Influence of mistuning bolted joints on dynamic characteristics of thin-walled cylinder
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摘要:
螺栓连接结构的性能退化是航空发动机安全运行必须考虑的问题，螺栓连接预紧失谐这个概念可以表征螺栓连接结构的性能退化，并用预紧失谐量和预紧失谐比例说明预紧失谐的状态。在此基础上，将预紧失谐的概念与螺栓连接改进薄层单元法相结合，研究失谐螺栓连接对薄壁圆筒动力特性的影响。针对预紧失谐对薄壁圆筒的确定性动力特性进行分析，包括固有特性、稳态响应的影响，考虑螺栓预紧力的随机性，研究失谐螺栓连接对薄壁圆筒的概率性动力特性分析。研究结果表明：薄壁圆筒同阶固有频率的分离程度随着预紧失谐量的减小而增大，随着预紧失谐比例的增大呈现“双峰”特点；预紧失谐使得薄壁圆筒响应峰值对应的频率减小但幅值增大，随机预紧失谐使得响应峰值点的频带更宽，并且输入参数为指数分布时，输出参数为威布尔分布。
Abstract:The performance degradation of bolted joints is a problem which should be considered for the safety of aero-engine. The concept of preload mistuning of bolted joints can characterize the performance degradation, and the preload mistuning amplitude and the preload mistuning ratio are used to illustrate the state of the preload mistuning. The influence of mistuning bolted joints on the dynamic characteristics of thin-walled cylinder was studied based on the combination of preload mistuning with the improved thin-layer element method of bolted joints. First of all, the deterministic analysis of the influence of preload mistuning on the thin-walled cylinder was proposed, including the influence of the natural frequency and steady-state response. Moreover, the influence of preload mistuning on the probabilistic response characteristics of thin-walled cylinder was researched considering the randomness of bolt preload. The results indicate that the separation degree of the same-order natural frequency of thin-walled cylinder increases with the decrease of preload mistuning amplitude, and presents a “double peak” characteristic with the increase of preload mistuning ratio. The preload mistuning makes the frequency corresponding to the response peak of thin-walled cylinder reduce but the amplitude increase. The random preload mistuning makes the frequency band of the response peak point wider, and when the input parameter is exponential distribution, the output parameter is Weibull distribution.
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图 6
$\phi $ 对薄壁圆筒固有频率的影响曲线($\beta $ =1/3)Figure 6. Influence of
$\phi $ on natural frequency of thin-walled cylinder ($\beta $ =1/3)
图 7
$\phi $ 和$\beta $ 对薄壁圆筒第1阶固有频率分离程度的影响Figure 7. Influence of
$\phi $ and$\beta $ on the first order natural frequency separation of thin-walled cylinder
图 9 预紧谐调与预紧失谐薄壁圆筒响应曲线
Figure 9. Response of thin-walled cylinder with tuning preload and mistuning preload
图 10
$\phi $ 和$\beta $ 对薄壁圆筒响应的影响Figure 10. Influence of
$\phi $ and$\beta $ on response of structure
图 14 薄壁圆筒加载点y 向和x向的随机响应曲线
Figure 14. Random response curves of load point in y and x direction of thin-walled cylinder
图 15 薄壁圆筒输入、输出参数的概率分布
Figure 15. Probability distribution of input and output parameters of thin-walled cylinder
表 1 圆筒和螺栓的材料参数
Table 1. Material parameters of cylinder and bolts
参数 数值 弹性模量 E/GPa 195 泊松比 $\nu $ 0.3 密度 $\rho $/(kg·m−3) 7850 表面粗糙度 ${R_{\rm{a}}}$/${\text{μm} }$ 0.9 屈服极限 ${\sigma _{0.2}}$/MPa 355 硬度 H/MPa 570 
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表 2 薄层单元的材料参数
Table 2. Material parameters of thin-layer elements
F/N E/GPa G/GPa 螺栓连接
区域对接面接触
区域螺栓连接
区域对接面接触
区域25 000 14.13 1.976 4.39 0.760 20 000 14.80 1.132 5.69 0.435 15 000 15.72 0.911 6.05 0.350 10 000 16.25 0.791 6.25 0.304 5 000 16.75 0.691 6.44 0.266
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表 3 不同
$\beta $ 和$\phi $ 下薄壁圆筒的前6阶固有频率Table 3. The first 6-order natural frequencies of thin-walled cylinder under different
$\beta $ and$\phi $ $\beta $ $\phi $/% 固有频率/Hz 第1阶 第2阶 第3阶 第4阶 第5阶 第6阶 0 0 1 399.28 2 864.41 3 536.57 4045.11 4685.78 4 956.10 1/6 −20 1 384.42 2 859.87 3 536.48 4 044.03 4 675.44 4 952.45 1 398.16 2 863.85 3 536.58 4 044.39 4 684.99 4 955.62 −40 1 378.25 2 858.42 3 536.44 4 043.66 4 671.14 4 951.28 1 397.71 2 863.68 3 536.57 4 044.12 4 684.67 4 955.47 −60 1 374.14 2 857.54 3 536.41 4 043.45 4 668.26 4 950.58 1 397.43 2 863.58 3 536.57 4 043.96 4 684.47 4 955.38 −80 1 370.21 2 856.73 3 536.39 4 043.25 4 665.50 4 949.95 1 397.18 2 863.49 3 536.57 4 043.82 4 684.29 4 955.29 1/3 −20 1 374.61 2 857.12 3536.42 4 042.99 4 668.81 4 950.14 1 390.24 2 861.32 3536.52 4 043.36 4 679.39 4 953.57 −40 1 363.38 2 854.69 3 536.35 4 042.28 4 661.21 4 948.11 1 386.70 2 860.34 3 536.49 4 042.77 4 676.84 4 952.76 −60 1 355.51 2 853.19 3 536.30 4 041.86 4 655.94 4 946.85 1 384.41 2 859.74 3 536.47 4 042.41 4 675.17 4 952.88 −80 1 347.69 2 851.80 3 536.26 4 041.48 4 650.74 4 945.67 1 382.27 28 59.19 3 536.45 4 042.09 4 673.59 4 951.83 1/2 −20 1 372.46 2 856.47 3 536.40 4 042.13 4 667.48 4 949.54 1 374.66 2 856.70 3 536.40 4 042.15 4 668.30 4 949.77 −40 1 359.79 2 853.78 3 536.32 4 041.15 4 659.13 4 947.25 1 364.37 2 854.12 3 536.33 4 041.17 4 660.80 4 947.67 −60 1 350.74 2 852.11 3 536.27 4 040.55 4 653.28 4 945.80 1 357.46 2 852.63 3 536.28 4 040.59 4 653.69 4 946.38 −80 1 341.57 2 850.55 3 536.22 4 040.02 4 647.45 4 944.44 1 350.82 2 851.20 3 536.23 4 040.06 4 650.73 4 945.18 2/3 −20 1 358.51 2 851.94 3 536.28 4 040.94 4 656.59 4 946.04 1 371.43 2 855.93 3 536.39 4 041.29 4 666.58 4 949.08 −40 1 340.96 2 847.80 3 536.15 4 039.58 4 643.47 4 942.73 1 358.56 2 853.07 3 536.30 4 040.03 4 657.91 4 946.65 −60 1329.11 2 845.25 3 536.07 4 038.77 4 634.36 4 940.73 1349.44 2 851.29 3 536.25 4 039.27 4 651.86 4 945.12 −80 1317.80 2 842.89 3 535.98 4 038.04 4 625.33 4 938.95 1340.23 2 849.63 3 536.20 4 038.58 4 625.85 4 943.68
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表 4 不同预紧力F下螺栓连接处的数据
Table 4. Data of bolted joints under different preloads F
F/kN 螺栓区域
半径/mm${A_2}$
/mm2${A_1}$
/mm2${K_{{\text{TL}}}}$/
(109 N·m)${E_2}$
/GPa${E_1}$
/GPa5 17.63 976.46 3969.26 9.351 16.350 0.689 10 17.63 976.46 3969.26 9.439 16.121 0.790 15 17.63 976.46 3969.26 9.485 15.722 0.911 20 17.63 976.46 3969.26 9.529 14.908 1.130 25 17.63 976.46 3969.26 9.573 11.559 1.980
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