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Involute Rack and Sector Pinion Gear Question 3

basserben

Student
Mar 17, 2025
2
This is a hobby related question, but one that has stirred up some debate in the world of airsoft replica tech work - and I believe the answer is best answered from the engineering front. I have a conclusion that I believe fits the science, but I wanted to see if the more knowledgeable among us lands in the same zip code as I did.

In an electric airsoft replica, the bb projectile is fired by a spring loaded, rack-driven piston. This piston is picked up (and later released) by a sector gear.

AEG.gif

In earlier days, the replicas were built with the piston rack so far forward, the sector gear would first engage the pickup rack tooth on the corner of the rack tooth, driving it upwards and frequently breaking off the rear of the rack entirely. To combat this, techs would shim the piston rearward to allow the faces of the gear teeth to meet properly at pickup. To do this, however, the second and a portion (or all of) the third teeth of the rack were removed to allow clearance for the sector gear teeth.

Over time, it was discovered that removing two entire teeth simply moved the issue to the fourth rack tooth, so standard operating procedure has been narrowed to removing the entire second tooth and 1/2 of the third.

My question is this - taking into account the sector gear information below, what is the most optimal angle for the sector gear to engage the rack pickup tooth, while trying for the best transmission of torque from tooth to tooth?

My research leads me to believe that, since involute gears have consistent torque throughout meshing (thus little to be gained by shimming the rack too far rearwards), removing the second rack tooth alone should be sufficient enough to allow clearance for the sector tooth to pickup the rack at roughly a 15° angle (11:30 position), which should allow face-to-face meshing while minimizing transfer issues between teeth - but I want to verify my findings, or improve on it if I'm wrong.

Sector Gear Information:
Module: .98436
Number of Teeth: 30 standard (built with 16)
Pressure Angle: 20°
Tip Diameter: 31.5mm
Base Diameter: 27.75mm
Pitch Circle Diameter: 29.52mm
 
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OP
for this application
contact ratio (# of teeth at contact)
should be higher than 1.2 ratio.

also center distance is important.

sector and rack gear location a important.
the angle would be to insure full contact while forward motion.
 
to obtain the the required # of teeth can mathematically be derived.
however it's much easier and faster to
draw it in cad.
the other issue with the rack breaking is
lack of thickness between the root diameter and the face of rack. a standard free body diagram of a beam or needs supported better.
 
OP
for this application
contact ratio (# of teeth at contact)
should be higher than 1.2 ratio.

also center distance is important.

sector and rack gear location a important.
the angle would be to insure full contact while forward motion.

I'm assuming an addendum of .984 on both the sector and rack that meet at the pitch point, and I'm calculating as if there is no significant axial shift (center distance). I wouldn't be sure how to measure axial distance with a rack, but thankfully the design doesn't appear to have much spacing involved.

I haven't dialed in the math precisely on the contact ratio, but it appears to be near 1.66.
 
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A sensible person would use an elliptical or cam gear so it engages at low speed and then accelerates the rack backwards. Generating the associated rack profile is not a major task, I did it at high school. Clue : bits of card and drawing pins.

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