What a Bearing Load Actually Is

Why this matters

Most techs picture a bearing as holding up the weight of the rotor. On a direct-coupled pump that picture is roughly right. On a belt-driven fan it is off by a factor of five, and the difference is the reason one shop replaces fan bearings every season while the shop across town does not. A bearing does not carry weight. It carries whatever the load path delivers to it, concentrated onto a handful of rolling elements, and its life responds to that number by a power law rather than a straight line. Get the load path wrong and you will replace the same bearing forever, correctly, and never fix anything.

Before you touch the machine

Rotating equipment is the highest stored-energy hazard in a service shop. Before you open a guard or put a hand near a shaft, isolate and lock the energy sources under 29 CFR 1910.147, then release stored energy and verify: a fan wheel coasts for minutes after the contactor drops, and a spring-loaded motor base holds belt tension that will snap the base into motion when the last belt comes off. Restrain or de-tension the base before removing belts. Guarding on belts, sheaves, shafts and couplings is covered by 29 CFR 1910.219 for general industry and 29 CFR 1926.300(b) on a construction site, and it goes back on before the machine runs. If you must open the motor terminal box, that is electrical work under 29 CFR 1910.333(b)(2), and you prove dead by the live-dead-live sequence in NFPA 70E-2021, 120.5. Never wear gloves or loose sleeves when working near a shaft that can turn.

The gate: compute the load where the bearing is, from the load path

There is one rule in this article, and everything else is it being run twice.

Trace the forces that reach the bearing seat, resolve them as a vector, and split them across the two bearings by statics. Do not start from the weight of the rotor.

For an overhung drive element - a sheave, a sprocket, a fan wheel hanging outboard of the bearings - the split is simple statics. With bearing span L and overhang a beyond the near bearing, the near bearing reacts F x (L + a) / L and the far bearing reacts F x a / L in the opposite direction. Note what that says: the near bearing carries more than the whole applied load, and the far bearing is pushed the other way. Nothing about that appears if you divide rotor weight by two.

What the bearing actually feels is a load zone, not a force

The applied force does not spread evenly around the bearing. Under a pure radial load, a bearing with normal internal clearance loads only the rolling elements inside an arc of roughly 120 degrees at the bottom of the load direction, which is about a third of the complement. Take the clearance to zero and the arc opens to about 180 degrees; add preload and it opens further. The condition matters: that 120-degree figure is for a radially loaded bearing with normal clearance and no meaningful misalignment, and it does not describe a bearing carrying a combined radial and axial load, where the geometry changes entirely.

Inside that zone, one element carries far more than the others. The common approximation for the most heavily loaded ball is Qmax of about 5 x Fr / Z, where Z is the ball count. That factor of 5 is derived for a radially loaded ball bearing at normal internal clearance; at zero clearance it falls to about 4.4, and under a combined load it does not apply at all. For a 9-ball bearing at 127 lbf radial, Qmax is about 70 lbf, so one ball out of nine is carrying 56 percent of the total, on a contact patch you could cover with a pencil point.

Why the exponent is the whole story

Bearing life is not proportional to load. The basic rating life in ISO 281 goes as (C / P) raised to a power p, where p is 3 for ball bearings and 10/3 for roller bearings, C is the basic dynamic load rating from the catalogue and P is the equivalent dynamic load. That formula is defined at 90 percent reliability under the standard's reference conditions for lubrication and cleanliness, so it tells you how life responds to load, not how many hours you will actually get.

The consequence is what you carry into the field. Double the load on a ball bearing and life falls to one eighth. On a roller bearing it falls to about one tenth. Raise the load by only half and a ball bearing keeps about 30 percent of its calculated life. This is why a small, invisible, well-intentioned change to a load path is a bigger reliability event than any lubricant decision you will make that day.

Outcome one: the direct-coupled pump

A close-coupled pump, flexible coupling, 40 lb rotating assembly carried between the two bearings, running at its best efficiency point. Weight splits roughly evenly, so call it 20 lbf per bearing. The hydraulic radial load on a well-matched single-volute casing near best efficiency is small, so the total sits around 25 lbf per bearing.

Run the gate and the answer is that the load is small, steady, and not the thing that will kill this bearing. The reliability conversation for this machine is about contamination, moisture in the lubricant, and seal condition, because at 25 lbf the fatigue clock is barely running. There is a second finding hiding here: a bearing this lightly loaded may be under the manufacturer's stated minimum load, where the rolling elements slide instead of roll on the way into the load zone. That is a real failure route with its own evidence, and a sibling article covers how to check for it.

Outcome two: the belt-driven fan motor

Same shop, a 3 hp motor at 1750 rpm driving a fan through a V-belt, 25 lb rotor, 4.0 in pitch diameter sheave overhung 2.0 in beyond the drive-end bearing, 6.0 in bearing span.

Torque is 5252 x hp / rpm in lb-ft, so 5252 x 3 / 1750 gives 9.0 lb-ft, which is 108 lb-in. Divide by the sheave pitch radius of 2.0 in and the tangential force is 54 lbf. That is only the force needed to transmit the torque. The shaft sees the vector sum of tight-side and slack-side tension, which is larger, and the multiplier depends on the arc of contact and the tension ratio the drive is set up for. The drive manufacturer's shaft-load table for this arc gives about 1.75, so the belt pull on the shaft is roughly 95 lbf. Take that number off your own drive maker's table, not off a rule of thumb, because a wrap under 180 degrees or a different belt section moves it.

Statics: the drive-end bearing reacts 95 x (6.0 + 2.0) / 6.0, which is 127 lbf, and the far bearing reacts 95 x 2.0 / 6.0, which is 32 lbf pushing the other way. Add the rotor weight share of 12.5 lbf per bearing, acting vertically while the belt pull acts horizontally, and the drive-end vector sum is about 127 lbf.

Same size machine as the pump. Five times the bearing load, and none of it is weight.

Running the gate on a maintenance decision

A tech chases a belt squeal by tightening the drive by half. The belt pull goes from 95 to about 143 lbf and the drive-end bearing load goes from 127 to 190 lbf.

Life ratio for a ball bearing is (127 / 190) cubed, which is 0.30. About 70 percent of the calculated life is gone. On a cylindrical roller bearing at the 10/3 exponent it is worse, about 26 percent remaining. Nothing looks different, nothing sounds different that day, and the bearing that used to make it three seasons now makes it one.

The correct move on a squeal is to check the tension against the drive manufacturer's tension-versus-deflection figure with a tension tester, on a locked-out machine with the guard off and the base restrained, and to check sheave groove wear, because a worn groove lets the belt ride down and squeal at correct tension. Tightening past the table is how a bearing problem gets manufactured.

How to verify you got this right

Three checks, in this order.

Does your force total close? The two bearing reactions from an overhung load must differ by exactly the applied load, and they act in opposite directions. In the fan case, 127 minus 32 is 95, the belt pull. If your two reactions add up to the applied load instead of differing by it, you have modelled an overhung load as if it sat between the bearings.

Is the dominant term the one you expected? Write the terms out and rank them. On the fan, belt pull at 127 lbf against a weight share of 12.5 lbf means weight is 10 percent of the problem and tension discipline is 90 percent of it. If your ranking says weight dominates on a belt-driven machine, re-check the sheave diameter, because a small sheave multiplies tangential force for the same torque.

Does the load zone evidence agree with your model? When the bearing comes out, the loaded arc on the stationary ring should sit centred on the direction your model says the resultant points. A load-zone band pointing somewhere your statics did not predict means there is a force in the path you have not accounted for, usually thermal growth in a piped assembly or a coupling pulling the shaft.

The failure mode of skipping all three is specific and common: you replace a fan bearing with a higher-rated one, which changes C but does nothing about P, gain the ratio you paid for and no more, and never discover that the drive has been running at double its rated tension for four years.

References

• ISO 281, basic dynamic load rating and rating life for rolling bearings, for the load-life exponents and the reference conditions they are defined under
• 29 CFR 1910.147 (control of hazardous energy) and 29 CFR 1910.219 (mechanical power-transmission apparatus guarding); 29 CFR 1926.300(b) for the construction counterpart on guarding
• NFPA 70E-2021, 120.5, for the live-dead-live verification sequence referenced for terminal-box work
• Drive manufacturer documentation for belt shaft-load factors and tension-versus-deflection values, which vary with belt section and arc of contact
• See related: Radial, Thrust and Combined Loads; How to Tell Whether a Bearing Is Loaded the Way It Was Meant to Be; Why a Bearing Fails in a Way That Names Its Own Cause