Mean Diameter of Screw given Torque in Lifting Load with Trapezoidal Threaded Screw Calculator

✖Torque for lifting load is described as the turning effect of force on the axis of rotation that is required in lifting the load.ⓘ Torque for lifting load [Mt_li]			+10% -10%
✖Load on screw is defined as the weight (force) of the body that is acted upon the screw threads.ⓘ Load on screw [W]			+10% -10%
✖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.ⓘ Coefficient of friction at screw thread [μ]			+10% -10%
✖Helix angle of screw is defined as the angle subtended between this unwound circumferential line and the pitch of the helix.ⓘ Helix angle of screw [α]			+10% -10%

✖Mean Diameter of Power Screw is the average diameter of the bearing surface - or more accurately, twice the average distance from the centreline of the thread to the bearing surface.ⓘ Mean Diameter of Screw given Torque in Lifting Load with Trapezoidal Threaded Screw [d_m]

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Formula

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Mean Diameter of Screw given Torque in Lifting Load with Trapezoidal Threaded Screw

Formula

`"d"_{"m"} = "Mt"_{"li"}/(0.5*"W"*(("μ"*sec((0.2618))+tan("α"))/(1-"μ"*sec((0.2618))*tan("α"))))`

Example

`"46.01324mm"="9265N*mm"/(0.5*"1700N"*(("0.15"*sec((0.2618))+tan("4.5°"))/(1-"0.15"*sec((0.2618))*tan("4.5°"))))`

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Mean Diameter of Screw given Torque in Lifting Load with Trapezoidal Threaded Screw Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mean Diameter of Power Screw = Torque for lifting load/(0.5*Load on screw*((Coefficient of friction at screw thread*sec((0.2618))+tan(Helix angle of screw))/(1-Coefficient of friction at screw thread*sec((0.2618))*tan(Helix angle of screw))))
d_m = Mt_li/(0.5*W*((μ*sec((0.2618))+tan(α))/(1-μ*sec((0.2618))*tan(α))))
This formula uses 2 Functions, 5 Variables

Functions Used

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., 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., sec(Angle)

Variables Used

Mean Diameter of Power Screw - (Measured in Meter) - Mean Diameter of Power Screw is the average diameter of the bearing surface - or more accurately, twice the average distance from the centreline of the thread to the bearing surface.
Torque for lifting load - (Measured in Newton Meter) - Torque for lifting load is described as the turning effect of force on the axis of rotation that is required in lifting the load.
Load on screw - (Measured in Newton) - Load on screw is defined as the weight (force) of the body that is acted upon the screw threads.
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.
Helix angle of screw - (Measured in Radian) - Helix angle of screw is defined as the angle subtended between this unwound circumferential line and the pitch of the helix.

STEP 1: Convert Input(s) to Base Unit

Torque for lifting load: 9265 Newton Millimeter --> 9.265 Newton Meter (Check conversion here)
Load on screw: 1700 Newton --> 1700 Newton No Conversion Required
Coefficient of friction at screw thread: 0.15 --> No Conversion Required
Helix angle of screw: 4.5 Degree --> 0.0785398163397301 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_m = Mt_li/(0.5*W*((μ*sec((0.2618))+tan(α))/(1-μ*sec((0.2618))*tan(α)))) --> 9.265/(0.5*1700*((0.15*sec((0.2618))+tan(0.0785398163397301))/(1-0.15*sec((0.2618))*tan(0.0785398163397301))))

Evaluating ... ...

d_m = 0.046013240188814

STEP 3: Convert Result to Output's Unit

0.046013240188814 Meter -->46.013240188814 Millimeter (Check conversion here)

FINAL ANSWER

46.013240188814 ≈ 46.01324 Millimeter <-- Mean Diameter of Power Screw

(Calculation completed in 00.004 seconds)

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Home » Engineering » Mechanical » Machine Design » Power Screws » Trapezoidal Thread » Mean Diameter of Screw given Torque in Lifting Load with Trapezoidal Threaded Screw

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< 21 Trapezoidal Thread Calculators

Helix Angle of Screw given Torque Required in Lowering Load with Trapezoidal Threaded Screw

Go Helix angle of screw = atan(((Load on screw*Mean Diameter of Power Screw*Coefficient of friction at screw thread*sec(0.2618))-(2*Torque for lowering load))/((Load on screw*Mean Diameter of Power Screw)+(2*Torque for lowering load*Coefficient of friction at screw thread*sec(0.2618))))

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

Go Helix angle of screw = atan((2*Torque for lifting load-(Load on screw*Mean Diameter of Power Screw*Coefficient of friction at screw thread*sec(0.2618)))/((Load on screw*Mean Diameter of Power Screw)+(2*Torque for lifting load*Coefficient of friction at screw thread*sec(0.2618))))

Coefficient of Friction of Screw given Torque Required in Lowering Load with Trapezoidal Thread

Go Coefficient of friction at screw thread = (2*Torque for lowering load+Load on screw*Mean Diameter of Power Screw*tan(Helix angle of screw))/(sec(0.2618)*(Load on screw*Mean Diameter of Power Screw-2*Torque for lowering load*tan(Helix angle of screw)))

Coefficient of Friction of Screw given Torque Required in Lifting Load with Trapezoidal Thread

Go Coefficient of friction at screw thread = (2*Torque for lifting load-Load on screw*Mean Diameter of Power Screw*tan(Helix angle of screw))/(sec(0.2618)*(Load on screw*Mean Diameter of Power Screw+2*Torque for lifting load*tan(Helix angle of screw)))

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

Go Helix angle of screw = atan((Load on screw*Coefficient of friction at screw thread*sec(15*pi/180)-Effort in lowering load)/(Load on screw+(Effort in lowering load*Coefficient of friction at screw thread*sec(15*pi/180))))

Load on Screw given Torque Required in Lowering Load with Trapezoidal Threaded Screw

Go Load on screw = Torque for lowering load/(0.5*Mean Diameter of Power Screw*(((Coefficient of friction at screw thread*sec((0.2618)))-tan(Helix angle of screw))/(1+(Coefficient of friction at screw thread*sec((0.2618))*tan(Helix angle of screw)))))

Torque Required in Lowering Load with Trapezoidal Threaded Screw

Go Torque for lowering load = 0.5*Mean Diameter of Power Screw*Load on screw*(((Coefficient of friction at screw thread*sec((0.2618)))-tan(Helix angle of screw))/(1+(Coefficient of friction at screw thread*sec((0.2618))*tan(Helix angle of screw))))

Torque Required in Lifting Load with Trapezoidal Threaded Screw

Go Torque for lifting load = 0.5*Mean Diameter of Power Screw*Load on screw*(((Coefficient of friction at screw thread*sec((0.2618)))+tan(Helix angle of screw))/(1-(Coefficient of friction at screw thread*sec((0.2618))*tan(Helix angle of screw))))

Mean Diameter of Screw given Torque in Lowering Load with Trapezoidal Threaded Screw

Go Mean Diameter of Power Screw = Torque for lowering load/(0.5*Load on screw*((Coefficient of friction at screw thread*sec((0.2618))-tan(Helix angle of screw))/(1+Coefficient of friction at screw thread*sec((0.2618))*tan(Helix angle of screw))))

Load on Screw given Torque Required in Lifting Load with Trapezoidal Threaded Screw

Go Load on screw = Torque for lifting load*(1-Coefficient of friction at screw thread*sec((0.2618))*tan(Helix angle of screw))/(0.5*Mean Diameter of Power Screw*((Coefficient of friction at screw thread*sec((0.2618))+tan(Helix angle of screw))))

Mean Diameter of Screw given Torque in Lifting Load with Trapezoidal Threaded Screw

Go Mean Diameter of Power Screw = Torque for lifting load/(0.5*Load on screw*((Coefficient of friction at screw thread*sec((0.2618))+tan(Helix angle of screw))/(1-Coefficient of friction at screw thread*sec((0.2618))*tan(Helix angle of screw))))

Efficiency of Trapezoidal Threaded Screw

Go 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))

Coefficient of Friction of Screw given Effort in Lowering Load

Go Coefficient of friction at screw thread = (Effort in lowering load+Load on screw*tan(Helix angle of screw))/(Load on screw*sec(0.2618)-Effort in lowering load*sec(0.2618)*tan(Helix angle of screw))

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

Go Helix angle of screw = atan((Effort in lifting load-Load on screw*Coefficient of friction at screw thread*sec(0.2618))/(Load on screw+(Effort in lifting load*Coefficient of friction at screw thread*sec(0.2618))))

Effort Required in Lowering Load with Trapezoidal Threaded Screw

Go Effort in lowering load = Load on screw*((Coefficient of friction at screw thread*sec((0.2618))-tan(Helix angle of screw))/(1+Coefficient of friction at screw thread*sec((0.2618))*tan(Helix angle of screw)))

Load on Screw given helix Angle

Go Load on screw = Effort in lowering load*(1+Coefficient of friction at screw thread*sec((0.2618))*tan(Helix angle of screw))/((Coefficient of friction at screw thread*sec((0.2618))-tan(Helix angle of screw)))

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

Go Load on screw = Effort in lifting load/((Coefficient of friction at screw thread*sec((0.2618))+tan(Helix angle of screw))/(1-Coefficient of friction at screw thread*sec((0.2618))*tan(Helix angle of screw)))

Effort Required in Lifting Load with Trapezoidal Threaded Screw

Go Effort in lifting load = Load on screw*((Coefficient of friction at screw thread*sec((0.2618))+tan(Helix angle of screw))/(1-Coefficient of friction at screw thread*sec((0.2618))*tan(Helix angle of screw)))

Coefficient of Friction of Screw given Efficiency of Trapezoidal Threaded Screw

Go Coefficient of friction at screw thread = tan(Helix angle of screw)*(1-Efficiency of power screw)/(sec(0.2618)*(Efficiency of power screw+tan(Helix angle of screw)*tan(Helix angle of screw)))

Coefficient of Friction of Screw given Effort for Trapezoidal Threaded Screw

Go Coefficient of friction at screw thread = (Effort in lifting load-(Load on screw*tan(Helix angle of screw)))/(sec(0.2618)*(Load on screw+Effort in lifting load*tan(Helix angle of screw)))

Coefficient of Friction of Power Screw given Efficiency of Trapezoidal Threaded Screw

Go Coefficient of friction at screw thread = (tan(Helix angle of screw))*(1-Efficiency of power screw)/(sec(0.253)*(Efficiency of power screw+(tan(Helix angle of screw))^2))

Mean Diameter of Screw given Torque in Lifting Load with Trapezoidal Threaded Screw Formula

Define a Trapezoidal Thread Screw?

Trapezoidal screws are also lead screws that use a trapezoidal thread form, but trapezoidal screws have a thread angle of 30° and are manufactured in metric dimensions. The size of a trapezoidal screw is designated by the screw shaft diameter and the pitch of the screw threads.

How to Calculate Mean Diameter of Screw given Torque in Lifting Load with Trapezoidal Threaded Screw?

Mean Diameter of Screw given Torque in Lifting Load with Trapezoidal Threaded Screw calculator uses Mean Diameter of Power Screw = Torque for lifting load/(0.5*Load on screw*((Coefficient of friction at screw thread*sec((0.2618))+tan(Helix angle of screw))/(1-Coefficient of friction at screw thread*sec((0.2618))*tan(Helix angle of screw)))) to calculate the Mean Diameter of Power Screw, Mean Diameter of Screw given Torque in Lifting Load with Trapezoidal Threaded Screw formula is defined as the average diameter of the bearing surface of the Screw. Mean Diameter of Power Screw is denoted by d_m symbol.

How to calculate Mean Diameter of Screw given Torque in Lifting Load with Trapezoidal Threaded Screw using this online calculator? To use this online calculator for Mean Diameter of Screw given Torque in Lifting Load with Trapezoidal Threaded Screw, enter Torque for lifting load (Mt_li), Load on screw (W), Coefficient of friction at screw thread (μ) & Helix angle of screw (α) and hit the calculate button. Here is how the Mean Diameter of Screw given Torque in Lifting Load with Trapezoidal Threaded Screw calculation can be explained with given input values -> 46013.24 = 9.265/(0.5*1700*((0.15*sec((0.2618))+tan(0.0785398163397301))/(1-0.15*sec((0.2618))*tan(0.0785398163397301)))).

FAQ

What is Mean Diameter of Screw given Torque in Lifting Load with Trapezoidal Threaded Screw?

Mean Diameter of Screw given Torque in Lifting Load with Trapezoidal Threaded Screw formula is defined as the average diameter of the bearing surface of the Screw and is represented as d_m = Mt_li/(0.5*W*((μ*sec((0.2618))+tan(α))/(1-μ*sec((0.2618))*tan(α)))) or Mean Diameter of Power Screw = Torque for lifting load/(0.5*Load on screw*((Coefficient of friction at screw thread*sec((0.2618))+tan(Helix angle of screw))/(1-Coefficient of friction at screw thread*sec((0.2618))*tan(Helix angle of screw)))). Torque for lifting load is described as the turning effect of force on the axis of rotation that is required in lifting the load, Load on screw is defined as the weight (force) of the body that is acted upon the screw threads, 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 & Helix angle of screw is defined as the angle subtended between this unwound circumferential line and the pitch of the helix.

How to calculate Mean Diameter of Screw given Torque in Lifting Load with Trapezoidal Threaded Screw?

Mean Diameter of Screw given Torque in Lifting Load with Trapezoidal Threaded Screw formula is defined as the average diameter of the bearing surface of the Screw is calculated using Mean Diameter of Power Screw = Torque for lifting load/(0.5*Load on screw*((Coefficient of friction at screw thread*sec((0.2618))+tan(Helix angle of screw))/(1-Coefficient of friction at screw thread*sec((0.2618))*tan(Helix angle of screw)))). To calculate Mean Diameter of Screw given Torque in Lifting Load with Trapezoidal Threaded Screw, you need Torque for lifting load (Mt_li), Load on screw (W), Coefficient of friction at screw thread (μ) & Helix angle of screw (α). With our tool, you need to enter the respective value for Torque for lifting load, Load on screw, Coefficient of friction at screw thread & Helix angle of screw and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Mean Diameter of Power Screw?

In this formula, Mean Diameter of Power Screw uses Torque for lifting load, Load on screw, Coefficient of friction at screw thread & Helix angle of screw. We can use 1 other way(s) to calculate the same, which is/are as follows -

Mean Diameter of Power Screw = Torque for lowering load/(0.5*Load on screw*((Coefficient of friction at screw thread*sec((0.2618))-tan(Helix angle of screw))/(1+Coefficient of friction at screw thread*sec((0.2618))*tan(Helix angle of screw))))

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