Re: Al Rotors - The definitive answer (Looong)

[Jeremy R King <kingjer@eng.auburn.edu>]

On Tue, 13 Feb 1996, Richard Funnell wrote:

> May I offer a couple of the minor corrections you mention.

snippage

> >without destroying everything is through FRICTION.  Friction is the most
> >important thing in stopping a car using brakes.  There are two places
> >this friction is important - one is between the rotor and pads, the other
> >is between the tire contact patch and the road.  If you think back to
> >your classes (physics), a frictional force (in our case - stopping force)
> >is equal to the normal force (normal as in perpendicular, not everyday)
> >times the coefficient of friction.  So, there are ONLY two ways to
> >increase a car's stopping force.  One is to increase the coefficient of
> >friction.  The other is to increase the normal force.  Before somebody
> >(Glen) jumps all over me on that one with, "What about swept area?"  Easy
> >- to come up with a total stopping force on one wheel at the rotor, you must
> >integrate the normal force at each point over the whole pad area.  Thus
> >the bigger the pad surface area is, the bigger the overall normal force
> >will be.
> 
> Yuo missed on this one.  The size of the pad surface doesn't have any
> obvious bearing on the total normal force.  A small pad will operate at a
> higher pressure to produce the same normal force, assuming a bunch of stuff
> to simplify the analysis (constant coefficient of friction across the pad
> surface, no change due to heating etc.)

Actually this isn't wholly wrong, simply misstated.  Instead of the last 
sentence saying "the overall normal force" will be bigger, it should 
read, "the bigger the resulting frictional force."  You're right in the 
fact that the normal force doesn't change (ie the amount of pressure on 
the brake pedal).  But a bigger pad with the same pedal pressure applied 
will generate a larger resulting frictional force (stopping force) 
because of the normal force being integrated over the whole pad surface.  
Simple mis-wording.

> >mass.  But you're dead wrong in saying that the mass difference from an
> >aluminum rotor to an iron one will make a significant difference in
> >stopping force due to reduced rotational inertia.  This effect will be
> >totally insignificant.  Glen is right on the money saying that the wheel
> >and tire have a much greater effect on this phenomenon.
> 
> I'm disappointed, Jeremy.  Why not actually do some simple calculations
> that say what the effect is.  I'm inclined to agree with your guess, but it
> still feels like a guess.

The math is done.  I didn't have time last night.

> >The one thing
> >Glen left out is the fact that the tire also has a frictional force
> >acting on it that wants to continue to rotate the wheel/tire/etc.  This
> >force is much greater than the rotational inertia of the rotational mass,
> >and much much greater than the rotational inertia of the wimpy little
> >rotor!  So where does this frictional force on the tire come from.
> >Simple - multiply the normal force on the tire (gee, would that be
> >weight?!!! as in MASS times acceleration
> 
> I guess you mean gravity here?

yep

> >) times the coefficient of
> >friction between the tire contact patch and road surface.  Again,
> >integrate the weight of the car over the contact patch - thus if the
> >contact patch is bigger, you get more overall normal force.
> 
> Not true.  See above.  The total normal force on the 4 tires is the weight
> of the car, period.

same correction as above - simple mis-wording.

> >Also note
> >here that the rubber compound of the tire
> 
> ... and the tread, and the carcass, etc.
> 
> >plays a key role in coefficient
> >of friction.  So, the heavier the car, the larger the normal force for a
> >given Cf and tire patch.  Thus a larger frictional force trying to keep
> >the tire/wheel/etc. spinning.

more snips

> >of the brake pads and thus reduce the coefficient of friction between the
> >pads and rotor (fade).  Here's where I think Aluminum makes its most
> >important contribution.  First of all, Aluminum is a softer metal than
> >iron.  Because it's softer, the coefficient of friction between an
> >Aluminum rotor and a given set of pads would be significantly higher than
> >the Cf between the same pads and an iron rotor.  MORE STOPPING FORCE!
> >This is, IMO, the main difference.
> 
> I can't buy this.  The normal force at the pads can be easily adjusted with
> a power assist mechanism or adjustment of mechanical advantage of the brake
> linkage.

stickin' to my guns on this one.  Haven't been able to find a Cf 
comparison yet, but still looking.

> >Another advantage (though not nearly
> >as significant) is Aluminum's higher specific heat.  It was pointed out
> >that an Aluminum rotor would get hotter than an iron one.  Not so.  The
> >higher specific heat of the aluminum allows it to conduct heat AWAY FROM
> >THE PADS to other parts of the rotor.
> 
> Specific heat is a measure of heat capacity, not conductance.

OK, should've read "k = thermal conductance"

> >This keeps the temperature at the
> >pad lower than it would be with an iron rotor.
> 
> Aluminum's better conductance would tend to help this way.
> 
> >BECAUSE Aluminum also
> >dissipates heat to air a lot better than iron.
> 
> Really?

Yep.  Cast iron tends to store heat while aluminum is very willing to 
give it off.  Ever heated a cast iron part up with a flame or grinding 
wheel, then done the same heating to a comparable aluminum part?  The 
aluminum part feels much warmer quicker.  That's because the aluminum is 
giving its heat to your hand and the cast iron is storing it.

> >So now the heat that is
> >better conducted away from the pad is now better convected and radiated
> >from the rotor into the air, which will carry this heat away.
> >
> >So why aren't all rotors aluminum?  For one thing, aluminum is less stiff
> >than iron.  And the stronger alloys (7075, 7079) tend to be very
> >brittle.  But the main drawback is that aluminum has about a third of the
> >cycle life of iron.  It is very subject to fatigue.  Since braking is a
> >very cycle-intensive process, aluminum is not the best choice for your
> >dependable, everyday commuter.  Since the racing life of a part (on a
> >race car) is very small compared to a passenger car, aluminum would be a
> >viable alternative.  Also, racing applications are tremendously sensitive
> >to unsprung weight,
> 
> As is the ride on your road car.

Not nearly as sensitive as a relatively lightweight race car.

> >where aluminum would provide yet another benefit.  I
> >think the answer lies with composite alloys, which would allow the
> >benefits and help remedy the weaknesses.
> >
> >Sorry this was so long.  I hope someone made it to the end.
> >
> >Jeremy R. King
> >Senior Mechanical Engineering Student
> >Suspension Team Leader - War Eagle Motorsports Formula SAE
> 
> After slogging through all this, you're still guessing at the relative
> effect of the rotor weight.
> 
> Richard Funnell,
> San Jose, California
> '83 urQ
> '87 560 SL
Jeremy