Re: ATM Pressure distribution between discs

[Jan Bentz <jbentz@inreach.com>]

Great idea-- After you knock this one off you can modify it to include 
rotating discs to apply it to a machine.   The predictions for a machine 
should be much closer to reality given that there are fewer 
uncontrolable variables.  

Jan Bentz

mdholm@telerama.com wrote:

>Hi ATM's
>
>I am thinking about a program to calculate the wear patterns of different 
>polishing strokes to help make hand figuring a bit more predictable.  I know 
>that in principle, polishing wear is a very complex phenominon, and that there 
>are a lot of polishing variations that would be hard to model.  I intend to 
>start out simple:
>
>    Only straight line motion, or motion that can be modeled as a series of 
>straight lines.  No spinning.  I will assume that spinning motion is 
>negligable.  Not strictly true, but, for most hand work, probably close.
>
>    The tool doesn't deform.
>
>    No added weight or pressure.
>
>    No velocity effects.  Wear is proportional to distance traveled in contact 
>x pressure.
>
>    Both the mirror and lap are circular.  For now, I will not deal with star 
>laps, etc., though in the future I would want to add that since is is a very 
>common technique.
>
>    The top disc has uniform mass distribution.
>
>    The mirror and lap can have different diameters.
>
>I don't intend, at the outset, to get too mathematically sophisticated about 
>this.  If it takes a lot of stupid arithmetic, that is what computers are for.  
>If I can get a coordinate system, boundary conditions and a function for each 
>area element, the computer can do the grunt work.
>
>The tricky part of this is dealing with the case where the top disc overhangs.  
>I think I can deal with the projected area part, but I am a bit stumped on the 
>pressure distribution.  Those of you who took Statics may even have done this 
>problem as an excercise.  Since I never took Statics, I am a bit at sea.  I 
>think there are two conditions I have to meet.  1. The sum of the pressure x 
>area elements has to equal the weight of the upper disc.  2. The sum of the 
>pressure moments has to equal the negative of the sum of the weight moments.  I 
>need to get the pressure at each area element where the discs are in contact.  
>I will assume, to start, that the top disc doesn't deform.  I expect to stay 
>well away from the teetering case where pressure would go infinite given the 
>ridgidity assumption.
>
>Anybody feel up to helping me with this one?  I am moderately fluent in 
>calculus, vectors and physics.
>
>(I realize also that wear may be a nonlinear function of pressure, but I have 
>to start somewhere, and a linear approximation may be good enough.)
>
>Mark Holm
>mdholm@telerama.com
>
>
>
>  
>