EB-20X Installation & Service Manual | Motor Data Package
36
Kollmorgen | kdn.kollmorgen.com | September 2020
This equation assumes ti is small compared to the thermal time constant for peak power of motor
(TCTP) for torque values significantly larger than the continuous torque (TC). This is not always a
good assumption. For cases where torque values significantly exceed TC, the following equation
is used:
T
OUT
T
C
=
1-e
-t
/Duty Cycle * TCTP
ON
1-e
-t
/TCTP
ON
where duty cycle = t
ON
/(t
ON
+ t
OFF
)
T
OUT
= output torque
T
C
= continuous torque at operating speed
t
ON
= time on
TCTP = thermal time constant for peak power of motor
The next equation expresses operating torques as a function of ON time. It also breaks the
operating cycle down into individual periods of ON time and OFF time. Substituting for duty cycle
and solving for tOFF, the
above
equation yields:
(EQ-2)
T
OFF
= -TCTP 1n 1-
(1-e
-t
/TCTP) T
OUT
ON
2
-t
ON
T
C
2
Thus, for a specific output torque and a given ON time, the required OFF time is known. This OFF
time is required so that the motor cools sufficiently so as not to exceed its thermal limits. The
calculated OFF time should precede the initial ON time to ensure that ultimate temperature is not
surpassed on the first cycle.
It may also be useful to calculate a time to ultimate temperature based on a one-time excursion
from ambient temperature. Consider the following pair of equations:
(EQ-3)
T
R
Actual Above Ambient =
T
R
Rated Above Ambient =
T
OUT
T
C
2
(EQ-4)
T
R
Rated = T
R
Ultimate (1 - e
-t
)
where TR Rated = time/TCTP
Substitute 3) into 4) and obtain:
To find the time to ultimate temperature, set TR Actual = TR Ultimate and solve for t. This yields
the following equation:
(EQ-5)
T
MAX
= -TCTP 1n 1-
2
T
OUT
T
C
where: t = max on time
TCTP = thermal time constant for peak power of motor
T
c
= continuous torque of the motor at the operating speed
T
OUT
= operating torque
