Products and services / SMT Accurate bearing models With an increase in the use of high-speed motors in automotive, in-depth understanding of transmission bearing behavior is vital odern transmissions increasingly require bearings that operate at higher speeds. For example, in electric vehicle transmissions, higher speeds are a result of a drive for improved efficiency. A common method for defining whether a bearing is operating at high speed is to use the DN value (diameter in mm x speed in RPM), in which the size of the bearing is also considered. A value of DN greater than 1,000,000 is generally taken to indicate high-speed operation. While reducing the size of the bearing can negate the impact of higher speeds, the bearing’s ability to carry load will then be reduced, so it is not possible to mitigate all the effects of high speed in this way. There are several important considerations for a bearing operating at high speed, namely overheating, cage failure and smearing. Heat is generated at the element-raceway contacts because, due to the geometry of the contact patch, the ball will be sliding in certain regions of the contact instead of rolling. If a bearing is not cooled adequately then this can eventually lead to the collapse of the fluid film between the element and the raceway, leading to even further heating and 1 subsequent damage. Smearing is another phenomenon caused by the contact between the element and raceway and is most likely to occur as a ball moves from an unloaded region to a loaded region of the bearing. As this transition occurs, the ball experiences high velocity sliding on the raceway and a rapid increase in normal load (thus friction force), both of which contribute to increased power loss. When the power loss per unit area in a contact patch exceeds a certain threshold, the surface of the raceway is at risk of experiencing smearing. Cage failure at high speeds is usually a result of fatigue from repeated impacts between the balls and the cage. If a bearing M 1. Ball-cage impacts (in red) and cage speeds (in blue) for an angular contact ball bearing. The cage speed changes when there is an impact between the cage and an element is not loaded equally at all points, the elements will orbit at different speeds. This will result in the elements orbiting faster than the cage in some regions, and orbiting slower at others, which will lead to ball-cage impacts. The magnitude of the impact forces, and thus the risk of cage failure, will depend on the cage design, cage material and loading conditions. Ideally, such problems are anticipated before anything is manufactured, hence the use of analytic and numerical methods as part of the design process. The analysis of high-speed bearings requires advanced models that can accurately calculate forces and moments on all the components of a bearing. QUASISTATIC MODELS Traditionally, quasistatic analytic models of ball bearings use two degrees of freedom, the two displacements of the ball in the radial plane through the ball center. It is then necessary to make further assumptions about the ball’s angular velocity to calculate sliding speeds at the contact patches. These assumptions work well for lower speeds or where only the stiffness of the bearing is required. At higher speeds, the error in the sliding speeds can generate significant errors in the calculation of the frictional forces. To accurately model high-speed bearings, a more advanced quasistatic model is required, in which the element has 6DOF. As well as the two ball displacements in the plane, the 6DOF model also treats the ball orbit speed and rotational vector as variables. The 36 Transmission Technology International / 2023