How to Find Radial and Axial Force on Bearings: A Step-by-Step Engineering Guide

The single most important question when selecting or troubleshooting a bearing is: what forces is it actually experiencing? Many engineers and technicians underestimate bearing loads by only accounting for obvious weight and ignoring factors such as belt tension, imbalance forces and axial thrust, which can lead to premature bearing failure.

This guide explains exactly how to identify, classify and calculate radial and axial forces on bearings, including the combined equivalent load formula used by engineers worldwide.

What Are Radial and Axial Forces on a Bearing?

Before calculating anything, you need to understand what these two fundamental force types mean in the context of a rotating shaft system.

Radial Force (Fr)

Radial force is any force that acts at a right angle to the axis of the shaft. Imagine a force pushing down (or sideways) onto the shaft from outside—like gravity pulling down on a horizontal shaft. The radial load is always the component of force that acts at 90° to the rotational axis, no matter what the orientation of the shaft is (horizontal, vertical, or angled).

Common sources of radial load:

• Weight of the shaft, gears, pulleys, and mounted components
• Belt tension (from V-belt, flat belt, or chain drives)
• Gear mesh forces (tangential and separating forces)
• Magnetic pull in electric motors
• Centrifugal force from unbalanced rotating masses

Axial Force (Fa) — Also Called Thrust Load

Axial force (also called thrust load) acts parallel to the shaft axis. It tries to push the shaft forward or backward along its own length. Axial loads are especially significant in vertical shaft applications or systems with helical gears and screw drives.

Common sources of axial load:

• Helical, bevel, or worm gear engagement
• Screw conveyors and lead screws
• Fan or propeller air/fluid pressure
• Gravity on vertically mounted shafts
• Misalignment-induced thrust

Radial force acts perpendicular to the bearing shaft axis. Axial force (thrust) acts parallel to the shaft axis. To find them: (1) draw a free body diagram of the shaft, (2) identify all external forces, (3) resolve each force into its radial and axial components, (4) use static equilibrium to find bearing reaction loads.

Why Getting Bearing Loads Right Matters

Using an incorrect load value doesn’t just mean choosing the wrong bearing size—it affects the entire service life calculation. According to ISO 281, bearing basic rating life is calculated as:

L10 = (C / P)^p × 10^6 revolutions

Where:

• C = Basic dynamic load rating (from bearing catalog)
• P = Equivalent dynamic load (calculated from radial + axial forces)
• p = 3 for ball bearings, 10/3 for roller bearings

If P is underestimated by 20%, your calculated life could be overestimated by 73% (for ball bearings). This is why accurate force identification is non-negotiable.

Step 1 — Draw a Free Body Diagram (FBD)

The first step in finding the loads on the bearings is to create a Free Body Diagram of the whole shaft assembly. This is a basic tool used in mechanical engineering. It separates the shaft and shows all the forces that are acting on it.

How to draw the FBD:

1. Sketch the shaft as a simple horizontal (or vertical) line
2. Mark the position of each bearing as a support point (A and B)
3. Mark the location of every load-applying component (gears, pulleys, fans, etc.)
4. Draw arrows for every external force: direction, magnitude (if known), and point of application
5. Note distances between all key points along the shaft

Once the FBD is complete, you have a clear picture of what forces exist and where they act.

Step 2 — Identify and Resolve All External Forces

Real-world loads almost never act purely radially or purely axially. You must resolve each external force into its radial (Fr) and axial (Fa) components using vector decomposition.

Belt and Chain Drive Forces

For a belt drive, the effective belt tension creates a radial load on the shaft. The total belt force is approximately:

F_belt = F_tight + F_slack

For a simplified estimate, many engineers use:

F_belt ≈ 2 × T / D

Where:

• T = Transmitted torque (N·m)
• D = Pulley pitch diameter (m)

This force acts radially, in the direction of the belt pull.

Gear Forces

For spur gears, the tangential force Ft and separating force Fr_gear combine as a radial load on the bearing:

Ft = 2T / d     (tangential force)
Fr_gear = Ft × tan(α)   (separating force, where α = pressure angle, typically 20°)

Helical gears also introduce an axial (thrust) component:

Fa_gear = Ft × tan(β)   (where β = helix angle)

Gravity / Component Weight

This is always a radial load, acting straight downward. For a horizontal shaft, the weight W of all components (shaft, gears, pulleys) creates a downward radial load distributed across the two bearings.

Step 3 — Calculate Bearing Reaction Loads Using Static Equilibrium

With all external forces identified and resolved, apply the equations of static equilibrium to find the reaction forces at each bearing.

For a shaft supported by two bearings (A and B) with forces in the vertical plane:

ΣFy = 0:   RA + RB = F1 + F2 + ... (sum of all radial loads)
ΣM_A = 0:  RB × L = F1 × a1 + F2 × a2 + ...

Solve for RB first, then substitute back to find RA.

Do this separately for each plane (vertical and horizontal), then combine:

Fr_total = √(R_vertical² + R_horizontal²)

For axial loads, sum all axial force components:

Fa_total = ΣFa (net axial force along shaft axis)

Step 4 — Worked Example: Industrial Fan Shaft

Let’s apply everything above to a real scenario—exactly the type of system encountered in HVAC and industrial applications.

Setup

An industrial fan shaft is supported by two pillow block bearings (A and B), 800 mm apart. The following loads act on the shaft:

Step 4.1 — Find Radial Reaction at Each Bearing

Taking moments about A (ΣM_A = 0):

RB × 800 = (700 × 400) + (1,200 × 650)
RB × 800 = 280,000 + 780,000
RB × 800 = 1,060,000
RB = 1,325 N

From ΣFy = 0:

RA + RB = 700 + 1,200 = 1,900 N
RA = 1,900 - 1,325 = 575 N

So Bearing A carries 575 N radial load, Bearing B carries 1,325 N radial load.

Step 4.2 — Axial Load

The fan generates 400 N of axial thrust. For a simple shaft with only one axial load, one bearing (typically the fixed/locating bearing) must absorb this entire axial load:

Fa = 400 N (absorbed by the designated fixed bearing)

Step 5 — Calculate Equivalent Dynamic Load (Combined Radial + Axial)

When a bearing experiences both radial and axial loads simultaneously, you cannot simply add them. Instead, use the equivalent dynamic load formula from ISO 281:

P = X · Fr + Y · Fa

Where:

• P = Equivalent dynamic load (N)
• Fr = Radial load on the bearing (N)
• Fa = Axial load on the bearing (N)
• X = Radial load factor (from bearing manufacturer’s catalog)
• Y = Axial load factor (from bearing manufacturer’s catalog)

How to Find X and Y Values

X and Y factors depend on:

1. The bearing type (ball, roller, tapered, angular contact)
2. The ratio of Fa/C0 (where C0 = static load rating from catalog)
3. The ratio of Fa/Fr

For a deep groove ball bearing (one of the most common types), typical values are:

When Fa/Fr ≤ 0.44, the bearing is considered radially dominated and P = Fr (axial load has negligible effect).

Worked Example (continued)

For Bearing B (Fr = 1,325 N, Fa = 400 N):

Fa/Fr = 400 / 1,325 = 0.302 → ≤ 0.44

Since the ratio is below 0.44:

P = X · Fr + Y · Fa = 1.0 × 1,325 + 0 × 400 = 1,325 N

The axial load has negligible influence here, so P = 1,325 N.

If Fa/Fr had been > 0.44 (say Fa = 700 N):

Fa/Fr = 700 / 1,325 = 0.528 → use X = 0.56, Y = 1.4
P = 0.56 × 1,325 + 1.4 × 700 = 742 + 980 = 1,722 N

In this case, the axial load significantly increases the equivalent load—highlighting why ignoring axial forces is dangerous.

Bearing Type and Load Handling Capability

Different bearing types are designed to handle different load combinations. Choosing the right type is just as important as calculating the load correctly.

Deep Groove Ball Bearings

• Best for: Primarily radial loads with moderate axial loads
• Axial capacity: Up to ~70% of radial capacity (depending on internal clearance)
• Typical applications: Electric motors, gearboxes, pumps

Angular Contact Ball Bearings

• Best for: Combined radial and axial loads, especially at high speeds
• Contact angle: 15°, 25°, or 40° (higher angle = more axial capacity)
• Typical applications: Machine tool spindles, compressors

Cylindrical Roller Bearings

• Best for: Heavy radial loads, high speeds
• Axial capacity: Very limited (not suitable for significant axial loads unless specifically designed)
• Typical applications: Large electric motors, rolling mills

Tapered Roller Bearings

• Best for: Heavy combined radial and axial loads
• Note: Must always be used in pairs (opposing configuration) to handle axial load in both directions
• Typical applications: Vehicle wheel hubs, gearboxes, conveyor systems

Thrust Bearings (Ball or Roller)

• Best for: Purely or predominantly axial loads
• Radial capacity: Minimal
• Typical applications: Vertical pump shafts, crane hooks, steering columns

Additional Loads Engineers Often Miss

Beyond the obvious forces, several “hidden” loads can significantly increase the actual load on a bearing:

1. Dynamic Imbalance Forces

If a rotating component (fan blade, grinding wheel, impeller) is not perfectly balanced, it generates a centrifugal imbalance force that rotates with the shaft. This force is radial in nature and increases with the square of rotational speed:

F_imbalance = m · e · ω²

Where m = unbalanced mass, e = eccentricity, ω = angular velocity (rad/s).

2. Misalignment Loads

Shaft misalignment (angular or parallel) between a driver and driven component adds additional bending moments and radial loads to the bearings. Even small misalignments—0.1° to 0.5°—can double the bearing load in severe cases.

3. Shock and Vibration Loads

Applications with frequent starts, stops, or impacts (crushers, presses, conveyors) experience dynamic load factors. A service factor (Ks) ranging from 1.2 to 3.0 is applied to the calculated load:

P_design = Ks × P

4. Thermal Expansion Effects

Temperature changes can alter shaft clearances and bearing preload, effectively changing the load distribution. This is especially critical in precision spindle applications.

Common Mistakes When Calculating Bearing Loads

Quick Reference: Step-by-Step Summary

How to find radial and axial force on bearings — 5 steps:

1. Draw a Free Body Diagram — sketch the shaft, mark bearing positions, and show all external forces
2. Resolve all forces — decompose each force into radial (⊥ to shaft) and axial (∥ to shaft) components
3. Apply static equilibrium — use ΣF = 0 and ΣM = 0 equations to find reaction forces at each bearing
4. Combine planar reactions — Fr_total = √(R_vertical² + R_horizontal²)
5. Calculate equivalent load — use P = X·Fr + Y·Fa with manufacturer X/Y factors

Frequently Asked Questions

Q: What is the difference between radial load and axial load on a bearing?

Radial load acts perpendicular to the shaft axis (like downward gravity on a horizontal shaft). Axial load (thrust load) acts parallel to the shaft axis, pushing it forward or backward.

Q: Can a bearing handle both radial and axial loads simultaneously?

Yes—bearings like angular contact ball bearings and tapered roller bearings are specifically designed for combined loading. Use the equivalent load formula P = X·Fr + Y·Fa to account for both.

Q: What happens if I use a bearing that is only rated for radial loads in an application with axial forces?

The bearing will experience stress in areas not designed to carry it, leading to rapid wear, overheating, and premature failure.

Q: How do I find the X and Y factors for the equivalent load formula?

X and Y values are published in every bearing manufacturer’s catalog (SKF, NSK, Timken, FAG, etc.) and vary by bearing type, internal geometry, and the Fa/C0 ratio.

Q: Do I need to consider both radial planes when calculating bearing loads?

Yes. For a shaft with forces in multiple directions, calculate reactions in the vertical plane and horizontal plane separately, then combine them: Fr = √(Rv² + Rh²).

Conclusion

Determining the radial and axial forces on a bearing is not guesswork. It is a systematic engineering process. To do this, start with a free body diagram, solve for all force components, apply equilibrium equations, and use the combined load formula P = X·Fr + Y·Fa. This will give you an accurate equivalent load. You can then use this to select the right bearing and predict its service life.

The most common mistake is to underestimate the load by only thinking about how heavy the parts are and not considering things like belt tension, how much force the gears can push, imbalance, and misalignment. To choose a reliable bearing, you need to do a correct load analysis.