Can I turn a part from hard clear plastic?

It will be interesting to see if the color of the screwdriver handle really matches the other plastic pieces on your lathe. They're all old; they have been exposed to different environments (light, heat, humidity); they probably aren't from the same plastic manufacturing lot. You might get lucky, maybe not.
 
It wouldn't be factory, but if the screwdriver thing doesn't work you could make three knobs of the red acrylic rod. At least they would all match.
Beat me to it...

Get something big enough to make all 3 plus one.

Make the replacement, then make the matching set.

Remove and replace the originals and keep them for "restoration", use it with the replacements.

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You can definitely turn and mill all sorts of plastic. Rule of thumb is if you can mount it in a lathe you can machine it. There is a plastics guy here on the forum. You might contact him and see if he has something that will work. The points about sharp tools, nice radius and slow turning are good. I drilled #45 hole in plexiglass at about 250 rpm. Got perfect. round shiny holes. Faster then that led to melting and grey holes. You can buy casting material and mold your own. That is a big thing in the art community. You might want to google acrylic art casting and see what you get.

The biggest thing is that you will have to experiment for your tools and machine. Get about triple the stuff you think you need and just starting turning. Plastic has a lot of deflection so stay choked up on the chuck and take light cuts. If i were doing the knobs, I would start with the 3/4" rod. Turn the thin end and taper up the the knob. That will keep you steady and tell you about your tools. Then part off and start over. Next time drill hole first and then turn knob. Keep repeating until you get it right. For a smooth look you really need to fire polish. You can practice that on the discards. And make extra all at the same time the same way so you have spares. Good Luck!
 
For a smooth look you really need to fire polish. You can practice that on the discards.
I disagree. Flame finishing puts a lot of stress at the surface and will craze much sooner than machine polishing. I have fabbed countless boat windshields and the difference shows up in the first year.
 
If you want a heat set insert you may want to anneal after you do that... maybe machine after that too.

Machining puts a lot of surface stresses into acrylic. For high load parts it's normal to anneal after machining. Like, for instance, submarine windows or things that work like them
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I disagree. Flame finishing puts a lot of stress at the surface and will craze much sooner than machine polishing. I have fabbed countless boat windshields and the difference shows up in the first year.
Never did a boat windshield Only small stuff and edges of plexiglass sheids that sit on the mill or attach to end of vise with magnets.
 
For anyone who's interested, I've contacted someone from another machining forum who happens to have TWO Rivett 1R watchmakers lathes. He had to do the exact same project I'm faced with - replicating the tailstock runner's knob and the lock knob on the tailstock's top. He says he made his with the plastic handle from a "rare MAC Tools screwdriver". Someone from this forum said they used a Millers Falls 805-series screwdriver to make yet another knob for yet another Rivett 1R tailstock. I currently have a Millers Falls screwdriver on its way to me via eBay. We'll see, I guess.
He supplied several closeup pics, complete with dimensions. I took the liberty of adding his dimensions to the photo he took, and here it is:
 

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It will be interesting to see if the color of the screwdriver handle really matches the other plastic pieces on your lathe. They're all old; they have been exposed to different environments (light, heat, humidity); they probably aren't from the same plastic manufacturing lot. You might get lucky, maybe not.
I was wondering about that. One thing I know is that the red plastic that Rivett used for their 1R watchmakers lathes and the red plastic from Millers Falls screwdrivers (and also from MAC Tools screwdrivers) are ALL from the same era - right after WW2. So I might strike out, but there's always that chance - it's not zero!
 
I don't know how big your end piece is, but here's a link to some 1" diameter red acrylic rod on ebay. Plenty to experiment with and to get things correct.
A few days ago I ordered some of the red acrylic rod from eBay, and it came in the mail yesterday! It looks great. I haven't tried turning it yet, but the color looks very close to the other red Permaloid knobs on the lathe. The good thing is the rod you suggested is 12" long, so there's enough material there to practice cutting a few times before getting it right.

By the way, a guy on another forum has a Rivett 1R watchmakers lathe, and he was kind enough to send me closeup pics of the plastic knob on his tailstock runner. The dimensions noted in the first picture are his measurements, not mine.


Notice that the female threads in the Rivett knob are cut directly into the plastic! I was going to use a threaded insert, but now that I see a real Rivett knob, I'd like to do the same with my (attempted) replica. I'm willing to try to turn plastic, but drilling & tapping? The thought makes me shudder...
 

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