The Orange Involute

Big Data need­ed more dri­ve­train pow­er. How do you get more of that sweet, sweet sen­sored brush­less power?

Portescap 22BL-8B-P17

More motor.

These are eBay-sup­plied Portescap 22BL-8B‑P motors, pre­cur­sors to the cur­rent Portescap line­up of 22 mm motors. With dif­fer­ent mag­nets on the rotor and a high­er ther­mal resis­tance of 13 °C/W, they are rat­ed for 20 W con­tin­u­ous rather than 70 W, but that’s still much more than a bee­tle weight (3 lb) robot needs, espe­cial­ly since dri­ve­train pow­er comes in short bursts.

22BL drawing

The mount­ing pat­tern in the dia­gram does­n’t quite match that in the pho­to. I’ll deal with that.

The more press­ing con­cern is the insane speed. The hob­by R/C world would describe this motor as a 1500 Kv “inrun­ner” with a no-load speed of 36800 RPM at 24V. With a con­tin­u­ous stall torque of 21.6 mNm and assum­ing 70 mm diam­e­ter wheels, each motor would have to be reduced at a ratio of 1:10.8 to be able to win a sta­t­ic push­ing match against anoth­er beetle.

Even with that much reduc­tion Big Data’s sec­ond com­ing would still have an esti­mat­ed top speed of over 10 m/s (20 mph). The max pow­er is lim­it­ed by heat, not wind­ings, so for short bursts the motors can dri­ve Big Data to a full 1 G of hor­i­zon­tal accel­er­a­tion at any speed with­in 90% of their top speed. Remem­ber that this is the fastest that a robot can accel­er­ate with­in the nor­mal lim­its of trac­tion (i.e., no tire adhe­sion, no mag­nets, no suc­tion, etc.).

Gear train design

This design calls for at least two stages of gear reduc­tion. I decid­ed on 8:42 on the first stage and 28:68 on the sec­ond for an over­all reduc­tion of 1:12.75, using spur gears with a 0.8 mm diame­tral pitch (“Mod­ule 0.8”) and a 20° pres­sure angle.

I did­n’t even know they made 8‑tooth pin­ion gears, but there they are from Stock Dri­ve Prod­ucts1. Unfor­tu­nate­ly, they don’t make a stepped spur gear with 42 and 28 teeth, so I had to make my own.

Planning mill tool paths

First I drew up the invo­lute gear pro­files as equa­tion dri­ven splines in Solid­Works and designed a machin­ing solu­tion using HSMX­press, my pre­ferred com­put­er-aid­ed machin­ing (CAM) package.

Roughing positive mold with a 6 mm tool

Then I milled the pos­i­tive mold cav­i­ty from Free­man Sup­ply’s “pur­ple machin­able wax,” which is basi­cal­ly hard­ened and plas­ti­cized paraf­fin. The machine is a Roland MDX-402 on loan to the Garage, the mak­er­space on Google’s Moun­tain View campus.

Finishing wax mold with a 0.4 mm tool

It gets pret­ty scary when I spin the 0.4 mm four-flute end mill to 15000 RPM and fin­ish the teeth at over 250 mm/min. The high feed rate keeps the tool from melt­ing the wax. Molten wax chips tend to stick back onto the mold and are tedious to get rid of.

No tools were bro­ken in the mak­ing of these gears.

Degassing silicone in wax mold cavity

Next I mix up some Quan­tum Sil­i­cone QM 270 and drop it in the pos­i­tive mold cav­i­ty. Under a strong vac­u­um, the air trapped under the sil­i­cone in the mold’s nooks and cran­nies bal­loon up and writhe to the sur­face, where they pop rather sat­is­fy­ing­ly (and silently!).

silicone ready to demold

I kept the back­side of the neg­a­tive mold flat using a sheet of acrylic. Sil­i­cone does­n’t stick to any­thing, so this worked well.

Silicone mold and polyurethane gears

Now the neg­a­tive mold is out and I have a reusable, flex­i­ble sil­i­cone neg­a­tive for plas­tic gears. I dump in some Inno­v­a­tive Poly­mers IE-3075 and a lot of the orangest dye I have ever seen. Unfor­tu­nate­ly, polyurethane does stick to acrylic.

gear separation

BAM, I got some gears. I love that the machin­ing marks from the orig­i­nal pos­i­tive wax mold are pre­served through the process to the final part.

Geartrain test fit

Seems to fit.

Thanks Dan for loan­ing us the Roland mill and thanks Michal for the superb CNC and resin cast­ing guide.

  1. I’m not link­ing to them because I’ve always had such a ter­ri­ble expe­ri­ence with them. I’m final­ly tak­ing my busi­ness away from SDP/SI for good. []
  2. Not MDX-40A, which takes G‑code, but the old­er mod­el that takes Roland Machine Lan­guage (RML). []