Modal Analysis Applications

Transcription

1 Modal Analysis and Controls Laboratory Mechanical Engineering Department University of Massachusetts Lowell Presentation Topics Structural Dynamic Modeling Tools MACL Research Overview Correlation Applications System Modeling Research System Modeling Applications Force Estimation Applications Reverse Modeling Technique - DO IT DO IT Equations Recent Work MACL Lab Resources New Research Concepts EMC Chile NRO Dryer Modal Analysis Applications Spring 2002 Dr. Peter Avitabile Dr. Peter Avitabile peter_avitabile@uml.edu Sunday, February 23,

2 Structural Dynamic Modeling Techniques Could you explain modal analysis and how is it used for solving dynamic problems? Illustration by Mike Avitabile Illustration by Mike Avitabile Illustration by Mike Avitabile Overview of Structural Dynamic Modeling Techniques 1 Dr. Peter Avitabile

3 Modal Analysis and Structural Dynamics DISK DRIVE INDUCED VIBRATIONS RESPONSE INPUT TIME FORCE OUTPUT TIME RESPONSE INPUT FORCE I F T BOARD CABINET RESPONSE F F T INPUT POWER SPECTRUM INPUT FORCE FAN INDUCED VIBRATIONS Modal Analysis is the study of the dynamic character of a system which is defined independently from the loads applied to the system and the response of the system. Structural dynamics is the study of how structures respond when subjected to applied loads. Many times, in one form or another, the modal characteristics of the structure is used to determine the response of the system. Overview of Structural Dynamic Modeling Techniques 2 Dr. Peter Avitabile

4 How Do Structures Respond Dynamically? The raw time response of a structure may seem complicated but it is really nothing more than the linear combination of the effects of all the modes that are excited by the specific input response due to a vertical bump superimposed on a random excitation high speed video showing drop load Overview of Structural Dynamic Modeling Techniques 3 Dr. Peter Avitabile

5 Response of a Simple Plate Simple time-frequency response relationship increasing rate of oscillation RESPONSE FORCE time frequency Overview of Structural Dynamic Modeling Techniques 4 Dr. Peter Avitabile

6 Response of a Simple Plate Measure many points on the plate simultaneously to view the actual response Different deformation patterns can be seen as the excitation sweeps from low frequency to high frequency Overview of Structural Dynamic Modeling Techniques 5 Dr. Peter Avitabile

7 Response of a Simple Plate Sine Dwell to Obtain Mode Shape Characteristics MODE 1 MODE3 MODE 2 MODE 4 Overview of Structural Dynamic Modeling Techniques 6 Dr. Peter Avitabile

8 Analytical Modal Analysis Equation of motion [ M ]{&& x } + [ C ]{ x& } + [ K ]{ x } { F (t)} n n n n n n = Eigensolution [ K ] λ[ M ]]{ x } { 0} n n n = n Overview of Structural Dynamic Modeling Techniques 7 Dr. Peter Avitabile

9 Finite Element Models Advantages Models used for design development No prototypes are necessary Disadvantages Modeling assumptions Joint design difficult to model Component interactions are difficult to predict Damping generally ignored Overview of Structural Dynamic Modeling Techniques 8 Dr. Peter Avitabile

10 Finite Element Models Analytical models are developed to describe the system mass and stiffness characteristics of a component or system The model is decomposed to express the part in terms of its modal characteristics - its frequency, damping and shapes The dynamic characteristics help to better understand how the structure will behave and how to adjust or improve the component or system design Overview of Structural Dynamic Modeling Techniques 9 Dr. Peter Avitabile

11 Experimental Modal Analysis [Y] MEASURED RESPONSE [F] APPLIED FORCE fref1 fref2 [H] FREQUENCY RESPONSE FUNCTIONS Advantages Modal characteristics are defined from actual measurements Damping can be evaluated Disadvantages Requires hardware Actual boundary conditions may be difficult to simulate Different hardware prototypes may vary Overview of Structural Dynamic Modeling Techniques 10 Dr. Peter Avitabile

12 Experimental Modal Analysis Measured frequency response functions from a modal test can also be used to describe the structure s dynamic properties - its frequency, damping and shapes DOF # 3 DOF #2 DOF # 1 MODE # 1 MODE # 2 MODE # 3 40 COHERENCE db Mag FRF INPUT POWER SPECTRUM -60 0Hz 800Hz AUTORANGING AVERAGING h h 23 3 h 31 h 33 h 32 h 33 Overview of Structural Dynamic Modeling Techniques 11 Dr. Peter Avitabile

13 Measured frequency response functions from a modal test or operating data can be used to develop a model of the dynamic characteristics of the system Experimental Data Reduction Overview of Structural Dynamic Modeling Techniques 12 Dr. Peter Avitabile

14 What Are Measurements Called FRFs? A simple inputoutput problem Magnitude Real 6 MODE # 1 MODE # 2 MODE # 3 DOF # 1 DOF # DOF # 3 Phase Imaginary Overview of Structural Dynamic Modeling Techniques 13 Dr. Peter Avitabile

15 Digital Signal Processing Flow Diagram INPUT ANALOG SIGNALS OUTPUT Actual time signals INPUT ANTIALIASING FILTERS AUTORANGE ANALYZER ADC DIGITIZES SIGNALS OUTPUT Analog anti-alias filter Digitized time signals INPUT APPLY WINDOWS OUTPUT Windowed time signals LINEAR INPUT SPECTRUM COMPUTE FFT LINEAR SPECTRA LINEAR OUTPUT SPECTRUM Compute FFT of signal AVERAGING OF SAMPLES INPUT POWER SPECTRUM COMPUTATION OF AVERAGED INPUT/OUTPUT/CROSS POWER SPECTRA CROSS POWER SPECTRUM OUTPUT POWER SPECTRUM Average auto/cross spectra COMPUTATION OF FRF AND COHERENCE Compute FRF and Coherence FREQUENCY RESPONSE FUNCTION COHERENC E FUNCTION Overview of Structural Dynamic Modeling Techniques 14 Dr. Peter Avitabile

16 Experimental Mode Shapes From FRFs MODE MODE Overview of Structural Dynamic Modeling Techniques 15 Dr. Peter Avitabile

17 Experimental Mode Shapes From FRFs a ij1 a ij2 a ij3 ω ω ω 1 ζ 1 2 ζ 2 ζ 3 3 HOW MANY POINTS??? The task for the modal test engineer is to determine the parameters that make up the pieces of the frequency response function RESIDUAL EFFECTS RESIDUAL EFFECTS HOW MANY MODES??? Mathematical routines help to determine the basic parameters that make up the FRF Overview of Structural Dynamic Modeling Techniques 16 Dr. Peter Avitabile

18 Flow Diagram for Response Why and How Do Structures Vibrate? INPUT TIME FORCE f(t) y(t) FFT IFT INPUT SPECTRUM OUTPUT SPECTRUM f(j ω) h(j ω) y(j ω) Overview of Structural Dynamic Modeling Techniques 17 Dr. Peter Avitabile

19 What is Operating Data? If an excitation is applied close to a mode, then that mode is excited - if not, then the response is the linear combination of all the modes excited Overview of Structural Dynamic Modeling Techniques 18 Dr. Peter Avitabile

20 What is Operating Data? The modes of the structure act like filters which amplify and attenuate input excitations on a frequency basis OUTPUT SPECTRUM y(j ω) f(j ω) INPUT SPECTRUM Overview of Structural Dynamic Modeling Techniques 19 Dr. Peter Avitabile

21 What is Operating Data? The raw time response of the structure may seem complicated but it is really nothing more than the linear combination of the effects of all the modes that are excited by the specific input response due to a vertical bump superimposed on a random excitation Overview of Structural Dynamic Modeling Techniques 20 Dr. Peter Avitabile

22 What Good is Modal Analysis? EXPERIMENTAL MODAL TESTING Repeat until desired characteristics are obtained MODAL PARAMETER ESTIMATION DEVELOP MODAL MODEL STRUCTURAL CHANGES REQUIRED Yes USE SDM TO EVALUATE STRUCTURAL CHANGES FINITE ELEMENT MODELING PERFORM EIGEN SOLUTION No DONE MASS SPRING DASHPOT RIB STIFFNER STRUCTURAL DYNAMIC MODIFICATIONS The dynamic model can be used for studies to determine the effect of structural changes of the mass, damping and stiffness Overview of Structural Dynamic Modeling Techniques 21 Dr. Peter Avitabile

23 What Good is Modal Analysis? Simulation, Prediction, Correlation, to name a few FREQUENCY RESPONSE MEASUREMENTS CORRECTIONS FINITE ELEMENT MODEL PARAMETER ESTIMATION EIGENVALUE SOLVER MODAL PARAMETERS MODEL VALIDATION MODAL PARAMETERS SYNTHESIS OF A DYNAMIC MODAL MODEL MASS, DAMPING, STIFFNESS CHANGES STRUCTURAL DYNAMICS MODIFICATION FORCED RESPONSE SIMULATION REAL WORLD FORCES MODIFIED MODAL DATA STRUCTURAL RESPONSE Overview of Structural Dynamic Modeling Techniques 22 Dr. Peter Avitabile

24 Correlation and Updating Models R V A C Analytical and experimental models are correlated and adjusted to provide MAC AND ORTHOGONALITY better component and system models MAC GUYAN FINITE ELEMENT MODEL [M], [K] [U n], [ ω 2 ] g [T u] = [U n ] [U a ] VECTOR CORRELATION M A C OR P O C MODE SWITCHING FEM 3 FEM 2 EXP1 EXP 2EXP 3EXP 4EXP 5 FEM 1 FEM 5 FEM 4 FINITE ELEMENT VECTOR CORRELATION F R A C FINITE ELEMENT DOF CORRELATION VECTOR CORRELATION EXPERIMENTAL CoMAC FINITE ELEMENT DOF CORRELATION Experimental Analytical DOF CORRELATION EXPERIMENTAL MODAL MODEL [E n] = [T u] [E a] CORTHOG EXPERIMENTAL IRS SEREP EXPERIMENTAL Overview of Structural Dynamic Modeling Techniques 23 Dr. Peter Avitabile

25 Correlation and Updating Models FINITE ELEMENT CoMAC CORTHOG M A C MODAL ASSURANCE CRITERIA MATRIX MODE SWITCHING COORDINATE MODAL ASSURANCE CRITERIA OR COORDINATE ORTHOGONALITY CRITERIA OR FEM 5 FEM 4 VECTOR CORRELATION FEM 3 FEM 2 Experimental Analytical PSEUDO ORTHOGONALITY CRITERIA MATRIX P O C 0 EXP1 EXP 2 EXP 3 EXP 4 EXP 5 FEM 1 DOF CORRELATION EXPERIMENTAL FINITE ELEMENT EXPERIMENTAL Vector tools Degree of freedom tools F R A C FREQUENCY RESPONSE ASSURANCE CRITERIA FINITE ELEMENT EXPERIMENTAL R V A C RESPONSE VECTOR ASSURANCE CRITERIA DOF CORRELATION Frequency tools VECTOR CORRELATION Overview of Structural Dynamic Modeling Techniques 24 Dr. Peter Avitabile

26 Correlation and Updating Models ANALYTICAL MODEL MODEL IMPROVEMENT REGIONS MODEL IMPROVEMENT REGIONS Models can be adjusted to better reflect actual measured system characteristics Joint stiffness can be more accurately identified Simplistic modeling assumptions can be modified to reflect the actual system Overview of Structural Dynamic Modeling Techniques 25 Dr. Peter Avitabile

27 System models are developed from component models which can be obtained from physical models, reduced models, modal models or measurement models All of these methods may be used to develop a system model System Models Overview of Structural Dynamic Modeling Techniques 26 Dr. Peter Avitabile

28 System Models Modal Models FULL SPACE PHYSICAL MODEL Reduced Models FULL SPACE PHYSICAL MODEL MODAL SPACE MODEL MODAL TIE MATRIX CONNECTION MODAL SPACE MODEL FULL SPACE PHYSICAL MODEL FULL SPACE PHYSICAL MODEL Modal/Physical Models Impedance Models FULL SPACE PHYSICAL MODEL TIE MATRIX FULL SPACE PHYSICAL MODEL CONNECTION MODAL SPACE MODEL FULL SPACE PHYSICAL MODEL FULL SPACE PHYSICAL MODEL Overview of Structural Dynamic Modeling Techniques 27 Dr. Peter Avitabile

29 Hybrid/Impedance Modeling In addition to more conventional system modeling approaches, measured frequency response functions can also be used to assemble systems and provide more realistic boundary conditions MACHINE CHUCK CONNECTION IMPEDANCE MEASURED AT MACHINE HYBRID MODELING CONNECTION IMPEDANCE SYNTHESIZED FROM FEM OF WORKPIECE REFERENCE IMPEDANCE SYNTHESIZED FROM FEM OF WORKPIECE calc3_xyz UNIV:1974:+Z 120 HYBRID db 100 (s2)/(kg) FEM db Hz (m/s2)/n Dof REFERENCE Dof CALCULATED Hz Overview of Structural Dynamic Modeling Techniques 28 Dr. Peter Avitabile

30 Dynamic Force Estimation Using both measured operating data and frequency response function, estimates of the dynamic forces driving the system can be estimated OPERATIONAL DISPLACEMENTS [Y] 10-1 Estimated force vs part Reference Estimated Lbf^ Estimated force vs part Reference Hz 200 Estimated Lbf^ [H] FREQUENCY RESPONSE FUNCTIONS Hz [F] Overview of Structural Dynamic Modeling Techniques 29 Dr. Peter Avitabile

31 System Response System response can be computed for both linear and non-linear systems by various methods. INPUT TIME FORCE FFT f(t) OUTPUT TIME RESPONSE y(t) IFT INPUT SPECTRUM FREQUENCY RESPONSE FUNCTION OUTPUT SPECTRUM f(j ω) h(j ω) y(j ω) Overview of Structural Dynamic Modeling Techniques 30 Dr. Peter Avitabile

32 System Disassembly and Cascaded Targets With a specified performance level, modification or adjustment of the system matrices is required CAB IMPEDANCES COMBINED STRUCTURE RESPONSE AMI FRAME IMPEDANCES SSO/MSSO These modified systems are then used for system disassembly to determine component required characteristics PHANTOM Overview of Structural Dynamic Modeling Techniques 31 Dr. Peter Avitabile

33 System Disassembly and Cascaded Targets Components may or may not have elemental topology The problem is difficult Overview of Structural Dynamic Modeling Techniques 32 Dr. Peter Avitabile

34 Recent Work - Telescopes 45m in Nobeyama, Japan & both Gemini 8m in Chile/Hawaii Overview of Structural Dynamic Modeling Techniques 33 Dr. Peter Avitabile

35 Recent Work - Computers and Peripherals Operating and modal data collected for massive storage devices - 40 terabyte Robust design options Overview of Structural Dynamic Modeling Techniques 34 Dr. Peter Avitabile

36 Future Work & Job Opportunities As equipment is designed to be lighter, quieter, more efficient, easier to manufacture, etc., there will always be structural dynamic issues to address. This is true in all industries and sectors - aerospace, automotive, commercial products, sporting goods equipment are just a short list of applications where structural dynamics plays a critical role in the design and analysis of equipment Overview of Structural Dynamic Modeling Techniques 35 Dr. Peter Avitabile

37 Could you explain modal analysis and how is it used for solving dynamic problems? Illustration by Mike Avitabile Illustration by Mike Avitabile Illustration by Mike Avitabile Overview of Structural Dynamic Modeling Techniques 36 Dr. Peter Avitabile