Copley Controls Xenus Plus Series - Page 136

Xenus Plus User Guide 16-01344 Rev 06
Copley Controls 136
A.1.3: Calculate Energy Returned for Each Deceleration
Use the following formulas to calculate the energy returned during each deceleration:
Rotary motor:
E
dec
= ½ J
t
(ω1
2
- ω2
2
)
Where:
E
dec
= Energy returned by the deceleration, in Joules.
J
t
= Load inertia on the motor shaft plus the motor inertia in kg m
2
.
ω
1
= Shaft speed at the start of deceleration in radians per second.
ω
2
= Shaft speed at the end of deceleration in radians per second.
ω = 2*π* (RPM / 60)
Linear motor:
E
dec
= ½ M
t
(V
1
2
- V
2
2
)
Where:
E
dec
= Energy returned by the deceleration, in Joules.
M
t
= Total mass of the load and the moving part of the motor in kg.
V
1
= Velocity at the start of deceleration in meters per second.
V
2
= Velocity at the end of deceleration in meters per second.
A.1.4: Determine the Amount of Energy Dissipated by the Motor
Calculate the amount of energy dissipated by the motor due to current flow though the motor winding
resistance using the following formulas.
P
motor
= 3/4 R
winding
(F / Kt)
2
Where:
P
motor
= Power dissipated in the motor in Watts.
R
winding
= Line to line resistance of the motor.
F = Force needed to decelerate the motor:
Nm for rotary applications
N for linear applications
Kt = Torque constant for the motor:
Nm/Amp for rotary applications
N/Amp for linear applications
E
motor
= P
motor
T
decel
Where:
E
motor
= Energy dissipated in the motor in Joules
T
decel
= Time of deceleration in seconds
A.1.5: Determine the Amount of Energy Returned to the Drive
Calculate the amount of energy that will be returned to the drive for each deceleration using the
following formula.
E
returned
= E
dec
- E
motor
Where:
E
returned
= Energy returned to the drive, in Joules
E
dec
= Energy returned by the deceleration, in Joules
E
motor
= Energy dissipated by the motor, in Joules