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Maximum Length of Path of Contact Formula

GoLength of Path of Contact Formula

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Path of Contact is the path traced by the contact point of a pair of tooth profiles. Check FAQs

P = (R w + r) \cdot \sin (Φ g)

P - Path of Contact?R_w - Radius of Pitch Circle of Wheel?r - Radius of Pitch Circle of Pinion?Φ_g - Pressure Angle of Gear?

Maximum Length of Path of Contact Example

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Here is how the Maximum Length of Path of Contact equation looks like with Values.

Here is how the Maximum Length of Path of Contact equation looks like with Units.

Here is how the Maximum Length of Path of Contact equation looks like.

11.9762 = (12.4 + 10.2) \cdot \sin (32)

11.9762mm = (12.4mm + 10.2mm) \cdot \sin (32°)

11.9762 = (12.4 + 10.2) \cdot \sin (32)

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Maximum Length of Path of Contact Solution

Follow our step by step solution on how to calculate Maximum Length of Path of Contact?

FIRST Step Consider the formula

P = (R w + r) \cdot \sin (Φ g)

Next Step Substitute values of Variables

∴

P = (12.4mm + 10.2mm) \cdot \sin (32°)

Next Step Convert Units

∴

P = (0.0124m + 0.0102m) \cdot \sin (0.5585rad)

Next Step Prepare to Evaluate

∴

P = (0.0124 + 0.0102) \cdot \sin (0.5585)

Next Step Evaluate

∴

P = 0.0119761753716684m

Next Step Convert to Output's Unit

∴

P = 11.9761753716684mm

LAST Step Rounding Answer

∴

P = 11.9762mm

Maximum Length of Path of Contact Formula Elements

Variables

Functions

Path of Contact

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

Radius of Pitch Circle of Wheel

Radius of Pitch Circle of Wheel is radial distance of the tooth measuring from the pitch circle to the bottom of the tooth space.

Symbol: R_w

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Pitch Circle of Wheel

Radius of Pitch Circle of Pinion

Radius of Pitch Circle of Pinion is the radial distance of the tooth measuring from the pitch circle to the bottom of the tooth space.

Symbol: r

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Pitch Circle of Pinion

Pressure Angle of Gear

Pressure Angle of Gear also known as the angle of obliquity is the angle between the tooth face and the gear wheel tangent.

Symbol: Φ_g

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Pressure Angle of Gear

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.

Syntax: sin(Angle)

Other Formulas to find Path of Contact

Go Length of Path of Contact

P = \sqrt{{R a}^{2} - {R w}^{2} \cdot {(\cos (Φ g))}^{2}} + \sqrt{{r a}^{2} - r^{2} \cdot {(\cos (Φ g))}^{2}} - (R w + r) \cdot \sin (Φ g)

Other formulas in Length category

Go Length of Arc of Contact

L = \frac{P}{\cos (Φ g)}

Go Length of Path of Approach

P 1 = \sqrt{{R a}^{2} - {R w}^{2} \cdot {(\cos (Φ g))}^{2}} - R w \cdot \sin (Φ g)

Go Length of Path of Recess

P 2 = \sqrt{{r a}^{2} - r^{2} \cdot {(\cos (Φ g))}^{2}} - r \cdot \sin (Φ g)

Go Maximum Length of Path of Approach

P 1 = r \cdot \sin (Φ g)

How to Evaluate Maximum Length of Path of Contact?

Maximum Length of Path of Contact evaluator uses Path of Contact = (Radius of Pitch Circle of Wheel+Radius of Pitch Circle of Pinion)*sin(Pressure Angle of Gear) to evaluate the Path of Contact, Maximum Length of Path of Contact formula is defined as the distance measured along the path of contact between two interacting gears, considering the wheel radius, gear radius, and the angle of rotation, to determine the maximum possible length of contact between the gears. Path of Contact is denoted by P symbol.

How to evaluate Maximum Length of Path of Contact using this online evaluator? To use this online evaluator for Maximum Length of Path of Contact, enter Radius of Pitch Circle of Wheel (R_w), Radius of Pitch Circle of Pinion (r) & Pressure Angle of Gear (Φ_g) and hit the calculate button.

FAQs on Maximum Length of Path of Contact

What is the formula to find Maximum Length of Path of Contact?

The formula of Maximum Length of Path of Contact is expressed as Path of Contact = (Radius of Pitch Circle of Wheel+Radius of Pitch Circle of Pinion)*sin(Pressure Angle of Gear). Here is an example- 11976.18 = (0.0124+0.0102)*sin(0.55850536063808).

How to calculate Maximum Length of Path of Contact?

With Radius of Pitch Circle of Wheel (R_w), Radius of Pitch Circle of Pinion (r) & Pressure Angle of Gear (Φ_g) we can find Maximum Length of Path of Contact using the formula - Path of Contact = (Radius of Pitch Circle of Wheel+Radius of Pitch Circle of Pinion)*sin(Pressure Angle of Gear). This formula also uses Sine (sin) function(s).

What are the other ways to Calculate Path of Contact?

Here are the different ways to Calculate Path of Contact-

Path of Contact=sqrt(Radius of Addendum Circle of Wheel^2-Radius of Pitch Circle of Wheel^2*(cos(Pressure Angle of Gear))^2)+sqrt(Radius of Addendum Circle of Pinion^2-Radius of Pitch Circle of Pinion^2*(cos(Pressure Angle of Gear))^2)-(Radius of Pitch Circle of Wheel+Radius of Pitch Circle of Pinion)*sin(Pressure Angle of Gear)

Can the Maximum Length of Path of Contact be negative?

Yes, the Maximum Length of Path of Contact, measured in Length can be negative.

Which unit is used to measure Maximum Length of Path of Contact?

Maximum Length of Path of Contact is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Maximum Length of Path of Contact can be measured.

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Maximum Length of Path of Contact Formula

​GoLength of Path of Contact Formula

Maximum Length of Path of Contact Example

Maximum Length of Path of Contact Solution

Maximum Length of Path of Contact Formula Elements

Other Formulas to find Path of Contact

Other formulas in Length category

How to Evaluate Maximum Length of Path of Contact?

FAQs on Maximum Length of Path of Contact

Variable Name

GoLength of Path of Contact Formula