Magnetorheological Fluid Technology

209Magnetorheological (MR) Brake System

where φ is a phase lag. In this case, the work per cycle of the optimal friction

torque T

opt

can be determined by

W T

t d t

cyc opt

cos( ) ( )

0

2

∫

= Θ ω ω

π

(7.49)

By introducing an equivalent damping coefcient C

eq

such that the work

per cycle due to this equivalent damping coefcient equals that of optimal

friction torque T

opt

, the following equation holds:

T t d t C t d t C

opt eq eq

cos( ) ( ) cos ( ) ( )

0

2

2 2

0

2

2

∫ ∫

Θ ω ω = Θ ω ω ω = Θ ωπ

π π

(7.50)

From Equation (7.50), the equivalent damping coefcient C

eq

is determined by

C

T t d t

T

J

eq

opt

opt

d

cos( ) ( )

4

4 2

0

2

2

∫

=

ω ω

Θωπ

=

Θωπ

=

π

ω

π

(7.51)

By assuming that the effec ...