船舶尾轴与机械密封装置工作状态耦合特性研究
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摘要
机械密封在船舶尾轴密封的应用越来越广泛,同时,由于主机的大型化、尾轴长度与重量的增加,尾轴运动特性更加复杂。为了确保船舶运行的可靠性,有必要准确分析影响尾轴动力学特性的因素,目前已经逐渐认识到轴承与密封装置影响尾轴的振动特性,在诸个非线性因素中,油膜力与密封力是关键的两个。
本文利用Jeffcott转子模型,分析密封力的单独作用、轴承油膜力与密封力耦合作用两种情况下转子的动力特性,主要研究内容如下。
(1)艉轴推进系统是非线性动力学系统,因此,首先介绍了非线性转子动力学相关的基本理论以及本文采用的非线性油膜力与密封力模型。
(2)研究单圆盘转子—密封系统的Jeffcott模型,求解密封力作用下系统的响应,讨论了振幅随转速的变化趋势,利用时程历程曲线图、轴心轨迹图及Poincare映射图、功率谱密度图反映系统的动力学特性,并分析密封压差、密封间隙、转子偏心量、密封长度四种因素对转子动力学特性的影响。
(3)运用转子—轴承—机械密封系统的模型,求解了油膜力与密封力的耦合作用下系统的响应,分析了振幅随转速的变化趋势,利用时程历程曲线图、轴心轨迹图、功率谱密度图、Poincare映射图来反映系统的动力学特性,分析密封压差、密封间隙、转子偏心量、密封长度、轴承间隙、轴承长度六种因素对转子运动的影响。通过比较分析得出保持系统稳定的参数范围,为推进系统设计与选型提供了理论依据。
(4)介绍了转子稳定性判断的常用的三种方法,即相平面法、最大Lyapunov指数法、Floquet乘子法,列出了求取对应系统最大Lyapunov指数和Floquet乘子的一般范式。
最后对全文的研究工作进行了总结,提出了今后需要进一步研究的方向与任务。
The mechanical seal is widely used in the stern seal of shaft. Meanwhile, the size of marines and the weight & length of stern shaft are becoming large, and dynamic properties of stern shaft are more complicate. So as to insure the reliability of operating, reasonable analysis of factors, which influences the dynamic properties of stern shaft, should be taken. It is gradually known that bearings and seals influence the vibration characteristics of stern shaft, and oil-film force and seal fluid force are two key factors among the given nonlinear ones.
The model of Jeffcott rotor is applied, and the dynamic response of rotor under the ict of seal fluid force is analyzed. Conclusions are summarized as follows:
(1) Because the shaft system in the dissertation is nonlinear dynamic system, it is introduced basic nonlinear theory used frequently in the study on dynamics of rotor, model of nonlinear oil-film force and seal-fluid force in the paper.
(2) Nonlinear response of single Jeffcott rotor excited by seal force is studied. It comes out that the amplitude varies with the rotor speed. The time histories, tracks of the rotor center, power density and Poincare maps are used to illustrate the dynamic characteristics and the influences of varying pressure, eccentricity, seal length and clearance.
(3) The response of the rotor-bearing-mechanical seal system is solved under the seal fluid force coupled with oil-film force. The discussion shows the amplitude is varied with the rotor speed. Time histories, tracks of the rotor center, power density and Poincare maps are used to demonstrate the dynamic features. The influences of varying pressure, eccentricity, seal length and clearance, rotor clearance and length are analyzed, and the range of parameters used to keep the system stable is gotten, which provides theoretical basis for design and choice of devices.
(4) Three methods to judge the stability of rotors are introduced, which are Phase plane method, Maximum Lyapunov exponent and Floquet multipliers. In final the methods of getting Maximum Lyapunov exponent and Floquet multipliers of corresponding systems are introduced.
At the end of the dissertation, research works to bring forth new ideas for the dissertation are summarized, and the research problems to go to a step further are pointed out.
本文利用Jeffcott转子模型,分析密封力的单独作用、轴承油膜力与密封力耦合作用两种情况下转子的动力特性,主要研究内容如下。
(1)艉轴推进系统是非线性动力学系统,因此,首先介绍了非线性转子动力学相关的基本理论以及本文采用的非线性油膜力与密封力模型。
(2)研究单圆盘转子—密封系统的Jeffcott模型,求解密封力作用下系统的响应,讨论了振幅随转速的变化趋势,利用时程历程曲线图、轴心轨迹图及Poincare映射图、功率谱密度图反映系统的动力学特性,并分析密封压差、密封间隙、转子偏心量、密封长度四种因素对转子动力学特性的影响。
(3)运用转子—轴承—机械密封系统的模型,求解了油膜力与密封力的耦合作用下系统的响应,分析了振幅随转速的变化趋势,利用时程历程曲线图、轴心轨迹图、功率谱密度图、Poincare映射图来反映系统的动力学特性,分析密封压差、密封间隙、转子偏心量、密封长度、轴承间隙、轴承长度六种因素对转子运动的影响。通过比较分析得出保持系统稳定的参数范围,为推进系统设计与选型提供了理论依据。
(4)介绍了转子稳定性判断的常用的三种方法,即相平面法、最大Lyapunov指数法、Floquet乘子法,列出了求取对应系统最大Lyapunov指数和Floquet乘子的一般范式。
最后对全文的研究工作进行了总结,提出了今后需要进一步研究的方向与任务。
The mechanical seal is widely used in the stern seal of shaft. Meanwhile, the size of marines and the weight & length of stern shaft are becoming large, and dynamic properties of stern shaft are more complicate. So as to insure the reliability of operating, reasonable analysis of factors, which influences the dynamic properties of stern shaft, should be taken. It is gradually known that bearings and seals influence the vibration characteristics of stern shaft, and oil-film force and seal fluid force are two key factors among the given nonlinear ones.
The model of Jeffcott rotor is applied, and the dynamic response of rotor under the ict of seal fluid force is analyzed. Conclusions are summarized as follows:
(1) Because the shaft system in the dissertation is nonlinear dynamic system, it is introduced basic nonlinear theory used frequently in the study on dynamics of rotor, model of nonlinear oil-film force and seal-fluid force in the paper.
(2) Nonlinear response of single Jeffcott rotor excited by seal force is studied. It comes out that the amplitude varies with the rotor speed. The time histories, tracks of the rotor center, power density and Poincare maps are used to illustrate the dynamic characteristics and the influences of varying pressure, eccentricity, seal length and clearance.
(3) The response of the rotor-bearing-mechanical seal system is solved under the seal fluid force coupled with oil-film force. The discussion shows the amplitude is varied with the rotor speed. Time histories, tracks of the rotor center, power density and Poincare maps are used to demonstrate the dynamic features. The influences of varying pressure, eccentricity, seal length and clearance, rotor clearance and length are analyzed, and the range of parameters used to keep the system stable is gotten, which provides theoretical basis for design and choice of devices.
(4) Three methods to judge the stability of rotors are introduced, which are Phase plane method, Maximum Lyapunov exponent and Floquet multipliers. In final the methods of getting Maximum Lyapunov exponent and Floquet multipliers of corresponding systems are introduced.
At the end of the dissertation, research works to bring forth new ideas for the dissertation are summarized, and the research problems to go to a step further are pointed out.
引文
[1]孙保苍.轴承-转子系统非线性动力学若干问题研究[M].南京:南京航空航天大学机械工程系.2002,12:8-64.
[2]李永.转子-轴承-密封系统的非线性振动与分岔[M].大连:大连理工大学,2007,6:8-44.
[3]闻梆春,顾家柳,夏松波等.高等转子动力学-理论、技术与应用.北京:机械工业出版社,2001.
[4]钟一谔,何衍宗,王正等.转子动力学.北京:清华大学出版社,1987.
[5]张文,郑铁生,马建敏等.油膜轴承瞬态非线性油膜力的力学建模及其表达式.自然科学进展,2002,12,(3):1-4.
[6]张直明,张言羊,谢友柏.滑动轴承的流体动力润滑理论.北京:高等教育出版社,1986.
[7]郭建萍,邱鹏庆,崔升等.有限长轴承非稳态油膜力建模及其非线性油膜失稳.振动工程学报,2001,14,(1):1-4
[8]孙保苍,席慧玲,周传荣.有限宽轴承-转子系统非线性行为研究.力学与实践,2004,26(4):1-4
[9]孙大成.润滑力学讲义.北京:中国友谊出版公司,1991.
[10]池长青.流体力学润滑.北京:国防工业出版社,1998.
[11]Leck A O.A Study of Contacting Mechanical Face Seal Performance Data using Mixed Friction Models[C].Proceedings of 12th ICFS 1989:271-289.
[12][苏]A.H.戈卢别夫.端面密封及动力密封[M].北京:化学工业出版社,1968:53-64.
[13]顾永泉.机械端面密封.北京:石油大学出版社,1994.
[14]徐华.机械密封对转子轴承系统动力学性能的影响.西安交通大学学报,2004,38(7):1-5.
[15]He Lidong,Xia Songbo.A study of the mechanism and application of damper seals in turbo machinery.In:Proceedings of the Asia-Pacific Vibration Conference 97,Korea,1997,836-841.
[16]A Muszynska.Stability of whirl and whip in rotor/bearing systems.Journal of Sound and vbration,1988,127(1):49-64.
[17]A Muszynska,D E Bently.Anti-swirl Arrangements prevent rotor/seal instability.Journal of Vibration,Acoustics,Stress and Reliability in Design,1989,v111,156-161.
[18]G.ADILETTA,A.R.GUIDO,C.ROSSI.Chaotic motions of a rigid rotor in short journal Bearings[J].Nonlinear Dynamics,1996(10):251-269.
[19]孙保苍,席慧玲,周传荣.有限宽轴承-转子系统非线性行为研究.力学与实践,2004,26(4):1-4.
[20]陈予恕,于千,孟泉.非线性转子的低频振动失稳机理分析,应用力学学报,1998,15(1):113-116
[21]陈予恕,孟泉.非线性转子-轴承系统的分岔,振动工程学报,1996,9(3):266-275.
[22]武新华,张新江,薛小平等.弹性转子-轴承系统的非线性动力学研究.中国机械工程,2001,12(11):1221-1223.
[23]孙保苍,周传荣,陈章耀.非稳态油膜力作用下轴承-转子系统非线性动力学行为研究.机械科学与技术,2003,22(5):708-709.
[24]Gardner M,Myers,Savage M.Analysis of limit-cycle response in fluid-film Jounal Bearing Using the Method of Multiple Scales.The Quarterly Journal of Mechanics and applied Mathematics,1985,38:27-45.
[25]Adams M L,Abu-Mahfouz IA.Exploratory research on chaos concepts as diagnostic tools for assessing rotating machinery vibration signatures.Proceeding of IfoMM Fourth International Conference on Rotor Dynamics,Chicago.USA,1994:29-39.
[26]成玫,孟光,荆建平.转子-轴承-密封系统的非线性动力学行为.振动与冲击,2006,25,(5):1-4
[27]李松涛,许庆余,万方义.迷宫密封转子系统非线性动力稳定性的研究.应用力学学报,2002,19(2):1-3.
[28]于千,陈予恕.非线性转子-密封系统的亚谐共振失稳机理研究.Journal of Vibration Engineering,1997,10(4):1-5.
[29]Sanchez N E,Nayfeh A H.Global behavior of biased nonlinear oscillator under external and parametric exciations.Journal of Sound and Vibration,1997,207(2):137-149.
[30]Padmanabhan C,Singh R.Analysis of periodically excited nonlinear system by a parametric continuation technique.Journal of Sound and Vibration,1995,184(1):35-58.
[31]刘恒,陈绍汀.非线性系统全局动态特性分析的PCM法及其在转子轴承系统中的应用.应用力学学报,1995,12(3):7-15.
[32]金俐,陆启韶,王琪.非光滑动力系统Floquet特征乘子的计算方法.应用力学学报,2004,21(3):2-6.
[33]张卫.运用Lyapunov第二方法研究转子系统的运动稳定性.暨南大学学报,2006,27(5):4-6.
[34]骆天舒,王双连,郭乙木.高维动力系统在转子稳定性分析中的应用.浙江大学学报,2007,41(6):1-4.
[35]张文.转子动力学理论基础.北京:科学出版社,1990.
[36]刘延柱,陈立群.非线性振动.西安:西安交通大学出版社,2001.
[37]高为炳.运动稳定性基础.北京:高等教育出版社,1985.
[38]孙祥,徐流美,吴清.MATLAB 7.0基础教程.北京:清华大学出版社.
[39]王能超.数值分析简明教程.北京:高等教育出版社,1984,10.
[40]Xiaoyao Shen,Jiuhong Jia,Mei Zhao.Experimental and numerical analysis of nonlinear dynamics of rotor-bearing-seal system[J].Nonlinear Dyn.,2008(53):31-44.
[41]Mei Cheng,Guang Meng,Jianping Jing.Non-linear dynamics of a rotor-bearing-seal system[J].Arch Appl Mech,2006(76):215-227
[42]Tom Lai.Development of Non-contacting,Non-leaking Spiral Groove Liqiud Face Seals[J].Lubrication Engineering,1994,50(8).
[43]T.G.Roust,An Experimental and Theoretical Study of Pressure and Thermal Distortions in a Mechanical Seal,ASLE Transactions,1986,29(2):151-159.
[44]Shaw J,Shaws.S.W..Instability and bifurcation in a rotating shaft.Jounal of Sound and Vibration,1989,132(2):227-244.
[45]Lund J.W,Nielsen H.B.Instability threshold of a unbalanced rigid rotor in short jounal bearing.Second International conference on Vibrations in Rotating Machinery,C263/80,IMECHE,Cambridge September,1980.
[46]A Muszyska,D E Bently.Frequency-swept rotating input perturbation techniques and identification of fluid force models in rotor/bearing/seal systems and fluid handing machines.Journal of Sound and Vibraton,1990,143(1):103-124.
[47]A Muszyska.Model testing of rotor/bearing systems.The international Jounal of Analytical and Experimental Model Analysis,1986,1(3):15-34.
[48]Songtao Li,Qingyu xu,Xiaolong Zhang.Nonlinear dynamic behaviors of a rotor-labyinth seal system.Nonlinear Dyn,2007,47(10):321-329.
[49]Guangchi Ying,Guang Meng,Jianping Jing.Turbocharger rotor dynamics with foundation excitation.Arch Appl Mech,2008,(10):1-4.
[50]向小东,郭耀煌.混沌时间序列最大Lyapunov指数的计算.预测,2001,20(5):2-3.
[51]杨银环.200MW汽轮机低压段转子一轴承系统的非线性动力学分析[M].哈尔滨:哈尔滨工业大学,2006,6.
[2]李永.转子-轴承-密封系统的非线性振动与分岔[M].大连:大连理工大学,2007,6:8-44.
[3]闻梆春,顾家柳,夏松波等.高等转子动力学-理论、技术与应用.北京:机械工业出版社,2001.
[4]钟一谔,何衍宗,王正等.转子动力学.北京:清华大学出版社,1987.
[5]张文,郑铁生,马建敏等.油膜轴承瞬态非线性油膜力的力学建模及其表达式.自然科学进展,2002,12,(3):1-4.
[6]张直明,张言羊,谢友柏.滑动轴承的流体动力润滑理论.北京:高等教育出版社,1986.
[7]郭建萍,邱鹏庆,崔升等.有限长轴承非稳态油膜力建模及其非线性油膜失稳.振动工程学报,2001,14,(1):1-4
[8]孙保苍,席慧玲,周传荣.有限宽轴承-转子系统非线性行为研究.力学与实践,2004,26(4):1-4
[9]孙大成.润滑力学讲义.北京:中国友谊出版公司,1991.
[10]池长青.流体力学润滑.北京:国防工业出版社,1998.
[11]Leck A O.A Study of Contacting Mechanical Face Seal Performance Data using Mixed Friction Models[C].Proceedings of 12th ICFS 1989:271-289.
[12][苏]A.H.戈卢别夫.端面密封及动力密封[M].北京:化学工业出版社,1968:53-64.
[13]顾永泉.机械端面密封.北京:石油大学出版社,1994.
[14]徐华.机械密封对转子轴承系统动力学性能的影响.西安交通大学学报,2004,38(7):1-5.
[15]He Lidong,Xia Songbo.A study of the mechanism and application of damper seals in turbo machinery.In:Proceedings of the Asia-Pacific Vibration Conference 97,Korea,1997,836-841.
[16]A Muszynska.Stability of whirl and whip in rotor/bearing systems.Journal of Sound and vbration,1988,127(1):49-64.
[17]A Muszynska,D E Bently.Anti-swirl Arrangements prevent rotor/seal instability.Journal of Vibration,Acoustics,Stress and Reliability in Design,1989,v111,156-161.
[18]G.ADILETTA,A.R.GUIDO,C.ROSSI.Chaotic motions of a rigid rotor in short journal Bearings[J].Nonlinear Dynamics,1996(10):251-269.
[19]孙保苍,席慧玲,周传荣.有限宽轴承-转子系统非线性行为研究.力学与实践,2004,26(4):1-4.
[20]陈予恕,于千,孟泉.非线性转子的低频振动失稳机理分析,应用力学学报,1998,15(1):113-116
[21]陈予恕,孟泉.非线性转子-轴承系统的分岔,振动工程学报,1996,9(3):266-275.
[22]武新华,张新江,薛小平等.弹性转子-轴承系统的非线性动力学研究.中国机械工程,2001,12(11):1221-1223.
[23]孙保苍,周传荣,陈章耀.非稳态油膜力作用下轴承-转子系统非线性动力学行为研究.机械科学与技术,2003,22(5):708-709.
[24]Gardner M,Myers,Savage M.Analysis of limit-cycle response in fluid-film Jounal Bearing Using the Method of Multiple Scales.The Quarterly Journal of Mechanics and applied Mathematics,1985,38:27-45.
[25]Adams M L,Abu-Mahfouz IA.Exploratory research on chaos concepts as diagnostic tools for assessing rotating machinery vibration signatures.Proceeding of IfoMM Fourth International Conference on Rotor Dynamics,Chicago.USA,1994:29-39.
[26]成玫,孟光,荆建平.转子-轴承-密封系统的非线性动力学行为.振动与冲击,2006,25,(5):1-4
[27]李松涛,许庆余,万方义.迷宫密封转子系统非线性动力稳定性的研究.应用力学学报,2002,19(2):1-3.
[28]于千,陈予恕.非线性转子-密封系统的亚谐共振失稳机理研究.Journal of Vibration Engineering,1997,10(4):1-5.
[29]Sanchez N E,Nayfeh A H.Global behavior of biased nonlinear oscillator under external and parametric exciations.Journal of Sound and Vibration,1997,207(2):137-149.
[30]Padmanabhan C,Singh R.Analysis of periodically excited nonlinear system by a parametric continuation technique.Journal of Sound and Vibration,1995,184(1):35-58.
[31]刘恒,陈绍汀.非线性系统全局动态特性分析的PCM法及其在转子轴承系统中的应用.应用力学学报,1995,12(3):7-15.
[32]金俐,陆启韶,王琪.非光滑动力系统Floquet特征乘子的计算方法.应用力学学报,2004,21(3):2-6.
[33]张卫.运用Lyapunov第二方法研究转子系统的运动稳定性.暨南大学学报,2006,27(5):4-6.
[34]骆天舒,王双连,郭乙木.高维动力系统在转子稳定性分析中的应用.浙江大学学报,2007,41(6):1-4.
[35]张文.转子动力学理论基础.北京:科学出版社,1990.
[36]刘延柱,陈立群.非线性振动.西安:西安交通大学出版社,2001.
[37]高为炳.运动稳定性基础.北京:高等教育出版社,1985.
[38]孙祥,徐流美,吴清.MATLAB 7.0基础教程.北京:清华大学出版社.
[39]王能超.数值分析简明教程.北京:高等教育出版社,1984,10.
[40]Xiaoyao Shen,Jiuhong Jia,Mei Zhao.Experimental and numerical analysis of nonlinear dynamics of rotor-bearing-seal system[J].Nonlinear Dyn.,2008(53):31-44.
[41]Mei Cheng,Guang Meng,Jianping Jing.Non-linear dynamics of a rotor-bearing-seal system[J].Arch Appl Mech,2006(76):215-227
[42]Tom Lai.Development of Non-contacting,Non-leaking Spiral Groove Liqiud Face Seals[J].Lubrication Engineering,1994,50(8).
[43]T.G.Roust,An Experimental and Theoretical Study of Pressure and Thermal Distortions in a Mechanical Seal,ASLE Transactions,1986,29(2):151-159.
[44]Shaw J,Shaws.S.W..Instability and bifurcation in a rotating shaft.Jounal of Sound and Vibration,1989,132(2):227-244.
[45]Lund J.W,Nielsen H.B.Instability threshold of a unbalanced rigid rotor in short jounal bearing.Second International conference on Vibrations in Rotating Machinery,C263/80,IMECHE,Cambridge September,1980.
[46]A Muszyska,D E Bently.Frequency-swept rotating input perturbation techniques and identification of fluid force models in rotor/bearing/seal systems and fluid handing machines.Journal of Sound and Vibraton,1990,143(1):103-124.
[47]A Muszyska.Model testing of rotor/bearing systems.The international Jounal of Analytical and Experimental Model Analysis,1986,1(3):15-34.
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