文章快速检索 高级检索

Modeling method of bolted joints of aero-engine based on thin-layer element
YAO Xingyu , WANG Jianjun , ZHAI Xue
School of Energy and Power Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Abstract: The bolted joints, which are commonly used in aero-engine structure, have important influences on dynamic characteristics of aero-engine. The thin-layer element method can simulate complex connection structure and maintain the structure integrity. Based on the thin-layer element method, the modeling principles of aero-engine bolted joints was studied and the influence law of material parameters of thin-layer element on bolted joints stiffness was researched. Then the material parameters of thin-layer element through theoretical derivation were determined. Finally it was applied to actual structure and compared with detailed finite elements model so as to verify the correctness and aspect of this method. The results indicate that the thin-layer element method can simulate aero-engine bolted joints excellently; the axial and bending stiffness are decided by axial elastic modulus of thin-layer element, and the shear stiffness is decided by the xy and xz plane shear modulus of thin-layer element; the material parameters of thin-layer element can be expressed by structural parameters of bolted joints.
Key words: bolted joints     thin-layer element method     aero-engine     joint stiffness     finite element

1 薄层单元法建模原理

 图 1 某航空发动机典型螺栓连接结构 Fig. 1 Typical aero-engine bolted joints structure

 图 2 薄壁圆筒螺栓连接结构 Fig. 2 Bolt joints thin-walled cylinder structure

 螺栓类型 普通 螺栓连接 带止口 螺栓连接 精密 螺栓连接 特殊结构 无 止口 在螺杆与 螺孔间无空隙 定位要求 低 一般 高 承载切向载荷方式 安装边 接触面摩擦 止口 螺杆与螺孔挤压 承载切向载荷大小 小 大 大 是否承载轴向载荷 是 是 是 是否承载弯曲载荷 是 是 是

1.1 薄层单元法有限元计算方程形成

1.2 轴向刚度

 图 3 螺栓连接结构轴向刚度定义 Fig. 3 Definition of axial stiffness of bolted joints structure

1.3 弯曲刚度

1.4 剪切刚度

 图 4 螺栓连接结构剪切刚度定义 Fig. 4 Definition of shear stiffness of bolted joints structure

2 薄层单元对连接刚度影响规律

2.1 建 模

 图 5 薄壁圆筒螺栓连接有限元模型 Fig. 5 Finite element model of thin-walled cylinder bolted joints

 单元 单元类型 密度/(kg·m-3) 材料属性 弹性模量/GPa 剪切模量/GPa 泊松比 x y z xy yz xz xy yz xz 薄层 SOLID185 7 850 正交各向异性 180 180 180 180 180 180 0 0 0 其他 SOLID185 7 850 各向异性 210 80.7 0.3

2.2 轴向刚度影响规律

2.2.1 剪切模量对轴向刚度的影响

 图 6 剪切模量对轴向刚度的影响 Fig. 6 Influence of shear modulus on axial stiffness
2.2.2 弹性模量对轴向刚度的影响

 图 7 不同方向弹性模量对轴向刚度的影响 Fig. 7 Influence of elastic modulus on axial stiffness

 图 8 Ex=160 GPa和1.8 GPa时机匣轴向位移图 Fig. 8 Axial displacement when Ex is 160 GPa and 1.8 GPa
2.3 弯曲刚度影响规律

2.3.1 剪切模量对弯曲刚度的影响

 图 9 剪切模量对弯曲刚度的影响 Fig. 9 Influence of shear modulus on bending stiffness
2.3.2 弹性模量对弯曲刚度的影响

 图 10 不同方向弹性模量对弯曲刚度的影响 Fig. 10 Influence of elastic modulus on bending stiffness

 图 11 Ex=130 GPa和1.8 GPa时机匣Von Mises位移图 Fig. 11 Von Mises displacement of casing when Ex is 130 GPa and 1.8 GPa
3 薄层单元法材料参数确定

3.1 螺栓连接轴向刚度理论表达式

 图 12 螺栓连接结构连接区域 Fig. 12 Connection region of bolted joints structure

 图 13 安装边厚度不同的螺栓连接结构 Fig. 13 Bolted joints structure of different thickness flange

3.2 结构参数对轴向刚度的影响

 图 14 精细有限元模型 Fig. 14 Detailed finite element model
3.2.1 螺栓数目对轴向刚度的影响

 图 15 螺栓个数对连接刚度影响 Fig. 15 Influence of bolt numbers on joint stiffness
3.2.2 螺栓预紧力对轴向刚度的影响

 图 16 螺栓预紧力对连接刚度影响 Fig. 16 Influence of bolt preload on joint stiffness
3.3 薄层单元材料参数理论表达式

 图 17 螺栓连接薄层单元 Fig. 17 Thin-layer element of bolted joints

4 应 用

4.1 精细有限元模型方法

 图 18 刚度变化规律 Fig. 18 Change law of stiffness

4.2 薄层单元法

4.3 对 比

1) 通过薄层单元法建立的薄壁圆筒螺栓连接结构的轴向刚度、弯曲刚度与精细有限元模型(标准值)相比,弯曲刚度与轴向刚度分别只相差6%和6.8%.

2) 精细有限元模型的轴向、弯曲刚度影响因素为螺杆直径、螺栓数目、螺栓孔位置、法兰边厚度、预紧力,而薄层单元法模型的影响因素则只有轴向弹性模量.

3) 薄层单元模型的单元数和节点数分别比精细有限元模型少78%和71%.

4) 薄层单元模型的计算时间相对精细有限元模型少98%.

 模型 轴向 弹性模量/GPa 弯曲刚度/ (N·m·rad-1) 轴向刚度/ (N·m-1) 刚度影响因素 单元数 节点数 计算时间/ min 精细有限元模型 210 9.16×107 3.35×109 螺杆直径、螺栓数目、螺栓孔位置、法兰边厚度、预紧力 88 333 95 917 49 薄层单元模型 2.62 9.71×107 3.58×109 轴向弹性模量 19 927 28 161 1 比例/% 6 6.8 78 71 98
5 结 论

1) 薄层单元法能很好地模拟航空发动机螺栓连接结构.

2) 薄层单元剪切模量对轴向、弯曲刚度几乎没有影响;横向弹性模量对轴向、弯曲刚度几乎没有影响.

3) 薄层单元轴向弹性模量对轴向、弯曲刚度起决定作用;薄层单元剪切模量对剪切刚度起决定作用.

4) 螺栓连接的螺栓数目与轴向连接刚度呈线性变化规律.

5) 当螺栓预紧力较小时,轴向刚度随着螺栓预紧力的增加线性增加;当预紧力增加到一定程度时,轴向刚度趋近不变,说明此时螺栓连接已接近于刚性连接.

6) 通过精细有限元模型与薄层单元模型结果的对比,薄层单元模型刚度值与精细有限元模型相差在7%以内,而且计算时间、模型规模较精细有限元模型均大幅减少.

 [1] Bickford J H.An introduction to the design and behavior of bolted joints[M].2nd ed.New York:Marcel Dekker,Inc.,1990:1-8. [2] Liu S G,Wang J,Hong J,et al.Dynamics design of the aero-engine rotor joint structures based on experimental and numerical study[C]//Proceedings of ASME Turbo Expo.New York:ASME,2010:GT2010-22199. [3] 樊宁.航空发动机连接结构刚度非线性及其对转子动力学影响[D].北京:北京航空航天大学,2013. Fan N.Studies on dynamic characteristics of the joint in the aero-engine rotor system[D].Beijing:Beijing University of Aeronautics and Astronautics,2013(in Chinese). [4] Belvin W K.Modeling of joints for the dynamic analysis of truss structures,NASA-L-16163[R].Washington,D.C.:NASA,1987. [5] Gregory D L,Martinez D R.On the development of methodologies for constructing predictive models of structures with joints and interfaces,SAND2001-0003P[R].Albuquerque:Sandia National Laboratories,2001. [6] Ibrahim R A,Pettit C L.Uncertainties and dynamic problems of bolted joints and other fasteners[J].Journal of Sound and Vibration,2005,279(3-5):857-936. Click browse the original [7] Groper M.Microslip macroslip in bolted joints[J].Experimental Mechanics,1985,25(2):171-174. Click browse the original [8] Gaul L,Nitsche R.The role of friction in mechanical joints[J].Applied Mechanics Reviews,2001,54(2):93-106. Click browse the original [9] Kim J,Yoon J C,Kang B S.Finite element analysis and modeling of structure with bolted joints[J].Applied Mathematical Modelling,2007,31(5):895-911. Click browse the original [10] Ahmadian H,Jalali H.Identification of bolted lap joints parameters in assembled structures[J].Mechanical Systems and Signal Processing,2007,21(2):1041-1050. Click browse the original [11] Boeswald M,Link M,Meyer S.Experimental and analytical investigations of non-linear cylindrical casing joints using base excitation testing[C]//2003 IMAC-XXI:Conference & Exposition on Structural Dynamics.Kissimmee:Society for Experimental Mechanics,2003:1-9. [12] Ahmadian H,Mottershead J E,James S,et al.Modelling and updating of large surface-to-surface joints in the AWE-MACE structure[J].Mechanical Systems and Signal Processing,2006,20(4):868-880. Click browse the original [13] Desai C S,Zaman M M,Lightner J G,et al.Thin-layer element for interfaces and joints[J].International Journal for Numerical and Analytical Methods in Geomechanics,1984,8(1):19-43. Click browse the original [14] Sharma K G,Desai C S.Analysis and implementation of thin-layer element for interfaces and joints[J].Journal of Engineering Mechanics,1992,118(12):2442-2462. Click browse the original [15] 马双超,臧朝平,兰海波.某航空发动机机匣的动力学模型修正[J].航空动力学报,2013,28(4):878-884. Ma S C,Zang C P,Lan H B.Dynamic model updating of an aero-engine casing[J].Journal of Aerospace Power,2013,28(4):878-884(in Chinese). Cited By in Cnki (3) | Click to display the text [16] Ahmadian H,Ebrahimi M,Mottershead J E,et al.Identification of bolted-joint interface models[C]// Proceedings of the 2002 International Conference on Noise and Vibration Engineering.Leuven:Katholieke Universiteit Leuven,2002:1741-1747. [17] Iranzad M,Ahmadian H.Identification of nonlinear bolted lap joint models[J].Computers and Structures,2012,96-97:1-8. Click browse the original [18] Pande G N,Sharma K G.On joint interface elements and associated problems of numerical ill-conditioning[J].International Journal for Numerical and Analytical Methods in Geomechanics,1979,3(3):293-300. Click browse the original [19] 黄耀英,吴中如,王德信.薄层单元基本假设和简化探讨[J].力学与实践,2008,30(2):49-52. Huang Y Y,Wu Z R,Wang D X.Discuss on fundamental assumption and simplification of thin-layer element[J].Mechanics in Engineering,2008,30(2):49-52(in Chinese). Cited By in Cnki (4) | Click to display the text [20] 栾宇.航天器结构中螺栓法兰连接的动力学建模方法研究[D].大连:大连理工大学,2012. Luan Y.Study on dynamic modeling of bolted flange connections in aerospace structures[D].Dalian:Dalian University of Technology,2012(in Chinese). Cited By in Cnki (1) [21] Williams J G,Anley R E,Nash D H,et al.Analysis of externally loaded bolted joints:Analytical, computational and experimental study[J].International Journal of Pressure Vessels and Piping,2009,86(7):420-427. Click browse the original [22] Pedersen N L,Pedersen P.Stiffness analysis and improvement of bolt-plate contact assemblies[J].Mechanics Based Design of Structures and Machines,2008,36(1):47-66. Click browse the original [23] Oskouei R H,Keikhosravy M,Soutis C.Estimating clamping pressure distribution and stiffness in aircraft bolted joints by finite-element analysis[J].Proceedings of the Institution of Mechanical Engineers,Part G:Journal of Aerospace Engineering,2009,223(7): 863-871. Click browse the original

#### 文章信息

YAO Xingyu, WANG Jianjun, ZHAI Xue

Modeling method of bolted joints of aero-engine based on thin-layer element

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(12): 2269-2279.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0796