Bearing Load Calculator

Bearing Load Calculator splitting a radial load between two shaft bearings, adding axial load through X and Y factors, then giving L10 life in hours and the lower s0 safety factor.

Bearing Load Calculator for Two-Bearing Shafts

The Bearing Load Calculator splits a shaft load between two bearings, turns each share into an equivalent load, and checks both bearings for fatigue life and static strength. It works for deep groove and angular contact ball bearings and for cylindrical, tapered and spherical roller bearings. Mechanics and designers use it to check whether a catalog bearing will last on a pulley shaft, a gearbox input or a pump.

Enter the radial load, any axial load on bearing A, the dynamic rating C and the shaft speed. The accordions add the bearing spacing, where the load sits, the service and belt factors, the static rating C0, reliability and a target life. Loads work in lbf or kN and lengths in inches or millimeters, converted at 224.81 lbf per kN.

Splitting the Shaft Load Between Bearings A and B

A shaft on two bearings acts like a simple beam, so each bearing carries the load times its distance to the other bearing, divided by the spacing. A load closer to bearing A puts more of it on A, and a load halfway between splits evenly. The calculator measures the load position from bearing A, so a negative distance or one past bearing B means the load hangs outside the span.

$$F_A = W \times \frac{L – x}{L} \qquad F_B = W \times \frac{x}{L}$$

With 600 lbf acting 3 in from bearing A on an 8 in span, A carries 375 lbf and B carries 225 lbf. Move a pulley outside the bearings, 10 in from A on that same span, and B carries 750 lbf while A is pulled the other way with 150 lbf. An overhung pulley loads the near bearing with more than the whole pulley load, which is why moving it closer to the bearing pays off.

The 600 lbf in that example already includes a service factor. Koyo’s load calculation guide multiplies the theoretical load by 1.0 to 1.2 for smooth running such as motors, 1.2 to 2.0 for normal duty, and 2.0 to 3.0 for heavy shock. Belt drives get a second factor for belt tension, from 1.2 to 1.5 for chain up to 4.0 to 5.0 for a flat belt.

Equivalent Load When Axial Force Joins In

Bearing life is rated for a pure radial load, so a combined load is first turned into one equivalent load P. The radial and axial parts are weighted by factors X and Y, which depend on the bearing type and on how large the axial share is. Bearing A is treated as the locating bearing, so it takes all of the axial load.

$$P = X F_r + Y F_a$$

For deep groove ball bearings, NSK’s catalog table reads the limit e and the factor Y from f0 times Fa divided by C0. While Fa divided by Fr stays at or below e, X is 1 and Y is 0, so the axial load does not count at all. Past e, X drops to 0.56 and Y runs from 2.30 down to 1.00 as the axial load grows.

In the default case, 120 lbf of axial load gives f0 times Fa over C0 of about 0.65, so e is about 0.26 and Y about 1.74. Fa over Fr on bearing A is 0.32, past e, so P rises to about 419 lbf from a 375 lbf radial share. Cylindrical roller bearings are handled differently, since the standard types take no axial load in the life formula and P is just the radial load.

From Equivalent Load to Hours

The basic rating life L10 is the number of revolutions that 90% of a group of identical bearings will reach. New Hampshire Ball Bearings defines C as the load a group of bearings will carry for one million revolutions. Life then falls with the cube of the load for ball bearings and with the 10/3 power for rollers.

$$L_{10} = \left(\frac{C}{P}\right)^p \text{ million revolutions}$$

$$L_{10h} = \frac{L_{10} \times 10^6}{60 \times n}$$

With C at 4,384 lbf and P at 419 lbf, bearing A reaches about 1,147 million revolutions, or 10,620 hours at 1,800 rpm. Without the axial load it would last about 14,800 hours, so that 120 lbf costs almost a third of the life. On a ball bearing, 10% more load cuts life by about 25%, and doubling the speed halves the hours.

For reliability above 90%, the calculator scales the life by the ISO 281 factor a1, using 0.25 at 99%. Accendo Reliability notes that the a1 table changed with ISO 281:2007, so older charts show slightly different values. The minimum C row works the formula backward to show the rating needed to reach your target life at your reliability.

The Static Check That Life Alone Misses

A slow or shock-loaded bearing can dent its raceways long before fatigue matters. The Bearing Load Calculator compares the static rating C0 with a static equivalent load P0, which NSK gives as 0.6 Fr plus 0.5 Fa for deep groove ball bearings, but never less than Fr.

$$s_0 = \frac{C_0}{P_0}$$

Koyo’s static load guide sets a minimum for that ratio depending on duty and bearing type. The default bearing A has a P0 of 375 lbf, since 0.6 Fr plus 0.5 Fa comes out lower than Fr, giving a safety factor of about 6.8.

Life figures from this method assume clean, well-lubricated bearings. The calculator’s alert notes that lubrication and contamination can still shorten real life, and a bearing that passes on paper can fail early if dirt or water gets in.