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 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" m-^ Conversion factors = 1000 = 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 rad r 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~^ revmin"^ = 1.6667x 10"^ rev s"^ = 6°s-i = 0.10472 rad s"^ Irevs-^ =360''s-^ = 6.2832 rad s-i 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 rad s-'^ rev s Conversion factors = 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 kg m '^ 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 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 hp Conversion factors = 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 NmA"^ Conversion factors = 141.612 oz in A"^ Derived motor constants - voltage Vr.p.m"^ SI units volts per revolutions per minute Conversion factors 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 ...282 Units and conversion factors Volume SI units cubic metre litre cubic millimetre m"' mm" m-^ Conversion factors = 1000 = 10^ mm^ = 6.1024 X 10^ in^ Linear velocity kms~^ m s~^ mms -1 SI units. .. kWh SI units joule kilowatt hour Conversion factors 1J = IWs = 2.7778 X 10-"^ kWh = 9.4781 ^ 10-^Btu kW h = 3.6 X 10^ J = 3.14121 X lO^Btu 284 Units and conversion factors Power W kW SI units. .. 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