Starting the fan and motor
During start up, the motor has to accelerate from zero to full speed. If there were no resistance this would be achieved rapidly, but with a fan the “inertia" of the rotating parts resists this acceleration. Fans, perhaps more than any other application, have high inertia relative to the power requirements. The power absorbed by a fan impeller varies as its speed cubed (see Chapter 4, Section 4.6 on fan laws) i. e.


















: Nioo"r"ioo 
Now p 
Njf] and P1C
Tioo 
N, 
Equ 13.2
I 
A 




If the torque developed by the motor were the same as that re The relationship is: Equ 13.3 
Now generally: 
T 7 
Equ 13.4 
Also 
T = p = 60 xiooo T 2iA Inertia referred to motor shaft: N. ‘2 
Equ 13.5 
Equ 13.6 
VNmy 
Torque referred to motor shaft: ,Nl Nm 
Tr =Tf 
2ttN "60” 
Equ 13.7 
Px1000 

© 2tiN A = — =———— T 60t 
This analysis assumes that 100% of the full load motor torque is available during the run up period. In fact the torque for acceleration is varying all the time from zero rev/min to full speed. Figure 13.17 shows this. The formula must therefore be amended by a factor “f which gives the 
» 2jiN lt . T =—— XL or t = 60 Tm 






Figure 13.19 Induction motor characteristics, stardelta starting 
% Fullload speed 
Figure 13.20 Induction motor characteristics, unsatisfactory torque 
% Fullload speed 
Frame 
Moment of inertia mr2 kgm2 

Size 
2Pole 
4Pole 
6Pole 
8Pole 
D63 
3.63×10" 
3.65 x 10" 
— 
— 
D71 
5.33 X104 
5.43×10" 
— 
— 
D80 
1.14 xtO’3 
1.56 x 103 
1.61 x 10 3 
— 
D90S 
1.61 x 10’3 
3.43 x10 3 
3.40 x 10 3 
3.40×10’3 
D90L 
1.99 x 103 
3.93 x10 3 
3.88 x10‘3 
3.88 x103 
D100L 
6.43 x 103 
1.15X102 
1.16 x 10’2 
1.16 x102 
D112M 
7.35 x10 3 
1.35 x 102 
1.38 x 102 
1.38 x 102 
D132S 
1.90 x 102 
3.10 x 102 
3.35 x10’2 
3.35 x 10 2 
D132M 
__ 
3.38 x 10 2 
4.15 x10 2 
4.15 x 10’2 
D160M 
4.63 x 10’2 
7.18×10 2 
1.02 x 101 
1.02 x10’1 
D160L 
5.20 x10 2 
8.53 x 102 
1.20×10’1 
1.20 x 10 1 
D180M 
6.00 x10 2 
9.83 x 102 
— 
— 
D180L 
__ 
1.52 x101 
1.99 x10’1 
1.99 x 10 1 
D200L 
1.87 x 10 ‘ 
1.88 x101 
3.59 x 10 1 
2.49×10’1 
D225S 
__ 
3.43 x 101 
__ 
4.16 x 101 
D225M 
2.04 x 10 1 
3.78 x 101 
4.71 x 101 
4.71 x 101 
Table 13.3 Typical moments of inertia for TEFV induction motors

Note: 1. These figures are for a range of light duty centrifugal impellers. They
Are of the backward inclined typed, spot/plug welded up to size 1900 mm diameter and fully welded above.
2. For other blade types refer to Table 13.5
3. Units are "engineers” i. e. mass kg x radius of gyration m
Table 13.4 Typical moments of inertia for a range of centrifugal fans
Impeller type 
Sizes 160 to 900 
Sizes 1120 to 2000 
Backward curved 
1.00 
1.05 
Forward curved 
1.09 
1.18 
Shrouded radial 
1.05 
1.10 
Open paddle 
1.12 
1.12 
Aerofoil 
1.21 
1.16 
Table 13.5 Typical multiplier for other blade forms 
Torque over the runup period and for this reason it is usual to assume an average 100% fullload torque available for the whole period. No correction is therefore necessary to the general formula. See Figure 13.18.
Stardelta starting induction motor
Normally used for motors between 7.5 kW and 45 kW this method reduces the line voltage (and hence current) on starting to prevent large surge currents. Unfortunately, it also reduces available torque as may be seen in Figure 13.19. An average value of torque available is 30% of the fullload value and therefore a correction factor of 3.33 may be used.
Note: Some motors, particularly between 15 kW and 30 kW, have a torque characteristic with a pronounced “dip” limiting the speed that may be attained in star. This is shown in Figure 13.20. Here the fan torque characteristic cuts the motor torque characteristic at a low speed and the motor will not accelerate beyond this point. Changing to delta connection at this speed will mean the line carrying a very high current for which the cables, fuses, and overloads must be adequately sized.
It is difficult to generalize in this case, but it may be assumed that the lowest value of the motor torque occurs at 30% fullload speed and is approximately 40% full load torque in star. Should the fan torque at this speed exceed this low value of motor torque, alternative starting methods should be used.
T =ilx— x1000x0.32 Equ 13.8
Nm 271
The torque absorbed by the fan at 30% motor speed referred to motor shaft.
Autotransformer starting
Autotransformer starting again reduces voltage current and torque, butin a greater number of stages (usually three, but can be two or four) thereby giving a higher average available torque. Tappings may be at 40%, 60%, 80% voltage and a correction factor of two is then used. Figure 13.21 gives typical characteristics.
Where:
Re = ratio of the applied voltage to the motor rated
Voltage
F = correction factor referred to in the text
Hence, assuming the correct voltage is applied, the approximate formula for each method of starting may be simplified to:
DOL induction
Example: A fan is driven by an induction motor and controlled by a direct online starter. It absorbs 5 kW and is fitted with a 51/2 kW motor. The run uptime calculated from Equation 13.10 is 18 seconds. If the motor power is increased to TA kW what will be the new starting time? 

300 
200 
1.1 ‘пф® 
M2 Pf 
— 2 
Im+’f 
T = 
Stardelta Induction 
N, X^x 
3.7 105 
T: 
Autotransformer N 
2.2 105 
V 
FT12 
L + l, 
T = 
N 
0.55 
‘hЈM2 
M2 
T = 
Pf 105 
Thus: Pf 
7.5 
= 1.5 

T = 
T = 
;—— ^—— x(—^xf Rg2 Pf x1000 I 60 J ^ 
N2 f? X—s x—— Rp x1.097 Pf 105 ^ 
Or 


































Note: kT has been calculated for a range of typical TEFV squirrel cage induction motors with directonline starting. The factors are expected to be somewhat smaller, and the starting times shorter, for induction motors with autotransformer starting or slip ring motors with statorrotor starters.
Posted in Fans Ventilation A Practical Guide
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