MEC751 Measurement Lab 2 Instrumented Cantilever Beam Goal: 1. To use a cantilever beam as a precision scale for loads between 0-500 gr. Using calibration procedure determine: a) Sensitivity (mv/gr) b) Overall instrument error (gr) c) Linearity error %FSO d) Hysteresis error %FSO e) Precision error %FSO 2. To investigate the dynamic behaviour of the beam Hardware: Data Acquisition Board: NI-PCI-6321 16 analog inputs, 250 ks/s, 16-bit resolution, ±10 V Two analog outputs, 90 ks/s, 16-bit resolution, ±10 V Connector Block - Screw Terminal (SCB-68 ) Cable Shielded (SHC68-68-EPM) Cable Cantilever beam Dimension of beam: 10 X 0.5 X 0.125 (inches) Material: Aluminum 6061
Hardware (continued) Signal Conditioning Manufacturer: Industrologic Model: SGAU Universal Strain Gauge Amplifier Gain: 90-1000. Gain factory set at approx X400 Single output with 2.5V offset The strain gauges Model SGD-7/350-LY13 (general purpose strain gauge) Excitation 5 volts DC Resistance: 350 ohm Dimensions: 30 L x 0.1 D x 0.3 mm W (1.2 L x 0.004 D x 0.012" W) Max strain 3% Gage factor: 2.0 +/-5% Number of gauges: 2 used in a half bridge configuration
Part 1 Preparing The Measurement System Wire the power supply to input of the signal conditioning circuit. Wire the output of the signal conditioning circuit to Connector Block (Use AI0 and AIGND to set up a RSE connection). All wires are color coded. Get TA s signature before turning on the power supply Get TA s signature before turning on the power supply Start a blank VI and add a DAQ Assistant to blockdiagram Configure the DAQ Assistant VI by double-clicking it. Choose the analog channel to read from (ai0) Range: for now leave as: -10/+10 V Terminal Configuration: RSE (Measurement made with respect to ground). g ( p g ) Timing Settings: Continuous Samples to Read (N): 100 Rate (sampling frequency): 1000 Hz Labview will ask permission to add a while loop. If not, add a while loop around DAQ Assistant. Wire a Waveform Graph and a numerical indicator to data port of DAQ Assistant. The number of decimal points in the indicator should match the resolution and accuracy of your voltage measurements. See the last page of this handout. Run the VI. What is the voltage reading?... mv Gently push on the beam. What is the min and max of the signal? Min.:...mV Max:...mV Max:...mV Based on these observations go back DAQ Assistant wizard and : Change the Signal Input Range to a more appropriate interval Use Custom Scaling to create a new scale Give the scale a name Chose linear Pick the two parameters, Slope and Y-intercept, such that at zero load the output is equal to zero and as you push down on the beam, the voltage increases. Run the VI. What is the voltage reading?... mv Gently push on the beam. What is the min and max of the signal? Min.:...mV Max: mv Max:...mV Get TA s signature before moving to the next part
Part 2 Collecting Calibration Data You are given a set of known weights. Use these to calibrate the insrumented beam so that it can be used as a precision scale. Allow 3-4 minutes for straing gauges to come to thermal equilibrium due to resistive heating. Use the table below to record the voltage reading of the Wheateston bridge for each weight. You must follow the sequence for each cycle. Allow the vibration die down as much as possible before recording your data. The data analysis will be done after the lab. Appendix B explains the process. Get TA s signature Once you have collected all the data You will be given an unknown weight. Record the voltage reading for this weight. Unknown Weight=... mv True Weight(gram) Cycle 1 Cycle 2 Cycle 3 Cycle 4 Cycle 5 80 160 240 320 400 480 500 480 400 320 240 160 80 0
Part 3 Natural Frequencies of the Aluminum Beam The aluminum beam is a continuous mechanical system and therefore, has infinite number of natural frequencies. Typically, modal analysis is used for determining natural frequencies of mechanical systems. This requires a specially instrumented hammer or shaker, accelerometer(s) and specialized algorithms (FRF) to accurately measure the modal shapes and frequency. Your goal in this lab is to determine the first fundamental frequency of the instrumented beam by applying an impulse load and observing the vibration that results. An ideal impulse force excites all modes of a structure, the response of the beam should contain all mode frequencies. However, an ideal impulse force is hard to achieve with this lab s setup and the vibration is only measured using a strain gauge. Nevertheless, you should be able to measure the first fundamental frequency. The first natural frequency of a cantilevered uniform beam (with negligible beam weight) with a load on the free end is given by: f 1 1 3 EI 2 0.236ml 3 E, Young s Modulus of Elasticity I, bending moment of inertia m, mass of the beam L, length of the beam Ref.: S. S. Rao, 'Mechanical Vibrations' 4th edition, Pearson Edition, Page 609 613.
Part 3 Natural Frequencies of the Aluminum Beam Measurement Add a Spectral Measurement express VI to the VI from last part. Set it up for power spectrum in DB with Hanning window and no averaging g. Wire a waveform graph to spectral measurement VI. Run the VI, tap the tip of the beam with a pen (Make sure the beam does not hit the lower stop) Can you see the power spectrum? For this type of measurements, you need a triggered data acquisition. For proper modal measurement, an instrumented hammer used as an external trigger. In this lab we use a software trigger instead. From Signal Manipulation palette, get a Trigger and Gate block. Set it up as shown in the figures. Wire the data from DAQ Assistant to Trigger VI and from Triggered Signal to Spectral measurement Remove the stop button for the while loop. Instead wire the data available port of the Trigger Express VI to the loop condition Move the Spectral express VI and its associated graph to the outside of while loop. Run the VI, tap the tip of the beam with a pen. The VI should stop automatically after collecting the date and you should be able to see the power spectrum. What is the approximate value of the first fundamental frequency?...hz Get TA s signature once you have confirmed this Change the data acquisition parameters so that you can get a frequency resolution of 0.5 Hz or better Put a report and Write to Measurement file VI outside the loop and run the VI again. You will use the graphs and data in your report.
Appendix A Calibration Procedure Use all of your 70 data points to create a XY graph of data. The x axis is the calibration weight and the y axis the voltage reading of the measurement system. Use MATLAB or Excel to plot the data and also find the best fit line (see Fig. 1). The equation of this line in the form of ffollowing equation is your calibration curve: y=ax+b Eq. 1 For each calibration weight (0, 80, 160,..., 500 gr), use the Eq. 1 to calculate the expected voltage output of the scale. The difference between each measurement and the corresponding expected value calculated using Eq. 1 is the deviation. Create a table of all deviations similar to Table 1. Now use Eq. 1 to represent all deviations in gram. Plot these versus calibration weight (see Figure 2). Overall instrument error is bounded by these two lines The accuracy limits includes all calibration errors and random errors associated with your measurements except drift and thermal stability. For now, youcam represent the repeatability error with the range of repeated measurements shown as Repeat in Table 1. (later, we use other statistical measures for this purpose) To separate the hysteresis and non-linearity errors, add the Average up-down columns as in Table 1. Once you have produced columns, create a graph similar to Figure 3. Nonlinearity and Hysterisis errors can be found from this graph.
Appendix A Calibration Procedure
Appendix B DAQ Board Specs AI Absolute Accuracy Table PCIe6321 http://sine.ni.com/ds/app/doc/p/id/ds 152/lang/en pp p