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Maximum Length of Arc of Approach Formula

GoLength of Arc of Contact Formula

GoMaximum Length of Arc of Contact Formula

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Length of Arc of Contact is the ratio of length of path of contact and the cosine of the pressure angle. Check FAQs

L = (R w + r) \cdot \tan (Φ g)

L - Length of Arc 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 Arc of Approach Example

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Here is how the Maximum Length of Arc of Approach equation looks like with Values.

Here is how the Maximum Length of Arc of Approach equation looks like with Units.

Here is how the Maximum Length of Arc of Approach equation looks like.

14.122 = (12.4 + 10.2) \cdot \tan (32)

14.122mm = (12.4mm + 10.2mm) \cdot \tan (32°)

14.122 = (12.4 + 10.2) \cdot \tan (32)

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Maximum Length of Arc of Approach Solution

Follow our step by step solution on how to calculate Maximum Length of Arc of Approach?

FIRST Step Consider the formula

L = (R w + r) \cdot \tan (Φ g)

Next Step Substitute values of Variables

∴

L = (12.4mm + 10.2mm) \cdot \tan (32°)

Next Step Convert Units

∴

L = (0.0124m + 0.0102m) \cdot \tan (0.5585rad)

Next Step Prepare to Evaluate

∴

L = (0.0124 + 0.0102) \cdot \tan (0.5585)

Next Step Evaluate

∴

L = 0.0141220473531475m

Next Step Convert to Output's Unit

∴

L = 14.1220473531475mm

LAST Step Rounding Answer

∴

L = 14.122mm

Maximum Length of Arc of Approach Formula Elements

Variables

Functions

Length of Arc of Contact

Length of Arc of Contact is the ratio of length of path of contact and the cosine of the pressure angle.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Arc 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

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

Other Formulas to find Length of Arc of Contact

Go Length of Arc of Contact

L = \frac{P}{\cos (Φ g)}

Go Maximum Length of Arc of Contact

L = (r + R w) \cdot \tan (α)

Other formulas in Length category

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 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)

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 Arc of Approach?

Maximum Length of Arc of Approach evaluator uses Length of Arc of Contact = (Radius of Pitch Circle of Wheel+Radius of Pitch Circle of Pinion)*tan(Pressure Angle of Gear) to evaluate the Length of Arc of Contact, Maximum Length of Arc of Approach formula is defined as the distance measured along the curve of a gear tooth from the starting point of engagement to the point where the gear tooth reaches its highest point of single tooth contact. Length of Arc of Contact is denoted by L symbol.

How to evaluate Maximum Length of Arc of Approach using this online evaluator? To use this online evaluator for Maximum Length of Arc of Approach, 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 Arc of Approach

What is the formula to find Maximum Length of Arc of Approach?

The formula of Maximum Length of Arc of Approach is expressed as Length of Arc of Contact = (Radius of Pitch Circle of Wheel+Radius of Pitch Circle of Pinion)*tan(Pressure Angle of Gear). Here is an example- 14122.05 = (0.0124+0.0102)*tan(0.55850536063808).

How to calculate Maximum Length of Arc of Approach?

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 Arc of Approach using the formula - Length of Arc of Contact = (Radius of Pitch Circle of Wheel+Radius of Pitch Circle of Pinion)*tan(Pressure Angle of Gear). This formula also uses Tangent (tan) function(s).

What are the other ways to Calculate Length of Arc of Contact?

Here are the different ways to Calculate Length of Arc of Contact-

Length of Arc of Contact=Path of Contact/cos(Pressure Angle of Gear)
Length of Arc of Contact=(Radius of Pitch Circle of Pinion+Radius of Pitch Circle of Wheel)*tan(Pressure Angle Of 2 Gears)

Can the Maximum Length of Arc of Approach be negative?

Yes, the Maximum Length of Arc of Approach, measured in Length can be negative.

Which unit is used to measure Maximum Length of Arc of Approach?

Maximum Length of Arc of Approach 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 Arc of Approach can be measured.

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Maximum Length of Arc of Approach Formula

​GoLength of Arc of Contact Formula

​GoMaximum Length of Arc of Contact Formula

Maximum Length of Arc of Approach Example

Maximum Length of Arc of Approach Solution

Maximum Length of Arc of Approach Formula Elements

Other Formulas to find Length of Arc of Contact

Other formulas in Length category

How to Evaluate Maximum Length of Arc of Approach?

FAQs on Maximum Length of Arc of Approach

Variable Name

GoLength of Arc of Contact Formula

GoMaximum Length of Arc of Contact Formula