有限元模型验证-仿真模型和模态试验数据比对

有限元(FE)模型可以在计算机上完成，大幅度减少原型制作，因此可以大大减少开发时间和成本。 但问题关键是这些有限元模型必须预测“真实”装置的特性。 FEM验证是将模拟数值与实际试验(即所谓的试验模态测试)的测得数据进行对比。 在大多数实际情况下，需要将有限元模型与试验数据进行核对，以获得可靠的验证模型，然后将其用于预测装置在负载下或进行小修改后的振动特性。 如果某个模型的仿真数据与试验数据不相符，那么该模型的设计就失去意义。

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有限元模型验证的典型试验装置

为进行有限元模型验证，需要进行相应的振动试验。先安装样品，然后在特定的位置以特定的方式对样品进行激励，该激励覆盖感兴趣的频率范围。这种方法可能不同于数值有限元模拟，后者只考虑样品的固有特性。而试验求解的是在假定的材料性质和边界条件下的一组运动微分方程。因此，严格地说，试验结果是样品在特定激励和边界条件下的响应，再通过曲线拟合从试验结果中提取模态，这是后处理的一部分。

Design cycle in RnD using modal testing for efficient FE model validation
Design cycle in RnD using modal testing for efficient FE model validation
Product development phase 01: FE model simulation
Product development phase 01: Build the bridge from design to real world, optimize simulation models based on real prototype measurement data
Product development phase 02: define measurement points
Product development phase 02: Define the modal test, measurement points matching the CAE requirements
Product development phase 03: define measurement parameters
Product development phase 03: Parametrize the measurement, specify bandwidth, resolution and excitation
Product development phase 04: Automatic laser scanning
Product development phase 4: Automatic laser scanning, sw-controlled focus compensates minor deviations from CAE to real geometry
Product development phase 05: 3d modes evaluation and visualization
Product development phase 05: Visualize and evaluate on behalf of frequency-selected 3D animations of deflection shapes
Product development phase 06: curve fit, modal parameter extraction (resonance frequencies, mode shapes and damping) and MAC analysis and FE correlation
Product development phase 06: curve fit, modal parameter extraction (resonance frequencies, mode shapes and damping) and MAC analysis and FE correlation
Product development phase 07: FE model update, optimization
Product development phase 07: FE model update, model optimization as closed loop design cycle
Design cycle in RnD using modal testing for efficient FE model validation
Design cycle in RnD using modal testing for efficient FE model validation
Product development phase 01: FE model simulation
Product development phase 01: Build the bridge from design to real world, optimize simulation models based on real prototype measurement data
Product development phase 02: define measurement points
Product development phase 02: Define the modal test, measurement points matching the CAE requirements
Product development phase 03: define measurement parameters
Product development phase 03: Parametrize the measurement, specify bandwidth, resolution and excitation
Product development phase 04: Automatic laser scanning
Product development phase 4: Automatic laser scanning, sw-controlled focus compensates minor deviations from CAE to real geometry
Product development phase 05: 3d modes evaluation and visualization
Product development phase 05: Visualize and evaluate on behalf of frequency-selected 3D animations of deflection shapes
Product development phase 06: curve fit, modal parameter extraction (resonance frequencies, mode shapes and damping) and MAC analysis and FE correlation
Product development phase 06: curve fit, modal parameter extraction (resonance frequencies, mode shapes and damping) and MAC analysis and FE correlation
Product development phase 07: FE model update, optimization
Product development phase 07: FE model update, model optimization as closed loop design cycle

基于扫描式激光测振仪的FE有限元验证

这个试验可信度高吗？在安装模态试验装置时，应复制有限元模型的边界条件，以便将有限元仿真和实测结果进行比较。测量参数（如频率带宽和所选测点）需要与任务相匹配。在建模过程中应避免或考虑到附加质量或钢化效应。扫描式激光测振仪，作为一种非接触式光学传感器，可为模态验证提供更有效输入。系统采用软件定义测点，具有超高的空间测试分辨率，全自动完成扫描测试，并迅速输出直观的2D/3D 振型。这也可以帮助减少后期数据评估和处理时可能出现的理解歧义。测点越多则更有利于数据后处理时进行曲线拟合，及对局部参数偏差的识别，如局部阻尼或质量分布的局部变化。

MAC analysis as result in FEM validation comparing model with modal test data
MAC analysis as result in FEM validation comparing model with modal test data

与仿真模型的有限元相关：频率、阻尼和MAC值

有限元模型和实测数据对比两个参数：通过求解模型中的运动微分方程所得到的特征值和特征向量，它们对应振动测试的共振频率和模态振型。最简单的方法是比较共振频率，视觉上比较特征向量和模态振型。MAC（模态置信准则）通常用于说明有限元模态分析的模态振型和实测模态振型的相关性，MAC的输入是模态振型而不是工作模态(ODS)，然后通过曲线拟合实测数据中提取出来，这是数据后处理的一部分。

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视频:为什么使用激光测振仪来验证有限元模型

对于简单的样品如铸造金属板，如果有限元模型选择合理，就可以非常准确地预测出其振动模态和共振频率。但是当组件和建模结构比较复杂时，情况就不同了。当存在多个部件，彼此通过关节进行连接，或者它们是由复合材料制成，那么仿真模型在设计初始并不可信，而是需要实测数据来进行验证。只有在所需的工作条件范围内正确地预测出模型的试验数据，改模型才可被称为已获得验证。因此，在大多数实际情况下，需要将有限元模型与试验数据进行核对，以获得可靠的验证模型，然后将其用于预测装置在负载下或进行小修改后的振动特性。 如果某个模型的仿真数据与试验数据不相符，那么该模型的设计就失去意义。

Setup of a micromechanical RF switch for FE model validation
Setup of a micromechanical RF switch for FE model validation
Mode shapes calculated by FEM for FE model validation on a mechanically-coupled piezoelectric disk-type MEMS resonator
Mode shapes calculated by FEM for FE model validation on a mechanically-coupled piezoelectric disk-type MEMS resonator
Measured deflection shapes from the piezoelectric disc-type MEMS resonator, measured by a scanning laser vibrometer for high frequency testing and FE model validation on MEMS
Measured deflection shapes from the piezoelectric disc-type MEMS resonator, measured by a scanning laser vibrometer for high frequency testing and FE model validation on MEMS
Eigen frequency of RF-MEMS switch for FEM simulation validation, G. Schrag University of Munich
Determination of Eigen frequency as one phase in the parameter extraction and calibration procedure of an energy-coupled simulation model of an RF-MEMS switch, G. Schrag University of Munich
Setup of a micromechanical RF switch for FE model validation
Setup of a micromechanical RF switch for FE model validation
Mode shapes calculated by FEM for FE model validation on a mechanically-coupled piezoelectric disk-type MEMS resonator
Mode shapes calculated by FEM for FE model validation on a mechanically-coupled piezoelectric disk-type MEMS resonator
Measured deflection shapes from the piezoelectric disc-type MEMS resonator, measured by a scanning laser vibrometer for high frequency testing and FE model validation on MEMS
Measured deflection shapes from the piezoelectric disc-type MEMS resonator, measured by a scanning laser vibrometer for high frequency testing and FE model validation on MEMS
Eigen frequency of RF-MEMS switch for FEM simulation validation, G. Schrag University of Munich
Determination of Eigen frequency as one phase in the parameter extraction and calibration procedure of an energy-coupled simulation model of an RF-MEMS switch, G. Schrag University of Munich

MEMS结构:激光测振仪如何验证FE模型

MEMS传感器的身影在日常用品中的随处可见，从胎压传感器到移动电话。计算机仿真模型对于MEMS器件的开发至关重要，但这些模型需要通过与精确试验数据的对比来验证和完善。通过基于激光的显微式激光测振仪和商用晶圆探针台，轻松获取MEMS器件真实的物理机械响应。

机械共振是MEMS器件最基本的动力学特性之一，已广泛用于陀螺仪，质量传感器，光学扫描仪，时钟振荡器等。MEMS谐振器的一个自然研究方向就是追求更高的谐振频率和寻找新的应用领域。静电和压电转导是两种主要驱动机理，这两种类型都可以使用高精度的激光测振仪在极高的频率下测试。

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有限元模型验证的测试服务&应用支持

为了解更多信息，您可登入我们官网，了解Polytec的测试解决方案：有限元网格导入，测试，比较，评估，后处理和记录全部模态试验数据。非接触式激光多普勒测振仪如何工作？如何使用扫描式激光测振仪进行2D或3D测试？我们专业团队期待您的垂询！对于形状复杂、体积较大的被测结构，采用基于机器人技术全自动测振站可以显著减少测试时间和成本。Polytec在全球设有多个结构测试中心，欢迎您与我们取得联系！

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