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Shaft Angle Formula

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Shaft angle is the measurement of the angle formed between the obliquely oriented neck with the vertical shaft. Check FAQs

θ = α 1 + α 2

θ - Shaft Angle?α₁ - Spiral Angle of Gear Teeth for Gear 1?α₂ - Spiral Angle of Gear Teeth for Gear 2?

Shaft Angle Example

With values

With units

Only example

Here is how the Shaft Angle equation looks like with Values.

Here is how the Shaft Angle equation looks like with Units.

Here is how the Shaft Angle equation looks like.

75.05 = 45 + 30.05

75.05° = 45° + 30.05°

75.05 = 45 + 30.05

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Shaft Angle Solution

Follow our step by step solution on how to calculate Shaft Angle?

FIRST Step Consider the formula

θ = α 1 + α 2

Next Step Substitute values of Variables

∴

θ = 45° + 30.05°

Next Step Convert Units

∴

θ = 0.7854rad + 0.5245rad

Next Step Prepare to Evaluate

∴

θ = 0.7854 + 0.5245

Next Step Evaluate

∴

θ = 1.3098696036215rad

LAST Step Convert to Output's Unit

∴

θ = 75.05°

Shaft Angle Formula Elements

Variables

Shaft Angle

Shaft angle is the measurement of the angle formed between the obliquely oriented neck with the vertical shaft.

Symbol: θ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Shaft Angle

Spiral Angle of Gear Teeth for Gear 1

The spiral angle of gear teeth for gear 1 is the angle between the tooth trace and an element of the pitch cone and corresponds to the helix angle in helical teeth.

Symbol: α₁

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Spiral Angle of Gear Teeth for Gear 1

Spiral Angle of Gear Teeth for Gear 2

The spiral angle of gear teeth for gear 2 is the angle between the tooth trace and an element of the pitch cone and corresponds to the helix angle in helical teeth.

Symbol: α₂

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Spiral Angle of Gear Teeth for Gear 2

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 Shaft Angle?

Shaft Angle evaluator uses Shaft Angle = Spiral Angle of Gear Teeth for Gear 1+Spiral Angle of Gear Teeth for Gear 2 to evaluate the Shaft Angle, Shaft Angle formula is defined as the total angle of rotation of a shaft in a toothed gear system, which is the sum of the angles of rotation of the individual gears, providing a critical parameter in the design and analysis of gear trains. Shaft Angle is denoted by θ symbol.

How to evaluate Shaft Angle using this online evaluator? To use this online evaluator for Shaft Angle, enter Spiral Angle of Gear Teeth for Gear 1 (α₁) & Spiral Angle of Gear Teeth for Gear 2 (α₂) and hit the calculate button.

FAQs on Shaft Angle

What is the formula to find Shaft Angle?

The formula of Shaft Angle is expressed as Shaft Angle = Spiral Angle of Gear Teeth for Gear 1+Spiral Angle of Gear Teeth for Gear 2. Here is an example- 4300.048 = 0.785398163397301+0.524471440224197.

How to calculate Shaft Angle?

With Spiral Angle of Gear Teeth for Gear 1 (α₁) & Spiral Angle of Gear Teeth for Gear 2 (α₂) we can find Shaft Angle using the formula - Shaft Angle = Spiral Angle of Gear Teeth for Gear 1+Spiral Angle of Gear Teeth for Gear 2.

Can the Shaft Angle be negative?

Yes, the Shaft Angle, measured in Angle can be negative.

Which unit is used to measure Shaft Angle?

Shaft Angle is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Shaft Angle can be measured.

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Shaft Angle Formula

Shaft Angle Example

Shaft Angle Solution

Shaft Angle Formula Elements

Other formulas in Toothed Gear Terminologies category

How to Evaluate Shaft Angle?

FAQs on Shaft Angle

Variable Name