Maximum Tooth Height above Pitch Polygon Calculator

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Design of Chain Drives

Design of Brakes

Design of Flywheel

Design of Friction Clutches

Design of Shafts

Design of Splines

Design of Springs

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Proportions of the Sprocket Wheel

Geometric Relationships for Chain

Polygonal Effect

Power Rating of Roller Chains

✖Pitch of Chain 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.ⓘ Pitch of Chain [P]			+10% -10%
✖Roller Radius of Chain is the distance between the center and the point on the circumference of the roller of a chain.ⓘ Roller Radius of Chain [R]			+10% -10%
✖Number of teeth on sprocket is defined as the number of teeth (which mesh with another compatible toothed part to the chain or convert torque and speed).ⓘ Number of teeth on sprocket [z]			+10% -10%

✖Maximum Sprocket Tooth Height is the maximum limit of the tooth height on the sprocket wheel.ⓘ Maximum Tooth Height above Pitch Polygon [ha_max]

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Formula

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Maximum Tooth Height above Pitch Polygon

Formula

`"ha"_{"max"} = 0.625*"P"-"R"+(0.8*"P"/"z")`

Example

`"8.715217mm"=0.625*"22mm"-"5.8mm"+(0.8*"22mm"/"23")`

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Maximum Tooth Height above Pitch Polygon Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

Maximum Sprocket Tooth Height - (Measured in Meter) - Maximum Sprocket Tooth Height is the maximum limit of the tooth height on the sprocket wheel.
Pitch of Chain - (Measured in Meter) - Pitch of Chain 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.
Roller Radius of Chain - (Measured in Meter) - Roller Radius of Chain is the distance between the center and the point on the circumference of the roller of a chain.
Number of teeth on sprocket - Number of teeth on sprocket is defined as the number of teeth (which mesh with another compatible toothed part to the chain or convert torque and speed).

STEP 1: Convert Input(s) to Base Unit

Pitch of Chain: 22 Millimeter --> 0.022 Meter (Check conversion here)
Roller Radius of Chain: 5.8 Millimeter --> 0.0058 Meter (Check conversion here)
Number of teeth on sprocket: 23 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ha_max = 0.625*P-R+(0.8*P/z) --> 0.625*0.022-0.0058+(0.8*0.022/23)

Evaluating ... ...

ha_max = 0.00871521739130435

STEP 3: Convert Result to Output's Unit

0.00871521739130435 Meter -->8.71521739130435 Millimeter (Check conversion here)

FINAL ANSWER

8.71521739130435 ≈ 8.715217 Millimeter <-- Maximum Sprocket Tooth Height

(Calculation completed in 00.020 seconds)

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Home » Physics » Design of Automobile Elements » Design of Chain Drives » Proportions of the Sprocket Wheel » Maximum Tooth Height above Pitch Polygon

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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Vishwakarma Government Engineering College (VGEC), Ahmedabad

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< 22 Proportions of the Sprocket Wheel Calculators

Pitch Circle Diameter given Top Diameter of Sprocket Wheel

Go Sproket Diameter of Pitch Circle = Top Diameter of Sprocket Wheel-Pitch of Chain*(1-(1.6/Number of teeth on sprocket))+2*Roller Radius of Chain

Top Diameter of Sprocket Wheel

Go Top Diameter of Sprocket Wheel = Sproket Diameter of Pitch Circle+Pitch of Chain*(1-(1.6/Number of teeth on sprocket))-2*Roller Radius of Chain

Number of Teeth given Maximum Tooth Height above Pitch Polygon

Go Number of teeth on sprocket = 0.8*Pitch of Chain/(Maximum Sprocket Tooth Height-0.625*Pitch of Chain+Roller Radius of Chain)

Maximum Tooth Height above Pitch Polygon

Go Maximum Sprocket Tooth Height = 0.625*Pitch of Chain-Roller Radius of Chain+(0.8*Pitch of Chain/Number of teeth on sprocket)

Chain Pitch given Maximum Tooth Height above Pitch Polygon

Go Pitch of Chain = Maximum Sprocket Tooth Height/(0.625-Roller Radius of Chain+0.8/Number of teeth on sprocket)

Pitch Circle Diameter given Average Velocity of Chain

Go Sproket Diameter of Pitch Circle = Average Chain Velocity*60/(pi*Speed of chain drive shaft in rpm)

Pitch Circle Diameter given Pitch

Go Sproket Diameter of Pitch Circle = Pitch of Chain/sin(3.035/Number of teeth on sprocket)

Roller Seating Radius given Roller Radius

Go Roller Seating Radius = (1.010*Roller Radius of Chain)+(0.00069*((2*Roller Radius of Chain)^(1/3)))

Tooth Flank Radius

Go Sprocket Tooth Flank Radius = 0.016*Roller Radius of Chain*((Number of teeth on sprocket)^2+180)

Roller Seating Radius given Root Diameter of Sprocket Wheel

Go Roller Seating Radius = (Sproket Diameter of Pitch Circle-Root Diameter of Sprocket Wheel)/2

Pitch Circle Diameter given Root Diameter of Sprocket Wheel

Go Sproket Diameter of Pitch Circle = Root Diameter of Sprocket Wheel+2*Roller Seating Radius

Number of Teeth given Minimum Tooth Flank Radius

Go Number of teeth on sprocket = (Minimum Tooth Flank Radius/(0.24*Roller Radius of Chain))-2

Root Diameter of Sprocket Wheel

Go Root Diameter of Sprocket Wheel = Sproket Diameter of Pitch Circle-2*Roller Seating Radius

Minimum Tooth Flank Radius

Go Minimum Tooth Flank Radius = 0.24*Roller Radius of Chain*(Number of teeth on sprocket+2)

Number of Teeth given Maximum Roller Seating Angle

Go Number of teeth on sprocket = 90/(120-(Maximum Roller Seating Angle*180/pi))

Number of Teeth given Minimum Roller Seating Angle

Go Number of teeth on sprocket = 90/(140-(Minimum Roller Seating Angle*180/pi))

Maximum Roller Seating Angle

Go Maximum Roller Seating Angle = (120-(90/Number of teeth on sprocket))*pi/180

Minimum Roller Seating Angle

Go Minimum Roller Seating Angle = (140-(90/Number of teeth on sprocket))*pi/180

Number of Teeth on Sprocket given Pitch Angle of Sprocket

Go Number of teeth on sprocket = 360/(Pitch Angle of Sprocket*(180/pi))

Minimum Tooth Height above Pitch Polygon

Go Minimum Tooth Height = 0.5*Pitch of Chain-Roller Radius of Chain

Pitch Angle of Sprocket

Go Pitch Angle of Sprocket = (360/Number of teeth on sprocket)/57.24

Minimum Roller Seating Radius

Go Minimum Roller Seating Radius = 2*0.505*Roller Radius of Chain

Maximum Tooth Height above Pitch Polygon Formula

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

Define a Sprocket?

A sprocket, sprocket-wheel, or chainwheel is a profiled wheel with teeth, or cogs, that mesh with a chain, track, or other perforated or indented material. The name 'sprocket' applies generally to any wheel upon which radial projections engage a chain passing over it.

How to Calculate Maximum Tooth Height above Pitch Polygon?

Maximum Tooth Height above Pitch Polygon calculator uses Maximum Sprocket Tooth Height = 0.625*Pitch of Chain-Roller Radius of Chain+(0.8*Pitch of Chain/Number of teeth on sprocket) to calculate the Maximum Sprocket Tooth Height, The Maximum Tooth Height above Pitch Polygon formula is defined as the maximum limit of the tooth on the sprocket wheel. Maximum Sprocket Tooth Height is denoted by ha_max symbol.

How to calculate Maximum Tooth Height above Pitch Polygon using this online calculator? To use this online calculator for Maximum Tooth Height above Pitch Polygon, enter Pitch of Chain (P), Roller Radius of Chain (R) & Number of teeth on sprocket (z) and hit the calculate button. Here is how the Maximum Tooth Height above Pitch Polygon calculation can be explained with given input values -> 8715.217 = 0.625*0.022-0.0058+(0.8*0.022/23).

FAQ

What is Maximum Tooth Height above Pitch Polygon?

The Maximum Tooth Height above Pitch Polygon formula is defined as the maximum limit of the tooth on the sprocket wheel and is represented as ha_max = 0.625*P-R+(0.8*P/z) or Maximum Sprocket Tooth Height = 0.625*Pitch of Chain-Roller Radius of Chain+(0.8*Pitch of Chain/Number of teeth on sprocket). Pitch of Chain 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, Roller Radius of Chain is the distance between the center and the point on the circumference of the roller of a chain & Number of teeth on sprocket is defined as the number of teeth (which mesh with another compatible toothed part to the chain or convert torque and speed).

How to calculate Maximum Tooth Height above Pitch Polygon?

The Maximum Tooth Height above Pitch Polygon formula is defined as the maximum limit of the tooth on the sprocket wheel is calculated using Maximum Sprocket Tooth Height = 0.625*Pitch of Chain-Roller Radius of Chain+(0.8*Pitch of Chain/Number of teeth on sprocket). To calculate Maximum Tooth Height above Pitch Polygon, you need Pitch of Chain (P), Roller Radius of Chain (R) & Number of teeth on sprocket (z). With our tool, you need to enter the respective value for Pitch of Chain, Roller Radius of Chain & 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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