FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Maximum Efficiency of Spiral Gears Formula

GoEfficiency of Spiral Gears Formula

GoEfficiency of Spiral Gears using Pitch Circle Diameter Formula

Fx Copy

LaTeX Copy

The Efficiency of an electric motor is defined as the ratio of usable shaft power to electric input power. Check FAQs

η = \frac{\cos (θ + Φ) + 1}{\cos (θ - Φ) + 1}

η - Efficiency?θ - Shaft Angle?Φ - Angle of Friction?

Maximum Efficiency of Spiral Gears Example

With values

With units

Only example

Here is how the Maximum Efficiency of Spiral Gears equation looks like with Values.

Here is how the Maximum Efficiency of Spiral Gears equation looks like with Units.

Here is how the Maximum Efficiency of Spiral Gears equation looks like.

0.8024 = \frac{\cos (29 + 24) + 1}{\cos (29 - 24) + 1}

0.8024 = \frac{\cos (29° + 24°) + 1}{\cos (29° - 24°) + 1}

0.8024 = \frac{\cos (29 + 24) + 1}{\cos (29 - 24) + 1}

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Physics » Category

Mechanical » Category

Theory of Machine » fx Maximum Efficiency of Spiral Gears

Maximum Efficiency of Spiral Gears Solution

Follow our step by step solution on how to calculate Maximum Efficiency of Spiral Gears?

FIRST Step Consider the formula

η = \frac{\cos (θ + Φ) + 1}{\cos (θ - Φ) + 1}

Next Step Substitute values of Variables

∴

η = \frac{\cos (29° + 24°) + 1}{\cos (29° - 24°) + 1}

Next Step Convert Units

∴

η = \frac{\cos (0.5061rad + 0.4189rad) + 1}{\cos (0.5061rad - 0.4189rad) + 1}

Next Step Prepare to Evaluate

∴

η = \frac{\cos (0.5061 + 0.4189) + 1}{\cos (0.5061 - 0.4189) + 1}

Next Step Evaluate

∴

η = 0.802434263893915

LAST Step Rounding Answer

∴

η = 0.8024

Maximum Efficiency of Spiral Gears Formula Elements

Variables

Functions

Efficiency

The Efficiency of an electric motor is defined as the ratio of usable shaft power to electric input power.

Symbol: η

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Efficiency

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

Angle of Friction

The angle of friction is the angle of a plane to the horizontal when a body placed on the plane will just start to slide.

Symbol: Φ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Friction

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other Formulas to find Efficiency

Go Efficiency of Spiral Gears

η = \frac{\cos (α 2 + Φ) \cdot \cos (α 1)}{\cos (α 1 - Φ) \cdot \cos (α 2)}

Go Efficiency of Spiral Gears using Pitch Circle Diameter

η = \frac{\cos (α 2 + Φ) \cdot d 2 \cdot N 2}{\cos (α 1 - Φ) \cdot d 1 \cdot N 1}

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 Maximum Efficiency of Spiral Gears?

Maximum Efficiency of Spiral Gears evaluator uses Efficiency = (cos(Shaft Angle+Angle of Friction)+1)/(cos(Shaft Angle-Angle of Friction)+1) to evaluate the Efficiency, Maximum Efficiency of Spiral Gears formula is defined as a measure of the optimal performance of spiral gears in transmitting power, taking into account the angle of friction and the pressure angle, to determine the maximum efficiency of the gear system in various mechanical applications. Efficiency is denoted by η symbol.

How to evaluate Maximum Efficiency of Spiral Gears using this online evaluator? To use this online evaluator for Maximum Efficiency of Spiral Gears, enter Shaft Angle (θ) & Angle of Friction (Φ) and hit the calculate button.

FAQs on Maximum Efficiency of Spiral Gears

What is the formula to find Maximum Efficiency of Spiral Gears?

The formula of Maximum Efficiency of Spiral Gears is expressed as Efficiency = (cos(Shaft Angle+Angle of Friction)+1)/(cos(Shaft Angle-Angle of Friction)+1). Here is an example- 0.802434 = (cos(0.50614548307826+0.41887902047856)+1)/(cos(0.50614548307826-0.41887902047856)+1).

How to calculate Maximum Efficiency of Spiral Gears?

With Shaft Angle (θ) & Angle of Friction (Φ) we can find Maximum Efficiency of Spiral Gears using the formula - Efficiency = (cos(Shaft Angle+Angle of Friction)+1)/(cos(Shaft Angle-Angle of Friction)+1). This formula also uses Cosine function(s).

What are the other ways to Calculate Efficiency?

Here are the different ways to Calculate Efficiency-

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))
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)

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit

Maximum Efficiency of Spiral Gears Formula

​GoEfficiency of Spiral Gears Formula

​GoEfficiency of Spiral Gears using Pitch Circle Diameter Formula

Maximum Efficiency of Spiral Gears Example

Maximum Efficiency of Spiral Gears Solution

Maximum Efficiency of Spiral Gears Formula Elements

Other Formulas to find Efficiency

Other formulas in Toothed Gear Terminologies category

How to Evaluate Maximum Efficiency of Spiral Gears?

FAQs on Maximum Efficiency of Spiral Gears

Variable Name

GoEfficiency of Spiral Gears Formula

GoEfficiency of Spiral Gears using Pitch Circle Diameter Formula