ON GOVERNORS
J. C. MAXWELL
From the Proceedings of the Royal Society, No.100, 1868.
A GOVERNOR is a part of a machine by means of which the velocity of the machine is kept nearly uniform, notwithstanding variations in the driving-power or the resistance.
Most governors depend on the centrifugal force of a piece connected with a shaft of the machine. When the velocity increases, this force increases, and either increases the pressure of the piece against a surface or moves the piece, and so acts on a break or a valve.
In one class of regulators of machinery, which we may call moderators[1], the resistance is increased by a quantity depending on the velocity. Thus in some pieces of clockwork the moderator consists of a conical pendulum revolving within a circular case. When the velocity increases, the ball of the pendulum presses against the inside of the case, and the friction checks the increase of velocity. In Watt’s governor for steam-engines the arms open outwards, and so contract the aperture of the steam-valve.
In a water-break invented by Professor J. Thomson, when the velocity is increased, water is centrifugally pumped up, and overflows with a great velocity, and the work is spent in lifting and communicating this velocity to the water.
In all these contrivances an increase of driving-power produces an increase of velocity, though a much smaller increase than would be produced without the moderator.
But if the part acted on by centrifugal force, instead of acting directly on the machine, sets in motion a contrivance which continually increases the resistance as long as the velocity is above its normal value, and reverses its action when the velocity is below that value, the governor will bring the velocity to the same normal value whatever variation (within the working limits of the machine) be made in the driving-power or the resistance.
I propose at present, without entering into any details of mechanism to direct the attention of engineers and mathematicians to the dynamical theory of such governors.
It will be seen that the motion of a machine with its governor consists in general of a uniform motion, combined with a disturbance which may be expressed as the sum of several component motions. These components may be of four different kinds:-
(1) The disturbance may continually increase.
(2) It may continually diminish.
(3) It may be an oscillation of continually increasing amplitude.
(4) It may be an oscillation of continually decreasing amplitude.
- ↑ See Mr C. W. Siemens “On Uniform Rotation,” Phil. Trans. 1866, p. 657.
