Developing a Virtual Model of a Second Order System to Simulation Real Laboratory Measurement Problems

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Proceedings of 24 IMECE: November 13-19, 24, Anaheim, CA

and RD&D Expo Developing a Virtual Model of a Second

Problems Peter Avitabile, Tracy Van Zandt University of

1 Proceedings of 24 IMECE: November 13-19, 24, Anaheim, CA 24 ASME International Mechanical Engineering Congress and RD&D Expo Developing a Virtual Model of a Second Order System to Simulation Real Laboratory Measurement Problems Peter Avitabile, Tracy Van Zandt University of Massachusetts Lowell 1 Dr. Peter Avitabile, Assistant Professor

2 The Problem Most of the student s educational exposure is to well behaved, deterministic problems with known results. Most courses expose students to - material in modules in book chapters - with exercises/problems at end of the chapter - majority of the material found in chapter/book 2 Dr. Peter Avitabile, Assistant Professor

3 The Problem Laboratory is the perfect place for students to become exposed to real world problems and solutions to those problems. Laboratory is the perfect place to put student s knowledge of basic STEM material to the test. However, many times the real world measurement is much more complicated than the textbook. Students often struggle with methods and procedures to solve a real measurement problem (with no answer at the back of the book) 3 Dr. Peter Avitabile, Assistant Professor

acceleration x(t) f(t) m k c Numerical processing of

4 A Typical MCK Measurement System A simple mass, spring, dashpot system is used to measure displacement and acceleration x(t) f(t) m k c Numerical processing of integration/differential needed to process data 4 Dr. Peter Avitabile, Assistant Professor

5 MCK Measurement System Requires extensive use of a wide variety of different analytical tools. Significant numerical data manipulation needed. Regression Analysis Data Cleansing Integration Differentiation 5 Dr. Peter Avitabile, Assistant Professor

6 MCK Measurement System The data acquisition system and transducers are intentionally selected such that the majority of possible errors exist in the data Drift Bias Offset Quantization Noise 1 Plot of Displacement for a Spring-Mass System c Displ (inch) Displ. Meas. Displ. Calc. Time (sec) Velocity Comparison Velocity (in/sec) Time (sec) 6 Dr. Peter Avitabile, Assistant Professor

7 MCK Measurement System The students are forced to integrate key STEM material and concepts to solve this problem Numerical processing Filtering Thinking is required!!! Phase (deg) Magnitude (db) Displacement (in) Displacment Comparisons Bode Diagram -.5 From: Input Point To: Output Point Time (sec) System: proj4_rc_2 Displacement(LVDT) Displacement(Accleraometer) Displacement Comparison I/O: Input Point to Output Point Frequency (rad/sec): 12.6 Magnitude (db): -3.3 Displacement (inches) Frequency (rad/sec) Measured Displacement Calculated Displacement Time (sec) 7 Dr. Peter Avitabile, Assistant Professor

8 The Virtual Measurement System The real test configuration has many problems that all simultaneously plague the measurement. Many times students are frustrated with the significant open-ended aspects of this exercise. This is due to the large number of items that simultaneously plague the measurement. 8 Dr. Peter Avitabile, Assistant Professor

9 The Virtual Measurement System In order to assist the student in understanding all of the individual effects, a virtual measurement system was developed. This enables the student to add individual effects and see the result on the measurement made. The pieces of the Virtual Measurement System are described in the following sections. 9 Dr. Peter Avitabile, Assistant Professor

10 The Virtual Measurement System The entire Simulink model 1 Dr. Peter Avitabile, Assistant Professor

11 The Virtual Measurement System The SDOF system portion 11 Dr. Peter Avitabile, Assistant Professor

12 The Virtual Measurement System The accelerometer measurement portion The LVDT & RC filter measurement portion 12 Dr. Peter Avitabile, Assistant Professor

13 The Virtual Measurement System The entire GUI Interface 13 Dr. Peter Avitabile, Assistant Professor

14 The Virtual Measurement System The system characteristic definition of mass, damping and stiffness along with IC and forcing function 14 Dr. Peter Avitabile, Assistant Professor

15 The Virtual Measurement System The accelerometer parameters can be entered along with the LVDT and RC filter setting 15 Dr. Peter Avitabile, Assistant Professor

16 Virtual Measurement System GUI User enters M, C, K system. User enters the amount of experimental distortion on the accel. (sensitivity, bias, drift) and displacement LVDT (sensitivity, bias, noise) and the low pass filter characteristics to virtually simulate the measurement environment. Data can be exported with ability to select which outputs and what effects are included on the measurement. 16 Dr. Peter Avitabile, Assistant Professor

17 Virtual Measurement Simulation The student can quickly study the measurement issues associated with drift, bias and offset. These effects are significant when numerically processing the data to perform differentiation and integration. Several cases are shown to illustrate the usefulness of the Virtual Measurement System. 17 Dr. Peter Avitabile, Assistant Professor

18 Virtual Measurement Simulation Differentiation of LVDT measurement and noise Displacement Displacement Displacement No Noise Small Noise More Noise d/dt d/dt Acceleration Acceleration Acceleration Dr. Peter Avitabile, Assistant Professor

19 Virtual Measurement Simulation Integration of the accelerometer measurement Acceleration Acceleration Acceleration No Drift or Offset Positive Offset Negative Drift Displacement Displacement Displacement Dr. Peter Avitabile, Assistant Professor

20 Summary Students tend to struggle when trying to process real world measurements. All of their STEM knowledge must come to bear to solve these types of problems. A Virtual Measurement System was developed to assist students in breaking down the measurement problem into pieces which all contribute to the distortion of the real measurement. 2 Dr. Peter Avitabile, Assistant Professor

1 1 1 ζ=.1% ζ=1% ζ=2% ζ=5% ζ=1% ζ=2% -9-18 ζ=2% ζ=1% ζ=5% ζ=2% ζ=1% ζ=.

21 1 1 1 ζ=.1% ζ=1% ζ=2% ζ=5% ζ=1% ζ=2% ζ=2% ζ=1% ζ=5% ζ=2% ζ=1% ζ=.1% Acknowledgements This project is partially supported by NSF Engineering Education Division Grant EEC Multi-Semester Interwoven Project for Teaching Basic Core STEM Material Critical for Solving Dynamic Systems Problems FIRST & SECOND ORDER SYSTEMS SIGNAL CONDITIONER RISE & SETTLING TIME FOURIER TRANSFORM DYNAMIC TESTING PULLS ALL THE PIECES TOGETHER!!! DIGITIAL DATA ACQUISITION ANALOG TO DIGITAL HAMMER TIP CHARACTERIZATION DIFFERENT PULSE SHAPES FOURIER SERIES & FFT x(t) k m c f(t) MODEL APPROXIMATION SDOF DYNAMIC SYSTEM MODEL FREE BODY DIAGRAM 2 d x dx & EQUATION OF MOTION m c kx f (t) dt = dt 1 ζωt h(t) = e sin ωdt mω * d a1 a1 h (s) = + * (s p ) (s p ) 1 1 DISPLACEMENT LVDT IMPACT HAMMER FORCE GAGE HAMMER TIP ACCELEROMETER yi 1 + y I i i = Ii ( xi+ 1 xi ) 2 QUANTIZATION SAMPLING T ALIASING I M LEAKAGE E WINDOWS TIME ACCELERATION NUMERICAL PROCESSING INTEGRATION / DIFFERENTIATION Y TRANSDUCER CALIBRATION REGRESSION ANALYSIS X F R E Q U E N C Y FREQUENCY ω/ω n ω/ω n LAPLACE & TRANSFER FUNCTION Peter Avitabile, Tracy Van Zandt 21 Dr. Peter Avitabile, Assistant Professor

Developing a Multisemester Interwoven Dynamic Systems Project to Foster Learning and Retention of STEM Material

Developing a Multisemester Interwoven Dynamic Systems Project to Foster Learning and Retention of STEM Material 100 10 1 ζ=0.1% ζ=1% ζ=2% ζ=5% ζ=10% ζ=20% 0-90 -180 ζ=20% ζ=10% ζ=5% ζ=2% ζ=1% ζ=0.1% Proceedings of 2004 IMECE: November 13-19, 2004, Anaheim, CA 2004 ASME International Mechanical Engineering Congress