A study of incomplete similar models for tyre fragment impact on fuselage structures
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摘要: 为降低机身结构抗冲击性能的实验成本，利用相似理论建立机身的非等比例缩放模型，开展模型实验是行之有效的方法。基于量纲分析的方法，建立Johnson-Cook线性应变率函数的修正关系；鉴于生产制造技术的限制，考虑扭曲厚度的非等比例机身模型对相似性行为的影响，采用指数函数法建立了非等比例模型的相似修正关系。通过对比实验中破片冲击过程的变形形态、靶板的应变时间历程曲线和最终变形轮廓，验证了数值模型的有效性。此外，分析了破片偏航姿态、机身材料、厚度和质量等因素对机身结构抗冲击性能的影响。结果表明：(1) 150 m/s的冲击速度下，破片冲击角度90º和着靶角度180º是最严苛的冲击条件。综合多种因素，分析认为3.5 mm厚的钛合金为机身结构的最佳选择，并以此作为全尺寸原型验证相似模型；另外，提出了一种可以快速获取缩比模型的设计方法。(2)应变率效应对轮胎破片冲击机身结构的影响并不显著，等比例缩放模型与原型结果吻合较好。(3)厚度扭曲的非等比例模型能够有效地预测原型结构的变形行为；虽然，在时间尺度上，模型与原型存在一定的偏差；但是，在空间尺度上，非等比例相似模型能够有效地修正扭曲厚度造成中心最大挠度的预测误差，修正后的最大误差不超过5.1%，这表明该方法能够有效地指导机身结构的相似模型设计。Abstract: In order to reduce the cost for the impact test of the full-size airframe structures, an incomplete similar model was established by the similarity theory. Based on dimensional analysis, the correction relation for the Johnson-Cook linear strain-rate function was formulated. Due to the limitation of manufacturing technology, the effect of the incomplete similar model with distorted thickness on similarity behaviors should be taken into account, so an exponential function was adopted to establish the correction formula for the distorted thickness model. The validity of the simulation model was then verified by comparisons relevant to the deformation on the fuselage, the strain-time curves of target plates and the final deformation profile. In addition, the influences of fragment angle, material property, distortion thickness and light weight on the deformation behavior of the fuselage structure were analyzed. The following main results were obtained. (1) Under the impact velocity of 150 m/s, the most severe impact conditions appear at the impact angle of 90° and the fragment attitude of 180º; by considering various factors, the 3.5-mm-thickness titanium alloy plate is regarded as the best choice for fuselage structures, and it is used as a full-size prototype to verify the similar method. Besides, it’s worth noting that an unconventional phenomenon takes place at the impact angle of 30º, while a reasonable explanation is given. (2) The effect of strain rate on the impact of tire fragments on the fuselage structure is not notable, so the incomplete similar model is in good agreement with the prototype results. (3) The incomplete scaled-down model corrected by this method can effectively predict the deformation behavior of prototype fuselage subjected to the impact of tyre fragments. Although there is a certain deviation between the model and the prototype on the time scale, on the spatial dimensions, the incomplete scaled-down model can effectively correct the prediction error for the maximum center deformation caused by the distortion thickness, and the corrected maximum error is less than 5.1%, indicating that the method can effectively guide the design for airframe structures.
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Key words:
- fuselage structure /
- similarity methods /
- incomplete similar model /
- structure impact
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图 1 高速摄影[2]和数值计算分别得到的橡胶轮胎破片以30º冲击角度和135 m/s的冲击速度撞击铝合金靶板后不同时刻的变形形貌
Figure 1. Deformation morphologies of the rubber tire fragment with the initial impact velocity of 135 m/s at the impact angle of 30º after its impacting on an aluminum alloy target at different times obtained by high-speed photography[2] and simulation
图 2 不同冲击角度下靶板的空间变形轮廓
Figure 2. Spatial deformation profiles of target plates at different impact angles
图 4 不同姿态的破片冲击靶板的空间位置
Figure 4. Spatial positions of the fragments with different attitudes impacting into target plates
图 6 靶板中心挠度的时间历程曲线
Figure 6. Deflection time history at the center points of target plates
图 7 轮胎破片正侵彻机身结构的有限元模型
Figure 7. The finite element model for a tire fragment impacting the fuselage
图 8 机身中心点的瞬时最大挠度的时间历程曲线
Figure 8. Time histories of the maximum instantaneous deflections at the centers of the fuselages
图 9 瞬时最大挠度时刻靶板中心的等效应力和有效塑性应变云图
Figure 9. Equivalent stress and plastic strain of the fuselage structures at the instant of the maximum transient deformation
图 12 对比未修正的等比例模型和原型的中心变形的时间历程曲线
Figure 12. Comparison of deformation-time curves between the uncorrected scaled models and the prototype
图 13 对比非等比例模型与原型的挠度时间历程曲线
Figure 13. Comparison of deformation-time curvesfor the center points of the plates
图 14 非等比例模型与原型靶板的最大变形时刻的轮廓图
Figure 14. The maximum deformation profiles of the plates for the incomplete scaling model and prototype
材料 $\rho $/(g·cm−3) E/GPa μ A/MPa B/MPa N C m Al 2024 2.71 72 0.33 225 406 0.34 0.015 1.0 Ti-6Al-4V 4.45 110 0.41 862 331 0.34 0.012 0.8 
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表 2 靶板中心点最终挠度的实验结果[2]与模拟结果的对比
Table 2. Comparison of the residual deformations at the centers of the target plates between experiment[2] and simulation
破片尺寸 靶板尺寸 β/(º) v/(m·s−1) 靶板中心点的最终挠度 实验值/mm[2] 模拟值/mm 相对偏差/% 30 mm×15 mm×60 mm 260 mm×260 mm×1.6 mm 30 135 2.9 2.4 18.6 30 mm×15 mm×60 mm 260 mm×260 mm×1.6 mm 30 136 8.6 10.1 17.4
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表 3 不同冲击条件下方形铝靶板中心的响应参数
Table 3. Response parameters at the centers of square aluminum plates under different impact conditions
β/(º) θ/(º) v/(m·s−1) 瞬时最大挠度/mm 最终挠度/mm 脉宽/ms 30 30 150 7.82 2.04 1.028 120 7.28 3.16 1.300 60 60 12.1 7.80 1.178 150 14.6 10.4 1.420 90 90 15.0 10.2 1.260 180 17.2 13.6 1.450
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表 4 机身的几何结构及响应参数
Table 4. Geometric structure and response parameters of the fuselage
材料 厚度/mm 质量/kg 瞬时最大挠度/cm Al01铝合金 4.0 92.9 9.35 5.0 116.2 7.91 6.0 139.4 6.77 钛合金 3.0 113.2 9.08 3.5 132.0 7.28 4.0 150.9 6.24
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表 5 对比模型与原型的瞬时最大挠度
Table 5. Comparison of the maximum displacement between the model and the prototype
对比源 比例因子 靶板厚度/mm 原型冲击速度/(m·s−1) 靶板挠度/cm 挠度相对偏差/% 模型修正速度/(m•s−1) 原型 1 3.500 150 7.28 模型 1/10 0.350 7.13 2.06 151.9 1/8 0.438 7.25 0.41 151.7 1/5 0.700 7.26 0.27 151.4 1/2 1.750 7.17 1.51 150.6
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表 6 不同指数对应的冲击速度和挠度
Table 6. Impact velocities and central deflections in relation to different exponents
n vm/(m·s−1) ${\alpha _{ {x_1 } } }=2.0$ $\alpha _{ {x_{2} } }=3.5$
$\left| { { {\text{δ} }_{ {x_1} } } - { {\text{δ} }_{ {x_2} } } } \right|/{ {\text{δ} }_{ {x_1} } }$/%$ {v_{{x_1}}} $/(m·s−1) ${ {\text{δ} }_{ {x_1} } }$/cm $ {v_{{x_2}}} $/(m·s−1) ${ {\text{δ} }_{ {x_2} } }$/cm 1.00 150 279.9 8.66 463.2 7.74 12 1.05 300.0 8.88 525.0 8.20 8 1.12 310.6 9.10 558.9 8.50 7 1.15 321.5 9.25 595.1 8.96 3
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表 7 对比原型与模型的靶板瞬时最大挠度
Table 7. Comparison of the maximum deflection between the prototype and models
模型 缩放因子 扭曲因子 机身板厚/mm 冲击速度/(m·s−1) 靶板挠度/cm 与原型挠度的相对偏差 /% 原型 1 1.00 3.5 150.0 7.28 扭曲非等
比例模型1/8 2.29 1.0 150.0 2.12 71.9 2.74 1.2 150.0 1.61 78.9 3.43 1.5 150.0 1.09 85.0 修正后的扭曲
厚度模型1/8 2.29 1.0 329.6 7.58 4.1 2.74 1.2 484.2 7.65 5.1 3.43 1.5 625.9 7.13 2.1
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