- #1
Lerch
- 7
- 0
Greetings All,
I am attempting to develop a software simulation of the dynamics involved in machine figuring concave parabolic telescope mirrors. As a member of the amateur telescope making community, we currently don't have any tools to do this other than the "trial and error" method.
You may be asking "So, what brings you here?" Well, long story short, I'm trying to model the situation, and I've already ran into problems and I need some guidance. Before I can ask my question, I need to describe the situation.
I have a polishing machine that looks like this:
http://lerch.no-ip.com/atm/Projects/Polisher/page_01.htm
The big piece of glass on the bottom is the telescope mirror which is 317mm in diameter. The mirror is on a turntable that spins at a fixed angular velocity. On top of the mirror is a polishing tool, 196mm in diameter. The tool is free to rotate about its center.
For the sake of keeping the initial simulation as simple as possible, I've assumed the following conditions:
#1 The surface of the mirror and tool are flat instead of curved
#2 The center of the tool is held at a fixed radius from the center of the mirror.
#3 The coefficient of kinetic friction is constant for all velocities.
#5 The angular velocity of the mirror is -4.189 radians per second
#6 At startup the tool has no angular velocity
My first goal for the simulation, "Predict the angular velocity of the tool" (which seemed simple enough).
First, I created a table elements, each containing the force tangent to the center of the tool:
http://lerch.no-ip.com/atm/Tang_Force.jpg
Next, I multiplied each table element by the radius in mm of the tool:
http://lerch.no-ip.com/atm/Tang_Force_X_Radius.jpg
Then I found the sum of the table, multiplied that by the force of friction, and divided the product by the inertia of the tool to give an initial angular acceleration. Thus completes time = 0, and now I'm stuck...
At time = 1, I have a tool angular velocity equal to the tool angular acceleration at time = 0, yes?
I know my force table calculations have to change, other wise I'd get infinite acceleration. I know that the change is related to the angular velocity for each point on the tool, compared to the angular velocity of the mirror at the same point., and this is where I'm stuck. I don't know how to make this comparison.
Any Suggestions on how to proceed?
Take Care,
James Lerch
http://lerch.no-ip.com/atm (My telescope construction,testing, and coating site)
"Anything that can happen, will happen" -Stephen Pollock from:
"Particle Physics for Non-Physicists: A Tour of the Microcosmos"
" Press on: nothing in the world can take the place of perseverance.
Talent will not; nothing is more common than unsuccessful men with talent.
Genius will not; unrewarded genius is almost a proverb.
Education will not; the world is full of educated derelicts.
Persistence and determination alone are omnipotent. "
Calvin Coolidge
I am attempting to develop a software simulation of the dynamics involved in machine figuring concave parabolic telescope mirrors. As a member of the amateur telescope making community, we currently don't have any tools to do this other than the "trial and error" method.
You may be asking "So, what brings you here?" Well, long story short, I'm trying to model the situation, and I've already ran into problems and I need some guidance. Before I can ask my question, I need to describe the situation.
I have a polishing machine that looks like this:
http://lerch.no-ip.com/atm/Projects/Polisher/page_01.htm
The big piece of glass on the bottom is the telescope mirror which is 317mm in diameter. The mirror is on a turntable that spins at a fixed angular velocity. On top of the mirror is a polishing tool, 196mm in diameter. The tool is free to rotate about its center.
For the sake of keeping the initial simulation as simple as possible, I've assumed the following conditions:
#1 The surface of the mirror and tool are flat instead of curved
#2 The center of the tool is held at a fixed radius from the center of the mirror.
#3 The coefficient of kinetic friction is constant for all velocities.
#5 The angular velocity of the mirror is -4.189 radians per second
#6 At startup the tool has no angular velocity
My first goal for the simulation, "Predict the angular velocity of the tool" (which seemed simple enough).
First, I created a table elements, each containing the force tangent to the center of the tool:
http://lerch.no-ip.com/atm/Tang_Force.jpg
Next, I multiplied each table element by the radius in mm of the tool:
http://lerch.no-ip.com/atm/Tang_Force_X_Radius.jpg
Then I found the sum of the table, multiplied that by the force of friction, and divided the product by the inertia of the tool to give an initial angular acceleration. Thus completes time = 0, and now I'm stuck...
At time = 1, I have a tool angular velocity equal to the tool angular acceleration at time = 0, yes?
I know my force table calculations have to change, other wise I'd get infinite acceleration. I know that the change is related to the angular velocity for each point on the tool, compared to the angular velocity of the mirror at the same point., and this is where I'm stuck. I don't know how to make this comparison.
Any Suggestions on how to proceed?
Take Care,
James Lerch
http://lerch.no-ip.com/atm (My telescope construction,testing, and coating site)
"Anything that can happen, will happen" -Stephen Pollock from:
"Particle Physics for Non-Physicists: A Tour of the Microcosmos"
" Press on: nothing in the world can take the place of perseverance.
Talent will not; nothing is more common than unsuccessful men with talent.
Genius will not; unrewarded genius is almost a proverb.
Education will not; the world is full of educated derelicts.
Persistence and determination alone are omnipotent. "
Calvin Coolidge