Number of Teeth given Maximum Roller Seating Angle Calculator

✖Maximum Roller Seating Angle is the angle at which the roller seats on the sprocket wheel, affecting the smooth transmission of power and motion.ⓘ Maximum Roller Seating Angle [α_max]

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✖Number of teeth on sprocket is the total count of teeth present on the circumference of the sprocket wheel, which affects the gear ratio and overall mechanism.ⓘ Number of Teeth given Maximum Roller Seating Angle [z]

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Formula

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Number of Teeth given Maximum Roller Seating Angle

Formula

z = \frac{90}{120 - (α max \cdot \frac{180}{π})}

Example

18 = \frac{90}{120 - (115 ° \cdot \frac{180}{π})}

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Number of Teeth given Maximum Roller Seating Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of Teeth on Sprocket = 90/(120-(Maximum Roller Seating Angle*180/pi))
z = 90/(120-(α_max*180/pi))
This formula uses 1 Constants, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Number of Teeth on Sprocket - Number of teeth on sprocket is the total count of teeth present on the circumference of the sprocket wheel, which affects the gear ratio and overall mechanism.
Maximum Roller Seating Angle - (Measured in Radian) - Maximum Roller Seating Angle is the angle at which the roller seats on the sprocket wheel, affecting the smooth transmission of power and motion.

STEP 1: Convert Input(s) to Base Unit

Maximum Roller Seating Angle: 115 Degree --> 2.0071286397931 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

z = 90/(120-(α_max*180/pi)) --> 90/(120-(2.0071286397931*180/pi))

Evaluating ... ...

z = 17.9999999999219

STEP 3: Convert Result to Output's Unit

17.9999999999219 --> No Conversion Required

FINAL ANSWER

17.9999999999219 ≈ 18 <-- Number of Teeth on Sprocket

(Calculation completed in 00.020 seconds)

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Home » Physics » Design of Automobile Elements » Design of Chain Drives » Mechanical » Proportions of the Sprocket Wheel » Number of Teeth given Maximum Roller Seating Angle

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

Kethavath Srinath has created this Calculator and 1000+ more calculators!

Verified by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

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< Proportions of the Sprocket Wheel Calculators

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

Pitch Circle Diameter given Pitch

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

Number of Teeth on Sprocket given Pitch Angle of Sprocket

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

Pitch Angle of Sprocket

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

Number of Teeth given Maximum Roller Seating Angle Formula

Number of Teeth on Sprocket = 90/(120-(Maximum Roller Seating Angle*180/pi))
z = 90/(120-(α_max*180/pi))

What is Maximum Roller Seating Angle?

The maximum roller seating angle is the greatest angle at which the chain roller can effectively contact the sprocket tooth without causing excessive stress or improper engagement. This angle is crucial for ensuring smooth operation, minimizing wear, and maintaining efficient power transmission in the chain drive system.

How to Calculate Number of Teeth given Maximum Roller Seating Angle?

Number of Teeth given Maximum Roller Seating Angle calculator uses Number of Teeth on Sprocket = 90/(120-(Maximum Roller Seating Angle*180/pi)) to calculate the Number of Teeth on Sprocket, Number of Teeth given Maximum Roller Seating Angle formula is defined as a method to determine the optimal number of teeth on a gear or roller, considering the maximum roller seating angle, to ensure efficient and smooth mechanical operation. Number of Teeth on Sprocket is denoted by z symbol.

How to calculate Number of Teeth given Maximum Roller Seating Angle using this online calculator? To use this online calculator for Number of Teeth given Maximum Roller Seating Angle, enter Maximum Roller Seating Angle (α_max) and hit the calculate button. Here is how the Number of Teeth given Maximum Roller Seating Angle calculation can be explained with given input values -> 18 = 90/(120-(2.0071286397931*180/pi)).

FAQ

What is Number of Teeth given Maximum Roller Seating Angle?

Number of Teeth given Maximum Roller Seating Angle formula is defined as a method to determine the optimal number of teeth on a gear or roller, considering the maximum roller seating angle, to ensure efficient and smooth mechanical operation and is represented as z = 90/(120-(α_max*180/pi)) or Number of Teeth on Sprocket = 90/(120-(Maximum Roller Seating Angle*180/pi)). Maximum Roller Seating Angle is the angle at which the roller seats on the sprocket wheel, affecting the smooth transmission of power and motion.

How to calculate Number of Teeth given Maximum Roller Seating Angle?

Number of Teeth given Maximum Roller Seating Angle formula is defined as a method to determine the optimal number of teeth on a gear or roller, considering the maximum roller seating angle, to ensure efficient and smooth mechanical operation is calculated using Number of Teeth on Sprocket = 90/(120-(Maximum Roller Seating Angle*180/pi)). To calculate Number of Teeth given Maximum Roller Seating Angle, you need Maximum Roller Seating Angle (α_max). With our tool, you need to enter the respective value for Maximum Roller Seating Angle 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 Number of Teeth on Sprocket?

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

Number of Teeth on Sprocket = 360/(Pitch Angle of Sprocket*(180/pi))
Number of Teeth on Sprocket = (Minimum Tooth Flank Radius/(0.24*Roller Radius of Chain))-2
Number of Teeth on Sprocket = 90/(140-(Minimum Roller Seating Angle*180/pi))

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