Dr Andrei Lozzi
Machine Design & CAD
MECH4460 & 5416
School of Aerospace Mechanical
& Mechatronic Engineering
Finite Element Exercise
Handed out: 2 pm, Thursday 3rd March 2016
To be collected: 2 pm, Thursday 24th March 2016
This assignment should take an average student 18 hours to complete to achieve a pass, which requires
just the application of principle.
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 may 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 functions later. You are then to use Simulation to develop two or more of the designs
described here. In this assignment it is best to seek understanding and begin with a plan, yet you can
unleash your native ingenuity. 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 our web site
www.aeromech.usyd.edu/units-of-study.php, then select MECH4460, course documents..
The Assignment
Problems. The SW files of the models referred to in these problems, shown on figure 1 to 5, 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 (ie 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
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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.
For each of the problems that you tackle your report must begin with a 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.
Some General advice
Cross-sections The shape and cross-sections of a part should reflect the 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 practical to increase I
by adding webs. If torque is being transmitted then a high polar moment of area is appropriate, that is a
tubular cross section. Where compressive forces are the problem, leading possibly to buckling, tubular
cross section is also most effective. Tensile forces may be dealt with just by simply increasing the
cross sectional area.
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 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 conclusions yourself.
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 are messier and have been used less often 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 it 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 new shapes.
Learn from others but do not copy them. Education and real world practice in design includes
examining other people’s work, understanding their ideas and how they executed them, so that you
may apply them and at best, improve on them. While working in industry, you must be careful not to
actually copy competitors’ designs, 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 its faults. Hence, my advice is not to spend too long on any
one problem, move on to others, then return to the troublesome ones with a fresh ideas.
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Work on two or more of the following three problems:
1 Cylinder block and head. In Fig 1 is shown a simplified single cylinder engine block and Fig 2 is
if its cylinder head. These are nominally assembled with four bolts, screws or studs, the selection,
diameter and length of which is for you to decide. You are to develop the detail design of the parts so
that when properly assembled together there will be a leak proof joint between them. All parts are
made from steel.
You must be aware that the clamping pressure is not uniformly distributed on the interface between
bolted plates. This is the state of affair no matter how thick the plates, the clamping force or the bolt
diameter may be. Considering the cylinder block and head that you are asked to develop, maybe the
contact pressure between them can never be made quite uniform, but engineers nevertheless have to
provide designs of the head & block interface such that they are leaks proof (to water, oil and hot high
pressure gases).
You are to apply your observations and research of real engines and your own considerable
imagination, to modify the two components that you are provided with here to arrive at an effective
clamping and sealing assembly. You may alter the location, diameter, length and anchor points of the
fasteners. You may add components and also alter the dimensions of the cylinder block and head. Only
the cylinder diameter and length should not be changed. Your final design should in principle be
practical, maybe reflect good current practice and if possible be novel.
Fig 1 A simplified engine cylinder block
Fig 2 – a cylinder head to match block in Fig 1.
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3.
Stress concentration at bolt threads. When a bolt and nut are preloaded (torqued up) there will be
tensile stress in the bolt and compressive stress in the nut. Since tensile stresses promote fatigue failures a great
deal of development has been done, and continues to be done, to limit the stress concentration caused by the
bottom of the groves, in the threads of the bolt. Fig 10 presents the standard proportions and dimensions for
internal and external ISO threads. Note that the external threads have a relatively wide fillet at the bottom of
their grooves, whereas the bottom of the threads in the nut have fillets of half that radii. Earlier standard allowed
flat bottoms in both internal and external threads, now fillets are required and for high stress bolts even greater
fillets radii and finer surface finish is required than those shown here. Figs 9 represent threads with some
clearance for proper function.
The bolt on Fig 8 is a SW model representing a simplified M20 bolt. It has been defined to have the tolerances
described in Fig 10. Real threads have to meet tolerances with respect to all other dimensions not just thread
width, but it would make the modelling excessively complex for this study. The fillets may make the meshing
and the FEA stress calculations ( ‘running’ the model) too demanding for our Cosmos installation and you may
find it necessary to replace the fillets with flats.
You are to investigate the stress concentration in the bolt threads, compare what you see to the values given in
the references. You are also to investigate geometric changes that one could make to the shape and proportions
of the bolt and nut, to limit or reduce the stress concentration. These parts are made from steel. This topic is
discussed more fully in MECH3460.
Fig 8. Bottom left - a simplified ISO bolt with a fillet undercut at
the end of the thread and under the head of the stem.
Fig 9. Right - a section through screw threads constructed in a
SW model with the 4% clearances.
Fig 10. Lower right – the standard proportions of ISO screw
threads, similar to the latest British and USA standards.
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Redesign of bulkhead
The rear bulkhead from our current Formula SAE car is shown at left. This component had to be designed
and manufactured in some haste, consequently it was not analysed in great detail.
We expect that we may be able to reduce its mass by possibly 1–2 kg. You are challenged to make a more
careful analysis, given the limitations of how it is mounted to the tubular chassis and the loads that it has
to carry.
Dimensions and forces are provided separately.
Marking scheme:
Clarity & completeness of report
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Tried less desirable designs .
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Found more desirable design .
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Tried solutions from lecture or other sources
Made appropriate observations
General Comments : .
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Alternative problems that may be chosen by students that have not attended MEC3460
Work on two or more of the following problems, in which all parts are made from steel:
Fig 1 –The steps shaft shown is used to transmit tension from one end (the near side circular face) to
the other end (far circular face). Apply means to reduce the stress concentration that takes place at the
concave corners, at the changes in diameter. Try circular fillets of different radii, compare the stress
concentration on your model to those tabulated at the back of many references, as that by Shigley and
Norton. The values given by these tables and graphs have been very well validated over many years.
You should try different parameters in setting up the FEA analysis to check for accuracy (with respect
to the references) and convergence. Progress slowly, recording all that you do, making one change at
the time. What design features do you propose if a rolling element bearing is to be fitted against the
right-hand shoulder. That is, this shoulder has to have a vertical face, only a very small radius fillet is
possible at the corner. If you have time, you may also compare the effectiveness of elliptical fillets to
circular ones.
Fig 2 - Examine the connections between vertical columns and horizontal base plates that are installed
at the train stations, tram, sport fields and other locations. Some of which may not be good designs.
For the vertical 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 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.
Fig 3 – A right angle L shaped bracket, shown here has to be stiffened and reinforced to carry a
horizontal and a vertical force each of 1000 N at the one hole shown. Four mounting holes are shown
on the vertical side of the bracket to fix it to a rigid wall, but you may chose different number and
locations of holes. You are required to modify the shape and thickness of this bracket such that with
the loads indicated its deflection is reduced by a factor of 30, while making the bracket light, simple
and practical. You may add webs, welds, bosses, lighting holes and alter plate thickness, in your quest to
achieve lightness, rigidity and practicality. The bracket is made from low carbon steel, Keep the
maximum von Mises stress below 80 N/mm2.
Fig 4 - shows a simplified gear wheel. The load generated at the teeth, which would be meshed with
the teeth of another gear wheel, is represented by just a tangential force at its pitch circle diameter. For
a typical helical gear, there would also be a radial and an axial force component, but these are omitted
here to make the outcome of design changes simpler and clearer. You may shorten the stubby shafts
and fix the two circular ends. Then apply about 2000N tangential load at the flat face. Examine the
stress distribution within a cross section that goes through the middle of the flat face and contains the
centre line of the shafts. See what it takes to reduce the variation in stress, and while the stress
becomes more uniform what happens to the deflection of the flat face, which of course means the
deflection of involute teeth from precise conjugate action.
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This shoulder has to accommodate a bearing, and has to retain some
vertical face. The bearing has a round at its inner diameter of 2 mm.
Fig 1
Fig 2
Fig 3
Fig 4
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How to judge when a solution may be said to be ‘practical’.
Adding more and more webs, as with adding more and more hold down bolt holes, will
make a welded and bolted joint stiffer and stiffer, but with each new web or bolt the
incremental improvement will be less and less. You have to decide when to stop adding
these features.
Consider using one web for each end of a plate, with the bolt hole closest to most heavily
loaded part of the weld, or build the bolt hole into the web. Minimize bending, or try to
place no part into bending.
Make table of attributes as you try different features, against their positions and quantities.
Identify and show your best solution up front, otherwise we may not select your best
answer from all your attempts. If you do not point out your best, we have to presume that
you cannot tell the difference.
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