The effect of friction on the behaviour of servo mechanisms at creep speeds

TLDR: Two methods of investigating the effects of static and Coulomb friction on the minimum smooth-running speed of a position-control system by using the differential analyser to solve the non-linear differential equations describing the behaviour of the system.

Abstract: Position-control servo mechanisms are frequently required to operate smoothly through a very wide range of speeds; the limitation to smooth running at creep speeds is invariably imposed by the non-linear friction in the bearings, gears, etc., associated with the output shaft. The object of the paper is to outline two methods of investigating the effects of static and Coulomb friction on the minimum smooth-running speed of a position-control system. The first method follows closely some recent work on non-linear mechanics and is particularly suited to the non-linear friction problem because it provides a qualitative picture of the behaviour of a system; the method has been applied to a simple mechanical filter-system. The second method uses the differential analyser to solve the non-linear differential equations describing the behaviour of the system. The use of the differential analyser for this problem presents some interesting features, and the running procedure of the machine for the case of the mechanical filter has been described in some detail. Some results are presented which were obtained with the differential analyser in connection with the behaviour of a typical automaticfollowing radar servo-system incorporating a metadyne-controlled motor at creep speeds. It is pointed out that, notwithstanding the rather special and complex nature of the system for this example, it is probable that the general nature of the results will not differ appreciably when other systems are used.