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Motors and Generators | Abb AC Servo motors
5
The basic equation that determines temperature rise is:
T = T
AMB
+ (P
Diss
x R
th
)(1 - e
-t/tTH
)
Where t = the motors’ “on” or operating time, an t
TH
= motors’ thermal time constant - which is a measure of how long it takes to reach
63.2% of the final or steady state temperature.
The exponential rise of temperature versus time can easily be plotted by using the following points:
1/2 t
TH
= 48%, t
TH
= 63%, 3x t
TH
= 95%, 5x t
TH
= 98%, 7x t
th
= 99.99%
This final point (7x t
th
) is the steady state temperature as calculated in the previous section. These points are shown on the curve in
figure 9.
Temperature rise
100%
Temperature
Final temperature
90%
50%
t = 0
t
TH
3t
TH
5t
TH
7t
TH
Time
≈48%
≈63.2%
≈95%
≈98%
≈99%
60%
Thermal time constant - time required to reach 63.2% of final temperature.
Figure 9 – Temperature Rise vs. Time
As an example, take the motor that has P
DISS
x R
th
= 92˚C with ambient of 40˚C, then temperature rise is shown below, and to determine
total temperature, the ambient of 40˚C must be added to these figures.
Thus:
With power applied, the motor winding heats up, attaining 63.2% of final temperature in one thermal time constant, and essentially
reaches final temperature in 7 time constants.
Time
∆Temp rise
+ Ambient
= Total temp.
1/2 tTH
48% x 92 = 44.1
+ 40
= 84.1
tTH
63.2% x 92 = 58.1
+ 40
= 98.1
3 tTH
95% x 92 = 87.4
+ 40
= 127.4
5 tTH
98% x 92 = 90.1
+ 40
= 130.1
7 tTH
99.9% x 92 = 92.9
+ 40
= 132.9
Abb AC Servo motors