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摘要:
针对导弹在延寿试验过程中振动谱设计精度低、与实际载荷剖面差距大的问题，提出一种基于逆虚拟激励法的导弹振动谱设计方法。首先，建立了导弹-悬架系统四自由度振动模型，推导出系统激励响应关系；然后，对系统时域响应数据进行Fourier变换，得到响应功率谱矩阵并对其进行分解，构造虚拟简谐响应；最后，基于逆虚拟激励法求得系统激励功率谱，并讨论了响应噪声及系统阻尼对识别精度的影响。实验结果表明：本文方法对于随机振动载荷的识别精度较高、鲁棒性好，零噪声识别误差为2.39%，30%噪声条件下识别误差为3.21%。本文方法同样适用于其他装备的振动试验谱的设计。
Abstract:Aimed at the low design precision and larger gap with actual load profile in missile life extension test, a missile vibration spectrum design based on inverse pseudo-excitation method was put forward. First, four-degree-of-freedom vibration model of missile-suspension system was established, and the system frequency response was inferred. Then, the time-domain response data was converted into the response matrix of power spectral density by means of Fourier transform, and harmonic response was constructed based on the decomposition of response matrix of power spectral density. Finally, the system excitation power spectrum was gained based on pseudo-excitation method. At the same time, the effect of response noise and system damping on identification precision was studied. The experimental results show that the inverse pseudo-excitation method has high identification precision and good robustness. When there is no noise, the identification error is 2.39%, and it reaches 3.21% when there is 30% noise. The design means of vibration spectrum is also applicable to other equipment.
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图 1 导弹-悬架系统四自由度振动模型
Figure 1. Four-degree-of-freedom vibration model of missile-suspension system
图 2 运输车前后轮及导弹质心垂直位移PSD
Figure 2. Vertical displacement PSD of front-rear wheels of vehicle and missile centroid
图 3 前轮识别功率谱密度及误差曲线
Figure 3. Identified PSD and identification error curves of front wheels
图 4 后轮识别功率谱密度及误差曲线
Figure 4. Identified PSD and identification error curves of rear wheels
图 5 30%噪声条件下前轮识别功率谱密度及误差曲线
Figure 5. Identified PSD and identification error curves of front wheels under condition of 30% noise
图 6 60%系统阻尼前轮识别功率谱密度及误差曲线
Figure 6. Identified PSD and identification error curves of front wheels under condition of 60% system damping
图 7 30%系统阻尼前轮识别功率谱密度及误差曲线
Figure 7. Identified PSD and identification error curves of front wheels under condition of 30% system damping
表 1 仿真参数
Table 1. Simulation parameters
变量 m1/kg m2/kg m3/kg k1/(kN·m-1) k2/(kN·m-1) k3/(kN·m-1) k4/(kN·m-1) c1/(Ns·m-1) c2/(Ns·m-1) l1/m l2/m A/m wo/(rad·s-1) v/(m·s-1) 数值 1 000 40 45 18 24 190 220 350 600 3 2 20 30 50 
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