电动桥式起重机负载升降过程的系统动力学模拟
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摘要
从系统的角度考虑电动桥式起重机起升机构工作过程中的动力学模拟问题。首先,由系统的拉格朗日函数、约束条件和电机的磁共能定义修正的拉格朗日函数;随后,应用Hamilton原理和三相感应电机瞬态模型得出起升机构工作过程中电动桥式起重机系统的运动方程。为验证模型的效果,本文还进行了转子串电阻速度控制系统控制下的32t电动桥式起重机吊运额定负载下降过程的数值模拟,分析了高速浮动轴扭转刚度以及制动过程中转子电阻的配置方案对系统动力响应的影响。模拟结果表明,制动过程中起升机构高速浮动轴所受载荷远大于起动过程中所受载荷,制动开始时在电机转子电路中增加一级较大的外串电阻有利于减小下降制动阶段系统中的动载。
The dynamics of electric overhead cranes during the lowering operation of the lifting mechanism were studied in a systematic view.By means of the transient model of the three-phase induction motor controlled by a speed control system and Hamilton's principal with a modified Lagrangian which consists of the ordinary Lagrangian and constraints of the crane system,and magnetic co-energy of the motor in the lifting mechanism,the equations of motion of the electric overhead cranes during the operation of the lifting mechanism were derived.The numerical simulations of the normal process for lowering a rated payload of an electric overhead crane of 32 tare presented.The effects of the torsional stiffness of the floating shaft in the high-speed link of the lifting mechanism and rotor resistance of the driving motor on dynamic responses of system are discussed.It is seen that the peak load acting on the high-speed link of lifting mechanism during braking is much greater than that when starting during a normal lowering operation for a rated payload and a bigger rotor resistance at the start of the braking process is favorable to decrease the dynamic loads applied to the electric overhead crane during braking.
The dynamics of electric overhead cranes during the lowering operation of the lifting mechanism were studied in a systematic view.By means of the transient model of the three-phase induction motor controlled by a speed control system and Hamilton's principal with a modified Lagrangian which consists of the ordinary Lagrangian and constraints of the crane system,and magnetic co-energy of the motor in the lifting mechanism,the equations of motion of the electric overhead cranes during the operation of the lifting mechanism were derived.The numerical simulations of the normal process for lowering a rated payload of an electric overhead crane of 32 tare presented.The effects of the torsional stiffness of the floating shaft in the high-speed link of the lifting mechanism and rotor resistance of the driving motor on dynamic responses of system are discussed.It is seen that the peak load acting on the high-speed link of lifting mechanism during braking is much greater than that when starting during a normal lowering operation for a rated payload and a bigger rotor resistance at the start of the braking process is favorable to decrease the dynamic loads applied to the electric overhead crane during braking.
引文
[1]GB/T 3811-2008起重机设计规范[S].(GB/T 3811-2008Design rules for cranes[S].(in Chinese))
[2]BS EN 13001-2:2004+A3:2009Crane safety—general design—Part 2:Load effects[S].
[3]ISO8686-5:1992 Cranes-design principles for loads and load combinations(Part 5):overhead travelling and portal bridge cranes[S].
[4]Jerman B,Podraj P,Kramar J.An investigation of slewing-crane dynamics during slewing motion-development and verification of a mathematical model[J].International Journal of Mechanical Sciences,2004,46(5):729-750.
[5]Wu J J.Dynamic responses of a three-dimensional framework due to a moving carriage hoisting a swinging object[J].International Journal for Numerical Methods in Engineering,2004,59(13):1679-1702.
[6]Sun G,Kleeberger M,Liu J.Complete dynamic calculation of lattice mobile crane during hoisting motion[J].Mechanism and Machine Theory,2005,40(4):447-466.
[7]Ju F,Choo Y S,Cui F S.Dynamic response of tower crane induced by the pendulum motion of the payload[J].International Journal of Solids and Structures,2006,43(2):376-389.
[8]Zrnic′ND-,Hoffmann K,Bonjak S M.Modelling of dynamic interaction between structure and trolley for mega container cranes[J].Mathematical and Computer Modelling of Dynamical Systems,2009,15(3):295-311.
[9]Niu C M,Zhang H W,Ouyang H.A comprehensive dynamic model of electric overhead cranes and the lifting operations[J].Proceedings of the Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science,2012,226(6):1484-1503.
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[12]Younesian D,Ghafoori E,Sadeghpour M.Nonlinear vibration of a three-dimensional moving gantry crane subjected to a travelling trolley hoisting a swinging object[J].Transactions of the Canadian Society for Mechanical Engineering,2010,34(3-4):333-350.
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[15]Sorensen K L,Singhose W,Dickerson S.A controller enabling precise positioning and sway reduction in bridge and gantry cranes[J].Control Engineering Practice,2007,15(7):825-837.
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[2]BS EN 13001-2:2004+A3:2009Crane safety—general design—Part 2:Load effects[S].
[3]ISO8686-5:1992 Cranes-design principles for loads and load combinations(Part 5):overhead travelling and portal bridge cranes[S].
[4]Jerman B,Podraj P,Kramar J.An investigation of slewing-crane dynamics during slewing motion-development and verification of a mathematical model[J].International Journal of Mechanical Sciences,2004,46(5):729-750.
[5]Wu J J.Dynamic responses of a three-dimensional framework due to a moving carriage hoisting a swinging object[J].International Journal for Numerical Methods in Engineering,2004,59(13):1679-1702.
[6]Sun G,Kleeberger M,Liu J.Complete dynamic calculation of lattice mobile crane during hoisting motion[J].Mechanism and Machine Theory,2005,40(4):447-466.
[7]Ju F,Choo Y S,Cui F S.Dynamic response of tower crane induced by the pendulum motion of the payload[J].International Journal of Solids and Structures,2006,43(2):376-389.
[8]Zrnic′ND-,Hoffmann K,Bonjak S M.Modelling of dynamic interaction between structure and trolley for mega container cranes[J].Mathematical and Computer Modelling of Dynamical Systems,2009,15(3):295-311.
[9]Niu C M,Zhang H W,Ouyang H.A comprehensive dynamic model of electric overhead cranes and the lifting operations[J].Proceedings of the Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science,2012,226(6):1484-1503.
[10]孙焕纯,宋亚新,张典仁.变质量,变阻尼,变刚度结构系统的动力响应[J].计算结构力学及其应用.1996,13(2):127-137.(SUN Huan-chun,SONG Ya-xin,ZHANG Dian-ren.Dynamic responses of a structure system with the variable mass,damping and stiffness[J].Journal of Computational Structural Mechanics and Applications,1996,13(2):127-137.(in Chinese))
[11]夏拥军,缪谦.计及二阶效应的门座起重机变幅工况动力学分析[J].计算力学学报,2010,27(4):711-715.(XIA Yong-jun,,MIAO Qian.Dynamic analysis of port crane in case of modifying amplitude with second order effect[J].Chinese Journal of Computational Mechanics,2010,27(4):711-715.(in Chinese))
[12]Younesian D,Ghafoori E,Sadeghpour M.Nonlinear vibration of a three-dimensional moving gantry crane subjected to a travelling trolley hoisting a swinging object[J].Transactions of the Canadian Society for Mechanical Engineering,2010,34(3-4):333-350.
[13]Abdel-Rahman E M,Nayfeh A H,Masoud Z N.Dynamics and control of cranes:A review[J].Journal of Vibration and Control,2003,9(7):863-908.
[14]Ebeid A M,Moustafa K A F,Hosam E.Electromechanical modelling of overhead cranes[J].International Journal of Systems Science,1992,23(12):2155-2169.
[15]Sorensen K L,Singhose W,Dickerson S.A controller enabling precise positioning and sway reduction in bridge and gantry cranes[J].Control Engineering Practice,2007,15(7):825-837.
[16]杨长骙.起重机械[M].北京:机械出版社,1984.(YANG Chang-kui.Crane Machinery[M].Beijing:Machine Press,1984.(in Chinese))
[17]徐克晋.金属结构[M].北京:机械出版社,1982.(XU Ke-jin.Steel Structures[M].Beijing:Machine Press,1982.(in Chinese))
[18]钱伟长.变分法及有限元[M].北京:科学出版社,1980.(QIAN Wei-chang.Variational Methods and the Finite Element Method[M].Beijing:Science Press,1980.(in Chinese))
[19]Krause P C.Analysis of Electric Machinery[M].McGraw-Hill New York,1986.
[20]俞载道.结构动力学基础[M].上海:同济大学出版社,1987.(YU Zai-dao.Fundamentals of Structural Dynamics[M].Shanghai:Tongji University Press,1987.(in Chinese))