sin(wt) y(t) Exciter Vibrating armature ENME599 1

Size: px

Start display at page:

Download "sin(wt) y(t) Exciter Vibrating armature ENME599 1"

Hollie Lynch
5 years ago
Views:

ENME599 1 LAB #3: Kinematic Excitation (Forced Vibration) of a SDOF system Students must read the laboratory instruction manual prior to the lab session.

1 ENME599 1 LAB #3: Kinematic Excitation (Forced Vibration) of a SDOF system Students must read the laboratory instruction manual prior to the lab session. The lab report must be submitted in the beginning of the following lab. Make sure you submit the Prelab prior to the actual lab session. The computer codes should be appended in the report. OBJECTIVES 1. Quantitative experimental analysis of the dynamic behavior of simple Single-Degree-of-Freedom, SDOF mechanical systems: a. Amplification of a harmonic excitation signal versus frequency b. Phase shift versus frequency 2. Studying forced response of simple SDOF mechanical systems for the case of kinematic excitation, 3. Comparison of the experimental and analytical results (the latter obtained from models derived in class), 4. Gaining experience with Experimental Modal Analysis. SAFETY and instrument protection: NOTE: Accelerometers used in this experiment are VERY DELICATE and EXPENSIVE (~$500/piece) devices. They can be easily damaged by shock (e.g., dropping or otherwise hitting a hard object). Please, HANDLE them with CARE. AGENDA 1. Using the Function Generator to find the natural frequency 2. Using Labview for Sine sweep 3. Experimental Modal Analysis Demonstration Introduction Considered is a mass M at the end of a cantilever beam (shown in Figure 1, right) of negligible mass with rectangular cross-section, as investigated in Lab #2. The left end of the beam is driven by an electrodynamic exciter. The end moves vertically and its POSITION is given by a function y b (t) y b (t) y b0 sin(t) The actual test setup is shown in Figure 2. The mass at the beam mid-span has been removed in this experiment. y b0 sin(wt) y(t) Exciter L Vibrating armature Figure 1. Simplified diagram of the tested system. Figure 2. Tested system (mid-span mass will be removed). RELEVANT EQUATIONS Steady state forced response: y p (t) D() sin[t ()] (1) Where:

2 ENME599 2 D() p o ( n 2 2 ) 2 (2n ) 2 (2) () arctan 2 n 2 n 2 Note: Refer to the class notes for the formulations of the Kinematic Excitations. (3) SETUP ACCELEROMETER LOCATIONS ON THE TESTED BEAM Inspect the locations and attachment of the accelerometers on the beam. Check that they are SECURED with a piece of electric tape (as instructed during the lab) y b0 sin(wt) y(t) Accelerometer mounted on the shaker s armature (Ch. 2) Exciter L Vibrating armature Accelerometer only or Accelerometer and test mass (Ch. 3) FOLLOW INSTRUCTOR S GUIDELINES FOR SETTING UP THE EQUIPMENT PRODEDURE FOR CONNECTING AND TURNING ON Note: Since we are using sensitive and expensive instrumentation, do not hesitate to ask for help if things do not work as explained in this instruction. 1. Inspect connections from the front panel BNC outputs of the channels used to the scope (Ch. 2 and Ch. 3) 2. Deflect the beam by approx. 10 mm and release it. You shall see an oscillating signal on the oscilloscope, at least in Ch. 3 (vibrating mass). If you experience difficulties, ask for help with the adjustments. SHAKER DESCRIPTION: Model 300 Shaker (APS Dynamics, Inc., The Model 300 Shaker is a small shaker designed for modal test excitation of structures and calibration excitation of accelerometers and velocity pick-up systems. The shaker features portability with a rugged self-cooled design. The unit includes an electrodynamic shaker capable of producing random or transient as well as sinusoidal acceleration waveforms. Force generated by the shaker is proportional to the instantaneous current supplied by the power amplifier. TURNING ON PROCEDURE 1. Make sure the Power is OFF 2. Turn the INPUT AMPLITUDE CONTROL knob maximum counter-clockwise (CCW) -> minimum amplification from the input signal to the output force (safe setting) 3. Turn Power on

3 ENME599 3 Desktop computer 1. Turn power on. 2. Select the user ID and password that will be provided during the lab. 3. Launch the LabView program (Consult with the instructor) Performing the task - the beam with mass and the accelerometers a. Compute the stiffness k of the tested beam (compare Lab 2). Use the analytical formula P *L3 3*E *I P k where L is the beam length, A is its cross-section area, I is the second moment of area ( moment of inertia ) and E is the Young s modulus (steel). Note: you can use results from Lab 2. k b. Record the value of mass (engraved) at the end of the beam, m =.... (gram). c. Compute the circular natural frequency n of the beam-mass system (neglect the beam mass) n and the analytical resonance frequency of the system f ra f ra n = note that for low system damping (e.g. < 0.2) f r n f d n f n n 2 ; 1. Using the Function Generator to find the natural frequency * find the natural frequency of the system by using the function generator (sine swept method) Make sure BNC cables from DAQ box is disconnected from the shaker amplifier Connect the generator output to Channel 1 on the scope and channel 0 on the DAQ Function Generator pull the offset knob Attenuator 20 db depressed a. Set generator output to +/- 1 V and have the instructor verify (fuse could be blown if improperly done) b. Connect the output of the generator to the input of the shaker amplifier c. Slowly sweep the frequency from 5 Hz to 20 Hz and find the natural frequency using the oscilloscope Team # Fn (Hz) Mass (g) 2. Using Labview for Sine sweep * we use the Labview program to perform the test IMPORTANT: The input voltage to the shaker amplifier must not exceed +/-1.4V). Please have the instructor double check the connections before you begin.

4 ENME599 4 Lab instructor will demonstrate the Labview program to actuate the shaker and capture the data. Follow instructor s instructions to setup and test. In the current experiment the recorded signals, stored as 4-column spreadsheet, are: (1) time reference, (2) output signal from the Digital-to-Analog Converter (DAC) which is fed to the shaker s input, Ch. 0 on DAQ box, (3) accelerometer on the shaker armature, i.e., excitation, Ch. 1 on DAQ, and (4) accelerometer at the end of the beam, i.e., response), Ch. 2 on DAQ, a. Estimate experimentally the resonance frequency of the system f re1. Do this by exciting the beam while varying the frequency in the vicinity of analytically computed n ; the maximum amplitude of the response occurs at f r. r f re1 n 2 (1 2 ) b. Set the data size to samples, sampling frequency to 1000 Hz, and a selected generator frequency. Choose Sine waveform. Record the amplitudes of the acceleration signals in Ch 1 of the DAQ box (armature vibration, column 2 in LabView) and Ch. 2 (excited mass, column 3 in LabView). Simultaneously, capture by pressing the Stop/Run key the acceleration signals in Ch. 2 and Ch. 3 of the oscilloscope. c. At the frequency of excitation specific to your experiment, using the captured oscilloscope information calculate the displacement amplitudes of the armature and the outboard mass. The lab instructor can be utilized to demonstrate how to get the most resolution from your oscilloscope. Recall the relationship t y(t) Y o sin(t) a()dd A o sin(t) Where A o, Y o are the amplitudes of acceleration and displacement, respectively, and is the frequency of the excitation. d. Compute the phase shift (it is recommended to express it in the ±180 range) using the capture oscilloscope data = 360 o = 2 [rad] = =.. rad Note: use degrees or radians whichever T r T r appropriate/convenient (Show this for at least one measurement in the lab write up) e. Compute the following values (conversion to the proper units): - shaker s armature (base vibr.) A oa =... V -> A oa =... m/s 2 ; =... rad/s ; Y oa =... mm - excited mass A om =... V -> A om =... m/s 2 ; =... rad/s ; Y om =... mm f. Obtain the signal transmissibility (amplification and phase shift) between the armature and outboard mass (acceleration signals in Ch 2 and Ch. 3) using the Labview Program. = D() = ; g. Compare your results obtained from the oscilloscope screen data to those obtained from the Labview analysis software. (pick 2 data points)

ENME599 5 h. Collect about 10 similar measurements appropriately spaced using the analysis program. Select frequencies between 0.5 and 2 f n with more points near the resonance.

5 ENME599 5 h. Collect about 10 similar measurements appropriately spaced using the analysis program. Select frequencies between 0.5 and 2 f n with more points near the resonance.. Tabulate the results as follows f i.i =1,.., fn 0.7 fn 0.9 fn 0.95 fn 1 fn 1.05 fn 1.1 fn 1.4 fn 1.6 fn 2 fn f [Hz] I [rad/s] A oa [V] A oa [g] A om [V] A om [g] i Note: In rows 4 9 compute results for only the first 2 columns. i. Record with Labview two representative sets of signals, one slightly below (0.95) and the other slightly above (1.05) the resonance frequency. Each set shall include three signals, i.e., generator, base acceleration and mass acceleration. 3. Experimental Modal Analysis Demo The TA will go over the EMA demonstration using the impact hammer and the accelerometers. Input: Output: Analyzer:

6 ENME599 6 Lab Assignment Due beginning of the next laboratory. Append Matlab or Mathematica codes. Make sure you put the correct UNITS for all your analysis (including figures). Answer the questions in the instruction section. 1. Plot representative waveforms recorded in Step 2 (Using Labview for Sine Input) of the instruction. Remember to express the accelerations in m/s 2 (rather than Volts). 2. Derive analytical expression for the transmissibility (magnitude and phase vs. frequency of excitation) of the kinematically excited beam. 3. Plot in the same graph the magnitude of transmissibility vs. excitation frequency obtained experimentally and analytically. The experimentally obtained magnitude of transmissibility is the amplification between the vibrations of the armature and outboard mass (acceleration signals in Ch 2 and Ch. 3). vs. frequency Plot on another graph the phase shift of transmissibility vs. excitation frequency obtained experimentally and analytically. 4. Briefly discuss any differences between observed transmissibility and phase shift found from experiments vs. analytical derivations. 5. Describe the experimental modal analysis (EMA) (based on the demonstration done by the TA) (More details are found in the Blackboard under Course Contents modal.pdf ). Describe the pros and cons of using either an impact hammer or a shaker system for the EMA. What are the assumptions associated with the EMA?

Physics 2310 Lab #2 Speed of Sound & Resonance in Air

Physics 2310 Lab #2 Speed of Sound & Resonance in Air Objective: The objectives of this experiment are a) to measure the speed of sound in air, and b) investigate resonance within air. Apparatus: Pasco