Roller Radius given Maximum Tooth Height above Pitch Polygon Calculator

✖Pitch of Chain is the distance between two consecutive identical links measured along the direction of the chain's length.ⓘ Pitch of Chain [P]			+10% -10%
✖Maximum Sprocket Tooth Height is the maximum height of a tooth on a sprocket in a chain, affecting the chain's overall performance and durability.ⓘ Maximum Sprocket Tooth Height [ha_max]			+10% -10%
✖Number of Teeth on Sprocket is the total count of teeth present on a sprocket in a chain drive system, used to transmit power and motion.ⓘ Number of Teeth on Sprocket [z]			+10% -10%

✖Roller Radius of Chain is the radius of the roller in a chain, which is a critical component in the geometric relationships for chain design.ⓘ Roller Radius given Maximum Tooth Height above Pitch Polygon [R]

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Formula

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Roller Radius given Maximum Tooth Height above Pitch Polygon

Formula

R = 0.625 \cdot P - ha max + 0.8 \cdot \frac{P}{z}

Example

6.000217 mm = 0.625 \cdot 22 mm - 8.515 mm + 0.8 \cdot \frac{22 mm}{23}

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Roller Radius given Maximum Tooth Height above Pitch Polygon Solution

STEP 0: Pre-Calculation Summary

Formula Used

Roller Radius of Chain = 0.625*Pitch of Chain-Maximum Sprocket Tooth Height+0.8*Pitch of Chain/Number of Teeth on Sprocket
R = 0.625*P-ha_max+0.8*P/z
This formula uses 4 Variables

Variables Used

Roller Radius of Chain - (Measured in Meter) - Roller Radius of Chain is the radius of the roller in a chain, which is a critical component in the geometric relationships for chain design.
Pitch of Chain - (Measured in Meter) - Pitch of Chain is the distance between two consecutive identical links measured along the direction of the chain's length.
Maximum Sprocket Tooth Height - (Measured in Meter) - Maximum Sprocket Tooth Height is the maximum height of a tooth on a sprocket in a chain, affecting the chain's overall performance and durability.
Number of Teeth on Sprocket - Number of Teeth on Sprocket is the total count of teeth present on a sprocket in a chain drive system, used to transmit power and motion.

STEP 1: Convert Input(s) to Base Unit

Pitch of Chain: 22 Millimeter --> 0.022 Meter (Check conversion here)
Maximum Sprocket Tooth Height: 8.515 Millimeter --> 0.008515 Meter (Check conversion here)
Number of Teeth on Sprocket: 23 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R = 0.625*P-ha_max+0.8*P/z --> 0.625*0.022-0.008515+0.8*0.022/23

Evaluating ... ...

R = 0.00600021739130435

STEP 3: Convert Result to Output's Unit

0.00600021739130435 Meter -->6.00021739130435 Millimeter (Check conversion here)

FINAL ANSWER

6.00021739130435 ≈ 6.000217 Millimeter <-- Roller Radius of Chain

(Calculation completed in 00.004 seconds)

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Home » Physics » Design of Automobile Elements » Design of Chain Drives » Mechanical » Geometric Relationships for Chain » Roller Radius given Maximum Tooth Height above Pitch Polygon

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Osmania University (OU), Hyderabad

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< Geometric Relationships for Chain Calculators

Pitch of chain given Pitch Circle Diameter

Go Pitch of Chain = Pitch Circle Diameter of Sprocket*sin(3.035/Number of Teeth on Sprocket)

Number of Teeth on Sprocket given Pitch Circle Diameter

Go Number of Teeth on Sprocket = 180*asin(Pitch of Chain/Pitch Circle Diameter of Sprocket)

Speed of Rotation of Driving Shaft given Velocity Ratio of Chain Drives

Go Angular Speed of Chain Driving Shaft = Velocity Ratio of Chain Drive*Angular Speed of Chain Driven Shaft

Velocity Ratio of Chain Drives

Go Velocity Ratio of Chain Drive = Angular Speed of Chain Driving Shaft/Angular Speed of Chain Driven Shaft

Roller Radius given Maximum Tooth Height above Pitch Polygon Formula

Roller Radius of Chain = 0.625*Pitch of Chain-Maximum Sprocket Tooth Height+0.8*Pitch of Chain/Number of Teeth on Sprocket
R = 0.625*P-ha_max+0.8*P/z

What is Pitch Polygon?

The pitch polygon is a geometric representation of the shape traced by the pitch circles of sprockets in a chain drive system when the sprockets rotate. It is used to analyze the engagement and movement of the chain with the sprockets. The pitch polygon helps in understanding how the chain interacts with the sprockets and ensures proper alignment and smooth operation.

How to Calculate Roller Radius given Maximum Tooth Height above Pitch Polygon?

Roller Radius given Maximum Tooth Height above Pitch Polygon calculator uses Roller Radius of Chain = 0.625*Pitch of Chain-Maximum Sprocket Tooth Height+0.8*Pitch of Chain/Number of Teeth on Sprocket to calculate the Roller Radius of Chain, Roller Radius given Maximum Tooth Height above Pitch Polygon formula is defined as a parameter that characterizes the size of a roller in a gear system, providing a way to determine the radius of the roller based on the maximum tooth height above the pitch polygon and other relevant factors. Roller Radius of Chain is denoted by R symbol.

How to calculate Roller Radius given Maximum Tooth Height above Pitch Polygon using this online calculator? To use this online calculator for Roller Radius given Maximum Tooth Height above Pitch Polygon, enter Pitch of Chain (P), Maximum Sprocket Tooth Height (ha_max) & Number of Teeth on Sprocket (z) and hit the calculate button. Here is how the Roller Radius given Maximum Tooth Height above Pitch Polygon calculation can be explained with given input values -> 6562.134 = 0.625*0.022-0.008515+0.8*0.022/23.

FAQ

What is Roller Radius given Maximum Tooth Height above Pitch Polygon?

Roller Radius given Maximum Tooth Height above Pitch Polygon formula is defined as a parameter that characterizes the size of a roller in a gear system, providing a way to determine the radius of the roller based on the maximum tooth height above the pitch polygon and other relevant factors and is represented as R = 0.625*P-ha_max+0.8*P/z or Roller Radius of Chain = 0.625*Pitch of Chain-Maximum Sprocket Tooth Height+0.8*Pitch of Chain/Number of Teeth on Sprocket. Pitch of Chain is the distance between two consecutive identical links measured along the direction of the chain's length, Maximum Sprocket Tooth Height is the maximum height of a tooth on a sprocket in a chain, affecting the chain's overall performance and durability & Number of Teeth on Sprocket is the total count of teeth present on a sprocket in a chain drive system, used to transmit power and motion.

How to calculate Roller Radius given Maximum Tooth Height above Pitch Polygon?

Roller Radius given Maximum Tooth Height above Pitch Polygon formula is defined as a parameter that characterizes the size of a roller in a gear system, providing a way to determine the radius of the roller based on the maximum tooth height above the pitch polygon and other relevant factors is calculated using Roller Radius of Chain = 0.625*Pitch of Chain-Maximum Sprocket Tooth Height+0.8*Pitch of Chain/Number of Teeth on Sprocket. To calculate Roller Radius given Maximum Tooth Height above Pitch Polygon, you need Pitch of Chain (P), Maximum Sprocket Tooth Height (ha_max) & Number of Teeth on Sprocket (z). With our tool, you need to enter the respective value for Pitch of Chain, Maximum Sprocket Tooth Height & 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.

How many ways are there to calculate Roller Radius of Chain?

In this formula, Roller Radius of Chain uses Pitch of Chain, Maximum Sprocket Tooth Height & Number of Teeth on Sprocket. We can use 3 other way(s) to calculate the same, which is/are as follows -

Roller Radius of Chain = (Pitch Circle Diameter of Sprocket+(Pitch of Chain*(1-(1.6/Number of Teeth on Sprocket)))-Top Diameter of Sprocket Wheel)/2
Roller Radius of Chain = Sprocket Tooth Flank Radius/(0.016*((Number of Teeth on Sprocket)^2+180))
Roller Radius of Chain = 0.5*Pitch of Chain-Minimum Tooth Height

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