Transcript Introduction

研究生平台课
工程测试理论与方法
(S201R006)
1 课程指导思想
2 教学团队
3 教学大纲和教学计划
4 教学对象、开设年限、教学基本形式、考
核方式
5 教材建设
6 课程建设
数字化、多媒体辅助教学
课程指导思想：
让理科学生接触工程，让工科学生深入理论。
培养研究生宽基础、深专业和独立科研能力
教学团队
杨志永(2010-)：堂上授课
汪 菲(2011-)：实验教学
刘习军(2004-)：实验教学
教学对象、开设年限、教学基本形式、考核方式
机械工程全体和部分力学专业，150人/年；
每年春季堂上授课32学时，闭卷考试；实验教学16学时，实验报告；
教学大纲和教学计划
它以机械工程中常见的机械量为对象，研究测试技术基础理论
及信号变换，测量、试验数据处理与分析等内容，内容包括信
号分析基础，力、振动、温度等传感器测量原理及相应的测量
电路、激振器等设备的使用方法，测试系统静动态特性及标定，
常见的机械工程量的测试方法等。通过学习使学生能根据测量
实际要求设计合理的测试系统，能够对测试系统的性能进行分
析，对测得的数据进行处理，初步具有综合利用测试技术基础
知识和技能来分析，解决工程实际的能力。
1）绪论 2
2）测试理论基础 4
3）传感器与激振器 10
4）采集与信号处理 10
5）现代测试系统 4
6) 复习，考试 2
7）实验 8
教材
刘习军 贾启芬 主编
汪菲 刘习军
教材
新增：振动基本理论与概念
新增：虚拟仪器（采集和数据处理）
更新：新的测试仪器的使用，如放大器
更新：成熟算法函数的使用，如
FFT/MATLAB
减少：基本的数学常识，如傅里叶变换
一加强了基本概念、基本理论方法的应用；二是通过实验加强了分析问
题的方法和思路，以增强逻辑思维能力和创新能力；三是引进新的测试
理论和方法及新技术，，提高起点，结合工程实际，以反映现代工程测
试技术的新特点
课程建设
（1）课堂教学方面：利用多媒体进行教学；注意突出重
点。利用有限的课时，侧重重点、难点的讲授；注重启发式
教学；注意各知识点的联系，引导学生自觉建立自己的知识
体系；对学生容易掌握的次要内容，安排自学，以节省课堂
教学时间。
（2）课后自学指导方面：在对学生进行自学指导的同时
注重学生自学能力的培养；指导他们在课后利用图书馆、网
络查阅相关资料，培养学生独立思考、深入探究问题的习惯
和能力。
（3）实验教学方面：针对课程实践性强的特点，在实验
教学方式上，采用边讲授理论，边实验的做法，以提高实验
效果。
数字化、多媒体辅助教学
采用多媒体与板书结合教学方式，辅助网上教
学资源E-learning（包括课件、作业、互动等）
课程建设
Experimental Modal Analysis
Test Procedure
• Excitation
• Shakers (Random, Sine)
or Hammer (Impulsive)
• Load cell for force meas.
• Response
• Accelerometers
• Laser (LDV)
• Cross-spectra averaging to
estimate FRFs
• Measurement system
• FFT analyzer (2-4 channel)
• PC & data-acquisition
front-end (2-1000
channels)
• “patching” -> nonsimultaneous data
课程建设
脉冲激励测验（锤击试验）
方法:
 Response measured at one point （在一点测试响应 ）
 Excitation of the structure at a number of points（用带传感器的锤
头在不同的点激励）

计算激励点和测点的频响函数

确定结构的模态
Amplitude
一阶模态
二阶模态
三阶模态
Beam
Acceleration
Force
Force
Force
Force
Force
Force
Force
Force
Force
Force
Force
Force
Press anywhere
to advance animation
课程建设
电池指示
传感器灵敏
度适调钮
过载显示
直流电源插座
参考信号
输出端
传感器灵
敏度范围
开关
加速度、速
度、位移开
关（下限频
率）
输入端
电源开关
增益旋钮
外部电源与内
部电池选择
输入端
上限频率
输出端
接地
课程建设
显示器
过载保护指示灯
BNT connector
放大器电源开关
菜单栏选择按键
BNC socket
Input Ch.1 to
4
RS-232 Host
DC 10-33V
TNC
connector
7-pin LEMO socket
BNC socket
RS-232 Next Unit
Battery
Output Ch.1 to 4
实验建设
在实践训练方面：
NI 9233
数据采
集卡
速度控制器
超声波电机
Bruel&Kjae
r2635电荷
放大器
Bruel&Kjaer8
001型阻抗头
实验建设
在实践训练方面：
Bruel&Kjae
r8230-c-003
压电式力传
感器
Bruel&Kjae
r2692-C-001
适调放大器
NI 9205
数据采
集卡
实验建设
在实践训练方面：
实验建设
在实践训练方面：
实验建设
在实践训练方面：
数控机床主轴的振动实验研究：(a) 以加工中心为对象，采用B&K
加速度传感器，用LMS动态测试仪进行系统动特性分析和系统固
有特征参数的辨识。 (b)用电涡流传感器，对机床主轴的径向跳动
进行测量和数据处理
实验建设
在实践训练方面：
实验建设
在实践训练方面：
实验建设
在实践训练方面：
实验建设
在实践训练方面：
实验建设
在实践训练方面：
System Identification: a Cornerstone of
Structural Design in the Aerospace and
Automotive Industries
本章教学目标：
1、熟悉测试系统的组成及基本要求；
2、熟悉测试系统的传递特性；
3、熟悉工程常见的几种振动。
一、测试系统的组成及基本要求
1、
定义： 测试过程是人们从客观事物中获取相
关信息的认识过程。
2、 组成
见下页
把被测量通过传感
器转换为电信号，
并进行处理
被测对象
非电
信息
测量装置
传感器
试验装置
使被测对象处于预
定状态下，并将其
有关方面的内在联
系充分显露出来，
以便进行有效测量
把输出信号进一步出来以
排除干扰，并清楚估计其
可靠程度，提高获得信息
的置信度。
电信号 变换及测量
装置
数据处理
装置
记录显示
装置
电源
输出环节，将测
得的有用信号及
其变化过程显示
或记录下来。
3、测试系统的基本要求
输
入
x(t)
传输特性h(t)
输出y(t)
 输入、输出、传输特性是有确定关系的三个量，当
已知其中任何两个量，即可求得第三个量。
 理想的测试装置应该具有单值的、确定的 输入输
出关系，其中以输入输出呈线性关系为最佳。
4、线性检测系统主要性质
（1）符合叠加原理
若：x1(t)
x2(t)
则：x1(t)＋x2(t)
y1(t)
y2(t)
y1(t)＋y2(t)
符合叠加原理，意味着作用于线性系统的各个输入
所产生的输出是互不影响的；一个输入的存在绝不影响另一
输入所引起的输出。而在分析众多输入同时加在系统所产生
的总效果时，可以先分别分析单个输入（假定其他输入不存
在）的效果，然后将这些效果叠加起来以表示总的效果。
（2）比例特性
常倍数输入的输出等于原输入所得输出的常倍
数。
若：x(t)
y(t)
按线性系统的比例特性，对于任意常
数a，
有：ax(t)
a y(t)
（3）频率保持特性
若输入为某一频率的简谐（正旋或余旋）信号
，则系统的稳态输出必是、也只是同频率的简谐信号。
如：已知系统是线性的和其输入的频率，那么依据频率保
持性，可以认定测得信号中只有与输入频率相同的成分才
真正是由该输入引起的输出，而其他频率成分都是噪声（
干扰信号），进而可以根据这一特性，采用相应的滤波技
术，在很强的干扰下，把有用的信息提取出来。
5、测试系统的性能

精确度：指示值和被测量真值的符合程度。

稳定性：随时间或环境条件变化的稳定程度。

测量范围：所能测的范围、动态还要考虑频率。

传递特性：输入与输出的对应关系。
Overview
 Objective: To discuss the vital importance of System
Identification in the Mechanical Design Engineering Process
 To identify the specific challenges for this kind of problems and
to illustrate the research needs
 Illustrate with typical products: cars, aircraft, satellites, …. where
adequate mechanical product behaviour is vital
Overview
 Introduction: the role of Structural Dynamics in
Mechanical Design Engineering
 Approach and methodology for Structural Dynamics
Analysis: Experimental Modal Analysis
 Modal Parameter Identification methods
 Applications of modal analysis
 Recent evolutions and challenges for the future
 Conclusions
Introduction
Mechanical Design Engineering
 Market Demand: Delivering products with the required
mechanical characteristics: Excel in
 Operational quality (performance specifications…)
 Reliability (load tolerance, fatigue, life-time…)
 Safety (vehicle crash, aircraft flutter….)
 Comfort (noise, vibration, harshness)
 Environmental impact (emissions, waste, noise,
recycling…)
 Process process challenges: Excel in
 Time-to-Market: reduce design cycle
 Reduce design costs
 Product customization
Introduction
Economic Impact: Some Figures
• Typical vehicle development programs require investment
budgets of 1 .. 4 B$
• New Mercedes C-class (Automotive Engineering Intl., Aug. 2000):
• 600 M$ development + 700M$ production facilities
• Developed in less than 4 years
• New Mini: 200M£ development costs (+ as much in marketing...)
• Chrysler minivan (“The Critical Path” by Brock Yates):
• 2 B$ development budget, of which 250 M$ R&D
• 36 different body styles, 2 wheelbases, 4 engines
Introduction
Time Pressure Increases Recall Risks
Warranty costs may explode the overall budget
•
•
•
2000 warranty cost (Mercedes-Benz) : 1.5 b$
Warranty cost exceeds R&D cost
Warranty cost x 3 in 2 years ...
Introduction
Mechanical Design Engineering
 Early Design Optimization is Essential
 Product design has to go beyond the “Form and Fit”
 Focus on “Functional Performance Engineering”
 For mechanical performances: structural analysis
 Static: strength, load analysis
 Kinematic: mechanisms, motion
 Dynamic: vibrations, fatigue, noise
 Basic approach: is through the use of structural models




A priori (Finite Element) and experimental (Modal)
Analyze the effect of dynamic loads
Understand the intrinsic structural dynamics behaviour
Derive optimal design modifications
Engine
Steering Wheel
Shake
Total Vehicle
System
TACTILE
Introduction: A Systems Approach
A Source-Transmitter-Receiver Model
Seat Vibration
VISUAL
Wheel & Tire
Unbalance
Road Input
Accessories
Noise at Driver’s
& Passenger’s
Ears
Environmental Sources
Source
X
System Transfer
=
Receiver
ACOUSTIC
Rearview mirror
vibration
Overview
 Introduction: the role of Structural Dynamics in
Mechanical Design Engineering
 Approach and methodology for Structural Dynamics
Analysis: Experimental Modal Analysis
 Modal Parameter Identification methods
 Applications of modal analysis
 Recent evolutions and challenges for the future
 Conclusions
Experimental Modal Analysis
Principles
 Structural dynamics modelling: relating force inputs to
displacement/acceleration outputs
ground
f (t)
1
f (t)
2
f (t)
n
k n+1
k2
k1
m 1
c
M x(t )  C x(t )  K x(t )  f (t )
m 2
m n
c
c2
1
x (t)
1
x (t)
2
ground
 Multiple D.o.F. System:
n+1
x (t)
n
 Continuous structures approximated by discrete number of
degrees of freedom -> Finite Element Matrix Formulation
 Majority of methods and applications: Linear and TimeInvariant models assumed
Experimental Modal Analysis
Principles
 Modal Analysis: Related to Eigenvalue Analysis
 Time domain equation
M x(t )  C x(t )  K x(t )  f (t )
 Laplace domain equation
( s 2 M  sC  K ) X (s)  F (s)
 Eigenvalue analysis -> system poles and Eigenvectors
 System pole -> Resonance frequency and damping value
k , *k   k k  j 1   k2 k
 Eigenvector -> Mode shape
 Transformation vectors to “Modal Space”
Experimental Modal Analysis
Principles
 Modal Shape: Eigenvector in the physical space: physical
interpretation (Example “Skytruck”)
Modal Analysis Principle;
Decomposition in Eigenmodes
 Modal Analysis: The modal superposition
a1 x
=
a2 x
+
+ …
+
+ …
+
x a3
x a4
Experimental Modal Analysis
Principles
 Modal Analysis: An input/output relation
 Transfer Function Formulation:
X ( s)  H ( s) F ( s)
H ( s )  [ s 2 M  sC  K ]1
 Model reduction (Finite number of modes):

B ( s, ) 
H (s) 
Ak  Qk {k }  Tk 
Ak
Ak*
H (s)  

*
s


s


k 1
k
k
k , *k   k k  j 1   k2 k
D ( s, )
n
Experimental Modal Analysis
Principles
 Experimental Analysis: using input/output measurements
Input
System
u(t)
U(ω)
H
Output
y(t)
Y(ω)
 Non-parametric estimates (FRF, IR) -> Data reduction
 Black box models (ARX, state-space)
 Modal models
 Standard experimental modal analysis approach: Fitting the
Transfer Function model by Frequency Response Function
measurements
Experimental Modal Analysis
Test Procedure
• Excitation
• Shakers (Random, Sine)
or Hammer (Impulsive)
• Load cell for force meas.
• Response
• Accelerometers
• Laser (LDV)
• Cross-spectra averaging to
estimate FRFs
• Measurement system
• FFT analyzer (2-4 channel)
• PC & data-acquisition
front-end (2-1000
channels)
• “patching” -> nonsimultaneous data
Experimental Modal Analysis:
Aircraft Test Setup Example
Inputs
Responses
Ground Vibration Test
(GVT) System
Responses
F3
F4
F1
F2
•
Force Inputs
((m/s2)/N)
Log
0.10
•
0.00 0.00
Hz
Linear
80.00
Hz
80.00
Hz
80.00
°
Phase
180.00 0.00
-180.00
0.00
 H11

 H 21
 H 31

 H 41
H12 H13 H14 

H 22 H 23 H 24 
H 32 H 33 H 34 

H 42 H 43 H 44 
1 row or column
suffices to determine
modal parameters
Reciprocity
H pq  H qp
Experimental Modal Analysis
A Typical Experiment
Vehicle Body Test
•
Input
System
Output
F
H
X
F : 2 inputs
•
•
Indicated by arrows
X : 240 outputs
•
All nodes in picture
 H has 480 elements
X=H*F
Vertical force
Horizontal force
Experimental Modal Analysis
Typical FRFs
Industrial
Gear box
Vehicle
Subframe
Experimental Modal Analysis
Typical FRFs
Engine block
driving point FRF
Engine block
FRF
Experimental Modal Analysis
Ambient Excitation Tests
 Many applications do not allow input/output tests
 No possibility to apply input
 Typical product loading difficult to realise (non-linear effects)
 Large ambient excitation levels present
 Specific approach:
 Use output-only data (responses)
 Assume white noise excitation
 Reduce output data to covariances or cross-powers
Experimental Modal Analysis
The Analysis Process
 Modal Analysis: identification of modal model parameters
from the FRF (or Covariances)
 Specific problems:
 Large number of inputs/outputs, long records (noisy data)
 Non-simultaneous I/O measurements
 High system orders, order truncation, modal overlap
 Low system damping (0.1 .. 10%), Large dynamic range
 Specific approach:
 Simultaneous (“global”) analysis of all reduced (FRF) data
 Order problem: Repeated analysis for increasing orders
-> The stabilisation diagram
Experimental Modal Analysis
Principles
 Experimental Modal Analysis: using FRF measurements in
a reduced set of structural locations
Overview
 Introduction: the role of structural dynamics in
Mechanical Design Engineering
 Approach and methodology for structural dynamics
analysis: experimental modal analysis
 Modal Parameter Identification methods
 Usually taking into account the physical model
 Use of raw time data exceptional -> reduced FRF models
 Time and frequency domain approaches
 Industrial and societal applications of modal analysis
 Recent evolutions and challenges for the future
 Conclusions
Modal Model Parameter Identification
Main Methods
 Frequency domain methods: rational polynomial FRF model
N
H(  ) 
  (  ).B
j 0
M
j
j
  j (  ).Aj
N
M
j 0
j 0
H ( )  [  j ( ).B j ][   j ( ). A j ]
j 0





Nonlinear in the unknowns
n
Common denominator methods
Ak
Ak*
H () 

Partial fraction expansion methods
j  *k
k 1 j   k
Linearized methods
State space formulations (“Eigensystem Realization”)

1
Modal Model Parameter Identification
Main Methods
• Linear frequency domain method
N
  (  )B
j 0
j
M
j
 H(  )  j (  )A j  0
j 0
• Weighted or not
• LS, TLS
• Maximum Likelihood: takes data variance into account -> Nonlinear error formulation -> iterative; Error bounds!!
• Continuous or discrete frequency domain
• Preferred approach: “PolyMAX”, Least Squares Discrete
Frequency Domain LS/TLS, originating from VUB.
Modal Model Parameter Identification
Main Methods
• Time domain: Complex damped exponential approach (UC)
Nm
[ Rk ]    r e
  r kt
r 1
{L}    e
T
r
*
r
  r *kt
{L}Tr *
• Impulse responses or correlations are solutions of the
“characteristic equation”
 
 
 



Rk I   Rk 1 W1   ...  Rk t Wt   0
• Poles: found as eigenvalues of [Wi] companion matrix
• Modeshapes: Least-squares fit of FRF matrix
Modal Model Parameter Identification
Main Methods
• Time domain: Discrete time state space model -> Subspace method
• In particular used with output-only data: stochastic subspace
xk 1   Axk   wk 
 y    Cx   v 
k
k
k
• Estimate [A] and [C] from
• output-only data (KUL…)
• covariances (INRIA):
[ A]  [ ][ ][ ]1
r  er t  r   r  ir
 r
 [C ] r
Modal Model Parameter Identification
Main Methods
 Stabilisation diagram: discrimination of physical poles
versus mathematical/spurious poles -> heuristic approach
Overview
 Introduction: the role of structural dynamics in
Mechanical Design Engineering
 Approach and methodology for structural dynamics
analysis: experimental modal analysis
 Modal Parameter Identification methods
 Applications of modal analysis
 Recent evolutions and challenges for the future
 Conclusions
EMA Example:
Aircraft Modal Analysis
• Component Development
• Engine, landing gear, ….
• Aircraft Ground Vibration Tests
•
•
•
•
Low frequency: 0 … 20… 40 Hz
> 50 orders, > 250 DOF
Model Validation & updating
Flutter prediction
EMA Example:
Aircraft Modal Analysis (Dash 8)
Frequency (Hz)
EMA Example:
Aircraft Modal Analysis for Aeroelasticity (Flutter)
Damping (%)
Airspeed (kts)
EMA Example:
Aircraft FE Model Correlation and Updating
6
FEM
FEM
Eigenfrequency
correlation
+ 5%
Analytical Frequencies [Hz]
5
4
- 5%
3
2
1
0
0
1
2
3
Measured Frequencies [Hz]
4
Mode shape
Correlation (MAC)
GVT
GVT
Courtesy H. Schaak, Airbus France
5
GVT
FEM
EMA Example:
Business Jet, Wing-Vane In-Flight Excitation
In-flight excitation, 2 wing-tip vanes
9 responses
2 min sine sweep
Higher order harmonics
Very noisy data
g/N
( )
Log
0.10
0.00 4.00
180.00 4.00
°
Phase
•
•
•
•
•
Hz
Linear
20.00
Linear
20.00
Hz
-180.00
PolyMAX
Hz
In-Operation Modal Analysis Example:
PZL-Sokol Helicopter Testing
•
•
•
•
Flight tests in different conditions (speed, climbing, hover…)
3 flights needed, 90 points
Correlation lab. / flight results
No problem with rotor frequencies
SNR GROUND TEST
MODE 6.40 Hz
CLIMBING FLIGHT TEST
MODE 6.37 Hz
MR-I ODS
6.4 Hz mode
EMA Example:
Car Body and Suspension Tests
•
•
)
Log
(
Body EMA for basic
bending and torsion
analysis (vehicle
stiffness)
0.00 25.00
179.98 25.00
Hz
Linear
75.00
Linear
75.00
Hz
°
Phase
(m/s2)/N
0.13
-179.96
25.00
Hz
75.00
Suspension EMA for a
rolling-noise problem :
Booming noise at 80Hz
Main contribution from
rear suspension mounts
EMA Example:
Civil Structures Dynamics
Input-output
testing
Øresund Bridge
Output-only
testing
Example:
Civil Structures - The Vasco da Gama Bridge
In-operation Modal Analysis
Covariance Driven
Stochastic Subspace
Overview
 Introduction: the role of structural dynamics in
Mechanical Design Engineering
 Approach and methodology for structural dynamics
analysis: experimental modal analysis
 Modal Parameter Identification methods
 Applications of modal analysis
 Recent evolutions and challenges for the future
 Conclusions
Industrial Model Analysis:
What are the issues and challenges?
• Optimizing the Test process
• Large structures (> 1000 points, in operating vehicles…)
– Novel transducers (MEMS, TEDS…)
– Optical measurements
• Complex structures, novel materials, high and distributed damping
(uneven energy distribution)
– Multiple excitation (MIMO Tests)
– Use of a priori information for experiment design
– Nonlinearity checks, non-linear model detection and
identification
– Excitation Design: Get maximal information in minimal time
Industrial Model Analysis:
What are the issues and challenges?
• Optimizing the Analysis process
• High model orders, numerical stability
• Discrimination between physical and “mathematical” poles
• Automated modal analysis
• Test and analysis duration and complexity
• Test-right-first-time
• Support user interaction with “smart results”
• Automating as much as possible the whole process
• Quantifying data and result uncertainty
-> bring intelligence in the test and analysis process
Innovation and Challenges:
Data Quality Assessment
Automatic Assessment and Classification of FRF Quality and Plausibility
x1
1
x2
x2
2
hid1
hid2
/
Amplitude
1.00
F
F
Coherence lfw :38:-Z/Multiple
Coherence rgw :38:-Z/Multiple
0.00
2.00
Hz
30.00
Coherence analysis (225 spectral lines X 540 DOFs)
Uncertainty and Reliability:
A Research Context
• Methods to assess uncertainty and variability of CAE models:
•
•
•
•
Input distribution -> response distribution
Fuzzy-FE, transformation method, Monte-Carlo…
Robust design and reliability considerations
What about test data confidence limits?
IN
OUT
Uncertainty in front craddle
•
•
•
Young’s modulus (190-210 GPa)
mass density (7600-8000 kg/m3)
shell thickness (1.6-2.4 mm)
Innovation and Challenges:
Automating Modal Parameter Estimation
•
•
•
Mimic the human operator (rules, implicit -> NN)?
Iterative methods (MLE)
Fundamental issue: discriminate mathematical and physical poles
• Indicators (damping value, p-z cancellation or correlation…)
• Fast stabilizing estimation methods
• Clustering techniques
PolyMAX
Industrial Model Analysis:
What are the issues and challenges?
• Novel applications
• Combined Ambient – I/O testing
• Nonlinear system detection and identification
• Build system-level models combining EMA and FE models
• Vibro-acoustic modal analysis: include cavity models
• Mechatronic and control
• End-of-line control
•
Model-based monitoring
• …..
Healthy structure
2nd mode shape
Damaged structure
Innovative Applications:
Building Hybrid System Models
Engine
&
Brackets
Hybrid
System
Synthesis
Subframe
&
Crossmember
HSS
Engine Mounts
Body
Vibro-acoustics
Bushings
Innovative Applications:
Vibro-Acoustic Modal Analysis
• Acoustic resonances, coupled structural-acoustical
behaviour can be modelled by vibro-acoustic modal models
K S

 0
 K C  x 
C S
 j 
f  
p
K  
 0
0
Cf
S
M

 x 
2
  p    M c
 

• Excitation by shakers and
loudspeakers -> Balancing of test
data needed (p/f, x/f, p/Q, x/Q)
• Non-symmetrical modal model
• Through structural acoustic
coupling
• Different right and left
eigenvectors
0
Mf
 x 
  
  p
 f 
 
 pq 
Vibro-Acoustic Modal Analysis
Example: Aircraft Interior Noise
f = 32.9 Hz
 = 8.5%
ATR42
f = 78.3 Hz
F100
 = 7.0%
Summary and Outlook
• Early product optimization is essential to meet market demands
• Mechanical Design Analysis and Optimization heavily rely on
Structural Models
• Experimental Modal Analysis is the key approach, it is a de-facto
standard in many industries
• While EMA is in essence a system identification problem,
particular test and analysis issues arise due to model size and
complexity
• Important challenges are related to supporting the industrial
demands (test time and accuracy) and novel applications
• Research efforts should also pay attention to “state-of-the-use”
breakthroughs
Structural Dynamics Testing on PULSE
using ME'scope
Structural Dynamic Testing
Structural Dynamic Testing
• Term differentiating it from Static Analysis and Testing
• Modal Analysis and Modal Testing
• Operational Deflection Shapes
Objectives
•
•
•
•
What is Modal Testing
Why do Modal Testing
How to do Modal Testing
Brüel & Kjær Solution to Modal Testing
Structural Dynamic Testing
Output
Modal Analysis vs Operational Deflection Shapes
• Modal Analysis
• artificial excitation (hammer, 1 or more shakers)
• input force is well known (“under our control”)
Input
• Operational Deflection Shapes
• investigation (visualisation) of structure behaviour
under “running conditions”
• input forces not known and complicated to describe
Introduction to Modal Testing
Present day demands
•
•
•
Increasing speed in transportation
Higher fuel economy
Both demands achieved by reducing the mass of
structures
Consequences
•
•
•
Structures become inherently weak
Resonances move down into frequency regions of
excitation forces
Structures fail because of dynamic loads
•
Statics studied for over a century
Modal Testing
What
Why
How
Definition of Modal Testing
To construct a mathematical model of
the vibrational properties and behaviour
of a structure by experimental means
Natural Frequency
Modal Damping
Residues
Modal Parameters
Theoretician
Experimentalist
•
•
Eigenvalue
Percent Damping
•
•
Natural Frequency
Loss Factor
•
Eigenvector
•
Mode Shape
Amplitude
First
Mode
Second
Mode
Third
Mode
Beam
Force
Modal Testing
What
Why
How
Brüel & Kjær Solution
Trouble Shooting
Frequency Response Function
High responses
Vibration response
during operation
SDM and FRS (Assumes validated Modal Model)
What if … scenarios
Structural Dynamics Modification

Mass

Stiffness

Tuned absorber

Move resonance frequency
Forced Response Simulation

How will a structure behave when
one or more forces are applied?
High response
Previous
response
Low response
Why do Modal Testing
• Trouble shooting
•
To reduce excessive vibration levels
• FE-modelling
•
•
•
•
•
To ensure resonances are away from excitation frequency
Validation by testing on prototypes
Refinement of the mathematical model through inclusion of damping
Prerequisite in aircraft industry
Today also commonly used in automotive industry
• Structural assembly analysis
•
To predict the dynamic behaviour of assembled sub-components
• Simulation of “what if” scenarios
•
•
Determination of forces
Response to complex excitation
Modal Testing
What
Why
How
How to do Modal Testing
Modeling
1



Geometry
Degree of Freedom definition
X or XYZ direction
Measurements
2



Frequency Response Functions
Hammer or shaker excitation
Coherence Function for validation
Curve fitting
3



Frequency
Damping
Residues
Validation
4




MAC (Modal Assurance Criteria)
Modal Confidence Factor
Phase Scatter
........
System Analysis
Determination of the inherent properties of the system

Output


Excitation of the system by a known force
Measurement of the Output
Relating the Output to the Input
Frequency Response Function:
Output Motion Response
H() =
=
=
Input
Force
Excitation
Input

The FRF shows the inherent properties of
a dynamic system — independent of the
excitation force and type
Frequency Response Function
[m /s²]
Tim e(R esp ons e) - Input
Wo rkin g : In put : Inp ut : FFT Analyzer
80
40
0
-40
-80
0
40 m
80 m
12 0m
[s]
16 0m
20 0m
24 0m
FFT
Frequency Domain
Output
[m /s²]
Time Domain
Au tosp ectru m(R esp ons e) - Input
Wo rkin g : In put : Inp ut : FFT Analyzer
10
1
10 0m
[(m /s²)/N]
Fre que ncy Res pons e H 1(Re spo nse,Excitation ) - In put (Mag nitu de)
Wo rkin g : In put : Inp ut : FFT Analyzer
10 m
10
1m
0
20 0
40 0
60 0
80 0
[H z]
1k
1,2 k
1,4 k 1,6 k
10 0m
[N ]
Input
Au tosp ectru m(Excita tion ) - In put
Wo rkin g : In put : Inp ut : FFT Analyzer
1
0
20 0
40 0
60 0
80 0
[H z]
1k
1,2 k
1,4 k 1,6 k
Inverse
FFT
[(m /s²)/N/s]
Im puls e Re spo nse h1(R esp ons e,Excitati on) - Inpu t (R eal Part)
Wo rkin g : In put : Inp ut : FFT Analyzer
2k

1k
0
-1k
-2k
0
40 m
80 m
12 0m
[s]
16 0m
20 0m
10 0m
10 m
1m
10 0u
0
[N ]
Tim e(Excita tion ) - In put
Wo rkin g : In put : Inp ut : FFT Analyzer
FFT
20 0
10 0
0
-10 0
-20 0
0
40 m
80 m
12 0m
[s]
16 0m
20 0m
24 0m
20 0
40 0
60 0
80 0
[H z]
1k
1,2 k
1,4 k 1,6 k
Frequency
Response
Function
Impulse
Response
Function
Output Motion Response
H() =
=
=
Input
Force
Excitation
24 0m
Modal Model – Global Parameters
Natural Frequency and Modal Damping
Frequency Domain
Time Domain
1
Decay Rate  = t
3 dB bandwidth
=2
3dB
Time
0
Frequency
Natural Frequency: 0 = 2pf0
Damping Ratio:


0
T
t
Natural Frequency:
Damping Ratio:
1
T


0
f0 
Modal Model – Local Parameters
Residues
Residue: The “strength” of the mode
H(0)
Amplitude
First
Mode
2
Second
Mode
Third
Mode
0
Frequency
Residue: R = H(0) · 
Driving point Residue: Riir = a · ir2
General Residue: Rijr = a · ir · jr
Beam
Force
The Driving point Residue
scales the Mode Shape
Excitation Technique
Shaker excitation
Hammer excitation
Excitation moved
Multichannel response or
response points may be moved
In
Out
In
Out
•
•
•
Small homogenous structures
Quick Polyreference technique
Fast method - no fixtures required
H11 H12.........H 1n 


.......... .......... .. 

H 
.......... .......... .. 


..........
..........
..


•
•
•
Large or complex structures
Various excitation signals
possible
Time consuming - installation
work to be done
H11.......... ... 


H
..........
...
21

H  
.......... ......... 


Hn1.......... ... 
Curve Fitting
Single Degree of Freedom (SDOF)


Simple structure
Few and widely spaced modes
Multi Degree of Freedom (MDOF)

[(m /s²)/N]
Fre que ncy Res pons e H 1(Re spo nse,Excitation ) - In put (Mag nitu de)
Wo rkin g : In put : Inp ut : FFT Analyzer

Multiple modes
Many and close modes
10
Local
10 0m

0
20 0
40 0
60 0
80 0
[H z]
1k
1,2 k
1,4 k 1,6 k
Based upon one single DOF
Global

Based upon multiple DOF’s
Polyreference


Symmetric structures exhibit multiple modes at the same frequency
One single peak does not necessarily mean one mode
How to do Modal Testing
Modeling



Geometry
Degree of Freedom definition
X or XYZ direction
Measurements


Frequency Response Functions
Hammer or shaker excitation
Curve fitting



Frequency
Damping
Residues
Validation




MAC (Modal Assurance Criteria)
Modal Confidence Factor
Phase Scatter
........
Modal Testing
What
Why
How
The Brüel & Kjær Solution
Vibration
Data
Modal Test
Consultant
PULSE
Modal
File
Transfer
Software
Brüel & Kjær Solution
PULSE Software
Predefined projects
•
for typical hammer, shaker tests
Contains predefined measurement setup
• trigger conditions, weighting functions, multibuffer
Easy data display using workbook layouts
• Time, Autospectra, FRF H1, H2, H3, Coherence
• FRF Display of Magnitude and Phase, Real and
Imaginary, Nyquist plot
PULSE Modal Test Consultant
Features and Benefits
• Geometry driven measurement
•
with the option of importing geometry from CAD data
• Intuitive graphic control of
analyzer parameters
• Cuts your setup and
measurement time in half
• Modal data acquisition your
way
•
comprehensive choice of Modal
Post-processing packages
PULSE Modal Test Consultant
The Modal Test Consultant
based on PULSE gives the
user:
• Openness
• Scalability
• Modularity
• Productivity
• Ease of use
OLE Automation
Brüel & Kjær PULSETM
PULSE Modal Test Consultant
Setting up measurements
Mounting
the transducer
• Transducer mounting
guided by geometry model
on screen
• Graphic supported set-up
of measurement
parameters
• Audio and visual
notification of
measurement status
Geometry
model
on screen
Time weighting
Overload
indication
• Automatic DOF labeling
• label while measuring
Easy Scaling and Set-up of Hammer Excitation
• Hit the test object in a number of different places and …..
1 Autorange or select Input Range
2 Select Trigger Level
• Hit the test object once and …..
3 Choose Time Weighting
4 Set Pre-trigger
PULSE Modal Test Consultant
Create Test Model from geometry
Geometry creation
•
•
Import geometry via DXF
and UFF file format
Easy-to-use geometry
drawing tools
Test Model
•
Assign DOFs to geometry
Export
•
•
Geometry model
DOF information
PULSE Modal Test Consultant
Measurements are guided by a geometrical model
PULSE Test Consultant for Modal
Set up of signal parameters using tables*
* The tables can be customizer to suit individual needs
PULSE Test Consultant for Modal
Set up Measurement conditions
Auto-ranging signals
•
using graphic support
Trigger conditions
•
•
Trigger level (impact test)
Pre-trigger
Time weighting
•
•
•
Transient
Exponential
Hanning, ...
Automated Transducer
Calibration
PULSE Modal Test Consultant
Data transfer to modal software
Data transfer of
•
•
geometry model and DOF
information
measurement data
Via file transfer
•
•
•
•
Universal File ASCII
Universal File Binary
Star Binary
SDF
Via OLE automation
•
Automatic transfer to ME´scope
Measurement data transfer to modal software
Via file transfer
•
•
•
•
Universal File ASCII
Universal File Binary
Star Binary
SDF
Via OLE automation
•
Automatic transfer to ME´scope
(Bridge to ME’scope)
PULSE Modal Test Consultant

Automatic Data Transfer to modal software
PULSE Modal Test Consultant
The Modal Test Consultant link PULSE to
major modal analysis post processing tools
• Reuse of existing software
• Post-processing of modal data as an integral
part of Modal Testing
OLE
Automation
ME’scopeTM
File
Transfer
STAR, I-DEASTM
OLE Automation
Brüel & Kjær PULSETM
PULSE Modal Test Consultant
Geometry driven reliable Modal Testing results
•
•
•
•
Create test model from geometry
Set up measurement conditions
Perform measurements
Transfer data to modal software
PULSE Bridge to ME’scope
Brüel & Kjær PULSETM
ME’scopeTM
Automatic Measurement Data Transfer
Load PULSE Project
Export to MEScope
Modal Software
Available through Brüel & Kjær:
STAR (Spectral Dynamics)
•
The STAR SystemTM Modal and Structural Analysis - Type 7750
ME’scopeTM (Vibrant Technology, Inc)
•
Brüel & Kjær ME’scope - Type 7754
I-DEASTM Master Series (MTS)
•
I-DEAS Test
Openness to other software:
ICATS (Imperial College, London)
LMS
Modal Analysis software
Beyond Modal Testing
Obtain modal parameters
• Natural Frequency
• Modal Damping
• Residues (Mode shape)
Validate modal parameters
• Phase Scatter
• MAC
• Modal Confidence Factor
Simulations
• Add mass
• Change stiffness
• Tuned absorbers
Validate FEM Models
Conclusion to Modal Testing
What
• Obtain Modal Model
Why
• Trouble shooting, FE Modeling,
Structural assembly analysis,
SDM and FRS
How
• Modeling, System Analysis
Measurements,Curve fitting,
Validation of Modal Model
Brüel & Kjær Solution
• PULSE Modal Bridge to ME’scope
• Modal Test Consultant
Operational Deflection Shapes
• Investigation (visualisation) of structure behaviour
under “running conditions”
• Powerfull trouble-shooting tool
• Phase information needed
• Data to be measured:
• phase assigned spectra (f.ex.between response point
and tacho (reference))
or
• FRF between response point / reference point
or
• Cross spectra
• No Curve - fitting
Measurement data transfer to ODS /modal sw
Via file transfer
•
•
•
•
Universal File ASCII
Universal File Binary
Star Binary
SDF
Via OLE automation
•
Automatic transfer to ME´scope
(Bridge to ME’scope)
Literature for Further Reading
• Frequency Analysis by R.B.Randall
(Brüel & Kjær Theory and Application Handbook BT 0007-11)
• Modal Analysis of Large Structures - Multiple Exciter
Systems by K. Zaveri
(Brüel & Kjær Theory and Application Handbook BT 0001-12)
• Modal Testing: Theory and Practice by D.J. Ewins
(Brüel & Kjær Theory and Application Handbook BT 0015-12)
• Dual Channel FFT Analysis by H. Herlufsen
(Brüel & Kjær Technical Review No. 1 & 2, 1984)
• Structural Testing, Part 1: Mechanical Mobility
Measurement by O. Døssing
(Brüel & Kjær Theory and Application Booklet BR 0458-12)
• Structural Testing, Part 2: Modal Analysis and Simulation
by O. Døssing
(Brüel & Kjær Theory and Application Booklet BR 0507-11)