17 / 52
close the system down. This, of course should not occur in normal
operation, and is dealt with in one of two ways:
A power transistor can connect a high capacity power dump
resistor across the smoothing capacitor to allow the excess energy
to be dissipated as heat in the power dump resistor. When the volt-
age across the smoothing capacitor reaches a safe level, the power
dump is switched off.
At the cost of considerable complexity the rectifier can reverse its
action and pass the capacitor’s stored energy from right to left into
the supply line. This is more efficient than the dissipative method
using a power dump
Which system is appropriate will depend on a number of factors.
The power dump method is used in the power systems or sys-
tems with a low duty cycle. For example, a payoff machine feeding
wire from a stock drum into a batch packaging winder at constant
tension would only be required to be in regeneration mode briefly
at the end of each production cycle as it slowed the stock drum to
zero speed. The rest of the cycle would see the drum at standstill or
in motoring mode.
A mine hoist, on the other hand, would spend a considerable
amount of time in the regeneration mode as the cage or skip was
being lowered. In this case a dissipative power dump would be a
profligate waste of energy.
ATrapezoid Move
Figure 3
section A shows the principle of operation (velocity versus
time). Themove commences with a period of acceleration at a constant
rate. This is followed by a plateau section at constant velocity. Finally,
this is followed by a controlled deceleration to complete the move.
Section B shows the corresponding torque versus time. Note
that the torque is constant during the acceleration and deceleration
in this case. The relationship between torque, inertia and accelera-
tion is given by:
DRIVES, MOTORS + SWITCHGEAR
Torque = Inertia X Acceleration
Or
T = J X
α
Where :
α
= Acceleration in radians/sec²
J = Inertia in kg.metre²
T = Torque in Newton.metres
Note that the Inertia is the sum of the motor rotor inertia plus the load
inertia. Inertia for small systems are often expressed more conveni-
ently in kg.cm² as this results more easily visualised numbers rather
than tiny decimal numbers.
1 Newton.m² = (100)² kg.cm²
= 10 000 kg.cm²
During the plateau section (constant velocity) the torque is only
required to overcome system friction.
Finally, deceleration requires negative torque as deceleration is
merely acceleration with a negative sign.
At this point, the torque drops to zero in this example. This would
not be true in the case of, say, a hoist which would have balance the
torque produced by the mass of the load.
Section C shows the resulting power produced by the motor.
During acceleration the power produced rises linearly with the (con-
stant) acceleration.
Power = Torque X Velocity
P = T
ω
where Power (P) is measured in Watts
Torque (T) is measured in Newton metres
Velocity (
ω
) is the angular velocity in radians/sec
More conveniently,
ω
can be expressed in Rev/sec or rev/minute.
Using
ω
in rev/sec
P = 2
πω
T (
ω
in rev/sec)
Using
ω
in rev/minute (RPM)
P = 2
πω
T (
ω
in RPM)
60
If the torque is not zero after the move, as would be the case with a
hoist, the power delivered by the motor is zero as there is no velocity.
In practice, system losses will consume a small amount of power.
This can be made zero by a brake fitted to the motor.
Section D shows a modification to the trapezoidmove. The begin-
ning and end of the acceleration and deceleration profile is modified
to provide a gentle start and stop. This is the so-called S curve. When
the load is driven by a gearbox with lost motion (backlash), the S
curve reduces the acceleration jerk at the velocity transition points.
Apart from reducing audible noise, gearbox life is extended. Move
time is, of course, extended in this case.
Figure 3: Trapezoid move profiles.
S Curve
Time
Time
Time
Time
Velocity
Velocity
Torque
Power
15
September ‘16
Electricity+Control