Mass of One Meter Length 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%
✖Belt Velocity is defined as the velocity of the belt used in a belt drive.ⓘ Belt Velocity [v_b]			+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 One Meter Length of V-Belt given Belt Tension in Loose Side [m_v]

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Formula

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Mass of One Meter Length of V-Belt given Belt Tension in Loose Side

Formula

`"m"_{"v"} = ("P"_{"1"}-(e^("μ"*"α"/sin("θ"/2)))*"P"_{"2"})/("v"_{"b"}^2*(1-(e^("μ"*"α"/sin("θ"/2)))))`

Example

`"0.759634kg/m"=("800N"-(e^("0.35"*"160.2°"/sin("62°"/2)))*"550N")/(("25.81m/s")^2*(1-(e^("0.35"*"160.2°"/sin("62°"/2)))))`

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Mass of One Meter Length of V-Belt given Belt Tension in Loose Side Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mass of Meter Length of V Belt = (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)/(Belt Velocity^2*(1-(e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley/sin(V belt angle/2)))))
m_v = (P₁-(e^(μ*α/sin(θ/2)))*P₂)/(v_b^2*(1-(e^(μ*α/sin(θ/2)))))
This formula uses 1 Constants, 1 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)

Variables Used

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 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.
Belt Velocity - (Measured in Meter per Second) - Belt Velocity is defined as the velocity of the belt used in a belt drive.

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
Belt Velocity: 25.81 Meter per Second --> 25.81 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

m_v = (P₁-(e^(μ*α/sin(θ/2)))*P₂)/(v_b^2*(1-(e^(μ*α/sin(θ/2))))) --> (800-(e^(0.35*2.79601746169439/sin(1.08210413623628/2)))*550)/(25.81^2*(1-(e^(0.35*2.79601746169439/sin(1.08210413623628/2)))))

Evaluating ... ...

m_v = 0.759634166315538

STEP 3: Convert Result to Output's Unit

0.759634166315538 Kilogram per Meter --> No Conversion Required

FINAL ANSWER

0.759634166315538 ≈ 0.759634 Kilogram per Meter <-- Mass of Meter Length of V Belt

(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 » Mass of One Meter Length of V-Belt given Belt Tension in Loose Side

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Osmania University (OU), Hyderabad

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< 11 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))))))

Mass of One Meter Length of V-Belt given Belt Tension in Loose Side

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

Coefficient of Friction in V-Belt given Belt Tension in Loose Side of Belt

Go Coefficient of Friction for Belt Drive = 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))/Wrap Angle on Pulley

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

Correction Factor for Industrial Services given Number of Belts Required

Go Correction Factor for Industrial Service = Number of Belts*(Correction Factor for Belt Length*Correction Factor for Arc of Contact*Power Rating of Single V-Belt)/Power transmitted by belt

Correction Factor for Arc of Contact given Number of Belts Required

Go Correction Factor for Arc of Contact = Power transmitted by belt*Correction Factor for Industrial Service/(Correction Factor for Belt Length*Number of Belts*Power Rating of Single V-Belt)

Correcting Factor for Belt Length given Number of Belts Required

Go Correction Factor for Belt Length = Power transmitted by belt*Correction Factor for Industrial Service/(Number of Belts*Correction Factor for Arc of Contact*Power Rating of Single V-Belt)

Number of V Belts Required for Given Applications

Go Number of Belts = Power transmitted by belt*Correction Factor for Industrial Service/(Correction Factor for Belt Length*Correction Factor for Arc of Contact*Power Rating of Single V-Belt)

Effective Pull in V-Belt

Go Effective Pull in V Belt = Belt Tension on Tight Side-Belt Tension on Loose Side

Mass of One Meter Length 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 Mass of One Meter Length of V-Belt given Belt Tension in Loose Side?

Mass of One Meter Length of V-Belt given Belt Tension in Loose Side calculator uses Mass of Meter Length of V Belt = (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)/(Belt Velocity^2*(1-(e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley/sin(V belt angle/2))))) to calculate the Mass of Meter Length of V Belt, Mass of One Meter Length of V-Belt given Belt Tension in Loose Side formula is defined as the mass of the belt per one meter length. Mass of Meter Length of V Belt is denoted by m_v symbol.

How to calculate Mass of One Meter Length of V-Belt given Belt Tension in Loose Side using this online calculator? To use this online calculator for Mass of One Meter Length 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) & Belt Velocity (v_b) and hit the calculate button. Here is how the Mass of One Meter Length of V-Belt given Belt Tension in Loose Side calculation can be explained with given input values -> 0.759634 = (800-(e^(0.35*2.79601746169439/sin(1.08210413623628/2)))*550)/(25.81^2*(1-(e^(0.35*2.79601746169439/sin(1.08210413623628/2))))).

FAQ

What is Mass of One Meter Length of V-Belt given Belt Tension in Loose Side?

Mass of One Meter Length of V-Belt given Belt Tension in Loose Side formula is defined as the mass of the belt per one meter length and is represented as m_v = (P₁-(e^(μ*α/sin(θ/2)))*P₂)/(v_b^2*(1-(e^(μ*α/sin(θ/2))))) or Mass of Meter Length of V Belt = (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)/(Belt Velocity^2*(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 & Belt Velocity is defined as the velocity of the belt used in a belt drive.

How to calculate Mass of One Meter Length of V-Belt given Belt Tension in Loose Side?

Mass of One Meter Length of V-Belt given Belt Tension in Loose Side formula is defined as the mass of the belt per one meter length is calculated using Mass of Meter Length of V Belt = (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)/(Belt Velocity^2*(1-(e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley/sin(V belt angle/2))))). To calculate Mass of One Meter Length 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) & Belt Velocity (v_b). 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 & Belt Velocity 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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