板带轧机空间振动特性研究
|
摘要
四/六辊板带轧机共振及颤振现象在全世界范围内一直未得到有效解决，且轧机设计理论也未能给出轧机振动特性技术参数。历来轧机振动研究不区分轧机辊系是否稳定，均以稳定轧机建立力学模型，将轧辊垂直、水平、轴向、扭转、交叉及摇摆的空间振动行为作为各单一振动的耦合模式加以分析。为了抑制甚至消除轧机振动，本文从区分轧机辊系的稳定性和空间振动行为的思路出发研究轧机振动特性。
首先，采用空间传递矩阵法作为轧机振动数值解析方法，并根据轧机多辊叠加的结构特点开发适合于轧机系统的多层多体系统空间传递矩阵法；同时以不同稳定性的两种二辊高刚度轧机为算例，利用上述方法对其进行空间振动解析并开展振动测试实验验证数值结果，最终建立空间传递矩阵法。
其次，建立1580四辊热轧机的空间振动力学模型和有限元模型，同时考虑轧机部件间阻尼影响，运用上述空间传递矩阵法和有限元法对具有不同稳定性的两种轧机进行空间振动特性数值解析和仿真，并对比其固有振动特性，分析结果表明辊系间隙对轧机固有频率和振型的重要影响。进行轧机在线振动测试实验，一方面验证以上数值计算和仿真结果，另一方面从轧机的拍振及共振现象认知中提出1580mm四辊板带热轧机的自激振动机理，即在大压下率条件下，辊缝前、后滑区内轧件对轧辊做功不等进而引发负阻尼自激振动。从控制轧制工艺参数和改进轧机结构两方面提出抑制轧机振动的方法。
最后，对650六辊冷轧机建立稳定性不同的两类轧机的空间振动模型，并利用空间传递矩阵法开展振动特性解析。开展650轧机的现场振动测试实验，验证数值结果的同时，探讨了引发薄带表面大斜浪板型的激励源并提出相应改进措施。
综上所述，轧机空间振动及其数值解析法、辊缝前后滑区内的负阻尼自激振动机理及轧机抑振法的提出对轧机振动理论研究和实际轧制生产抑振具有重要的理论意义和工程应用价值。
The resonant and chatter vibrations of4/6-h cold and hot rolling mills worldwidehave not been solved yet so far. Technical parameters about natural vibrationcharacteristics of rolling mills have not been given in design theory of the mill. Thestability of the roll system is not concerned in traditional research about mill vibrations,namely that the mechanical model of the mill is all built on stable rolling mill. Meanwhile,the spatial vibration behaviors involving vertical, horizontal, axial, torsional, cross andswinging vibration are analyzed as coupled vibration behaviors of single vibration. Tocontrol or even eliminate mill vibration, the new research about mill vibration is from thethought of stability of roll system and spatial behaviors of the mill.
First, the spatial transfer matrix method is selected for vibration analysis of the mill.The multilayer and multi-body spatial transfer matrix method is built according to thestructural characteristics of more rolls. The two2-h rolling mills with different stability ofroll system are taken as examples and the spatial vibration analysis is conducted usingmentioned method. Meanwhile, the field test experiment is done as well to validatenumerical results. Finally, the spatial vibration transfer matrix method is built.
Secondly, considering the effect of damping, the spatial vibration models of the1580hot plate4-h mill, including mechanical model and FEM model, are built. For two rollingmills with different stability of roll system, the numerical analysis and simulation aboutspatial vibration characteristics are conducted using transfer matrix method and finiteelement method. The comparison between vibration characteristics of two mills is doneand the effect of clearance on natural frequency and mode shape is demonstrated. Thefield test experiment is done to validate numerical calculation and simulation. Meanwhile,the self-excited vibration mechanism for the1580mill is proposed form the recognition ofbeat and resonant vibration phenomenon, i.e., self-excited vibration caused by negativedamping occurring in forward and backward slip zone of roll gap is generated due tounequal work that the strip exerts on the roll under heavy reduction rate. Vibration controlmethods are proposed from technical parameter controlling and modification of mill structure.
Finally, the spatial vibration models of two650cold plate4-h mills with differentstability of roll system are built and the numerical analysis about spatial vibrationcharacteristics is conducted using transfer matrix method. The field test experiment isdone simultaneously to validate numerical results and discuss excitation source whichcauses big inclined wave on strip surface, and the corresponding modified vibrationcontrol methods are proposed.
In conclusion, the spatial vibration and its numerical analytical method, self-excitedvibration mechanism caused by negative damping occurring in forward and backward slipzone, and presentation of vibration control method have a great theoretical andengineering application value for the theoretical research of mill vibration and practicalproduction vibration controlling.
首先，采用空间传递矩阵法作为轧机振动数值解析方法，并根据轧机多辊叠加的结构特点开发适合于轧机系统的多层多体系统空间传递矩阵法；同时以不同稳定性的两种二辊高刚度轧机为算例，利用上述方法对其进行空间振动解析并开展振动测试实验验证数值结果，最终建立空间传递矩阵法。
其次，建立1580四辊热轧机的空间振动力学模型和有限元模型，同时考虑轧机部件间阻尼影响，运用上述空间传递矩阵法和有限元法对具有不同稳定性的两种轧机进行空间振动特性数值解析和仿真，并对比其固有振动特性，分析结果表明辊系间隙对轧机固有频率和振型的重要影响。进行轧机在线振动测试实验，一方面验证以上数值计算和仿真结果，另一方面从轧机的拍振及共振现象认知中提出1580mm四辊板带热轧机的自激振动机理，即在大压下率条件下，辊缝前、后滑区内轧件对轧辊做功不等进而引发负阻尼自激振动。从控制轧制工艺参数和改进轧机结构两方面提出抑制轧机振动的方法。
最后，对650六辊冷轧机建立稳定性不同的两类轧机的空间振动模型，并利用空间传递矩阵法开展振动特性解析。开展650轧机的现场振动测试实验，验证数值结果的同时，探讨了引发薄带表面大斜浪板型的激励源并提出相应改进措施。
综上所述，轧机空间振动及其数值解析法、辊缝前后滑区内的负阻尼自激振动机理及轧机抑振法的提出对轧机振动理论研究和实际轧制生产抑振具有重要的理论意义和工程应用价值。
The resonant and chatter vibrations of4/6-h cold and hot rolling mills worldwidehave not been solved yet so far. Technical parameters about natural vibrationcharacteristics of rolling mills have not been given in design theory of the mill. Thestability of the roll system is not concerned in traditional research about mill vibrations,namely that the mechanical model of the mill is all built on stable rolling mill. Meanwhile,the spatial vibration behaviors involving vertical, horizontal, axial, torsional, cross andswinging vibration are analyzed as coupled vibration behaviors of single vibration. Tocontrol or even eliminate mill vibration, the new research about mill vibration is from thethought of stability of roll system and spatial behaviors of the mill.
First, the spatial transfer matrix method is selected for vibration analysis of the mill.The multilayer and multi-body spatial transfer matrix method is built according to thestructural characteristics of more rolls. The two2-h rolling mills with different stability ofroll system are taken as examples and the spatial vibration analysis is conducted usingmentioned method. Meanwhile, the field test experiment is done as well to validatenumerical results. Finally, the spatial vibration transfer matrix method is built.
Secondly, considering the effect of damping, the spatial vibration models of the1580hot plate4-h mill, including mechanical model and FEM model, are built. For two rollingmills with different stability of roll system, the numerical analysis and simulation aboutspatial vibration characteristics are conducted using transfer matrix method and finiteelement method. The comparison between vibration characteristics of two mills is doneand the effect of clearance on natural frequency and mode shape is demonstrated. Thefield test experiment is done to validate numerical calculation and simulation. Meanwhile,the self-excited vibration mechanism for the1580mill is proposed form the recognition ofbeat and resonant vibration phenomenon, i.e., self-excited vibration caused by negativedamping occurring in forward and backward slip zone of roll gap is generated due tounequal work that the strip exerts on the roll under heavy reduction rate. Vibration controlmethods are proposed from technical parameter controlling and modification of mill structure.
Finally, the spatial vibration models of two650cold plate4-h mills with differentstability of roll system are built and the numerical analysis about spatial vibrationcharacteristics is conducted using transfer matrix method. The field test experiment isdone simultaneously to validate numerical results and discuss excitation source whichcauses big inclined wave on strip surface, and the corresponding modified vibrationcontrol methods are proposed.
In conclusion, the spatial vibration and its numerical analytical method, self-excitedvibration mechanism caused by negative damping occurring in forward and backward slipzone, and presentation of vibration control method have a great theoretical andengineering application value for the theoretical research of mill vibration and practicalproduction vibration controlling.
引文
[1]苏小新.铝板带单机架双卷取四辊热轧机的应用前景[J].有色金属加工,2000,1:9-11.
[2] Cao J G, Liu S J, Zhang J, et al. ASR Work Roll Shifting Strategy for Schedule-Free Rolling in HotWide Strip Mills[J]. Journal of Materials Processing Technology,2011,11(211):1768-1775.
[3]王国栋，刘向华，王君.我国中厚板生产技术20年[J].轧钢,2004,6(2):5-9.
[4]李学通，吴志贺，杜凤山，等.四辊平整机轧制过程辊系变形有限元分析[J].塑性工程学报,2008,2(15):126-130.
[5] Okamura Y, Hoshino I. State Feedback Control of the Strip Steering for Aluminum Hot RollingMill[J]. Control Engineering Practice,1997,8(5):1035-1042.
[6]钟掘，杨勇学，古可，等.1600高速铝带轧机扭振研究[J].冶金设备,1986,3:1-7.
[7] Yukio K, Yasuhiro S, Nobuo N, et al. Analysis of Chatter in Tandem Cold Rolling Mills[J]. ISIJInternational,2003(43):77-84.
[8] Zhong J, Yan H Z, Duan J A, et al. Industrial Experiments and Findings on Temper RollingChatter[J]. Journal of Materials Processing Technology,2002(120):275-280.
[9] Kim Y S, Zhang N, Ji J C, et al. The Effect of Tension Variation in the Dynamic Roll Gap on ColdRolling Mill Stability[C].9th International Rolling Conference, Venice, Italy,2003: Poster#37.
[10] Hu P H, Ehmann K. Stability Analysis of Chatter on a Tandem Rolling Mill[J]. Journal ofManufacturing Processes,2000,4(2):217-224.
[11] Tamaoki T, Takanezawa M, Kimoto M, et al. Study on Online Analysis of Transfer Function ofVariable-Speed Rolling Mill Motor with Shaft Torsional Vibration Systems[J]. IEEJ Transactionson Industry Applications,2011,6(131):844-857.
[12]叶黔元，郑七振，鲁晓燕.冷连轧机的振动分析及改善方法[J].振动工程学报,2004(17):825-827.
[13]唐华平，李旭宇，钟掘.轧机扭转自激振动分析[J].湘潭矿业学院学报,2002,2(17):21-24.
[14] Nizio J, Swiatoniowski A. Numerical Analysis of the Vertical Vibrations of Rolling Mills and theirNegative Effect on the Sheet Quality[J]. Journal of Materials Processing Technology,2005(162-163):546-550.
[15]杨其俊，连家创.高速冷带轧机垂直自激振动稳定性分析的数值计算方法[J].振动与冲击,1996,3(15):16-21.
[16] Alok1D. Case Study Systematic Approach for Elimination of Vibrations in Gap FormerWire-Section to Speed-Up the Machine[J]. Quarterly Journal of Indian Pulp and Paper TechnicalAssociation,2010(4),151-154.
[17]范小彬，臧勇，王会刚.热连轧机水平振动特性研究[J].钢铁,2010,9(45):62-66.
[18]唐华平，钟掘.单辊驱动轧机水平自激振动定性分析[J].机械工程学报,2001,8(37):55-59.
[19] Yun I S, Wilson W R D. Review of Chatter Studier in Cold Rolling[J]. Journal of Machine Tools&Manufacture,1998,(38):1499-1530.
[20]杜国君，张忠建，高崇一.考虑打滑和双间隙影响的厚板轧机主传动系统扭振[J].钢铁,2013,2(48):39-43.
[21]申延智，刘宏民，熊杰，等.厚板轧机含间隙主传动系统混沌动力学分析[J].工程力学,2010,7(27):232-236.
[22]申延智，杜国君，张渡仙，等.基于辊缝耦合的轧机主传动系统扭振研究[J].钢铁,2010,4(45):56-59.
[23]李怀志.考虑齿轮啮合刚度的轧机主传动系统动力学特性研究[D].沈阳：东北大学硕士学位论文2008：7-11.
[24]陈勇辉，刘世元，廖广兰.四辊冷带轧机三倍频颤振机理的研究[J].机械工程学报,2003,6(39):118-123.
[25]陈勇辉，李巍华，史铁林，等.四辊冷带轧机五倍频再生颤振机理的研究颤振[J].钢铁,2003,15(31):55-57.
[26] Wei L Q, Qu Z H, Zhang X Y, et al. Influence of Rolling Lubrication on Self-Excited Vibration in1420Continuous Cold Rolling Mill[C].9th International Rolling Conference, Venice, Italy,2003:(paper number28, no pages).
[27]高亚男，彭艳，孙建亮，等.1580热连轧机F2精轧机振动综合测试与分析[J].钢铁,2013,1(48):1-7.
[28]杨其俊，连家创，段振勇.四辊冷轧机减振装置的研究[J].钢铁,1996,11(31):71-75.
[29]许石民，孙登月.板带材生产工艺及设备[M].北京：冶金工业出版社，2008.
[30]林鹤，邹家祥，岳海龙.四辊冷轧机第三倍频颤振[J].钢铁,1999,1(34):56-59.
[31] Tlusty J, Chandra G, Critchley S. Chatter in Cold Rolling[J]. CIRP Annals-ManufacturingTechnology,1982,1(31):195-199.
[32] Panjkovic V, Gloss R, Steward J, et al. Causes of Chatter in a Hot Strip Mill: Observation,Qualitative Analysed and Mathematical Modelling[J]. Journal of Materials Processing Technology,2012(212):954-961.
[33]钟掘，严珩志.带钢表面振纹的工业实验与发现[J].中国有色金属学报,2000,2(10):291-296.
[34]段吉安，钟掘.高速轧机工作界面的负阻尼特性[J].中南工业大学学报,2002,4(33):401-404.
[35] Swiatoniowski A, Bar A. Parametrical Excitement Vibration in Tandem Mills—MathematicalModel and its Analysis[J]. Journal of Materials Processing Technology,2003,2(134):214-224.
[36] Tang H P, Wang D Y, Zhong J. Investigation into the Electromechanical Coupling Unstability of aRolling Mill[J]. Journal of Materials Processing Technology,2002,1-3(129):294-298.
[37] In S Y, William R D W, Kornel E. Review of Chatter Studies in Cold Rolling[J]. InternationalJournal of Machine Tools and Manufacture.1998,12(38):1499-1530.
[38]史荣，赵静，彭艳，等.基于实验研究的轧机垂扭耦合振动分析[J].实验力学,2012,3(27):319-325.
[39]闫晓强，史灿，曹曦，等. CSP轧机扭振与垂振耦合研究[J].振动、测试与诊断,2008,4(28):377-381.
[40]马彬城，马维金，王俊元，等.高速轧机耦合振动问题研究进展及评述[J].制造业自动化,2013,12(35):55-58.
[41]闫晓强，刘丽娜，史灿，等. CSP轧机弯扭耦合振动频率研究[J].振动与冲击,2009,3(28):182-185.
[42]闫晓强，刘丽娜，曹曦，等. CSP轧机万向接轴弯扭耦合振动[J].北京科技大学学报,2008,10(30):1158-1162.
[43]马小英.板带轧机辊系横向动力学研究[D].秦皇岛：燕山大学硕士学位论文2003：22-35.
[44]钟掘，唐华平.高速轧机若干振动问题——复杂机电系统耦合动力学研究[J].振动、测试与诊断,2002,1(22):1-8.
[45]闫晓强.热连轧机机电液耦合振动研究[J].机械工程学报,2011,17(47):61-65.
[46]杨文军.轧机伺服液压缸测试系统研究[D].武汉：武汉科技大学硕士学位论文2012：22-33.
[47] Dyja H, Markowski J, Stoinski D. Asymmetry of the Roll Gap as a Factor Improving Work of theHydraulic Gauge Control in the Plate Rolling Mill[J]. Journal of Materials ProcessingTechnology,1996,1-4(60):73-80.
[48]王益群.2030冷连轧机速度控制系统的建模及电动机负载转矩的计算[J].机械工程学报,2005,3(41):128-133.
[49]刘仙.冷连轧机速度系统鲁棒控制研究[D].秦皇岛：燕山大学硕士学位论文2003：45-58.
[50] Malloci I, Daafouz J, Lung C, et al. Switched System modeling and Robust Steering Control of theTail End Phase in a Hot Strip Mill[J]. Nonlinear analysis: Hybrid Systems,2009,3(3):239-250.
[51]孙文权，杨荃，邵健，等.单机架冷轧机全干扰耦合模型的分步解耦设计[J].钢铁研究学报,2010,8(22):8-12.
[52] Linghu K Z, He A R, Yang Q, et al. Dynamic Decoupling for Combined Shape and Guage ControlSystem in Wide Strip Rolling Process[J]. Journal of Iron and Steel Research, International,2008,2(15):28-31.
[53] Hu P H, Kornel E. Regenerative Effect in Rolling Chatter [J]. Journal of ManufacturingProcesses[J].2001,2(3):82-93.
[54]陈勇辉，史铁林，林梅香.四辊冷带轧机再生颤振稳定性的统一理论[J].中国机械工程,2003,16(14):1408-1412.
[55] Shi P M, Li J Z, Jiang J S, et al. Nonlinear Dynamics of Torsional Vibration for Rolling Mill'sMain Drive System Under Parametric Excitation [J]. Journal of Materials Processing Technology,2013,1(20):7-12.
[56]刘浩然，侯东晓，时培明，等.轧机辊系滞后非线性垂直振动系统的振动特性[J].机械工程学报,2011,13(47):65-70.
[57] Sun J L, Peng Y, Liu H M. Non-Linear Vibration and Stability of Moving Strip WithTime–Dependent Tension in Rolling Process[J]. Journal of Iron and Steel Research, International,2010,6(17):11-15.
[58] Kugi A, Schlacher K, Novak R. Nonlinear control in rolling ills: a new perspective[J]. IEEEtransactions on industry application,2001,5(37):1394-1402.
[59]邹家祥，徐乐江.冷连轧机系统振动控制[M].北京：冶金工业出版社，1998,79-83.
[60]申光宪，束学道，李明著.轧机微尺度理论和实际[M].北京：科学出版社，2005.
[61]刘习军，贾启芬.工程振动理论与测试技术[M].北京：高等教育出版社，2004.
[62]沙明红，赖应无，张德臣.1780热连轧机机座系统的动力学分析[J].辽宁科技大学学报,2010,3(33):230-232.
[63] Vignolo L, DeLuca A, Tedesco S, et al. An Innovative Approach to Dynamic Chatter Control andSuppression in Cold Rolling[C]. Venice: Committee of9th International Rolling Conference,2013:paper number#23.
[64]倪振华.振动力学[M].西安：西安交通大学出版社，1986.
[65]范小彬，臧勇，王永涛.国内外板带轧机机座振动问题研究的进展[J].重型机械,2006,1:1-5.
[66]申光宪，安瑞臣，谢朝辉.高刚度轧机重载滚子轴承低寿命问题的研究[J].机械工程学报,1996,32(2):95-100.
[67]魏立群，瞿志豪，柳谋渊，等.1420冷连轧机组自激振动分析[J].钢铁,2005,11(40):37-39.
[68]瞿志豪，柴绍宽，叶黔元.1420冷连轧机的动态特性及颤振分析[J]. Journal of Vibaration andShock,2006,4(25):25-29.
[69]闫晓强.可逆式冷轧机振动机理研究[J].振动与冲击,2010,9(29):231-234.
[70] Ye Z H, Wang L Q, Gu L, et al. Effect of Tilted Misalignment on Loading Characteristics ofCylindrical Roller Bearing [J]. Mechanism and Machine Theory[J].2013,(69):153-167.
[71]段秀明，杨清娟.轧机用四列圆柱滚子轴承的选用要点[J].一重技术,2007,1:7-9.
[72]苏玉达.降低窄带钢热轧机轴承消耗的措施[J].轧钢机械,2003,3(20),57-58.
[73]张祖德.带钢热轧机轴承的使用寿命研究[J].冶金设备,2008特刊,10-12.
[74]崔磊.铝箔轧机弯辊控制系统对工作辊表面及带材表面质量的影响[J].有色金属加工,2013,2(42):59-62.
[75]李一耕.镀膜圆柱滚子轴承的热机耦合分析[D].秦皇岛：燕山大学硕士学位论文2011：34-46.
[76] Lockhart, Howard M. Protecting bearings in rolling mills [C]. Proceedings of the Iron and SteelTechnology Conference and Exposition,2012:2005.
[77]陈占福，申光宪，束学道.2030铝箔轧机工作辊止推轴承寿命及事故分析[J].重型机械,1999,2:6-8.
[78]周纪华，叶煦琳，史小路，等.四辊轧机支承辊止推轴承烧损原因测试[J].北京科技大学学报,1995,5(17):444-450.
[79]束学道，申光宪.2350铝箔轧机工作辊轴向力测试及止推轴承短寿分析[J].冶金设备,2001,5:1-5.
[80]詹大桂.1270四辊防交叉轧机研制与止推轴承烧损分析[D].秦皇岛：燕山大学硕士学位论文2012：14.
[81]谢朝晖.三铰拉杆方柱型高刚度轧机的设计与工业性测试研究[D].秦皇岛：燕山大学硕士学位论文1991：22-40.
[82]紺野洋司,渋谷聡,田中伸治.圧延プロセスの非定常負荷発生機構の解明と抑制策[J].川崎製鐵技報,2001,33(1):37-42.
[83]黒田彰夫.進化したPair Cross(PC)ミル,製鉄機械特集,産業機械,2006,(8):43-46.
[84]蒋基洪，戎司旦.液压衬板技术在宝钢CM04机组平整机上的应用,重型机械,1999,4:13-14.
[85]申光宪，黄孟魁，束学道等.空间自位高刚度轧机[P].国家发明专利: ZL97101305.5,2001.
[86]申光宪.構成要素の変位を静定的に考慮した圧延機の最適設計に関する研究[D].东京：日本东京大学博士论文2010：10-30.
[87] Shen G X, Li M. Statically Determinate Characteristics of Micro-Displacement in a Four-HighMill [J], Journal of Materials Processing Technology,2009,11(209):5002-5007.
[88]邹家祥.轧钢机械[M].北京：冶金工业出版社，2004.
[89]申光宪，李明，史荣，等.四辊轧机辊系偏移距机理的不确定性和微尺度静定性[J].机械工程学报,2010,46(10):69-74.
[90] Huang Q X, Shen G X, Chen Z F, et al. Self-aligning Even Load Mechanism of Multi-RowBearings of Large Strip Rolling Mill[J]. Chinese Journal of Mechanical Engineering,2006,19(2),246-250.
[91]陈占福，申光宪，束学道.大型轧机滚动轴承延寿理论与方法研究[J].中国机械工程,2001,10(12),1089-1092.
[92]黄庆学，申光宪，陈占福.宝钢2050mm轧机组合轴承载荷特性的边界元解析及试验研究[J].机械工程学报,2001,2(37),43-47.
[93]芮筱亭，贠来峰，陆毓琪，等.多体系统传递矩阵法及其工程应用[M].北京：科学出版社，2008.
[94]陆佑方.柔性多体系统动力学[M].北京：高等教育出版社，1996.
[95] He B, Rui X T, Wang G P. Riccati Discrete Time Transfer Matrix Method of Multibody System forElastic Beam undergoing Large Overall Motion[J]. Multibody System Dynamics,2007,18(4),579-598.
[96]刘延柱，洪嘉振，杨海兴.多刚体系统动力学[M].北京：高等教育出版社，1989.
[97] Zienkiewicz O C. The Finite Element Method[M]. New York: Mcgraw-Hill Book Company,1987.
[98] Wittenburg J. Dynamics of Systems of Rigid bodies[M]. Stuttgart: B.G.Teubner,1977.
[99] Schiehen W. Multibody Systems Handbook[M]. Berlin：Springer-Verlag,1990.
[100] Kane T R, Likins P W, Levinson D A. Spacecraft Dynamics[M]. New York: Mcgraw-Hill BookCompany,1983.
[101] Pestel E C, Leckie F A. Matrix Method in Elastomechanics[M]. New York: Mcgraw-Hill BookCompany,1963.
[102] Uhrig R. Elastostatik und Elastokinetik in Matrizenschreibweise das Verfrahren derunertragungsmatrizen[M]. Berlin：Springer-Verlag,1973.
[103] Pilkey W D, Chang P Y. Modern Formulas for Statics and Dynamics[M]. New York:Mcgraw-Hill Book Company,1978.
[104] Holzer H. Die Berechnung der Drehschwingungen[M]. Berlin：Springer,1921.
[105] Proh M A. A General Method for Calculating Critical Speeds of Flexbile Rotors[J]. Journal ofApplied Mechanics,1945,12(3):142-148.
[106] Horner G C, Pilkey W D. The Riccati Transfer Matrix Method[J]. Journal of Mechanics Design,ASME,1978,1(100):297-302.
[107]铁摩辛柯S.工程中的振动问题[M].杨D H，译.北京：人民铁道出版社，1978.
[108]川井忠彦.振动矩阵分析方法[M].刘锡荟，译.北京：中国建筑工业出版社，1971.
[109]骆振黄.工程振动导引[M].上海：上海交通大学出版社，1989.
[110]谷口修,振动工程大全[M].北京：机械工业出版社，1983.
[111]邹家祥，徐乐江.冷连轧机系统振动控制[M].北京：冶金工业出版社，1998,79-83.
[112]哈尔滨工业大学等校压力加工教研室编著.金属压力机工原理[M].北京：中国工业出版社，1962.
[113]申光宪，李明.微尺度静定性四辊轧机:中国，CN200810080014.3[P].2009-05-13.
[2] Cao J G, Liu S J, Zhang J, et al. ASR Work Roll Shifting Strategy for Schedule-Free Rolling in HotWide Strip Mills[J]. Journal of Materials Processing Technology,2011,11(211):1768-1775.
[3]王国栋，刘向华，王君.我国中厚板生产技术20年[J].轧钢,2004,6(2):5-9.
[4]李学通，吴志贺，杜凤山，等.四辊平整机轧制过程辊系变形有限元分析[J].塑性工程学报,2008,2(15):126-130.
[5] Okamura Y, Hoshino I. State Feedback Control of the Strip Steering for Aluminum Hot RollingMill[J]. Control Engineering Practice,1997,8(5):1035-1042.
[6]钟掘，杨勇学，古可，等.1600高速铝带轧机扭振研究[J].冶金设备,1986,3:1-7.
[7] Yukio K, Yasuhiro S, Nobuo N, et al. Analysis of Chatter in Tandem Cold Rolling Mills[J]. ISIJInternational,2003(43):77-84.
[8] Zhong J, Yan H Z, Duan J A, et al. Industrial Experiments and Findings on Temper RollingChatter[J]. Journal of Materials Processing Technology,2002(120):275-280.
[9] Kim Y S, Zhang N, Ji J C, et al. The Effect of Tension Variation in the Dynamic Roll Gap on ColdRolling Mill Stability[C].9th International Rolling Conference, Venice, Italy,2003: Poster#37.
[10] Hu P H, Ehmann K. Stability Analysis of Chatter on a Tandem Rolling Mill[J]. Journal ofManufacturing Processes,2000,4(2):217-224.
[11] Tamaoki T, Takanezawa M, Kimoto M, et al. Study on Online Analysis of Transfer Function ofVariable-Speed Rolling Mill Motor with Shaft Torsional Vibration Systems[J]. IEEJ Transactionson Industry Applications,2011,6(131):844-857.
[12]叶黔元，郑七振，鲁晓燕.冷连轧机的振动分析及改善方法[J].振动工程学报,2004(17):825-827.
[13]唐华平，李旭宇，钟掘.轧机扭转自激振动分析[J].湘潭矿业学院学报,2002,2(17):21-24.
[14] Nizio J, Swiatoniowski A. Numerical Analysis of the Vertical Vibrations of Rolling Mills and theirNegative Effect on the Sheet Quality[J]. Journal of Materials Processing Technology,2005(162-163):546-550.
[15]杨其俊，连家创.高速冷带轧机垂直自激振动稳定性分析的数值计算方法[J].振动与冲击,1996,3(15):16-21.
[16] Alok1D. Case Study Systematic Approach for Elimination of Vibrations in Gap FormerWire-Section to Speed-Up the Machine[J]. Quarterly Journal of Indian Pulp and Paper TechnicalAssociation,2010(4),151-154.
[17]范小彬，臧勇，王会刚.热连轧机水平振动特性研究[J].钢铁,2010,9(45):62-66.
[18]唐华平，钟掘.单辊驱动轧机水平自激振动定性分析[J].机械工程学报,2001,8(37):55-59.
[19] Yun I S, Wilson W R D. Review of Chatter Studier in Cold Rolling[J]. Journal of Machine Tools&Manufacture,1998,(38):1499-1530.
[20]杜国君，张忠建，高崇一.考虑打滑和双间隙影响的厚板轧机主传动系统扭振[J].钢铁,2013,2(48):39-43.
[21]申延智，刘宏民，熊杰，等.厚板轧机含间隙主传动系统混沌动力学分析[J].工程力学,2010,7(27):232-236.
[22]申延智，杜国君，张渡仙，等.基于辊缝耦合的轧机主传动系统扭振研究[J].钢铁,2010,4(45):56-59.
[23]李怀志.考虑齿轮啮合刚度的轧机主传动系统动力学特性研究[D].沈阳：东北大学硕士学位论文2008：7-11.
[24]陈勇辉，刘世元，廖广兰.四辊冷带轧机三倍频颤振机理的研究[J].机械工程学报,2003,6(39):118-123.
[25]陈勇辉，李巍华，史铁林，等.四辊冷带轧机五倍频再生颤振机理的研究颤振[J].钢铁,2003,15(31):55-57.
[26] Wei L Q, Qu Z H, Zhang X Y, et al. Influence of Rolling Lubrication on Self-Excited Vibration in1420Continuous Cold Rolling Mill[C].9th International Rolling Conference, Venice, Italy,2003:(paper number28, no pages).
[27]高亚男，彭艳，孙建亮，等.1580热连轧机F2精轧机振动综合测试与分析[J].钢铁,2013,1(48):1-7.
[28]杨其俊，连家创，段振勇.四辊冷轧机减振装置的研究[J].钢铁,1996,11(31):71-75.
[29]许石民，孙登月.板带材生产工艺及设备[M].北京：冶金工业出版社，2008.
[30]林鹤，邹家祥，岳海龙.四辊冷轧机第三倍频颤振[J].钢铁,1999,1(34):56-59.
[31] Tlusty J, Chandra G, Critchley S. Chatter in Cold Rolling[J]. CIRP Annals-ManufacturingTechnology,1982,1(31):195-199.
[32] Panjkovic V, Gloss R, Steward J, et al. Causes of Chatter in a Hot Strip Mill: Observation,Qualitative Analysed and Mathematical Modelling[J]. Journal of Materials Processing Technology,2012(212):954-961.
[33]钟掘，严珩志.带钢表面振纹的工业实验与发现[J].中国有色金属学报,2000,2(10):291-296.
[34]段吉安，钟掘.高速轧机工作界面的负阻尼特性[J].中南工业大学学报,2002,4(33):401-404.
[35] Swiatoniowski A, Bar A. Parametrical Excitement Vibration in Tandem Mills—MathematicalModel and its Analysis[J]. Journal of Materials Processing Technology,2003,2(134):214-224.
[36] Tang H P, Wang D Y, Zhong J. Investigation into the Electromechanical Coupling Unstability of aRolling Mill[J]. Journal of Materials Processing Technology,2002,1-3(129):294-298.
[37] In S Y, William R D W, Kornel E. Review of Chatter Studies in Cold Rolling[J]. InternationalJournal of Machine Tools and Manufacture.1998,12(38):1499-1530.
[38]史荣，赵静，彭艳，等.基于实验研究的轧机垂扭耦合振动分析[J].实验力学,2012,3(27):319-325.
[39]闫晓强，史灿，曹曦，等. CSP轧机扭振与垂振耦合研究[J].振动、测试与诊断,2008,4(28):377-381.
[40]马彬城，马维金，王俊元，等.高速轧机耦合振动问题研究进展及评述[J].制造业自动化,2013,12(35):55-58.
[41]闫晓强，刘丽娜，史灿，等. CSP轧机弯扭耦合振动频率研究[J].振动与冲击,2009,3(28):182-185.
[42]闫晓强，刘丽娜，曹曦，等. CSP轧机万向接轴弯扭耦合振动[J].北京科技大学学报,2008,10(30):1158-1162.
[43]马小英.板带轧机辊系横向动力学研究[D].秦皇岛：燕山大学硕士学位论文2003：22-35.
[44]钟掘，唐华平.高速轧机若干振动问题——复杂机电系统耦合动力学研究[J].振动、测试与诊断,2002,1(22):1-8.
[45]闫晓强.热连轧机机电液耦合振动研究[J].机械工程学报,2011,17(47):61-65.
[46]杨文军.轧机伺服液压缸测试系统研究[D].武汉：武汉科技大学硕士学位论文2012：22-33.
[47] Dyja H, Markowski J, Stoinski D. Asymmetry of the Roll Gap as a Factor Improving Work of theHydraulic Gauge Control in the Plate Rolling Mill[J]. Journal of Materials ProcessingTechnology,1996,1-4(60):73-80.
[48]王益群.2030冷连轧机速度控制系统的建模及电动机负载转矩的计算[J].机械工程学报,2005,3(41):128-133.
[49]刘仙.冷连轧机速度系统鲁棒控制研究[D].秦皇岛：燕山大学硕士学位论文2003：45-58.
[50] Malloci I, Daafouz J, Lung C, et al. Switched System modeling and Robust Steering Control of theTail End Phase in a Hot Strip Mill[J]. Nonlinear analysis: Hybrid Systems,2009,3(3):239-250.
[51]孙文权，杨荃，邵健，等.单机架冷轧机全干扰耦合模型的分步解耦设计[J].钢铁研究学报,2010,8(22):8-12.
[52] Linghu K Z, He A R, Yang Q, et al. Dynamic Decoupling for Combined Shape and Guage ControlSystem in Wide Strip Rolling Process[J]. Journal of Iron and Steel Research, International,2008,2(15):28-31.
[53] Hu P H, Kornel E. Regenerative Effect in Rolling Chatter [J]. Journal of ManufacturingProcesses[J].2001,2(3):82-93.
[54]陈勇辉，史铁林，林梅香.四辊冷带轧机再生颤振稳定性的统一理论[J].中国机械工程,2003,16(14):1408-1412.
[55] Shi P M, Li J Z, Jiang J S, et al. Nonlinear Dynamics of Torsional Vibration for Rolling Mill'sMain Drive System Under Parametric Excitation [J]. Journal of Materials Processing Technology,2013,1(20):7-12.
[56]刘浩然，侯东晓，时培明，等.轧机辊系滞后非线性垂直振动系统的振动特性[J].机械工程学报,2011,13(47):65-70.
[57] Sun J L, Peng Y, Liu H M. Non-Linear Vibration and Stability of Moving Strip WithTime–Dependent Tension in Rolling Process[J]. Journal of Iron and Steel Research, International,2010,6(17):11-15.
[58] Kugi A, Schlacher K, Novak R. Nonlinear control in rolling ills: a new perspective[J]. IEEEtransactions on industry application,2001,5(37):1394-1402.
[59]邹家祥，徐乐江.冷连轧机系统振动控制[M].北京：冶金工业出版社，1998,79-83.
[60]申光宪，束学道，李明著.轧机微尺度理论和实际[M].北京：科学出版社，2005.
[61]刘习军，贾启芬.工程振动理论与测试技术[M].北京：高等教育出版社，2004.
[62]沙明红，赖应无，张德臣.1780热连轧机机座系统的动力学分析[J].辽宁科技大学学报,2010,3(33):230-232.
[63] Vignolo L, DeLuca A, Tedesco S, et al. An Innovative Approach to Dynamic Chatter Control andSuppression in Cold Rolling[C]. Venice: Committee of9th International Rolling Conference,2013:paper number#23.
[64]倪振华.振动力学[M].西安：西安交通大学出版社，1986.
[65]范小彬，臧勇，王永涛.国内外板带轧机机座振动问题研究的进展[J].重型机械,2006,1:1-5.
[66]申光宪，安瑞臣，谢朝辉.高刚度轧机重载滚子轴承低寿命问题的研究[J].机械工程学报,1996,32(2):95-100.
[67]魏立群，瞿志豪，柳谋渊，等.1420冷连轧机组自激振动分析[J].钢铁,2005,11(40):37-39.
[68]瞿志豪，柴绍宽，叶黔元.1420冷连轧机的动态特性及颤振分析[J]. Journal of Vibaration andShock,2006,4(25):25-29.
[69]闫晓强.可逆式冷轧机振动机理研究[J].振动与冲击,2010,9(29):231-234.
[70] Ye Z H, Wang L Q, Gu L, et al. Effect of Tilted Misalignment on Loading Characteristics ofCylindrical Roller Bearing [J]. Mechanism and Machine Theory[J].2013,(69):153-167.
[71]段秀明，杨清娟.轧机用四列圆柱滚子轴承的选用要点[J].一重技术,2007,1:7-9.
[72]苏玉达.降低窄带钢热轧机轴承消耗的措施[J].轧钢机械,2003,3(20),57-58.
[73]张祖德.带钢热轧机轴承的使用寿命研究[J].冶金设备,2008特刊,10-12.
[74]崔磊.铝箔轧机弯辊控制系统对工作辊表面及带材表面质量的影响[J].有色金属加工,2013,2(42):59-62.
[75]李一耕.镀膜圆柱滚子轴承的热机耦合分析[D].秦皇岛：燕山大学硕士学位论文2011：34-46.
[76] Lockhart, Howard M. Protecting bearings in rolling mills [C]. Proceedings of the Iron and SteelTechnology Conference and Exposition,2012:2005.
[77]陈占福，申光宪，束学道.2030铝箔轧机工作辊止推轴承寿命及事故分析[J].重型机械,1999,2:6-8.
[78]周纪华，叶煦琳，史小路，等.四辊轧机支承辊止推轴承烧损原因测试[J].北京科技大学学报,1995,5(17):444-450.
[79]束学道，申光宪.2350铝箔轧机工作辊轴向力测试及止推轴承短寿分析[J].冶金设备,2001,5:1-5.
[80]詹大桂.1270四辊防交叉轧机研制与止推轴承烧损分析[D].秦皇岛：燕山大学硕士学位论文2012：14.
[81]谢朝晖.三铰拉杆方柱型高刚度轧机的设计与工业性测试研究[D].秦皇岛：燕山大学硕士学位论文1991：22-40.
[82]紺野洋司,渋谷聡,田中伸治.圧延プロセスの非定常負荷発生機構の解明と抑制策[J].川崎製鐵技報,2001,33(1):37-42.
[83]黒田彰夫.進化したPair Cross(PC)ミル,製鉄機械特集,産業機械,2006,(8):43-46.
[84]蒋基洪，戎司旦.液压衬板技术在宝钢CM04机组平整机上的应用,重型机械,1999,4:13-14.
[85]申光宪，黄孟魁，束学道等.空间自位高刚度轧机[P].国家发明专利: ZL97101305.5,2001.
[86]申光宪.構成要素の変位を静定的に考慮した圧延機の最適設計に関する研究[D].东京：日本东京大学博士论文2010：10-30.
[87] Shen G X, Li M. Statically Determinate Characteristics of Micro-Displacement in a Four-HighMill [J], Journal of Materials Processing Technology,2009,11(209):5002-5007.
[88]邹家祥.轧钢机械[M].北京：冶金工业出版社，2004.
[89]申光宪，李明，史荣，等.四辊轧机辊系偏移距机理的不确定性和微尺度静定性[J].机械工程学报,2010,46(10):69-74.
[90] Huang Q X, Shen G X, Chen Z F, et al. Self-aligning Even Load Mechanism of Multi-RowBearings of Large Strip Rolling Mill[J]. Chinese Journal of Mechanical Engineering,2006,19(2),246-250.
[91]陈占福，申光宪，束学道.大型轧机滚动轴承延寿理论与方法研究[J].中国机械工程,2001,10(12),1089-1092.
[92]黄庆学，申光宪，陈占福.宝钢2050mm轧机组合轴承载荷特性的边界元解析及试验研究[J].机械工程学报,2001,2(37),43-47.
[93]芮筱亭，贠来峰，陆毓琪，等.多体系统传递矩阵法及其工程应用[M].北京：科学出版社，2008.
[94]陆佑方.柔性多体系统动力学[M].北京：高等教育出版社，1996.
[95] He B, Rui X T, Wang G P. Riccati Discrete Time Transfer Matrix Method of Multibody System forElastic Beam undergoing Large Overall Motion[J]. Multibody System Dynamics,2007,18(4),579-598.
[96]刘延柱，洪嘉振，杨海兴.多刚体系统动力学[M].北京：高等教育出版社，1989.
[97] Zienkiewicz O C. The Finite Element Method[M]. New York: Mcgraw-Hill Book Company,1987.
[98] Wittenburg J. Dynamics of Systems of Rigid bodies[M]. Stuttgart: B.G.Teubner,1977.
[99] Schiehen W. Multibody Systems Handbook[M]. Berlin：Springer-Verlag,1990.
[100] Kane T R, Likins P W, Levinson D A. Spacecraft Dynamics[M]. New York: Mcgraw-Hill BookCompany,1983.
[101] Pestel E C, Leckie F A. Matrix Method in Elastomechanics[M]. New York: Mcgraw-Hill BookCompany,1963.
[102] Uhrig R. Elastostatik und Elastokinetik in Matrizenschreibweise das Verfrahren derunertragungsmatrizen[M]. Berlin：Springer-Verlag,1973.
[103] Pilkey W D, Chang P Y. Modern Formulas for Statics and Dynamics[M]. New York:Mcgraw-Hill Book Company,1978.
[104] Holzer H. Die Berechnung der Drehschwingungen[M]. Berlin：Springer,1921.
[105] Proh M A. A General Method for Calculating Critical Speeds of Flexbile Rotors[J]. Journal ofApplied Mechanics,1945,12(3):142-148.
[106] Horner G C, Pilkey W D. The Riccati Transfer Matrix Method[J]. Journal of Mechanics Design,ASME,1978,1(100):297-302.
[107]铁摩辛柯S.工程中的振动问题[M].杨D H，译.北京：人民铁道出版社，1978.
[108]川井忠彦.振动矩阵分析方法[M].刘锡荟，译.北京：中国建筑工业出版社，1971.
[109]骆振黄.工程振动导引[M].上海：上海交通大学出版社，1989.
[110]谷口修,振动工程大全[M].北京：机械工业出版社，1983.
[111]邹家祥，徐乐江.冷连轧机系统振动控制[M].北京：冶金工业出版社，1998,79-83.
[112]哈尔滨工业大学等校压力加工教研室编著.金属压力机工原理[M].北京：中国工业出版社，1962.
[113]申光宪，李明.微尺度静定性四辊轧机:中国，CN200810080014.3[P].2009-05-13.