Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction Solution

STEP 0: Pre-Calculation Summary
Formula Used
Worm Gear Efficiency = (cos(Pressure Angle of Worm Gear)-Coefficient of Friction for Worm Gear*tan(Lead Angle of Worm))/(cos(Pressure Angle of Worm Gear)+Coefficient of Friction for Worm Gear*cot(Lead Angle of Worm))
η = (cos(Φ)-μ*tan(γ))/(cos(Φ)+μ*cot(γ))
This formula uses 3 Functions, 4 Variables
Functions Used
cos - Trigonometric cosine function, cos(Angle)
tan - Trigonometric tangent function, tan(Angle)
cot - Trigonometric cotangent function, cot(Angle)
Variables Used
Worm Gear Efficiency - Worm Gear Efficiency is simply the ratio of output power from the worm gear to the Input power to the gear.
Pressure Angle of Worm Gear - (Measured in Radian) - Pressure Angle of Worm Gear is known as the angle of obliquity is the angle between the tooth face and the gear wheel tangent.
Coefficient of Friction for Worm Gear - Coefficient of Friction for Worm Gear is the ratio defining the force that resists the motion of one body in relation to another body in contact with it.
Lead Angle of Worm - (Measured in Radian) - The Lead Angle of Worm is defined as the angle between a tangent to the thread at the pitch diameter and a plane normal to the worm axis.
STEP 1: Convert Input(s) to Base Unit
Pressure Angle of Worm Gear: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Coefficient of Friction for Worm Gear: 0.2 --> No Conversion Required
Lead Angle of Worm: 14.03 Degree --> 0.244869694054758 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
η = (cos(Φ)-μ*tan(γ))/(cos(Φ)+μ*cot(γ)) --> (cos(0.5235987755982)-0.2*tan(0.244869694054758))/(cos(0.5235987755982)+0.2*cot(0.244869694054758))
Evaluating ... ...
η = 0.489708646447362
STEP 3: Convert Result to Output's Unit
0.489708646447362 --> No Conversion Required
FINAL ANSWER
0.489708646447362 <-- Worm Gear Efficiency
(Calculation completed in 00.011 seconds)

Credits

Created by Ojas Kulkarni
Sardar Patel College of Engineering (SPCE), Mumbai
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7 Design of Worm Gear Calculators

Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction
Worm Gear Efficiency = (cos(Pressure Angle of Worm Gear)-Coefficient of Friction for Worm Gear*tan(Lead Angle of Worm))/(cos(Pressure Angle of Worm Gear)+Coefficient of Friction for Worm Gear*cot(Lead Angle of Worm)) Go
Rubbing speed of Worm Gear
Rubbing Speed of Worm Gear = pi*Pitch Circle Diameter of Worm Gear*Speed of Worm Gear/(60*cos(Lead Angle of Worm)) Go
Lead angle of Worm Gear given lead of worm and pitch circle diameter of worm
Lead Angle of Worm = atan(Lead of Worm/(pi*Pitch Circle Diameter of Worm Gear)) Go
Lead angle of Worm Gear given number of starts and diametral quotient
Lead Angle of Worm = atan(Number of starts on worm/Diametral Quotient) Go
Lead of Worm Gear given axial module and number of starts on worm
Lead of Worm = pi*Axial Module*Number of starts on worm Go
Diametral Quotient of Worm Gear
Diametral Quotient = Pitch Circle Diameter of Worm Gear/Axial Module Go
Lead of Worm Gear given axial pitch and number of starts on worm
Lead of Worm = Axial Pitch of Worm*Number of starts on worm Go

Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction Formula

Worm Gear Efficiency = (cos(Pressure Angle of Worm Gear)-Coefficient of Friction for Worm Gear*tan(Lead Angle of Worm))/(cos(Pressure Angle of Worm Gear)+Coefficient of Friction for Worm Gear*cot(Lead Angle of Worm))
η = (cos(Φ)-μ*tan(γ))/(cos(Φ)+μ*cot(γ))

What is the range of efficiency in worm gear?

The efficiency of worm gear typically ranges between 50% to 98%. The efficiency is inversely proportional to speed ratio, provided the coefficient of friction is constant.

How to Calculate Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction?

Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction calculator uses Worm Gear Efficiency = (cos(Pressure Angle of Worm Gear)-Coefficient of Friction for Worm Gear*tan(Lead Angle of Worm))/(cos(Pressure Angle of Worm Gear)+Coefficient of Friction for Worm Gear*cot(Lead Angle of Worm)) to calculate the Worm Gear Efficiency, Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction is simply calculated as the [output shaft power /Input shaft power]. The output power is the (input power - power losses). Power losses in gear systems are associated primarily with tooth friction and lubrication churning losses. Worm Gear Efficiency is denoted by η symbol.

How to calculate Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction using this online calculator? To use this online calculator for Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction, enter Pressure Angle of Worm Gear (Φ), Coefficient of Friction for Worm Gear (μ) & Lead Angle of Worm (γ) and hit the calculate button. Here is how the Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction calculation can be explained with given input values -> 0.489709 = (cos(0.5235987755982)-0.2*tan(0.244869694054758))/(cos(0.5235987755982)+0.2*cot(0.244869694054758)).

FAQ

What is Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction?
Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction is simply calculated as the [output shaft power /Input shaft power]. The output power is the (input power - power losses). Power losses in gear systems are associated primarily with tooth friction and lubrication churning losses and is represented as η = (cos(Φ)-μ*tan(γ))/(cos(Φ)+μ*cot(γ)) or Worm Gear Efficiency = (cos(Pressure Angle of Worm Gear)-Coefficient of Friction for Worm Gear*tan(Lead Angle of Worm))/(cos(Pressure Angle of Worm Gear)+Coefficient of Friction for Worm Gear*cot(Lead Angle of Worm)). Pressure Angle of Worm Gear is known as the angle of obliquity is the angle between the tooth face and the gear wheel tangent, Coefficient of Friction for Worm Gear is the ratio defining the force that resists the motion of one body in relation to another body in contact with it & The Lead Angle of Worm is defined as the angle between a tangent to the thread at the pitch diameter and a plane normal to the worm axis.
How to calculate Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction?
Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction is simply calculated as the [output shaft power /Input shaft power]. The output power is the (input power - power losses). Power losses in gear systems are associated primarily with tooth friction and lubrication churning losses is calculated using Worm Gear Efficiency = (cos(Pressure Angle of Worm Gear)-Coefficient of Friction for Worm Gear*tan(Lead Angle of Worm))/(cos(Pressure Angle of Worm Gear)+Coefficient of Friction for Worm Gear*cot(Lead Angle of Worm)). To calculate Efficiency of Worm Gear given lead angle, pressure angle and coefficient of friction, you need Pressure Angle of Worm Gear (Φ), Coefficient of Friction for Worm Gear (μ) & Lead Angle of Worm (γ). With our tool, you need to enter the respective value for Pressure Angle of Worm Gear, Coefficient of Friction for Worm Gear & Lead Angle of Worm 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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