Length of Open Belt Drive Calculator

✖Radii of Smaller Pulley is a straight line from the center to the circumference of pulley.ⓘ Radii of Smaller Pulley [r₂]			+10% -10%
✖Radii of larger pulley is a straight line from the center to the circumference of pulley.ⓘ Radii of Larger Pulley [r₁]			+10% -10%
✖Distance between centers of two pulleys is the horizontal distance between larger and smaller pulley.ⓘ Distance Between Centers of Two Pulleys [x]			+10% -10%

✖The total length of belt is the length of the belt in the belt drive.ⓘ Length of Open Belt Drive [L_belt]

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Formula

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Length of Open Belt Drive

Formula

`"L"_{"belt"} = pi*("r"_{"2"}+"r"_{"1"})+2*"x"+(("r"_{"1"}-"r"_{"2"})^2)/"x"`

Example

`"80.45639m"=pi*("6m"+"10m")+2*"0.55m"+(("10m"-"6m")^2)/"0.55m"`

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Length of Open Belt Drive Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Length of Belt = pi*(Radii of Smaller Pulley+Radii of Larger Pulley)+2*Distance Between Centers of Two Pulleys+((Radii of Larger Pulley-Radii of Smaller Pulley)^2)/Distance Between Centers of Two Pulleys
L_belt = pi*(r₂+r₁)+2*x+((r₁-r₂)^2)/x
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Total Length of Belt - (Measured in Meter) - The total length of belt is the length of the belt in the belt drive.
Radii of Smaller Pulley - (Measured in Meter) - Radii of Smaller Pulley is a straight line from the center to the circumference of pulley.
Radii of Larger Pulley - (Measured in Meter) - Radii of larger pulley is a straight line from the center to the circumference of pulley.
Distance Between Centers of Two Pulleys - (Measured in Meter) - Distance between centers of two pulleys is the horizontal distance between larger and smaller pulley.

STEP 1: Convert Input(s) to Base Unit

Radii of Smaller Pulley: 6 Meter --> 6 Meter No Conversion Required
Radii of Larger Pulley: 10 Meter --> 10 Meter No Conversion Required
Distance Between Centers of Two Pulleys: 0.55 Meter --> 0.55 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_belt = pi*(r₂+r₁)+2*x+((r₁-r₂)^2)/x --> pi*(6+10)+2*0.55+((10-6)^2)/0.55

Evaluating ... ...

L_belt = 80.4563915483458

STEP 3: Convert Result to Output's Unit

80.4563915483458 Meter --> No Conversion Required

FINAL ANSWER

80.4563915483458 ≈ 80.45639 Meter <-- Total Length of Belt

(Calculation completed in 00.004 seconds)

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< 20 Belt Drive Calculators

Length of Open Belt Drive

Go Total Length of Belt = pi*(Radii of Smaller Pulley+Radii of Larger Pulley)+2*Distance Between Centers of Two Pulleys+((Radii of Larger Pulley-Radii of Smaller Pulley)^2)/Distance Between Centers of Two Pulleys

Cross Belt Drive Length

Go Length Belt Drive = pi*(Radii of Smaller Pulley+Radii of Larger Pulley)+2*Distance Between Centers of Two Pulleys+(Radii of Smaller Pulley+Radii of Larger Pulley)^2/Distance Between Centers of Two Pulleys

Frictional Force in V Belt Drive

Go Force of Friction = Coefficient of Friction b/w Belt & Sides of Groove*Total Reaction in Plane of Groove*cosec(Angle of Groove/2)

Relation between Pitch and Pitch Circle Diameter of Chain Drive

Go Pitch Circle Diameter of Gear = Pitch of Chain Drive*cosec((180*pi/180)/Number of Teeth on Sprocket)

Angle Made by Belt with Vertical Axis for Cross Belt Drive

Go Angle made by Belt with Vertical Axis = (Radii of Smaller Pulley+Radii of Larger Pulley)/Distance Between Centers of Two Pulleys

Angle Made by Belt with Vertical Axis for Open Belt Drive

Go Angle made by Belt with Vertical Axis = (Radii of Larger Pulley-Radii of Smaller Pulley)/Distance Between Centers of Two Pulleys

Initial Tension in Belt

Go Initial Tension of Belt = (Tension in Tight Side of Belt+Tension in Slack Side of Belt+2*Centrifugal Tension of Belt)/2

Normal Reaction between Belt and Sides of Groove

Go Normal Reaction between Belt and Sides of Groove = Total Reaction in Plane of Groove/(2*sin(Angle of Groove/2))

Torque Exerted on Driven Pulley

Go Torque Exerted on Pulley = (Tension in Tight Side of Belt-Tension in Slack Side of Belt)*Diameter of Follower/2

Torque Exerted on Driving Pulley

Go Torque Exerted on Pulley = (Tension in Tight Side of Belt-Tension in Slack Side of Belt)*Diameter of Driver/2

Power Transmitted by Belt

Go Power Transmitted = (Tension in Tight Side of Belt-Tension in Slack Side of Belt)*Velocity of Belt

Velocity for Transmission of Maximum Power by Belt

Go Velocity of Belt = sqrt(Maximum Tension of Belt/(3*Mass of Belt per Unit Length))

Length of Belt that Passes over Follower

Go Length of Belt over Follower = pi*Speed of Follower*Diameter of Follower Pulley

Length of Belt that Passes over Driver

Go Length of Belt over Driver = pi*Diameter of Driver Pulley*Speed of Driver

Maximum Tension of Belt

Go Maximum Tension of Belt = Maximum Safe Stress*Belt Width*Belt Thickness

Total Percentage Slip in Belt

Go Total Percentage of Slip = Slip between Driver and Belt+Slip between Belt and Follower

Centrifugal Tension in Belt

Go Centrifugal Tension of Belt = Mass of Belt per Unit Length*Velocity of Belt

Angle of Contact for Cross Belt Drive

Go Angle of Contact = 180*pi/180+2*Angle made by Belt with Vertical Axis

Angle of Contact for Open Belt Drive

Go Angle of Contact = 180*pi/180-2*Angle made by Belt with Vertical Axis

Maximum Tension for Transmission of Maximum Power by Belt

Go Maximum Tension of Belt = 3*Centrifugal Tension of Belt

Length of Open Belt Drive Formula

What is a belt drive used for?

Belt drive, in machinery, a pair of pulleys attached to usually parallel shafts and connected by an encircling flexible belt (band) that can serve to transmit and modify rotary motion from one shaft to the other.

Difference Between Open Belt Drive and Cross Belt Drive?

In open belt drive, driving shaft and driven shaft rotate in same direction. In crossed belt drive, driving shaft and driven shaft rotate in opposite direction.

How to Calculate Length of Open Belt Drive?

Length of Open Belt Drive calculator uses Total Length of Belt = pi*(Radii of Smaller Pulley+Radii of Larger Pulley)+2*Distance Between Centers of Two Pulleys+((Radii of Larger Pulley-Radii of Smaller Pulley)^2)/Distance Between Centers of Two Pulleys to calculate the Total Length of Belt, Length of Open Belt Drive is based on two factors: the center-to-center distance between pulleys and the arc of contact between the belt and the pulleys, which depends on the relative pulley diameters. Total Length of Belt is denoted by L_belt symbol.

How to calculate Length of Open Belt Drive using this online calculator? To use this online calculator for Length of Open Belt Drive, enter Radii of Smaller Pulley (r₂), Radii of Larger Pulley (r₁) & Distance Between Centers of Two Pulleys (x) and hit the calculate button. Here is how the Length of Open Belt Drive calculation can be explained with given input values -> 80.45639 = pi*(6+10)+2*0.55+((10-6)^2)/0.55.

FAQ

What is Length of Open Belt Drive?

Length of Open Belt Drive is based on two factors: the center-to-center distance between pulleys and the arc of contact between the belt and the pulleys, which depends on the relative pulley diameters and is represented as L_belt = pi*(r₂+r₁)+2*x+((r₁-r₂)^2)/x or Total Length of Belt = pi*(Radii of Smaller Pulley+Radii of Larger Pulley)+2*Distance Between Centers of Two Pulleys+((Radii of Larger Pulley-Radii of Smaller Pulley)^2)/Distance Between Centers of Two Pulleys. Radii of Smaller Pulley is a straight line from the center to the circumference of pulley, Radii of larger pulley is a straight line from the center to the circumference of pulley & Distance between centers of two pulleys is the horizontal distance between larger and smaller pulley.

How to calculate Length of Open Belt Drive?

Length of Open Belt Drive is based on two factors: the center-to-center distance between pulleys and the arc of contact between the belt and the pulleys, which depends on the relative pulley diameters is calculated using Total Length of Belt = pi*(Radii of Smaller Pulley+Radii of Larger Pulley)+2*Distance Between Centers of Two Pulleys+((Radii of Larger Pulley-Radii of Smaller Pulley)^2)/Distance Between Centers of Two Pulleys. To calculate Length of Open Belt Drive, you need Radii of Smaller Pulley (r₂), Radii of Larger Pulley (r₁) & Distance Between Centers of Two Pulleys (x). With our tool, you need to enter the respective value for Radii of Smaller Pulley, Radii of Larger Pulley & Distance Between Centers of Two 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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