unit and formulas

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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2/41.29

General information

THERMODYNAMICS



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



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



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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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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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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