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

✖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%
✖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.ⓘ Wrap Angle on Pulley [α]			+10% -10%
✖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 Loose Side is defined as the belt's tension on the belt's loose side.ⓘ Belt Tension on Loose Side [P₂]			+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 of V-Belt given Belt Tension in Loose Side [v_b]

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

STEP 0: Pre-Calculation Summary

Formula Used

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))))))
v_b = sqrt((P₁-(e^(μ*α/sin(θ/2)))*P₂)/(m_v*(1-(e^(μ*α/sin(θ/2))))))
This formula uses 1 Constants, 2 Functions, 7 Variables

Constants Used

e - Napier's constant Value Taken As 2.71828182845904523536028747135266249

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)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

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 Tight Side - (Measured in Newton) - Belt Tension on Tight Side is defined as the belt's tension on the belt's tight 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.
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 Loose Side - (Measured in Newton) - Belt Tension on Loose Side is defined as the belt's tension on the belt's loose 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.

STEP 1: Convert Input(s) to Base Unit

Belt Tension on Tight Side: 800 Newton --> 800 Newton No Conversion Required
Coefficient of Friction for Belt Drive: 0.35 --> No Conversion Required
Wrap Angle on Pulley: 160.2 Degree --> 2.79601746169439 Radian (Check conversion here)
V Belt Angle: 62 Degree --> 1.08210413623628 Radian (Check conversion here)
Belt Tension on Loose Side: 550 Newton --> 550 Newton No Conversion Required
Mass of Meter Length of V Belt: 0.76 Kilogram per Meter --> 0.76 Kilogram per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

v_b = sqrt((P₁-(e^(μ*α/sin(θ/2)))*P₂)/(m_v*(1-(e^(μ*α/sin(θ/2)))))) --> sqrt((800-(e^(0.35*2.79601746169439/sin(1.08210413623628/2)))*550)/(0.76*(1-(e^(0.35*2.79601746169439/sin(1.08210413623628/2))))))

Evaluating ... ...

v_b = 25.8037873000393

STEP 3: Convert Result to Output's Unit

25.8037873000393 Meter per Second --> No Conversion Required

FINAL ANSWER

25.8037873000393 ≈ 25.80379 Meter per Second <-- Belt Velocity

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

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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

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

Belt Velocity of V-Belt given Belt Tension in Loose Side calculator uses 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)))))) to calculate the Belt Velocity, The Belt Velocity of V-Belt given Belt Tension in Loose Side formula is a measure of the rotational speed of the belt at which the rotational force is being transferred from one pulley to another. Belt Velocity is denoted by v_b symbol.

How to calculate Belt Velocity of V-Belt given Belt Tension in Loose Side using this online calculator? To use this online calculator for Belt Velocity of V-Belt given Belt Tension in Loose Side, enter Belt Tension on Tight Side (P₁), Coefficient of Friction for Belt Drive (μ), Wrap Angle on Pulley (α), V Belt Angle (θ), Belt Tension on Loose Side (P₂) & Mass of Meter Length of V Belt (m_v) and hit the calculate button. Here is how the Belt Velocity of V-Belt given Belt Tension in Loose Side calculation can be explained with given input values -> 25.80379 = sqrt((800-(e^(0.35*2.79601746169439/sin(1.08210413623628/2)))*550)/(0.76*(1-(e^(0.35*2.79601746169439/sin(1.08210413623628/2)))))).

FAQ

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

The Belt Velocity of V-Belt given Belt Tension in Loose Side formula is a measure of the rotational speed of the belt at which the rotational force is being transferred from one pulley to another and is represented as v_b = sqrt((P₁-(e^(μ*α/sin(θ/2)))*P₂)/(m_v*(1-(e^(μ*α/sin(θ/2)))))) or 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)))))). Belt Tension on Tight Side is defined as the belt's tension on the belt's tight side, Coefficient of Friction for Belt Drive is the ratio defining the force that resists the motion of the belt over the pulley, Wrap Angle on Pulley is the angle between the run-up and run-off of the belt on the pulley, V Belt Angle is defined as the angle included between the side faces of the V cross-section belt, Belt Tension on Loose Side is defined as the belt's tension on the belt's loose 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.

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

The Belt Velocity of V-Belt given Belt Tension in Loose Side formula is a measure of the rotational speed of the belt at which the rotational force is being transferred from one pulley to another is calculated using 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)))))). To calculate Belt Velocity of V-Belt given Belt Tension in Loose Side, you need Belt Tension on Tight Side (P₁), Coefficient of Friction for Belt Drive (μ), Wrap Angle on Pulley (α), V Belt Angle (θ), Belt Tension on Loose Side (P₂) & Mass of Meter Length of V Belt (m_v). With our tool, you need to enter the respective value for Belt Tension on Tight Side, Coefficient of Friction for Belt Drive, Wrap Angle on Pulley, V Belt Angle, Belt Tension on Loose Side & Mass of Meter Length of V Belt 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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