Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt Calculator

✖V Belt Angle is defined as the angle included between the side faces of the V cross-section belt.ⓘ V belt angle [θ]			+10% -10%
✖Belt Tension on Tight Side is defined as the belt's tension on the belt's tight side.ⓘ Belt Tension on Tight Side [P₁]			+10% -10%
✖Mass of Meter Length of V Belt is the mass of 1-meter length of the belt simply mass per unit length of the belt.ⓘ Mass of Meter Length of V Belt [m_v]			+10% -10%
✖Belt Velocity is defined as the velocity of the belt used in a belt drive.ⓘ Belt Velocity [v_b]			+10% -10%
✖Belt Tension on Loose Side is defined as the belt's tension on the belt's loose side.ⓘ Belt Tension on Loose Side [P₂]			+10% -10%
✖Coefficient of Friction for Belt Drive is the ratio defining the force that resists the motion of the belt over the pulley.ⓘ Coefficient of Friction for Belt Drive [μ]			+10% -10%

✖Wrap Angle on Pulley is the angle between the run-up and run-off of the belt on the pulley.ⓘ Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt [α]

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Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt Solution

STEP 0: Pre-Calculation Summary

Formula Used

Wrap Angle on Pulley = sin(V belt angle/2)*ln((Belt Tension on Tight Side-Mass of Meter Length of V Belt*Belt Velocity^2)/(Belt Tension on Loose Side-Mass of Meter Length of V Belt*Belt Velocity^2))/Coefficient of Friction for Belt Drive
α = sin(θ/2)*ln((P₁-m_v*v_b^2)/(P₂-m_v*v_b^2))/μ
This formula uses 2 Functions, 7 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)
ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

Wrap Angle on Pulley - (Measured in Radian) - Wrap Angle on Pulley is the angle between the run-up and run-off of the belt on the pulley.
V belt angle - (Measured in Radian) - V Belt Angle is defined as the angle included between the side faces of the V cross-section belt.
Belt Tension on Tight Side - (Measured in Newton) - Belt Tension on Tight Side is defined as the belt's tension on the belt's tight side.
Mass of Meter Length of V Belt - (Measured in Kilogram per Meter) - Mass of Meter Length of V Belt is the mass of 1-meter length of the belt simply mass per unit length of the belt.
Belt Velocity - (Measured in Meter per Second) - Belt Velocity is defined as the velocity of the belt used in a belt drive.
Belt Tension on Loose Side - (Measured in Newton) - Belt Tension on Loose Side is defined as the belt's tension on the belt's loose side.
Coefficient of Friction for Belt Drive - Coefficient of Friction for Belt Drive is the ratio defining the force that resists the motion of the belt over the pulley.

STEP 1: Convert Input(s) to Base Unit

V belt angle: 62 Degree --> 1.08210413623628 Radian (Check conversion here)
Belt Tension on Tight Side: 800 Newton --> 800 Newton No Conversion Required
Mass of Meter Length of V Belt: 0.76 Kilogram per Meter --> 0.76 Kilogram per Meter No Conversion Required
Belt Velocity: 25.81 Meter per Second --> 25.81 Meter per Second No Conversion Required
Belt Tension on Loose Side: 550 Newton --> 550 Newton No Conversion Required
Coefficient of Friction for Belt Drive: 0.35 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

α = sin(θ/2)*ln((P₁-m_v*v_b^2)/(P₂-m_v*v_b^2))/μ --> sin(1.08210413623628/2)*ln((800-0.76*25.81^2)/(550-0.76*25.81^2))/0.35

Evaluating ... ...

α = 2.80297658045815

STEP 3: Convert Result to Output's Unit

2.80297658045815 Radian -->160.598728134294 Degree (Check conversion here)

FINAL ANSWER

160.598728134294 ≈ 160.5987 Degree <-- Wrap Angle on Pulley

(Calculation completed in 00.004 seconds)

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Home » Engineering » Mechanical » Machine Design » Design of Belt Drives » V Belt Drives » V Belt Characteristics and Parameters » Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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Vishwakarma Government Engineering College (VGEC), Ahmedabad

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< V Belt Characteristics and Parameters Calculators

Belt Velocity of V-Belt given Belt Tension in Loose Side

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

Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt

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

Belt Tension in Loose Side of V-Belt

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

Belt Tension in Tight Side of V-Belt

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

Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt Formula

Types of Belt Drives?

There are five different kinds of belt drive that can be found and those are:
Open belt drive.
Closed or crossed belt drive.
Fast and loose cone pulley.
Stepped cone pulley.
Jockey pulley drive.

How to Calculate Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt?

Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt calculator uses Wrap Angle on Pulley = sin(V belt angle/2)*ln((Belt Tension on Tight Side-Mass of Meter Length of V Belt*Belt Velocity^2)/(Belt Tension on Loose Side-Mass of Meter Length of V Belt*Belt Velocity^2))/Coefficient of Friction for Belt Drive to calculate the Wrap Angle on Pulley, The Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt formula is defined as the angle between the run-up and run-off of the belt on the pulley. Wrap Angle on Pulley is denoted by α symbol.

How to calculate Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt using this online calculator? To use this online calculator for Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt, enter V belt angle (θ), Belt Tension on Tight Side (P₁), Mass of Meter Length of V Belt (m_v), Belt Velocity (v_b), Belt Tension on Loose Side (P₂) & Coefficient of Friction for Belt Drive (μ) and hit the calculate button. Here is how the Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt calculation can be explained with given input values -> 9201.629 = sin(1.08210413623628/2)*ln((800-0.76*25.81^2)/(550-0.76*25.81^2))/0.35.

FAQ

What is Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt?

The Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt formula is defined as the angle between the run-up and run-off of the belt on the pulley and is represented as α = sin(θ/2)*ln((P₁-m_v*v_b^2)/(P₂-m_v*v_b^2))/μ or Wrap Angle on Pulley = sin(V belt angle/2)*ln((Belt Tension on Tight Side-Mass of Meter Length of V Belt*Belt Velocity^2)/(Belt Tension on Loose Side-Mass of Meter Length of V Belt*Belt Velocity^2))/Coefficient of Friction for Belt Drive. V Belt Angle is defined as the angle included between the side faces of the V cross-section belt, Belt Tension on Tight Side is defined as the belt's tension on the belt's tight side, Mass of Meter Length of V Belt is the mass of 1-meter length of the belt simply mass per unit length of the belt, Belt Velocity is defined as the velocity of the belt used in a belt drive, Belt Tension on Loose Side is defined as the belt's tension on the belt's loose side & Coefficient of Friction for Belt Drive is the ratio defining the force that resists the motion of the belt over the pulley.

How to calculate Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt?

The Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt 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 Pulley = sin(V belt angle/2)*ln((Belt Tension on Tight Side-Mass of Meter Length of V Belt*Belt Velocity^2)/(Belt Tension on Loose Side-Mass of Meter Length of V Belt*Belt Velocity^2))/Coefficient of Friction for Belt Drive. To calculate Angle of Wrap of V-Belt given Belt Tension in Loose Side of Belt, you need V belt angle (θ), Belt Tension on Tight Side (P₁), Mass of Meter Length of V Belt (m_v), Belt Velocity (v_b), Belt Tension on Loose Side (P₂) & Coefficient of Friction for Belt Drive (μ). With our tool, you need to enter the respective value for V belt angle, Belt Tension on Tight Side, Mass of Meter Length of V Belt, Belt Velocity, Belt Tension on Loose Side & Coefficient of Friction for Belt Drive 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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