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Dr Andrei Lozzi Machine Design & CAD MECH3460

School of Aerospace Mechanical & Mechatronic Engineering

Finite Element Exercise MECH3460

Handed out: 11 am 31st July 2017 To be collected: 4 pm 21st August 2017. From assignment boxes, Level 3 Mech Eng Building. No assignment will be marked after this time. This assignment should take an average student 18 hours to complete to achieve a pass, which requires the application of relevant principles.

All students are required to submit a signed statement of compliance, with this University’s policy on plagiarism, with all work submitted for assessment.

Preliminary Tutorials. You should begin by reviewing a selection of FEA tutorials made

available online whenever the SolidWorks Simulation software is ‘added in’ to a SW application.

They are accessible by selecting Help\SolidWorks, Simulation, Simulation tutorials. Examine the

range of topics covered by the tutorials to get an overview of what is available, in case you need to

apply some of their operations later. You are then to use Simulation to develop some or all of the

designs described here. In this assignment you can unleash your native ingenuity, but it is best to

seek understanding and begin with a plan. Some changes will make things worse, some better. It is

as important for you to understand what makes things worse as it is what makes things better. With

a little care you will be able, maybe in a seesaw fashion, to progressively improve your designs.

It may be necessary to ‘add in’ Simulation, if it had not been used in your PC before. After SW is

running, start a new part, from the top menu select - Tools, add in, then Simulation. More advanced

tutorials and user manuals of SW and SWS in pdf format, may be copied from

http://web.aeromech.usyd.edu.au/MECH3460, then select MECH3460, course documents..

The Assignment

Problems. The files of the SW models referred to in these problems, shown on figure 1 to 4, are

also included in the above folder. You may assume that these models are adequately functional but

they need to have their stress distribution improved and for some their deflection reduced. You are

to select two or more of these and develop their detail designs along the lines prescribed.

What to submit. You are to submit a written report (i.e. on paper not by email) that shows and

describes how you progressed, from beginning to end, comparing design changes with

improvements or otherwise. Use objective aspects such as deflection, stress, mass, complexity or

other indicators that may be relevant. You really must try one geometric change at the time, if you

do not you will not know for sure what change has caused what effect. Keep your SW and SWS

files and studies in the event that we ask you to provide them to us, for examination.

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For each of the problems that you tackle your report must begin with an executive summary of your

preferred design. You must make clear what you have learned from your analysis and what is your

best design, do not leave that to the reader or marker, they may get it wrong.

Materials. All parts may be assumed to be made from a mid-strength steel or aluminium alloy. For

a given type of load, the size, shape of the component and the Young’s modulus of the material,

will determine the deformation within the component and overall deflection. Which also of course

means the strain and stress distribution within it. To control deformation and or stress levels, we

can modify size and shape, which is what you asked to do in these exercises.

Selecting alloys, within the steel or aluminium range, of higher or lower strength will not alter the

stress and deformation. To make a component safe, we need to select a material and or heat

treatment that will give a strength sufficiently higher than the highest stress within the part. The

SW files for all the parts provided for analysis are contained in the folder made available to you.

Some General advice

Cross-sections. The shape and cross-sections of a part should reflect the sort of loads transmitted

through it. For example, where the bending moment is high, one can reduce the normal stresses on

the surfaces, by increasing the second moment of area (I) of the section. In a welded part, it is often

practical to increase I by adding webs where the bending moment is highest. If torque is being

transmitted then a high polar moment of area J is appropriate, that is a tubular cross section. Where

compressive forces are the problem, leading possibly to buckling, tubular cross section are also

most effective. Tensile forces may be dealt with just by simply increasing the cross sectional area

that is subject to the tension.

Improvements in a design may be said to have taken place if the under and over-stressed areas are

reduced. For some, an ideal design is one where a part is completely uniformly stressed, that is

where the safety margin against failure is the same everywhere. We may strive for this condition,

but we may never quite achieve it in practice, except possibly in the simplest of cases.

The critical point is to notice is that FEA does not reveal what is creating the stresses, and what

are appropriate ways to control them, you have to arrive at those observations and conclusions

yourself.

Deflections. A good design is also relatively stiff, that is it undergoes a relatively small amount of

deflection under load. Deflection often gets neglected, partly because it has less dramatic

consequences if it becomes excessive, causing just malfunction rather than catastrophic failure, and

partly because before FEA, deflection calculations were less often used, as they are messier than

their stress counterpart. You may therefore be surprised by the magnitude of the deflections and

distortions that occurs in mechanical components, and the ingenuity that is required just to keep

them within acceptable limits.

Stress concentration. There is a simple rule to follow to obtain improved uniformity of stress in a

component, add material where the stress is high and take it away where the stress is low! It is

really quite simple to say, but we quickly come up against the limits of our imagination at changing

and inventing shapes.

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Learn from others but do not copy them. In education and in the real world, the practice of

design includes examining other people’s work, understanding their ideas and how they are

executed, so that you may apply those ideas, and at best improve on them. While working in

industry, you must be careful not to actually copy competitors’ designs and patents, as opposed to

just learn from them, or you may end up in court. For this class you can and should discuss and

develop ideas with others, but submit your own unique designs. Also, please note that there is no

perfect design; you can spend your life chasing just some ideal, only to have someone pointing out

simple faults. Hence my advice is not to spend too long on any one problem, move on to others

then maybe return to the troublesome problems, with fresh ideas.

Work on at least two of the following Four problems:

1 Coil spring are increasingly used in

the front suspension of cars. As shown in

the figure at right, some are subjected to

normal axial compression together with

transverse shear forces. We need to

estimate the combined stiffness when

the transverse displacement is about 20%

of that in the axial direction.

See Heissing & Ersoy, ‘Chassis Handbook’

p241-247, e-book, Scitech library.

By refining the features of this spring, such as

attaching a bar to the ends of the wire, so that axial

forces can be applied, at top and bottom, at the

centre of the coil. Compare your results with that

for deflection, stress and stiffness, provided by

standard references for coil springs.

Then, find the stiffness for a transverse force.

Thereafter arrive at a combined stiffness for a

transverse displacement 1/5th of the axial one.

A more typical spring for this application has wire

diameter of 14mm, mean coil diameter of 83 mm

and 8 active coils.

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2 Column examine the connections

between vertical columns and horizontal

base plates, installed at the train stations,

tram, sport fields and other locations. For the

I column and base plate shown here, you are

to reduce the deflection, stress and stress

concentration by modifying how the column

is connected to the base plate. You may

choose the size and shape of the base plate,

locations and number of bolt holes, add webs

and other features. To apply a load to this

weldment you may attach a thick rectangular

plate to the top of the column and apply two

horizontal 10 kN forces to that plate. These

forces have to be parallel to the base plate

but perpendicular to each other.

3 Gear wheel Shows at right is a simplified gear

wheel. The loads generated at the teeth, which

would be meshed with the teeth of another gear

wheel, are represented by a tangential and a radial

force at a rectangular area, at its pitch circle.

You may shorten and fix the two circular ends of

the stub shafts. Apply 1000 N vertically and the

same tangentially, distributed uniformly over the

rectangular flat face. Stress is to be limited to 200

N/mm2. You may make the shaft hollow to

achieve more uniform stress. Examine the stress

distribution within a cross section perpendicular to

the circular outline. See what it takes to reduce

stress concentration, and while the stress becomes

more uniform what happens to the deflection at the

flat face.

The sketches at bottom left on page 6 represent

some practical advice on how to design gear

wheels, taken from one of P. Orlov’s 5 volumes.

The figure at lower right is the reduction gear of a

RR Merlin. Please note the RR gear designs.

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4 Pressure vessel. Above is a model representing a simplified valve body, cylinder or

pressure vessel, as used in hydraulic and pneumatic systems. This model has some features

that often seen in these types of components. All these components are typically subjected

to high internal pressure, which nearly always cycles between medium to very high levels.

Although they are analysed by modern methods they surprisingly experience fatigue

failures, which when it happens in an airliner, becomes very inconvenient.

In conventional components, tensile failures typically begin on the outside surface at some

high stress area, from there progresses inwardly.

You are asked to examine and compare Von Mises stresses on the inside surface with that

on the outside of this model. Apply an internal pressure between 10 and 200 atmospheres.

Consider some of the examples included in a PowerPoint shown to the class, and possibly

provide an explanation for their failures.

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