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Contact Ratio Formula

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The contact ratio represents the average number of teeth meshing at the same time. Check FAQs

CR = \frac{P}{P c}

CR - Contact Ratio?P - Path of Contact?P_c - Circular Pitch?

Contact Ratio Example

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With units

Only example

Here is how the Contact Ratio equation looks like with Values.

Here is how the Contact Ratio equation looks like with Units.

Here is how the Contact Ratio equation looks like.

1.125 = \frac{18}{16}

1.125 = \frac{18mm}{16mm}

1.125 = \frac{18}{16}

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Contact Ratio Solution

Follow our step by step solution on how to calculate Contact Ratio?

FIRST Step Consider the formula

CR = \frac{P}{P c}

Next Step Substitute values of Variables

∴

CR = \frac{18mm}{16mm}

Next Step Convert Units

∴

CR = \frac{0.018m}{0.016m}

Next Step Prepare to Evaluate

∴

CR = \frac{0.018}{0.016}

LAST Step Evaluate

∴

CR = 1.125

Contact Ratio Formula Elements

Variables

Contact Ratio

The contact ratio represents the average number of teeth meshing at the same time.

Symbol: CR

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Contact Ratio

Path of Contact

The path of contact is the path traced by the contact point of a pair of tooth profiles.

Symbol: P

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Path of Contact

Circular Pitch

A circular pitch is the distance along the pitch circle or pitch line between corresponding profiles of adjacent teeth.

Symbol: P_c

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Circular Pitch

Other formulas in Toothed Gear Terminologies category

Go Torque Exerted on Gear Shaft

τ = P t \cdot \frac{d pitch circle}{2}

Go Work Output on Driven

w = R \cdot \cos (α 2 + Φ) \cdot π \cdot d 2 \cdot N 2

Go Work Output on Driver

w = R \cdot \cos (α 1 - Φ) \cdot π \cdot d 1 \cdot N 1

Go Addendum of Pinion

A p = \frac{Z p}{2} \cdot (\sqrt{1 + \frac{T}{Z p} \cdot (\frac{T}{Z p} + 2) \cdot {(\sin (Φ gear))}^{2}} - 1)

How to Evaluate Contact Ratio?

Contact Ratio evaluator uses Contact Ratio = Path of Contact/Circular Pitch to evaluate 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 evaluate Contact Ratio using this online evaluator? To use this online evaluator for Contact Ratio, enter Path of Contact (P) & Circular Pitch (P_c) and hit the calculate button.

FAQs on Contact Ratio

What is the formula to find Contact Ratio?

The formula of Contact Ratio is expressed as Contact Ratio = Path of Contact/Circular Pitch. Here is an example- 1.125 = 0.018/0.016.

How to calculate Contact Ratio?

With Path of Contact (P) & Circular Pitch (P_c) we can find Contact Ratio using the formula - Contact Ratio = Path of Contact/Circular Pitch.

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