Simplified Morton Effect analysis for synchronous spiral instability

It’s been known for many years that thermal temperature gradients across a rotor can alter the amplitude and phase of synchronous vibration. This is due to bowing of the shaft caused by a temperature difference between one side of the shaft and the other. The earliest published recognition of this phenomenon was by Newkirk [1], where the temperature difference was a result of frictional heating from the rotor rubbing on non-rotating elements of the machine. A rub of this type could involve labyrinth seals, armatures, impellers, slip rings, etc. Residual rotor imbalance produces vibration, which may produce a rub. The rub generates heat locally on the shaft surface and bows the shaft, causing additional imbalance and leading to increased vibration and heat, and so on. This could be described as a type of thermal runaway. Another way a temperature difference in the shaft can be produced is through non-uniform viscous shearing action in the oil film of a journal bearing. This particular type of thermal action is referred to as the Morton Effect [2]. An excellent review of literature on this topic is given by de Jongh [3]. The Morton Effect is a thermal condition that exists to a various extent in all fluid film journal bearings. Figure 1 depicts a cylindrical sleeve bearing with an orbiting journal. An essential underlying condition of the Morton Effect is that the shaft orbital motion is synchronous with rotation. In Figure 1a the shaft is at its closest approach to the stationary bearing liner. In this position, the maximum amount of viscous shearing heat is generated at the location of minimum film thickness. This is a fundamental aspect of hydrodynamic lubrication. This particular spot on the shaft surface is marked with a red circle and subsequently referred to as the “high spot.” The 4 successive orbital positions displayed in Figure 1 (every 90 degrees of shaft rotation) show that the “high spot” is the only spot on the shaft that experiences the smallest possible film thickness, and its accompanying maximum heat input during the course of one complete shaft orbit and revolution. The result is that different regions of the shaft surface are exposed to different amounts of time averaged heat input during each revolution. This produces a fixed (relative to the shaft) temperature difference across the shaft. The temperature difference is proportional to the size of the orbit. When the orbit size is zero, and the shaft only spins, all regions of the shaft surface are exposed to identical amounts of heat during each revolution. This means there is no temperature difference created, except for the shallow skin temperature effects that cycle with each revolution. As orbit size increases, however, the variation in heat input becomes greater. The temperature difference across the shaft increases as orbit size increases. Most rotating machines are not affected by the aforementioned orbit-induced temperature difference in a journal bearing. Some particular machine configurations, however, are sensitive. A common trait is a large amount of overhung weight outboard of one or both bearings. Examples include turbochargers and turboexpanders with large overhung impellers, high-power compressors with large heavy coupling hubs, and electrical generators with overhung exciters. Shaft bowing at the bearing throws the overhung weight out of balance. If the machine is running at a speed where vibration amplitude at the bearing is sensitive to imbalance of the overhung weight, a Morton Effect instability becomes likely.