Contact Ratio Calculator

✖The path of contact is the path traced by the contact point of a pair of tooth profiles.ⓘ Path of Contact [P]			+10% -10%
✖A circular pitch is the distance along the pitch circle or pitch line between corresponding profiles of adjacent teeth.ⓘ Circular Pitch [P_c]			+10% -10%

✖The contact ratio represents the average number of teeth meshing at the same time.ⓘ Contact Ratio [CR]

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Contact Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Contact Ratio = Path of Contact/Circular Pitch
CR = P/P_c
This formula uses 3 Variables

Variables Used

Contact Ratio - The contact ratio represents the average number of teeth meshing at the same time.
Path of Contact - (Measured in Meter) - The path of contact is the path traced by the contact point of a pair of tooth profiles.
Circular Pitch - (Measured in Meter) - A circular pitch is the distance along the pitch circle or pitch line between corresponding profiles of adjacent teeth.

STEP 1: Convert Input(s) to Base Unit

Path of Contact: 18 Millimeter --> 0.018 Meter (Check conversion here)
Circular Pitch: 16 Millimeter --> 0.016 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

CR = P/P_c --> 0.018/0.016

Evaluating ... ...

CR = 1.125

STEP 3: Convert Result to Output's Unit

1.125 --> No Conversion Required

FINAL ANSWER

1.125 <-- Contact Ratio

(Calculation completed in 00.004 seconds)

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< Toothed Gear Terminologies Calculators

Addendum of Pinion

LaTeX Go Addendum of Pinion = Number of Teeth on Pinion/2*(sqrt(1+Number of Teeth on Wheel/Number of Teeth on Pinion*(Number of Teeth on Wheel/Number of Teeth on Pinion+2)*(sin(Pressure Angle of Gear))^2)-1)

Work Output on Driven

LaTeX Go Work Output = Resultant Reaction at Point of Contact*cos(Spiral Angle of Gear Teeth for Gear 2+Angle of Friction)*pi*Pitch Circle Diameter of Gear 2*Speed of Gear 2

Work Output on Driver

LaTeX Go Work Output = Resultant Reaction at Point of Contact*cos(Spiral Angle of Gear Teeth for Gear 1-Angle of Friction)*pi*Pitch Circle Diameter of Gear 1*Speed of Gear 1

Torque Exerted on Gear Shaft

LaTeX Go Torque Exerted on Wheel = Tangential Force*Diameter of Pitch Circle/2

Contact Ratio Formula

LaTeX Go

Contact Ratio = Path of Contact/Circular Pitch
CR = P/P_c

What is length of path of contact?

Path of contact is the locus of the point of contact on two mating teeth from the beginning of engagement to the end of it. Thus CD is the path of contact. It is also called as contact length. It is the tangent to both the base circles and passes through the pitch point.

How is circular pitch calculated?

Circular Circular pitch is the distance from a point on one tooth to the corresponding point on the next tooth measured along the pitch circle. Its value is equal to the circumference of the pitch circle divided by the number of teeth in the gear.

How to Calculate Contact Ratio?

Contact Ratio calculator uses Contact Ratio = Path of Contact/Circular Pitch to calculate the Contact Ratio, Contact Ratio formula is defined as a dimensionless quantity that characterizes the tooth overlap in a gear mesh, providing a measure of the extent to which the teeth of one gear overlap with those of another gear in a toothed gear system. Contact Ratio is denoted by CR symbol.

How to calculate Contact Ratio using this online calculator? To use this online calculator for Contact Ratio, enter Path of Contact (P) & Circular Pitch (P_c) and hit the calculate button. Here is how the Contact Ratio calculation can be explained with given input values -> 1.125 = 0.018/0.016.

FAQ

What is Contact Ratio?

Contact Ratio formula is defined as a dimensionless quantity that characterizes the tooth overlap in a gear mesh, providing a measure of the extent to which the teeth of one gear overlap with those of another gear in a toothed gear system and is represented as CR = P/P_c or Contact Ratio = Path of Contact/Circular Pitch. The path of contact is the path traced by the contact point of a pair of tooth profiles & A circular pitch is the distance along the pitch circle or pitch line between corresponding profiles of adjacent teeth.

How to calculate Contact Ratio?

Contact Ratio formula is defined as a dimensionless quantity that characterizes the tooth overlap in a gear mesh, providing a measure of the extent to which the teeth of one gear overlap with those of another gear in a toothed gear system is calculated using Contact Ratio = Path of Contact/Circular Pitch. To calculate Contact Ratio, you need Path of Contact (P) & Circular Pitch (P_c). With our tool, you need to enter the respective value for Path of Contact & Circular Pitch 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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