User`s guide

EE Pro for TI-89, 92 Plus
Equations - Motors and Generators
132
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ωω
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31.7 DC Shunt Motor
These seven equations describe the principal characteristics of a DC shunt motor. The first equation expresses the
terminal voltage Vt in terms of the field current IIf and field resistance Rf along with the external field resistance
Re. The second equation defines the terminal voltage Vt in terms of the back emf (expressed in terms of the
machine constant K, flux swept
φ
, and angular velocity
ω
m) and the IR drop in the armature circuit.
Vt Rf IIf
=+⋅Re
bg
Eq. 31.7.1
Vt K m Ra Ia=⋅⋅ + ⋅
φω
Eq. 31.7.2
The third equation refers to the torque available at the load TL due to the current Ia in the armature minus the loss of
torque Tloss due to friction and other reasons.
TL K Ia Tloss=⋅⋅−
φ
Eq. 31.7.3
The fourth equation gives the definitive relationship between the back emf Ea, K,
φφ
and
ωω
m.
Ea K m=⋅ ⋅
ωφ
Eq. 31.7.4
The next equation displays the reciprocal quadratic relationship between
ωω
m, Vt, K,
φφ
, armature resistance Ra,
adjustable resistance Rd and T.
ω
φ
φ
m
Vt
K
Ra Rd T
K
=
⋅
−
+⋅
⋅
bg
b
g
2
Eq. 31.7.5
The last two equations compute torque T in terms of Tloss, load torque TL, flux
φφ
, Ia, and K.
T Tloss TL
=+
Eq. 31.7.6
TK Ia=⋅⋅
φ
Eq. 31.7.7
Example 31.7 -
Find the back emf for a motor with a machine constant of 2.1, rotating at 62 rad/s in a flux of
2.4 Wb.
Entered Values Calculated Results