Trifilar Suspension Lab experiment

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Mechanical Engineering Science 5 – Dynamics Lab Report

Trifilar Suspension

Abstract

By using the trifilar suspension set up it is possible to calculate the moment of inertia of rigid bodies. By completing the experiment and acquiring actual data results these can then be compared to the theoretical values calculated to show the difference.  

Introduction

“The Mass Moment of Inertia of a solid measures the solid's ability to resist changes in rotational speed about a specific axis, the larger the Mass Moment of Inertia the smaller the angular acceleration about that axis for a given torque.

The mass moment of inertia depends on a reference axis, and is usually specified with two subscripts. This helps to provide clarity during three-dimensional motion where rotation can occur about multiple axes.” [1]

“The actual trifilar suspension is an assembly that is used to determine the moment of inertia of a body about an axis passing through the body’s mass centre, perpendicular to the plane of motion”[2]

Image shows trifilar suspension set up: [image taken from http://www.tpub.com/content/MIL-SPEC/MIL-S/MIL-S-81963B/MIL-S-81963B00038.htm]

Occurrence in Industry

The type of motion looked at in this experiment can be seen in many areas of engineering, making it important to understand the components involved in simple harmonic motion so as to be able to design products accordingly, the following are just a few examples of where the theory is used.

Car Suspensions: As the suspension of car moves up and down in the y axis as time progresses the content of the experiment relates closely to working of suspension making it easier to design successful systems.

Pendulums – Although not often seen in today’s world the content of this experiment relates closely to the operations of pendulums, again making the design process and understandings of their workings easier and clearer.

Oil Pumping – Again the motion involved in some large scale oil pumps is not dissimilar to content covered in this experiment making it important to understand how the moment of inertia relates to periodic time.

The Aim of this Lab experiment was to calculate the polar moment of inertia of an assembly and using the results to predict the periodic time of a trifilar suspension. By using objects of known dimensions and mass and using the parallel axis theorem it will be possible to look in greater detail at the mass moment of inertia and obtain a value for it.

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Theory

The moment of inertia of solid objects can be calculated by integrating the second moment of inertia of mass about a selected axis. The general formula used for inertia is:

Where

 = moment of inertia in kgm2 about the mass centre

        

 = mass in kg

        

 = radius of gyration in m about the mass centre 

In order to calculate the inertia of an assembly, the local inertia needs to be increased by ...

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