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


Formulas

HORSEPOWER CALCULATIONS:

HP  = TN
63000
Where:    

T    = Torque in (lb-in)

N    = Base Speed (RPM)

——————————————————————————————–

HP = TN
5250
Where:    

T = Torque in (lb-in)

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)

————————————————————————————————

FOR A GIVEN WEIGHT

WK² = W x D2
8
Where:    

WK2 = inertia (lb-ft2)

W = weight  (lbs)

D  = diameter (ft)

————————————————————————————————

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

——————————————————————————————–

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

——————————————————————————————–

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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