Finite-element model of thermal loads on an oil-starved journal bearing
Bearing assemblies (run dry at start-up) with a larger radial clearance take longer to seize than those with smaller clearances.
Start-up frictional torque rises 50-fold when bearings seize to shafts. (W = 4,400, N = 250 rpm, R = 25.5 mm, C = 0.0125 mm, L = 51 mm).
M. M. Khonsari
Director, Center for Rotating Machinery
Mechanical Engineering Dept.
Louisiana State Univ.
Baton Rouge, La.
E. R. Booser
A large commercial air conditioner turns on after sitting over winter, but its compressor locks up within seconds of starting. The unit is fairly new and had worked fine last season. So what happened? Forensics revealed that running clearance had completely closed between a compressor sleeve bearing and mating shaft. The culprit: thermally induced seizure (TIS).
TIS is most common in hydrodynamic bearings, especially those that operate in the boundary or mixed-lubrication regimes. But it can also happen to fully lubricated bearings. Equipment that sits idle for a while between operations is particularly susceptible because oil can creep away or volatilize over time, leaving bearings completely dry at start-up. In fact, anything that interferes with lubricant properly reaching bearings can trigger TIS, including a clogged oil filter.
Bearings starved of lubricant generate excessive frictional heat. For example, a hydrodynamic journal bearing with a full film of lubricant separating surfaces typically has a friction coefficient, ƒ of about 0.001 to 0.008. Without lubricant, that same contact surface -- depending on material properties of the friction pair -- may have an ƒ of 0.1 to 0.25. Higher-than-normal heat loads at the contact surface cause a shaft to grow radially. Most designs constrain the bearing outer surface in a housing so bearings grow inward towards the shaft, further closing clearances and ultimately seizing parts together.
It turns out the thermomechanical process responsible for TIS is complex and nonlinear. A finite-element model of a journal bearing undergoing TIS shows that while the shaft expands uniformly, the bearing tends to assume an "ovalized" shape. The distortion boosts frictional force between the shaft and bushing inner surface which, in turn, generates even more heat. Once this extra contact area forms, shaft torque required to overcome friction rises nonlinearly with time and accelerates rapidly until the bearing seizes. A 1-in.-diameter shaft run at 250 rpm and starved of oil may take only 20 to 30 sec to seize, for example.
Empirical relations from FE models can predict time to seizure, ts (sec)of dry journal bearings and shafts at start-up:
For 500 ≤ R/C ≤ 1,000
For 1,000 < R/C ≤ 5,100where:
where ω = angular speed (rads/sec), W = load (N), R = shaft radius (mm), C = radial clearance (mm), ƒ = coefficient of friction, α = coefficient of thermal expansion (m/m-°K), k = shaft thermal conductivity (W/m-°K), κ = shaft thermal diffusivity (mm2/sec), and L = bearing length.
Consider a journal bearing with R = 20 mm, C = 0.008 mm, L = 50 mm, W = 5,000 N, N= 1,000 rpm, k = 52 W/m-°K, α = 0.5 X 10-5 m/m-°K, and ρCp = 1.23 X 106. In this case, R/C = 2,500, so use the second equation. It estimates a ts of 10.5 sec with a startup friction coefficient of ƒ = 0.1. In other words, the bearing system will fail by seizure in that time unless oil reaches the contact area to reduce friction.
These empirical relationships can also help engineers design bearing assemblies that take longer to seize when starved of lube. For instance, doubling radial clearance in the above design extends seizure time to about 22 sec. Increasing clearance to, say, R/C = 500 may avoid seizure altogether because of more room for expansion and reduced thermal load with a smaller contact area between the shaft and bearing bore. However, the extra heat from running dry for a longer time accelerates wear and may overheat, even melt bearing materials, possibly leading to catastrophic failure of equipment. With increasing running clearance also comes less control of rotor vibration.