Appendix 1: Units and conversion factors

Appendix 1: 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.

Length SI units

Conversion factors Kilometre Metre Millimetre Micrometre Nanometre

Km m mm mm nm

¼ 103 km ¼ 103 mm ¼ 106 mm ¼ 109 nm ¼ 25.4 mm ¼ 0.3048 m

lm

1 in 1 ft

Area SI units

Conversion factors

2

m mm2

¼ 106 mm2 ¼ 10.764 ft2

2

Square metre Square millimetre

1m

Volume SI units

Conversion factors

3

m L mm3

Cubic metre Litre Cubic millimetre

¼ 1000 L ¼ 109 mm3 ¼ 6.1024  104 in3

3

1m

Linear Velocity SI units 1

km s m s1 mm s1

Kilometres per second Metres per second Millimetres per second

Conversion factors 1

¼ 103 mm s1 ¼ 3.6 km h1

1ms

Linear Acceleration SI units ms

2

Metres per second squared

Conversion factors 2

1ms

¼ 39.370 in s2

291

292

Appendix 1: Units and conversion factors

Plane Angle Units

Conversion factors Radian Revolution Angular degree Angular minute Angular second

rad rev o

‘ ‘’

¼ 57.296o ¼ 1.7453  102 rad ¼ 2.7778  103 rev ¼ 6.2832 rad

1 rad 1o 1 rev

Angular Velocity Units 1

Conversion factors

Radians per second Revolutions per second Revolutions per minute Degree per minute

rad s rev s1 rev min1 o min1

rad s

1

¼ 0.15915 rev s1 ¼ 9.5493 rev min1 ¼ 1.6667  102 rev s1 ¼ 6o s1 ¼ 0.10472 rad s1 ¼ 360o s1 ¼ 6.2832 rad s1

1 rev min1 1 rev s1

Angular Acceleration Units 2

rad s rev s2

Conversion factors

Radians per second square Revolutions per second squared

1

1 rad s

1 rev s2

¼ 0.15915 rev s2 ¼ 9.5493 rev min1 s1 ¼ 6.2832 rad s2

Mass SI units g kg

Conversion factors Gram Kilogram

1 kg

¼ 103 g ¼ 2.2046 lb (mass)

Force SI units N

Conversion factors Newton

1N

¼ 0.22481 lbf ¼ 7.2330 poundals

Torque SI units Nm

Conversion factors Newton metre

1Nm

¼ 0.7376 lb ft ¼ 8.85075 lb in ¼ 141.612 oz in

Appendix 1: Units and conversion factors 293

Moment of Inertia SI units 2

kgm g m2

Conversion factors

Kilogram metre squared Gram centimetre squared

¼ 107 g cm2 ¼ 27.0616  103 kg m2

2

1 kg m 1 oz in s2

Energy SI units

Conversion factors

J kW h

Joule Kilowatt hour

¼ 1Ws ¼ 2.7778  107 kWh ¼ 9.4781  104 Btu ¼ 3.6  106 J ¼ 3.14121  103 Btu

1J 1 kW h

Power SI units

Conversion factors

W kW

Watt Kilowatt

¼ 1 J s1 ¼ 0.73756 lb ft s1 ¼ 735.5 W

1W 1 hp

Rotational Power Relevant equations

Units

Derived as the product of torque and the angular speed: Power (P) ¼ Torque (T)  Angular speed (n) ¼Tn W; ¼ 0.10472 T n W; ¼ 7.3948  104 T n W;

P P P

Nm; rad s1 Nm; rev min1 oz in; rev min1

Derived Motor Constant - Torque Unit 1

Nm A

Newton metres per amp

Conversion factors 1 NmA

1

¼ 141.612 oz in A1

Derived Motor Constants - Voltage Unit 1 1

V (rev min )

Volts per revolutions per minute

Conversion factors 1 V rev

1

¼ 9.55  103 V rad1s

min

Derived Motor Constant - Damping Unit 1

N m rad s

Newton meter per radian per second 1 N m rad

Conversion factors 1

s

¼ 0.105 Nm rev1 min