三相五环减速器的研究
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摘要
三环减速器是在渐开线少齿差行星传动的基础上开发的一种新型传动装置。由于其独特的传动原理和结构特点,而受到广泛关注。三环减速器的传动机构不能实现动平衡,而引起振动和噪声较大,针对这些问题,提出了能实现惯性力和惯性力矩同时平衡的三相五环减速器,并对其进行了理论研究和实验研究。
首先,对三相五环减速器的传动原理进行研究,并建立了少齿差内啮合行星齿轮的啮合方程,通过对三相五环减速器传动机构的力分析,来计算内齿环板和输入轴的受力情况,验证三相五环传动方案可实现完全动平衡。
其次,研究了插齿刀加工下的少齿差内啮合行星齿轮的设计方法,应用MATLAB编制少齿差内啮合变位系数的牛顿迭代公式的计算程序,来得到啮合角最小,满足重合度和齿廓不重叠干涉系数要求的变位系数,与实际加工情况一致。通过对三相五环减速器装配条件分析和传动效率计算,来指导参数设计和结构设计。
再次,利用Cosmos/Works,对三相五环减速器的关键零件内齿环板、输入轴和偏心套进行了有限元的静态分析和模态分析,验证了强度和振动满足设计要求。通过Solidworks的虚拟装配,验证了结构设计的合理性。
最后,对研制出的三相五环减速器样机进行了传动性能和振动的实验研究,实验采用微机采集数据和处理信号。实验结果表明:三相五环减速器样机具有较高的传动效率,箱体的振动较三环减速器有明显的降低。
The three-ring gear reducer (TRGR) is a new type of transmission device developed on the basis of involute few teeth difference (FTD) planetary transmission. Due to its distinctive transmission principle and structural character, the study on TRGR attracts wide attention. This article focuses on the current TRGR vibration and noise problems caused by transmission mechanism which leads to non-dynamic balance. So it puts forth and further makes theoretical and experimental research on three-phrase five-ring gear reducer as a solution.
Firstly, the article studies the principle of TRGR transmission and establishes the few teeth inside engaged planetary gear mesh equation. By analyzing the stress on the drive gear, it calculates and analyzes the stress on tooth ring flat-plate and input shaft, and proves the transmission program can completely effect the dynamic balance.
Secondly, the design uses the technique of the few teeth inside engaged planetary gear under the slotting cutter treatment, which is, with the application of the calculate programmer of Newton iterative formula of few teeth difference inside engaged gear modification coefficient of MATLAB regimentation, the minimum engagement angle can be achieved as well as the modification coefficient between contact ratio and the interference coefficient of tooth profile which is consistent with the actual situation. It also calculates the reducer's assembly condition and the reducer's transmission efficiency which can guide the parameter and structural design.
Thirdly, by applying Cosmos/Works, the finite element static and modal analysis on the key parts of internal tooth ring flat-plate, input axle and eccentric strap is made, which shows that they can meet the demand of intensity and vibration in design specification. Through using the virtual assembly of Solidworks, verify the structural design is reasonable.
At last, the article focuses on the developed model machine’s data collection and signal processing in the experiment on transmission performance and vibration which are carried out by microcomputer. The experiment declares that the three-phase five-ring gear reducer has a high efficiency on transmission and a much lower vibration compared with the old one.
首先,对三相五环减速器的传动原理进行研究,并建立了少齿差内啮合行星齿轮的啮合方程,通过对三相五环减速器传动机构的力分析,来计算内齿环板和输入轴的受力情况,验证三相五环传动方案可实现完全动平衡。
其次,研究了插齿刀加工下的少齿差内啮合行星齿轮的设计方法,应用MATLAB编制少齿差内啮合变位系数的牛顿迭代公式的计算程序,来得到啮合角最小,满足重合度和齿廓不重叠干涉系数要求的变位系数,与实际加工情况一致。通过对三相五环减速器装配条件分析和传动效率计算,来指导参数设计和结构设计。
再次,利用Cosmos/Works,对三相五环减速器的关键零件内齿环板、输入轴和偏心套进行了有限元的静态分析和模态分析,验证了强度和振动满足设计要求。通过Solidworks的虚拟装配,验证了结构设计的合理性。
最后,对研制出的三相五环减速器样机进行了传动性能和振动的实验研究,实验采用微机采集数据和处理信号。实验结果表明:三相五环减速器样机具有较高的传动效率,箱体的振动较三环减速器有明显的降低。
The three-ring gear reducer (TRGR) is a new type of transmission device developed on the basis of involute few teeth difference (FTD) planetary transmission. Due to its distinctive transmission principle and structural character, the study on TRGR attracts wide attention. This article focuses on the current TRGR vibration and noise problems caused by transmission mechanism which leads to non-dynamic balance. So it puts forth and further makes theoretical and experimental research on three-phrase five-ring gear reducer as a solution.
Firstly, the article studies the principle of TRGR transmission and establishes the few teeth inside engaged planetary gear mesh equation. By analyzing the stress on the drive gear, it calculates and analyzes the stress on tooth ring flat-plate and input shaft, and proves the transmission program can completely effect the dynamic balance.
Secondly, the design uses the technique of the few teeth inside engaged planetary gear under the slotting cutter treatment, which is, with the application of the calculate programmer of Newton iterative formula of few teeth difference inside engaged gear modification coefficient of MATLAB regimentation, the minimum engagement angle can be achieved as well as the modification coefficient between contact ratio and the interference coefficient of tooth profile which is consistent with the actual situation. It also calculates the reducer's assembly condition and the reducer's transmission efficiency which can guide the parameter and structural design.
Thirdly, by applying Cosmos/Works, the finite element static and modal analysis on the key parts of internal tooth ring flat-plate, input axle and eccentric strap is made, which shows that they can meet the demand of intensity and vibration in design specification. Through using the virtual assembly of Solidworks, verify the structural design is reasonable.
At last, the article focuses on the developed model machine’s data collection and signal processing in the experiment on transmission performance and vibration which are carried out by microcomputer. The experiment declares that the three-phase five-ring gear reducer has a high efficiency on transmission and a much lower vibration compared with the old one.
引文
1戴红鹃,周红良,曾励.少齿差行星齿轮传动技术现状及发展.机械工程师.2005,12(30):32~33
2 D.W.Dudley.The Evolution of the Gear Art.AGMA.Washitong,1989:1~15
3 Yang Jianmin,Zhang Ce,Lin Zhongqin,Chen Guanlong. Theoretical explanation for lower order harmonic resonance phenomenon of three- ring transmissions. Journal of Shang hai jiao tong University.2003,8(1) :71~74
4 Yuan Mao Huang,C.D.Hong.Analysis of Torsional Vibration Systems by the Extended Transfer Matrix Method. Transactions of the ASME,Journal of Vibration and Acoustics.1999,121(2):250~255
5崔亚辉,马朝峰.封闭式行星传动的动力学分析.机械工程.2006,17(4):62~63
6 L.Litvin.Modern Theory of Gearing and Application.Proceedings of 2~(nd) World Conference on Gearing.Paris,1996:23~26
7徐茂.三环减速器在冶金领域应用探讨.包钢科技.2002,28(4):50~51
8辛绍杰,李华敏,梁永生.用于抽油机的新型三环减速器.石油机械.2000,28(3):26~29
9黄文振.三环减速器振动问题研究.机械工程学报.1994,30(2):64~68
10崔建昆,白国振.三环减速器环板惯性力平衡和实验研究.机械.1998,25(1):21~23
11郑甲红,冯丽萍.内齿行星轮传动的平衡.机械.2003,30(3):29~30
12崔建昆,曾志.三环减速器摆动力及摆动力矩的计算平衡.机械设计与研究.1996,(3):39~40
13 L.Moriwaki,T.Fukuda,Y.Watada,K.Saito.Global Local Finite Element Method(GLFEM) in Gear Tooth Stress Analysis .Transactions of the ASME,Journal of mechanical Design.1993,115(4) :1008~1012
14 F.L.Litvin,J.-S. Chen,J.Lu. ,R.F.Handschuh.Application of Finite Element Analysis for Determination of Load Share,Real Contact Ratio,Precision of Motion and Stress Analysis.Transactions of the ASME,Journal of Mechanical Design.1996,118(4) :561~567
15 J.J.Coy,CHC.Chao.A Method of Selecting Grid Size to Account for Hertz Deformation in Finite Element Analysis of Spur Gear.Transactions of theASEM,Journal of Mechanical Design.1982,104(2):759~766
16 H.Von Eiff,K.H.Hirschmann,G.Lechner.Influence of Gear Tooth Geometry on Tooth Stress of External and Internal Gears.Transactions of the ASME,Journal of Mechanical Design.1996,112(4) :575~583
17 Wang Shitong,Yan Huanxin,Liu Rongqiang,Li Huamin.Experimental Study on Load Equilibration and Vibration in 3-Ring-Gear Reducer. Journal of Harbin Institute of Technology.1997,4(3):43~47
18 Xin Shaojie ,Li Huamin,Li Xiangjiu.Dynamics analysis on new type two-stage three-ring gear reducer on pumping units.1st International Conference on Mechanical Engineering ,2000.11,shanghai
19 Huamin Li,Yongsheng Liang,Shaojie Xin. Study on Load Equilibrating and Vibration reducing of Three-Ring Gear Reducer. 8~(th) International ASME Power Transmission and Gearing Conference.2000,14456:1~5
20余跃海,张策.内啮合齿轮几何设计CAD系统及其在三环减速器系列设计中的应用.机械科学与技术.2005,24(4):475~478
21黄华梁,戴杜,龙有亮.三环式少齿差行星齿轮减速器的内啮合变位.机械设计.2004,21(1):23~25
22基于CAD的三环少齿差内啮合行星齿轮传动变位方法的研究.机械传动.2004,27(5):15~17
23 Wu Junfei,Li Guixian,Lin Shaofen,Li Huamin,Chen Xiujie.Interference of Internal Involute Bevoloid Gears with Parallel Axes.Journal of Harbin Institute of Technology.1999,6(3):32~36
24崔建昆,张光辉.平行曲柄输入式少齿差行星齿轮传动.机械.1996,23(1):37~38,48
25 Li Lixing,He Weidong,Li Xin.Study on Double Crank Ring-Plate-Type Cycloid Drive.Tenth World Congress on the Theory of Machine and Mechanisms.Oulu University,Finland,1999:2380~2385
26陈宗源,刘昭文,王志德,郭思玲.三环式减速(或增速)装置.发明专利公告号:CN 85106692A,1987:1~5
27杨耀峰,纪岗昌,王乃信.不同型式的内齿行星齿轮传动的理论研究.机械科学与技术.1995,14(4):27~30
28商冠华.浮动式齿差减速器.实用新型专利公告号:CN2034218U,1989:1~5
29唐国良,汪署浩.双曲柄单齿环少齿差行星减速器.实用新型专利公告号:CN2059200U,1990:1~5
30唐国良,汪署浩.双曲柄双齿环少齿差行星减速器.实用新型专利公告号:CN2118208U,1992:1~8
31萧南平.全对称平移连杆减速箱.实用新型专利公告号:CN 2293683Y,1992:1~5
32李华敏,梁永生,辛绍杰.完全平衡、均载减振两级三环齿轮减速器.实用新型专利公告号:ZL00234570.6,2002:1~5
33唐倩,李润方,雷闻宇,廖小云.少齿差内啮合齿轮轮齿接触问题研究.机械传动.1998,22(1):21~23
34崔建昆,曾志.三环减速器的工作原理与功率流分析.机械传动.1996,20(2),增刊:65~68
35 H.N.Ozguzen,D.R.Houser.Dynamic Analysis of High Speed Gears by Using Loaded Static Transmission Error.Journal of Sound and Vibration.1998,(125): 71~83
36 W.lewis.Investigations of Strength of Gear Teeth.Proceeding of the Engineers Club of Philadelphia.1983:16~23
37 K.L.Wang,H.S.Cheng.A Numerical Solution to the Dynamic Load,Film Thickness,and Surface Temperature in Spur Gears.Transactions of the ASME,Journal of Mechanical Design.1981:177~187
38 K.Nagaya,S.Uematsu.Effect of Moving Speed of Dynamic Loads on the Deflection of Gear Teeth.Transactions of the ASME,Journal of Mechanical Design.1981:357~363
39 M.F.Spott.Estimating Dynamic Loads on Gear Teeth. Transactions of the ASME,Journal of Mechanical Design.1984,56:84~88
40 A.H.Elkholy.Tooth Load Sharing in High-Contact Ratio Spur Gear. Transactions of the ASME,Journal of Mechanical Design,Transmissions,and Automation in Design.1985,107:11~16
41 W.D.Mark.Use of the Generalized Transmission Error in the Equations of Motion of Gear Systems. Transactions of the ASME,Journal of Mechanical Design,Transmissions,and Automation in Design.1987,109:191~283
42 H.H.Lin,R.L.Huston.On Dynamic Load in Parallel Shaft Transmission:Part II-Modeling and Analysis. Transactions of the ASME,Journal of Mechanical Design,Transmissions,and Automation in Design.1988,110:226~229
43 A.Abiud,B.G.Belnikolovsky. Study of the Dynamic Loads in Machines with SpurGears:Part1,Eighth World Congress on the Theory of Machine and Mechanisms.Prague,Czechoslovakia,1991:531~534
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48辛绍杰.油膜浮动均载的完全平衡两级三环减速器的研究.哈尔滨工业大学博士学位论文.2002,16~39
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52宋轾民,张俊,张永心,张策.计入内齿板变形的环式减速器弹性动力分析.机械工程学报.2006,42(9):29~32
53朱孝录.齿轮传动设计手册.化学工业出版社.2002
54冯晓宁,李忠浩.渐开线少齿差传动设计参数的选择.机械传动.1995,19(1):11~14
55梁永生,李华敏,李瑰贤.用插齿刀加工的少齿差内啮合变位系数的确定.哈尔滨工业大学学报.1999,30(4):34~36,39
56吴春英,周志明,王乃信,梁治国.内齿行星齿轮传动装配条件的分析.机械传动1995,19(4):23~26
57蔡玉强,田海英,孟宪举.基于Pro/E的三环减速器装配的参数化设计.机械设计与制造.2006,(7):53~55
58王万娇,李润方,林腾蛟,刘文,谢永春.新型双环减速器机构虚拟装配及运动学仿真.机械研究与应用.2006,19(4):116~118
59崔亚辉,张道勇,贾晓雯.三环传动的性能仿真及可视化.重型机械.2005,30(2):46~48
2 D.W.Dudley.The Evolution of the Gear Art.AGMA.Washitong,1989:1~15
3 Yang Jianmin,Zhang Ce,Lin Zhongqin,Chen Guanlong. Theoretical explanation for lower order harmonic resonance phenomenon of three- ring transmissions. Journal of Shang hai jiao tong University.2003,8(1) :71~74
4 Yuan Mao Huang,C.D.Hong.Analysis of Torsional Vibration Systems by the Extended Transfer Matrix Method. Transactions of the ASME,Journal of Vibration and Acoustics.1999,121(2):250~255
5崔亚辉,马朝峰.封闭式行星传动的动力学分析.机械工程.2006,17(4):62~63
6 L.Litvin.Modern Theory of Gearing and Application.Proceedings of 2~(nd) World Conference on Gearing.Paris,1996:23~26
7徐茂.三环减速器在冶金领域应用探讨.包钢科技.2002,28(4):50~51
8辛绍杰,李华敏,梁永生.用于抽油机的新型三环减速器.石油机械.2000,28(3):26~29
9黄文振.三环减速器振动问题研究.机械工程学报.1994,30(2):64~68
10崔建昆,白国振.三环减速器环板惯性力平衡和实验研究.机械.1998,25(1):21~23
11郑甲红,冯丽萍.内齿行星轮传动的平衡.机械.2003,30(3):29~30
12崔建昆,曾志.三环减速器摆动力及摆动力矩的计算平衡.机械设计与研究.1996,(3):39~40
13 L.Moriwaki,T.Fukuda,Y.Watada,K.Saito.Global Local Finite Element Method(GLFEM) in Gear Tooth Stress Analysis .Transactions of the ASME,Journal of mechanical Design.1993,115(4) :1008~1012
14 F.L.Litvin,J.-S. Chen,J.Lu. ,R.F.Handschuh.Application of Finite Element Analysis for Determination of Load Share,Real Contact Ratio,Precision of Motion and Stress Analysis.Transactions of the ASME,Journal of Mechanical Design.1996,118(4) :561~567
15 J.J.Coy,CHC.Chao.A Method of Selecting Grid Size to Account for Hertz Deformation in Finite Element Analysis of Spur Gear.Transactions of theASEM,Journal of Mechanical Design.1982,104(2):759~766
16 H.Von Eiff,K.H.Hirschmann,G.Lechner.Influence of Gear Tooth Geometry on Tooth Stress of External and Internal Gears.Transactions of the ASME,Journal of Mechanical Design.1996,112(4) :575~583
17 Wang Shitong,Yan Huanxin,Liu Rongqiang,Li Huamin.Experimental Study on Load Equilibration and Vibration in 3-Ring-Gear Reducer. Journal of Harbin Institute of Technology.1997,4(3):43~47
18 Xin Shaojie ,Li Huamin,Li Xiangjiu.Dynamics analysis on new type two-stage three-ring gear reducer on pumping units.1st International Conference on Mechanical Engineering ,2000.11,shanghai
19 Huamin Li,Yongsheng Liang,Shaojie Xin. Study on Load Equilibrating and Vibration reducing of Three-Ring Gear Reducer. 8~(th) International ASME Power Transmission and Gearing Conference.2000,14456:1~5
20余跃海,张策.内啮合齿轮几何设计CAD系统及其在三环减速器系列设计中的应用.机械科学与技术.2005,24(4):475~478
21黄华梁,戴杜,龙有亮.三环式少齿差行星齿轮减速器的内啮合变位.机械设计.2004,21(1):23~25
22基于CAD的三环少齿差内啮合行星齿轮传动变位方法的研究.机械传动.2004,27(5):15~17
23 Wu Junfei,Li Guixian,Lin Shaofen,Li Huamin,Chen Xiujie.Interference of Internal Involute Bevoloid Gears with Parallel Axes.Journal of Harbin Institute of Technology.1999,6(3):32~36
24崔建昆,张光辉.平行曲柄输入式少齿差行星齿轮传动.机械.1996,23(1):37~38,48
25 Li Lixing,He Weidong,Li Xin.Study on Double Crank Ring-Plate-Type Cycloid Drive.Tenth World Congress on the Theory of Machine and Mechanisms.Oulu University,Finland,1999:2380~2385
26陈宗源,刘昭文,王志德,郭思玲.三环式减速(或增速)装置.发明专利公告号:CN 85106692A,1987:1~5
27杨耀峰,纪岗昌,王乃信.不同型式的内齿行星齿轮传动的理论研究.机械科学与技术.1995,14(4):27~30
28商冠华.浮动式齿差减速器.实用新型专利公告号:CN2034218U,1989:1~5
29唐国良,汪署浩.双曲柄单齿环少齿差行星减速器.实用新型专利公告号:CN2059200U,1990:1~5
30唐国良,汪署浩.双曲柄双齿环少齿差行星减速器.实用新型专利公告号:CN2118208U,1992:1~8
31萧南平.全对称平移连杆减速箱.实用新型专利公告号:CN 2293683Y,1992:1~5
32李华敏,梁永生,辛绍杰.完全平衡、均载减振两级三环齿轮减速器.实用新型专利公告号:ZL00234570.6,2002:1~5
33唐倩,李润方,雷闻宇,廖小云.少齿差内啮合齿轮轮齿接触问题研究.机械传动.1998,22(1):21~23
34崔建昆,曾志.三环减速器的工作原理与功率流分析.机械传动.1996,20(2),增刊:65~68
35 H.N.Ozguzen,D.R.Houser.Dynamic Analysis of High Speed Gears by Using Loaded Static Transmission Error.Journal of Sound and Vibration.1998,(125): 71~83
36 W.lewis.Investigations of Strength of Gear Teeth.Proceeding of the Engineers Club of Philadelphia.1983:16~23
37 K.L.Wang,H.S.Cheng.A Numerical Solution to the Dynamic Load,Film Thickness,and Surface Temperature in Spur Gears.Transactions of the ASME,Journal of Mechanical Design.1981:177~187
38 K.Nagaya,S.Uematsu.Effect of Moving Speed of Dynamic Loads on the Deflection of Gear Teeth.Transactions of the ASME,Journal of Mechanical Design.1981:357~363
39 M.F.Spott.Estimating Dynamic Loads on Gear Teeth. Transactions of the ASME,Journal of Mechanical Design.1984,56:84~88
40 A.H.Elkholy.Tooth Load Sharing in High-Contact Ratio Spur Gear. Transactions of the ASME,Journal of Mechanical Design,Transmissions,and Automation in Design.1985,107:11~16
41 W.D.Mark.Use of the Generalized Transmission Error in the Equations of Motion of Gear Systems. Transactions of the ASME,Journal of Mechanical Design,Transmissions,and Automation in Design.1987,109:191~283
42 H.H.Lin,R.L.Huston.On Dynamic Load in Parallel Shaft Transmission:Part II-Modeling and Analysis. Transactions of the ASME,Journal of Mechanical Design,Transmissions,and Automation in Design.1988,110:226~229
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