Relation between Pitch and Pitch Circle Diameter of Chain Drive Calculator

✖Pitch of chain drive is the distance between regularly spaced objects such as the distance between two regular threads.ⓘ Pitch of Chain Drive [P_{chain drive}]			+10% -10%
✖The number of teeth on sprocket is the count of the number of teeth on the sprockets.ⓘ Number of Teeth on Sprocket [t_sprocket]			+10% -10%

✖The Pitch Circle Diameter of Gear is an imaginary circle concentric to a toothed wheel, along which the pitch of the teeth is measured.ⓘ Relation between Pitch and Pitch Circle Diameter of Chain Drive [d_pitch]

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Formula

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Relation between Pitch and Pitch Circle Diameter of Chain Drive

Formula

`"d"_{"pitch"} = "P"_{"chain drive"}*cosec((180*pi/180)/"t"_{"sprocket"})`

Example

`"0.478339m"="0.05m"*cosec((180*pi/180)/"30")`

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Relation between Pitch and Pitch Circle Diameter of Chain Drive Solution

STEP 0: Pre-Calculation Summary

Formula Used

Pitch Circle Diameter of Gear = Pitch of Chain Drive*cosec((180*pi/180)/Number of Teeth on Sprocket)
d_pitch = P_{chain drive}*cosec((180*pi/180)/t_sprocket)
This formula uses 1 Constants, 2 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sec - Secant is a trigonometric function that is defined ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine., sec(Angle)
cosec - The cosecant function is a trigonometric function that is the reciprocal of the sine function., cosec(Angle)

Variables Used

Pitch Circle Diameter of Gear - (Measured in Meter) - The Pitch Circle Diameter of Gear is an imaginary circle concentric to a toothed wheel, along which the pitch of the teeth is measured.
Pitch of Chain Drive - (Measured in Meter) - Pitch of chain drive is the distance between regularly spaced objects such as the distance between two regular threads.
Number of Teeth on Sprocket - The number of teeth on sprocket is the count of the number of teeth on the sprockets.

STEP 1: Convert Input(s) to Base Unit

Pitch of Chain Drive: 0.05 Meter --> 0.05 Meter No Conversion Required
Number of Teeth on Sprocket: 30 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_pitch = P_{chain drive}*cosec((180*pi/180)/t_sprocket) --> 0.05*cosec((180*pi/180)/30)

Evaluating ... ...

d_pitch = 0.478338611675281

STEP 3: Convert Result to Output's Unit

0.478338611675281 Meter --> No Conversion Required

FINAL ANSWER

0.478338611675281 ≈ 0.478339 Meter <-- Pitch Circle Diameter of Gear

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Belt, Rope and Chain Drives » Belt Drive » Relation between Pitch and Pitch Circle Diameter of Chain Drive

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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

Relation between Pitch and Pitch Circle Diameter of Chain Drive Formula

Pitch Circle Diameter of Gear = Pitch of Chain Drive*cosec((180*pi/180)/Number of Teeth on Sprocket)
d_pitch = P_{chain drive}*cosec((180*pi/180)/t_sprocket)

What is the pitch of a roller chain?

In terms of conveyor chain, the pitch is usually defined as the distance between links, as measured from the center of the roller pin on one link to the center of the roller pin on the next link. Note that some precision link conveyors refer to the pitch as the link size.

How to Calculate Relation between Pitch and Pitch Circle Diameter of Chain Drive?

Relation between Pitch and Pitch Circle Diameter of Chain Drive calculator uses Pitch Circle Diameter of Gear = Pitch of Chain Drive*cosec((180*pi/180)/Number of Teeth on Sprocket) to calculate the Pitch Circle Diameter of Gear, The relation between pitch and pitch circle diameter of chain drive is the mathematical relation between pitch and pitch circle diameter. Pitch Circle Diameter of Gear is denoted by d_pitch symbol.

How to calculate Relation between Pitch and Pitch Circle Diameter of Chain Drive using this online calculator? To use this online calculator for Relation between Pitch and Pitch Circle Diameter of Chain Drive, enter Pitch of Chain Drive (P_{chain drive}) & Number of Teeth on Sprocket (t_sprocket) and hit the calculate button. Here is how the Relation between Pitch and Pitch Circle Diameter of Chain Drive calculation can be explained with given input values -> 0.478339 = 0.05*cosec((180*pi/180)/30).

FAQ

What is Relation between Pitch and Pitch Circle Diameter of Chain Drive?

The relation between pitch and pitch circle diameter of chain drive is the mathematical relation between pitch and pitch circle diameter and is represented as d_pitch = P_{chain drive}*cosec((180*pi/180)/t_sprocket) or Pitch Circle Diameter of Gear = Pitch of Chain Drive*cosec((180*pi/180)/Number of Teeth on Sprocket). Pitch of chain drive is the distance between regularly spaced objects such as the distance between two regular threads & The number of teeth on sprocket is the count of the number of teeth on the sprockets.

How to calculate Relation between Pitch and Pitch Circle Diameter of Chain Drive?

The relation between pitch and pitch circle diameter of chain drive is the mathematical relation between pitch and pitch circle diameter is calculated using Pitch Circle Diameter of Gear = Pitch of Chain Drive*cosec((180*pi/180)/Number of Teeth on Sprocket). To calculate Relation between Pitch and Pitch Circle Diameter of Chain Drive, you need Pitch of Chain Drive (P_{chain drive}) & Number of Teeth on Sprocket (t_sprocket). With our tool, you need to enter the respective value for Pitch of Chain Drive & Number of Teeth on Sprocket 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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