Hi, I'm working on a school project designing a gearbox with the following setup: -200 rpm motor with 0.45 N/m torque -5kg weight that is hung from one of 5 pulleys, we get to choose which. They are 20, 30, 40, 50, 60 mm diameter. -The design will be 3D printed out of ABS -The fastest time to lift the weight wins. I've done calculations for each pulley, requiring a GB with ratios of: 1.09, 1.635, 2.18, 2.725 , 3.27 As far as I can tell, they will all lift the weight at the same speed, unless you factor in GB losses. (Friction etc...) So: Do I go high speed (with smallest pulley), high torque (biggest pulley), or somewhere in between?

I assume that you are setting the ratio to have the motor run at the maximum power point, which for a DC motor is typically 50% of no-load speed. I would go with the design that has the fewest stages, to try to reduce friction losses. Do a free body diagram on each gear to see what the reaction forces are an make some assumptions about friction to estimate losses. It doesn't really matter if the assumptions are perfect, as long as they are consistent you should be able to compare options. Since it is going to be built with 3d printing you may want to investigate non-traditional gear teeth forms. There are some cool articles on direct gear design by a guy named kapelevich. assymetric teeth and stuff - very cool. Also look at planetary. the radial symmetry reduces some, but not all, of the bearing loads. Good luck

Thanks, that's a good start. I get the feeling that friction on teeth will always just cancel out, but I will do the math to be sure (friction from Higher load/lower rpm = friction from lower load/higher rpm??). I considered helical or herringbone gears, and planetary too, but was concerned about friction. Is there generally higher friction associated with these gear types? (More tooth contact with the helical/herringbone... but again less force)

If you feel confident in those calculations then it seems to me that you should pick the GB ratio that can be best matched of those ratios with one gear reduction and you have your pulley size. If you find one that hits then you have it. If not then use a combination of three gears to find best match to pulley size.

friction on the teeth is, to a first order approximation, zero, since involute teeth have rolling contact. Of course in practice there is friction, but it is tricky to calculate. There are correlations available, but I think most of them are based on particular materials. Since it is going to be 3d printed in ABS i am assuming you mean FDM. This has some roughness and so it may be best to have larger teeth rather than smaller so that the roughness is a smaller proportion of the tooth shape. Using herringbone/ helical gears improves the contact ratio, but helicals produce side thrust. Since one of the ratios you calculated is 1.09, your best bet may be to take the 9% hit and direct drive the pulley - no bearings, no gears mean no tooth friction and no bearing friction and it may more than compensate for the slightly sub-optimum ratio.

I don't understand your project's objective: 1. Do you have to design and use a gearbox? 2. Do you have to show the fastest time to lift the weight? 3. Both are correct? Without defining a clear objective it's very difficult to solve any engineering problem. Another question, by what means are you going to drive the DC motor?

@guy: Yes the gearbox must be designed and tested. The fastest time to lift the weight is the winner. The AC gearmotor can be found here: http://www.mcmaster.com/#6142k73/=anb5gs Presumably powered form a 15 amp 115v outlet. @maniacal_engineer: Agreed, upon calculating those ratios, I thought the 1.09 would be a cheeky solution, not sure how many marks I would get for design though! The thrust issues aside, would it be safe to assume equal losses in spur gears and equivalent helical gears? Does a helical gear roll in the same way that an involute spur gear does?

The thrust loads come from the axial component of the face normal force on the tooth. So at extreme angles you would get wedging - like a morse taper - with high friction loads. I think it is a 1/cos factor. A small taper angle herringbone - less than 10 degrees say - can improve smoothness of the mesh with only a little extra friction. If the bearings in the gearbox are just plastic on plastic, and not roller bearings or good plain bearings (Igus, sintered bronze on hard steel etc) then the direct drive solution IS the best design solution. Low part count, nothing to make, nothing to break - what's not to like. Also, I had assumed a DC motor. the shaded pole AC motor has a different torque/speed curve so you might want to look at starting torque to make sure that it can start as well as run steady state.