计及臂间搭接与摩擦影响的箱形伸缩臂整体稳定性研究
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摘要
伸缩臂是轮式起重机最重要的工作部件,其稳定性计算是设计分析的关键。目前,伸缩臂的稳定性计算主要依据中国起重机设计规范《GB3811-83》,其伸缩臂的计算长度是以未考虑油缸影响的变截面梯形柱模型采用能量方法推导而得,理论上既不严密也不够精确。新修订的起重机设计规范的计算模型采用的仍是变截面阶梯柱,但求解采用精确的微分方程得到阶梯柱递推公式形式的精确解析解,在理论上更严密一些,但也没有考虑油缸和伸缩臂搭接处摩擦的影响,与伸缩臂实际工作状态不完全相符。因此,求解考虑油缸和摩擦影响的伸缩臂的稳定性是十分必要。
本文通过对臂间搭接与摩擦影响的箱形伸缩臂稳定性分析研究,可知在伸缩吊臂的搭接处产生摩擦力,从而使伸缩吊臂的轴向力由箱形臂与油缸共同成承受,箱形臂自身在承受一定的轴向力的同时承受全部的弯矩。由此受力关系推导出由单个多级油缸支承至顶部的箱形伸缩臂欧拉临界力的递推公式,定性并定量地分析变截面梯形柱、考虑油缸和计及摩擦影响时吊臂整体失稳欧拉临界力的差异。
本文采用微分方程法和精确有限元法两种方法求解伸缩吊臂在计及臂间搭接与摩擦影响时起升平面外的欧拉临界力的精确解,同时辅以弹性支座法验证其理论的准确性。本文给出单个油缸支承在顶部时伸缩臂欧拉临界力精确解的递推公式;通过比较用微分方程法、弹性支座法、有限元法三种方法确定伸缩臂的临界力;并求出了伸缩臂在不同支承情况下的失稳特征方程,同时给出了伸缩臂的计算长度系数;并详细的阐述了采用精确有限元法求解伸缩臂的欧拉临界力的求解过程。
根据《GB3811-83》规范的有关计算参数和图表,用本研究结果同原起重机设计规范、变截面梯形柱模型和考虑油缸支承作用的伸缩臂模型进行比较,分析结果表明,计及臂间搭接与摩擦影响的伸缩臂欧拉临界力介于变截面梯形柱模型欧拉临界力与考虑油缸作用的多节伸缩臂模型的欧拉临界力之间,与伸缩吊臂的实际工作情况相符合。
Telescopic boom is the most important component of wheel crane, whose stability calculation is the key of design and analysis. At present, stability calculation of telescopic boom mainly according to Chinese crane design specifications《GB3811-83》, and calculation length of telescopic arm is derived by energy method according to the variable cross-section ladder model without considering the impact of fuel tank, therefore, it is theoretically neither rigor nor precision. The revised crane design specifications still uses variable cross-section ladder model; although it got precise analytical solutions in the form of ladder recurrence formula, which is more rigor theoretically, it did not consider the friction impact of fuel tank and telescopic boom’s lap so that it is completely not consistent with the actual working conditions. Therefore, it is very necessary to work out the stability of telescopic boom with considering fuel tank and friction.
Crane’s telescopic boom is usually composed of a number of variable cross-section box-arms that are connected by sliders, which allows axial expansion. Its fuel tank generally lies inside of the telescopic boom, and bears axial force together with box-arms, while the latter at the same time bear all the bearing moment. Therefore, telescopic boom’s Euler critical force is different from that of both the variable cross-section ladder model and the multi-telescopic boom model only considering fuel tank. It depends on the moment of inertia of lazy arm’s section and the axial force, friction, box-arm bears. Meanwhile, with different support forms of fuel tanks, Euler critical force would also be different. The issue mentioned above is that this paper will focus on.
In this paper, two methods, differential equation method and precision FEM, are introduced to get Euler critical force’s precision solution of telescopic boom with considering the effects of arm lap and friction outside the lifting plane. Then, elastic support method is applied to verify the accuracy of theory. In this paper, the recurrence formula of Euler critical force’s precision solution of telescopic boom with a single fuel tank at its top is proposed; critical force of telescopic boom is determined by three methods: differential equations method, elastic support method and FEM; work out the instability characteristic equation of telescopic boom in different support; and describe in detail the solution process of telescopic boom’s Euler critical force using precision FEM.
According to the relevant parameters and charts in standard《GB3811-83》, comparison of results between this paper and both the variable cross-section ladder model and the telescopic boom model with considering fuel tank support in the standard shows that Euler critical force of telescopic boom with considering arm lap and friction is between that of those two models mentioned above, which is consistent with the real work of telescopic boom.
本文通过对臂间搭接与摩擦影响的箱形伸缩臂稳定性分析研究,可知在伸缩吊臂的搭接处产生摩擦力,从而使伸缩吊臂的轴向力由箱形臂与油缸共同成承受,箱形臂自身在承受一定的轴向力的同时承受全部的弯矩。由此受力关系推导出由单个多级油缸支承至顶部的箱形伸缩臂欧拉临界力的递推公式,定性并定量地分析变截面梯形柱、考虑油缸和计及摩擦影响时吊臂整体失稳欧拉临界力的差异。
本文采用微分方程法和精确有限元法两种方法求解伸缩吊臂在计及臂间搭接与摩擦影响时起升平面外的欧拉临界力的精确解,同时辅以弹性支座法验证其理论的准确性。本文给出单个油缸支承在顶部时伸缩臂欧拉临界力精确解的递推公式;通过比较用微分方程法、弹性支座法、有限元法三种方法确定伸缩臂的临界力;并求出了伸缩臂在不同支承情况下的失稳特征方程,同时给出了伸缩臂的计算长度系数;并详细的阐述了采用精确有限元法求解伸缩臂的欧拉临界力的求解过程。
根据《GB3811-83》规范的有关计算参数和图表,用本研究结果同原起重机设计规范、变截面梯形柱模型和考虑油缸支承作用的伸缩臂模型进行比较,分析结果表明,计及臂间搭接与摩擦影响的伸缩臂欧拉临界力介于变截面梯形柱模型欧拉临界力与考虑油缸作用的多节伸缩臂模型的欧拉临界力之间,与伸缩吊臂的实际工作情况相符合。
Telescopic boom is the most important component of wheel crane, whose stability calculation is the key of design and analysis. At present, stability calculation of telescopic boom mainly according to Chinese crane design specifications《GB3811-83》, and calculation length of telescopic arm is derived by energy method according to the variable cross-section ladder model without considering the impact of fuel tank, therefore, it is theoretically neither rigor nor precision. The revised crane design specifications still uses variable cross-section ladder model; although it got precise analytical solutions in the form of ladder recurrence formula, which is more rigor theoretically, it did not consider the friction impact of fuel tank and telescopic boom’s lap so that it is completely not consistent with the actual working conditions. Therefore, it is very necessary to work out the stability of telescopic boom with considering fuel tank and friction.
Crane’s telescopic boom is usually composed of a number of variable cross-section box-arms that are connected by sliders, which allows axial expansion. Its fuel tank generally lies inside of the telescopic boom, and bears axial force together with box-arms, while the latter at the same time bear all the bearing moment. Therefore, telescopic boom’s Euler critical force is different from that of both the variable cross-section ladder model and the multi-telescopic boom model only considering fuel tank. It depends on the moment of inertia of lazy arm’s section and the axial force, friction, box-arm bears. Meanwhile, with different support forms of fuel tanks, Euler critical force would also be different. The issue mentioned above is that this paper will focus on.
In this paper, two methods, differential equation method and precision FEM, are introduced to get Euler critical force’s precision solution of telescopic boom with considering the effects of arm lap and friction outside the lifting plane. Then, elastic support method is applied to verify the accuracy of theory. In this paper, the recurrence formula of Euler critical force’s precision solution of telescopic boom with a single fuel tank at its top is proposed; critical force of telescopic boom is determined by three methods: differential equations method, elastic support method and FEM; work out the instability characteristic equation of telescopic boom in different support; and describe in detail the solution process of telescopic boom’s Euler critical force using precision FEM.
According to the relevant parameters and charts in standard《GB3811-83》, comparison of results between this paper and both the variable cross-section ladder model and the telescopic boom model with considering fuel tank support in the standard shows that Euler critical force of telescopic boom with considering arm lap and friction is between that of those two models mentioned above, which is consistent with the real work of telescopic boom.
引文
1汤茂旭,刘木南.轮式起重机起重臂的发展历程.建筑机械化.2007,(2):29~32
2张魁元,王雪.汽车起重机伸缩臂的维护和修理. 2004, (11):28~30
3沈玉风,孟庆华.汽车起重机六边形截面箱形伸缩臂计算研究.2001,(15):23-27
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5朱渝春,冯贤桂.伸缩臂式起重机回转侧向动载荷的计算.工程机械. 2005,(2):11~14
6顾迪民.起重机械事故分析和对策.人民出版社. 2001: 210-224
7 GB3811-83起重机设计规范.中国标准出版社, 1983:76~82
8陆念力,孟晓平,顾迪民.具有外伸臂的多跨连续附着压杆的非线性变形及整体稳定性计算.工程机械. 1996, (9):3~6
9 Q.S.Li. Buckling analysis of multi-step non-uniform columns, Advances in Structure Engineering, volume(3), 139-144, (2000)
10 Georage.A.Kardomateas, George.J.Simitses. Comparative studies on the buckling of isotropic, orthotropic, and sandwich columns, Mechanics of Advanced Materials and Structures, volume(1), 309-327, (2004)
11王硕哲,顾迪民.伸缩油缸对箱形吊臂受力状况的影响.起重运输机械.1983,(11):34~37
12 Loannis G. Raftoyiannis,John Ch. Ermopoulos. Stability of Tapered and Stepped steel Columns with Initial Imperfections. Engineering Structures. 2005,27(8):1248~1257
13胡铁华,唐洪学,马成林.箱形伸缩吊臂设计变量对性能参数的影响线.建筑学报.1996,(9):9~13
14 S.P.Timoshenko, J.M.Gere .Theory of elastic stability, 2nd ed,McGraw-Hill, 1961:203~236
15 Otsuka Hiromitsu, Koga Tatsuzo. Buckling of circular cylindrical shell under beam-like bending experiment, Transactions of the Japan Society for Aeronautical and Space Sciences. 1998,(41):38~45
16 P.Timoshenko, J.M.Gere .Theory of elastic stability, 2nd ed,McGraw-Hill,1961:203~236
17 Sung-Bo Kim, Moon-Young Kim. Improved formulation for spatial stability and free vibration of thin-walled tapered beams and space frames. Engineering Structures. 2000, (22) 446~458
18 Nam-Il Kim , Kwang-Jin Seo b, Moon-Young Kim. Free vibration and spatial stability of non-symmetric thin-walled curved beams with variable curvatures. International Journal of Solids and Structures,2003(40) 3107–3128
19 Guo-Qiang Li. A tapered Timoshenko–Euler beam element for analysis of steel portal frames. Journal of Constructional Steel Research ,2002, (58) 1531~1544
20 S. Naguleswaran. Transverse vibration and stability of an Euler–Bernoulli beam with step change in cross-section and in axial force. Journal of Sound and Vibration,2004 (270)1045~1055
21杨学银,钢结构稳定性探讨.工程科学.2007,(02):26-27
22刘光栋,罗汉泉.杆系结构稳定.人民交通出版社.1988:1-4
23 Klaus-Jürgen Bathe. Advances in Nonlinear Finite Element Analysis of Automobiles. 1997, 64(5): 881-891
24 Klaus-Jurgen Bathe.Finite Element procedures. Prentice Hall, Inc. 1996,(6):485~628
25蓝天,姚卓智.桅杆结构的非线形分析.中国建筑研究院结构所. 1980,(2):2~4
26楚中毅,陆念力,楚兰英等.梁杆结构稳定性分析的一种精确有限元方法及其优化.建筑机械.2001, (9):68~73
27陆念力,兰朋.二阶理论条件下的梁杆系统精确有限元方程及应用.哈尔滨建筑大学学报.1998,(4):21~25
28陈玮璋.起重机金属结构.人民交通出版社, 1987:134~176
29孙焕纯,王跃方.对桁架结构稳定分析经典理论的讨论.计算力学学报. 2005,(3): 316~320
30楚中毅,陆念力,车仁炜.一种梁杆结构稳定性分析的精确有限元法.哈尔滨建筑大学学报. 2002, 35(4): 25~28
31 David H. Ellis , Scott R. Swengel, George W. Archibald,etal. A sociogram for the cranes of the world. Behavioural Processes. 1998,(43): 125~151
32陆念力,兰朋,白桦.起重机箱型伸缩臂稳定性分析的精确理论解.哈尔滨建筑大学学报.2000,33(2):89~93
33兰朋.二阶应力作用下梁杆精确有限元方程及其在非线性分析和稳定计算中的应用.《哈尔滨建筑大学硕士论文》.1996 :32~45
34陆念力,孟晓平,顾迪民.梁杆系统精确有限元方程及其在几何非线性分析和稳定计算中的应用.建筑机械.1996,(3) 18~21
35 Nianli Lu,HongSheng Zhang,Peng Lan. Precise theoretical solution of Euler’s critical load for crane telescopic boom with cylinder supporting. 2007.9,(2):10~14
36张月红.具有油缸支承的起重机箱形伸缩臂的稳定性研究.《哈尔滨工业大学硕士论文》.2006.7
37 Samir Z. Al-Sadder. Exact Expressions for Stability Functions of a General Non-prismatic Beam-column Member. Journal of Constructional Steel Reaserch. 2004, 60(11): 582~584
38 S.R.Bodner, M.B.Rubin. Modelling the buckling of axially compressed elastic cylindrical shells, AIAA Journal, volume2005 ,(43):103-110
39桂敦光.起重机吊臂液压缸拉伤分析.工程机械.1995,(7):35~36
40张质文,虞和谦,王金诺等.起重机设计手册.北京:中国铁道出版社,1998
41 S.P.铁摩辛柯.弹性稳定理论(第二版).科学出版社.1965
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43纪爱敏. QY25K型汽车起重机伸缩吊臂的有限元分析.工程机械.2003, (1): 24~29
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53 Kim Moon-Young a, Kim Sung-Bo, Kim Nam-II. Spatial stability of shear deformable curved beams with non-symmetric thin-walled sections. Stability formulation and closed-form solutions. Computers and Structures. 2005,(83):58~68
2张魁元,王雪.汽车起重机伸缩臂的维护和修理. 2004, (11):28~30
3沈玉风,孟庆华.汽车起重机六边形截面箱形伸缩臂计算研究.2001,(15):23-27
4谷礼新,郑海斌,彭卫平.塔式起重机起重臂结构和稳定性有限元分析.机电工程技术. 2005, 34(8):28~36
5朱渝春,冯贤桂.伸缩臂式起重机回转侧向动载荷的计算.工程机械. 2005,(2):11~14
6顾迪民.起重机械事故分析和对策.人民出版社. 2001: 210-224
7 GB3811-83起重机设计规范.中国标准出版社, 1983:76~82
8陆念力,孟晓平,顾迪民.具有外伸臂的多跨连续附着压杆的非线性变形及整体稳定性计算.工程机械. 1996, (9):3~6
9 Q.S.Li. Buckling analysis of multi-step non-uniform columns, Advances in Structure Engineering, volume(3), 139-144, (2000)
10 Georage.A.Kardomateas, George.J.Simitses. Comparative studies on the buckling of isotropic, orthotropic, and sandwich columns, Mechanics of Advanced Materials and Structures, volume(1), 309-327, (2004)
11王硕哲,顾迪民.伸缩油缸对箱形吊臂受力状况的影响.起重运输机械.1983,(11):34~37
12 Loannis G. Raftoyiannis,John Ch. Ermopoulos. Stability of Tapered and Stepped steel Columns with Initial Imperfections. Engineering Structures. 2005,27(8):1248~1257
13胡铁华,唐洪学,马成林.箱形伸缩吊臂设计变量对性能参数的影响线.建筑学报.1996,(9):9~13
14 S.P.Timoshenko, J.M.Gere .Theory of elastic stability, 2nd ed,McGraw-Hill, 1961:203~236
15 Otsuka Hiromitsu, Koga Tatsuzo. Buckling of circular cylindrical shell under beam-like bending experiment, Transactions of the Japan Society for Aeronautical and Space Sciences. 1998,(41):38~45
16 P.Timoshenko, J.M.Gere .Theory of elastic stability, 2nd ed,McGraw-Hill,1961:203~236
17 Sung-Bo Kim, Moon-Young Kim. Improved formulation for spatial stability and free vibration of thin-walled tapered beams and space frames. Engineering Structures. 2000, (22) 446~458
18 Nam-Il Kim , Kwang-Jin Seo b, Moon-Young Kim. Free vibration and spatial stability of non-symmetric thin-walled curved beams with variable curvatures. International Journal of Solids and Structures,2003(40) 3107–3128
19 Guo-Qiang Li. A tapered Timoshenko–Euler beam element for analysis of steel portal frames. Journal of Constructional Steel Research ,2002, (58) 1531~1544
20 S. Naguleswaran. Transverse vibration and stability of an Euler–Bernoulli beam with step change in cross-section and in axial force. Journal of Sound and Vibration,2004 (270)1045~1055
21杨学银,钢结构稳定性探讨.工程科学.2007,(02):26-27
22刘光栋,罗汉泉.杆系结构稳定.人民交通出版社.1988:1-4
23 Klaus-Jürgen Bathe. Advances in Nonlinear Finite Element Analysis of Automobiles. 1997, 64(5): 881-891
24 Klaus-Jurgen Bathe.Finite Element procedures. Prentice Hall, Inc. 1996,(6):485~628
25蓝天,姚卓智.桅杆结构的非线形分析.中国建筑研究院结构所. 1980,(2):2~4
26楚中毅,陆念力,楚兰英等.梁杆结构稳定性分析的一种精确有限元方法及其优化.建筑机械.2001, (9):68~73
27陆念力,兰朋.二阶理论条件下的梁杆系统精确有限元方程及应用.哈尔滨建筑大学学报.1998,(4):21~25
28陈玮璋.起重机金属结构.人民交通出版社, 1987:134~176
29孙焕纯,王跃方.对桁架结构稳定分析经典理论的讨论.计算力学学报. 2005,(3): 316~320
30楚中毅,陆念力,车仁炜.一种梁杆结构稳定性分析的精确有限元法.哈尔滨建筑大学学报. 2002, 35(4): 25~28
31 David H. Ellis , Scott R. Swengel, George W. Archibald,etal. A sociogram for the cranes of the world. Behavioural Processes. 1998,(43): 125~151
32陆念力,兰朋,白桦.起重机箱型伸缩臂稳定性分析的精确理论解.哈尔滨建筑大学学报.2000,33(2):89~93
33兰朋.二阶应力作用下梁杆精确有限元方程及其在非线性分析和稳定计算中的应用.《哈尔滨建筑大学硕士论文》.1996 :32~45
34陆念力,孟晓平,顾迪民.梁杆系统精确有限元方程及其在几何非线性分析和稳定计算中的应用.建筑机械.1996,(3) 18~21
35 Nianli Lu,HongSheng Zhang,Peng Lan. Precise theoretical solution of Euler’s critical load for crane telescopic boom with cylinder supporting. 2007.9,(2):10~14
36张月红.具有油缸支承的起重机箱形伸缩臂的稳定性研究.《哈尔滨工业大学硕士论文》.2006.7
37 Samir Z. Al-Sadder. Exact Expressions for Stability Functions of a General Non-prismatic Beam-column Member. Journal of Constructional Steel Reaserch. 2004, 60(11): 582~584
38 S.R.Bodner, M.B.Rubin. Modelling the buckling of axially compressed elastic cylindrical shells, AIAA Journal, volume2005 ,(43):103-110
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