----- Original Message -----
From: Jeffrey L. Walker
To: Klrlist (E-mail) DSN_klr650@egroups.com>; Weaver, Mark
; Jim & Shannon Morehead
Sent: Monday, June 19, 2000 1:06 PM
Subject: Re: [DSN_klr650] Tire cupping, revisited and complex for
non-engineer types NKLR
>
> > I never claimed that there isn't a POINT of instantaneous zero velocity,
> > just that the entire contact patch does not have zero velocity relative
to
> > the pavement.
> >
>
> Nope, just the great majority of it, where the tire is flattened to the
> pavement. There is an "entry region" and "exit region" where their will
be
> some slippage between the two surfaces, but this is very small in
comparison
> to the area of the contact patch. Consider this extreme example of a
> similar system; a tank's tracks. All along the bottom of the track where
it
> is flat their is no relative velocity between the surfaces. Also, bear in
> mind that as an element of the tire (a differential mass if you will)
enters
> the contact patch, it is not only translating, but rotating, therefore
moves
> up or down rather rapidly, so the amount of time that it slips is very
short
> in comparison to the amount of time that element spends in the contact
> patch.
>
> Yes, the slippage that occurs is a wear mechanism, but I don't think that
> you have described why tires cup. This wear mechanism you describe would
> provide even wear on the tire, not uneven wear.
>
> I consider the dynamic system like this; With vulcanized rubber and
> pressurized air in the tire, there is a coefficient of restitution, or
> spring constant for the system. There is also a damping constant, (which
I
> have no clue as to what it is, but it must exist and offhand I'd say the
> system is underdamped.) The normal force between the tire and the
surface,
> and the force due to static friction contribute to the forcing function.
> (Alternating stresses on each side of the contact patch, compression and
> tension.) Therefore, this is an oscillatory system. I don't know how
many
> degrees of freedom. I do know that the natural frequencies of the system
> are influenced by the rotational velocity of the tire, and the tire tread
> pattern. Perhaps it is then a "beating phenomenon" that creates the tire
> cupping, or simple resonance. This I don't know. As Tom pointed out,
this
> is a very complicated dynamic system, so I'm sure I don't have much hope
> creating a mathematical model, even with finite element analysis. So you
> see, it is because of the zero velocity point that tire cupping occurs, as
> this is the point at which the forcing function occurs, and my original
> explanation is valid, with refinement.
>
> Mr. Morehead, I might respectfully suggest that you check the validity of
> your own arguments before you make disparaging allusions to the
intelligence
> of others. I am not infallible, and I do appreciate corrections to any
> theory I might propose, as this is a very important part of the learning
> process and I still have much to learn. However you came across as rather
> unprofessional. If you have any doubt as to the professional conduct and
> ethics of an engineer, then I refer you to the National Society of
> Professional Engineers Code of Ethics:
>
>
http://www.nspe.org/ethics/eh1-code.asp
>
> More specifically:
>
> Engineers shall:
>
> 6. Conduct themselves honorably, responsibly, ethically, and lawfully so
as
> to enhance the honor, reputation, and usefulness of the profession.
>
> and
>
> 7. Engineers shall not attempt to injure, maliciously or falsely, directly
> or indirectly, the professional reputation, prospects, practice, or
> employment of other engineers.
>
>
> Respectfully,
>
> Jeff Walker
>