With MadeinSpace investigating the potential of manufacturing in space a question for power nerds arises, is it possible to use stereo lithography style 3-D printers to create useful tools and objects for space bound explorers? Theoretically the answer would be yes it is possible to develop stereo-lithography printers that work in space. This yes comes with a number of caveats, starting with the challenges of working with fluids in a micro-gravity environment, without the aid of gravity, liquids tend to bunch up and create floating globs that can cause chaos on space craft. (see vacuum toilets). Ensuring that liquids stay in place can be done one of three ways*, store it in a container, use the force of air to position the fluid, or finally using centripetal force to "push" the liquid to the outside of a rotating body. Using air to control the position of the photo reactive resin would most likely lead to a range of headaches that would make developing such a technology extremely prohibitive. The remaining two options are two manufacture the entire object in a sealed container, similar to more traditional approaches in stereo lithography manufacture, but that doesn't involve any "fun" math, so I'm going to ignore this option, initially and go for the math approach, spinning a 3-D printer around a center point to simulate the effect of gravity.
In the image above we see a cut away that helps to highlight a concern of trying to create the effect of gravitational pull using centripetal acceleration (read spinning things around a center point). The liquid reservoir will not simply lie flat within in its container while it is being spun out, similar to the water in a bucket curving if you spin it around, the concave shape of the liquid must be controlled, if it is too extreme the printer won't behave correctly. Calculating the shape of the liquid in the container is relatively simple, as energy is conserved the photo reactive resin will take the path of least resistance, ie. the shape of the water will roughly follow the curvature of the path of the spinning object, you can see this effect in the image above. An engineer properly designing this printing system is limited by two things, the maximum allowable difference in the depth of the photo-curable resin and the maximum allowable radius of rotation that can occur within the volume of a space craft, for example the ISS.
The proposed Centrifuge Accommodations Module, canceled after the 2003 Columbia disaster, was intended to have a 2.5 meter diameter centrifuge to allow for experiments on organisms and materials under various intensities of simulated gravity, while this diameter might not occupy the entire volume of the module, it provides a reasonable outer bound for diameter of the centrifuged printer system.
Calculating the height difference of the photo curable resin from the diameter of rotation is now a matter of trigonometry.
The image to the right is a zoomed in perspective of the totally not to scale reference image from above.
Here we are defining R as being 1.25 meters,
X is going to be defined off of the FormLabs Form1 printer for two reasons, 1) I know the number off hand it makes my life a bit easier 2) I want to suck up to a perspective employer. X is defined as half the value of the width of the resin reservoir, or 0.0625m
(the Form1 is 12.5 cm accross)
With these two variables we have 2 sides of a right triangle making the last variable pretty easy to calculate the change in height.
which can be
rewritten as,
Plugging in the numbers we can now calculate the difference in height of the fluid from the center to the outside. Where we find the liquid would be 1.56 mm deeper at the edge of rotation, and as it is almost as easy to calculate a large range of cases as it is just this particular case, the below graph shows the variation in fluid height as a result of the radius of rotation.
It is reasonable to assume that if the printer is allowed to rotate at a radius of at least 0.7 meters, where the height difference between the fluid is less than 3mm that the printer would be capable of operating in a micro-gravity setting.
Alternatively engineers could build a system that closely resembles more traditional Stero Lithogrpahy rapid prototyping where the top of the printer is covered in a material transparent to UV light.
The purple represents the UV transparent cover, the blue is the working fluid. As the container is fully enclosed the liquid cannot go anywhere during printing seeing as it already fills the volume of its container. The challenge for this design is the removal of the relatively large volume of leftover photo-curable resin at the end of the process.
While this was a fun thought experiment there are some legitimate concerns of using stereo lithography in a micro-gravity environment.
Do the benefits of this type of printer outweigh the complexity and cost requirements. How would cosmic rays and solar particles effect the quality of the photo-curable resin while it is in storage, considering the intense energies of these particles it is worth determining how much of the resin would become non-viable during storage over time.
inks
http://www.cns.gatech.edu/~predrag/courses/PHYS-4421-10/Lautrup/shapes.pdf page 59 (or 2 via scrolling) provides the useful math
open source physics textbook http://www.saylor.org/site/wp-content/uploads/2013/02/PHYS101_OpenStaxCollege_College-Physics.pdf
another reference http://cnx.org/content/m42084/latest/?collection=col11406/latest
http://en.wikipedia.org/wiki/Bucket_argument
In the image above we see a cut away that helps to highlight a concern of trying to create the effect of gravitational pull using centripetal acceleration (read spinning things around a center point). The liquid reservoir will not simply lie flat within in its container while it is being spun out, similar to the water in a bucket curving if you spin it around, the concave shape of the liquid must be controlled, if it is too extreme the printer won't behave correctly. Calculating the shape of the liquid in the container is relatively simple, as energy is conserved the photo reactive resin will take the path of least resistance, ie. the shape of the water will roughly follow the curvature of the path of the spinning object, you can see this effect in the image above. An engineer properly designing this printing system is limited by two things, the maximum allowable difference in the depth of the photo-curable resin and the maximum allowable radius of rotation that can occur within the volume of a space craft, for example the ISS.
The proposed Centrifuge Accommodations Module, canceled after the 2003 Columbia disaster, was intended to have a 2.5 meter diameter centrifuge to allow for experiments on organisms and materials under various intensities of simulated gravity, while this diameter might not occupy the entire volume of the module, it provides a reasonable outer bound for diameter of the centrifuged printer system.
Calculating the height difference of the photo curable resin from the diameter of rotation is now a matter of trigonometry.
The image to the right is a zoomed in perspective of the totally not to scale reference image from above.
Here we are defining R as being 1.25 meters,
X is going to be defined off of the FormLabs Form1 printer for two reasons, 1) I know the number off hand it makes my life a bit easier 2) I want to suck up to a perspective employer. X is defined as half the value of the width of the resin reservoir, or 0.0625m
(the Form1 is 12.5 cm accross)
With these two variables we have 2 sides of a right triangle making the last variable pretty easy to calculate the change in height.
which can berewritten as,
Plugging in the numbers we can now calculate the difference in height of the fluid from the center to the outside. Where we find the liquid would be 1.56 mm deeper at the edge of rotation, and as it is almost as easy to calculate a large range of cases as it is just this particular case, the below graph shows the variation in fluid height as a result of the radius of rotation.
It is reasonable to assume that if the printer is allowed to rotate at a radius of at least 0.7 meters, where the height difference between the fluid is less than 3mm that the printer would be capable of operating in a micro-gravity setting.
Alternatively engineers could build a system that closely resembles more traditional Stero Lithogrpahy rapid prototyping where the top of the printer is covered in a material transparent to UV light.
The purple represents the UV transparent cover, the blue is the working fluid. As the container is fully enclosed the liquid cannot go anywhere during printing seeing as it already fills the volume of its container. The challenge for this design is the removal of the relatively large volume of leftover photo-curable resin at the end of the process.
While this was a fun thought experiment there are some legitimate concerns of using stereo lithography in a micro-gravity environment.
Do the benefits of this type of printer outweigh the complexity and cost requirements. How would cosmic rays and solar particles effect the quality of the photo-curable resin while it is in storage, considering the intense energies of these particles it is worth determining how much of the resin would become non-viable during storage over time.
inks
http://www.cns.gatech.edu/~predrag/courses/PHYS-4421-10/Lautrup/shapes.pdf page 59 (or 2 via scrolling) provides the useful math
open source physics textbook http://www.saylor.org/site/wp-content/uploads/2013/02/PHYS101_OpenStaxCollege_College-Physics.pdf
another reference http://cnx.org/content/m42084/latest/?collection=col11406/latest
http://en.wikipedia.org/wiki/Bucket_argument
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