Electrical Machines - Questions and Answers
 Information courtesy of ALSTOM.

CONVERSION FACTORS

Multiply By To obtain Length
Centimetres  x 0.3937  = Inches
Fathoms  x 6.0  = Feet
Feet  x 12.0  = Inches
Feet  x 0.3048  = Metres
Inches  x 2.54  = Centimetres
Kilometres  x 0.6214  = Miles
Metres  x 3.281  = Feet
Metres  x 39.37  = Inches
Metres  x 1.094  = Yards
Miles  x 5280.0  = Feet
Miles  x 1.609  = Kilometres
Rods  x 5.5  = Yards
Yards  x 0.9144  = Metres

Area

Acres  x 43560.0  = Square feet
Acres  x 4840.0  = Square yards
Circular Mils  x 7.854 x 107  = Square inches
Circular Mils  x 7.854  = Square mils
Square Centimeters  x 0.155  = Square inches
Square Feet  x 144.0  = Square inches
Square Feet  x 0.0929  = Square meters
Square Inches  x 6.452  = Square centimeters
Square Metres  x 1.196  = Square yards
Square Miles  x 640.0  = Acres
Square Mils  x 1.273  = Circular mils
Square Yards  x 0.8361  = Square meters

Volume

Cubic Feet  x 0.0283  = Cubic Metres
Cubic Feet  x 7.481  = Gallons
Cubic Inches  x 0.5541  = Ounces (fluid)
Cubic Metres  x 35.31  = Cubic Feet
Cubic Metres  x 1.308  = Cubic Yards
Cubic Yards  x 0.7646  = Cubic Metres
Gallons  x 0.1337  = Cubic Feet
Gallons  x 3.785  = Litres
Litres   x 0.2642  = Gallons
Litres  x 1.057  = Quarts (liquid)
Ounces (Fluid)  x 1.805  = Cubic Inches
Quarts (liquid)  x 0.9463  = Litres

Mass

Multiply By To obtain Length Weight
Grams  x 0.0353  = Ounces
Kilograms  x 2.205  = Pounds
Newtons  x 0.2248  = Pounds (force)
Ounces  x 28.35  = Grams
Pounds  x 453.6  = Grams
Pounds (force)  x 4.448  = Newtons
Tons (short)  x 907.2  = Kilograms
Tons (short)  x 2000.0  = Pounds

Torque

Gram-centimetres  x 0.0139  = Ounce-inches
Newton-metres  x 0.7376  = Pound-feet
Newton-metres  x 8.851  = Pound-inches
Ounce-inches  x 72.0  = Gram-centimetres
Pound-feet  x 1.3558  = Newton-metres
Pound-inches  x 0.113  = Newton-metres

Energy or Work

Btu  x 778.2  = Foot-pounds
Btu  x 252.0  = Gram-calories

Power

Btu per hour  x 0.293  = Watts
Horsepower  x 33000.0  = Foot-pounds
Horsepower  x 550.0  = Foot-pounds
Horsepower  x 746.0  = Watts
Kilowatts  x 1.341  = Horsepower

Plane Angle

Degrees  x 0.0175  = Radians
Minutes  x 0.01667  = Degrees
Minutes  x 2.9 x 104  = Radius
Quadrants  x 90.0  = Degrees
Quadrants  x 1.5708  = Radians
Radians  x 57.3  = Degrees
Pounds are U.S. avoirdupois
Gallons and quarts are U.S.

SYMBOLS

Metric

D = Displacement: metres peak-to-peak
V = Velocity: meters/second peak
A = Acceleration: G's peak
1G = Force of gravity = 9.806 65 m/sec2
Hz = Hertz: cycles/second

Formulas

D = 0.318 V/Hz
D = 19.607 A/(Hz)2
V = 3.1416 (Hz) (D)
V = 61.440 A/Hz
A = 0.051 (Hz)2 (D)
A = 0.016 (V) (Hz)

USEFUL 3-PHASE FORMULAE

kW = kVA x power factor
kW =       HP x 746      
1000 x efficiency
kW = line amps x line volts x 1,732 x PF x efficiency
1000

 

kVA = kW
PF
kVA =          HP x 746         
1000 x efficiency x PF
kVA = line amps x line volts x 1.732
1000

 

Line amps =             kW x 1000            
line volts x 1.732 x PF x eff.
Line amps =              HP x 746             
line volts x 1.732 x eff. x PF

 

HP = kW x 1000 x efficiency
746
HP = kVA x 1000 x efficiency x PF
746
HP = line amps x line volts x 1,732 x eff. x PF
746

VIBRATION LIMITS

All motors comply with the requirements of SABS 948 (revised), which states that:

When a completely assembled motor (mounted horizontally) is run on no-load at rated voltage and speed, the amplitude of vibration on the bearings, on a horizontal plane through the shaft centre line, shall not exceed the maximum value tabulated below:

Speed
r/min		 Amplitude
(peak to peak)
mm max.		 Speed
r/min		 Amplitude
(peak to peak)
mm max.
3000 24 1000 55
2800 25 900 59
2600 27 850 61
2400 29 800 63
2200 31 750 65
1500 41 700 68
1400 43 650 71
1300 45 600 74
1200 48    

VIBRATION IDENTIFICATION GUIDE FOR ASSEMBLED UNIT

Case Frequency Relative to Machine RPM Phase-Strobe Picture Amplitude Notes
Unbalance 1 x rpm Single steady reference mark Radial - steady proportional to unbalance Common cause of vibration
Defective anti-friction bearing 10 to 100 x rpm Unstable Measure velocity 0.2 to 1.0 in/sec radial

Velocity largest at defective bearing. As failure approaches velocity signal increases, frequency decreases.
Sleeve bearing 1 x rpm Single reference mark Not large

Shaft and bearing mark amplitudes about the same.
Misalignment coupling or bearing 2 x rpm. Sometimes 1 or 3 rpm Usually 2 steady reference marks Sometimes 1 or 3. High axial

Axial vibration can be twice race. Use dial indicator as check.
Bent shaft 1 or 2 x rpm 1 or 2 High axial  
Defective gears High rpm x gear teeth   Radial

Use velocity measurement.
Mechanical looseness 1 or 2 x rpm 1 or 2 Proportional to looseness

Radial vibration largest in direction of looseness
Defective belt Belt rpm x 1 or 2   Erratic

Strobe light will freeze belt.
Electrical Power line frequency x 1 or 2 (3600 or 7200 rpm) 1 or 2 rotating marks Usually low

Vibration stops instantly when power is turned off.
Oil whip Less than rpm Unstable Radial - unsteady

Frequency may be as low as half rpm.
Aerodynamic 1 x rpm or number of blades on fan x rpm    

May cause trouble in case of resonance.
Beat frequency 1 x rpm Rotates at beat rate Variable at beat rate

Caused by two machines running at close rpm.
Resonance Specific criticals Single reference mark High

Phase changes with reference mark speed. Amplitude decreases above and below resonant speed. Resonance can be removed from operative range by stiffening.

GREASE RELIEF SYSTEMS

Frames D315L and all 355 frames incorporate full grease relief systems as a standard feature. A similar grease relief system can be incorporated in the foot mounted versions of framesD250-31 5M as an optional extra.

SILENCERS

The sound pressure levels reflected on pages 91 and 92 are typical for the GEC range of motors, using standard external fan and cowl arrangement. As an optional extra, a special fan and/or silencer unit can be supplied which will reduce the sound pressure level on any motor in the 80.355 range to 85 dba measured at 1 m reference radius.

Gieck Conversion Factors

Decimal multiples and fractions of units

da = deca = 10
h = hecto = 10
k = kilo = 10
M = mega = 106
G = giga = 109
T = tera = 1012
P = peta = 1015
E = exa = 1018
d = deci = 10-1
c = centi = 10-2
m = milli = 10-3
= micro = 10-6
n = nano = 10-9
p = pico = 10-12
f = femto = 10-15
a = atto = 10-18

Units of Length

  m m mm cm dm km
1 m = 1 106 10 10 10 10-3
1 m = 10-6 1 10-3 10-4 10-5 10-9
1 mm = 10-3 10 1 10-1 10-2 10-6
1 cm = 10-2 104 10 1 10-1 10-5
1 dm = 10-1 105 10 10 1 10-4
1 km = 103 109 106 105 104 1

Units of Length

  mm m nm
( o
A		 )1)
pm
(    o
mA		 )2)
1 mm = 1 10 106 107 109 1010
1 m = 10-3 1 10 104 106 107
1 nm = 10-6 10-3 1 10 10 104
(    o
1 A		 ) =
10-7 10-4 10-1 1 10 10
1 pm = 10-9 10-6 10-3 10-2 1 10
(       o
1 mA		 ) =
10-10 10-7 10-4 10-3 10-1 1
1)

o
A
=		 o
Angstrm
2)       o
1 mA
= 1 XE = 1 X-unit

Units of area

  m m mm cm dm km
1 m = 1 1012 106 104 10 10-6
1 m = 10-12 1 10-6 10-8 10-10 10-18
1 mm = 10-6 106 1 10-2 10-4 10-12
1 cm = 10-4 108 10 1 10-2 10-10
1 dm = 10-2 1010 104 10 1 10-8
1 km = 106 1018 1012 1010 108 1

Units of Volume

  m mm cm dm 1) km
1 m = 1 109 106 103 10-9
1 mm = 10-9 1 10-3 10-6 10-18
1 cm = 10-6 103 1 10-3 10-15
1 dm = 10-3 106 103 1 10-12
1 km = 109 1018 1015 1012 1

Units of mass

  kg kg g dt t=Mg
kg = 1 106 10 10-2 10-3
mg = 10-6 1 10-3 10-8 10-9
g = 10-3 10 1 10-5 10-6
dt = 10 108 105 1 10-1
1t = 1 Mg = 10 109 106 10 1

Units of time

  s ns s ms min
1 s = 1 109 106 10 16.66x10-3
1 ns = 10-9 1 10-3 10-6 16.66x10-12
1 s = 10-6 10 1 10-3 16.66x10-9
1 ms = 10-3 106 10 1 16.66x10-6
1 min = 60 60x109 60x106 60x10 1
1 h = 3600 3.6x1012 3.6x109 3.6x106 60
1 d = 86.4x10 86.4x1012 86.4x109 86.4x106 1440

Units of force (gravitational force also)

  N2) kN MN (kgf) (dyn)
1 N = 1 10-3 10-6 0.102 105
1 kN = 10 1 10-3 0.102x10 108
1 MN = 106 10 1 0.102x106 1011

1) 1 dm = 1 l = 1 liter
2) 1 N = 1 kg m/s = 1 Newton

Units of pressure

  Pa N/mm bar (kgf/cm) (torr)
1 Pa = N/m = 1 10-6 10-5 1.02x10-5 0.0075
1 N/mm = 106 1 10 10.2 7.5x10
1 bar = 105 0.1 1 1.02 750
(1 kgf/cm = 1 at) = 98 100 9.81x10-2 0.981 1 736
(1 torr) 1) = 133 0.133x10-3 1.33x10-3 1.36x10-3 1

Units of work

  J kW h (kgf m) (kcal) (hp h)
1 J2) = 1 0.278x10-6 0.102 0.239x10-3 0.378x10-6
1 kW h = 3.60x106 1 367x10 860 1.36
(1 kgf m) = 9.81 2.72x10-6 1 2.345x10-3 3.70x10-6
(a kcal) = 4186.8 1.16x10-3 426.9 1 1.58x10-3
(1 hp h) = 2.65x106 0.736 0.27x106 632 1

Units of Power

  W kW (kgf m/s) (kcal/h) (hp)
1 W3) = 1 10-3 0.102 0.860 1.36x10-3
1 kW = 1000 1 102 860 1.36
(1 kgf m/s) = 9.81 9.81x10-3 1 8.43 13.3x10-3
(1 kcal h) = 1.16 1.16x10-3 0.119 1 1.58x10-3
(1 hp) = 736 0.736 75 632 1

Unit of mass for jewels

1 carat = 200 mg = 0.2 x 10-3kg = 1/5000 kg

Unit of fineness for precious metals

24 carat ∆ 1000.00  18 carat ∆ 750.00 
14 carat ∆ 583.33 8 carat ∆ 333.33

Units of temperature

T = (  t  + 273.15) K = 5 .   TR   K
C 9 Rank
TR = ( tF + 459.67) Rank = 9 . T Rank
F 5 K
t = 5 ( tf - 32)C = ( T - 273.15)C
9 F K
tF = ( 9 .  t  + 32)F = (   TR   - 459.67)F
5 C Rank

T, TR, t and tF are the temperatures in the scales for Kelvin, Rankine, Celsius, Fahrenheit.

1) 1 torr = 1/760 atm = 1.333 22 mbar = 1 mm Hg at t = 0C
2) 1 J = N m = 1 W s
3) 1 W = 1 J/s = 1 N m/s

Conversion
Anglo-American to metric units

Units of length

  in ft yd mm m km
1 in = 1 0.08333 0.02778 25.4 0.0254 -
1 ft = 12 1 0.3333 304.8 0.3048 -
1 yd = 36 3 1 914.4 0.9144 -
1 mm = 0.03937 3281x10-6 1094x10-6 1 0.001 10-6
1 m = 39.37 3.281 1.094 1000 1 0.001
1 km = 39370 3281 1094 106 1000 1

Units of area

  sq in sq ft sq yd cm dm m
1 sq in = 1 6.944x10-3 0.772x10-3 6.452 0.06452 64.5x10-5
1 sq ft = 144 1 0.1111 929 9.29 0.0929
1 sq yd = 1296 9 1 8361 83.61 0.8361
1 cm = 0.155 1.076x10-3 1.197x10-4 1 0.01 0.0001
1 dm = 15.5 0.1076 0.01196 100 1 0.001
1 m = 1550 10.76 1.196 10000 100 1

Units of volume

  cu in cu ft cu yd cm dm m
1 cu in = 1 5.786x10-4 2.144x10-5 16.39 0.01639 1.64x10-5
1 cu ft = 1728 1 0.037 28316 28.32 0.0283
1 cu yd = 46656 27 1 764555 764.55 0.7646
1 cm = 0.06102 3532x10-8 1.31x10-6 1 0.001 10-6
1 dm = 61.02 0.03532 0.00131 1000 1 0.001
1 m = 61023 35.32 1.307 106 1000 1

Units of mass

  dram oz lb g kg Mg
1 dram = 1 0.0625 0.003906 1.772 0.00177 1.77x10-6
1 oz = 16 1 0.0625 28.35 0.02832 28.3x10-6
1 lb = 256 16 1 453.6 0.4531 4.53x10-4
1 g = 0.5643 0.03527 0.002205 1 0.001 10-6
1 kg = 564.3 35.27 2.205 1000 1 0.001
1 Mg = 564.3x10 35270 2205 106 1000 1

Units of work

  ft lb kgf m J = W s kW h kcal Btu
1 ft lb = 1 0.1383 1.356 376.8x10-9 324x10-6 1.286x10-3
1 kgf m = 7.233 1 9.807 2.725x10-6 2.344x10-3 9.301x10-3
1 J = 1 Ws = 0.7376 0.102 1 277.8x10-9 239x10-6 948.4x10-6
1 kW h = 2.655x106 367.1x10 3.6x106 1 860 3413
1 kcal = 3.087x10 426.9 4187 1.163x10-5 1 3.968
1 Btu = 778.6 107.6 1055 293x10-6 0.252 1

Units of power

  hp kgf m/s J/s=W kW kcal/s Btu/s
1 hp = 1 76.04 745.7 0.7457 0.1782 0.7073
1 kgf m/s = 13.15x10-3 1 9.807 9.807x10-3 2.344x10-3 9.296x10-3
1 J/s = 1W = 1.341x10-3 0.102 1 10-3 239x10-6 948.4x10-6
1 kW = 1.341 102 1000 1 0.239 0.9484
1 kcal/s = 5.614 426.9 4187 4.187 1 3.968
1 Btu/s = 1.415 107.6 1055 1.055 0.252 1

Other units

1 mil = 10-3 in = 0.0254 mm
1 sq mil = 10-6 sq in = 645.2 m
1 yard = 3 ft = 0.914 m
1 English mile = 1760 yds = 1609 m
1 Nautical mile = 1852 m
1 Geographical mile = 7420 m
1 long ton = 2240 lb = 1.016 Mg
1 short ton (US) = 2000 lb = 0.9072 Mg
1 long ton = 2240 lbf = 9.96 MN
1 short ton (US) = 2000 lbf = 9.00 MN
1 Imp. gallon (Imperial gallon) = 4.546 dm
1 US gallon = 3.785 dm
1 BTU/ft = 9.547 kcal/m = 39.964 kJ/m
1 BTU/lb = 0.556 kcal/kg = 2.327 kJ/kg
1 lbf/ft = 4.882 kgf/m = 47.8924 N/m
1 lbf/in (p.s.i.) = 0.0703 kgf/cm = 0.6896 N/cm
1 chain = 22 yds = 20.11 m
1 Hundredweight (GB) (cwt) = 112 lbf = 498 kN
1 Quarter (GB) = 28 lbf = 124.5 kN
1 Stone (GB) = 14 lbf = 62.3 kN