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Efficiency of Trapezoidal Threaded Screw Formula

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Efficiency of power screw refers to how well it converts rotary energy into linear energy or motion. Check FAQs

η = \tan (α) \cdot \frac{1 - μ \cdot \tan (α) \cdot \sec (0.2618)}{μ \cdot \sec (0.2618) + \tan (α)}

η - Efficiency of power screw?α - Helix angle of screw?μ - Coefficient of friction at screw thread?

Efficiency of Trapezoidal Threaded Screw Example

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Here is how the Efficiency of Trapezoidal Threaded Screw equation looks like with Values.

Here is how the Efficiency of Trapezoidal Threaded Screw equation looks like with Units.

Here is how the Efficiency of Trapezoidal Threaded Screw equation looks like.

0.3322 = \tan (4.5) \cdot \frac{1 - 0.15 \cdot \tan (4.5) \cdot \sec (0.2618)}{0.15 \cdot \sec (0.2618) + \tan (4.5)}

0.3322 = \tan (4.5°) \cdot \frac{1 - 0.15 \cdot \tan (4.5°) \cdot \sec (0.2618)}{0.15 \cdot \sec (0.2618) + \tan (4.5°)}

0.3322 = \tan (4.5) \cdot \frac{1 - 0.15 \cdot \tan (4.5) \cdot \sec (0.2618)}{0.15 \cdot \sec (0.2618) + \tan (4.5)}

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Efficiency of Trapezoidal Threaded Screw Solution

Follow our step by step solution on how to calculate Efficiency of Trapezoidal Threaded Screw?

FIRST Step Consider the formula

η = \tan (α) \cdot \frac{1 - μ \cdot \tan (α) \cdot \sec (0.2618)}{μ \cdot \sec (0.2618) + \tan (α)}

Next Step Substitute values of Variables

∴

η = \tan (4.5°) \cdot \frac{1 - 0.15 \cdot \tan (4.5°) \cdot \sec (0.2618)}{0.15 \cdot \sec (0.2618) + \tan (4.5°)}

Next Step Convert Units

∴

η = \tan (0.0785rad) \cdot \frac{1 - 0.15 \cdot \tan (0.0785rad) \cdot \sec (0.2618)}{0.15 \cdot \sec (0.2618) + \tan (0.0785rad)}

Next Step Prepare to Evaluate

∴

η = \tan (0.0785) \cdot \frac{1 - 0.15 \cdot \tan (0.0785) \cdot \sec (0.2618)}{0.15 \cdot \sec (0.2618) + \tan (0.0785)}

Next Step Evaluate

∴

η = 0.332231242145882

LAST Step Rounding Answer

∴

η = 0.3322

Efficiency of Trapezoidal Threaded Screw Formula Elements

Variables

Functions

Efficiency of power screw

Efficiency of power screw refers to how well it converts rotary energy into linear energy or motion.

Symbol: η

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Efficiency of power screw

Helix angle of screw

Helix angle of screw is defined as the angle subtended between this unwound circumferential line and the pitch of the helix.

Symbol: α

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Helix angle of screw

Coefficient of friction at screw thread

Coefficient of friction at screw thread is the ratio defining the force that resists the motion of the nut in relation to the threads in contact with it.

Symbol: μ

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Coefficient of friction at screw thread

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)

sec

Secant is a trigonometric function that is defined ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine.

Syntax: sec(Angle)

Other formulas in Trapezoidal Thread category

Go Effort Required in Lifting Load with Trapezoidal Threaded Screw

P li = W \cdot (\frac{μ \cdot \sec ((0.2618)) + \tan (α)}{1 - μ \cdot \sec ((0.2618)) \cdot \tan (α)})

Go Load on Screw given Effort Required in Lifting Load with Trapezoidal Threaded Screw

W = \frac{P li}{\frac{μ \cdot \sec ((0.2618)) + \tan (α)}{1 - μ \cdot \sec ((0.2618)) \cdot \tan (α)}}

Go Helix Angle of Screw given Effort Required in Lifting Load with Trapezoidal Threaded Screw

α = a \tan (\frac{P li - W \cdot μ \cdot \sec (0.2618)}{W + (P li \cdot μ \cdot \sec (0.2618))})

Go Coefficient of Friction of Screw given Effort for Trapezoidal Threaded Screw

μ = \frac{P li - (W \cdot \tan (α))}{\sec (0.2618) \cdot (W + P li \cdot \tan (α))}

How to Evaluate Efficiency of Trapezoidal Threaded Screw?

Efficiency of Trapezoidal Threaded Screw evaluator uses Efficiency of power screw = tan(Helix angle of screw)*(1-Coefficient of friction at screw thread*tan(Helix angle of screw)*sec(0.2618))/(Coefficient of friction at screw thread*sec(0.2618)+tan(Helix angle of screw)) to evaluate the Efficiency of power screw, The Efficiency of Trapezoidal Threaded Screw formula is defined as a way of describing the amount of useful output a process or machine can generate as a percentage of the input required to make it go. Efficiency of power screw is denoted by η symbol.

How to evaluate Efficiency of Trapezoidal Threaded Screw using this online evaluator? To use this online evaluator for Efficiency of Trapezoidal Threaded Screw, enter Helix angle of screw (α) & Coefficient of friction at screw thread (μ) and hit the calculate button.

FAQs on Efficiency of Trapezoidal Threaded Screw

What is the formula to find Efficiency of Trapezoidal Threaded Screw?

The formula of Efficiency of Trapezoidal Threaded Screw is expressed as Efficiency of power screw = tan(Helix angle of screw)*(1-Coefficient of friction at screw thread*tan(Helix angle of screw)*sec(0.2618))/(Coefficient of friction at screw thread*sec(0.2618)+tan(Helix angle of screw)). Here is an example- 0.332231 = tan(0.0785398163397301)*(1-0.15*tan(0.0785398163397301)*sec(0.2618))/(0.15*sec(0.2618)+tan(0.0785398163397301)).

How to calculate Efficiency of Trapezoidal Threaded Screw?

With Helix angle of screw (α) & Coefficient of friction at screw thread (μ) we can find Efficiency of Trapezoidal Threaded Screw using the formula - Efficiency of power screw = tan(Helix angle of screw)*(1-Coefficient of friction at screw thread*tan(Helix angle of screw)*sec(0.2618))/(Coefficient of friction at screw thread*sec(0.2618)+tan(Helix angle of screw)). This formula also uses Tangent (tan), Secant (sec) function(s).

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