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Threadless Ballscrew - 3D printed
@palatisCool stuff bro, thanks for the math!I am sure this will help a lot of people.
damn where does the image go?let me just re-upload it...
math behind traveling distance calculation:given the diameter of the shaft D, and bearing angle ϴ, how far does it travel if the shaft takes a full turn?the bearing travels a helical path alone the center of the shaftif we expand the cylinder (the shaft often has a cylindrical shape... if yours doesn't, you're in trouble.) into a plane, we get a right triangle with it's hypotenus equals the circumferences of the cylinder C, distance traveled by the ball bearing alone the helical path T, the angle towards the direction of movement ϴ, and movement along the shaft h.the shaft with diameter D has a circumferences of C = D * π, the distance the nut has traveled is:h = tan(ϴ) * D * πfor example, 1. a 8mm shaft with 20 degree ball bearing angle will travelh = tan(20 degree) * 8mm * π ~= 0.364 * 8mm * 3.1415 ~= 9.147mmafter a full turn.2. a 8mm shaft with 10 degree ball bearing angle will travelh = tan(10 degree) * 8mm * π ~= 0.176 * 8mm * 3.1415 ~= 4.4315mmafter a full turn.3. a 16mm shaft with 10 degree ball bearing angle will travelh = tan(10 degree) * 16mm* π ~= 0.176 * 16mm * 3.1415 ~= 8.8631mmafter a full turn.=============now, say you want the nut to travel h mm after a full turn of the shaft, how do you calculate the correct angle for it?taken the above equationh = tan(ϴ) * D * π,rearrange thattan(ϴ) = h / (D * π),ϴ = tan^-1(h / (D * π))for example, you want the nut to travel 4mm alone a 16mm shaft:ϴ = tan^-1(4 / (16 * π)) ~= tan^-1(0.00795) ~= 4.55 degree=============HOWEVER, 1. bearings got play and tolerance2. shafts got tolerance3. 3D printed parts got tolerance4. friction of "steel against steel" is not very high...how long a specific "ball bearing bearing nut" will travel per shaft turn may vary from nut to nut.the above equations just give you an idea on how to design your own nut, for precision cnc you ALWAYS has to calibrate your machine.=============dunno if we have something like rubber coated bearings or not?I know there're POM bearing wheel out there (such as the wheel used in V-slot or other aluminium extrusions), but POM is a low friction (ie, slippery) material...maybe i'll get the tires from those mini 4WD and try them out...
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