14.5.3.1. Rolling Bearing - Analytic

When the load is applied to bearing, bearing stiffness can be calculated by measuring the amount of deformation between the ball and the raceway (Inner/Outer). In order to calculate the amount of deformation between the ball and the raceway, it is necessary ball and raceway CM maker information. Using the maker information, it is possible to know the position and orientation of the ball and raceway.

Figure 14.212: Bearing components

Bearing components

Contact point is calculated by radius of the ball and the raceway and curvature center of the Inner Race / Outer Race.

Figure 14.213: Get direction and orientation

Get direction and orientation

Position and orientation of the ball and the raceway is as follows.

(14–37)

It is possible to calculate the amount of penetration, using the position of the ball and raceway,

(14–38)

When the ball and raceway are contact with each other, it can be connected between curvatures center of inner race and outer race in a straight line. It called contact angle. Direction of the contact angle is normal direction of contact force.

Figure 14.214: Calculate deformation

Calculate deformation

Contact direction formulation is described in Equation 14–2.

(14–39)

The Penetration velocity and tangential velocity are as follows.

(14–40)

The contact force is calculated as follows.

(14–41)

Figure 14.215: Force Generalization

Force Generalization

Generalizing the force described in Equation 14–42.

(14–42)

Transform the calculated values to the global coordinates

Figure 14.216: Transform to global

Transform to global