Formulas Motor Ac

Appendix B: Formulas and Conversions

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Appendix B: Formulas and Conversions

General Information
The following information is a summary of typical formulas and conversion factors used in the rotating machinery industry. This information can be used as a basis for sizing drives and evaluating application types and factors. However, these formulas are to be used for estimating purposesonly. They do not include allowance for machine friction, windage, or other machine factors. When sizing a drive, always consider all machine factors (i.e. electrical, mechanical, and environmental) and motor factors (e.g., full load amperes and speed range).

Horsepower Formulas
General Formula Torque × Speed HP = ---------------------------------------5252 where: Torque = lb-ft Speed = rpm5252 = a proportional constant Conveyors Force × Velocity HP ( Vertical ) = ------------------------------------------33,000

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where: Force = force or weight (lb) Velocity = fpm Force × Velocity × Coef of Friction HP ( Horizontal ) = --------------------------------------------------------------------------------------------33,000 where: Force = force or weight (lb)Velocity = fpm Fans and Blowers CFM × Pressure BHP = ------------------------------------------------33,000 × Eff of Fan where: BHP = CFM = cubic feet per minute EffofFan = efficiency of fan (%/100) Pressure = lb/ft2 CFM × Pressure BHP = -----------------------------------------229 × Eff of Fan where: BHP = CFM = cubic feet per minute EffofFan = efficiency of fan (%/100) Pressure = lb/in2 CFM × PSI HP= --------------------------------------------6356 × Eff of Fan where: CFM = cubic feet per minute EffofFan = efficiency of fan (%/100) PSI = pressure in inches of water Pumps GPM × Head × Specific Gravity BHP = ----------------------------------------------------------------------------------3960 × Eff of Pump where: BHP =

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GPM = gallons perminute Head = measurement of pressure in ft EffofPump = efficiency of pump (%/100) SpecificGravity = 1.0 (water) Efficiency of pump (positive displacement) may vary between 50 and 80% depending on size Efficiency of pump (centrifugal) = 500 to 100 GPM = 70 to 75% 1000 to 1500 GPM = 75 to 80% Over 1500 GPM = 80 to 85% GPM × PSI × Specific Gravity BHP =------------------------------------------------------------------------------1713 × Eff of Pump Affinity laws for centrifugal applications:
Flow 1 RPM 1 ---------------- = --------------Flow RPM 2 2 Pres ( RPM ) 2 1 1 -------------- = ----------------------Pres 2 ( RPM 2 ) 2 BHP ( RPM ) 2 1 1 --------------- = ----------------------BHP 2 ( RPM 2 ) 2

Torque Formulas
General Formulas HP × 5252 T = ------------------------Speed where: T =torque in lb-ft HP = horsepower Speed = speed in rpm Torque = Force × Radius where: Torque = torque in lb-ft Force = force in lb Radius = radius in ft WK × ∆RPM Torque = ----------------------------------308 × t

2

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where: Torque = torque in lb-ft WK2 = inertia reflected to the motor shaft (lb-ft2) ∆rpm = change in speed (rpm) t = time to accelerate (seconds)

ACMotor Formulas
120 × Frequency Speed = -------------------------------------------Number of Poles where: Speed = synchronous speed in rpm Frequency = applied frequency in Hz NumberofPoles = number of poles per phase ( Sync Speed – FL Speed ) × 100 Slip = ---------------------------------------------------------------------------------Sync Speed where: Slip = slip in % SyncSpeed = synchronous speedin rpm FLSpeed = full load speed in rpm

Electrical Formulas
Power (DC Circuits) I×E HP = ----------746 where: I = intensity of current (amperes) E = EMF or voltage (volts) Power (AC Circuits) I×E kVA = ----------1000 where: kVA = kilovolt amperes (1 phase) I = intensity of current (amperes) E = EMF or voltage (volts)

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I × E × 1.73 kVA =...