Banebots 42mm gearbox: Recommendations for use

[Joe Johnson]

As readers of these fora know, the 56mm Banebots transmission has a failure mode that involves the double D joint between the last carrier stage and the output shaft.

The 42mm gearbox shares this same failure mode.

I have done some testing and I have the following recommendation with regard to the use of these gearboxes:


My analysis is below. I think the numbers are somewhat conservative but I don’t think they are way out of line with what teams will see.

This will be my advice to teams in summary:
42mm w/FP: If you plan to stall the motor, use ratio less than 145:1
42mm w/BB: If you plan to stall the motor, use ratio less than 214:1

Note that even though you cannot BUY a 144:1 gearbox it is possible to build one if you buy a 256:1 and combine it with parts from a 36:1 BUT... BE WARNED doing so is probably marginal if used with a FP motor

Finally, I do not include dynamic effects in these calculations. If you are expecting the mechanism to have significant impact loads, I recommend even lower ratios.

As always, your mileage may vary.

Joe J.

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Rockwell C to Tensile Yield:
RC 22 – 115 Ksi
RC 23 – 117 Ksi
RC 24 – 119 Ksi
RC 25 – 123 Ksi
RC 26 – 125 Ksi

42mm
Carrier hardness:
RC 23.6, 23.8, 24.3
Gear Brass:
RA 37.7, 35.4, 35.8 <<suspect due to small surface to test
Shaft:
RC 43.1, 40.6, 43.7

Given the analysis of the D on the 56mm gearbox, due to scaling, the 42mm D should take 54% of 350in-lbs failure for the 56mm gearbox. But the yield of the carrier on the 42mm gearbox is harder (119Ksi rather than 64Ksi) so it should 186% stronger due to better material. The net effect should be that the joint should fail at almost exactly the same value as the 56mm gearbox (350in-lbs).

If that is true, then I predict that the 42mm gearbox with a FP motor (with 12V stall = .42N-m = 3.7in-lbs) will fail if the effective ratio (the ratio including losses due to efficiency) is 95:1 or higher.

In order to get 95:1 it will take 4 stages. I usually use 85% per planetary stage as my efficiency when I design a gearbox output, but in this case I will use 90% per stage in order to be safe (more torque getting through means more stress on the output). Given that, I predict that the FP motor on the 42mm gearbox with a ratio of 145:1 or greater will fail.

Similarly for the BB motor in the kit (12V stall = .28N-m = 2.5in-lbs) will fail if the effective ratio (the ratio including losses due to efficiency) is higher than 140:1.

In order to get 140:1 it will take 4 stages. Again using 90% per, predict that the BB motor on the 42mm gearbox with a ratio of 214:1 or greater will fail.

Note that these are not one time failure predictions but a failure that will fail upon repeated cycling back and forth.

Now to the actual torque to failure test: I used a 256:1 gearbox. The input torque required to fail the gearbox with the output shaft locked was .6N-m (5.3in-lbs). The peak (after failure, the torque grows as the shaft plows through the carrier) was 1.0N-m

This is scarily close to the stall torque of the FP motor and not too far away from the BB motor. Also, this does not include any dynamic loading of the gearbox.

But, based on the 5.3in-lbs failure, I get that the D joint fails at 5.3in-lbs * (4 * .85)^4 = 710in-lbs. Note while this is higher than the 350in-lbs predicted above, that number was not 1 time failure load, but a load that if cycled caused failure, so I am not too worried at this difference.