Rotating machines form the basis of systems for propulsion, power transmission and generation, compressors, energy storage, manufacturing spindles, vacuum generation, and a range of process plant. They have to operate in a dynamically stable manner and within vibration limits in order that they may function safely over short to long timescales, often involving transient conditions. They may also be expected to operate under variable external conditions of load, speed, and temperature. In order to withstand these variations and disturbances, machines need to be designed with appropriate bearings, seals, and working sections having suitably large clearances to avoid rotor–stator rubs. In hydrodynamic journal bearings, lubricant shearing is necessary to generate static load-carrying capacity, though dynamic conditions will result in journal orbiting within the radial clearance. A dynamic heat source will then be generated in the lubricant film and the manner of the heat transfer will depend...

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