Thermal runaway — where it appears
Named by 6 essays across one field — each of them below, with the objects they name alongside it.
Also named here as viscous heating — the same set of essays touches all of them, so they are one junction rather than several.
The film that heats itself
The oil in a bearing is not at the temperature of the metal around it. It is tens of kelvin hotter, the rise contains no length whatever, and whether the heating runs away or settles down depends on something that is not a property of the oil at all — whether the machine driving it holds the speed or holds the force.
A lost steady state still holds the film
Push a self-heating oil film one per cent past the stress at which it can no longer settle and it does not run away at once. It warms to the temperature the vanished steady state would have had, sits there as if nothing were wrong, and only then goes — after a delay that grows as one over the square root of the overload, and during nearly all of which the load could still be taken back.
A motor turns the runaway into a jump
A self-heating oil film has a fold at fixed stress and none at fixed speed, and a real motor is neither: its torque falls along a line as its speed rises. Put that line across the film's own torque–speed curve and the runaway disappears for any motor at all. What replaces it depends on the line's slope. A drive softer than one fourteenth of the cold oil's resistance jumps to a hot state and keeps a memory of the load; a stiffer one does neither. And the boundary between the two falls exactly where the motor is turning at a quarter of its no-load speed, which no motor near its rated speed can reach.
A rotor's inertia slows the jump and cannot make it ring
Give the motor driving a self-heating oil film a rotor that has to spin up, and there are two clocks: the film's diffusion time and the rotor's. Two clocks are what an oscillator is usually made of, and this pair cannot make one. Every eigenvalue stays real at every inertia, because the film and the rotor only ever push each other the same way. What inertia does instead is add its own delay to the film's, and in a real machine, where the rotor is hundreds of times slower, the delay past the fold is almost entirely the rotor's.
A slow sensor makes the bearing cycle
Derate the motor driving a self-heating oil film on the temperature of its housing, which warms over minutes, and a protection meant to hold the bearing cool instead makes it cycle for ever: jump hot, warm the housing until the hot state is lost, drop cool, let the housing cool until the cool state is lost, jump again. The period belongs to the housing, the amplitude belongs to the film, and the derating strength decides only whether the cycle happens at all.
A warm bush stops the bearing hunting
A bearing whose motor is derated on its housing's temperature can hunt, jumping between a cool film and a hot one on the housing's clock. Let the bush warm with the housing, and a second feedback joins the first, of the kind that usually makes things run away. It does the opposite: a warm wall is a stiffer drive, the stiffening closes the S the cycle runs round, and past a bush coupling of about a third the bearing settles, warm and derated, however the protection is set.
Named alongside it
The objects these essays reach for when they reach for this one.
BifurcationLubrication filmStabilityViscous heatingModel limitUnsteadyHysteresisOperating pointTemperatureDissipationOscillationBoundary condition