Expanding the twin pulse swing free profile
The twin-pulse motion profile is still perhaps the simplest profile in existence for reducing residual vibration. Its primary drawback is that of narrow bandwidth, i.e., it is effective for attenuating only a very narrow range of frequencies about its design frequency. This has led to the inclusion of more pulses to improve robustness to frequency variation. However, one cost of adding pulses is extending the duration of the resulting motion. This paper presents several techniques whereby the basic twin-pulse motion profile can be expanded to reduce its frequency sensitivity while still preserving its advantages. These techniques include intentionally mis-aligning the null points of ideal twin pulses and a convolved boxcar function, then adding a trapezoidal profile component, finally culminating in what we term a misaligned boxcar/trapezoidal/twin pulse (M- BC:TZ:TP) motion profile. This expanded profile and a basic twin-pulse profile were both evaluated on a ten-pendula system with natural frequencies varying over a range of nearly 10%. Simulation results showed an overall reduction of 97% with the expanded twin-pulse profile, and notably all ten frequencies were attenuated; only one frequency was attenuated with the standard twin-pulse profile. Experiments using a linear rail transport system and the ten pendula device validated the simulation. These expanded profiles retain the simplicity and short duration of the twin-pulse with increased robustness to frequency variations.