Pitch Circle Diameter given Pitch Solution

STEP 0: Pre-Calculation Summary
Formula Used
Sproket Diameter of Pitch Circle = Pitch of Chain/sin(3.035/Number of teeth on sprocket)
Ds = P/sin(3.035/z)
This formula uses 1 Functions, 3 Variables
Functions Used
sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
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.
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).
STEP 1: Convert Input(s) to Base Unit
Pitch of Chain: 22 Millimeter --> 0.022 Meter (Check conversion here)
Number of teeth on sprocket: 23 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Ds = P/sin(3.035/z) --> 0.022/sin(3.035/23)
Evaluating ... ...
Ds = 0.16720640683947
STEP 3: Convert Result to Output's Unit
0.16720640683947 Meter -->167.20640683947 Millimeter (Check conversion here)
FINAL ANSWER
167.20640683947 โ‰ˆ 167.2064 Millimeter <-- Sproket Diameter of Pitch Circle
(Calculation completed in 00.004 seconds)

Credits

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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 Pitch Formula

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

Define 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 Pitch Circle Diameter given Pitch?

Pitch Circle Diameter given Pitch calculator uses Sproket Diameter of Pitch Circle = Pitch of Chain/sin(3.035/Number of teeth on sprocket) to calculate the Sproket Diameter of Pitch Circle, The Pitch Circle Diameter given Pitch formula is defined as the diameter of the circle which passes through the centre of all the studs, wheel bolts or wheel rim holes. Sproket Diameter of Pitch Circle is denoted by Ds symbol.

How to calculate Pitch Circle Diameter given Pitch using this online calculator? To use this online calculator for Pitch Circle Diameter given Pitch, enter Pitch of Chain (P) & Number of teeth on sprocket (z) and hit the calculate button. Here is how the Pitch Circle Diameter given Pitch calculation can be explained with given input values -> 167206.4 = 0.022/sin(3.035/23).

FAQ

What is Pitch Circle Diameter given Pitch?
The Pitch Circle Diameter given Pitch formula is defined as the diameter of the circle which passes through the centre of all the studs, wheel bolts or wheel rim holes and is represented as Ds = P/sin(3.035/z) or Sproket Diameter of Pitch Circle = Pitch of Chain/sin(3.035/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 & 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 Pitch Circle Diameter given Pitch?
The Pitch Circle Diameter given Pitch formula is defined as the diameter of the circle which passes through the centre of all the studs, wheel bolts or wheel rim holes is calculated using Sproket Diameter of Pitch Circle = Pitch of Chain/sin(3.035/Number of teeth on sprocket). To calculate Pitch Circle Diameter given Pitch, you need Pitch of Chain (P) & Number of teeth on sprocket (z). With our tool, you need to enter the respective value for Pitch 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.
How many ways are there to calculate Sproket Diameter of Pitch Circle?
In this formula, Sproket Diameter of Pitch Circle uses Pitch of Chain & Number of teeth on sprocket. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • 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
  • 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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