Research on Anti-Impact Scaling Test Method for Supporting Structure of Large Equipment
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摘要: 为给某核动力大型设备支撑结构的抗冲击设计提供试验依据，确保其抗冲击能力满足相关规范要求，需选用该大型设备及其支撑结构缩比模型作为抗冲击技术研究对象，在标准中型冲击机上进行冲击试验。依据π定理对该大型设备支撑结构缩比模型抗冲击试验进行理论分析，获得3种可以选用的试验工况；通过改变缩比模型加速度值使得缩比模型的支撑结构根部最大应力强度与原型达到一致，解决了π定理推导中的试验条件难题。本研究建立的分析方法可为大型设备的支撑结构冲击机缩比试验提供参考。Abstract: In order to provide experimental basis for anti-impact design of the supporting structure of large nuclear power equipment and ensure that its impact resistance meets the requirements of relevant specifications, it is necessary to select the scaling model of the large equipment and its supporting structure as the research object of impact resistance technology and carry out impact test on standard medium-sized impact machine. According to the π theorem, the impact resistance test of the scaling model of the supporting structure of the large equipment is theoretically analyzed, and three optional test conditions are obtained; By changing the acceleration value of the scaling model, the maximum stress strength at the root of the supporting structure of the model is consistent with that of the prototype, and the difficult problem of test conditions in the derivation of π theorem is solved. The analysis method established in this study can provide a reference for the scaling test of the impact machine of the supporting structure of large equipment.
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Key words:
- Large structure /
- Scaling test /
- Impact
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图 3 支撑结构根部受垂向冲击时的主应力强度变化图
Figure 3. Variation Diagram of Principal Stress Intensity at the Root of Supporting Structure under Vertical Impact
图 7 设备支撑根部受外力冲击时应力强度变化图
Figure 7. Variation Diagram of Stress Intensity at the Root of Equipment Supporting Structure under Impact of External Force
图 8 设备支撑结构垂向冲击缩比尺寸与加速度比值拟合曲线
Figure 8. Fitting Curve of Vertical Impact Scaling Size and Acceleration Ratio of Equipment Supporting Structure
图 9 双自由度系统受半正弦脉冲的位移
Figure 9. Displacement of Two-degree-of-freedom System with Half Sine Pulse
图 10 设备支撑结构根部受横向外力作用时的主应力强度变化图
Figure 10. Variation Diagram of Principal Stress Intensity at the Root of Equipment Supporting Structure under Lateral External Force
图 11 大型设备支撑根部受横向冲击力作用时的应力强度变化图
Figure 11. Variation Diagram of Stress Intensity at the Root of Large Equipment Supporting Structure under Lateral Impact Force
表 1 π定理推导下3种工况缩比模型支撑结构与原型关系对比
Table 1. Comparison between Supporting Structure and Prototype with Scaling Model under Three Working Conditions under π Theorem Derivation
参数 工况1 工况2 工况3 材料 一致 一致 $ E''' = n\lambda E $，$ G''' = n\lambda G $ 质量 ${m' = m/{n^{\rm{3}}}}$ ${m'' = m/n}$ ${m''' = \lambda m}$ 尺寸 $ \begin{array}{l} {{x'} = x/n},\\ {{l'} = l/n} \end{array}$ $ \begin{array}{l}{x'' = x/n},\\{l'' = l/n}\end{array}$ $\begin{array}{l}{x''' = x/n},\\{l''' = l/n}\end{array} $ 面积 $ {A' = A/{n^{\rm{2}}}}$ $ {A'' = A/{n^{\rm{2}}}}$ $ {A''' = A/{n^{\rm{2}}}}$ 外部激励加速度 $ {a' = na}$ $ {a'' = a/n}$ $ {a''' = a/n}$ 外部激励频率 $ {\omega _{\rm{0}}' = n{\omega _{\rm{0}}}}$ ${\omega _0^{''} = {\omega _{\rm{0}}}}$ ${\omega _0^{'''} = {\omega _{\rm{0}}}}$ 测量时间 $ {{t'} = t/n}$ $ {t'' = t}$ $ {t''' = t}$ 自身频率 $ {{\omega '} = n\omega }$ $ {\omega '' = \omega }$ $ {\omega ''' = \omega }$ 所测应力强度 $ {{\sigma '} = \sigma }$ $ {\sigma '' = \sigma }$ $ {\sigma ''' = n\lambda \sigma }$ 所测应变 $ {{\varepsilon '} = \varepsilon }$ $ {\varepsilon '' = \varepsilon }$ $ {\varepsilon ''' = \varepsilon }$ 上标“'”、“''”、“'''”分别为缩比模型支撑结构工况1、工况2、工况3 
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表 2 该大型设备及其支撑结构主振频率
Table 2. Main Vibration Frequency of the Large Equipment and Its Supporting Structure
阶数 频率/Hz 主振频率参与质量/t 方向 1 12.49 65.6 X 2 12.52 66.4 Z 3 37.36 52.6 ROT-Y 4 41.79 19.1 X 5 42.42 18.4 Z 6 60.38 82.1 Y 7 162.18 78.7 Z 8 184.71 0.0062 Y “ROT-Y”—绕Y轴转动方向
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表 3 单自由度系统缩比模型与原型加速度比值关系
Table 3. Ratio Relationship between Scaling Model and Prototype Acceleration of Single-degree-of-freedom System
缩比尺寸 缩比模型与原型加速度比值 1 1 1/2 1.015 1/4 1.077 1/6 1.193 1/8 1.380
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表 4 π定理扩展法缩比模型与原型关系对比
Table 4. Comparison between Scaling Model and Prototype under π Theorem Extension Method
材料 缩比模型与原型一致 质量 ${\overline m = m/{n^{\rm{3}}}}$ 尺寸 ${\overline x = x/n},\;\;\;{\overline l = l/n}$ 圆筒厚度 ${\overline h = h/n}$ 外部激励加速度 ${\overline a = \psi a}$ 外部激励频率 ${\overline {{\omega _0}} = {\omega _{\rm{0}}}}$ 自身频率 ${\overline \omega = n\omega }$ 上标“—”表示由π定理扩展法得到的参数
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表 5 横向分析各模态有效质量和比例因子
Table 5. Effective Mass and Scale Factor of Each Mode in Transverse Analysis
频率/Hz 比例因子 有效质量/t 12.49 1 65.65 41.86 0.540 19.13 185.19 0.0065 0.003 194.71 0.035 0.084 292.63 0.0017 0.000187 424.39 0.086 0.481
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表 6 双自由度系统缩比模型与缩比模型加速度比值关系
Table 6. Ratio Relationship between Scaling Model and Scaling Model Acceleration of Two-degree-of-freedom System
缩比尺寸 缩比模型与原型加速度比值 1 1 1/2 1.006 1/4 1.012 1/6 1.022 1/8 1.033
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