Effort Required in Lowering Load with Trapezoidal Threaded Screw Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)))
Plo = W*((μ*sec((0.2618))-tan(α))/(1+μ*sec((0.2618))*tan(α)))
This formula uses 2 Functions, 4 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
Effort in lowering load - (Measured in Newton) - Effort in lowering load is the force required to overcome the resistance to lower 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
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
Plo = W*((μ*sec((0.2618))-tan(α))/(1+μ*sec((0.2618))*tan(α))) --> 1700*((0.15*sec((0.2618))-tan(0.0785398163397301))/(1+0.15*sec((0.2618))*tan(0.0785398163397301)))
Evaluating ... ...
Plo = 128.630484214521
STEP 3: Convert Result to Output's Unit
128.630484214521 Newton --> No Conversion Required
FINAL ANSWER
128.630484214521 128.6305 Newton <-- Effort in lowering load
(Calculation completed in 00.004 seconds)

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Osmania University (OU), Hyderabad
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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))

Effort Required in Lowering Load with Trapezoidal Threaded Screw Formula

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)))
Plo = W*((μ*sec((0.2618))-tan(α))/(1+μ*sec((0.2618))*tan(α)))

Define a Trapezoidal Screw Thread?

Trapezoidal thread forms are screw thread profiles with trapezoidal outlines. They are the most common forms used for leadscrews (power screws). They offer high strength and ease of manufacture. They are typically found where large loads are required, as in a vise or the leadscrew of a lathe. Standardized variations include multiple-start threads, left-hand threads, and self-centering threads (which are less likely to bind under lateral forces).

How to Calculate Effort Required in Lowering Load with Trapezoidal Threaded Screw?

Effort Required in Lowering Load with Trapezoidal Threaded Screw calculator uses 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))) to calculate the Effort in lowering load, The Effort Required in Lowering Load with Trapezoidal Threaded Screw formula is defined as the amount of force that is to be applied to lower the load and this force is transmitted as a torque. Effort in lowering load is denoted by Plo symbol.

How to calculate Effort Required in Lowering Load with Trapezoidal Threaded Screw using this online calculator? To use this online calculator for Effort Required in Lowering Load with Trapezoidal Threaded Screw, enter 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 Effort Required in Lowering Load with Trapezoidal Threaded Screw calculation can be explained with given input values -> 128.6305 = 1700*((0.15*sec((0.2618))-tan(0.0785398163397301))/(1+0.15*sec((0.2618))*tan(0.0785398163397301))).

FAQ

What is Effort Required in Lowering Load with Trapezoidal Threaded Screw?
The Effort Required in Lowering Load with Trapezoidal Threaded Screw formula is defined as the amount of force that is to be applied to lower the load and this force is transmitted as a torque and is represented as Plo = W*((μ*sec((0.2618))-tan(α))/(1+μ*sec((0.2618))*tan(α))) or 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 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 Effort Required in Lowering Load with Trapezoidal Threaded Screw?
The Effort Required in Lowering Load with Trapezoidal Threaded Screw formula is defined as the amount of force that is to be applied to lower the load and this force is transmitted as a torque is calculated using 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))). To calculate Effort Required in Lowering Load with Trapezoidal Threaded Screw, you need 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 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.
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