0.3 Strain gages and force measurement  (Page 4/4)

6.2 temperature sensitivity

Using a quarter bridge configuration, apply a load to the beam and measure the voltage output.

Apply heat uniformly to the beam (140 F max) near the gages and observe any changes in the voltage output. Donot apply heat to the gages directly! Why does the voltage (which corresponds to the measured strain) change? Repeat the procedureusing a full-bridge configuration. Compare the sensitivity of the quarter bridge and full bridge configurations to temperaturevariations. How would you expect the half bridge to behave?

Part 7: dynamic characteristics

Up to this part of the lab, you have examined the static characteristics of the strain-gage bridge. Now you willmodify the VI that you developed for Temperature Measurement and First-Order Dynamic Response to measure the dynamic characteristics of a signal from the strain-gage bridge. You willexcite the dynamics of the cantilever beam by plucking it. You will use your VI to display the response of the vibrating beam.

7.1 differential model

The first mode of vibration of the cantilever beam can be modeled using a simple mass-spring-damper model. Thismodel results in a second-order differential equation that describes the dynamics of the system. You will observe that theresponse of the strain–gages to an initial deflection is a damped sinusoid. This is the expected response for a second-order system.Using acquired data; you will compute and display values for the damping ratio and the natural frequency of the first vibrationalmode of the beam.

7.2 damping ratio and damped natural frequency

Figure 5 shows the response of a second-order system to an initial condition. This response plot will be used todefine the damping ratio and the natural frequency for this system.From the amplitudes x1and xn, the damping ratio can becalculated using the following expression:

The damped natural frequencycan be determined by measuring the period of the damped oscillations. An accuratemeasurement of the period T is obtained by considering several periods:

Onceandare known, the natural frequency of oscillation can be calculated by

7.3 programming exercise

You will modify your VI to automate the calculation ofandfor the cantilever beam.

1. Your TA will direct you to a subVI named“Damping Ratio”that is has been started for you.

2. To place the subVI on your block diagram, open the functions palette and select Select a VI…

3. Connect the Data wire from the DAQ Assistant to the Measured Data input of the Damping RatiosubVI.

4. Open the block diagram by double-clicking the subVI icon. (The block diagram is shown in Figure 18.)

5. You will need to modify the block diagram for the VI to work. Refer to equations 8-11 as you design a blockdiagram that will calculate the Damping Ratio of your signal.

6. You will notice that the necessary inputs for the subVI are placed along the left of the block diagram. Theoutputs are placed along the right of the block diagram. The Peak Detector VI is used to locate the peaks (or valleys) of the signal.The locations of the peaks are given as indexed data points. For example, if the first peak occurs in between the sixth and seventhdata points, the location will be 6.5. The time at which this peak occurs can be calculated using the sample rate.

7. For more information about the Peak Detector or other VIs, press Ctrl+H to activate the context helpwindow.

(Hint: you may want to use the index array function to pull values such as x1, xn, t1 and tn out of theamplitude and location arrays.)

This exercise is meant to give you a feel for the possibilities for data acquisition, processing, and displayusing computer software tools. Be sure to save a copy of your data for plotting. You will need it for your writing assignment.

Part 8: design of a force transducer

For your course project, you will design a force transducer for measuring the thrust of a model rocket motor.This exercise is intended to help you initiate the design process. You may assume that the maximum thrust that will be sensed by yourtransducer is 5 lb.

Cantilever-beam force transducer

Assume that you will use a cantilever-beam configuration similar to what was used in this lab. A fullstrain-gage bridge will be used. The width of two gages side-by-side is 1/2 inch. A good design will result in 2000microstrains under the maximum load and will have a natural frequency above 100 Hz. Meeting both of these objectives might notbe possible with a cantilever-beam design. You are to determine the thickness of the cross section where the gages are to be mountedand the distance from where the motor is mounted to the center of the gages (i.e., the length of the cantilever).

Spreadsheet analysis

Develop a spreadsheet to perform your calculations. A spreadsheet will simplify the evaluation ofdifferent designs. This analysis will be a good starting point for the analysis of your project. Note: Your project will involvedifferent loads and different dimensions than the transducer used in this lab. The calculations, however, are the same.

Lab report

For this lab you will write the Results and Discussion of Results sections of a full report. As you perform thelab, think about what data should be saved or recorded for presentation and why these data are important. For some of yourdata, tabulation is sufficient (e.g., calculated strain vs. measured strain). Other data should be recorded using LabVIEW(e.g., dynamic response of strain when the beam is plucked). Make sure that you include your thoughts about the results you obtainedand why they are important. Discuss their agreement with your expectations.