考虑结合部特征的ϕ150 mm口径反射镜模型修正

崔鼎; 邓兆祥; 叶长春; 鲜玉强

doi:10.11884/HPLPB201931.190012

考虑结合部特征的ϕ150 mm口径反射镜模型修正

doi: 10.11884/HPLPB201931.190012

崔鼎^{1, 2,},
邓兆祥^{2, 3},
叶长春¹,
鲜玉强¹

1.
中国工程物理研究院应用电子学研究所, 四川绵阳 621999
2.
重庆大学汽车工程学院, 重庆 400044
3.
重庆大学机械传动国家重点实验室, 重庆 400044

基金项目:

军委科技委国防科技创新特区资助项目 C-2017-JKW-14

详细信息

作者简介:
崔鼎(1986—), 男，博士研究生，助理研究员，从事光机结构设计与优化研究；cdguycui2003@aliyun.com

中图分类号: TB122;TH128
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- 被引次数: 0
出版历程
- 收稿日期: 2019-01-14
- 修回日期: 2019-03-27
- 刊出日期: 2019-09-15

Model updating of a ϕ150 mm mirror including joint parts

1.
Institute of Applied Electronics, CAEP, P. O. Box 919-1012, Mianyang 621999, China
2.
School of Automotive Engineering, Chongqing University, Chongqing 400044, China
3.
The State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China

摘要

摘要: 针对ϕ150 mm口径反射镜受结合部的非线性因素影响导致结构分析模型精度较差的问题，提出了线性的动力学等效建模与参数修正方法。首先，在实际装配和约束环境下测试并获得了反射镜结构的试验模态参数。然后，根据界面结合部的动力学特征，对反射镜结构按照镜框固定连接模型、镜面螺钉夹持模型以及间隙等效模型进行了等效建模。最后，以试验模态参数为修正目标，采用优化方法对反射镜结构的动力学等效模型进行了参数修正，并采用模型分层和分步修正的思路，依据结合部特征将修正模型细分为两部分，提高模型参数的修正效率。结果表明，参数修正后的固有频率平均误差为1.5%，模态置信度均大于0.8，提升了反射镜结构的动力学模型精度，验证了线性化等效建模方法的正确性。
- 反射镜 /
- 动力学模型 /
- 结合部 /
- 模型修正 /
- 模态
Abstract: For the problem of precision deficiency of the analysis model caused by nonlinear factors of the joint parts in the ϕ150 mm mirror, the equivalent linearized model and the model updating method were presented. First, the experimental modal parameters of the ϕ150 mm mirror within 800 Hz were tested and obtained under the actual assembly and boundary conditions. Then, according to the dynamic characteristics of the interface joints, the equivalent finite element model of the mirror was classified as the connection model of fixed parts, the screw model and the equivalent gap model of the clamping parts, which were modeled by beam elements, rigid elements and spring elements. Finally, taking the measured experimental data including natural frequencies and modal shapes as the objective function, the dynamic model of the ϕ150 mm mirror was corrected by using optimization method. At the same time, the modified model was divided into two parts according to the characteristics of the joints by adopting the idea of hierarchical and step-by-step modification to improve the efficiency of the correction process. The results indicate that the average error of natural frequencies within 800 Hz after model updating is 1.6%, and the minimum value of modal assurance criterion is greater than 0.8, which improves the accuracy of the dynamic model for the reflective mirror. And the equivalent linearized model is also verified.
- mirror /
- dynamic modeling /
- joint part /
- model updating /
- modal

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图 1 反射镜模型

Figure 1. Schematic diagram of the reflective mirror

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图 2 反射镜的试验模态振型

Figure 2. Experimental modal shapes

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图 3 反射镜的有限元模型

Figure 3. Finite element model of the reflective mirror

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图 4 反射镜的模型参数修正过程

Figure 4. Flow chart of model updating for reflective mirror

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图 5 整体装配模型的灵敏度分析

Figure 5. Sensitivity analysis of the assembly model

下载: 全尺寸图片幻灯片

表 1 初始模型的计算误差

Table 1. Calculation errors of the initial model

order	frequency/Hz		frequency error/%	MAC
order	experimental model	initial model	frequency error/%	MAC
1	147.6	145.2	1.6	0.98
2	185.4	171.2	7.7	0.92
3	343.1	374.1	9.0	0.92
4	657.6	640.2	2.6	0.67
5	734.7	687.1	6.5	0.46

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表 2 修正变量的初值与修正结果

Table 2. Initial value and modified results

variable	E₁ /MPa	E₂ /MPa	R/mm	E₃ /MPa	E₄/MPa	K₁ /(N·mm^-1)	K₂ /(N·mm^-1)	K₃ /(N·mm^-1)	K₄ /(N·mm^-1)
initial value	100	2×10⁶	14	3×10⁴	1.5×10⁴	1×10³	1×10⁴	1×10³	1×10³
modified value	120	8.2×10⁶	18	2.63×10⁴	8.3×10³	800	1.92×10⁴	1.45×10³	1×10⁵

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表 3 镜框固定连接模型的修正结果

Table 3. Modified results of the fixed connection model

No.	frequency/Hz		frequency error/%	MAC
No.	experimental model	updated model	frequency error/%	MAC
1	211.4	217.5	2.9	0.99
2	244.2	249	2.0	0.99
3	562.6	571.4	1.6	0.94
4	751.1	759.2	1.1	0.99
5	1 197.6	1 174.9	1.9	0.87
6	1 688.5	1 636.6	3.1	0.96
7	1 843.2	1 816.9	1.4	0.90

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表 4 整体装配模型的模型修正结果

Table 4. Modified results of the assembly model

No	frequency error/%			MAC
No	1st step	2nd step	3rd step	1st step	2nd step	3rd step
1	0.06	0.06	0.06	0.98	0.98	0.98
2	7.1	4.1	4.8	0.92	0.92	0.92
3	0.2	0.15	2.4	0.95	0.95	0.95
4	0.09	5.4	0.09	0.75	0.87	0.98
5	4.6	1.5	0.008	0.44	0.81	0.82

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