Number of Threads in Engagement with Nut given Unit Bearing Pressure Calculator

✖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%
✖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%
✖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 [d_c]			+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 Threads in Engagement with Nut given Unit Bearing Pressure [z]

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Number of Threads in Engagement with Nut given Unit Bearing Pressure Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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.
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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

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)
Nominal diameter of screw: 50 Millimeter --> 0.05 Meter (Check conversion here)
Core diameter of screw: 42 Millimeter --> 0.042 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

z = 4*W_a/((pi*S_b*((d^2)-(d_c^2)))) --> 4*131000/((pi*24900000*((0.05^2)-(0.042^2))))

Evaluating ... ...

z = 9.10131724508394

STEP 3: Convert Result to Output's Unit

9.10131724508394 --> No Conversion Required

FINAL ANSWER

9.10131724508394 ≈ 9.101317 <-- Number of Engaged Threads

(Calculation completed in 00.020 seconds)

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Created by Kumar Siddhant

Indian Institute of Information Technology, Design and Manufacturing (IIITDM), Jabalpur

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< Design of Screw and Nut Calculators

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

Number of Threads in Engagement with Nut given Unit Bearing Pressure Formula

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

Importance of Thread Engagement

Thread engagement is important because it directly relates to the integrity of the joint. For little engagement, the mode of failure may be the nut member stripping out or breaking of the externally threaded fastener (bolt or screw).
For high engagement, the torque needed to drive the screw rises leading to inadequate clamp load or even breaking fasteners during assembly.

How to Calculate Number of Threads in Engagement with Nut given Unit Bearing Pressure?

Number of Threads in Engagement with Nut given Unit Bearing Pressure calculator uses Number of Engaged Threads = 4*Axial load on screw/((pi*Unit bearing pressure for nut*((Nominal diameter of screw^2)-(Core diameter of screw^2)))) to calculate the Number of Engaged Threads, The Number of Threads in Engagement with Nut given Unit Bearing Pressure refers to the minimum number of engaged threads required to support the Axial Load when the specification and properties of the material are known. Number of Engaged Threads is denoted by z symbol.

How to calculate Number of Threads in Engagement with Nut given Unit Bearing Pressure using this online calculator? To use this online calculator for Number of Threads in Engagement with Nut given Unit Bearing Pressure, enter Axial load on screw (W_a), Unit bearing pressure for nut (S_b), Nominal diameter of screw (d) & Core diameter of screw (d_c) and hit the calculate button. Here is how the Number of Threads in Engagement with Nut given Unit Bearing Pressure calculation can be explained with given input values -> 9.101317 = 4*131000/((pi*24900000*((0.05^2)-(0.042^2)))).

FAQ

What is Number of Threads in Engagement with Nut given Unit Bearing Pressure?

The Number of Threads in Engagement with Nut given Unit Bearing Pressure refers to the minimum number of engaged threads required to support the Axial Load when the specification and properties of the material are known and is represented as z = 4*W_a/((pi*S_b*((d^2)-(d_c^2)))) or Number of Engaged Threads = 4*Axial load on screw/((pi*Unit bearing pressure for nut*((Nominal diameter of screw^2)-(Core diameter of screw^2)))). 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, Nominal diameter of screw is defined as the diameter of the cylinder touching the external threads of the screw & 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.

How to calculate Number of Threads in Engagement with Nut given Unit Bearing Pressure?

The Number of Threads in Engagement with Nut given Unit Bearing Pressure refers to the minimum number of engaged threads required to support the Axial Load when the specification and properties of the material are known is calculated using Number of Engaged Threads = 4*Axial load on screw/((pi*Unit bearing pressure for nut*((Nominal diameter of screw^2)-(Core diameter of screw^2)))). To calculate Number of Threads in Engagement with Nut given Unit Bearing Pressure, you need Axial load on screw (W_a), Unit bearing pressure for nut (S_b), Nominal diameter of screw (d) & Core diameter of screw (d_c). With our tool, you need to enter the respective value for Axial load on screw, Unit bearing pressure for nut, Nominal diameter of screw & Core diameter 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 Number of Engaged Threads?

In this formula, Number of Engaged Threads uses Axial load on screw, Unit bearing pressure for nut, Nominal diameter of screw & Core diameter of screw. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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