Control Systems 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) |
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) |
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DENSITY VALUES FOR COMMON MATERIALS |
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| MATERIAL | DENSITY lbs/in3 (p) |
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Aluminum |
0.0924 |
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Bronze |
0.3200 |
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Cast Iron |
0.2600 |
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Nylon |
0.0510 |
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Paper |
0.0250 to 0.0420 |
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Steel |
0.2820 |
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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 Index • Next “Transients and Electrical Noise in Drive Applications”
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