## Control Systems Application Guide

Complete Application Guide

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# Gear Torque Formulas

HORSEPOWER CALCULATIONS:

 HP  = TN 63000 Where: T    = Torque in (lb-in) N    = Base Speed (RPM)

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 HP = TN 5250 Where: T = Torque in (lb-ft) N = Base Speed (RPM)

HP CALCULATIONS for CENTER DRIVEN WINDERS:

 HP = TV x     B/U 33000 Where: T = Web Tension  (lbs) V = Line Speed (ft/min) B/U = Build Up Ratio = full roll diameter core diameter

ACCELERATION TORQUE CALCULATION:

When a machine must be accelerated to a given speed in a certain amount of time, the drive system HP may have to supply additional torque during acceleration to compensate for the load inertia.  The acceleration torque must be added to the normal torque requirements of the machine.

 T = WK2 x ΔN 380t Where: T  = acceleration Torque (lb-ft) ΔN = change in speed (rpm) t  = acceleration time (seconds) WK²  = total system inertia (lb-ft2) includes motor, reducer & load

INERTIA:

Inertia is a measure of a body’s resistance to changes in velocity.  The factor WK2 (inertia) is the weight of a rotating object multiplied by the square of the radius of gyration K.

FOR A SOLID CYLINDER

 T = ρ x L x D4 1467 Where: WK2 = inertia (lb-ft2) ρ = density (lb-in³) L = length (in) D = diameter (in)

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FOR A GIVEN WEIGHT

 WK² = W x D2 8 Where: WK2 = inertia (lb-ft2) W = weight  (lbs) D  = diameter (ft)

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FOR A HOLLOW CYLINDER

 WK2 or WR2 = W x (R22 – R12 ) 2 Where: WK2 = inertia (lb-ft2) W   = weight (lbs) R2   = outer radius (ft) R1   = inner radius (ft)

 DENSITY VALUES FOR COMMON MATERIALS MATERIAL DENSITY lbs/in3 (p) Aluminum 0.0924 Bronze 0.3200 Cast Iron 0.2600 Nylon 0.0510 Paper 0.0250 to 0.0420 Steel 0.2820 Rubber 0.0341

GEAR REDUCERS:

 OUTPUT SPEED (RPM)  = INPUT SPEED (RPM) GEAR RATIO

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OUTPUT TORQUE (LB-FT) = INPUT TORQUE (LB-FT) x EFFICIENCY x GEAR RATIO

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 INERTIA REFLECTED TO MOTOR SHAFT = TOTAL LOAD INERTIA (GEAR RATIO)2

Previous “Line Reactors and Drive Isolation Transformers”Back To IndexNext “Transients and Electrical Noise in Drive Applications”

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