Wrap Angle for Big Pulley Calculator

✖Diameter of Big Pulley is the distance from side to side of the flat of the Big pulley.ⓘ Diameter of Big Pulley [D]			+10% -10%
✖Diameter of Small Pulley is the distance from side to side of the flat of the Small pulley.ⓘ Diameter of Small Pulley [d]			+10% -10%
✖Centre Distance between Pulleys is the distance between the centres of the big pulley and the small pulley.ⓘ Centre Distance between Pulleys [C]			+10% -10%

✖Wrap Angle on Big Pulley is the angle that the Belt wraps around the Big Pulley.ⓘ Wrap Angle for Big Pulley [α_b]

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Formula

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Wrap Angle for Big Pulley

Formula

`"α"_{"b"} = 3.14+(2*(asin(("D"-"d")/(2*"C"))))`

Example

`"199.339°"=3.14+(2*(asin(("810mm"-"270mm")/(2*"1600mm"))))`

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Wrap Angle for Big Pulley Solution

STEP 0: Pre-Calculation Summary

Formula Used

Wrap Angle on Big Pulley = 3.14+(2*(asin((Diameter of Big Pulley-Diameter of Small Pulley)/(2*Centre Distance between Pulleys))))
α_b = 3.14+(2*(asin((D-d)/(2*C))))
This formula uses 2 Functions, 4 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
asin - The inverse sine function, is a trigonometric function that takes a ratio of two sides of a right triangle and outputs the angle opposite the side with the given ratio., asin(Number)

Variables Used

Wrap Angle on Big Pulley - (Measured in Radian) - Wrap Angle on Big Pulley is the angle that the Belt wraps around the Big Pulley.
Diameter of Big Pulley - (Measured in Meter) - Diameter of Big Pulley is the distance from side to side of the flat of the Big pulley.
Diameter of Small Pulley - (Measured in Meter) - Diameter of Small Pulley is the distance from side to side of the flat of the Small pulley.
Centre Distance between Pulleys - (Measured in Meter) - Centre Distance between Pulleys is the distance between the centres of the big pulley and the small pulley.

STEP 1: Convert Input(s) to Base Unit

Diameter of Big Pulley: 810 Millimeter --> 0.81 Meter (Check conversion here)
Diameter of Small Pulley: 270 Millimeter --> 0.27 Meter (Check conversion here)
Centre Distance between Pulleys: 1600 Millimeter --> 1.6 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

α_b = 3.14+(2*(asin((D-d)/(2*C)))) --> 3.14+(2*(asin((0.81-0.27)/(2*1.6))))

Evaluating ... ...

α_b = 3.47912268773137

STEP 3: Convert Result to Output's Unit

3.47912268773137 Radian -->199.339046415256 Degree (Check conversion here)

FINAL ANSWER

199.339046415256 ≈ 199.339 Degree <-- Wrap Angle on Big Pulley

(Calculation completed in 00.004 seconds)

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Home » Engineering » Mechanical » Machine Design » Design of Belt Drives » Introduction of Belt Drives » Wrap Angle for Big Pulley

Credits

Created by Kethavath Srinath

Osmania University (OU), Hyderabad

Kethavath Srinath has created this Calculator and 1000+ more calculators!

Verified by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

Urvi Rathod has verified this Calculator and 1900+ more calculators!

< 15 Introduction of Belt Drives Calculators

Velocity of belt given tension of belt in tight side

Go Belt Velocity = sqrt((((e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))*Belt Tension on Loose Side)-Belt Tension on Tight Side)/(Mass of Meter Length of Belt*((e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))-1)))

Angle of Wrap given Belt Tension in Tight Side

Go Wrap Angle on Pulley = ln((Belt Tension on Tight Side-Mass of Meter Length of Belt*Belt Velocity^2)/(Belt Tension on Loose Side-(Mass of Meter Length of Belt*Belt Velocity^2)))/Coefficient of Friction for Belt Drive

Mass per unit length of belt

Go Mass of Meter Length of Belt = (Belt Tension on Tight Side-((e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))*Belt Tension on Loose Side))/((Belt Velocity^2)*(1-(e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))))

Coefficient of Friction in between Surfaces given Belt Tension in Tight Side

Go Coefficient of Friction for Belt Drive = ln((Belt Tension on Tight Side-Mass of Meter Length of Belt*Belt Velocity^2)/(Belt Tension on Loose Side-Mass of Meter Length of Belt*Belt Velocity^2))/Wrap Angle on Pulley

Belt Tension in Loose Side of Belt given Tension in Tight Side

Go Belt Tension on Loose Side = ((Belt Tension on Tight Side-(Mass of Meter Length of Belt*Belt Velocity^2))/(e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley)))+(Mass of Meter Length of Belt*Belt Velocity^2)

Belt tension in tight side

Go Belt Tension on Tight Side = ((e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))*(Belt Tension on Loose Side-(Mass of Meter Length of Belt*Belt Velocity^2)))+(Mass of Meter Length of Belt*Belt Velocity^2)

Length of Belt

Go Belt Length = (2*Centre Distance between Pulleys)+(pi*(Diameter of Big Pulley+Diameter of Small Pulley)/2)+(((Diameter of Big Pulley-Diameter of Small Pulley)^2)/(4*Centre Distance between Pulleys))

Wrap Angle for Small Pulley

Go Wrap Angle on Small Pulley = 3.14-(2*(asin((Diameter of Big Pulley-Diameter of Small Pulley)/(2*Centre Distance between Pulleys))))

Center Distance from Small Pulley to Big Pulley given Wrap Angle of Small Pulley

Go Centre Distance between Pulleys = (Diameter of Big Pulley-Diameter of Small Pulley)/(2*sin((3.14-Wrap Angle on Small Pulley)/2))

Wrap Angle for Big Pulley

Go Wrap Angle on Big Pulley = 3.14+(2*(asin((Diameter of Big Pulley-Diameter of Small Pulley)/(2*Centre Distance between Pulleys))))

Center Distance from Small Pulley to Big Pulley given Wrap Angle of Big Pulley

Go Centre Distance between Pulleys = (Diameter of Big Pulley-Diameter of Small Pulley)/(2*sin((Wrap Angle on Big Pulley-3.14)/2))

Diameter of Small Pulley given Wrap Angle of Small Pulley

Go Diameter of Small Pulley = Diameter of Big Pulley-(2*Centre Distance between Pulleys*sin((3.14-Wrap Angle on Small Pulley)/2))

Diameter of Big Pulley given Wrap Angle of Small Pulley

Go Diameter of Big Pulley = Diameter of Small Pulley+(2*Centre Distance between Pulleys*sin((3.14-Wrap Angle on Small Pulley)/2))

Diameter of Small Pulley given Wrap Angle of Big Pulley

Go Diameter of Small Pulley = Diameter of Big Pulley-(2*Centre Distance between Pulleys*sin((Wrap Angle on Big Pulley-3.14)/2))

Diameter of Big Pulley given Wrap Angle for Big Pulley

Go Diameter of Big Pulley = Diameter of Small Pulley+(2*Centre Distance between Pulleys*sin((Wrap Angle on Big Pulley-3.14)/2))

Wrap Angle for Big Pulley Formula

Wrap Angle on Big Pulley = 3.14+(2*(asin((Diameter of Big Pulley-Diameter of Small Pulley)/(2*Centre Distance between Pulleys))))
α_b = 3.14+(2*(asin((D-d)/(2*C))))

Define a Wrap Angle?

The wrap angle is defined as the angle between the run-up and run-off of the belt on the pulley. In addition, the greater curvature causes greater bending stresses in the belt, which also limits the transmittable belt force. So-called idler pulleys can be used to increase the wrap angle.

How to Calculate Wrap Angle for Big Pulley?

Wrap Angle for Big Pulley calculator uses Wrap Angle on Big Pulley = 3.14+(2*(asin((Diameter of Big Pulley-Diameter of Small Pulley)/(2*Centre Distance between Pulleys)))) to calculate the Wrap Angle on Big Pulley, The Wrap Angle for Big Pulley formula is defined as the angle between the run-up and run-off of the belt on the pulley. Wrap Angle on Big Pulley is denoted by α_b symbol.

How to calculate Wrap Angle for Big Pulley using this online calculator? To use this online calculator for Wrap Angle for Big Pulley, enter Diameter of Big Pulley (D), Diameter of Small Pulley (d) & Centre Distance between Pulleys (C) and hit the calculate button. Here is how the Wrap Angle for Big Pulley calculation can be explained with given input values -> 11421.29 = 3.14+(2*(asin((0.81-0.27)/(2*1.6)))).

FAQ

What is Wrap Angle for Big Pulley?

The Wrap Angle for Big Pulley formula is defined as the angle between the run-up and run-off of the belt on the pulley and is represented as α_b = 3.14+(2*(asin((D-d)/(2*C)))) or Wrap Angle on Big Pulley = 3.14+(2*(asin((Diameter of Big Pulley-Diameter of Small Pulley)/(2*Centre Distance between Pulleys)))). Diameter of Big Pulley is the distance from side to side of the flat of the Big pulley, Diameter of Small Pulley is the distance from side to side of the flat of the Small pulley & Centre Distance between Pulleys is the distance between the centres of the big pulley and the small pulley.

How to calculate Wrap Angle for Big Pulley?

The Wrap Angle for Big Pulley formula is defined as the angle between the run-up and run-off of the belt on the pulley is calculated using Wrap Angle on Big Pulley = 3.14+(2*(asin((Diameter of Big Pulley-Diameter of Small Pulley)/(2*Centre Distance between Pulleys)))). To calculate Wrap Angle for Big Pulley, you need Diameter of Big Pulley (D), Diameter of Small Pulley (d) & Centre Distance between Pulleys (C). With our tool, you need to enter the respective value for Diameter of Big Pulley, Diameter of Small Pulley & Centre Distance between Pulleys and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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