Mass per unit length of belt 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%
✖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 Belt is the mass of 1-meter length of the belt simply mass per unit length of the belt.ⓘ Mass per unit length of belt [m]

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Formula

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Mass per unit length of belt

Formula

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

Example

`"0.599657kg/m"=("800N"-((e^("0.35"*"160.2°"))*"550N"))/((("25.81m/s")^2)*(1-(e^("0.35"*"160.2°"))))`

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Mass per unit length of belt Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))))
m = (P₁-((e^(μ*α))*P₂))/((v_b^2)*(1-(e^(μ*α))))
This formula uses 1 Constants, 6 Variables

Constants Used

e - Napier's constant Value Taken As 2.71828182845904523536028747135266249

Variables Used

Mass of Meter Length of Belt - (Measured in Kilogram per Meter) - Mass of Meter Length of 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.
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)
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 = (P₁-((e^(μ*α))*P₂))/((v_b^2)*(1-(e^(μ*α)))) --> (800-((e^(0.35*2.79601746169439))*550))/((25.81^2)*(1-(e^(0.35*2.79601746169439))))

Evaluating ... ...

m = 0.599656954727705

STEP 3: Convert Result to Output's Unit

0.599656954727705 Kilogram per Meter --> No Conversion Required

FINAL ANSWER

0.599656954727705 ≈ 0.599657 Kilogram per Meter <-- Mass of Meter Length of Belt

(Calculation completed in 00.004 seconds)

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Home » Engineering » Mechanical » Machine Design » Design of Belt Drives » Introduction of Belt Drives » Mass per unit length of belt

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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

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< 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))))

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 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))

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))

Mass per unit length 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 Mass per unit length of belt?

Mass per unit length of belt calculator uses 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)))) to calculate the Mass of Meter Length of Belt, The Mass per unit length of belt formula is defined as the mass of the belt per one meter length. Mass of Meter Length of Belt is denoted by m symbol.

How to calculate Mass per unit length of belt using this online calculator? To use this online calculator for Mass per unit length of belt, enter Belt Tension on Tight Side (P₁), Coefficient of Friction for Belt Drive (μ), Wrap Angle on Pulley (α), Belt Tension on Loose Side (P₂) & Belt Velocity (v_b) and hit the calculate button. Here is how the Mass per unit length of belt calculation can be explained with given input values -> 0.599657 = (800-((e^(0.35*2.79601746169439))*550))/((25.81^2)*(1-(e^(0.35*2.79601746169439)))).

FAQ

What is Mass per unit length of belt?

The Mass per unit length of belt formula is defined as the mass of the belt per one meter length and is represented as m = (P₁-((e^(μ*α))*P₂))/((v_b^2)*(1-(e^(μ*α)))) or 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)))). 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, 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 per unit length of belt?

The Mass per unit length of belt formula is defined as the mass of the belt per one meter length is calculated using 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)))). To calculate Mass per unit length of belt, you need Belt Tension on Tight Side (P₁), Coefficient of Friction for Belt Drive (μ), Wrap Angle on Pulley (α), 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, 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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