# Bevel/Miter Gear Mounting Distances

So we are playing around with bevel and miter gears for our gearboxes. We can’t seem to find an easy to understand formula for determining the proper mounting distances.

Right now we are using the 15t bevel gear from VEX Pro and are trying to design a simple 90 degree 1:1 mesh.

Are there any handy formulas that you all use to determine the mounting distances?

We are familiar with spur gear mounting distances, mating proper DP, etc.

Can anyone help or give examples?

The mounting distance is usually listed with the product for miter gears. In the case of the Vex ones, this is 1.250". You can find it in the drawing here: http://content.vexrobotics.com/vexpro/pdf/217-3344-Drawing-20140211.PDF

Ok. I see the drawing file and the distances listed. I can see that the bevel gears are 12 DP gears so 15 teeth divided by 12 gives me 1.25 in. for the mounting distances.

Do the same rules for spur gear mounting distances apply to bevel and miter gears as well?

For example, if I wanted to use a bevel gear with a 15 tooth input and a 30 tooth output and they were both 12 DP gears would my mounting distance be:

15 / 12 = 1.25
30 /12 = 2.5

Mounting distance = 3.75

Is that correct?

No, each gear mounts the appropriate distance from the inside corner for the number of teeth it has. If you were to “unfold” the box, you would have the sum of these two distances (plus the fold itself) as the distance between the holes. The “pitch cone” of each gear should intersect the inside corner of the gearbox at the same point, and those two cones should share a line where they are tangent to each other.

There is no way to determine the mounting distances for miter or bevel gears solely from the tooth information. The mounting distances are dependent on the shape and size of the gear’s hub and should be specified in drawings or data tables with the gears. Many of these gears are made with standard hub sizes so if that information isn’t available from the seller it might be available in the manufactures product catalogs.

That makes sense. I have seen gear sets with the distances marked on them. I just didn’t know whether or not if there was a simple formula to use.

When designing these you will need to have the bearing flanges on the miter/bevel side to take the axial load into the structure. I would also recommend a thrust bearing, an Oilite bronze bearing is ideal for this application. The Bearing Flange is 1/16" thick, and the Oilite Bearings are normally 1/16" thick in this size range. So make sure to account for another 0.125" behind each gear.

The Vex miter gears have a smaller hub behind the main hub that protrudes out 1/16". You can put a thrust bearing/washer on that to save space, and/or forgo putting the thrust loads on the ball bearing.

This depends on what you are designing. If you are designing a swerve drive, yes, you need a thrust bearing so that the gearbox can support the robot weight. On the other hand, if all you are doing is turning the motor sideways then driving another gear or sprocket, or are transferring torque from one direction to another (e.g. a lobster drive), there will not be a significant axial load.

Miter and Bevel Gears require fairly tight tolerances to avoid excessive gear tooth wear. These Gears mating at an angle do induce thrust loads.

Skipping the inclusion of a \$1 bronze or brass thrust washer is fine if your design, machining, and assembly tolerances are close to perfect. However, repeatable perfect machining and assembly don’t seem to be a common characteristic during a rushed build season.

The thrust washer both distributes the thrust loads, and also provide a less hard wear surface between the steel gear & steel bearing. This is simply good engineering practice for use of these gears, your welcome to use it or ignore it.

I thought miter/bevel gears by nature exert large axial forces? In a swerve drive you can have a thrust bearing on the module and a separate one on the miter/bevel gears to take two different thrust loads.

There is a little bit of hand waving here, but for the typical FRC

swerve that uses 12DP 15T bevels with some reduction after to the wheel (the rough size modules 118, 1717, 973, 1625, etc… have run ) it’s okay to use the radial bearing (typical an FR6/FR8 here) to handle these axial loads. If doing this make sure the gear is necked down such as the Vex bevel so it’s not rubbing the outer race.

Starting fresh, and not having a massive pile of anecdotal data for these exact bevels to reference, I’d design in better thrust management (or do the math for what thrust you bearing can take and compare that to the loads generated).

A 1" diameter bevel gear driven at the same speed as a 2" wheel delivering 100lb of force to that wheel still only sees a 50 lb thrust load. Increasing wheel size or reduction after the bevel stage, or reducing final force output, reduces this thrust load. Since the radial bearings typically take several hundred pounds radially, sounds reasonable that the groove is deep enough (min. ~30 degree span) to support that small of a thrust load as well. Sounds like some of those swerves did rely on the radial bearing in this way.

Edit: did wheel to bevel diameter ratio backwards. Fixed by multiplying thrust loads by 4.

Just dug out Shigley & Mithell Machine Design Text

For the VEX Miter gears the average gear tooth diameter is 0.926 inches, or a radius of 0.463 inch. For Miter gears both Pitch angles are 45°

= (Torque/0.463) (1) (.707)

CIM Motor Torque at maximum power is 172 oz* in

Axial Gear Force = 172 (Ounce*In) * (.707) / 0.463 in = 262 oz or 16.4 lbs.

Directly driven by a CIM Motor. If there are typical swerve speed reduction stages of 4:1 or so ahead of the miter gears, you can multiply this axial force by that ratio as well.

The argument to tangent is the pressure angle of the teeth, not the pitch cone angle. tan(20°) is around 0.36 resulting in a reduction in your figures by a factor of 3.

= (Torque/0.463) (.364) (.707)

Axial Gear Force = 172 (Ounce*In) * (.364)(.707) / 0.463 in
= 95.6 oz or 5.9 lbs

With a Swerve drive gear reduction, this is still a substantial force on a small FR6ZZ

One counter example is 1640, who has been re-iterating their swerve modules for the last few years and have one of the most fully developed systems (in my opinion). They still incorporate thrust bearings into their modules. It’s only about \$3.50 per bearing, so not really a large resource cost.

Anyone designing swerve modules should check out their wiki, it’s a fountain of information. DEWBOT XI Drive Train - DEW Robotics

Much smaller than the thrust loads applied to the bearings in all traction wheeled skid steers.

If you’re particularly worried about the thrust loads and you’re using the Vex miter gears…you’ll notice they already include a small shoulder on the back side for a standard sized 0.0625" thick thrust bushing. Adding this bushing will not modify the mount distance.

They don’t advertise this feature but it’s there.