Has anyone tried to wire cut the developed shape of a piston ring ? I am thinking of trying it so I'm just throwing this in to see if it is not just another barking mad idea by yours truly. Couldn't find much useful on the internet so I thought I'd just give it a whirl.
Comments would be appreciated.
Above photo - I tried all sorts of developments (geometric, log, hyperbolic - Arrrrghhh!) but eventually settled on the simplest linear method :-
I drew 36 polyline chords occupying 5° each to substitute for half of a ring - the numbers chosen were for simplicity at this stage and came about after an awful lot of mucking about.
Numbered 35 to zero. The numbers and colours are to help me keep track during the subsequent rotate commands.
This is a Ø25mm ring - but merely for trial purposes.
An open ring will obviously have a larger radius opposite the split and at the tip of the split it would be exactly the bore radius. So there must be a constantly changing radius - since Hooke's law would be linear I went with that - it turns out it's not - because of the nature of the ring - see later.
I chose to rotate all segments starting at the top and rotating 0.35° - followed by rotate previous - remove #35 and rotate 0.34° and so on - thereby diminishing the resultant curve to zero adjustment over the 180° of the ring - so the angle between chords constantly diminished by 0.01° per step and the final is zero so that the last radius generated by chords #0 and #1 is the cylinder diameter.
This actually came out at R14.5 opposite the gap and R12.5 at the gap tip.
If you wanted a bigger gap then start with a bigger number than 0.35° like say 0.5° - in which case I would recommend using 50 segments at 0.01° change in increment - it simplifies keeping track of all the rotate commands if you manage to get lost. (You could use 25 even numbered segments at 0.02° increments.)
I then joined all the polylines to form a single polyline, mirrored it about the centreline and joined the two halves followed by the "spline" function to redefine the curve completely. It redefined it into ±260 short arc lengths of ±0.3mm length - that's sufficient detail to be very accurate.
Obviously since the chords are actually shorter than a true circular path, the circumference came out as 78.4448mm and should have been 78.539816mm (25π) so I scaled up the developed shape by 1.0012112 to get the exact right length - I could have pitched the cords to the effective diameter - but I still would have expected some error which would require scaling to cure it so I didn't bother.)
Next I offset the developed outer shape inwards by 2mm (ring width - probably excessive for a Ø25 piston)
Now that circumference should be 65.9734 (21π) but it comes in at 66.6101
So I tried developing the inside shape by the same method and got something similar. Worse it was not altogether parallel to the outer profile by up to 0.02mm no matter how I scaled and fiddled with it.
The reason is obviously the nature of stressing a split ring - the outer circumference is going to go into tension (thus making it longer) and the inner is going to go into compression (thus making it shorter).
Probably the thing to do is develop the effective diameter (in this case (Ø23) and offset 1mm either way. The true developed shape is therefore going to have a slightly shorter outer circumference (because it's going to stretch) and the inner a slightly longer than theoretical (because it's going to be compressed) these errors are likely to be very tiny.
In any case you are almost certainly going to finesse the gap ends for ring gap clearance.
I am thinking of trying this unless someone points out why it is a truly stupid idea (at worst you can cut it oversize and finish the OD afterwards closed on a mandrel a'la Mr. Chaddocks fixture.
Does anyone have any references that might be useful - also things like the ratio of ring width, ring thickness, open gap, materials etc.
Regards, Ken
Comments would be appreciated.
Above photo - I tried all sorts of developments (geometric, log, hyperbolic - Arrrrghhh!) but eventually settled on the simplest linear method :-
I drew 36 polyline chords occupying 5° each to substitute for half of a ring - the numbers chosen were for simplicity at this stage and came about after an awful lot of mucking about.
Numbered 35 to zero. The numbers and colours are to help me keep track during the subsequent rotate commands.
This is a Ø25mm ring - but merely for trial purposes.
An open ring will obviously have a larger radius opposite the split and at the tip of the split it would be exactly the bore radius. So there must be a constantly changing radius - since Hooke's law would be linear I went with that - it turns out it's not - because of the nature of the ring - see later.
I chose to rotate all segments starting at the top and rotating 0.35° - followed by rotate previous - remove #35 and rotate 0.34° and so on - thereby diminishing the resultant curve to zero adjustment over the 180° of the ring - so the angle between chords constantly diminished by 0.01° per step and the final is zero so that the last radius generated by chords #0 and #1 is the cylinder diameter.
This actually came out at R14.5 opposite the gap and R12.5 at the gap tip.
If you wanted a bigger gap then start with a bigger number than 0.35° like say 0.5° - in which case I would recommend using 50 segments at 0.01° change in increment - it simplifies keeping track of all the rotate commands if you manage to get lost. (You could use 25 even numbered segments at 0.02° increments.)
I then joined all the polylines to form a single polyline, mirrored it about the centreline and joined the two halves followed by the "spline" function to redefine the curve completely. It redefined it into ±260 short arc lengths of ±0.3mm length - that's sufficient detail to be very accurate.
Obviously since the chords are actually shorter than a true circular path, the circumference came out as 78.4448mm and should have been 78.539816mm (25π) so I scaled up the developed shape by 1.0012112 to get the exact right length - I could have pitched the cords to the effective diameter - but I still would have expected some error which would require scaling to cure it so I didn't bother.)
Next I offset the developed outer shape inwards by 2mm (ring width - probably excessive for a Ø25 piston)
Now that circumference should be 65.9734 (21π) but it comes in at 66.6101
So I tried developing the inside shape by the same method and got something similar. Worse it was not altogether parallel to the outer profile by up to 0.02mm no matter how I scaled and fiddled with it.
The reason is obviously the nature of stressing a split ring - the outer circumference is going to go into tension (thus making it longer) and the inner is going to go into compression (thus making it shorter).
Probably the thing to do is develop the effective diameter (in this case (Ø23) and offset 1mm either way. The true developed shape is therefore going to have a slightly shorter outer circumference (because it's going to stretch) and the inner a slightly longer than theoretical (because it's going to be compressed) these errors are likely to be very tiny.
In any case you are almost certainly going to finesse the gap ends for ring gap clearance.
I am thinking of trying this unless someone points out why it is a truly stupid idea (at worst you can cut it oversize and finish the OD afterwards closed on a mandrel a'la Mr. Chaddocks fixture.
Does anyone have any references that might be useful - also things like the ratio of ring width, ring thickness, open gap, materials etc.
Regards, Ken
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