STRAIN GAGE ACCELEROMETER EXPERIMENT Objective The objective of this laboratory experiment is to determine the characteristics of a strain gage type accelerometer, including its natural frequency, damping ratio and sensitivity. Equipment 1. ENTRAN Strain gage accelerometer 2. ENTRAN PS-15 Bridge balance unit 3. B & K Piezoelectric accelerometer 4. Piezoelectric accelerometer charge amplifier 5. CROWN Electro-dynamic shaker 6. CROWN Power amplifier 7. HP Signal generator 8. HP Dual-beam oscilloscopePre-lab Assignment Derive the differential equation governing accelerometer response to a sinusoidal input. From this equation, prove that the relative displacement of the accelerometer seismic mass with respect to the accelerometer housing z, is a function of the input acceleration, the magnification factor, and the accelerometer natural frequency; Also determine the phase lag relation. This should be done by each student independently prior to the laboratory period and included in your report as an appendix. Review pp. 73, 87-95, 487-488 of Figliola and Beasley Procedure 1. Study and understand the equipment set-up, and draw a block diagram showing all components and connections. 2. Turn on the CROWN power amplifier, HP signal generator, HP scope, ENTRAN bridge power supply, and piezoelectric charge amplifier. 3. Make sure that FULL SCALE = 20 on the charge amplifier. NOTE: the sensitivity of the piezoelectric accelerometer as output by the charge amplifier is given by: sg' SCALE FULLVolts 5=PIEZOK , where FULL SCALE is the setting the user makes on the charge amplifier. (i.e. with the "FULL SCALE" knob set at 20, if the accelerometer is forced at ±10 g, the charge amplifier will produce an output signal of Peak-to-Peak Volts 5Volts 2.5sg' 10sg' 20Volts 5=±=±× ). 4. Record the voltage excitation from the ENTRAN PS-15 Bridge Power Supply. Denote this number as eV (Volts). 5. Use the function generator (Freq. Button) to set the minimum sine frequency to 100 Hz (the shaker is not linear below 100 Hz), turn the function generator amplitude up to ±10 g by adjusting Amp. Button to a level of 380 mV on the function generator. 6. Verify that the ±10 g input at 100 Hz is set by measuring the piezoelectric accelerometer output on CH2 of the oscilloscope screen (Voltage Button -> Measure Voltage Peak-Peak CH2) and verify that it is indeed 5 Volts peak-to-peak. NOTE: This level of input ±10 g vibration is to remain constant for all further test readings, and must be checked before taking data at each frequency. 7. Determine natural frequency of strain gage accelerometer: Determine the strain gage accelerometer natural frequency, by noting the frequency at which its output lags that of the piezoelectric accelerometer by 90°. Use a Lissajous pattern to do this.A Lissajous pattern is generated when the two signals are combined (this can be done by pushing the “main-delayed” button and selecting the XY mode on the screen, see sheets near experimental hardware for more clarification). Adjust the frequency on the function generator until the Lissajous pattern is a circle. Note the value of frequency at which this occurs as being the natural frequency of the strain gage accelerometer πω2nnf = . 8. Collect data for transducer sensitivity calculation: Record the strain gage accelerometer output at frequencies ranging from 100 Hz to 3000 Hz, in increments of 100 Hz. Use the Freq. Button on the function generator to increment the frequency. At each new frequency, adjust the amplitude of the function generator using the Amp. Button so that CH2 on the scope reads 5 Vp-p. For example, at 200 Hz, you will need to change the amplitude on the function generator to approximately 0.370 V in order that the signal on CH2 registers as 5 Vp-p on the scope. Record the peak-to-peak voltage of CH1 at each frequency. Fine tune the amplitude on the function generator for all other frequencies measured in order to ensure that 5 Vp-p = ±±±±10 g is the constant input at each new frequency and complete the entries in the table below. Forcing Frequency (Hz) Function Generator Voltage Amplitude (mV) Scope CH2 Peak-Peak Voltage (should be const. @ 5 Vp-p) Scope CH1 Peak-Peak Voltage (mV) 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 3000Data Analysis 1. Explain why a piezoelectric accelerometer can be used as the reference standard for calibration of the strain gage accelerometer in this experiment. 2. Report the natural frequency, nf (Hz) and nnf 2πω= (rad/sec) of the strain gage accelerometer you found via step 7 in the test procedure. How does your measured value compare to those expected from the ENTRAN website or other strain gage type accelerometers ? 3. From your experimental data of step 8 of the procedure, determine the average DC sensitivity of the strain gage accelerometer, in units of SGK [mV/g]. Compare the value you computed for SGK to the manufacturer’s reported average value of =vendorK 2.72 mV/g. Formulate a percentage error 100×−=vendorSGvendorKKKe and explain any discrepancies you discover. 4. From the experimental data of steps 7 & 8 of the procedure, determine the damping ratio ζ of the strain gage accelerometer by plotting your data against the equation for the magnitude ratio given below (Figliola & Beasley Eqn. 3.21 and Fig. 3.16):  +−==2221010) 2()1(120))((20rrLOGMLOGdBζω When plotting your experimental data, you must normalize as follows: Plot  × 20g(mV/g) (mV) OUTPUT*2010SGKLOG on a log y-scale vs. frequency on a linear x-scale in order to have a properly scaled plot from which to determine the damping ratio from. By plotting your data overlaid with some theoretical dB magnitude curves (via Eqn. 3.21 above), you may infer what damping ratio the transducer has. How does the value of damping you measured