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PMMA or Poly(methyl methacrylate) is a transparent thermoplastic also called acrylic glass or perspex. wikipedia.

Chemically, it is the synthetic polymer of methyl methacrylate. It is sold under many trade names, including Policril, Plexiglas, Gavrieli, Vitroflex, Limacryl, R-Cast, Per-Clax, Perspex, Plazcryl, Acrylex, Acrylite, Acrylplast, Altuglas, Polycast, Oroglass, Optix and Lucite and is commonly called acrylic glass, simply acrylic, perspex or plexiglas. Acrylic, or acrylic fiber, can also refer to polymers or copolymers containing polyacrylonitrile.

It is commonly used to make laser cut parts for 3D Printer kits, on account of price and relative strength vs cost, though a Prusa i3 box frame, made of wood, is actually a much stronger frame, regardless of 1/Appearance, a 'value added' feature sought by those who buy 'Acrylic 3D Printers', 2/ Relative strength, compared with Aluminium frame or Steel frame, Alumium Sheet frame is only slightly heavier but more expensive and much more rigid and 'stable', Steel is much heavier, while not more expensive for the steel, laser cutting of the P3Steel adds substantial cost, while the Wanhao Duplicator uses bench pressed steel to save money and avoid expensive laser tool-head costs.

Extrusion for FDM (3D Printing)

Nophead managed to print with it How? by setting the hot end temperature at 220C, and heated bed to 100C. It wouldn't stick in a cold environment.

This is probably very incomplete maybe incorrect info. Follow the link/do more research if you want to extrude from an all metal nozzle!

macc24 was able to print it on non-reprap printer with 250°C on nozzle, and 85°C on buildtak-like bed surface. Raft or brim may be needed. PMMA likes to warp. He could not get it to stick on glass bed.

Printing on Acrylic sheets

Because, you know, you want to print a 3d design on a nice flat sheet, which may be transparent! What filaments adhere best at room temeperature? And in a heated build chamber? </br> It should be noted that actually placing the acrylic sheet on a heated bed wont have any positive effect. You want the top to be hotter, not the base!

Manually working with it

Perspex can easily be sawed and filed with a metal saw. For accuracy in sawing, use a shallow sawing angle. With fast(electric) sawing/drilling care has to be taken that it doesn't go over the melting temperature.

However sawing it yourself can be time consuming, it may be a good oppertunity to look up and visit a nearby hackerspace.

It can be polished. Another method used sanding well and then applying heat to use melting as last polishing step.(cant find link)

If there are no defects and it is well-polished, presumably it can be used as lens/optics.(to some degree)