Page 622 - Mechatronics with Experiments

608 MECHATRONICS
t cycle
t acc t dec

F t

··
x t

x · t

x
t

P t

FIGURE 8.4: Typical output force to load and
E t motion profile and regenerative energy
opportunity for energy recovery during the
deceleration phase of the motion.

The force–motion relationship from Newton’s second law is
F(t) = m ⋅ ̈ x(t) (8.5)
The mechanical power delivered to the inertia is
P (t) = F(t) ⋅ ̇ x(t) (8.6)
m
which is supplied by the electric motor and drive combination.
Notice that when the force and speed are in the same direction, the mechanical power
delivered to the inertia is positive, and the motor-drive operates in motoring mode, that is
to convert electrical energy to mechanical energy. Similarly, when the direction of force
is opposite to the direction of speed, the mechanical power is negative, which means the
inertia gives out energy intead of taking energy. This mechanical energy is converted to
electrical energy by the motor since it acts like a generator under this condition.
P (t) = P (t) = F(t) ⋅ ̇ x(t) (8.7)
e
m
P (t) = P (t) = F(t) ⋅ ̇ x(t) > 0 motoring mode (8.8)
e
m
P (t) = P (t) = F(t) ⋅ ̇ x(t) < 0 generating mode (8.9)
m
e
In motoring mode, the motor-drive provides energy to the load. In generator mode, the
motor drive takes away energy from the load. This energy must be either stored, returned to
line, or dissipated in resistors. One of the most common approaches in servo applications
is to store a small portion of the energy in the DC bus capacitor and dissipate the rest
as heat over external resistors added specifically for this purpose. In applications where