感謝山衛科技同意轉載「山衛科技電子報」系列專題文章，本篇文章原始連結為http://www.samwells.com/bc/news-tw/news-tech-news-tw/480-news-tech-news-tw-2015-01-01-validation-of-fe-models-with-the-3d-ccanning-vibrometer
隨著時代的進步與市場的要求，產品的開發週期與上市時間越來越短暫，如何在最短的時間完成產品的設計與開發，成為了所有研發者面臨最大的挑戰。電腦輔助工程分析(CAE)正好可以符合這樣的需求，但CAE分析常因邊界條件或是參數設定誤差，造成分析果與實際狀況往往有著一定程度的落差。Model validation正是為了使分析模型與實際狀況一致所發展的技術，所謂的Model validation就是利用實驗量測結果FRF去計算MAC矩陣去驗證與修正CAE模型的正確性。
本文主要與大家分享利用3D掃描式雷射都普勒干涉儀進行全場的振動量測，利用此系統的好處在於快速且準確度高，不用擔心因為加速規黏貼的方向有偏移而產生誤差。完成量測後再將各點測得之FRF帶入LMS Test.Lab進行模態分析與利用Matlab進行MAC計算，以了解CAE模型與實際狀況的差異進而進行模型修改。下期文章將進一步與大家分享如何無縫一次性的在LMS. Test.Lab平台上快速的完成模態測試、相關性分析與模型更新的流程，讓您快速的建立最正確的CAE模型。
Introduction
Complex FE modeling over wide frequency ranges is used to determine the eigenfrequencies and eigenvectors during model validation. Such models are an important means of realistically mapping the effect of design changes onto the final product.
In the traditional experimentation setup, acceleration sensors are used for vibration measurement and modal hammers or shakers are used to provide excitation. For complex structures, such a setup is complex, costly and susceptible to error. Measurement and excitation points must be defined with care, to ensure that all eigenfrequencies are excited and to produce adequate resolution of the corresponding eigenvectors. 3-D laser vibrometry is an interesting alternative, enabling a much larger number of measuring points to be attained with less effort and expense and without introducing additional mass influences into the system.
Mounting and Sample Excitation
Integral measurements with a laser vibrometer require that all measuring points are optically accessible. The most convenient solution would be a 3-D laser vibrometer mounted on a robot. Additionally, mirrors can be used to divert the laser beam, or the vibrometer or measurement object can be repositioned to measure otherwise hidden points. Preprogramming a robot to move the laser measuring heads around the measurement object enables complex structures to be measured. Optionally, the measurement object – including the excitation source used – can be pivot-mounted, though it is important then to ensure adequate stability of the arrangement. The resultant data sets are then combined with the Stitching feature of the scanning vibrometer software to reproduce a full body vibration map.
A measurement object, such as the transmission casing in this example, can be suspended from straps (Fig. 1) or in an upright mounting arrangement (Fig. 2), with the shaker and the structure isolated from the environment by rubber feet. The quality of the mounting variants can be assessed by comparing the so-called Driving Point Function (DPF), the quotient of the spectrum of the system response at the point of excitation and that of the introduced force. Here a clearly defined sequence of resonances and antiresonances, a falling or rising trend and an adequately large gap between the rigid body and structure modes should be identifiable (Fig. 3). 
These criteria are met for both mounting variants. The rigid body modes occur in both variants at around 30 Hz, but in the upright mounting variant, some resonances are less distinct and between 600 Hz and 1000 Hz additional peaks are present. The upright mounting method’s advantage of a quicker setup is offset by the disadvantage of overestimating the modal damping values and additional resonances. As well as the mounting method, the stinger used to join the structure and shaker also has a major influence on the experiment result (Fig. 4). The blue curve relates to a stinger variant with two clamp sets and the green curve relates to a variant with a simple stud screw clamp fixture. The results are similar in principle, though the simpler variants exhibit additional resonances in the low frequency range and much less distinct resonances in the high frequency range. Consequently, the short, thin, rigid-fixed stinger is better suited to the structure under investigation and to measurements in the frequency range above 1200 Hz.
These criteria are met for both mounting variants. The rigid body modes occur in both variants at around 30 Hz, but in the upright mounting variant, some resonances are less distinct and between 600 Hz and 1000 Hz additional peaks are present. The upright mounting method’s advantage of a quicker setup is offset by the disadvantage of overestimating the modal damping values and additional resonances. As well as the mounting method, the stinger used to join the structure and shaker also has a major influence on the experiment result (Fig. 4). The blue curve relates to a stinger variant with two clamp sets and the green curve relates to a variant with a simple stud screw clamp fixture. The results are similar in principle, though the simpler variants exhibit additional resonances in the low frequency range and much less distinct resonances in the high frequency range. Consequently, the short, thin, rigid-fixed stinger is better suited to the structure under investigation and to measurements in the frequency range above 1200 Hz.Vibration Measurement and Evaluation
After specifying the experiment setup, the PSV-400-3D Scanning Vibrometer is applied to the transmission casing to determine the system responses at 600 measuring points and frequencies up to 4000 Hz. The associated transfer functions can be imported into LMS Test.LAB using the UFF format and evaluated there. In the evaluated range up to 3500 Hz, 16 eigenfrequencies were identified which can be classified as reliable, based on Auto-MAC and modal synthesis. The additional peaks in the upright mounting variant can be identified as non-structure modes by Auto-MAC analysis.
Correlation with the FE Model
Modal analysis is conducted by the Block-Lanczos method available in MD Nastran. To correlate the two models (Fig. 5), the experimental data is imported into MATLAB using the UFF format while the numerical data is imported by use of the MATLAB/Nastran interface IMAT FEA. The two datasets are then automatically positioned and correlated. For the first 16 eigenfrequencies, this results in a mean MAC correlation (Fig. 6) of 91% and a mean frequency variation of 1.28%. The MAC correlation is better in the low modes, while the frequency correlation is better in the higher modes.Summary
The example shows that 3-D laser vibrometry can efficiently determine the modal parameters of a complex structure within a short space of time, particularly when the measurement object – including the excitation source – is rotated for measurements from different directions. By selecting suitable stingers, the vibration excitation can be reliably applied even in high frequency ranges. It is possible to validate the FE model with the setup described here all across the evaluation range. The variations are within the limit values which can be attained with CAD data-based FE models.
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