## Friction Null Band

Digital computers are based on binary circuits. Binary circuits are either on or off, with a corresponding value of one (1) or (0) zero.  This characteristic of digital computing can pose a problem in many instances of modeling physical phenomena such as the effects of friction. As the simulated velocity on which the friction is based approaches zero any friction associated with opposing the velocity is either on or off. If the magnitude of the friction is large, it can produce an excessive force which acts to reverse the sign of the velocity. This type of velocity reversal is what is commonly referred to as oscillatory solution behavior.

This characteristic of digital computers was recognized early in the development of the SMAC program (Reference 1). To avoid the possibility of oscillatory behavior a friction null band was implemented in many of the friction equations to reduce or eliminate the possible oscillatory effects of friction on digital computers at low simulated velocities.  When the relative velocity on which a friction term is based is at or below the friction null band the corresponding magnitude of the friction force is reduced linearly to be zero at zero velocity.

Care must be exercised in the application of large values for the intervehicle friction coefficient (Card 13, Field 7). In particular, the corresponding friction null band that is defined by Field 4 of card 13 must be sufficiently large to insure that the calculated change in the relative velocity, within the given time interval of integration (Card 1, Field 4), does not exceed the width of the null band and, thereby, produce a full reversal of the intervehicle friction force. Such full friction reversals can, of course, produce erroneous oscillatory response predictions, which, as a minimum effect, can produce erroneous directions for the resultant acceleration. Examination of the time-histories of the acceleration components can serve as a check for the existence of such erroneous oscillations.

It should be noted that round-off values near zero for the calculated relative velocity can produce full friction reversals and corresponding oscillations with any friction coefficient (card 13, field 7) in the case of a zero entry for card 13, field 4.

More: Impulsive Constraint "Snag"