Core Diameter of Screw given Unit Bearing Pressure Calculator

✖Nominal diameter of screw is defined as the diameter of the cylinder touching the external threads of the screw.ⓘ Nominal diameter of screw [d]			+10% -10%
✖Axial load on screw is the instantaneous load applied to the screw along its axis.ⓘ Axial load on screw [W_a]			+10% -10%
✖Unit bearing pressure for nut is the average pressure acting on the contact surface of the thread in a Screw-Nut pair.ⓘ Unit bearing pressure for nut [S_b]			+10% -10%
✖A number of Engaged Threads of a screw/bolt are the count of threads of the screw/bolt that are currently in engagement with the nut.ⓘ Number of Engaged Threads [z]			+10% -10%

✖Core diameter of screw is defined as the smallest diameter of the thread of the screw or nut. The term “minor diameter” replaces the term “core diameter” as applied to the thread of a screw.ⓘ Core Diameter of Screw given Unit Bearing Pressure [d_c]

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Formula

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Core Diameter of Screw given Unit Bearing Pressure

Formula

`"d"_{"c"} = sqrt(("d")^2-(4*"W"_{"a"}/("S"_{"b"}*pi*"z")))`

Example

`"41.90125mm"=sqrt(("50mm")^2-(4*"131000N"/("24.9N/mm²"*pi*"9")))`

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Core Diameter of Screw given Unit Bearing Pressure Solution

STEP 0: Pre-Calculation Summary

Formula Used

Core diameter of screw = sqrt((Nominal diameter of screw)^2-(4*Axial load on screw/(Unit bearing pressure for nut*pi*Number of Engaged Threads)))
d_c = sqrt((d)^2-(4*W_a/(S_b*pi*z)))
This formula uses 1 Constants, 1 Functions, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Core diameter of screw - (Measured in Meter) - Core diameter of screw is defined as the smallest diameter of the thread of the screw or nut. The term “minor diameter” replaces the term “core diameter” as applied to the thread of a screw.
Nominal diameter of screw - (Measured in Meter) - Nominal diameter of screw is defined as the diameter of the cylinder touching the external threads of the screw.
Axial load on screw - (Measured in Newton) - Axial load on screw is the instantaneous load applied to the screw along its axis.
Unit bearing pressure for nut - (Measured in Pascal) - Unit bearing pressure for nut is the average pressure acting on the contact surface of the thread in a Screw-Nut pair.
Number of Engaged Threads - A number of Engaged Threads of a screw/bolt are the count of threads of the screw/bolt that are currently in engagement with the nut.

STEP 1: Convert Input(s) to Base Unit

Nominal diameter of screw: 50 Millimeter --> 0.05 Meter (Check conversion here)
Axial load on screw: 131000 Newton --> 131000 Newton No Conversion Required
Unit bearing pressure for nut: 24.9 Newton per Square Millimeter --> 24900000 Pascal (Check conversion here)
Number of Engaged Threads: 9 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_c = sqrt((d)^2-(4*W_a/(S_b*pi*z))) --> sqrt((0.05)^2-(4*131000/(24900000*pi*9)))

Evaluating ... ...

d_c = 0.0419012470082511

STEP 3: Convert Result to Output's Unit

0.0419012470082511 Meter -->41.9012470082511 Millimeter (Check conversion here)

FINAL ANSWER

41.9012470082511 ≈ 41.90125 Millimeter <-- Core diameter of screw

(Calculation completed in 00.004 seconds)

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Home » Engineering » Mechanical » Machine Design » Power Screws » Design of Screw and Nut » Core Diameter of Screw given Unit Bearing Pressure

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Created by Parul Keshav

National Institute of Technology (NIT), Srinagar

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Osmania University (OU), Hyderabad

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< 25 Design of Screw and Nut Calculators

Nominal Diameter of Screw given Transverse Shear Stress at Root of Nut

Go Nominal diameter of screw = Axial load on screw/(pi*Transverse shear stress in nut*Thread Thickness*Number of Engaged Threads)

Transverse Shear Stress at Root of Nut

Go Transverse shear stress in nut = Axial load on screw/(pi*Nominal diameter of screw*Thread Thickness*Number of Engaged Threads)

Thread Thickness at Core Diameter of Screw given Transverse Shear Stress

Go Thread Thickness = Axial load on screw/(pi*Transverse Shear Stress in Screw*Core diameter of screw*Number of Engaged Threads)

Number of Threads in Engagement with Nut given Transverse Shear Stress

Go Number of Engaged Threads = Axial load on screw/(pi*Thread Thickness*Transverse Shear Stress in Screw*Core diameter of screw)

Core Diameter of Screw given Transverse Shear Stress in Screw

Go Core diameter of screw = Axial load on screw/(Transverse Shear Stress in Screw*pi*Thread Thickness*Number of Engaged Threads)

Axial Load on Screw given Transverse Shear Stress

Go Axial load on screw = (Transverse Shear Stress in Screw*pi*Core diameter of screw*Thread Thickness*Number of Engaged Threads)

Transverse Shear Stress in Screw

Go Transverse Shear Stress in Screw = Axial load on screw/(pi*Core diameter of screw*Thread Thickness*Number of Engaged Threads)

Axial Load on Screw given Transverse Shear Stress at Root of Nut

Go Axial load on screw = pi*Transverse shear stress in nut*Thread Thickness*Nominal diameter of screw*Number of Engaged Threads

Overall Efficiency of Power Screw

Go Efficiency of power screw = Axial load on screw*Lead of Power Screw/(2*pi*Torsional Moment on Screw)

Lead of Screw given Overall Efficiency

Go Lead of Power Screw = 2*pi*Efficiency of power screw*Torsional Moment on Screw/Axial load on screw

Core Diameter of Screw given Direct Compressive Stress

Go Core diameter of screw = sqrt((4*Axial load on screw)/(pi*Compressive stress in screw))

Helix Angle of Thread

Go Helix angle of screw = atan(Lead of Power Screw/(pi*Mean Diameter of Power Screw))

Mean diameter of Screw given Helix Angle

Go Mean Diameter of Power Screw = Lead of Power Screw/(pi*tan(Helix angle of screw))

Lead of Screw given Helix angle

Go Lead of Power Screw = tan(Helix angle of screw)*pi*Mean Diameter of Power Screw

Core Diameter of Screw given Torsional Shear Stress

Go Core diameter of screw = (16*Torsional Moment on Screw/(pi*Torsional shear stress in screw))^(1/3)

Torsional Shear Stress of Screw

Go Torsional shear stress in screw = 16*Torsional Moment on Screw/(pi*(Core diameter of screw^3))

Torsional Moment in Screw given Torsional Shear Stress

Go Torsional Moment on Screw = Torsional shear stress in screw*pi*(Core diameter of screw^3)/16

Direct Compressive Stress in Screw

Go Compressive stress in screw = (Axial load on screw*4)/(pi*Core diameter of screw^2)

Axial Load on Screw given Direct Compressive Stress

Go Axial load on screw = (Compressive stress in screw*pi*Core diameter of screw^2)/4

Nominal Diameter of Power Screw given Mean Diameter

Go Nominal diameter of screw = Mean Diameter of Power Screw+(0.5*Pitch of power screw thread)

Pitch of Screw given Mean Diameter

Go Pitch of power screw thread = (Nominal diameter of screw-Mean Diameter of Power Screw)/0.5

Mean Diameter of Power Screw

Go Mean Diameter of Power Screw = Nominal diameter of screw-0.5*Pitch of power screw thread

Nominal Diameter of Power Screw

Go Nominal diameter of screw = Core diameter of screw+Pitch of power screw thread

Core Diameter of Power Screw

Go Core diameter of screw = Nominal diameter of screw-Pitch of power screw thread

Pitch of Power Screw

Go Pitch of power screw thread = Nominal diameter of screw-Core diameter of screw

Core Diameter of Screw given Unit Bearing Pressure Formula

Core diameter of screw = sqrt((Nominal diameter of screw)^2-(4*Axial load on screw/(Unit bearing pressure for nut*pi*Number of Engaged Threads)))
d_c = sqrt((d)^2-(4*W_a/(S_b*pi*z)))

Define core diameter?

The smallest diameter of the thread of the screw or nut. The term “minor diameter” replaces the term “core diameter” as applied to the thread of a screw and also the term “inside diameter” as applied to the thread of a nut.

How to Calculate Core Diameter of Screw given Unit Bearing Pressure?

Core Diameter of Screw given Unit Bearing Pressure calculator uses Core diameter of screw = sqrt((Nominal diameter of screw)^2-(4*Axial load on screw/(Unit bearing pressure for nut*pi*Number of Engaged Threads))) to calculate the Core diameter of screw, Core Diameter of Screw given Unit Bearing Pressure is defined as the smallest diameter of the thread of the screw or nut. The term “minor diameter” replaces the term “core diameter” as applied to the thread of a screw. Core diameter of screw is denoted by d_c symbol.

How to calculate Core Diameter of Screw given Unit Bearing Pressure using this online calculator? To use this online calculator for Core Diameter of Screw given Unit Bearing Pressure, enter Nominal diameter of screw (d), Axial load on screw (W_a), Unit bearing pressure for nut (S_b) & Number of Engaged Threads (z) and hit the calculate button. Here is how the Core Diameter of Screw given Unit Bearing Pressure calculation can be explained with given input values -> 41901.25 = sqrt((0.05)^2-(4*131000/(24900000*pi*9))).

FAQ

What is Core Diameter of Screw given Unit Bearing Pressure?

Core Diameter of Screw given Unit Bearing Pressure is defined as the smallest diameter of the thread of the screw or nut. The term “minor diameter” replaces the term “core diameter” as applied to the thread of a screw and is represented as d_c = sqrt((d)^2-(4*W_a/(S_b*pi*z))) or Core diameter of screw = sqrt((Nominal diameter of screw)^2-(4*Axial load on screw/(Unit bearing pressure for nut*pi*Number of Engaged Threads))). Nominal diameter of screw is defined as the diameter of the cylinder touching the external threads of the screw, Axial load on screw is the instantaneous load applied to the screw along its axis, Unit bearing pressure for nut is the average pressure acting on the contact surface of the thread in a Screw-Nut pair & A number of Engaged Threads of a screw/bolt are the count of threads of the screw/bolt that are currently in engagement with the nut.

How to calculate Core Diameter of Screw given Unit Bearing Pressure?

Core Diameter of Screw given Unit Bearing Pressure is defined as the smallest diameter of the thread of the screw or nut. The term “minor diameter” replaces the term “core diameter” as applied to the thread of a screw is calculated using Core diameter of screw = sqrt((Nominal diameter of screw)^2-(4*Axial load on screw/(Unit bearing pressure for nut*pi*Number of Engaged Threads))). To calculate Core Diameter of Screw given Unit Bearing Pressure, you need Nominal diameter of screw (d), Axial load on screw (W_a), Unit bearing pressure for nut (S_b) & Number of Engaged Threads (z). With our tool, you need to enter the respective value for Nominal diameter of screw, Axial load on screw, Unit bearing pressure for nut & Number of Engaged Threads 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 Core diameter of screw?

In this formula, Core diameter of screw uses Nominal diameter of screw, Axial load on screw, Unit bearing pressure for nut & Number of Engaged Threads. We can use 4 other way(s) to calculate the same, which is/are as follows -

Core diameter of screw = Nominal diameter of screw-Pitch of power screw thread
Core diameter of screw = sqrt((4*Axial load on screw)/(pi*Compressive stress in screw))
Core diameter of screw = (16*Torsional Moment on Screw/(pi*Torsional shear stress in screw))^(1/3)
Core diameter of screw = Axial load on screw/(Transverse Shear Stress in Screw*pi*Thread Thickness*Number of Engaged Threads)

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