Wind Turbine Gearbox Vibration Analysis

When a gearbox vibrates as a whole, the severity of the vibration can be detected at the outer surface of the gearbox housing. While some vibration is normal, higher levels of vibration can be caused by the wearing or failure of the gearbox components. For this reason, gearboxes often incorporate vibration sensors to detect conditions that require maintenance or repair.

Gearbox vibration can be complicated and multidirectional since the gearbox and its mounting
assembly are neither completely rigid nor completely elastic. However, the fundamental concepts of weighted average of mass centers, Newton’s Second Law, and elastic forces help explain the
relationship between component wear or failure and the vibration of the gearbox.

Each gear as a whole can be considered as a system of mass particles. A properly functioning gear has a mass center at the geometric center of the gear. This means that the mass of the gear material is evenly distributed within the space that the gear takes. In a well-designed and manufactured gear, the mass center of the gear is also its rotational center.

A worn or failed gear, however, has a mass center that deviates from the geometric center of the gear because the material of the gear is no longer evenly distributed within the space that the gear takes. The mass center of a worn gear is no longer the same as the center around which the gear turns.

Once these gears start to rotate, each mass center will change its location relative to both its rotational center and the gearbox housing, resulting in a reciprocating motion during each rotational cycle.

Because the mass center of the gearbox as a whole is the weighted average of the mass centers of all the gearbox components, when the mass center of any gearbox component changes, it affects the mass center of the entire gearbox. This mass center changes its location relative to the gearbox base in a reciprocating motion, causing vibration. The velocity of this motion changes in both direction and magnitude over time.

A change of either the magnitude or the direction of the velocity of the mass center constitutes the acceleration of the gearbox as a whole. According to Newton’s Second Law, this acceleration is associated with a force which is external to the gearbox.

This external force is the resultant of two forces acting on the gearbox. They are gravitational forces and contact forces. While the change of gravitational force is insignificant, the contact or elastic force from the gearbox base does change significantly during the reciprocating cycle.

An elastic force is caused by, and positively proportional to, the deformation of the contact
materials. In the case of gearbox vibrations, the reciprocating movement of the gearbox tends to
manifest itself most significantly in the direction in which the restricting rigidity is the weakest. The bolted joints between the gearbox housing and its mounts are normally less rigid than the housing itself.

These bolted joints function as quasi-elastic elements, providing the reciprocating resultant force
that concurs and sustains the gearbox vibration. Significant and constant gearbox vibration will not only further damage the worn or failed gearbox components, but may also cause the failure of the bolted joints that connect the gearbox to its base.

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