# Why Off-Center Torque Has a Major Effect on Bearings: Explained

Recently, an engineer asked a question about the calculation of overturning torque. We provided a rough estimation method from a very general perspective in bearing load calculation. However, such calculation often differs greatly from the actual internal forces in the bearing and does not meet the requirements in some engineering minutiae.

On the other hand, the overturning torque of the bearing in the field is often caused by misalignment (exceptions exist in some designs that require withstand overturning torque). In practical engineering, we often say that misalignment can cause significant damage to the bearing.

But why is this so? This is an excellent opportunity to introduce the impact of overturning torque on bearing loads and explain why misalignment can cause substantial damage to the bearing.

Below is a basic analysis of the bearing load under overturning torque:

The diagram below simply illustrates the load state of the bearing system under the overturning torque. To simplify the analysis, we use a deep groove ball bearing as an example, considering only the scenario with overturning torque.

In the diagram, the force F1 applies an overturning torque F1*h1 to the bearing on the shaft with the force arm h1. For deep groove ball bearings, in a tilted state, the contact between the internal rolling element and the raceway is different from pure radial load and axial load. The contact between the rolling body and the raceway is estimated to leave a tilted trace.

Within the plane of maximum overturning torque (the plane of F1 and h1 in the diagram), the contact between the bearing rolling body and the raceway appears off-centered. This load situation is similar to angular contact bearings, where the line connecting the two points of contact between the rolling body and the raceway and the vertical direction forms the contact angle α,β is the angle between the line connecting the contact point and the center of the fulcrum and the vertical direction.

At this moment, the system is in overall equilibrium, so there should be a balance of torques.

F1*h1=Fa*h2*cosβ

Herein, h2 refers to the distance between the contact point and the axis support point (in this case, we choose the center of support point F1). This distance actually varies with the change in the tilt angle.

We assume the situation in the figure to be stable and balanced for subsequent analysis. Alternatively, the outer radius D/2 of the bearing can be used to estimate h2, because the difference between them is relatively small on this scale (the maximum difference is the depth of the bearing raceway).

Therefore, we can roughly estimate the axial force Fa exerted on the bearing at this time:

Fa=(F1*h1)/(h2*cosβ)

The contact force F2 between the bearing raceway and rolling element should be:

F2=Fa/sinα=(F1*h1)/(h2*cosβ*sinα)

The above calculations yield the overturning torque and the bearing force on the force arm plane. Upon determining this force, further relevant calculations can be performed.

However, these calculations are obtained under certain conditions. In this computation, we use a semi-bearing as an example, first treating the entire system as a rigid body, and assuming that the inner and outer rings of the bearing and the related components are rigidly connected.

If these premises are incorporated into the calculation, it would necessitate the introduction of complex tools such as finite element analysis, and of course, discrepancies will arise compared to our manual calculations.

## Why does overturning torque greatly affect the bearing?

Through the above calculations, we have a general understanding of the potential force a bearing may experience in the presence of an overturning torque. From the calculation of F2, it can be seen that the magnitude of F2 is influenced by F1, h1, h2, Sinα, and Cosβ.