124 D. P. Rohe Fig. 12.1 Small spring shown on an penny for size reference (SLDV) was used to measure the response of the spring to vibration excitation. The SLDV has advantages over traditional mounted sensors in that it does not mass load the test article. In addition, its sensor footprint is very small, so it can measure the motion of individual coils of the spring resulting in better mode shape resolution [2]. The natural frequencies and deflection shapes of several modes were extracted using the SLDV. 12.2 Spring Dynamic Testing The spring is much smaller than the objects usually tested in the modal laboratory at Sandia National Laboratories. The wire diameter of the spring was approximately 75 m, and the stretched length of the spring was about 0.5 cm. The mass of the spring was approximately 2 mg. Given that the smallest accelerometer owned by the modal laboratory at Sandia National Laboratories was over 100 times as massive as the spring, and any fixture onto which the accelerometer could be mounted would likely be equally as massive, the approach of identifying spring natural frequencies by measuring on the fixture itself was discarded. Instead, the laser vibrometer system would be used to measure directly on the spring itself. A simple fixture was designed to hold the spring during testing, as shown in Fig. 12.2. The fixture consisted of a rectangular base with two cylindrical pins. The fixture was excited using base excitation from a modal shaker (BCKType 4809). In order to determine whether fixture modes would contaminate the spring data, preliminary finite element analysis of the fixture was performed, showing the first mode of the fixture above 100 kHz. This was well above the bandwidth of interest for the test so for this work the fixture was assumed to be rigid. Rather than trying to measure the force applied to the fixture by the shaker, a transmissibility approach was used instead. A reference accelerometer was mounted to the shaker alongside the fixture to serve as the input acceleration. The SLDV was set up in 1D mode with a single laser head. A 3D measurement was initially considered to get the in-plane responses; however, it was unclear whether the laser system would be accurate enough to triangulate three laser points onto the thin wire of the spring. In the author’s experience the typical alignment accuracy for the laser system is on the order of 0.1–0.5 mm, which is larger than the wire diameter. Additionally, only one set of close-up hardware (close-up module and lenses) were available to use at the time. Once testing started, it became clear that it would be useful to have an inplane measurement to help identify the many modes in the bandwidth, but it was found that re-mounting the spring so the perpendicular face would be visible to the laser would result in changing natural frequencies. An alternative would be to move the laser head, but this would require re-aligning the laser to the part. Because a large number of springs were to be tested, this idea was discarded. Instead, a small piece of first-surface mirror was placed next to the spring on the shaker at a 45 degree angle allowing the laser system to measure two perpendicular sides of the spring. The final test setup can be seen in Fig. 12.3. A representative view from the laser system is shown in Fig. 12.4. The SLDV was set up to measure 21 points on each face of the spring. This was supplemented by measurement points on the fixture to verify that it was in fact moving rigidly over the bandwidth of interest. For each test the transfer function between these fixture points and the reference accelerometer was verified to be close to 1. Because the spring is small and
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