# 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.

 NiL

 N,

 Equ 13.1

 Where: Pi Pico Ni N100

 Power at any instant power at full speed speed at any instant full speed

 F

 For vee belt-driven fans there will be additional small power losses in the bearings and belt (varying directly as the speed), but for the following analysis, these are ignored. It is usual for electric motor manufacturers to produce torque speed curves. It is therefore necessary to calculate the torque required by the fan.

 I*-

 Figure 13.14 Comparison of space required for an axial flow fan fitted with an “inside-out” and conventional motor respectively

 : Nioo"r"ioo

 Now p

Njf] and P1C

 Tioo

 N,

Equ 13.2

 I
 A
 It will be seen that this is a square relationship. We may there­fore draw a curve of torque versus speed. This starts at the ori­gin, for when N, = 0 then T = 0. N100 and T100 will be the full speed and corresponding torque taken by the fan under the stated conditions of gas air density and point of operation (damper closure etc). In fact, with a fan impeller mounted on a shaft running in bearings, there will be a small amount of torque at the instant of starting. This is due to the “stiction” in the bear­ings and is known as the “break away torque”. It is only of any significance with sleeve bearings and again will be ignored in the present analysis.

 Figure 13.15 View of forward curved centrifugal fan fitted with “inside-out" motor Courtesy of PM°DM Precision Motors Deutsche Minebea GmbH

 If the torque developed by the motor were the same as that re- quired by the fan, then they would be in balance, and the fan would neither accelerate nor slow down. During the run up pe- riod, therefore, the excess of motor torque over torque required is available for accelerating the fan to full speed. 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
 Tm-Tf = + K Where: Tia = Torque available for acceleration Tjm — Torque developed by motor Ti, = Torque required by fan I = Inertia of rotating parts Ai = Acceleration all at any instant We may determine the run up time from the fc Analysis: M = Mass of rotating parts (kg) R = Radius of gyration (m) I = Inertia of rotating parts (kg. m2) = N = Rotational speed (rev/min) T = Run up time (S) T = Torque (Nm) A = Angular acceleration (rad/s2) P = Power (kW) W = Angular velocity (rad/sec) Tn = 2tiN 60 Suffix F = Fan M = Motor T = Total I = Instantaneous 100 = Full speed
 © 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 =—— X-L or t = 60 Tm
 % Full-load speed Figure 13.17 Torque available for acceleration

 Average torque available for acceleration (average of all ordi­nates taken over very small Increments of speed). In the examples which follow “f is approximated for some of the most popular types of motor and starter. However, there is no substitute for a detailed analysis when actual fan and motor torque/speed curves are drawn to scale on the same base. This will enable “f to be accurately assessed. The time allowablefor starting is dependent on a number of fac­tors. Acceleration produces additional stresses in the fan im­peller and shaft but these are not usually of significance. More important are the effects of higher motor winding temperatures, suitability of starter overload relays, and the ability of power lines to accept the additional current. Usually a time of around 18 seconds is therefore recommended, but this may not be achieved with very large units. The whole installation must then be discussed between fan, motor, and starter manufacturers to achieve the best solution. To assist in the calculation of these times, it is necessary to have accurate values of the inertia of both motors and fans. However, typical values are given in Tables 13.2,13.3 and 13.4, which may be used for initial calculations at the project stage. They should be replaced by actual values, once the fan and motor manufacturers have been selected. In most cases the power absorbed by the fan will be within a small percentage of the motor installed power. Assuming them to be equal, at this stage of the analysis, we may then plot curves for the motor and fan. The various types of motor and starter may now be considered and factors “f” determined to give approximate run up times: Direct-on-line (DOL) induction motor This method of starting is usually employed up to about 7.5 kW, and for motors of this size the torque/speed characteristic is generally as shown in Figure. 13.15. As may be seen the avail­able torque varies from 200% to 0% of the motor full-load

 Figure 13.19 Induction motor characteristics, star-delta starting

 Figure 13.20 Induction motor characteristics, unsatisfactory torque

 Frame Moment of inertia mr2 kgm2 Size 2-Pole 4-Pole 6-Pole 8-Pole D63 3.63×10" 3.65 x 10" — — D71 5.33 X10-4 5.43×10" — — D80 1.14 xtO’3 1.56 x 10-3 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 10-3 3.93 x10 3 3.88 x10‘3 3.88 x10-3 D100L 6.43 x 10-3 1.15X10-2 1.16 x 10’2 1.16 x102 D112M 7.35 x10 3 1.35 x 10-2 1.38 x 10-2 1.38 x 10-2 D132S 1.90 x 10-2 3.10 x 10-2 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 10-1 1.02 x10’1 D160L 5.20 x10 2 8.53 x 10-2 1.20×10’1 1.20 x 10 1 D180M 6.00 x10 2 9.83 x 10-2 — — D180L __ 1.52 x10-1 1.99 x10’1 1.99 x 10 1 D200L 1.87 x 10- ‘ 1.88 x10-1 3.59 x 10 1 2.49×10’1 D225S __ 3.43 x 101 __ 4.16 x 10-1 D225M 2.04 x 10 1 3.78 x 10-1 4.71 x 10-1 4.71 x 101

Table 13.3 Typical moments of inertia for TEFV induction motors

 Moment of inertia mr2 kgm2 Width Extra narrow Narrow Medium Wide Extra wide 160 7.19 x10’3 1.10 x102 180 9.61 x 10 3 1.44 x 10’2 200 1.26 x 10*2 2.04 x 10’2 224 1.73×10 2 2.88 x10 2 250 2.29×1 O’2 2.41 x 10’2 3.38 x 10 2 A> E 280 2.47×10 2 2.74 x 10 2 3.83 x 10’2 ‘*5 315 4 .15 x10’2 4.28×1 O’2 4.76×10 2 5.01 x 10’2 7.26 x 10 2 0) A. 355 6.10 x 10’2 6.35 x IO-2 7.06 x 10 2 7.43 x 10 2 1.17 x 101 Fc 400 8.89×10’2 9.26 x 10 2 1.03 x 10 1 1.07 x 10 1 1.69 x 10’1 E 450 1.35 x 10 1 1.41 x 10 1 1.57×10′ 1.74 x IO’1 2.69 x 10’1 4) N 500 2.31 x 10’1 2.43 x 10’1 2.70 x 10 1 3.00 x10-‘ 4.81 x 10 1 C Re 560 4.32 x10’1 4.55 x 10’1 5.04 x 10 1 5.60 x 10 1 9.53 x 10’1 630 7.18 x 10"1 7.64 x 10’1 8.49 x 10 1 1.01 1.53 710 1.21 1.29 1.43 1,83 2.78 800 2.49 2.68 2.98 3.21 5.12 900 4.31 4.63 4.67 5.19 7.65 1000 1.39x 10 1.49 x 10 1.66 x 10 1.74 x 10 2.82 x 10 1120 2.1 x 10 2.28 x 10 2.53 x 10 2.66 x 10 4.71 x 10 1250 3,58×10 4.01 x 10 7.53 x 10 1400 5.93×10 6.43 x 10 1.10 x 102 1600 1.05 x 102 1.98 x102 1800 1.58 x 102 2.91 x 102 2000 2.69 x 102 4.74 x102

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 run-up period and for this reason it is usual to assume an average 100% full-load torque available for the whole period. No correction is therefore necessary to the gen­eral formula. See Figure 13.18.

Star-delta 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 full-load 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% full-load 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 =il-x— x1000x0.32 Equ 13.8

Nm 271

The torque absorbed by the fan at 30% motor speed referred to motor shaft.

Auto-transformer 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 on-line 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?

 .Locke I motor torq Ue Pul -out torque I Full-loac Torque N T Pull-up tore [ue Far^2! ЗяS’-‘-»’"""
 300
 200
 1.1 ‘пф®
 M2 Pf
 — |2
 Im+’f
 T =
 Star-delta Induction
 N, X^-x
 3.7 105
 T:
 Auto-transformer N
 2.2 105
 V
 FT12
 L + l,
 T =
 N
 0.55
 ‘-h|ЈM2
 M2
 T =
 Pf 105
 Thus: Pf
 7.5
 = 1.5
 RNfl 2 L + if F Nf ^ 2“ Im + lf
 T =
 T =
 ;—— ^—— x(—^xf Rg2 Pf x1000 I 60 J ^
 N2 f? X—s x—— Rp x1.097 Pf 105 ^
 Or
 Equ 13.10

 Equ 13.11

 100

 Equ 13.12

 20

 80

 Slip ring stator rotor

 Figure 13.21 Induction motor characteristics, auto-transformer starting

 Slip-ring motors/stator-rotor starting This is one of the most satisfactory methods of fan starting since by inserting resistance in the rotor circuit, the torque char­acteristic is arranged such that maximum is available when re­quired. Figure 13.22 shows a higher torque is available than in most other cases. The correction factor may be as low as 0.4 although 0.5 is a reasonable figure to use.

 Equ 13.13

 In all cases it is good practice to limit the value of t to about 18 seconds. The value of Pf to insert in the formula is that relating to the conditions of start up. It is important to note that these approximate formulae make the assumption that the fan absorbed power and the motor rat­ing are almost equal and certainly within 10% of each other. If a larger motor is installed then this will reduce the starting time. Strictly speaking a new correction factor should be assessed. However, an indication of the starting time, likely to result, may be obtained by the use of the graph in Figure 13.23. Simply by multiplying the time calculated by the use of equations 13.10 to 13.13 by the factor kT, the reduced time may be calculated.

 % Full-load speed Figure 13.22 Slip-ring motor characteristics, stator-rotor starting

 % Full-load speed Figure 13.23 Indication of reduction in starting time

 Correct voltage selection is also important, and care should be taken to ensure that the motor is rated at the line voltage. For example, a motor wound for 440 volts connected to a 380 ^38qA2 Volt supply will develop only I I x100, i. e. 75% of normal Torque, but more important, in star connection, the torque avail­able for starting the fan may be as low as 20% of the direct on-line value. Summary: From the above remarks it can be seen that a general formula may be derived to calculate the run-up time of any AC motor, i. e.:

 Equ 13.9

 .-.kT =0.61 •• Used =18×0.61 = 11 seconds

Note: kT has been calculated for a range of typical TEFV squirrel cage induction motors with direct-on-line 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 stator-rotor starters.

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