Study on Mechanism of Size Effect and Dynamic Characteristics of Rod-fastened Rotors with Crack
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摘要: 在利用相似规律设计不同尺寸拉杆转子时,由于尺寸变化,存在明显尺寸效应,含裂纹缺陷的转子尺度律机理尚不明确。本文基于量纲分析法,探究了裂纹扩展的尺寸效应机理。分析了不同尺寸机型,裂纹拉杆应力强度因子的分布规律与刚度变化规律;对比分析了不同尺寸机型对裂纹转子固有频率漂移现象的敏感性;最后提出了一种用拉杆预紧力的下降表征裂纹扩展过程的研究方法,通过实验比较了不同裂纹拉杆分布形式下转子固有频率的漂移现象。研究结论为拉杆转子的系列化设计与设备维护提供了理论基础。Abstract: In designing the rod-fastened rotors in terms of the similarity principle, there is a significant size effect due to dimensional changes and the mechanism of the scaling law of the rotors with crack defects is not clear. Based on the dimensional analysis method, the mechanism of size effect of crack propagation has been analyzed. The distribution law of the stress intensity factor and the change in stiffness was analyzed for the different size cracked rods during crack propagation. The sensitivity of natural frequencies drifting in cracked rotors of different size models was compared. Finally, a method which can simulate the crack propagation process by using the pre-tightening force reduction of rod-fastened rotors has been proposed. The phenomenon in natural frequencies drifting under different cracked rod distribution forms has also been compared with the experimental. The conclusions provide a theoretical basis for the serial design and equipment maintenance of the rod-fastened rotors.
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Key words:
- rod-fastened rotors /
- crack propagation /
- size effect /
- dynamic characteristics /
- natural frequency
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表 1 影响裂纹扩展速率的因素
影响裂纹尖端状态的量 影响材料属性的量 表征拉杆结构的量 应力强度因子幅值ΔK 材料的弹性模量E 拉杆名义尺寸d 应力比R=Kmin/Kmax 断裂韧性Kc 裂纹尖端尺寸d′ 加载频率f 泊松比υ 裂纹长度l 加载时间t 屈服强度σy 表 2 量纲矩阵
量纲指数 影响因素 F L T a1 ΔK 1 -3/2 0 a2 R 0 0 0 a3 f 0 0 -1 a4 t 0 0 1 a5 E 1 -2 0 a6 Kc 1 -3/2 0 a7 σy 1 2 0 a8 l 0 1 0 a9 d 0 1 0 a10 d′ 0 1 0 表 3 拉杆转子系统量纲矩阵
量钢指数 结构参数 F L T a1 E 1 -2 0 a2 L1 0 1 0 a3 kb1 1 -1 0 a4 mb 1 -1 2 a5 ρ 1 -4 2 a6 ω 0 0 -1 a7 F0 1 0 0 a8 nt 0 0 0 a9 υ 0 0 0 a10 Rdisk 0 1 0 a11 Rrod 0 1 0 a12 md 1 -1 0 a13 Ldisk 0 1 0 a14 R1 0 1 0 a15 kb2 1 -1 0 表 4 拉杆转子结构参数
结构参数 原型机参数 1.3倍放大机型 2.3倍缩小机型 轴头段质量mb/kg 1 000 2 197 82.2 轴头段长度L1/m 1.5 1.95 0.652 轴头段半径R1/m 0.2 0.26 0.087 拉杆半径Rrod/m 0.08 0.104 0.035 左轴承刚度kb1/(N·m-1) 1×108 1.3×108 0.435×108 弹性模量E/GPa 210 210 210 材料密度ρ/(kg·m-3) 7 800 7 800 7 800 轮盘质量md/kg 4 200 9 227.4 345.2 轮盘长度Ldisk/m 0.32 0.416 0.139 轮盘半径Rdisk/m 0.75 0.975 0.326 裂纹拉杆处界面相对刚度nt 0.8 0.8 0.8 右轴承刚度kb2/(N·m-1) 1×108 1.3×108 0.435×108 泊松比υ 0.3 0.3 0.3 拉杆预紧力F0/N 1.5×106 1.95×106 0.284×106 表 5 拉杆转子预紧力与裂纹尺寸对应关系
裂纹尺寸/mm 0 0.1 0.2 0.3 0.4 0.5 预紧力/N 7 000 6 936 6 856 6 738 6 591 6 389 -
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