Analyse Dynamic Engineering SystemsEngineering Science

By Brendan Burr

Brendan Burr BTEC Higher National Certificate in ElectronicsAnalyse Dynamic Engineering Systems

Table of Contents

TABLE OF CONTENTS - 2 -

TASK 1 - 3 -

A wheel and axle is mounted on horizontal frictionless bearings. The total mass is 90 Kg and the radius of gyration about the axis of rotation is 250mm. The diameter of the axle is 76mm. A mass of 16Kg is attached to the hanging end of a light string wrapped round the axel and is then released. Calculate the angular acceleration produced on the wheel. - 3 -

Solution:- - 3 -

TASK 2 - 3 -

A train of total mass 200 tonnes starts from rest and accelerates up an incline of 1 in 80. If the locomotive exerts a steady tractive effort of 100kN and the friction resistance to motion is 25kN, what will be the speed of the train after it has travelled 300m? - 5 -

Solution:- - 5 -

TASK 3 - 8 -

3.1 A helical spring is suspended from a rigid support and a mass of 0.9Kg is attached to its lower end causing the spring to extend 100mm. This mass is then removed and replaced by a body of unknown mass. When the body is allowed to oscillate vertically it is found to complete 72 vibrations in one minute. Calculate the value of the unknown mass and determine the maximum acceleration given that its maximum displacement from the equilibrium position is 150mm. - 8 -

Solution:- - 8 -

3.2 Explain what is meant by damping and sketch an amplitude of vibration against time graph for an undamped and damped vibrating system. Describe a system such as a car suspension, or any mechanical system of your choice, in terms of the mathematical model for a damped vibrating system. - 10 -

Solution:- - 10 -

EVALUATION - 12 -

CONCLUSION - 13 -

Books - 14 -

Catalogues - 14 -

Websites - 14 -

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Brendan Burr BTEC Higher National Certificate in ElectronicsAnalyse Dynamic Engineering Systems

Task 1

A wheel and axle is mounted on horizontal frictionless bearings. The total mass is 90 Kg and the radius of gyration about the axis of rotation is 250mm. The diameter of the axle is 76mm. A mass of 16Kg is attached to the hanging end of a light string wrapped round the axel and is then released. Calculate the angular acceleration produced on the wheel.

Solution:-

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Brendan Burr BTEC Higher National Certificate in ElectronicsAnalyse Dynamic Engineering Systems

There is no way of checking this answer.

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Brendan Burr BTEC Higher National Certificate in ElectronicsAnalyse Dynamic Engineering Systems

Task 2

A train of total mass 200 tonnes starts from rest and accelerates up an incline of 1 in 80. If the locomotive exerts a steady tractive effort of 100kN and the friction resistance to motion is 25kN, what will be the speed of the train after it has travelled 300m?

Solution:-

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Brendan Burr BTEC Higher National Certificate in ElectronicsAnalyse Dynamic Engineering Systems

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Brendan Burr BTEC Higher National Certificate in ElectronicsAnalyse Dynamic Engineering Systems

Check:-

Find the value for acceleration by transposition:

By using the following formula, using our known value for Acceleration:

We can get a value for Velocity, which should equal the same value as before.

This proves that my answer is correct.

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Brendan Burr BTEC Higher National Certificate in ElectronicsAnalyse Dynamic Engineering Systems

Task 3

3.1 A helical spring is suspended from a rigid support and a mass of 0.9Kg is attached to its lower end causing the spring to extend 100mm. This mass is then removed and replaced by a body of unknown mass. When the body is allowed to oscillate vertically it is found to complete 72 vibrations in one minute. Calculate the value of the unknown mass and determine the maximum acceleration given that its maximum displacement from the equilibrium position is 150mm.

Solution:-

Known Mass:

Unknown Mass:

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Brendan Burr BTEC Higher National Certificate in ElectronicsAnalyse Dynamic Engineering Systems

Check:-

So when the Force is added to the Strain Energy there is equilibrium. Hence cancelling one another out and leaving 0!

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Brendan Burr BTEC Higher National Certificate in ElectronicsAnalyse Dynamic Engineering Systems

3.2 Explain what is meant by damping and sketch an amplitude of vibration against time graph for an undamped and damped vibrating system. Describe a system such as a car suspension, or any mechanical system of your choice, in terms of the mathematical model for a damped vibrating system.

Solution:-

Damping is a very straightforward concept.  Simply put, damping is the rate at which something dissipates energy. The higher the damping, the higher the rate of energy dissipation.The images below illustrate different levels of damping in a pictorial form. In these plots, what you see is vibration, and the faster this vibration dies down, the higher the damping. Damping factor is a measure of damping performance.

Extremely poor dampingDamping factor = ~.006

Poor dampingDamping factor = ~.005This graph shows the response of a freely hung piece of 1/2" drywall.  While superior to the steel shown above, damping is still poor.  The poor damping of common building materials such as drywall or wood products is responsible for a lot of the sound isolation problems that the world has today.

Good dampingDamping factor ~0.10This graph shows the damping of two sheets of drywall laminated with an older damping technology. Damping is vastly improved relative to the raw drywall.

Excellent dampingDamping factor = ~0.60

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Brendan Burr BTEC Higher National Certificate in ElectronicsAnalyse Dynamic Engineering Systems

In an undamped system there is no loss in amplitude, as represented in the following graph.

Vehicle Suspension System:The shock absorbers duty is to absorb or dissipate energy. One design consideration, when designing or choosing a shock absorber, is where that energy will go. In most dashpots, energy is converted to heat inside the viscous fluid. In hydraulic cylinders, the hydraulic fluid will heat up, while in air cylinders, the hot air is usually exhausted to the atmosphere. In other types of dashpots, such as electromagnetic types, the dissipated energy can be stored and used later. In general terms, shock absorbers help cushion vehicles on uneven roads.

With no shock absorber and no outside effects, the vehicle would continue bouncing and become uncontrollable (represented by the magenta waveform). A soft shock absorber would produce the blue waveform, which simulates the car bouncing slightly but soon becoming stable.When the shock absorber is even stiffer, the vehicle would return to a controllable state very quickly (represented by the green waveform).The red waveform represents a minimal disturbance in the cabin of the vehicle, as it would return to a controllable state even more quickly.

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Brendan Burr BTEC Higher National Certificate in ElectronicsAnalyse Dynamic Engineering Systems

EvaluationI found this assignment difficult at first, but once I knew what formula and processes to use, it became easier.Starting with Task 1, I found that it was difficult to comprehend the question without having an illustration, so this is how I began the solution. I primarily calculated the Angular Acceleration with an incorrect method, because I wasn’t aware that the Angular Acceleration was the same for both the axle and wheel. With this in mind an equation for each could be merger together, transposed and then a value for Acceleration could be achieved, which could then be divided by the known Radius to provide the Angular Acceleration.Looking back with my new knowledge, I understand fully where the two formulas have come from and that each equals the same thing and can therefore be manipulated in the same way I have done in my workings.There wasn’t a suitable check for my answer in Task 1, other than actually practically experimenting with a real axle and wheel.

I managed to complete Task 2 within an hour after receiving an example which was quite different from the Assignment. I managed to successfully transpose the formula from the example to get an answer for the final velocity, which seemed like a suitable and realistic figure. I couldn’t comprehend a check for this task even after researching a lot in books and online, but received one when the whole class seemed to be having difficulty with the question and had a walkthrough of what needed to be done. I then applied the check to my answer using the Force method rather than the Energy method, and received an identical (even down to eight decimal points) answer for the velocity. In the end I found the check extremely easy to work out, and it used previous knowledge it just required a small and almost insignificant direction to get me on the right path.

Task 3 presented many problems and hours of working out. This wasn’t through my own miscalculation but with an error in the question.There are methods to calculate the Stiffness of the spring by using the either the frequency or calculating the square root of the spring stiffness over the mass. Unfortunately I found that doing this either way would cause a different result for the radial speed. I worked out the spring stiffness with the information given in the question about the mass and the overall extension. This gave me a stiffness of 88.29N/m, which could then be used to calculate the mass of the unknown weight, which I got as 1.35Kg (which appeared like a suitably round figure). I could then calculate the radial speed from the values now obtained for the stiffness and mass. Using this I calculated the maximum acceleration to be -9.81m/s^2, which seemed ideal considering this was the constant value of gravity.I calculated this within an hour, but thought that because it was the precise figure of gravity, I should check my workings thoroughly. During so, I noticed that I hadn’t used the frequency of 72 oscillations a minute (1.2Hz), and decided to redo the earlier stages of calculation to get the maximum acceleration, where I got -8.527338203m/s^2. I then began to question my original workings because of the difference, and searched through pages of text book and notes to find an appropriate check for the answer. After hours of searching, I noticed an equation that had been given to us which stated that

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Brendan Burr BTEC Higher National Certificate in ElectronicsAnalyse Dynamic Engineering Systems

when the Force is added to the Strain Energy there will be equilibrium, hence they should cancel one another out and equal zero.Using this equation I entered the appropriate values in for the frequency equalling 1.2Hz, as follows:

And then did the same for my primary calculations and received the following:

This proves that the question is incorrect as the frequency does not equal 72 oscillations a minute! This took a considerable amount of my time to determine the error with the question and could have potentially compromised another assignment.

ConclusionTo conclude, I found this assignment relatively straightforward, looking back. I find the Science Unit is based on knowledge that many mechanical students gain from previous years, however it is really an alien subject for electrical students. Once the knowledge is taught in a way that is understandable, for example through worked examples or tutorials which have answers, the assignment can be very straightforward. There is clearly a gap in basic knowledge with this unit which was to such an extent that it came close to compromising the entire course. This wasn’t through the teaching methods directly but a definite sacrifice due to the restricted time we have with the lecturer, which is a direct descendant of the guided learning hours being minimised to 45 hours from 60, which was a decision made by the college!This year I have always dedicated my spare time to this course, and without a doubt have spent hundreds of hours ensuring I obtain the best grades possible. This is not always possible though, due to the constraints and availability of knowledge, which is especially relevant to this unit, it sometimes isn’t possible to answer many different types of questions without receiving some support from lecturers. I personally feel that I have only had slight help on Task 1, but because of the marking scheme, the entire assignment will be compromised as a result, which I feel is wrong.

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Brendan Burr BTEC Higher National Certificate in ElectronicsAnalyse Dynamic Engineering Systems

Bibliography

Through guidance from my lecturer, the following text books, catalogues and websites I was able to complete this assignment:

Books

BTEC National Engineering (Mike Tooley & Lloyd Dingle) ISBN: 978-0-7506-8521-4Success in Electronics (Tom Duncan & John Murray)ISBN: 0-7195-4015-1Higher Engineering Mathematics (John Bird) ISBN: 0-7506-8152-7

Catalogues

N/A

Websites

http://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Dampinghttp://www.greengluecompany.com/understandingDamping.phphttp://www.lightandmatter.com/html_books/3vw/ch02/ch02.htmlhttp://en.wikipedia.org/wiki/Shock_absorberhttp://en.wikipedia.org/wiki/Damping

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