Torsional Stiffness of Shaft given Time Period of Vibration Calculator

✖Mass Moment of Inertia of Disc is the rotational inertia of a disc that resists changes in its rotational motion, used in torsional vibration analysis.ⓘ Mass Moment of Inertia of Disc [I_d]			+10% -10%
✖Time Period is the time taken by the shaft to complete one oscillation or vibration about its axis in a torsional vibration system.ⓘ Time Period [t_p]			+10% -10%

✖torsional stiffness is the ability of an object to resist twisting when acted upon by an external force, torque.ⓘ Torsional Stiffness of Shaft given Time Period of Vibration [q]

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Torsional Stiffness of Shaft given Time Period of Vibration Solution

STEP 0: Pre-Calculation Summary

Formula Used

Torsional Stiffness = ((2*pi)^2*Mass Moment of Inertia of Disc)/(Time Period)^2
q = ((2*pi)^2*I_d)/(t_p)^2
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Torsional Stiffness - (Measured in Newton per Meter) - torsional stiffness is the ability of an object to resist twisting when acted upon by an external force, torque.
Mass Moment of Inertia of Disc - (Measured in Kilogram Square Meter) - Mass Moment of Inertia of Disc is the rotational inertia of a disc that resists changes in its rotational motion, used in torsional vibration analysis.
Time Period - (Measured in Second) - Time Period is the time taken by the shaft to complete one oscillation or vibration about its axis in a torsional vibration system.

STEP 1: Convert Input(s) to Base Unit

Mass Moment of Inertia of Disc: 6.2 Kilogram Square Meter --> 6.2 Kilogram Square Meter No Conversion Required
Time Period: 6.7325383 Second --> 6.7325383 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

q = ((2*pi)^2*I_d)/(t_p)^2 --> ((2*pi)^2*6.2)/(6.7325383)^2

Evaluating ... ...

q = 5.400000012306

STEP 3: Convert Result to Output's Unit

5.400000012306 Newton per Meter --> No Conversion Required

FINAL ANSWER

5.400000012306 ≈ 5.4 Newton per Meter <-- Torsional Stiffness

(Calculation completed in 00.018 seconds)

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Home » Physics » Theory of Machine » Vibrations » Torsional Vibrations » Mechanical » Natural Frequency of Free Torsional Vibrations » Torsional Stiffness of Shaft given Time Period of Vibration

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National Institute Of Technology (NIT), Hamirpur

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< Natural Frequency of Free Torsional Vibrations Calculators

Moment of Inertia of Disc using Natural Frequency of Vibration

LaTeX Go Mass Moment of Inertia of Disc = Torsional Stiffness/((2*pi*Natural Frequency)^2)

Torsional Stiffness of Shaft given Natural Frequency of Vibration

LaTeX Go Torsional Stiffness = (2*pi*Natural Frequency)^2*Mass Moment of Inertia of Disc

Torsional Stiffness of Shaft given Time Period of Vibration

LaTeX Go Torsional Stiffness = ((2*pi)^2*Mass Moment of Inertia of Disc)/(Time Period)^2

Moment of Inertia of Disc given Time Period of Vibration

LaTeX Go Mass Moment of Inertia of Disc = (Time Period^2*Torsional Stiffness)/((2*pi)^2)

Torsional Stiffness of Shaft given Time Period of Vibration Formula

LaTeX Go

Torsional Stiffness = ((2*pi)^2*Mass Moment of Inertia of Disc)/(Time Period)^2
q = ((2*pi)^2*I_d)/(t_p)^2

What causes torsional vibration?

Torsional vibrations are an example of machinery vibrations and are caused by the superposition of angular oscillations along the whole propulsion shaft system including propeller shaft, engine crankshaft, engine, gearbox, flexible coupling and along the intermediate shafts.

How to Calculate Torsional Stiffness of Shaft given Time Period of Vibration?

Torsional Stiffness of Shaft given Time Period of Vibration calculator uses Torsional Stiffness = ((2*pi)^2*Mass Moment of Inertia of Disc)/(Time Period)^2 to calculate the Torsional Stiffness, Torsional Stiffness of Shaft given Time Period of Vibration formula is defined as the measure of a shaft's resistance to twisting forces, which is essential in determining the shaft's ability to withstand torsional vibrations, and is a critical parameter in the design and analysis of rotating machines and mechanical systems. Torsional Stiffness is denoted by q symbol.

How to calculate Torsional Stiffness of Shaft given Time Period of Vibration using this online calculator? To use this online calculator for Torsional Stiffness of Shaft given Time Period of Vibration, enter Mass Moment of Inertia of Disc (I_d) & Time Period (t_p) and hit the calculate button. Here is how the Torsional Stiffness of Shaft given Time Period of Vibration calculation can be explained with given input values -> 5.4 = ((2*pi)^2*6.2)/(6.7325383)^2.

FAQ

What is Torsional Stiffness of Shaft given Time Period of Vibration?

Torsional Stiffness of Shaft given Time Period of Vibration formula is defined as the measure of a shaft's resistance to twisting forces, which is essential in determining the shaft's ability to withstand torsional vibrations, and is a critical parameter in the design and analysis of rotating machines and mechanical systems and is represented as q = ((2*pi)^2*I_d)/(t_p)^2 or Torsional Stiffness = ((2*pi)^2*Mass Moment of Inertia of Disc)/(Time Period)^2. Mass Moment of Inertia of Disc is the rotational inertia of a disc that resists changes in its rotational motion, used in torsional vibration analysis & Time Period is the time taken by the shaft to complete one oscillation or vibration about its axis in a torsional vibration system.

How to calculate Torsional Stiffness of Shaft given Time Period of Vibration?

Torsional Stiffness of Shaft given Time Period of Vibration formula is defined as the measure of a shaft's resistance to twisting forces, which is essential in determining the shaft's ability to withstand torsional vibrations, and is a critical parameter in the design and analysis of rotating machines and mechanical systems is calculated using Torsional Stiffness = ((2*pi)^2*Mass Moment of Inertia of Disc)/(Time Period)^2. To calculate Torsional Stiffness of Shaft given Time Period of Vibration, you need Mass Moment of Inertia of Disc (I_d) & Time Period (t_p). With our tool, you need to enter the respective value for Mass Moment of Inertia of Disc & Time Period 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 Torsional Stiffness?

In this formula, Torsional Stiffness uses Mass Moment of Inertia of Disc & Time Period. We can use 2 other way(s) to calculate the same, which is/are as follows -

Torsional Stiffness = (2*pi*Natural Frequency)^2*Mass Moment of Inertia of Disc
Torsional Stiffness = Restoring Force/Angular Displacement of Shaft

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