White, R., "Measurement Techniques for Estimating Critical Speed of Drivelines," SAE Technical Paper 2017-01-1800, 2017.
Several analytical tools exist for estimating a driveshaft’s critical speed, from simple elementary beam theory to sophisticated FEA models. Ultimately, nothing is better than a test, because no one will argue with the outcome from a well-designed measurement. Impact response measurements are easy, but they tend to over predict the critical speed. A test which sweeps the shaft speed up until failure is telling, but the speed causing failure is strongly dependent on even small amounts of variation in rotor unbalance. Waterfall plots of shaft displacement measurements offer the best indication of critical speed, however sometimes the resonance isn’t unmistakable or multiple resonances exist, making the critical speed unclear. A method less susceptible to system variation is offered here, fitting shaft orbit measurements to the theoretical single degree of freedom equation. The procedure is to first make an impact response measurement using an accelerometer and modal hammer, then select a maximum speed for the speed sweep several hundred rpm below the resonance. A test is then run with a slow speed sweep up to the previously determined maximum speed and then back down while measuring the shaft’s deflection with displacement transducers. The radii of the orbits are computed and the orbit radius vs. shaft speed is plotted. The single degree of freedom equation parameters are adjusted to fit to these data, resulting in estimates for critical speed, damping, unbalance to stiffness ratio and an offset (half static runout).