Improving SRTD With Resonance Phase Settings

Experiments and Papers

Author Philip Van Baren

Phase Control vs. Frequency Control:

Traditionally, when test engineers performed “sine resonance track and dwell” tests they have controlled the frequency of the resonance with little concern for the phase of the resonance. There is some good reasoning to this. Since a resonance occurs when a material’s vibrations are reinforced (constructive interference) by the “reflected” waves in the material, it can be assumed that the ideal phase value for a resonance is 90°. Consider a cantilevered beam (fastened to shaker on one end; other end (perhaps with a mass attached) free to vibrate) vibrating in its fundamental mode; in which the end of the beam is at its peak amplitude while the shaker head is at its equilibrium position (Figure 1 and Figure 2). Therefore, controllers would often set the default phase setting for a resonance to 90°.


Figure 1: Resonating cantilevered beam – profile


Figure 2: Resonating cantilevered beam – 3D

However, in reality this theoretical phase value of 90° could be different. The phase value may be affected by the location of the accelerometer or due to a lag in the reading of instrumentation. When these real‐life factors are considered, the test engineer should be concerned about the phase value of the resonance.

In addition to this, there is a significant difference between how a fatiguing product affects frequency-tracking versus phase-tracking tests. When a product begins to fatigue, the frequency values of its resonances will decrease, but its phase value for the resonance will not. So if one uses frequency-tracking SRTD, then when the product begins to fatigue the test will no longer be dwelling at the resonance of the product because that resonance value has changed. But if one uses phase-tracking SRTD, then when the product begins to fatigue the test will continue to maintain the same phase, but allow the frequency value to adjust with the changing resonant frequency of the product. Therefore, phase-tracking is advantageous as it allows the test’s frequency value to match the changing resonant frequency.

For these two reasons (real-life phase values are not always 90°; and phase-control allows the test to adjust the test frequency to match the changing resonant frequency of the product) test engineers ought to consider utilizing a phase‐tracking control method for SRTD tests. Vibration Research has developed a method that allows the test engineer to manually track the phase value in order to determine the maximum transmissibility value at a particular resonance (transmissibility value is the value that gives the most damaging acceleration to the product). This method is Advanced User-Defined SRTD Phase-Tracking Control.

Resonance Tracking Methods:

There are a few options available to the test engineer for Sine-Resonance-Track-Dwell (SRTD) testing. To understand these options, consider a swept sine test that was conducted on a thin metal beam in which accelerations were measured on the end of the beam (Figure 3).


Figure 3: Tear drop accelerometer attached to beam’s “short arm”

In this case, a resonance table was produced from the swept sine test that indicated that the fundamental mode of the long arm had a resonance at 69.7 Hz; in which the measured Transmissibility value was 31 G/G and the measured phase was -71.6° (Figure 4).


Figure 4: Resonance Table for Metal Beam (long arm), showing fundamental resonance at 69.7 Hz with a peak transmissibility of 31 G/G and a phase of -71.6°

a) Phase-Tracking: 90° Default

Since the theoretical phase of linear spring-mass systems is 90°, many controllers will set the phase automatically to 90°. With Vibration Research’s VibrationVIEW software the test engineer can choose to set the phase automatically to 90° by clicking on the “phase-tracking” checkbox (Figure 5). In this case the SRTD test will lock the phase to 90° and allow the resonance frequency to drift slightly as the test proceeds to dwell at the resonant frequency.


Figure 5: Phase‐Tracking Setting selected for “lawnmower blade test” – phase is automatically set to 90°

b) Resonance Frequency Track and Dwell: Using the Measured Phase Value

Commonly in SRTD testing the test engineer will control the resonance frequency (resonance track) since it is important to test the product at its resonance frequency. In this case, the controller tries to accurately measure the phase of the resonance during the swept sine test. This measured value (example: -71.6°) is recorded in the resonance table (Figure 4). This measured value, however, may not be entirely accurate. The inaccuracies are due mostly to the lag in reading of instrumentation. Therefore, the phase results from one swept sine may differ (sometimes significantly) from the phase results of a different swept sine. For example, a series of swept sine tests were conducted in which very similar resonance frequencies and transmissibility values were produced, but the phase values were quite different (see Error! Reference source not found. below: 8.5 degree variance in sweeps). If the test engineer desires to dwell at a specific resonant frequency, then this technique is commonly utilized even though the measured phase value may be off from the true phase value. In addition, this method dwells at a particular frequency with the goal of meeting the resonant frequency. However, the resonant frequency may change slightly as the product fatigues.

Sweep
Method

Sweep Rate
(oct/min)

Resonance Freq
(Hz)

Resonance
Transmissibility (G/G)

Resonance Phase
(degree)

Up

3

70.6

32

-91.5

Up

3

70.8

32

-101.9

Up

3

70.5

32

-79.1

Up

3

70.6

32

-90.3

Up

3

70.5

32

-79.7

Up

3

70.6

32

-89.9

Up

3

70.8

32

-102.9

Up

3

70.6

32

-89.6

Up

3

70.6

32

-88.4

Up

3

70.5

32

-78.9

AVG

3

70.6

32

-89.22

STDEV

0

0.110050493

0

8.531744644

Table 1: Results of variety of swept sine tests on thin metal beam. Note variability of measured resonance phase

c) Manual Phase‐Tracking Control

In the “metal beam” test example, the actual phase of the resonance that produced the peak transmissibility was not the default value (-90°) or the predicted value by the software (-71.6°). As can be seen in Figure 6, the peak transmissibility was a completely different value (-82.5°).


Figure 6: Transmissibility Metal Beam Tip (Long End of Beam) to Shaker Head vs. Phase of Resonance. Standard SRTD predicts a phase of ‐71.6° (peak transmissibility of 31 G/G) and the “phase tracking” sets the phase to a default of ‐90°. Meanwhile, a new feature, Advanced User-Defined SRTD Phase Tracking control, allows the engineer to adjust the phase to ‐82.5° to obtain the true peak transmissibility (32.4 G/G).

Since the true phase of the resonance may not be the default value of 90°, a test engineer may not want to utilize option 1: Phase-tracking at the default value. Since the resonance frequency of the test product may change as it fatigues, it may not be desirable to conduct SRTD testing by using option 2: Resonance Frequency Track and Dwell while using the Measured Phase Value. With Vibration Research’s newest VibrationVIEW software the test engineer will be able to adjust the phase value during the test to help obtain the highest peak transmissibility. This method is valuable because it allows the test engineer to dwell at a resonance using the correct phase value while allowing the frequency value to adjust slightly for changes that occur in the product’s resonance as it fatigues.

Metal Beam and Lawnmower Blade Tests:

The effect of phase-tracking on the peak transmissibility can be shown from experimental results. One test conducted on a simple product was the “thin metal beam” test (Figure 7). Resonance data was collected from both the “short arm” and the “long arm”. A second test was conducted on a more complex beam – a lawnmower blade, in which there is a twist in the beam (Figure 8 and 9). The lawnmower blade was specifically chosen because it resembles a “turbine blade”; an object that tends to be a non-linear system.


Figure 7: Thin metal beam attached to shaker


Figure 8: Lawn mower blade attached to large shaker


Figure 9: CAD drawing of lawnmower blade

Experimental Results:

a) Thin Metal Beam

When the Advanced User-Defined SRTD Phase‐Tracking method was used with the thin metal beam, the phase was manually adjusted to -82.5°. The SRTD test then dwelt at that phase value, applying to the product a peak transmissibility of 32.4 G/G. The resonant frequency-tracking method would have set the resonant frequency to 69.7 Hz and would have dwelt there with a phase value of -71.6°. This would have produced approximately a peak transmissibility of 31 G/G. The Advanced User-Defined SRTD Phase-Tracking method gives approximately a 4.5% increase in the peak transmissibility value compared to the resonant frequency-tracking method (Figure 10).


Figure 10: Advanced User-Defined SRTD Phase-Tracking Control obtained a higher peak transmissibility than the ‘Default 90°’ method or the Resonant Frequency-Tracking method

a) Lawnmower Blade

When the Advanced User-Defined SRTD Phase-Tracking method was used with the lawnmower blade, the phase was manually adjusted to -92°. The SRTD test then dwelt at that phase value (resonant frequency of 71.6 Hz). At this phase setting and frequency setting, the product experienced a peak transmissibility near 54 G/G. The resonant frequency-tracking method would have set the resonant frequency to 72.5 Hz and would have dwelt there with a phase value of -105°. This would have produced approximately a peak transmissibility of 51 G/G. The Advanced User-Defined SRTD Phase-Tracking method gives approximately a 5.9% increase in the peak transmissibility value compared to the resonant frequency-tracking method (Figure 11).


Figure 11: Screenshot of VibrationVIEW software, showing the use of Advanced User‐Defined SRTD Phase-Tracking Control to obtain a higher peak transmissibility. The peak transmissibility occurs around -90° and not the predicted -105°.

Conclusion

Consequently, these results indicate that the test engineer ought to manually control the SRTD phase-tracking in order to find the most accurate location for the peak transmissibility of a resonance. In order to obtain a phase of the resonance that will provide the highest possible transmissibility level for that resonance, the test engineer should use a manual control feature to “tweak” the phase as necessary in order to obtain the highest possible transmissibility level for that resonance. This will serve as an improvement over the traditional “phase‐tracking” tool or the “resonant frequency-tracking” method. A new add‐on feature from Vibration Research in its VibrationVIEW Software (Version 11) is the Advanced User-Defined SRTD phase-tracking control that allows the test engineer to manually find the peak transmissibility at a particular resonant frequency by adjusting and controlling the phase value.

Test engineers would benefit from using Vibration Research’s VibrationVIEW software with the add-on feature, Advanced User-Defined SRTD phase-tracking control, in order to conduct the most precise test – a test that maximizes the transmissibility value of the resonances while maintaining high quality control.

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