Parker Aries AR-04CE - Energy Dissipated in Motor Winding Resistance; Energy Dissipated in Load

Parker Hannifin
Appendix B External Power-Dump Resistor Selection - 97 -
Energy Dissipated in Motor Winding Resistance
Some energy is dissipated in the motor windings. Because the energy is
converted to wasted heat in the motor, it is referred to as copper losses.
The energy during deceleration can be derived from the mass, deceleration
rate, motor resistance, and motor force constant. If some of the parameters
are not known, the energy dissipated in the motor windings (E
W
) can
conservatively be assumed zero (Ø).
This is based on current and motor winding resistance.
()
DM
DF
LF
DMW
tR
tk
vMM
tRIE ⋅⋅
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⋅
⋅+
⋅=⋅=
2
2
2
1
2
1
Where
E
W
= energy dissipated in the motor windings (Joules) – copper losses
I = current through the windings (Amps
rms
)
R
M
= line to line motor resistance (Ohms)
t
D
= deceleration time (Seconds)
M
F
= mass of forcer in kilograms (kg)
M
L
= mass of load in kilograms (kg)
k
F
= motor force constant (N/Amp
rms
)
Energy Dissipated in Load
The load dissipates energy through friction losses, viscous damping, and
other motor/load related losses. These losses are known as load losses. If
some of the parameters are not known, the energy dissipated in the load (E
L
)
can conservatively be assumed zero (Ø).
This can be derived from the force required during the constant velocity
portion of the move profile, either measured or calculated.
DL
tvFE ⋅⋅=
2
1
Where
E
L
= energy dissipated by the load (Joules) – load losses
F = force at constant velocity in Newtons (N)
v = velocity in meters per second (m/s)
t
D
= deceleration time (Seconds)