Page 58 - Electric Drives and Electromechanical Systems

Chapter 2 Analysing a drive system 51

The standard friction model is satisfactory for slow-moving, or very large loads, Fig
2.8A. However, in the case of high speed servo application the variation of the Coulomb
friction with speed may need to be considered. The Coulomb friction at a standstill is
higher than its value just above a standstill; this is termed the stiction (or static friction).
The static frictional force is the result of the interlocking of the microscopic irregularities
of two surfaces that will impede any relative motion. The stiction has to be overcome
before the load will move. An additional component to the overall friction is the viscous
friction which increases with the speed; if this is combined with Coulomb friction and
stiction, the resultant characteristic (known as the general kinetic friction model)is
shown in Fig. 2.8B (Papadopoulos and Chasparis, 2004). This curve can be defined as:
8
< F f ð _ xÞ _ xs0
>
F f ¼ F e _ x ¼ 0; € x ¼ 0; jF e j < F s (2.27)
>
F s sgnðF e Þ x ¼ 0; € xs0; jF e j > F s
: _
where F e is any external force and F s is the breakaway force, which is defined as the limit
between static friction (or stiction) and the kinetic friction. The classical friction model is
given by,
F f _ x ¼ F c sgn _ x þ B _ x (2.28)
where F c is the Coulomb friction level and B the viscous friction coefficient. The sgn
function is defined as,
8
_
< þ1 x > 0
>
sgn _ x ¼ 0 _ x ¼ 0 (2.29)
> _
: 1 x < 0

FIG. 2.8 The friction between two surfaces, using the classical or general kinematic model. F s is the breakaway or
stiction frictional force, and F c is the coulomb frictional force. (A) The classical friction model. (B) The general
kinetic friction model.