Shaft Angle Calculator

✖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.ⓘ Spiral Angle of Gear Teeth for Gear 1 [α₁]			+10% -10%
✖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.ⓘ Spiral Angle of Gear Teeth for Gear 2 [α₂]			+10% -10%

✖Shaft angle is the measurement of the angle formed between the obliquely oriented neck with the vertical shaft.ⓘ Shaft Angle [θ]

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Formula

✖

Shaft Angle

Formula

`"θ" = "α"_{"1"}+"α"_{"2"}`

Example

`"75.05°"="45°"+"30.05°"`

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Shaft Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Shaft Angle = Spiral Angle of Gear Teeth for Gear 1+Spiral Angle of Gear Teeth for Gear 2
θ = α₁+α₂
This formula uses 3 Variables

Variables Used

Shaft Angle - (Measured in Radian) - Shaft angle is the measurement of the angle formed between the obliquely oriented neck with the vertical shaft.
Spiral Angle of Gear Teeth for Gear 1 - (Measured in Radian) - 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.
Spiral Angle of Gear Teeth for Gear 2 - (Measured in Radian) - 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.

STEP 1: Convert Input(s) to Base Unit

Spiral Angle of Gear Teeth for Gear 1: 45 Degree --> 0.785398163397301 Radian (Check conversion here)
Spiral Angle of Gear Teeth for Gear 2: 30.05 Degree --> 0.524471440224197 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = α₁+α₂ --> 0.785398163397301+0.524471440224197

Evaluating ... ...

θ = 1.3098696036215

STEP 3: Convert Result to Output's Unit

1.3098696036215 Radian -->75.05 Degree (Check conversion here)

FINAL ANSWER

75.05 Degree <-- Shaft Angle

(Calculation completed in 00.004 seconds)

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< 22 Toothed Gear Terminologies Calculators

Efficiency of Spiral Gears using Pitch Circle Diameter

Go Efficiency = (cos(Spiral Angle of Gear Teeth for Gear 2+Angle of Friction)*Pitch Circle Diameter of Gear 2*Speed of Gear 2)/(cos(Spiral Angle of Gear Teeth for Gear 1-Angle of Friction)*Pitch Circle Diameter of Gear 1*Speed of Gear 1)

Efficiency of Spiral Gears

Go Efficiency = (cos(Spiral Angle of Gear Teeth for Gear 2+Angle of Friction)*cos(Spiral Angle of Gear Teeth for Gear 1))/(cos(Spiral Angle of Gear Teeth for Gear 1-Angle of Friction)*cos(Spiral Angle of Gear Teeth for Gear 2))

Addendum of Pinion

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)

Addendum of Wheel

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

Work Output on Driven

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

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

Maximum Efficiency of Spiral Gears

Go Efficiency = (cos(Shaft Angle+Angle of Friction)+1)/(cos(Shaft Angle-Angle of Friction)+1)

Resisting Force Acting Tangentially on Driven

Go Resisting Force acting Tangentially on Driven = Resultant Reaction at Point of Contact*cos(Spiral Angle of Gear Teeth for Gear 2+Angle of Friction)

Force Applied Tangentially on Driver

Go Force Applied Tangentially on Driver = Resultant Reaction at Point of Contact*cos(Spiral Angle of Gear Teeth for Gear 1-Angle of Friction)

Axial Thrust on Driven

Go Axial Thrust on Driven = Resisting Force acting Tangentially on Driven*tan(Spiral Angle of Gear Teeth for Gear 2)

Axial Thrust on Driver

Go Axial Thrust on Driver = Force Applied Tangentially on Driver*tan(Spiral Angle of Gear Teeth for Gear 1)

Radius of Base Circle of Pinion

Go Radius of Base Circle of Pinion = Radius of Pitch Circle of Pinion*cos(Pressure Angle of Gear)

Radius of Base Circle of Wheel

Go Radius of Base Circle of Wheel = Radius of Pitch Circle of Wheel*cos(Pressure Angle of Gear)

Addendum of Rack

Go Addendum of Rack = (Number of Teeth on Pinion*(sin(Pressure Angle of Gear))^2)/2

Tangential Force on Gear Shaft

Go Tangential Force = Maximum Tooth Pressure*cos(Pressure Angle of Gear)

Normal Force on Gear Shaft

Go Normal Force = Maximum Tooth Pressure*sin(Pressure Angle of Gear)

Shaft Angle

Go Shaft Angle = Spiral Angle of Gear Teeth for Gear 1+Spiral Angle of Gear Teeth for Gear 2

Gear Ratio

Go Gear Ratio = Radius of Pitch Circle of Wheel/Radius of Pitch Circle of Pinion

Torque Exerted on Gear Shaft

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

Gear Ratio given Number of Teeth on Wheel and Pinion

Go Gear Ratio = Number of Teeth on Wheel/Number of Teeth on Pinion

Module

Go Module = Diameter of Pitch Circle/Number of Teeth on Wheel

Contact Ratio

Go Contact Ratio = Path of Contact/Circular Pitch

Shaft Angle Formula

Shaft Angle = Spiral Angle of Gear Teeth for Gear 1+Spiral Angle of Gear Teeth for Gear 2
θ = α₁+α₂

What is a gear shaft?

The gear shaft is the axle of the gear, providing the rotation that allows one gear to engage with and turn another. The process is often known as gear reduction and is essential to transferring horsepower from the engine to the drive mechanism.

How to Calculate Shaft Angle?

Shaft Angle calculator uses Shaft Angle = Spiral Angle of Gear Teeth for Gear 1+Spiral Angle of Gear Teeth for Gear 2 to calculate the Shaft Angle, Shaft angle is the measurement of the angle formed between the obliquely oriented neck with the vertical shaft. Shaft Angle is denoted by θ symbol.

How to calculate Shaft Angle using this online calculator? To use this online calculator 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. Here is how the Shaft Angle calculation can be explained with given input values -> 4300.048 = 0.785398163397301+0.524471440224197.

FAQ

What is Shaft Angle?

Shaft angle is the measurement of the angle formed between the obliquely oriented neck with the vertical shaft and is represented as θ = α₁+α₂ or Shaft Angle = Spiral Angle of Gear Teeth for Gear 1+Spiral Angle of Gear Teeth for Gear 2. 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 & 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.

How to calculate Shaft Angle?

Shaft angle is the measurement of the angle formed between the obliquely oriented neck with the vertical shaft is calculated using Shaft Angle = Spiral Angle of Gear Teeth for Gear 1+Spiral Angle of Gear Teeth for Gear 2. To calculate Shaft Angle, you need Spiral Angle of Gear Teeth for Gear 1 (α₁) & Spiral Angle of Gear Teeth for Gear 2 (α₂). With our tool, you need to enter the respective value for Spiral Angle of Gear Teeth for Gear 1 & Spiral Angle of Gear Teeth for Gear 2 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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