Bearings Video Lecture | Design of Machine Elements - Mechanical Engineering

in this video we're going to discuss
bearings and how to size them and how to
design them before we can begin we need
to set some definitions about what a
bearing is a bearing is any two parts
that have relative motion to each other
and we classify bearings in several
different categories the first one is a
plane bearing the plane bearing has two
materials that rub directly against each
other
there's several different examples so
typically one part is structural
material like a steel or a cast iron and
the other part is a bearing material and
it's supposed to be something that won't
wear out and has very low friction so
bronze is a good example or there's a
material called Babbitt that has tin or
lead infused in it that makes it um very
slippery and lots of friction and low
coefficient of friction plain berries
are pit bearings are typically
custom-designed for each individual
application within the plane bearing
category there are bushings which are
radial plane bearings so there only
thing they're allowing is rotational
motion and they're a complete closed
cylinder thrust bearings support axial
loads entirely and then journal bearings
is when a shaft rotates freely in a
supported sleeve or shell so maybe this
it goes all the way around to be a
complete cylinder but very often it
doesn't and very often especially in the
journal bearing there's some sort of
lubrication that's occurring in the
bearing to allow the the journal to
rotate freely the other type of bearing
that we consider is a roller air element
bearing and these are almost always
composed of hardened steel balls or
rollers and the hole and the rollers are
captured between hardened steel raceways
and the the translation of motion comes
from rolling so you get the effect of
wheels working to reduce the friction
these are very rarely designed custom
for an application much more often these
are selected
from manufacturing catalogs and they're
made in large bulks and you purchase the
type that fits your application so a
plane bearing you're going to design the
bearing to match your shaft and a roller
element bearing you're going to design
your shaft to fit a particular bearing
roller element bearings can support all
kinds of different loads there are
different types of roller element
bearings and we'll talk about several
common styles for supporting radial
thrust radial loads or thrust loads or
combinations of radial and thrust loads
I think it's really important as we
consider this to realize the
understanding of what a bearing is
really doing and this is Anthony GM
Mitchell is a major bearing designer he
had a lot to do with the construction of
journal bearings and all that they do
and this is what he had to say to the
machine designer all bearings are of
course only necessary evils contributing
nothing to the product or function of
the machine and any virtues they can
have are only of a negative order their
merits consist in absorbing as little
power as possible wearing out as slowly
as possible occupying as little space as
possible and costing as little possible
as possible so that's a good thing for
us to understanding having a good
bearing doesn't in doesn't increase our
power of production or anything like
that it stops the decrease of our power
production it's a good perspective to
happen now looking at different types of
bearing material here are some just
examples of different types of Babbitt
and how hard they are and the type of of
where they would be used
okay so let's look at three different
types of lubricated plane bearings so
lubrication is absolutely the key to
reducing both friction and wear and in
hydrostatic lubrication you have a
continuous supply of a high-pressure
loop a lubricant and a very low
coefficient of friction actually for
zero relative velocity if you're moving
very slowly the coefficient of friction
is almost nothing and with a relative
velocity it's normally around point zero
zero two which is a very small
coefficient of friction hydrodynamic
lubrication is there's enough lubricant
to allow the moving surfaces to actually
pump the lubricant between the surfaces
so there's a dynamic film of liquid in
other words if I stop the rotation of
the shaft the film disappears from
between the shaft and the bearing but as
I spin the shaft
I'll force a film in between the shaft
and the housing this means when
everything is stopped where could occur
so where only occurs during startup and
shutdown this is why you do eventually
have we're in a car engine for instance
everything is perfectly fine as long as
the car is running but during the
startup and start down you might be
tearing up your journals just a little
bit as you start and then the last one
is hydro elasto hydrodynamic lubrication
so this is specifically used to to
lubricate things like gear teeth or
things or cams anything that's going to
have a point contact and so if you have
a point contact all of the force has to
be distributed to practically no area so
you have to have some sort of
deformation when that deformation occurs
you have some local deflection and this
patch where the local deflection occurs
is where the film can develop so even
though you don't have film on most of
the contact you will develop a film
exactly where the deflection occurs
here's an example of a hydrostatic
example the the best example of this for
practical life might be some of the the
domes for stadiums are rolled out and on
using hydro static pressure so you're
gonna pump enough pressure into it to
actually float the entire roof on a film
a thin film of oil and then you can
slide it with very little work once you
get it going elastro hydro static again
there's gears and cams and the figure
figure eleven point two shows you that
as your speed increases you get closer
and closer to a full film lubrication
and so there's actually a perfect spot
of relative velocity that you're going
to get a full film and slow velocity and
you're going to have the least amount of
friction and so that's what we'll design
for we will not discuss elasto hydra
hydro static friction in this course
what we'll spend the rest of this
lecture discussing is hydro dynamic
friction and this includes journal
bearings so figure a shows a shaft
resting in oil without the shaft
spinning as the shaft begins to spin
notice that it moves to the right as
we're looking at it during the startup
so now we're going to start having
boundary lubrication and the contact
point leads leaves the center line it
leads the center line meaning it's in
front of it and it also is no longer on
the center line as Omega increases you
get enough speed you'll actually start
pumping oil inside right right here now
there's oil getting pumped inside
between the bearing housing and the
journal and this is going to allow the
entire journal to float and now the
shaft is going to follow or laugh
the center line of the of the housing so
there's a lot of work that's gone on to
model exactly how this happens and and
the key thing we want to do is decide
what cut type of tolerance we want right
here and that's going to be highly
dependent on the speed of the shaft so
we need to know the speed of the shaft
we need to know the forces generated by
the friction of the of the lubrication
as it drives itself under the shaft and
all of that's going to help us to
dictate what type of lubricant we should
use what type of tolerances we should
have on the shaft versus the housing and
how everything ought to work together so
so here's another example during the the
process there's going to be some place
where we have a maximum force and a
minimum thickness so as we look here
here is the minimum thickness of the
lubrication there's the maximum
thickness and this is some starting
angle and we're going to figure out
exactly where the highest and lowest
pressures and everything else goes
notice while we're at this diagram we
also can see the s intricity of the
journal in relation to the bearing
housing and obviously that's has
something to do with the clearance
so for any particular point I can find
what the velocity of the fluid is that
the velocity of the fluid right here is
zero at stationary the velocity of the
fluid right here is the speed of the
journal at that location those two
changes in velocities help me understand
forces and that's going to be how we're
going to generate the force that the
looper can exert onto the journal this
is a graph that shows how P moves as a
function of theta so we're again we're
considering running and now we're going
to say theta is equal to zero when we're
when we're in line with the s with the a
centricity in other words the shaft if I
were to draw a line from the center of
the shaft to the center of the housing
that's going to be my theta is equal to
zero and we can see that there is a
location there's a theta max that
produces a P max which is the maximum
force being exhibit exerted on the
journal and we also can see across the
width of the journal that the maximum P
is exerted right there in the middle
this is going to help us find the
maximum pressure so that's what we're
looking for all right so here's the
steps to design a hydrostatic bearing
usually I already know the forces that
need to be on the shaft and the
rotational speed of the shaft what I'm
looking for our diameters and clearances
so I'm going to start with making a
random selection and then I'm going to
use that to calculate in order the vissa
viscosity requirements that allows me to
choose a lubricant then I'm going to
find the average pressure I'm going to
find the location of the maximum
pressure then I'll find the maximum
pressure then I'll find the angle of
torques to the applied load then I'll
find stationary and rotating torques
calculate the power loss and calculate
the coefficient of the bearing so just
so you know where we're going and then
that gives me the minimum film thickness
and finally I can have a factor of
safety to make sure that my film never
gets too thin and we
we're out the park so this is what we'll
do what I'm going to do in the next few
slides is discuss how to find some of
these the maximum pressure and then in
class we'll go through an example where
we do all of these steps in a specific
design scenario obviously when I make my
random selection I won't be right yet so
after I get my factor of safety then
I'll have to iterate and go through
again probably at least a couple times
if not many times to get to the right
answer so going back to the beginning
usually the applied force on the shaft
and the rotational speed of the shaft
are known so the first thing we're going
to do is define a dimensionless
parameter we'll call it k epsilon and it
is a function of P which is the
resultant force that's something I know
the clearance diameter that's the
maximum amount of clearance this is
again something I know the maximum
clearance between the shaft and the
housing I need to find the absolute
viscosity which is the kinematic film a
sensitive this is something I'm gonna
make a decision about we'll look at a
chart to show you how to make that
decision then I'm going to find the
speed of the journal and this in prime
is in units of revolutions per second so
we'll translate anything we have from
revolutions per minute into revolutions
per second and then two more the length
of the bearing which is L and D is the
diameter and all of those and then we
need all of those will help me know this
dimensionless parameter this K epsilon
once I know that I'm going to find an
effect number and the aquavit number is
a function of this K that we just found
and from that I can get the average
pressure this is a design decision and
I'll talk a little bit more about it in
the next couple of slides but typically
I'm gonna say I desire a particular
Vick number and once I've found so I'm
gonna find viscosity specifically I'm
going to choose the correct viscosity
and clearance difference to allow the
oxic number to be where I want it to be
and maybe this equation does a better
job of even showing how that ought to
happen if I change the D over L that's
going to influence the aquavit number if
I change C D over D that's going to
influence so these ratios are really
what's doing the influencing of the oxic
number now this is epsilon is the a
centricity ratio of the shaft to the
bearing and it's a function of the AH
quick numbered matter of fact that's
really what we're trying to describe
with the oxic number and this equation
if you look at it very clearly looks
like something that's been kurt thin and
it has this is the experiential number
this is curve fit based on existing data
of how things have actually happened we
do have a theoretical number but since
the theoretical number doesn't quite
match reality in this course we're
always going to use this number this
approximation using doc Fick number to
calculate our s intricity ratio so let's
take a look here's the oxic number as it
goes from zero to a hundred here's the
theoretical curve here is the
experiential curve this is the one that
had the log in it and these are data
points of where things seem to fall so
the experience will curve much better
matches reality also we can look at how
the AH quick number is influenced by P
max over P average and the ratio of the
torques so here's the experiential
there's the theoretical so there seems
to be like there still a ways to go in
the theory behind the AH quick number
again the larger the oxic number the
more shift we're gonna have in theta
here are the guidelines if we have a
moderate loading condition then we're
gonna aim to have an offic number less
than 30 if we have a heavy loading
condition we're gonna aim for the
awkward number to be less than 60 and if
we have a severe loading will aim for
the oxford number to be less than 90 as
I said before there's a lot of steps to
go through here and this is best shown
using example so in class we'll start
with these