基于模态试验的PCB板结构动态性能的等效建模

汤贺鑫; 张巍; 管照阳; 刘愚; 郭小军; 罗凤旺; 李江; 张莹

基于模态试验的PCB板结构动态性能的等效建模

昆明物理研究所, 云南昆明 650223

详细信息

作者简介:
汤贺鑫（1997-），男，硕士研究生，主要研究方向：光机结构系统设计及仿真。Email：845477573@qq.com

中图分类号: TN214
计量
- 文章访问数: 144
- HTML全文浏览量: 100
- PDF下载量: 19
- 被引次数: 0
出版历程
- 收稿日期: 2021-09-06
- 修回日期: 2022-01-14
- 刊出日期: 2022-03-20

Equivalent Modeling of PCB for Dynamic Properties Based on The Modal Test

Kunming Institute of Physics, Kunming 650223, China

摘要

摘要: PCB因其基板内部结构的复杂性以及元器件种类众多且分布无规律性导致有限元模型建立困难，为此本文针对某车载热像仪主处理板上元器件的分布及结构特点，提出了一种基于自由模态试验数据的PCB板动态性能等效建模的方法。该方法对基板采用其原几何尺寸建立，对元器件的处理方式根据其物理属性以及在基板上分布特点按不同方法处理，最终需保持等效模型的质量与实际相等，并利用了自由模态试验数据以及最小二乘法推导出了基板的等效刚度以及泊松比的计算方法。通过正弦扫频试验获取主处理板的响应曲线，利用半功率带宽法计算前两阶响应对应的阻尼比，将阻尼比有限元分析软件中，获得等效模型数值计算的响应曲线，与试验的响应曲线对比，结果表明该等效建模方法满足实际工程需求，为类似产品的等效建模提供了可借鉴的思路。
- PCB /
- 等效模型 /
- 模态试验 /
- 半功率带宽法
Abstract: It is difficult to establish a finite element model for a PCB owing to the complexity of the internal structure of the substrate, the large variety of components, and irregular distribution. To solve these issues, this article proposes the distribution and structural characteristics of the components on the main processing board of a vehicle thermal imaging camera as an equivalent modeling method of PCB board dynamic performance based on free modal test data. This method uses the original geometric size of the substrate and the components are processed in different ways according to their physical properties and distribution characteristics on the substrate. Finally, the quality of the equivalent model must be kept equal to the actual model, and the free mode is used. The experimental data and least square method were used to deduce the equivalent stiffness of the substrate and the calculation of Poisson's ratio, respectively. The response curve of the main processing board was obtained through a sine frequency sweep test. The damping ratio corresponding to the first two-order responses was calculated using the half-power bandwidth method, and the damping ratio finite element analysis software was used to obtain the response curve of the equivalent model numerical calculation. A comparison of the response curves shows that the equivalent modeling method meets the actual engineering requirements and provides a reference for the equivalent modeling of similar products.
- PCB /
- equivalent modeling /
- modal testing /
- half-power bandwidth method

HTML全文

图 1 主处理电路板

Figure 1. Main processing circuit board

下载: 全尺寸图片幻灯片

图 2 主处理板等效模型

Figure 2. Equivalent model of main processing circuit board

下载: 全尺寸图片幻灯片

图 3 自由模态试验电路板悬挂示意图

Figure 3. PCB with free boundary conditions

下载: 全尺寸图片幻灯片

图 4 力锤敲击位置标记示意图

Figure 4. Grid of hammer hitting points

下载: 全尺寸图片幻灯片

图 5 传感器安装位置示意图

Figure 5. Schematic diagram of sensor installation position

下载: 全尺寸图片幻灯片

图 6 试验测取测点振动响应曲线图

Figure 6. Vibration response curve of test points

下载: 全尺寸图片幻灯片

图 7 主处理板约束状态等效模型

Figure 7. Equivalent model of constraint state of main processing board

下载: 全尺寸图片幻灯片

图 8 通过有限元分析软件计算的测点振动响应曲线图

Figure 8. Vibration response curve of measuring point calculated by finite element analysis software

下载: 全尺寸图片幻灯片

表 1 材料参数

Table 1. Material parameters

Material Name	Density ρ/(kg/m³)	Young’s modulus E/(×10¹⁰ Pa)	Poisson’s ratio υ
Metal Packaged Chips（x）	2100	3.9	0.12
Plastic packaged Chips（y）	1800	1.7	0.35
Connector（z）	2850	1.7	0.42
PCB Substrate（b）	3050	E_b	υ_b
Zone 1	8113	E_b	υ_b
Zone 2	7489	E_b	υ_b

下载: 导出CSV

表 2 自由边界条件下试验测得主处理板的前六阶模态频率

Table 2. The first six-order modal frequencies of the main processing board measured under the free boundary conditions

Mode	Frequency/Hz	Mode	Frequency/Hz
Mode 1	105.299	Mode 4	268.954
Mode 2	145.354	Mode 5	316.982
Mode 3	227.892	Mode 6	425.658

下载: 导出CSV

表 3 自由边界条件下试验与数值计算的主处理板前6阶模态

Table 3. The first six modes of the main processing plate under the free boundary conditions of the experiment and numerical calculation

Mode	Frequency/Hz Discrepancy/%	Test mode shape	Numerical mode shape
Numerical 1 vs Test 1	109.87 vs 105.299 4.34
Numerical 2 vs Test 2	135.95 vs 145.354 -6.47
Numerical 3 vs Test 3	236.54 vs 227.892 3.79
Numerical 4 vs Test 4	276.75 vs 268.954 2.90
Numerical 5 vs Test 5	314.32 vs 316.982 -0.84
Numerical 6 vs Test 6	428.93 vs 425.658 0.77

下载: 导出CSV

表 4 约束状态下主处理板等效模型的频率、峰值响应以及误差

Table 4. Frequency, peak and discrepancy of the equivalent model of the main processing board under constraints

Mode	Numerical results	Test results	Discrepancy
Mode 1	297.5 Hz	295 Hz	0.85%
First-Order Peak	73.02 g	72.912g	0.15%
Mode 2	575 Hz	555 Hz	3.60%
Second-Order Peak	13.65 g	13.085 g	4.32%

下载: 导出CSV

参考文献(13)

[1]	陶亮, 赵劲松, 刘传明, 等. 高可靠性红外热像仪的设计方法[J]. 红外技术, 2014, 36(12): 941-948. http://hwjs.nvir.cn/article/id/hwjs201412001 TAO Liang, ZHAO Jinsong, LIU Chuan-ming, et al. Design methods of high reliability thermal imagers[J]. Infrared Technology, 2014, 36(12): 941-948. http://hwjs.nvir.cn/article/id/hwjs201412001
[2]	尹俊辉, 徐立, 杨再超, 等. 基于有限元方法的印制电路板的模态分析[C]//中国力学大会-2017暨庆祝中国力学学会成立60周年大会论文集, 2017: 233-238. YIN Junhui, XU Li, YANG Zaichao, et al. Modal analysis of the PCB base on finite element method[C]//Chinese Mechanics Conference - 2017 and Proceedings of the Conference Celebrating the 60th Anniversary of the Chinese Society of Mechanics, 2017: 233-238.
[3]	LEE Y C, WANG B T, LAI Y S, et al. Finite element model verification for packaged printed circuit board by experimental modal analysis[J]. Microelectronics Reliability, 2008, 48(11-12): 1837-1846. doi: 10.1016/j.microrel.2008.07.068
[4]	姜宇, 肖鸿, 刘兴鹏, 等. 一种新型宽带单面异向介质结构的分析与设计[J]. 电子测量与仪器学报, 2009(8): 27-31. https://www.cnki.com.cn/Article/CJFDTOTAL-DZIY200908007.htm JIANG Yu, XIAO Hong, LIU Xingpeng, et al. Analysis and design of novel broadband metamaterial structure[J]. Journal of Electronic Measurement and Instrument, 2009(8): 27-31. https://www.cnki.com.cn/Article/CJFDTOTAL-DZIY200908007.htm
[5]	Pitarresi J M, Primavera A A. Comparison of modeling techniques for the vibration analysis of printed circuit cards[J]. Journal of Electronic Packing, 1992, 114(4): 378-383. doi: 10.1115/1.2905468
[6]	WU J, ZHANG R R, Radons S. Vibration analysis of medical devices with a calibrated FEA model[J]. Computers & Structures, 2002, 80(12): 1081-1086. https://www.sciencedirect.com/science/article/pii/S0045794902000676
[7]	刘孝保, 杜平安, 夏汉良, 等. 一种面向动态分析的PCB板等效建模方法[J]. 仪器仪表学报, 2011(4): 145-151. https://www.cnki.com.cn/Article/CJFDTOTAL-YQXB201104024.htm LIU Xiaobao, DU Ping'an, XIA Hanliang, et al. Dynamic property analysis-oriented PCB equivalent modeling method[J]. Chinese Journal of Scientific Instrument, 2011(4): 145-151. https://www.cnki.com.cn/Article/CJFDTOTAL-YQXB201104024.htm
[8]	刘孝保, 杜平安. 基于实验的PCB板动态性能等效建模方法[J]. 电子科技大学学报, 2013, 42(5): 787-790. https://www.cnki.com.cn/Article/CJFDTOTAL-DKDX201305029.htm LIU Xiaobao, DU Ping'an. Equivalent modeling method of PCB for dynamic property based on experimental data[J]. Journal of University of Electronic Science and Technology of China, 2013, 42(5): 787-790. https://www.cnki.com.cn/Article/CJFDTOTAL-DKDX201305029.htm
[9]	TANG W, REN J, FENG G, et al. Study on vibration analysis for printed circuit board of an electronic apparatus[C]//2007 International Conference on Mechatronics and Automation. IEEE, 2007: 855-860.
[10]	Karthiheyan S, Verma V K, Saravanan S, et al. Dynamic response characteristics and fatigue life prediction of printed circuit boards for random vibration environments[J]. Journal of Failure Analysis and Prevention, 2020, 20(4): 920-929.
[11]	杨强, 杜平安, 周元, 等. PCB板动态分析等效建模方法[J]. 电子科技大学学报, 2015(3): 475-480. https://www.cnki.com.cn/Article/CJFDTOTAL-DKDX201503028.htm YANG Qiang, DU Ping'an, ZHOU Yuan, et al. Equivalent modeling method for PCB's dynamic property analysis[J]. Journal of University of Electronic Science and Technology of China, 2015(3): 475-480. https://www.cnki.com.cn/Article/CJFDTOTAL-DKDX201503028.htm
[12]	施荣明, 朱广荣, 吴飒, 等. 军用装备实验室环境试验方法第16部分: 振动试验[S]. GJB 150.16A-2009. SHI Rongming, ZHU Guangrong, WU Sa, et al. Laboratory Environmental Test Methods for Military Materiel-Part 16: Vibration Test[S]. GJB 150.16A-2009.
[13]	Singiresu S Rao. 机械振动[M]. 4版, 北京: 清华大学出版社, 2009 Singiresu S Rao. Mechanical Vibrations[M]. Fourth Edition, Beijing: Tsinghua University Press, 2009.