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Pitch Circle Diameter given Top Diameter of Sprocket Wheel Calculator

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✖Top Diameter of Sprocket Wheel is the diameter of the top part or the outermost part of a sprocket wheel.ⓘ Top Diameter of Sprocket Wheel [da]
+10%
-10%
✖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%
✖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%
✖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%
✖Sproket Diameter of Pitch Circle is the diameter of the pitch circle (passing through rollers centre) of the sprocket.ⓘ Pitch Circle Diameter given Top Diameter of Sprocket Wheel [Ds]
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Formula
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Pitch Circle Diameter given Top Diameter of Sprocket Wheel

Formula
`"D"_{"s"} = "d"_{"a"}-"P"*(1-(1.6/"z"))+2*"R"`

Example
`"103.1304mm"="112mm"-"22mm"*(1-(1.6/"23"))+2*"5.8mm"`

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Pitch Circle Diameter given Top Diameter of Sprocket Wheel Solution

STEP 0: Pre-Calculation Summary
Formula Used
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
Ds = da-P*(1-(1.6/z))+2*R
This formula uses 5 Variables
Variables Used
Sproket Diameter of Pitch Circle - (Measured in Meter) - Sproket Diameter of Pitch Circle is the diameter of the pitch circle (passing through rollers centre) of the sprocket.
Top Diameter of Sprocket Wheel - (Measured in Meter) - Top Diameter of Sprocket Wheel is the diameter of the top part or the outermost part of a 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.
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).
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.
STEP 1: Convert Input(s) to Base Unit
Top Diameter of Sprocket Wheel: 112 Millimeter --> 0.112 Meter (Check conversion here)
Pitch of Chain: 22 Millimeter --> 0.022 Meter (Check conversion here)
Number of teeth on sprocket: 23 --> No Conversion Required
Roller Radius of Chain: 5.8 Millimeter --> 0.0058 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Ds = da-P*(1-(1.6/z))+2*R --> 0.112-0.022*(1-(1.6/23))+2*0.0058
Evaluating ... ...
Ds = 0.103130434782609
STEP 3: Convert Result to Output's Unit
0.103130434782609 Meter -->103.130434782609 Millimeter (Check conversion here)
FINAL ANSWER
103.130434782609 ≈ 103.1304 Millimeter <-- Sproket Diameter of Pitch Circle
(Calculation completed in 00.004 seconds)
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Home » Physics » Design of Automobile Elements » Design of Chain Drives » Proportions of the Sprocket Wheel » Pitch Circle Diameter given Top Diameter of Sprocket Wheel

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Osmania University (OU), Hyderabad
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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

Pitch Circle Diameter given Top Diameter of Sprocket Wheel Formula

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
Ds = da-P*(1-(1.6/z))+2*R

Define a Roller Chain?

Roller chain or bush roller chain is the type of chain drive most commonly used for transmission of mechanical power on many kinds of domestic, industrial and agricultural machinery, including conveyors, wire- and tube-drawing machines, printing presses, cars, motorcycles, and bicycles.Roller chain or bush roller chain is the type of chain drive most commonly used for transmission of mechanical power on many kinds of domestic, industrial and agricultural machinery, including conveyors, wire- and tube-drawing machines, printing presses, cars, motorcycles, and bicycles.

How to Calculate Pitch Circle Diameter given Top Diameter of Sprocket Wheel?

Pitch Circle Diameter given Top Diameter of Sprocket Wheel calculator uses 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 to calculate the Sproket Diameter of Pitch Circle, The Pitch Circle Diameter given Top Diameter of Sprocket Wheel formula is defined as diameter of circle which passes through centre of all studs, wheel bolts or wheel rim holes. Sproket Diameter of Pitch Circle is denoted by Ds symbol.

How to calculate Pitch Circle Diameter given Top Diameter of Sprocket Wheel using this online calculator? To use this online calculator for Pitch Circle Diameter given Top Diameter of Sprocket Wheel, enter Top Diameter of Sprocket Wheel (da), Pitch of Chain (P), Number of teeth on sprocket (z) & Roller Radius of Chain (R) and hit the calculate button. Here is how the Pitch Circle Diameter given Top Diameter of Sprocket Wheel calculation can be explained with given input values -> 103130.4 = 0.112-0.022*(1-(1.6/23))+2*0.0058.

FAQ

What is Pitch Circle Diameter given Top Diameter of Sprocket Wheel?
The Pitch Circle Diameter given Top Diameter of Sprocket Wheel formula is defined as diameter of circle which passes through centre of all studs, wheel bolts or wheel rim holes and is represented as Ds = da-P*(1-(1.6/z))+2*R or 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 is the diameter of the top part or the outermost part of a sprocket wheel, 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, 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) & Roller Radius of Chain is the distance between the center and the point on the circumference of the roller of a chain.
How to calculate Pitch Circle Diameter given Top Diameter of Sprocket Wheel?
The Pitch Circle Diameter given Top Diameter of Sprocket Wheel formula is defined as diameter of circle which passes through centre of all studs, wheel bolts or wheel rim holes is calculated using 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. To calculate Pitch Circle Diameter given Top Diameter of Sprocket Wheel, you need Top Diameter of Sprocket Wheel (da), Pitch of Chain (P), Number of teeth on sprocket (z) & Roller Radius of Chain (R). With our tool, you need to enter the respective value for Top Diameter of Sprocket Wheel, Pitch of Chain, Number of teeth on sprocket & Roller Radius of Chain 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 Sproket Diameter of Pitch Circle?
In this formula, Sproket Diameter of Pitch Circle uses Top Diameter of Sprocket Wheel, Pitch of Chain, Number of teeth on sprocket & Roller Radius of Chain. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Sproket Diameter of Pitch Circle = Pitch of Chain/sin(3.035/Number of teeth on sprocket)
  • Sproket Diameter of Pitch Circle = Root Diameter of Sprocket Wheel+2*Roller Seating Radius
  • Sproket Diameter of Pitch Circle = Average Chain Velocity*60/(pi*Speed of chain drive shaft in rpm)
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