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Bearing Load & Support Placement

What each bearing carries, and why an overhung wheel can push its inner bearing backwards with more force than the load itself. Sandwiching a load halves the bearing forces; overhanging it multiplies them.

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The arrangement

Outboard is a wheel or sprocket hanging past the end of its bearings. Sandwiched is the same part with a bearing on each side of it.

in

Center to center. VEX holes are 0.5" apart, so a whole number of holes is what you can actually build.

in

Measured outward past the bearing for an outboard load, inward from it for a sandwiched one.

The load

lbf

The sideways force at that point. For a drive wheel this is roughly the robot's weight on that corner, plus whatever pushing force it is making.

Used only for the deflection comparison at the bottom. The bearing forces do not depend on it at all. That is worth knowing on its own.

Results

Inner bearing, next to the load

—lbf

Outer bearing

—lbf

Which way the outer one pushes

—

Worst bearing, against the load itself

—

How far the load moves

—thou

Cheapest thing to change

—

Bearings and the forces on them

Bearings and the forces on them
4 holes

Arrows show which way each bearing pushes on the shaft, and their length is to scale with each other. Drag to change the spacing in whole VEX holes and watch the two forces trade against each other.

Show the numbers behind this chart

What every buildable bearing spacing does to the two bearing forces and to how far the load moves, so the trade-off is visible as numbers rather than a claim.

How this is calculated

A shaft is not held up by magic. Whatever pushes on it has to be balanced by the supports, and there are only two rules, both of which you can check on your fingers.

  • The forces have to add to nothing.
  • The turning effects have to add to nothing, measured about any point you like.

Sandwiched: the easy case

Put the load between the bearings and each one takes a share, split by how close it is. Halfway between, they take half each. A quarter of the way along, the near one takes three quarters. Neither ever carries more than the whole load, and neither ever pushes backwards.

near = load × far distance ÷ span

Outboard: the case that surprises everyone

Now hang the load past the end. Take moments about the outer bearing: the load is pulling down at a distance of the span plus the overhang, and the only thing available to balance it is the inner bearing. So

inner = load × (span + overhang) ÷ span

which is bigger than the load, always. And now the forces do not add up: the inner bearing is pushing up harder than the load pushes down. Something has to make up the difference, and the only thing left is the outer bearing, which must pull the other way:

outer = −load × overhang ÷ span

Put numbers on it. A 10 lbf load an inch past two bearings an inch apart: the inner bearing carries 20 lbf and the outer one pulls down with 10. A 10 lbf load has produced 30 lbf of bearing force out of nowhere, and it did that purely from the geometry.

This is what is happening when an overhung wheel pulls its inner bearing block off the C-channel, or wears the hole into an oval, with a load nowhere near strong enough to explain it.

The trade nobody mentions

The obvious fix is to move the bearings further apart, and for bearing forces that works. The span is on the bottom of both fractions, so wider spacing means gentler forces.

It makes the deflection worse. Two bearings are not a rigid wall; they resist the overhang's twisting with a pair of opposite forces, and the length of shaft between them bends under that pair. A longer piece of shaft is a floppier spring, so it rotates further, and the overhang rides that rotation out to the wheel. With bearings two inches apart holding a wheel half an inch out, four fifths of the wobble is the span rotating rather than the stub bending.

So the two things you can change pull against each other:

  • Narrow spacing: less movement, much higher bearing forces.
  • Wide spacing: gentle bearing forces, more movement.

There is no best answer in between, because this model treats the bearings and the C-channel as immovable. On a real robot they are not, and it is the narrow-spacing case that splays blocks and wallows out holes. Which is why the honest recommendation is usually neither number:stop overhanging it. Put a bearing on both sides of the wheel and both problems go away at once. That is why VEX drivetrains sandwich their wheels between two C-channels, and it is not for neatness.

What this does not cover

  • Bearing strength. VEX publishes no load rating for a bearing block, so this page tells you the force and cannot tell you whether the bearing survives it. Use it to compare arrangements, and trust what you see on the robot for the rest.
  • The screws. The force reaching the C-channel goes through two small screws in one direction. That is frequently the actual weak point.
  • Shock. Every figure here is the steady load. A drivetrain being rammed sees several times this for an instant.

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                                Sources & assumptions

                                The bearing forces are pure statics. They follow from the two balance rules and nothing else: no material property, no VEX-specific figure, and notably not the shaft size. A 1/8" shaft and a 1/4" shaft in the same arrangement put identical forces into their bearings.

                                The deflection figure is derived and assumes steel at 29,000,000 psi. See thedeflection tool for what that assumption is worth.

                                No bearing load rating is used or implied, because VEX does not publish one. This page reports forces, not verdicts about survival.

                                Checked numerically. The reactions, the sign reversal on the outer bearing and the spacing trade-off are all verified inscripts/verify-beam.mjs against an independent solution, with force and moment balance checked directly, and deflection checked against a numerical integration of the beam's curvature.

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