To: ME 107A Consulting Group
From: National Satellites, Inc.
Re: Accelerometer Calibration Test Stand
We would like your assistance in the modification and characterization of a calibration test stand. The test stand is designed to permit calibration of motion sensors such as accelerometers and velocimeters. We have constructed a prototype of the calibration test stand, but we need an expert to characterize its vibrational characteristics, suggest a modification of the test stand to achieve a specific resonance frequency, and determine the practicality of the calibration procedure.
The test stand is a double guided beam which permits flexibility in only one mode of vibration. We have provided the option to add mass to the free end of the stand and to interchange the top beam so as to modify the stiffness. The test stand is instrumented with a linear-variable differential transformer (LVDT) for displacement measurement, a pair of strain gauges mounted on the fixed beam, a voice-coil and magnet arrangement which can be used as either a source of excitation or as a velocimeter, and an accelerometer.
The calibration procedure which we plan to use involves subjecting the beam to steady-state harmonic motion and monitoring the resulting displacement of the beam's free-end. This permits determination of the instantaneous velocity and acceleration at the free end where the instruments to be calibrated are located. However, in calibrating the velocimeter provided, the free response to the test stand must be used. We would like an assessment of which of these techniques, operating in the forced or free mode, is most practical and accurate for the calibration process. Please provide calibration factors for the velocimeter and accelerometer as functions of frequency within the 2 to 30 Hz range.
We currently have the test stand instrumented with an LVDT, which measures tip displacement directly, and a set of strain gauges, which can infer displacement from strain. We would prefer just using the strain gauges since they are less expensive and less sensitive to misalignments. Please predict the linear relationship between strain and beam-tip displacement based on Euler-Bernoulli beam theory and then experimentally measure the relationship. Is the measured relationship consistent with theory? Based on these measurements plus an uncertainty analysis, do you recommend that we rely on indirect displacement measurements using the strain gauges in our final design?
We would also like you to characterize the vibrational characteristics of the test stand. The designer suggests that the dynamics of the test stand are adequately represented by the single-degree-of-freedom model consisting of an ideal linear spring, mass, and viscous damping elements. Please attempt to apply this model to our current test stand to evaluate the natural frequency, damped natural frequency, resonant frequency, and damping ratio. To evaluate the self-consistency of this model, determine the associated stiffness and effective mass of the stand from the experimental data, and compare these to values predicted from Euler-Bernoulli beam theory an the linear second-order spring-mass-damper model. For at least one configuration, you should determine the vibrational characteristics using both free and forced response, and compare the results.
Your lab group will be given a particular natural frequency which is our desired operating frequency for the actual test stand. Please indicate how the test stand should be configured (which of the various removable beams and how much additional mass should be added) in order to provide the desired response.
Please provide us with a summary report within two weeks of completing the experiments. We look forward to getting your response.