摆杆活齿传动振动建模与分析
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摘要
摆杆活齿传动是在摆动活齿传动基础上研究开发的一种新型活齿传动形式。它是一种用于传递两同轴运动和动力的新型传动,具有多齿啮合、承载能力强、全滚动啮合传动效率高、传动比大、输出刚度大等特点,这些特点使摆杆活齿传动具有很好的应用前景。
论文根据摆杆活齿传动的结构特点,推导出摆杆活齿传动中心轮齿廓方程和活齿受力计算公式。根据振动系统建模方法,建立了摆杆活齿传动系统的振动分析模型。
依据摆杆活齿传动啮合副结构特点,基于Hertz理论建立了摆杆活齿传动啮合副的啮合刚度模型,结合模型推导出各啮合副刚度计算公式,利用Matlab软件程序计算分析了摆杆活齿传动各主要结构参数对各啮合副啮合刚度的影响规律。
针对摆杆活齿传动机构的动力学特点,首次采用集中参数法建立了摆杆活齿减速器的3自由度扭转振动模型。按照等效前后动能和势能不变的原则,推导出等效转动惯量和啮合副等效扭转刚度,并利用Matlab软件程序计算分析等效啮合刚度的变化规律及摆杆活齿传动结构参数对等效啮合刚度的影响规律。利用动力学模型对摆杆活齿传动样机的振型进行了求解和分析。
综合考虑摆杆活齿传动的输入轴弹性、输出轴轴承弹性以及激波器与活齿啮合副、活齿与中心轮啮合副的弹性等因素的影响,利用牛顿第二定律并结合变形协调方程,建立了摆杆活齿传动系统的动力学模型,并对摆杆活齿传动系统振动的固有频率进行了求解和分析。
Swing-rod movable teeth drive, which is exploited on the foundation of swing movable teeth drive, is a new type of movable teeth drive. It, which is used to transit rotary motion and power between two shifts with the same axis, is a new type of drive. The swing-rod movable teeth drive has the advantage of more meshing, strong load-carrying capacity, high transmission efficiency by full rotation, large angular velocity ratio, large outputting rigidity etc. These characteristics make swing-rod movable teeth drive have great application vistas.
According to the structure characteristic of swing-rod movable teeth drive, the center roller teeth profile equation and stress calculated formula of movable teeth of swing-rod movable teeth drive are deduced. By means of modeling of vibration system, the vibration analysis system of swing-rod movable teeth drive is built.
According to the structure characteristic of swing-rod movable teeth drive meshing pair and the theory of Hertz, the meshing rigidity model of swing-rod movable teeth drive meshing pair is founded. The meshing rigidity of each meshing pair is deduced. By using of Matlab the regularity that structure parameters of swing-rod movable teeth drive affect meshing rigidity of each meshing pair is analyzed.
Contraposing to dynamic characteristic of swing-rod movable teeth drive organization, the 3 freedoms torsional dynamic model of swing-rod movable teeth reducer is founded, which adopt concentrate parametric method for the first time for the first time. Base on the principle of kinetic energy and potential energy which are fixedness fore-and-after equivalent, the equivalent torsional inertia and the equivalent torsional rigidity of meshing are deduced. The regularities which are the change of equivalent torsional rigidity ofmeshing and the influence of the equivalent meshing rigidity on structure parameters of swing-rod movable teeth drive are calculated and analyzed by using of Matlab. The model analysis is worked out.
The elasticity of driving axis, the elasticity of outputting axis bearing and the elasticity of movable teeth are taken into consideration. The dynamic model of swing-rod movable teeth drive system is founded by using of Newton’s second law and compatibility of deformation equation. The natural frequency of vibration system is calculated and analyzed.
论文根据摆杆活齿传动的结构特点,推导出摆杆活齿传动中心轮齿廓方程和活齿受力计算公式。根据振动系统建模方法,建立了摆杆活齿传动系统的振动分析模型。
依据摆杆活齿传动啮合副结构特点,基于Hertz理论建立了摆杆活齿传动啮合副的啮合刚度模型,结合模型推导出各啮合副刚度计算公式,利用Matlab软件程序计算分析了摆杆活齿传动各主要结构参数对各啮合副啮合刚度的影响规律。
针对摆杆活齿传动机构的动力学特点,首次采用集中参数法建立了摆杆活齿减速器的3自由度扭转振动模型。按照等效前后动能和势能不变的原则,推导出等效转动惯量和啮合副等效扭转刚度,并利用Matlab软件程序计算分析等效啮合刚度的变化规律及摆杆活齿传动结构参数对等效啮合刚度的影响规律。利用动力学模型对摆杆活齿传动样机的振型进行了求解和分析。
综合考虑摆杆活齿传动的输入轴弹性、输出轴轴承弹性以及激波器与活齿啮合副、活齿与中心轮啮合副的弹性等因素的影响,利用牛顿第二定律并结合变形协调方程,建立了摆杆活齿传动系统的动力学模型,并对摆杆活齿传动系统振动的固有频率进行了求解和分析。
Swing-rod movable teeth drive, which is exploited on the foundation of swing movable teeth drive, is a new type of movable teeth drive. It, which is used to transit rotary motion and power between two shifts with the same axis, is a new type of drive. The swing-rod movable teeth drive has the advantage of more meshing, strong load-carrying capacity, high transmission efficiency by full rotation, large angular velocity ratio, large outputting rigidity etc. These characteristics make swing-rod movable teeth drive have great application vistas.
According to the structure characteristic of swing-rod movable teeth drive, the center roller teeth profile equation and stress calculated formula of movable teeth of swing-rod movable teeth drive are deduced. By means of modeling of vibration system, the vibration analysis system of swing-rod movable teeth drive is built.
According to the structure characteristic of swing-rod movable teeth drive meshing pair and the theory of Hertz, the meshing rigidity model of swing-rod movable teeth drive meshing pair is founded. The meshing rigidity of each meshing pair is deduced. By using of Matlab the regularity that structure parameters of swing-rod movable teeth drive affect meshing rigidity of each meshing pair is analyzed.
Contraposing to dynamic characteristic of swing-rod movable teeth drive organization, the 3 freedoms torsional dynamic model of swing-rod movable teeth reducer is founded, which adopt concentrate parametric method for the first time for the first time. Base on the principle of kinetic energy and potential energy which are fixedness fore-and-after equivalent, the equivalent torsional inertia and the equivalent torsional rigidity of meshing are deduced. The regularities which are the change of equivalent torsional rigidity ofmeshing and the influence of the equivalent meshing rigidity on structure parameters of swing-rod movable teeth drive are calculated and analyzed by using of Matlab. The model analysis is worked out.
The elasticity of driving axis, the elasticity of outputting axis bearing and the elasticity of movable teeth are taken into consideration. The dynamic model of swing-rod movable teeth drive system is founded by using of Newton’s second law and compatibility of deformation equation. The natural frequency of vibration system is calculated and analyzed.
引文
1 曲继方.活齿传动理论.北京:机械工业出版社,1993:1-20
2 邵忍平, 何大为, 黄欣娜.机械系统动力学.北京:机械工业出版社,2005:1-115
3 周加龙.摆杆活齿传动的优化设计及建模仿真研究.[燕山大学工学硕士学位论文].2003:1-26
4 Р·М·Игнамищев Общиесвепения О Синусощарикоъгх Передачах. Вестник Мaщиностроения,1986,No2
5 崔建伟, 李变荣, 徐斌.螺旋钢球活齿传动的原理及特点.煤炭科学技术,2003, 31(6):5-7,10
6 Keith S. Subtractive and Additive Differential Gear Reduction System. United States Patent,4338830,1986
7 Eyer E., Dipl. -1ng et al. DEUTSCHES PATENTAMT, P3920317.4,1990
8 Edward C. Tibbals, Jr., High Point, N. C.. Wobble Type Axial Speed Reducer Apparatus. United States Patent,4563915
9 陈仕贤.活齿波齿传动啮合原理与齿形设计.北京航空学院学报,1978,(11):37-61
10 周有强, 王宏猷.套筒活齿少齿差传动装置.中国专利,专利号:CN2075729U
11 麻彪.结构参数优化及齿廓修形.[中国矿业大学硕士学位论文].1990:1-35
12 曲继方.摆动活齿减速机.中国专利,专利号:CN2075729U
13 严明.移位滚柱减速机的纯滚动结构及其应用.机械传动(增刊),1996,(2):43-44
14 刘生林, 吴序堂.推杆减速器的优化设计.机械设计,1999,17(1):44-46
15 梁尚明.摆动活齿传动研究.[四川大学工学博士学位论文].2001:1-9
16 李瑰贤.滚柱活齿传递受力分析的研究.机械设计,2002,(1):18-22
17 唐琼, 栾振辉.摆动活齿泵的流量脉动.煤矿机械,2005,(8):44-45
18 韩敏.圆形活齿行星传动的研究.设计与研究,2005,(5):31-32
19 陈兵奎, 牟萑.空间凸轮活齿行星传动.机械工程学报,2004,40(1):29-32
20 陈仕贤, 陈勃, 冯骥.复式滚动活齿传动(CORT 传动).机器人技术与应用,2005, (2):31-38
21 张佑林.活齿端面谐波齿轮啮合原理的研究.机械设计与研究,2005,21(6):56-58
22 蔡海鹏, 杨坤玉.推杆活齿的受力分析和尺寸设计.轴承,2003,(8):8-10
23 曾强, 李鹏.空间凸轮活齿传动的应力应变分析.机械工程师,2004,10:59-62
24 Li Mingshan, Liu Xiangjiu, Dong Zhifeng and Zhou Youqiang. An Equivalent Me- chanism Method for Analyzing Forces in the Movable Sleeve Tooth Transmission with Small Tooth Difference .Proceedings of Ninth World Congress on the Theory of Mechanisms,Milan,Italy,1995:105-211
25 鹏程.少齿差摆动活齿传动的模糊可靠性优化设计.现代机械,2006,(1):20-21,24
26 骆行.滚子活齿行星传动的模糊可靠性优化设计.机械设计与制造,2004,(5):7-8
27 王洪星.活齿减速器齿廓共轭问题.北京航空学院学报,1988,(2):22-25
28 Tadao, Tsukada, Isamu, Takasu. An Optimum Design of Planetary Reduction Gear Using Roller as Teeth. Bullentin of the JSME,1980,123(183):1530-1538
29 安子军, 王广欣.摆线钢球行星传动的模糊可靠性设计.机械传动,2004,28(5): 17-19
30 Wu Xutang etc. Tooth Profiles Analysis and Parameter Determination of Push Rod Reducer. Chinese Journal of Mechanical Engineering,1996,22(3):3-4,12
31 Peng Zhang, Zijun An. Research on rigidity and torsional vibration model of cycloid steel ball transmission system. Daizhong Su. Proceedings of International Conference on Advanced Design and Manufacture. Harbin, 2006. United Kingdom, ADMEC, Notting Trent University, 2006:907-911
32 Zhou JJ, Chen ZC. Creative design of movable tooth gear drive. Huang T. 11th World Congress in Mechanism and Machine Science, TianJin, 2004. BeiJing, China Machine Press,2004:796-799
33 梁尚明.摆动活齿的研究.[四川大学博士论文].2000:1-24
34 安子军, 周加龙.摆杆活齿传动参数优化设计研究.机械设计,2006,30(2):30-31
35 余跃庆, 李哲.现代机械动力学.北京:北京工业大学出版社,1998:1-6
36 Dubowsky S. On Predictiong the Dynamic Effects of Clearances in Planar Mechanics. Trans. ASME, J. Eng. Ind.,1974,96(1):317-323
37 Dubowsky S, Gardner T N., Design and Analysis of Multilink Flexible Mechanismswith Multiple Clearance Connections. Trans. ASME,. J. Eng. Ind.,1997,99B:88-96
38 Funabashi H, Ogawa K, Horie M. A Dynamic Analysis of Mechanisms with Clearances. Bull. JSME,1978,21:1652-1659
39 Hua Chen, Weishan Chen, Junkao Liu. Dynamics analysis and simulation of the 3-PRS parallel manipulator. Daizhong Su. Proceedings of the International Conference on Advanced Design and Manufacture, Harbin, 2006. United Kingdom, Advanced Design and Mannufacturing Eengineering Centre, Nottingham Trent University,2004:53-57
40 Horie M et al. A Dynamic Characteristic of Planar Link Mechanisms with Clearances. Bull. JSME,1986,29:1888-1894
41 Meirovitch L. Element of Vibration Analysis. Second Edition U.S.A.McGRAW-Hill Book Company,1986:30-55
42 Bishop R E D, Johnson D C. The Mechanics of Vibration. Cambridge: Cambridge Univ. Press,1960:1-10
43 廖伯瑜, 周新民, 尹志宏.现代机械动力学及其工程应用.北京:机械工业出版社, 2004:1-35
44 Zienkiewicz O C. The finite element method in engineering. 3rd ed. New York: McCraw-Hill,1997:1-5
45 R J Melosh. Basis for Derivation of Matrices for the Direct Stiffness Method. AIAAJ,1963,(7):6-12
46 R Courant. Varaiational Methods for the Solution of Problems of Equilibrium and Vibrations. Bullentin of the American Mathematical Society,1943,(49):199-205
47 徐秉业,黄炎等.弹塑性力学及其应用.北京:机械工业出版社,1984:180-185
48 Love, A.E.H..A Treatise on the Mathematical Theory of Elasticity. Dover,1944:1-20
49 白象忠.材料力学.北京:中国建材工业出版社,2003:46-151
50 安子军, 周加龙.新型摆杆活齿传动齿形综合研究.机械传动,2003,27(2):12-13
51 张大卫, 王刚, 黄田.RV 减速机动力学建模与结构参数分析.机械工程学报,2001, 37(1):69-74
52 严细海, 张策, 李充宁, 等.RV 减速器的扭转振动的固有频率及其主要影响因素.机械科学与技术,2004,23(8):991-994
53 哈尔滨理工大学教研室.理论力学.北京:高等教育出版社,2003:233-318
54 梁尚明, 张均富, 徐礼钜, 等.摆动活齿传动系统振动的动力学模型.振动工程学报,2003,16(3):285-288
55 陈塑寰.结构动态设计的矩阵摄动理论.北京:科学出版社,1999:11-15
2 邵忍平, 何大为, 黄欣娜.机械系统动力学.北京:机械工业出版社,2005:1-115
3 周加龙.摆杆活齿传动的优化设计及建模仿真研究.[燕山大学工学硕士学位论文].2003:1-26
4 Р·М·Игнамищев Общиесвепения О Синусощарикоъгх Передачах. Вестник Мaщиностроения,1986,No2
5 崔建伟, 李变荣, 徐斌.螺旋钢球活齿传动的原理及特点.煤炭科学技术,2003, 31(6):5-7,10
6 Keith S. Subtractive and Additive Differential Gear Reduction System. United States Patent,4338830,1986
7 Eyer E., Dipl. -1ng et al. DEUTSCHES PATENTAMT, P3920317.4,1990
8 Edward C. Tibbals, Jr., High Point, N. C.. Wobble Type Axial Speed Reducer Apparatus. United States Patent,4563915
9 陈仕贤.活齿波齿传动啮合原理与齿形设计.北京航空学院学报,1978,(11):37-61
10 周有强, 王宏猷.套筒活齿少齿差传动装置.中国专利,专利号:CN2075729U
11 麻彪.结构参数优化及齿廓修形.[中国矿业大学硕士学位论文].1990:1-35
12 曲继方.摆动活齿减速机.中国专利,专利号:CN2075729U
13 严明.移位滚柱减速机的纯滚动结构及其应用.机械传动(增刊),1996,(2):43-44
14 刘生林, 吴序堂.推杆减速器的优化设计.机械设计,1999,17(1):44-46
15 梁尚明.摆动活齿传动研究.[四川大学工学博士学位论文].2001:1-9
16 李瑰贤.滚柱活齿传递受力分析的研究.机械设计,2002,(1):18-22
17 唐琼, 栾振辉.摆动活齿泵的流量脉动.煤矿机械,2005,(8):44-45
18 韩敏.圆形活齿行星传动的研究.设计与研究,2005,(5):31-32
19 陈兵奎, 牟萑.空间凸轮活齿行星传动.机械工程学报,2004,40(1):29-32
20 陈仕贤, 陈勃, 冯骥.复式滚动活齿传动(CORT 传动).机器人技术与应用,2005, (2):31-38
21 张佑林.活齿端面谐波齿轮啮合原理的研究.机械设计与研究,2005,21(6):56-58
22 蔡海鹏, 杨坤玉.推杆活齿的受力分析和尺寸设计.轴承,2003,(8):8-10
23 曾强, 李鹏.空间凸轮活齿传动的应力应变分析.机械工程师,2004,10:59-62
24 Li Mingshan, Liu Xiangjiu, Dong Zhifeng and Zhou Youqiang. An Equivalent Me- chanism Method for Analyzing Forces in the Movable Sleeve Tooth Transmission with Small Tooth Difference .Proceedings of Ninth World Congress on the Theory of Mechanisms,Milan,Italy,1995:105-211
25 鹏程.少齿差摆动活齿传动的模糊可靠性优化设计.现代机械,2006,(1):20-21,24
26 骆行.滚子活齿行星传动的模糊可靠性优化设计.机械设计与制造,2004,(5):7-8
27 王洪星.活齿减速器齿廓共轭问题.北京航空学院学报,1988,(2):22-25
28 Tadao, Tsukada, Isamu, Takasu. An Optimum Design of Planetary Reduction Gear Using Roller as Teeth. Bullentin of the JSME,1980,123(183):1530-1538
29 安子军, 王广欣.摆线钢球行星传动的模糊可靠性设计.机械传动,2004,28(5): 17-19
30 Wu Xutang etc. Tooth Profiles Analysis and Parameter Determination of Push Rod Reducer. Chinese Journal of Mechanical Engineering,1996,22(3):3-4,12
31 Peng Zhang, Zijun An. Research on rigidity and torsional vibration model of cycloid steel ball transmission system. Daizhong Su. Proceedings of International Conference on Advanced Design and Manufacture. Harbin, 2006. United Kingdom, ADMEC, Notting Trent University, 2006:907-911
32 Zhou JJ, Chen ZC. Creative design of movable tooth gear drive. Huang T. 11th World Congress in Mechanism and Machine Science, TianJin, 2004. BeiJing, China Machine Press,2004:796-799
33 梁尚明.摆动活齿的研究.[四川大学博士论文].2000:1-24
34 安子军, 周加龙.摆杆活齿传动参数优化设计研究.机械设计,2006,30(2):30-31
35 余跃庆, 李哲.现代机械动力学.北京:北京工业大学出版社,1998:1-6
36 Dubowsky S. On Predictiong the Dynamic Effects of Clearances in Planar Mechanics. Trans. ASME, J. Eng. Ind.,1974,96(1):317-323
37 Dubowsky S, Gardner T N., Design and Analysis of Multilink Flexible Mechanismswith Multiple Clearance Connections. Trans. ASME,. J. Eng. Ind.,1997,99B:88-96
38 Funabashi H, Ogawa K, Horie M. A Dynamic Analysis of Mechanisms with Clearances. Bull. JSME,1978,21:1652-1659
39 Hua Chen, Weishan Chen, Junkao Liu. Dynamics analysis and simulation of the 3-PRS parallel manipulator. Daizhong Su. Proceedings of the International Conference on Advanced Design and Manufacture, Harbin, 2006. United Kingdom, Advanced Design and Mannufacturing Eengineering Centre, Nottingham Trent University,2004:53-57
40 Horie M et al. A Dynamic Characteristic of Planar Link Mechanisms with Clearances. Bull. JSME,1986,29:1888-1894
41 Meirovitch L. Element of Vibration Analysis. Second Edition U.S.A.McGRAW-Hill Book Company,1986:30-55
42 Bishop R E D, Johnson D C. The Mechanics of Vibration. Cambridge: Cambridge Univ. Press,1960:1-10
43 廖伯瑜, 周新民, 尹志宏.现代机械动力学及其工程应用.北京:机械工业出版社, 2004:1-35
44 Zienkiewicz O C. The finite element method in engineering. 3rd ed. New York: McCraw-Hill,1997:1-5
45 R J Melosh. Basis for Derivation of Matrices for the Direct Stiffness Method. AIAAJ,1963,(7):6-12
46 R Courant. Varaiational Methods for the Solution of Problems of Equilibrium and Vibrations. Bullentin of the American Mathematical Society,1943,(49):199-205
47 徐秉业,黄炎等.弹塑性力学及其应用.北京:机械工业出版社,1984:180-185
48 Love, A.E.H..A Treatise on the Mathematical Theory of Elasticity. Dover,1944:1-20
49 白象忠.材料力学.北京:中国建材工业出版社,2003:46-151
50 安子军, 周加龙.新型摆杆活齿传动齿形综合研究.机械传动,2003,27(2):12-13
51 张大卫, 王刚, 黄田.RV 减速机动力学建模与结构参数分析.机械工程学报,2001, 37(1):69-74
52 严细海, 张策, 李充宁, 等.RV 减速器的扭转振动的固有频率及其主要影响因素.机械科学与技术,2004,23(8):991-994
53 哈尔滨理工大学教研室.理论力学.北京:高等教育出版社,2003:233-318
54 梁尚明, 张均富, 徐礼钜, 等.摆动活齿传动系统振动的动力学模型.振动工程学报,2003,16(3):285-288
55 陈塑寰.结构动态设计的矩阵摄动理论.北京:科学出版社,1999:11-15