ASEE Conference – June 2007 – Hawaii AN INTEGRATED UNDERGRADUATE DYNAMIC SYSTEMS TEACHING METHODOLOGY UTILIZING ANALYTICAL AND EXPERIMENTAL APPROACHES FIRST & SECOND ORDER SYSTEMS DIGITIAL DATA ACQUISITION SIGNAL CONDITIONER RISE & SETTLING TIME DYNAMIC TESTING PULLS ALL THE ANALOG DIGITAL PIECES TOGETHER !!! TO FOURIER TRANSFORM IMPACT HAMMER QUANTIZATION F R SAMPLING T E ALIASING I FORCE GAGE Q LEAKAGE M HAMMER TIP CHARACTERIZATION U HAMMER TIP E DIFFERENT PULSE SHAPES WINDOWS E N FOURIER SERIES & FFT ACCELEROMETER C Y TIME MODEL APPROXIMATION LVDT x(t) f(t) m SDOF DYNAMIC k c SYSTEM MODEL ACCELERATION FREE BODY DIAGRAM + FREQUENCY 2 y y ( ) d x dx I = I + i + 1 i x − x m + c + k x = f ( t ) i i − 1 i + 1 i & EQUATION OF MOTION 2 dt 2 dt NUMERICAL PROCESSING 1 h ( t ) = e − ζω t sin ω t DISPLACEMENT INTEGRATION / DIFFERENTIATION ω d m d * a a h ( s ) = 1 + 1 ( s − p ) ( s − p * ) TRANSDUCER 1 1 CALIBRATION 100 ζ=0.1% Y ζ=1% ζ=2% ζ=5% 10 REGRESSION ANALYSIS ζ=10% 0 ζ=20% 1 X -90 ζ=20% ω/ω n ζ=10% ζ=5% ζ=2% ζ=1% ζ=0.1% LAPLACE & TRANSFER FUNCTION -180 ω/ω n Peter Avitabile Mechanical Engineering Department University of Massachusetts Lowell Dr. Peter Avitabile, Associate Professor Integrating Undergraduate Dynamic Systems 1 Mechanical Engineering Department
The Problem Students generally do not understand how basic STEM (Science, Technology, Engineering and Math) material fits into all of their engineering courses Relationship of basic material to subsequent courses is unclear to the student. Practical relevance of the material is not clear. Students hit the “reset button” after each course not realizing the importance of STEM material Dr. Peter Avitabile, Associate Professor Integrating Undergraduate Dynamic Systems 2 Mechanical Engineering Department
The Problem Student Comment: Professor Thoughts: Professor, why didn’t you tell us that the material covered Hmmmmm... in other courses was going to be really important for the work we need to do in this Dynamic Systems course ? Professor clearly sees Student views material how pieces fit together in a disjointed fashion Dr. Peter Avitabile, Associate Professor Integrating Undergraduate Dynamic Systems 3 Mechanical Engineering Department
How to Solve the Problem A new multisemester interwoven dynamic systems project has been initiated This is to better integrate the material from differential equations, mathematical methods, laboratory measurements and dynamic systems This is done across several semesters/courses to help students better understand the relationship of basic STEM material to an ongoing problem Dr. Peter Avitabile, Associate Professor Integrating Undergraduate Dynamic Systems 4 Mechanical Engineering Department
Some Key Components of This Work Analytical Modeling Tools/GUIs Website and Online Acquisition System Projects Integration/Differentiation w/contaminants Fourier Series using LabVIEW Design of a Dynamic Measurement System 1 st and 2 nd Order System Characterization (many additional smaller projects – see paper) Dr. Peter Avitabile, Associate Professor Integrating Undergraduate Dynamic Systems 5 Mechanical Engineering Department
Webpage --- dynsys.uml.edu Project Overview Technical Papers Tutorials cover a wide assortment Tutorials of integrated material – both Online Acquisition paper tutorials with Matlab and Labview modules with voice Downloads annotated multimedia overviews Acknowledgements People Dr. Peter Avitabile, Associate Professor Integrating Undergraduate Dynamic Systems 6 Mechanical Engineering Department
Webpage --- dynsys.uml.edu Complete Imagemap of all materials available Dr. Peter Avitabile, Associate Professor Integrating Undergraduate Dynamic Systems 7 Mechanical Engineering Department
Analytical Modeling Tools/GUIs Theoretical Aspects of First and Second Order Systems First Order Systems - Modeling Step Response with ODE and Block Diagram Second Order Systems - Step, Impulse, Initial Condition with ODE and Block Diagrams Mathematical Modeling Considerations - Fourier Series, Integration/Differentiation, Regression Analysis Miscellaneous Materials - Simulink and MATLAB Primer Materials - LabVIEW Tutorial Materials - Virtual Measurement Modeling Simulations - Integration/Differentiation Considerations with Contamination Dr. Peter Avitabile, Associate Professor Integrating Undergraduate Dynamic Systems 8 Mechanical Engineering Department
Analytical Modeling Tools/GUIs MATLAB & LabVIEW Dr. Peter Avitabile, Associate Professor Integrating Undergraduate Dynamic Systems 9 Mechanical Engineering Department
Online Measurement System RUBE Accelerometer LVDT Response Under Basic Excitation x m c k Variable Damping Measurement Devices Variable Mass System Excitation Characteristics Impact Force Variable Stiffness = = + + k k k k k k EQ EQ LEAF LEAF COIL COIL Initial Displacement Dr. Peter Avitabile, Associate Professor Integrating Undergraduate Dynamic Systems 10 Mechanical Engineering Department
Online Measurement System RUBE Response Under Basic Excitation RUBE I RUBE II Dr. Peter Avitabile, Associate Professor Integrating Undergraduate Dynamic Systems 11 Mechanical Engineering Department
Online Measurement System RUBE Dr. Peter Avitabile, Associate Professor Integrating Undergraduate Dynamic Systems 12 Mechanical Engineering Department
Online Measurement System RUBE System can be remotely run Stiffness is changed for each run Sampling rate can be set Impact is available Initial displacements – three inputs LVDT and accelerometers can be turned on and off as desired Data saved and captured to browser Dr. Peter Avitabile, Associate Professor Integrating Undergraduate Dynamic Systems 13 Mechanical Engineering Department
Contaminants Cause Difficulty Students learn with problems that make them think Dr. Peter Avitabile, Associate Professor Integrating Undergraduate Dynamic Systems 14 Mechanical Engineering Department
Learn by Doing (not Listening) Fourier series come to life with LabVIEW Dr. Peter Avitabile, Associate Professor Integrating Undergraduate Dynamic Systems 15 Mechanical Engineering Department
Dynamic Measurement System Design Integration of all material to design system Comparison of Non-Colocated Accelerometer, Laser and Strain Gage Approximations of Tip Displacement of Cantilever Micrometer Cantilever Beam Accelerometer Strain Gage Laser Measurement Dr. Peter Avitabile, Associate Professor Integrating Undergraduate Dynamic Systems 16 Mechanical Engineering Department
Dynamic Systems Projects Projects integrated in with Lecture Material - Analytical project to force understanding of ODE and Laplace along with MATLAB/Simulink - RUBE used to strengthen understanding through system identification on less that perfect measurements Accelerometer LVDT - Filtering data through 1 st order RC filter in x m Simulink c k Dr. Peter Avitabile, Associate Professor Integrating Undergraduate Dynamic Systems 17 Mechanical Engineering Department
Brief Summarizing Statements Only a brief smattering of material presented here The 30 page paper has much more material. The website has a significant amount of material (tutorials, exercises, GUIs, etc) along with the online measurement system Dr. Peter Avitabile, Associate Professor Integrating Undergraduate Dynamic Systems 18 Mechanical Engineering Department
Acknowledgements This project is partially supported by NSF Engineering Education Division Grant EEC-0314875 Multi-Semester Interwoven Project for Teaching Basic Core STEM Material Critical for Solving Dynamic Systems Problems FIRST & SECOND ORDER SYSTEMS DIGITIAL DATA ACQUISITION SIGNAL CONDITIONER RISE & SETTLING TIME DYNAMIC TESTING PULLS ALL THE PIECES TOGETHER !!! ANALOG TO DIGITAL FOURIER TRANSFORM IMPACT HAMMER QUANTIZATION F R SAMPLING T E ALIASING I Q FORCE GAGE LEAKAGE M HAMMER TIP CHARACTERIZATION U HAMMER TIP E WINDOWS E DIFFERENT PULSE SHAPES N FOURIER SERIES & FFT ACCELEROMETER C Y TIME MODEL APPROXIMATION LVDT x(t) f(t) m SDOF DYNAMIC k c SYSTEM MODEL ACCELERATION FREE BODY DIAGRAM + FREQUENCY 2 y y ( ) d x dx I = I + i + 1 i x − x + + = i i − 1 i + 1 i m c k x f ( t ) 2 & EQUATION OF MOTION 2 dt dt NUMERICAL PROCESSING 1 − ζω h ( t ) = e t sin ω t DISPLACEMENT INTEGRATION / DIFFERENTIATION d m ω d a a * = + h ( s ) 1 1 − − * ( s p ) ( s p ) TRANSDUCER 1 1 CALIBRATION 100 ζ=0.1% Y ζ=1% ζ=2% ζ=5% 10 REGRESSION ANALYSIS ζ=10% 0 ζ=20% 1 X -90 ζ=20% ω/ω n ζ=10% ζ=5% ζ=2% ζ=1% ζ=0.1% LAPLACE & TRANSFER FUNCTION -180 ω/ω n Peter Avitabile, John White, Stephen Pennell Dr. Peter Avitabile, Associate Professor Integrating Undergraduate Dynamic Systems 19 Mechanical Engineering Department
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