学数学系齿轮研究小组.齿轮啮合理论的数学基础(三) [J].应用数学学报, 1976, 1(1):84~88.
[49]吴大任,骆家舜著.齿轮啮合理论[M].北京:科学出版社, 1985.
[50]陈兵奎.二次包络摆线行星传动装置[P].中国, ZL200610054263.6[P], 2006.4.30.
[51]房婷婷.摆线包络行星传动啮合理论研究[D]. 2007.
[52]陈兵奎.锥形摆线轮行星传动装置[P].中国, ZL20063117879.0, 2005.02.16.
[53]陈兵奎,王淑妍,李朝阳.双圆盘摆线轮行星传动装置[P].中国, 200510057463.2, 2005.12.23.
[54]贺敬良,吴序堂等.交错轴渐开线锥形齿轮副啮合原理研究[J].机械工程学报, 2004, 40(04): 81-84.
[55]毛世民,吴序堂等.点接触内啮合直齿锥齿轮全成形加工原理[J].制造技术与机床, 1991,(10): 14-17.
[56]毋荣亮.圆弧齿线双圆弧齿轮的基本啮合原理[J].太原工业大学学报, 1997, 28(03): 73-78+111.
[57]陶昇元等.诺维可夫齿轮的啮合原理与计算[J].合肥工业大学学报, 1959.
[58]段德荣.圆弧齿轮啮合原理的误差[J].机械传动, 1996, (03): 8-12+55.
[59] Y. Chen, G. Xing, X. Peng,“The Space Curve Mesh Equation and its kinematics Experiment”, Proceedings of 12th IFToMM World Congress, Besan?on France, 2007, 6: 18-21.
[60] Y. Chen, X. Peng, G. Xing,“Dynamics Modeling and Experiment on Micro-Elastic-Meshing- Wheel Mechanism”, Proceeding of ITIC’2006, Hangzhou China, 2006,11(56):7.
[61] Yang-zhi Chen, Xiang Xiao-yong, Luo Liang;“A Corrected Equation of Space Curve Meshing”; Mech. Mach. Theory, 2009, 44 (7): 1348-1359.
[62] CHEN Yang-zhi, LUO Liang, HU Qiang“Contact Ratio of Space-Curve Meshing-Wheel Transmission Mechanism”; Journal of Mechanical Design, 2009, 131 (7): 074501-5.
[63] Y. Chen, X. Liu, D.G..Chetwynd, P. Huang,“Investigation of a novel elastic–mechanical wheel transmission under light conditions”, Mech. Mech. Theory, 2008, 43: 1462-1477.
[64] Yang-zhi Chen, Qiang Hu, Lei-hou Sun,“The Design Criterion of the Space-Curve Meshing- Wheel Mechanism Based on Elastic Deformation of the Tine”, Journal of Mechanical Design, 2010, 132 (5): 054502 -6.
[65] CHEN Yang-zhi, LUO Liang, HU Qiang,“The Parameters of SCMW mechanism for helix–shaped driving tine”, Chinese Journal of Mechanical Engineering, 2009.
[66]黄小平等.齿轮纯滚动啮合的原理与实现[J].机械传动, 2001, 25(03): 5-8.
[67]杨兰春.渐开线内齿轮副的设计与计算[M].北京:机械工业出版社, 1995.1.
[68]李瑰贤著.空间几何建模及工程应用[M].北京:高等教育出版社, 2007.
[69]章易程,李蔚聂等.渐开线内齿轮副相对滑动率的研究[J].机械传动, 2001, 25(02): 25-27+ 40.
[70]章易程,李蔚聂等.渐开线外齿轮副相对滑动率的研究[J].机械设计, 2001,(07): 27-29.
[71]赵亚平等.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, 2006, 17(S2): 40-43.
[72]饶振刚.行星传动机构设计[M].北京:国防工业出版社, 1994.6.
[73]刘晖.基于参数化的齿轮传动接触有限元分析[D].大连交通大学, 2004.11.
[74]李润方等.接触问题数值方法[M].重庆大学出版社, 1992,(03): 11-14.
[75]关天明,张东升,蕾蕾. FA新型摆线针轮行星传动受力分析方法与齿面接触状态有限元分析[J].机械设计, 2005, 22(3):31-43.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |