考虑运动副间隙的平面四杆机构动力学建模与仿真
摘要
在机械系统中,运动副是机构构件连接的中间环节,它不仅要将构件连接起来还要保证构件间能有一定的相对运动。运动副元件间一般需要采用动配合,这就必然存在一定的运动副间隙。为此,本论文对考虑间隙的平面四杆机构动力学问题和仿真方面进行了分析和研究。
首先介绍了机构动力学中的运动副间隙模型的近期研究成果,遇到的主要问题和未来的发展趋势。详细的阐述了运动副间隙模型中的“二状态”和“三状态”模型的建模方法。针对运动副间隙对四杆机构的运动影响,选择了“连续接触模型”进行分析。并以考虑单一间隙的平面四杆机构为例,建立存在间隙的运动微分方程,通过数值积分求出一个运动周期的解,从而确定运动副元素的分离判断准则。同时对平面四杆机构动力学特性进行了分析,比较了理想无间隙与考虑间隙机构的不同动态特性。为了进一步的研究间隙运动副的动力学特性,对单一的间隙转动副和移动副系统进行分析,建立动力学微分方程。对不同间隙值,不同接触阻尼系数下的间隙运动副的接触力动态特性进行了仿真分析。同样利用“连续接触模型”对考虑多间隙的平面四杆机构进行了分析,其中,考虑每个运动副处均存在间隙,研究存在四个间隙的平面四杆机构的运动特性,利用完整系统的拉格朗日方程建立了机构的动力学方程组,用龙格-库塔法编制了求解该微分方程组的求解程序,对四杆机构的动态性能参数进行了仿真分析。从而说明运动副间隙大大影响了机构的运动特性,使机构的实际运动和理想运动之间产生偏差,并且使运动副之间产生碰撞,从而引起构件的振动,加速磨损,降低工作效率。
The joints which connect two mechanic components of mechanisms can make sure the machines move relatively. Therefore, the presence of clearance in the joints of mechanisms must be considered. The clearance can cause contact and separation between the joint elements. So that, there will cause windages between the ideal movements and practical movements, increase the force between two machine elements. Then internal dynamic contacts can cause unusual vibration and noise, accelerate fatigue and wear and seriously reduce the machine efficiency. So, the influence of machine with clearance can not be neglected to some machine systems. So this work mainly studies the analysis of dynamic model and simulation of a deployable truss structure with clearances.
Firstly, recent researches were reviewed and discussed, several typical dynamics model of pairs with clearances were compared and discussed in respect of impact, damping, friction, etc in detail. Expound the“two-state”and“three-state”clearance model particularly. Considering the influence of machine with clearance,chose the continous contact model to analyse. On the basis of analysis for planar four-bar linkages with clearances, the dynamic differential equations were established. The numerical analysis methods were used to solve the problems, so that the impact-separate rule for the elements of joints were established, meanwhile, compared the dynamic characteristics of mechanisms between clearance considered and no-clearance considered. To be continue, two typical joints with clearance were established, the rotate joint and the remove joint, analysed their dynamics differential equations, compared the dynamic charateristics with different clearances, different damp, some important conclusions were drown. Finally analyse the planar linkages with four clearances using the continuous contact model, established the dynamic differential equations using Larange equations. By solving these problems, which not only show the bad effects clearances have on the stability of mechanism, but the methods to reduce the effects as well.
首先介绍了机构动力学中的运动副间隙模型的近期研究成果,遇到的主要问题和未来的发展趋势。详细的阐述了运动副间隙模型中的“二状态”和“三状态”模型的建模方法。针对运动副间隙对四杆机构的运动影响,选择了“连续接触模型”进行分析。并以考虑单一间隙的平面四杆机构为例,建立存在间隙的运动微分方程,通过数值积分求出一个运动周期的解,从而确定运动副元素的分离判断准则。同时对平面四杆机构动力学特性进行了分析,比较了理想无间隙与考虑间隙机构的不同动态特性。为了进一步的研究间隙运动副的动力学特性,对单一的间隙转动副和移动副系统进行分析,建立动力学微分方程。对不同间隙值,不同接触阻尼系数下的间隙运动副的接触力动态特性进行了仿真分析。同样利用“连续接触模型”对考虑多间隙的平面四杆机构进行了分析,其中,考虑每个运动副处均存在间隙,研究存在四个间隙的平面四杆机构的运动特性,利用完整系统的拉格朗日方程建立了机构的动力学方程组,用龙格-库塔法编制了求解该微分方程组的求解程序,对四杆机构的动态性能参数进行了仿真分析。从而说明运动副间隙大大影响了机构的运动特性,使机构的实际运动和理想运动之间产生偏差,并且使运动副之间产生碰撞,从而引起构件的振动,加速磨损,降低工作效率。
The joints which connect two mechanic components of mechanisms can make sure the machines move relatively. Therefore, the presence of clearance in the joints of mechanisms must be considered. The clearance can cause contact and separation between the joint elements. So that, there will cause windages between the ideal movements and practical movements, increase the force between two machine elements. Then internal dynamic contacts can cause unusual vibration and noise, accelerate fatigue and wear and seriously reduce the machine efficiency. So, the influence of machine with clearance can not be neglected to some machine systems. So this work mainly studies the analysis of dynamic model and simulation of a deployable truss structure with clearances.
Firstly, recent researches were reviewed and discussed, several typical dynamics model of pairs with clearances were compared and discussed in respect of impact, damping, friction, etc in detail. Expound the“two-state”and“three-state”clearance model particularly. Considering the influence of machine with clearance,chose the continous contact model to analyse. On the basis of analysis for planar four-bar linkages with clearances, the dynamic differential equations were established. The numerical analysis methods were used to solve the problems, so that the impact-separate rule for the elements of joints were established, meanwhile, compared the dynamic characteristics of mechanisms between clearance considered and no-clearance considered. To be continue, two typical joints with clearance were established, the rotate joint and the remove joint, analysed their dynamics differential equations, compared the dynamic charateristics with different clearances, different damp, some important conclusions were drown. Finally analyse the planar linkages with four clearances using the continuous contact model, established the dynamic differential equations using Larange equations. By solving these problems, which not only show the bad effects clearances have on the stability of mechanism, but the methods to reduce the effects as well.
引文
[1] 张策. 机械动力学[M]. 高等教育出版社,2000.4
[2] 文荣等. 空间伸展机构动力学研究[J]. 导弹与航天运载技术, 1996,2:1-10
[3] 文荣等. 带间隙空间结构的动力学特性分析[J]. 中国空间科学技术, 1998, 1:7-12
[4] 陈滨等. 含铰接间隙与杆件柔性的空间伸展机构单元的动力学建模与计算模拟,第一部分:动力学建模[J]. 导弹与航天运载技术, 1997,1:27-37
[5] 陈滨等. 含铰接间隙与杆件柔性的空间伸展机构单元的动力学建模与计算模拟,第二部分:系统动态特性的计算模拟结果[J]. 导弹与航天运载技术, 1997,3:34-40
[6] Dubowsky S, Freudenstein F. Dynamic Analysis of Mechanical Systems with Clearance,Part1:Formation of Dynamic Model[J], Journal of Engineering for industry, 1971,93B(1):305-309
[7] Dubowsky S, FreudensteinF.Dynamic Analysis of Mechanical Systems with Clearance,Part 2:Dynamic Response[J], Trans. ASME, J.Eng.Ind, 1971, 93B(1): 310-316
[8] Dubowsky S, Gardner T N. Dynamic Interactions of Link Elasticity and Clearance Connections in Planar Mechanical Systems[J]. Journal of Engineering for industry, 1975,97B (2):652-661
[9] Dubowsky S et al. On the Development of Criteria for the Prediction of Impact in the Design of High Speed Systems with Clearances[A]. Proc. 5th world Cong[C]. IFTOMM, Canada,1979,968-971
[10] Dubowsky S et al. An Analytical and Experimental Study of the Prediction of Impacts in Planar Mechanical Systems with Clearances[J]. Trans.AMSE, J. Mech. Transmiss. Automat. Des.,1984,106(4):444-451
[11] Dubowsky S. On Predicting the Dynamic Effects of Clearances in Planar Mechanisms[J]. Trans. ASME, J. Eng. Ind. ,1974,96(1):317-323
[12] Dubowsky S. On Predicting the Dynamic Effects of Clearances in One-Dimensional Closed Loop Systems[J]. Trans. ASME, J. Eng. Ind. ,1974,96B:324-329
[13] Dubowsky S,Young S C. An Experimental and Analytical Study of Connection Forces in High-speed Mechanisms[J]. Journal of Engineering for industry,1975,97B:1166-1175
[14] Dubowsky S,Gardner T N., Design and Analysis of Multilink Flexible Mechanisms with Multiple Clearance Connections[J]. Trans. ASME, J.Eng. Ind. ,1977,99B:88-96
[15] Dubowsky S,Moening M F. An Experimental and Analytical Study of Impact Forces in Elastic Mechanical Systems with Clearances[J]. Mech.Mach.Theory, 1978,13:451-465
[16] Dubowsky S et al. The Dynamic Modeling of Flexible Spatial Mechine Systems with Clearance Connections[J]. Trans. ASME, J.Mech. Transmiss. Automat. Des.,1987,109:87-94
[17] Horie M. Dynamic Characteristics of Planar Link Mechanisms with Clearance[J]. Bulletin of JSME, 1986,29:1888-1894
[18] Funabashi H, Ogawa K, Horie M et al. A Dynamic Analysis of the Plane Crank-and-rocker Mechanisms with Clearances. Bulletin of the JSME, 1988, 23(177):446-452
[19] 李哲. 考虑运动副间隙和构件弹性的平面连杆机构动力学研究(博士学位论文).北京:北京工业大学,1991
[20] 唐锡宽,金德闻. 机械动力学[M]. 北京:高等教育出版社,1984
[21] 俞武勇,季林红等. 含间隙机构运动副的动力学模型[J]. 机械科学与技术. 2001,20(5):665-669
[22] Hunt K H, et al. Coefficient of Restitution Interpreted as Damping in Vibroimpact[J]. Journal of Applied Mechanics. 1975,42E:440-445
[23] Herbert R G, et al. Shape and Frequency Composition of Pulses from an Impact Pair[J]. Journal of Engineering for Industry. 1977,99B(8):513-518
[24] Yigit A S, et al. Spring-dashpot Models for the Dynamics of a Radially Rotating Beam with Impact[J]. Journal of sound and Vibration. 1990,142(3):515-525
[25] Lee T W, et al. On the Dynamic Interactions of Interm Intent Motion Mechanisms, part 1:Dynamic model and response[J]. Journal of Mechanisms, Transmissions, and Automation in Design, 1983,105(3):527-539
[26] Wang Yu,et al. Dynamic Analysis of Flexible Mechanisms with Clearance[J] Journal of Mechanical Design. 1996,118:592-594
[27] Furuhashi T, et al. Research on Dynamic of Four-bar Linkage with Clearance at Turning Pairs (4th Report, Forces Acting at Joints of Crank-lever Mechanism)[J]. Bulletin of the JSME,1978,21(158):1299-1305
[28] Eleonor D. Stoenescu,Dan B. Marghitu. Dynamic Analysis of a Planar Rigid-linkMechanism with Rotating Slider Joint and Clearance. Journal of sound and Vibration. 2003(266):394-404
[29] Mansour W M, et al. Impact Spectra and Intensities for High-speed Mechanisms[J]. Journal of Engineering for Industry, 1975,97B(2):347-353
[30] Zakhariev E. Dynamics of Rigid Multibody Systems with Clearance in the Joints[J]. Mechanics of Structures and Machine, 1999,27(1):63-87
[31] Earles S.W.E, et al. Motion Analysis of a Rigid-link Mechanism with Clearance at a Bearing, Using Lagrangian Mechanics and Digital Computation[A]. In: Conference on Mechanisms,ME[C],London,England,1972:83-89
[32] Jungkeun R, et al. Dynamic Response of a Revolute Joint with Clearance[J]. Mechanics and Machinery Theory, 1996,31(1):121-134
[33] Bajkow skiJ ,et al. Application FEM in Modeling Rigid and Flexible Systems with Joint Clearances[J]. Shock and Vibration Digest, 2000,32(1):63-68
[34] 张跃明等. 考虑构件弹性和转动副间隙的空间机构动力学研究[J]. 机械科学与技术, 1999,18(4):532-534
[35] Seneviratne L D, et al. Analysis of a Four-bar Mechanism with a Radially Compliant Clearance Joint[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 1996,210(3):372-378
[36] 余跃庆,李哲. 现代机械动力学[M]. 北京工业大学出版社,1998.12
[37] 王国庆,刘宏昭等 . 含间隙连杆机构非线性行为研究 . 机械设计 , 2005,33(4):23-25
[38] 王国庆,刘宏昭等. 非线性接触模型在多间隙机构混沌分析中的应用. 机械科学与技术,2005,24(6):636-638
[39] 黄铁球,吴德隆等. 带间隙伸展机构的非线性动力学建模. 中国空间科学技术, 1999(1):7-13
[40] 黄铁球,阎绍泽等. 空间站伸展机构的非线性动态相应分析. 非线性动力学学报,1998,5(1):36-41
[41] 朱巨才,符炜. 用无质量杆-弹簧阻尼组合模型(MLSD 模型)对间隙机构进行分析的方法探讨. 机械科学与技术,2004,23(4):450-453
[42] P. Flores,J. Ambrosio. Revolute Joints with Clearance in Multibody Systems[J]. Computers and Structures, 2004(82)1359-1369
[43] P. Flores,J. Ambrosio. A Study on Dynamics of Mechanical Systems Including Joints with Clearance and Lubrication[J]. Mechanism and Mechine theory, 2006(41):247-261
[44] 尉立肖,刘才山. 圆柱铰间隙运动学分析及动力学仿真. 北京大学学报(自然科学版),2005,41(5):679-687
[45] 阎绍泽,申永胜等. 考虑杆件柔性和铰间隙的可展结构动力学数值模拟. 清华大学学报(自然科学版), 2003,43(2):145-148
[46] 黄昭度,纪辉玉. 分析力学[M]. 北京:清华大学出版社,1985
[47] 王振发. 分析力学[M]. 北京:科学出版社,2002
[48] 程强,师忠秀等. 含间隙平面连杆机构的运动精度概率分析. 青岛大学学报(工程技术版), 2005,20(2):67-74
[49] Ming-June Tsai, Tiea-Hsing Lai. Kinematic Sensitivity Analysis of Linkage with Joint Clearance Based on Transmission Quality[J]. Mechanism and Machine Theory, 2004(39):1189-1206
[50] 靳春梅.含间隙机构非线性动态特性、控制及实验研究[D].西安:西安交通大学,2001.4
[2] 文荣等. 空间伸展机构动力学研究[J]. 导弹与航天运载技术, 1996,2:1-10
[3] 文荣等. 带间隙空间结构的动力学特性分析[J]. 中国空间科学技术, 1998, 1:7-12
[4] 陈滨等. 含铰接间隙与杆件柔性的空间伸展机构单元的动力学建模与计算模拟,第一部分:动力学建模[J]. 导弹与航天运载技术, 1997,1:27-37
[5] 陈滨等. 含铰接间隙与杆件柔性的空间伸展机构单元的动力学建模与计算模拟,第二部分:系统动态特性的计算模拟结果[J]. 导弹与航天运载技术, 1997,3:34-40
[6] Dubowsky S, Freudenstein F. Dynamic Analysis of Mechanical Systems with Clearance,Part1:Formation of Dynamic Model[J], Journal of Engineering for industry, 1971,93B(1):305-309
[7] Dubowsky S, FreudensteinF.Dynamic Analysis of Mechanical Systems with Clearance,Part 2:Dynamic Response[J], Trans. ASME, J.Eng.Ind, 1971, 93B(1): 310-316
[8] Dubowsky S, Gardner T N. Dynamic Interactions of Link Elasticity and Clearance Connections in Planar Mechanical Systems[J]. Journal of Engineering for industry, 1975,97B (2):652-661
[9] Dubowsky S et al. On the Development of Criteria for the Prediction of Impact in the Design of High Speed Systems with Clearances[A]. Proc. 5th world Cong[C]. IFTOMM, Canada,1979,968-971
[10] Dubowsky S et al. An Analytical and Experimental Study of the Prediction of Impacts in Planar Mechanical Systems with Clearances[J]. Trans.AMSE, J. Mech. Transmiss. Automat. Des.,1984,106(4):444-451
[11] Dubowsky S. On Predicting the Dynamic Effects of Clearances in Planar Mechanisms[J]. Trans. ASME, J. Eng. Ind. ,1974,96(1):317-323
[12] Dubowsky S. On Predicting the Dynamic Effects of Clearances in One-Dimensional Closed Loop Systems[J]. Trans. ASME, J. Eng. Ind. ,1974,96B:324-329
[13] Dubowsky S,Young S C. An Experimental and Analytical Study of Connection Forces in High-speed Mechanisms[J]. Journal of Engineering for industry,1975,97B:1166-1175
[14] Dubowsky S,Gardner T N., Design and Analysis of Multilink Flexible Mechanisms with Multiple Clearance Connections[J]. Trans. ASME, J.Eng. Ind. ,1977,99B:88-96
[15] Dubowsky S,Moening M F. An Experimental and Analytical Study of Impact Forces in Elastic Mechanical Systems with Clearances[J]. Mech.Mach.Theory, 1978,13:451-465
[16] Dubowsky S et al. The Dynamic Modeling of Flexible Spatial Mechine Systems with Clearance Connections[J]. Trans. ASME, J.Mech. Transmiss. Automat. Des.,1987,109:87-94
[17] Horie M. Dynamic Characteristics of Planar Link Mechanisms with Clearance[J]. Bulletin of JSME, 1986,29:1888-1894
[18] Funabashi H, Ogawa K, Horie M et al. A Dynamic Analysis of the Plane Crank-and-rocker Mechanisms with Clearances. Bulletin of the JSME, 1988, 23(177):446-452
[19] 李哲. 考虑运动副间隙和构件弹性的平面连杆机构动力学研究(博士学位论文).北京:北京工业大学,1991
[20] 唐锡宽,金德闻. 机械动力学[M]. 北京:高等教育出版社,1984
[21] 俞武勇,季林红等. 含间隙机构运动副的动力学模型[J]. 机械科学与技术. 2001,20(5):665-669
[22] Hunt K H, et al. Coefficient of Restitution Interpreted as Damping in Vibroimpact[J]. Journal of Applied Mechanics. 1975,42E:440-445
[23] Herbert R G, et al. Shape and Frequency Composition of Pulses from an Impact Pair[J]. Journal of Engineering for Industry. 1977,99B(8):513-518
[24] Yigit A S, et al. Spring-dashpot Models for the Dynamics of a Radially Rotating Beam with Impact[J]. Journal of sound and Vibration. 1990,142(3):515-525
[25] Lee T W, et al. On the Dynamic Interactions of Interm Intent Motion Mechanisms, part 1:Dynamic model and response[J]. Journal of Mechanisms, Transmissions, and Automation in Design, 1983,105(3):527-539
[26] Wang Yu,et al. Dynamic Analysis of Flexible Mechanisms with Clearance[J] Journal of Mechanical Design. 1996,118:592-594
[27] Furuhashi T, et al. Research on Dynamic of Four-bar Linkage with Clearance at Turning Pairs (4th Report, Forces Acting at Joints of Crank-lever Mechanism)[J]. Bulletin of the JSME,1978,21(158):1299-1305
[28] Eleonor D. Stoenescu,Dan B. Marghitu. Dynamic Analysis of a Planar Rigid-linkMechanism with Rotating Slider Joint and Clearance. Journal of sound and Vibration. 2003(266):394-404
[29] Mansour W M, et al. Impact Spectra and Intensities for High-speed Mechanisms[J]. Journal of Engineering for Industry, 1975,97B(2):347-353
[30] Zakhariev E. Dynamics of Rigid Multibody Systems with Clearance in the Joints[J]. Mechanics of Structures and Machine, 1999,27(1):63-87
[31] Earles S.W.E, et al. Motion Analysis of a Rigid-link Mechanism with Clearance at a Bearing, Using Lagrangian Mechanics and Digital Computation[A]. In: Conference on Mechanisms,ME[C],London,England,1972:83-89
[32] Jungkeun R, et al. Dynamic Response of a Revolute Joint with Clearance[J]. Mechanics and Machinery Theory, 1996,31(1):121-134
[33] Bajkow skiJ ,et al. Application FEM in Modeling Rigid and Flexible Systems with Joint Clearances[J]. Shock and Vibration Digest, 2000,32(1):63-68
[34] 张跃明等. 考虑构件弹性和转动副间隙的空间机构动力学研究[J]. 机械科学与技术, 1999,18(4):532-534
[35] Seneviratne L D, et al. Analysis of a Four-bar Mechanism with a Radially Compliant Clearance Joint[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 1996,210(3):372-378
[36] 余跃庆,李哲. 现代机械动力学[M]. 北京工业大学出版社,1998.12
[37] 王国庆,刘宏昭等 . 含间隙连杆机构非线性行为研究 . 机械设计 , 2005,33(4):23-25
[38] 王国庆,刘宏昭等. 非线性接触模型在多间隙机构混沌分析中的应用. 机械科学与技术,2005,24(6):636-638
[39] 黄铁球,吴德隆等. 带间隙伸展机构的非线性动力学建模. 中国空间科学技术, 1999(1):7-13
[40] 黄铁球,阎绍泽等. 空间站伸展机构的非线性动态相应分析. 非线性动力学学报,1998,5(1):36-41
[41] 朱巨才,符炜. 用无质量杆-弹簧阻尼组合模型(MLSD 模型)对间隙机构进行分析的方法探讨. 机械科学与技术,2004,23(4):450-453
[42] P. Flores,J. Ambrosio. Revolute Joints with Clearance in Multibody Systems[J]. Computers and Structures, 2004(82)1359-1369
[43] P. Flores,J. Ambrosio. A Study on Dynamics of Mechanical Systems Including Joints with Clearance and Lubrication[J]. Mechanism and Mechine theory, 2006(41):247-261
[44] 尉立肖,刘才山. 圆柱铰间隙运动学分析及动力学仿真. 北京大学学报(自然科学版),2005,41(5):679-687
[45] 阎绍泽,申永胜等. 考虑杆件柔性和铰间隙的可展结构动力学数值模拟. 清华大学学报(自然科学版), 2003,43(2):145-148
[46] 黄昭度,纪辉玉. 分析力学[M]. 北京:清华大学出版社,1985
[47] 王振发. 分析力学[M]. 北京:科学出版社,2002
[48] 程强,师忠秀等. 含间隙平面连杆机构的运动精度概率分析. 青岛大学学报(工程技术版), 2005,20(2):67-74
[49] Ming-June Tsai, Tiea-Hsing Lai. Kinematic Sensitivity Analysis of Linkage with Joint Clearance Based on Transmission Quality[J]. Mechanism and Machine Theory, 2004(39):1189-1206
[50] 靳春梅.含间隙机构非线性动态特性、控制及实验研究[D].西安:西安交通大学,2001.4