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Project 2
Introduction
In this project you will perform a probabilistic analysis
for the same disk slider problem that you have been working on for
project #1. Manufacturers of disk drives do not define and set the air
gap between disk and slider and find out about fluid-dynamic forces. In
reality, a manufacturer controls the external force that pushes the
slider down towards the disk and the fluid-dynamic effects will then lead
to a gap such that fluid-dynamic force is in equilibrium with the
external force.
The Finite-Element Model
The calculation of the air gap such that the
fluid-dynamic forces exactly balance the external forces is a non-linear
problem that would require an iterative search algorithm This is a rather
time consuming procedure involving a lot of Finite-Element analyses. To
save computational time we make use of the fact that the logarithm of the
air gap size and the logarithm of the external force can be very well
approximated by a quadratic function, as illustrated in the figure 1. You
will be given ANSYS macro files, which help you solve project #2. These
files include the file “EvalClearance.mac”. This ANSYS macro
calculates the fluid-dynamic force for 3 settings of the air gap size and
then fits the air gap size as a quadratic function of the external
forces. It then uses the fitted quadratic relationship at the given
external force to obtain the size of the air gap corresponding to the
external force.
In the ANSYS Finite-Element analysis the external force
is a parameter called “EXTERNALFORCE” and the angle of attack
of the slider is a parameter called “ALPHA”. Similarly, the
length of the slider is called “LENGTH” and the width of the
slider is called “WIDTH”. The air gap size for which the
external force is in equilibrium with the fluid-dynamic force is called
“B2EQUI.
Random input variables
Due to manufacturing imperfections several of the input
variables entering the Finite-Element model are subjected to scatter,
namely:
Length and Width
- The
manufacturing process generally has a standard deviation for all characteristic
dimensions of ±1 μm. This particularly affects the
length and the width of the slider, which have a nominal value of
2.0 mm and 0.4 mm respectively. The variability of the dimensions is
very well described by a Gaussian distribution, with the mean value
being identical to the respective nominal value.
Angle
- The angle of slider can
only be manufactured with a certain accuracy. The nominal value of
the angle is 2.5º. The manufacturer wants to make sure that the
angle does not drop below 2.3º and that it does not exceed a
value of 2.75º. Extensive quality tests of the manufacturing
process have shown that for the parts coming off the manufacturing
line the angle follows a Gaussian distribution with only 3830 out of
1,000,000 devices dropping below the lower limit of the angle and
only 429 out of 1,000,000 devices exceeding the upper limit of the
angle. Sliders with an angle outside the range from 2.3º and
2.75º are discarded and will not be put into a disk drive.
External Force
- The external force is
small – it has a nominal value of 2.0e-3 N - and controlling
it requires a fair amount of process control in the manufacturing of
the arm carrying the slider. The mean value of the external force is
the same as the nominal value and it has a coefficient of variation
of 10%. Since the force can only have positive values it is
reasonable to assume that the variability can be described by a
lognormal distribution.
All of these manufacturing uncertainties will contribute
to the fact that also the resulting air gap b 2 under equilibrium is
subjected to scatter.
Individual Project
Use ANSYS to obtain statistics information about b2
when length, width, alpha and external force have probabilistic
distributions.
Group Project
Find the optimal configuration of a quality control check
that is intended to minimize the costs of the disk drive and write a
report about your findings. Please follow the same format as previous
report.
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