EE Pro for TI-89, 92 Plus
Equations - Motors and Generators
135
ω
φ
φ
m
Vt
K
Ra T
K
=
⋅
−
⋅
⋅
b
g
2
Eq. 31.9.5
Example
31.9
– Find the machine constant for a permanent motor rotating at 62.5 rad/s in a magnetic flux field of
1.26 Wb. Assume a 110 V back emf.
Entered Values
Calculated Results
Solution
- The first equation is needed to compute the solution. Select it by highlighting and pressing
¸
. Press
„
to display the input screen, enter all the known variables and press
„
to solve the
equation.
-PQYP8CTKCDNGU
'C
A8
φφ
A9D
ω
ω
O
ATU
%QORWVGF4GUWNV
-
31.10 Induction Motor I
These eleven equations define the relationships amongst key variables used in evaluating the performance of an
induction motor.
The first equation expresses the relationship between the radian frequency induced in the rotor
ω
ω
r, the angular speed
of the rotating magnetic field of the stator
ω
ω
s, the number of poles p, and the mechanical angular speed
ω
ω
m.
ω
ω
ω
r
s
p
m
=
− ⋅
2
Eq. 31.10.1
The second, third and fourth equations describe the slip s using
ω
ω
r and
ω
ω
s,
ω
ω
m, p, the induced rotor power per
phase Pr, and the power transferred to the rotor per phase Pma.
s
p
m
s
= − ⋅
1
2
ω
ω
Eq. 31.10.2
Pr
Pma
s
=
Eq. 31.10.3
ω
ω
r
s
s
= ⋅
Eq. 31.10.4
Pma is defined in the fifth equation in terms of the rotor current Ir and the rotor phase voltage Ema.
Pma
Ir Ema
= ⋅ ⋅
3
Eq. 31.10.5
The sixth and seventh equations account for the mechanical power Pme in terms of p,
ω
ω
m,
ω
ω
s, Pma, and torque T.