unit and formulas
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8/12/2019 Unit and Formulas
1/41.28
General information
Units of measurement and standard formulae
ELECTRICITY AND ELECTROMAGNETISM
Quantity UnitsUnits and expressionsnot recommended
Name French name Symbol Definition SINon SI,but accepted Conversion
Frequency Frquence f 1 Hz (hertz)Priode T
Electric current Courant lectrique(intensit de)
I A (ampere)
Electric potential Potentiel lectrique V V (volt)Voltage Tension U Electromotive force Force lectromotrice E Phase angle Dphasage " U = Um cos # t rad degree
i = im cos ( # t - " )Power factor Facteur de puissance cos " Reactance Ractance X Z = IZI j "
Resistance Rsistance R = R + j X $ (ohm)IZ I = % R2 + X2
Impedance Impdance Z 1 C #
Self inductance Inductance propre (self) L & H (henry)
Capacitance Capacit C Q F (farad)
Quantity of electricity Charge lectrique,Quantit d'lectricit
Q Q = '( dt C (coulomb) A.h1 A.h = 3600 C
Resistivity Rsistivit ) R.S $ .m $ /m
Conductance Conductance G 1 S (siemens) 1/ $ = 1S
No. of turns (coil) Nombre de tours (spires)de l'enroulement
N
No. of phases Nombre de phases m No. of pairs of poles Nombre de paires de ples p Magnetic field Champ magntique H A/m
Magnetic potential difference Diffrence de potentiel
magntique
Um A
Magnetomotive force Force magntomotrice F, Fm F = * H s d s Solnation, courant totalis H H = NI
Magnetic inductionMagnetic flux density
Induction magntique,Densit de flux magntique
B T (Tesla) = Wb/m 2 (gauss) 1 G = 10 -4 T
Magnetic flux Flux magntique,Flux d'induction magntique
& & = s Bn ds Wb (weber) (maxwell)1 max = 10 -8 Wb
Magnetic vector potential Potentiel vecteur magntique A Wb/mPermeability Permabilit d'un milieu = o r B = H H/mPermeability of vacuum Permabilit du vide o o = 4+10 -7 H/mPermittivity Permittivit , = , o , r 1 F/m
36 + 10 9
X = L# -
L =I
C =V
) =I
G =R
f =
, o = F/m
The unit AT (ampere-turns)is incorrect because it treats"turn" as a physical unit
j is defined as j 2 = -1# pulsation = 2 + . f
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8/12/2019 Unit and Formulas
2/41.29
General information
THERMODYNAMICS
Quantity UnitsUnits and expressionsnot recommended
Name French name Symbol Definition SINon SI,but accepted Conversion
Temperature Temprature T K (kelvin) temperatureThermodynamic Thermodynamique Celsius, . , C
T = . + 273.15
1.8
Temperature rise Ecart de temprature / T K C 1 C = 1 KHeat flux density Densit de flux thermique q, " & W/m 2
A
Thermal conductivity Conductivit thermique 0 W/m.KTotal heat transmission Coefficient de transmission K " = K (Tr 2 - Tr 1 ) W/m 2.Kcoefficient thermique global
Heat capacity Capacit thermique C dQ J/K dT
Specific heat capacity Capacit thermique c C massique m J/kg.K
Internal energy Energie interne U J
q =
C =
c =
NOISE AND VIBRATION
Quantity UnitsUnits and expressionsnot recommended
Name French name Symbol Definition SINon SI,but accepted Conversion
Sound power level Niveau de puissance Lw LW = 10 lg (P/P o ) dB lg logarithm to base 10acoustique (P o = 10
-12 W) (decibel) lg10 = 1Sound pressure level Niveau de pression Lp Lp = 20 lg (P/P o ) dB
acoustique (P o = 2 x10-5 Pa)
DIMENSIONS
Quantity UnitsUnits and expressionsnot recommended
Name French name Symbol Definition SINon SI,but accepted Conversion
Angle (plane angle) Angle (angle plan) ! , 1 , T , " degree : 180 : + radminute : 'second : "
2 3.14 rad
Length Longueur I cm, dm, dam, hmBreadth Largeur b working diag.: 1 inch = 1" = 25.4 mmHeight Hauteur h m (metre) milimetre (mm) 1 foot = 1' = 304.8 mmRadius Rayon r m
Longueur curviligne s micrometre micron angstrm : A = 0.10 nm
Area Aire, superficie A, S m2 1 square inch = 6.45 10 -4 m 2Volume Volume V m3 litre : l UK gallon = 4.546 10 -3 m 3
liter : L US gallon = 3.785 10 -3 m 3
C : Degree Celsius. C : temperature in C. F : temperature in F . F - 32. C =
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8/12/2019 Unit and Formulas
3/41.30
General information
Quantity Units Units and expressionsnot recommended
Name French name Symbol Definition , SINon SI,but accepted Conversion
Time Temps t minute : min Symbols ' and " are reservedIntervalle de temps, dure s (second) hour : h for angles.
Period (periodic time) Priode (dure d'un cycle) T day : d minute not written as mnAngular velocity Vitesse angulaire # d "
Circular frequency Pulsation dt Angular acceleration Acclration angulaire ! d #
dt
Speed Vitesse u, v, w, ds 1 km/h = dt 0.277778 m/s
Velocity Clrit c 1 m/min =
0.0166 m/sAcceleration Acclration a dv
(ou dclration) dt Acceleration Acclrationof free fall de la pesanteur g = 9.81 m/s 2 approxRevolution per minute Frquence de rotation n s -1 min -1 tr/mn, RPM, TMMass Masse m tonne : t kilo, kgs, KG
kg (kilogramme) 1 t = 1000 kg 1 pound : 1 lb = 0.4536 kgMass density Masse volumique ) d m
dV
Linear density Masse linique ) e d m d L
Surface mass Masse surfacique ) A d m d S
Momentum Quantit de mouvement P p = m.v kg.m/sMoment of inertia Moment d'inertie J, I I = 3 m.r 2 kg.m 2 MD2 kg.m 2
4
pound per square foot = 1 lb.ft 2
= 42.1 x 10 -3 kg.m 2
Force Force F N (newton) kgf = kgp = 9.81 NWeight Poids G G = m.g pound force = IbF = 4.448 NMoment of force, Moment d'une force M M = F.r N.m mdaN, mkg, N.mTorque T 1 mkg = 9.81 N.m
1 ft.lbF= 1.356 N.m1 in.lbF= 0.113 N.m
Pressure Pression p F F bar S A Pa (pascal) 1 bar = 10 5 Pa
Normal stress Contrainte normale 4 Pa kg/mm 2, 1 daN/mm 2 = 10 MPaShear stress Contrainte tangentielle, 5 Leroy-Somer use psi = pound per square inch
Cission the MPa = 10 6 Pa 1 psi = 6894 PaFriction coefficient Facteur de frottement incorrectly = friction
coefficient Work Travail W W = F.I 1 N.m = 1 W.s = 1 JEnergy Energie E Wh = 3600 J 1 kgm = 9,81 JPotential energy Energie potentielle Ep J (joule) (watt-hour) 1 cal = 4.18 J (calorie)Kinetic energy Energie cintique Ek 6 /2 J # 2 1 Btu = 1055 JQuantity of heat Quantit de chaleur Q (British thermal unit)Power Puissance P W 1 ch = 736 W
t 1 HP = 746 WVolumetric flow Dbit volumique q v dV m3 /s
dt Efficiency Rendement 7 < 1 %Dynamic viscosity Viscosit dynamique 7, Pa.s poise, 1 P = 0.1 Pa.sKinematic viscosity Viscosit cinmatique 8 7 stokes, 1 St = 10 -4 m 2 /s
)
# = rad/s
rad/s 2! =
m/s
v =
a = m/s 2
kg/m 3
kg/m
J =
kg/m 2
W (watt)P =
q v =
m2 /s8 =
1 kgf/cm 2 = 0.981 bar1 psi = 6894 N/m 2 = 6894 Pa1 psi = 0.06894 bar1 atm = 1.013 x 10 5 Pa
p = =
MECHANICS
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8/12/2019 Unit and Formulas
4/41.31
General information
Unit conversions
Symbol Definition Symbol Definition
FJ inertia factor M Max maximum permissible torque
N.m
FM operating factor expressed in % M S max maximum output selection torque
N.m
Frpermissible radial force
NM uS
torque required for the application during output N.m
h/d daily operating timein hours per day M nS rated output torque
i exact reduction of gearbox n min , n maxminimum output rotational speed of gearbox,maximum output rotational speed of gearbox
min -1
i u reduction available to the application n uE useful input rotational speed of gearbox,
min-1
J C/M moment of inertia of the load
applied to the motor shaftn uS
useful output rotational speed of gearboxmin -1
J M moment of inertia of the motor P standard motor power
kW
K overall duty factor P n rated powerkWK1 duty factor
dependent upon the inertiaP uE
input power required for the applicationkW
K2 duty factordependent upon the operating factor
P uS output power required for the application
kW
KPmaximum possible duty factor
for the geared motorP t
rated thermal power of gearboxkW
K.thermal power
correction factor s/h starts per hour
M torque transmitted by the geared motorN.m
. ambient temperatureC
Z (s/h) starting frequencyof the application (s/h)
Units MKSA (SI = International system) AGMA (US system)
Length 1 m = 3.2808 ft 1 mm = 0.03937 in 1 ft = 0.3048 m 1 in = 25.4 mm
Mass 1 kg = 2.2046 lb 1 lb = 0.4536 kg
Torque 1 N.m = 0.7376 lb.ft 1 N.m = 141.6 oz.in 1 lb.ft = 1.356 N.m 1 oz.in = 0.00706 N.m
Force 1 N = 0.2248 lb 1 lb = 4.448 N
Moment of inertia 1 kg.m 2 = 23.73 lb.ft 2 1 lb.ft 2 = 0.04214 kg.m 2
Power 1 kW = 1.341 HP 1 HP = 0.746 kW
Pressure 1 kPa = 0.14505 psi 1 psi = 6.894 kPa
Magnetic flux 1 T = 1 Wb / m 2 = 6.45210 4 line / in 2 1 line / in 2 = 1.55010 -5 Wb / m 2
Magnetic losses 1 W / kg = 0.4536 W / lb 1 W / lb = 2.204 W / kg
GLOSSARY
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