Units and conversion factors

Units and conversion factors
The tables below give the definitions and conversion factors for quantities which
are widely found in the design of motion control systems. Unless otherwise specified, ounces (oz) and pounds (lb) are considered to be units offeree.
Length

km
m
mm
/xm
nm

SI units
kilometre
metre
millimetre
micrometre
namometre

Im

1 in
1ft
Imil

Conversion factors
= 10"^ km
=10^ mm
=10^/xm
=10^ nm
= 25.4 mm
= 0.3048 m

= 10"^ in
= 25.4 /xm

Area

m^
mm^

SI units
square metre
square millimetre

Im^

281

Conversion factors
^
= 10^ mm^
= 10.764 ft^


282

Units and conversion factors

Volume
SI units
cubic metre
litre

cubic millimetre

m"'
mm"

1 m-^

Conversion factors
= 1000 1
= 10^ mm^
= 6.1024 X 10^ in^

Linear velocity

kms~^
m s~^
mms -1

SI units
kilometres per second
metres per second
millimetres per second

1ms

Conversion factors
= 10^ mm s ^
= 3.6kmh-i
= 39.370 in s-i

Linear acceleration
SI units
metres per second
squared

ms

=T

1ms

Conversion factors
= 39.370 in s"^

Plane angle
SI units
radian
revolution
angular degree
angular minute
angular second

rad
rev

1 rad
r

1 rev

Conversion factors
= 57.296°
=1.7453 X 10-2 rad
= 2.7778 X 10-^ rev
= 6.2832 rad

Angular velocity

rads"^
rev s"^
rev min"
mm

-1

SI units
radians per second
revolutions per second
revolutions per minute
degree per minute

Conversion factors
=0.15915 rev s-^
= 9.5493 rev min~^
1 revmin"^ = 1.6667x 10"^ rev s"^
= 6°s-i
= 0.10472 rad s"^
Irevs-^
=360''s-^
= 6.2832 rad s-i

1 rad s-i


283

Units and conversion factors
Angular acceleration

rad s '^
rev s~^
°s-i

SI units
radians per sec per sec
revolutions per sec per sec
degrees per sec per sec

1 rad s-'^
1 rev s

Conversion factors
= 0 . 15915 rev s""^
= 9.5493 rev niin
= 360° s-2
= 6.2832 rad s-^

Mass

g

kg

SI units
gram
kilogram

1kg

Conversion factors
= 10^g
= 2.2046 lb (mass)

SI units
newton
kilogram force

IN

Conversion factors
= 0.22481 Ibf
= 7.2330 poundals

Force

N
kgf
Torque

Nm

SI units
newton metre

INm

Conversion factors
= 0.7376 lb ft
= 8.85075 lb in
= 141.612 oz in

Moment of inertia

kgm'-^
gm^

SI units
kilogram metre squared
gram centimetre squared

1 kg m '^
1 oz in s2

Conversion factors
= 10^ gem '^
= 7.0616x10^ kg m^

Energy

J
kWh

SI units
joule
kilowatt hour

Conversion factors
1J
= IWs
= 2.7778 X 10-"^ kWh
= 9.4781 ^ 10-^Btu
1 kW h
= 3.6 X 10^ J
= 3.14121 X lO^Btu


284

Units and conversion factors

Power

W
kW

SI units
watt
kilowatt

1W
1 hp

Conversion factors
= 1 Js"n.
= 0.73756 lb ft s"^
= 735.5 W

Rotational power
Derived as the product of torque and the angular speed:
power (P) = torque (T) x angular speed (n)
P = Tn
P = 0.10472 Tn
P = 7.3948 X 10-^

W; Nm; rad s-^
W; Nm; rev min~^
W; oz in; revmin"^

Tn

Derived motor constant - torque

NmA-=ir

SI units
newton metres per amp

1 NmA"^

Conversion factors
= 141.612 oz in A"^

Derived motor constants - voltage

Vr.p.m"^

SI units
volts per revolutions per
minute

Conversion factors
1 Vr.p.m.~^= 9.55x10"^ V rad~^s~^

Derived motor constants - damping

N m r a d ^s

SI units
Newton metres per radian
per second

Conversion factors
I N m r a d ^= 104.72 Nm krpm-^-1