Curve
Generating
Baldwin
There are
many ways to curve generate a telescope mirror. Each method is performed to
make the mirror concave and the tool convex. You are finished when the mirror
is the correct depth and the mirror and tool move over each other in spherical
contact. Also, when you are in spherical contact the bubbles and material will
move uniformly between the two without spots where they seem to not move on
either the tool or the mirror. The correct depth will be when where s is the sagitta,
or depth of the curve, r is the
radius of the mirror, and R is the
radius of curvature of the mirror. R
is twice the focal length. To measure the sagitta,
place a straightedge across the mirror passing over the center and measure the
gap between the center of the mirror and the straightedge. You can also use a
spherometer.
For example, for a 12”
mirror with a 60” focal length, R = 120”,
r = 6”, so , or 0.150”. While you are working you
can compare your glass with a template. To make a template, pivot a pencil
using a tape measure at the correct radius of curvature to make a curve that
will match your final mirror result. Grind until the mirror matches the
template.
Here are a
few methods that we at the SAS ATM shop have used.
1] Full-Sized
Tool on Top Method. Grit and water are applied to the mirror, which is on
the barrel face up. The tool is placed over the mirror and pressure is applied
over edge of tool as it passes over
center of mirror. Use 60 grit if it is a large mirror, 80 grit if it is a
smaller mirror. Walk around the barrel as you do this. As you walk around the
barrel, occasionally rotate the tool in
the same direction as you are walking around the barrel and the mirror in the
opposite direction. With time the mirror will become concave and the tool will
become convex.
2] Sub-diameter
Tool on Top Method. Same grit as in method 1, only this time your tool is
smaller than your mirror. We do that sometimes. The tool is on top, and as you
pass over the center of the mirror with the near-edge of the tool, your weight
is on the edge of the tool. This will wear away at the edge of the tool and the
center of the mirror, making the mirror eventually concave and the tool convex.
3] Mirror
on Top Method. This should be done with a full-sized tool. The mirror is
passed over the tool so that the center of the mirror passes over the edge of
the tool. Weight is over the middle of the mirror, which will eventually wear
away at the center of the mirror and edge of the tool, making the mirror
concave and the tool convex.
4] Horizontal Pendulum Arm Method.
This is the greatest way we have used so far for removing large amounts of
glass from large, fast telescope mirrors. Mike Lavieri supplied us with a 1 HP
motor, reducing pulleys, pillow blocks and shaft, as well as the diamond
grinding wheel. At the end of a 2X6 arm the motor turns the diamond grinding
wheel at 3500 RPM. With a water feed, the system removes glass quickly and cooly, and “quite safely”. The 2X6 is attached to another
2X6 with alignment holes which enable us to adjust the system to any radius of
curvature we desire. Dave Wilson supplied us with the stainless steel shaft
mounted with pillow block to the wall as a pivot. The mirror is held solidly
with its face pointing horizontally facing the grinding wheel. The grinding
wheel pivots across and back revolving about the pivot in a “perfect” circle
grinding a depth of no more than 1/20 inch into the glass. Then the mirror is
rotated slightly and the grinding wheel is passed again. Once the mirror has
had a complete rotation accomplished, a small ground circle exists on it and it
is moved forward 1/20 inch and it is repeated. Each time we finish a series,
the mirrors spherical cut is larger, and this is continued until the mirror has
been fully ground spherical edge to edge. It is smooth, clean, accurate, and
takes zillions of years out of your hogging out time. Jeff’s 24” f/3.6 was
hogged out in a day and was extremely spherical when finished. Here is a shot
of that assembly.
Update: I
now have a mill and I connected the shaft to the mill stand. Below is a more
current photo.
Here are
three videos of us working the horizontal pendulum.
https://www.youtube.com/watch?v=k5ddX2NZ0ik
https://www.youtube.com/watch?v=lonAulU-kWA
https://www.youtube.com/watch?v=pQ1RUDxobss
7] Metal
Ring Method. A iron ring, such as a pipe end cap, can be used to curve
generate mirrors. The ring ought to be roughly 1/3 to ½ the diameter of the
mirror, and grinding center over center strokes with it using large grits, such
as 60 grit, will curve generate a mirror. You will have to cast a tool for it
when finished. Below is a photo of using a barbell weight on our mirror making
machine to curve a 32” f/3.67 mirror to an f/3.1. The weight is 1/3 the
diameter of the mirror and the center over center strokes are performed 5.5
times per mirror rotation. We also move the center over center condition over
to 16% off-center and 25% off-center now and then to keep the middle from
deepening faster than the rest of the mirror. Click here to see a movie.
When you
use your tool to curve generate, then you already will have a matching tool to
continue to use. If you use one of the methods that doesn’t use a tool, then
you will have to make a matching tool to continue working your mirror. See the section on making a tool.