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Mean Diameter of Screw When Torque Required in Lowering a Load is Given (Acme Thread) Solution

STEP 0: Pre-Calculation Summary
Formula Used
mean_diameter_of_screw = Torque/(0.5*Force*((Coefficient of Friction*sec((14.5*pi/180))-tan(Helix Angle*pi/180))/(1+Coefficient of Friction*sec((14.5*pi/180))*tan(Helix Angle*pi/180))))
dmean = τ/(0.5*F*((μ*sec((14.5*pi/180))-tan(α*pi/180))/(1+μ*sec((14.5*pi/180))*tan(α*pi/180))))
This formula uses 2 Constants, 2 Functions, 4 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249
Functions Used
tan - Trigonometric tangent function, tan(Angle)
sec - Trigonometric secant function, sec(Angle)
Variables Used
Torque - Torque is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force. It is characterized by τ. (Measured in Newton Meter)
Force - Force is the instantaneous load applied perpendicular to the specimen cross section. (Measured in Newton)
Coefficient of Friction- The Coefficient of Friction (μ) is the ratio defining the force that resists the motion of one body in relation to another body in contact with it. This ratio is dependent on material properties and most materials have a value between 0 and 1.
Helix Angle - Helix Angle denotes the standard pitch circle unless otherwise specified. Application of the helix angle typically employs a magnitude ranging from 15° to 30° for helical gears, with 45° capping the safe operation limit. (Measured in Degree)
STEP 1: Convert Input(s) to Base Unit
Torque: 50 Newton Meter --> 50 Newton Meter No Conversion Required
Force: 1000 Newton --> 1000 Newton No Conversion Required
Coefficient of Friction: 0.2 --> No Conversion Required
Helix Angle: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
dmean = τ/(0.5*F*((μ*sec((14.5*pi/180))-tan(α*pi/180))/(1+μ*sec((14.5*pi/180))*tan(α*pi/180)))) --> 50/(0.5*1000*((0.2*sec((14.5*pi/180))-tan(0.5235987755982*pi/180))/(1+0.2*sec((14.5*pi/180))*tan(0.5235987755982*pi/180))))
Evaluating ... ...
dmean = 0.507435862196624
STEP 3: Convert Result to Output's Unit
0.507435862196624 Meter --> No Conversion Required
0.507435862196624 Meter <-- Mean diameter of screw
(Calculation completed in 00.016 seconds)

efficiency = tan(Helix Angle*pi/180)*(1-Coefficient of Friction*tan(Helix Angle*pi/180)*sec(14.5*pi/180))/(Coefficient of Friction*sec(14.5*pi/180)+tan(Helix Angle*pi/180)) Go
load = Torque/(0.5*Mean diameter of screw*(((Coefficient of Friction*sec((14.5*pi/180)))-tan(Helix Angle*pi/180))/(1+(Coefficient of Friction*sec((14.5*pi/180))*tan(Helix Angle*pi/180))))) Go
torque = 0.5*Mean diameter of screw*Force*(((Coefficient of Friction*sec((14.5*pi/180)))-tan(Helix Angle*pi/180))/(1+(Coefficient of Friction*sec((14.5*pi/180))*tan(Helix Angle*pi/180)))) Go
Mean Diameter of Screw When Torque Required in Lowering a Load is Given (Acme Thread)
mean_diameter_of_screw = Torque/(0.5*Force*((Coefficient of Friction*sec((14.5*pi/180))-tan(Helix Angle*pi/180))/(1+Coefficient of Friction*sec((14.5*pi/180))*tan(Helix Angle*pi/180)))) Go
Coefficient of Friction When Torque Required in Lowering a Load is Given(for Acme Thread)
coefficient_of_friction = (2*Torque+Force*Mean diameter of screw*tan(Helix Angle*pi/180))/sec(14.5*pi/180)*(Force*Mean diameter of screw-2*Torque*tan(Helix Angle*pi/180)) Go
Helix Angle When Torque Required in Lowering a Load is Given (For Acme Thread)
helix_angle = atan((Force*Mean diameter of screw*Coefficient of Friction*sec(14.5*pi/180)-2*Torque)/(Force*Mean diameter of screw+2*Torque*Coefficient of Friction*sec(14.5*pi/180))) Go
Coefficient of Friction When Effort in Lowering a Load is Given (for Acme Thread)
coefficient_of_friction = (Effort+Force*tan(Helix Angle*pi/180))/(Force*sec(14.5*pi/180)-Effort*sec(14.5*pi/180)*tan(Helix Angle*pi/180)) Go
effort = Force*((Coefficient of Friction*sec((14.5*pi/180))-tan(Helix Angle*pi/180))/(1+Coefficient of Friction*sec((14.5*pi/180))*tan(Helix Angle*pi/180))) Go
load = Effort/((Coefficient of Friction*sec((14.5*pi/180))-tan(Helix Angle*pi/180))/(1+Coefficient of Friction*sec((14.5*pi/180))*tan(Helix Angle*pi/180))) Go
Helix Angle When Load and coefficient of friction is Given
helix_angle = atan((Force*Coefficient of Friction*sec(14.5*pi/180)-Effort)/(Force+(Effort*Coefficient of Friction*sec(14.5*pi/180)))) Go

Mean Diameter of Screw When Torque Required in Lowering a Load is Given (Acme Thread) Formula

mean_diameter_of_screw = Torque/(0.5*Force*((Coefficient of Friction*sec((14.5*pi/180))-tan(Helix Angle*pi/180))/(1+Coefficient of Friction*sec((14.5*pi/180))*tan(Helix Angle*pi/180))))
dmean = τ/(0.5*F*((μ*sec((14.5*pi/180))-tan(α*pi/180))/(1+μ*sec((14.5*pi/180))*tan(α*pi/180))))

Acme screw threads are manufactured for assemblies that require the carrying of heavy loads. Acme screw threads were designed to replace the Square thread, which is difficult to manufacture.

How to Calculate Mean Diameter of Screw When Torque Required in Lowering a Load is Given (Acme Thread)?

Mean Diameter of Screw When Torque Required in Lowering a Load is Given (Acme Thread) calculator uses mean_diameter_of_screw = Torque/(0.5*Force*((Coefficient of Friction*sec((14.5*pi/180))-tan(Helix Angle*pi/180))/(1+Coefficient of Friction*sec((14.5*pi/180))*tan(Helix Angle*pi/180)))) to calculate the Mean diameter of screw, The Mean Diameter of Screw When Torque Required in Lowering a Load is Given (Acme Thread) is Given formula is defined as the average diameter of the bearing surface of the Screw. Mean diameter of screw and is denoted by dmean symbol.

How to calculate Mean Diameter of Screw When Torque Required in Lowering a Load is Given (Acme Thread) using this online calculator? To use this online calculator for Mean Diameter of Screw When Torque Required in Lowering a Load is Given (Acme Thread), enter Torque (τ), Force (F), Coefficient of Friction (μ) and Helix Angle (α) and hit the calculate button. Here is how the Mean Diameter of Screw When Torque Required in Lowering a Load is Given (Acme Thread) calculation can be explained with given input values -> 0.507436 = 50/(0.5*1000*((0.2*sec((14.5*pi/180))-tan(0.5235987755982*pi/180))/(1+0.2*sec((14.5*pi/180))*tan(0.5235987755982*pi/180)))).

FAQ

What is Mean Diameter of Screw When Torque Required in Lowering a Load is Given (Acme Thread)?
The Mean Diameter of Screw When Torque Required in Lowering a Load is Given (Acme Thread) is Given formula is defined as the average diameter of the bearing surface of the Screw and is represented as dmean = τ/(0.5*F*((μ*sec((14.5*pi/180))-tan(α*pi/180))/(1+μ*sec((14.5*pi/180))*tan(α*pi/180)))) or mean_diameter_of_screw = Torque/(0.5*Force*((Coefficient of Friction*sec((14.5*pi/180))-tan(Helix Angle*pi/180))/(1+Coefficient of Friction*sec((14.5*pi/180))*tan(Helix Angle*pi/180)))). Torque is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force. It is characterized by τ, Force is the instantaneous load applied perpendicular to the specimen cross section, The Coefficient of Friction (μ) is the ratio defining the force that resists the motion of one body in relation to another body in contact with it. This ratio is dependent on material properties and most materials have a value between 0 and 1. and Helix Angle denotes the standard pitch circle unless otherwise specified. Application of the helix angle typically employs a magnitude ranging from 15° to 30° for helical gears, with 45° capping the safe operation limit.
How to calculate Mean Diameter of Screw When Torque Required in Lowering a Load is Given (Acme Thread)?
The Mean Diameter of Screw When Torque Required in Lowering a Load is Given (Acme Thread) is Given formula is defined as the average diameter of the bearing surface of the Screw is calculated using mean_diameter_of_screw = Torque/(0.5*Force*((Coefficient of Friction*sec((14.5*pi/180))-tan(Helix Angle*pi/180))/(1+Coefficient of Friction*sec((14.5*pi/180))*tan(Helix Angle*pi/180)))). To calculate Mean Diameter of Screw When Torque Required in Lowering a Load is Given (Acme Thread), you need Torque (τ), Force (F), Coefficient of Friction (μ) and Helix Angle (α). With our tool, you need to enter the respective value for Torque, Force, Coefficient of Friction and Helix Angle 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 screw?
In this formula, Mean diameter of screw uses Torque, Force, Coefficient of Friction and Helix Angle. We can use 10 other way(s) to calculate the same, which is/are as follows -
• helix_angle = atan((Force*Mean diameter of screw*Coefficient of Friction*sec(14.5*pi/180)-2*Torque)/(Force*Mean diameter of screw+2*Torque*Coefficient of Friction*sec(14.5*pi/180)))
• coefficient_of_friction = (2*Torque+Force*Mean diameter of screw*tan(Helix Angle*pi/180))/sec(14.5*pi/180)*(Force*Mean diameter of screw-2*Torque*tan(Helix Angle*pi/180))
• mean_diameter_of_screw = Torque/(0.5*Force*((Coefficient of Friction*sec((14.5*pi/180))-tan(Helix Angle*pi/180))/(1+Coefficient of Friction*sec((14.5*pi/180))*tan(Helix Angle*pi/180))))
• load = Torque/(0.5*Mean diameter of screw*(((Coefficient of Friction*sec((14.5*pi/180)))-tan(Helix Angle*pi/180))/(1+(Coefficient of Friction*sec((14.5*pi/180))*tan(Helix Angle*pi/180)))))
• helix_angle = atan((Force*Coefficient of Friction*sec(14.5*pi/180)-Effort)/(Force+(Effort*Coefficient of Friction*sec(14.5*pi/180))))
• coefficient_of_friction = (Effort+Force*tan(Helix Angle*pi/180))/(Force*sec(14.5*pi/180)-Effort*sec(14.5*pi/180)*tan(Helix Angle*pi/180))
• load = Effort/((Coefficient of Friction*sec((14.5*pi/180))-tan(Helix Angle*pi/180))/(1+Coefficient of Friction*sec((14.5*pi/180))*tan(Helix Angle*pi/180)))
• effort = Force*((Coefficient of Friction*sec((14.5*pi/180))-tan(Helix Angle*pi/180))/(1+Coefficient of Friction*sec((14.5*pi/180))*tan(Helix Angle*pi/180)))
• torque = 0.5*Mean diameter of screw*Force*(((Coefficient of Friction*sec((14.5*pi/180)))-tan(Helix Angle*pi/180))/(1+(Coefficient of Friction*sec((14.5*pi/180))*tan(Helix Angle*pi/180))))
• efficiency = tan(Helix Angle*pi/180)*(1-Coefficient of Friction*tan(Helix Angle*pi/180)*sec(14.5*pi/180))/(Coefficient of Friction*sec(14.5*pi/180)+tan(Helix Angle*pi/180))
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Among many, Mean Diameter of Screw When Torque Required in Lowering a Load is Given (Acme Thread) calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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