EE6604 - DC Machines 2.1 Output Equation

1. EE6604
DESIGNOF ELECTRICAL MACHINES
ELECTRICAL AND ELECTRONICS ENGINEERING
SRI KRISHNA KUMAR S
HTS953
AP/EEE

2. UNITII DC MACHINES
Output Equations
1 1
11
Main Dimensions
Choice of Specific Electric and Magnetic Loading 1 1
Magnetic Circuits Calculations
1 1Carter’s Coefficient
Net length of Iron
Real & Apparent flux densities
1
1
Selection of number of poles 1
Design of Armature
1
Design of commutator and brushes
Performance prediction using design values 1

3. 2.1. Output equation of a DC machine
Output equation relates the output and main dimensions of the machine. Actually it relates the power developed in the
armature and main dimensions.
E : EMF induced or back EMF
Ia : armature current
Φ:Average value of flux / pole
Z : Total number of armature conductors
N : Speed in rpm
n : Speed in rps
P : Number of poles
A : number of armature paths or circuits
D : Diameter of the armature
L : Length of the armature core

4. Power developed in the armature in kW, Pa= E Ia x 10-3
=(φZNP/60 A)× Ia× 10-3
2.1. Output equation of a DC machine

5. 2.1. Output equation of a DC machine
•Find the dimensions of a 200kW, 250V, 6 pole, 1000 rpm DC generator. The maximum value
of flux density in air gap is 0.87wb/m2 and the ampere conductors per metre length of
armature periphery are 31000. Ratio of pole arc to pole pitch is 0.67 and efficiency 91%.
Assume that the ratio of core length to pole pitch = 0.75. (AU MAY 2008)

6. Power developed in the armature in kW, Pa= E Ia x 10-3
=(φZNP/60 A)× Ia× 10-3
=(Pφ)×(IaZ/A)×N x 10-3/60
=(Pφ)×(IaZ/A)×n x 10-3....... (1)
The term P φ represents the total flux and is called the magnetic loading. Magnetic
Loading per unit area of the armature surface is called the specific magnetic loading or average value of the
flux density in the air gap Bav.
2.1. Output equation of a DC machine

7. Power developed in the armature in kW, Pa= E Ia x 10-3
=(φZNP/60 A)× Ia× 10-3
=(Pφ)×(IaZ/A)×N x 10-3/60
=(Pφ)×(IaZ/A)×n x 10-3....... (1)
The term P φ represents the total flux and is called the magnetic loading. Magnetic
Loading per unit area of the armature surface is called the specific magnetic loading or average value of the
flux density in the air gap Bav.
Bav = Pφ /π DL Wb/m2 or tesla denoted by T
Therefore Pφ = Bav π DL ................ (2)
2.1. Output equation of a DC machine

8. Power developed in the armature in kW, Pa= E Ia x 10-3
=(φZNP/60 A)× Ia× 10-3
=(Pφ)×(IaZ/A)×N x 10-3/60
=(Pφ)×(IaZ/A)×n x 10-3....... (1)
The term P φ represents the total flux and is called the magnetic loading. Magnetic
Loading per unit area of the armature surface is called the specific magnetic loading or average value of the
flux density in the air gap Bav. That is,
Bav = Pφ /π DL Wb/m2 or tesla denoted by T
Therefore Pφ = Bav π DL ................ (2)
The term (Ia Z/A) represents the total ampere-conductors on the armature and is called the electric loading.
2.1. Output equation of a DC machine

9. Power developed in the armature in kW, Pa= E Ia x 10-3
=(φZNP/60 A)× Ia× 10-3
=(Pφ)×(IaZ/A)×N x 10-3/60
=(Pφ)×(IaZ/A)×n x 10-3....... (1)
The term P φ represents the total flux and is called the magnetic loading. Magnetic
Loading per unit area of the armature surface is called the specific magnetic loading or average value of the
flux density in the air gap Bav. That is,
Bav = Pφ /π DL Wb/m2 or tesla denoted by T
Therefore Pφ = Bav π DL ................ (2)
The term (Ia Z/A) represents the total ampere-conductors on the armature and is called the electric loading.
Electric loading/unit length of armature periphery is called the specific electric loading q. That is,
q= IaZ / π A D Amp-cond / m
2.1. Output equation of a DC machine

10. Power developed in the armature in kW, Pa= E Ia x 10-3
=(φZNP/60 A)× Ia× 10-3
=(Pφ)×(IaZ/A)×N x 10-3/60
=(Pφ)×(IaZ/A)×n x 10-3....... (1)
The term P φ represents the total flux and is called the magnetic loading. Magnetic
Loading per unit area of the armature surface is called the specific magnetic loading or average value of the
flux density in the air gap Bav. That is,
Bav = Pφ /π DL Wb/m2 or tesla denoted by T
Therefore Pφ = Bav π DL ................ (2)
The term (Ia Z/A) represents the total ampere-conductors on the armature and is called the electric loading.
Electric loading/unit length of armature periphery is called the specific electric loading q. That is,
q= IaZ / π A D Amp-cond / m
Therefore Ia Z/A = q π D ............ (3)
2.1. Output equation of a DC machine

11. Power developed in the armature in kW, Pa= E Ia x 10-3
=(φZNP/60 A)× Ia× 10-3
=(Pφ)×(IaZ/A)×N x 10-3/60
=(Pφ)×(IaZ/A)×n x 10-3....... (1)
The term P φ represents the total flux and is called the magnetic loading. Magnetic
Loading per unit area of the armature surface is called the specific magnetic loading or average value of the
flux density in the air gap Bav. That is,
Bav = Pφ /π DL Wb/m2 or tesla denoted by T
Therefore Pφ = Bav π DL ................ (2)
The term (Ia Z/A) represents the total ampere-conductors on the armature and is called the electric loading.
Electric loading/unit length of armature periphery is called the specific electric loading q. That is,
q= IaZ / π A D Amp-cond / m
Therefore Ia Z/A = q π D ............ (3)
Substitution of equations 2 and 3 in 1, leads to
kW = Bav π DL × q π D × (n × 10-3)
2.1. Output equation of a DC machine

12. Power developed in the armature in kW, Pa= E Ia x 10-3
=(φZNP/60 A)× Ia× 10-3
=(Pφ)×(IaZ/A)×N x 10-3/60
=(Pφ)×(IaZ/A)×n x 10-3....... (1)
The term P φ represents the total flux and is called the magnetic loading. Magnetic
Loading per unit area of the armature surface is called the specific magnetic loading or average value of the
flux density in the air gap Bav. That is,
Bav = Pφ /π DL Wb/m2 or tesla denoted by T
Therefore Pφ = Bav π DL ................ (2)
The term (Ia Z/A) represents the total ampere-conductors on the armature and is called the electric loading.
Electric loading/unit length of armature periphery is called the specific electric loading q. That is,
q= IaZ / π A D Amp-cond / m
Therefore Ia Z/A = q π D ............ (3)
Substitution of equations 2 and 3 in 1, leads to
kW = Bav π DL × q π D × (n × 10-3)
= B q D2 L n
= π2Bav q C0 D2 L N 10-3
Where C0= π2Bav q 10-3 is called the output coefficeint of the DC machine
2.1. Output equation of a DC machine