Tooth Flank Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Sprocket Tooth Flank Radius = 0.016*Roller Radius of Chain*((Number of teeth on sprocket)^2+180)
Re = 0.016*R*((z)^2+180)
This formula uses 3 Variables
Variables Used
Sprocket Tooth Flank Radius - (Measured in Meter) - Sprocket Tooth Flank Radius is the radius of curvature of the flanks of a sprocket tooth.
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
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
Re = 0.016*R*((z)^2+180) --> 0.016*0.0058*((23)^2+180)
Evaluating ... ...
Re = 0.0657952
STEP 3: Convert Result to Output's Unit
0.0657952 Meter -->65.7952 Millimeter (Check conversion here)
FINAL ANSWER
65.7952 Millimeter <-- Sprocket Tooth Flank Radius
(Calculation completed in 00.020 seconds)

Credits

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

Tooth Flank Radius Formula

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

Define Tooth Flank Radius?

In theory, the radius, , of the boundary N-circle is a trade-off between a desirable high contact strength and low friction between the teeth flanks of the gear, , and the pinion.

How to Calculate Tooth Flank Radius?

Tooth Flank Radius calculator uses Sprocket Tooth Flank Radius = 0.016*Roller Radius of Chain*((Number of teeth on sprocket)^2+180) to calculate the Sprocket Tooth Flank Radius, The Tooth Flank Radius formula is defined as a trade-off between a desirable high contact strength and low friction between the teeth flanks of the gear, , and the pinion. Sprocket Tooth Flank Radius is denoted by Re symbol.

How to calculate Tooth Flank Radius using this online calculator? To use this online calculator for Tooth Flank Radius, enter Roller Radius of Chain (R) & Number of teeth on sprocket (z) and hit the calculate button. Here is how the Tooth Flank Radius calculation can be explained with given input values -> 65795.2 = 0.016*0.0058*((23)^2+180).

FAQ

What is Tooth Flank Radius?
The Tooth Flank Radius formula is defined as a trade-off between a desirable high contact strength and low friction between the teeth flanks of the gear, , and the pinion and is represented as Re = 0.016*R*((z)^2+180) or Sprocket Tooth Flank Radius = 0.016*Roller Radius of Chain*((Number of teeth on sprocket)^2+180). 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 Tooth Flank Radius?
The Tooth Flank Radius formula is defined as a trade-off between a desirable high contact strength and low friction between the teeth flanks of the gear, , and the pinion is calculated using Sprocket Tooth Flank Radius = 0.016*Roller Radius of Chain*((Number of teeth on sprocket)^2+180). To calculate Tooth Flank Radius, you need Roller Radius of Chain (R) & Number of teeth on sprocket (z). With our tool, you need to enter the respective value for 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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