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# Sizing the Teeth of the Ring Gear in an Epicyclic Gear Train

## Sizing the Teeth of the Ring Gear in an Epicyclic Gear Train

(OP)
I'm outside my area of expertise, so I apologize if this question is a little basic. I'm modeling an epicyclic gear train, and have hit a snag. I can model the spur gears, but I'm having trouble finding a good reference on how to size the teeth on the ring gear. I've exhausted Google searches, so time to call in the professionals. Can someone point me to an appropriate reference?

Example calculation
DiametralPitch = 16
PressureAngle = 14.5 degrees
SunNumberTeeth = 20
PlanetNumberTeeth = 16
NumberPlanetGears = 4

SunDedendum = 1.157/#DiametralPitch = 0.072"
SunPitchDiameter = #SunNumberTeeth/#DiametralPitch = 1.25"
SunBaseDiameter = #SunPitchDiameter*cos(#PressureAngle) = 1.210"
SunRootDiameter = #SunPitchDiameter-2*#SunDedendum = 1.105"
SunBaseCircumference = 3.1415927*#SunBaseDiameter = 3.802"
SunGearToothSpacing = 360*degree/#SunNumberTeeth = 18 degrees
SunGearToothWidth = 18*degree/2 = 9 degrees (at Base Circle)

PlanetDedendum = #SunDedendum = 0.072"
PlanetPitchDiameter = #PlanetNumberTeeth/#DiametralPitch = 1.000"
PlanetBaseDiameter = #PlanetPitchDiameter*cos(#PressureAngle) = 0.968"
PlanetRootDiameter = #PlanetPitchDiameter-2*#PlanetDedendum = 0.855"
PlanetBaseCircumference = 3.1415927*#PlanetBaseDiameter = 3.042"
PlanetGearToothSpacing = 360*degree/#PlanetNumberTeeth = 22.5 degrees
PlanetGearToothWidth = 18*degree/2 = 9 degrees (at Base Circle)

RingNumberTeeth = #SunNumberTeeth+2*#PlanetNumberTeeth = 52
RingPitchDiameter = #RingNumberTeeth/#DiametralPitch = 3.25"
RingBaseDiameter = #RingPitchDiameter*cos(#PressureAngle) = 3.146"
RingRootDiameter = #RingPitchDiameter+2*#RingDedendum = 3.391"
RingBaseCircumference = 3.1415927*#RingBaseDiameter = 9.885"
RingGearToothSpacing = 360*degree/#RingNumberTeeth = 6.923 degrees
SunGearToothWidth = ?

### RE: Sizing the Teeth of the Ring Gear in an Epicyclic Gear Train

Can you be more specific in what you mean by "modeling" and/or "sizing" the ring gear teeth? What are the requirements of your application? Are you concerned with efficiency, weight, fatigue life, noise, cost?

The data in your OP looks like the design is pretty straight forward. Depending on the specific operating requirements, you might want to tweak the geometries a bit to optimize performance and balance fatigue life.

### RE: Sizing the Teeth of the Ring Gear in an Epicyclic Gear Train

(OP)
@tbuelna, thanks for the reply. My sticking point was how to calculate the width of the gear teeth. For two spur gears to mesh, half of the circumference is tooth and half is root which is very straightforward. I tried the same philosophy with a ring gear and got interference. I just realized I need to match the widths at the pitch circle and it is looking much better, so I guess I solved my own problem.

In this case, I'm building a mechanism to roll/unroll a narrow banner, so it's a pretty light-duty application. I'm planning on 3-D printing it, so the tolerances won't be very tight. I'm also 1) learning about gearing, 2) learning to use the OnShape CAD package, and 3) contributing my design to the OnShape community for others to use in whatever project they are doing, so I want to do it right.

### RE: Sizing the Teeth of the Ring Gear in an Epicyclic Gear Train

The tooth thickness and mating tooth space should allow for some amount of backlash.

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