The Lundberg And Palmgren Theory: Predicting The Life Of A Ball Bearing
If you work with ball bearings then you’ll know that being aware of a bearing’s estimated lifespan is important to budgeting appropriately and achieving maximum efficiency. In the 1940s Gustaf Lundberg and Arvid Palmgren devised the first widely used, official formula for figuring out the lifespan of an individual bearing and, over time this has been innovated by SKF to cater for newer kinds of bearings. This article will take a look at the history of the formula and how it has been updated in recent times.
History
The formula was first devised in 1947 at SKF using the Weibull probability theory of fatigue and marked an absolute breakthrough in the engineering world. For the first time bearings could be selected on a rational basis for specific applications which matched their projected lifespan. As time went on developments in engineering and particularly tribology meant that the theory had to be rendered to compensate.
Better steel manufacturing meant that stainless steel ball bearings were cleaner and better functioning, improved lubrication meant that less wear occurred in roller bearings and the advent of high precision bearings introduced quality to the bearing industry not seen before. Such improvements in the ball bearing meant that the Lundberg and Palmgren formula had to be adapted accordingly.
Performance improvements were catered for by increasing dynamic load ratings. Application of adjustment factors were used to account for operational conditions like special bearing materials or lubrication. For a long time these adjustments worked and the calculations served the industry well, but in recent times the equation has needed to be innovated in order to keep up with engineering developments.
Recent Innovations
Currently powerful computers and the latest calculation techniques are used to figure out the life of ball bearings. The Lundgren ad Palmgren theory was innovated by the rolling contact fatigue life model published by Eustathios Ioannides and Tedric Harris. This model introduced:
- A threshold value of the local stress, a fatigue limit, below which no fatigue is expected to occur in bearing.
- Considering the stressed volume below a contact as an array of small volume elements, each experiencing individual local stresses.
SKF bearings are now assessed under the SKF Life Equation which introduces a new and higher standard into life span calculations. This is the latest manifestation of SKF’s Lundberg and Palmgren theory and according to SKF,
“manages to describe the complex tribo-system in which the bearing operates using a few key a parameters. This is an important feature of the model that concentrates on the effect of a few important factors that have significant consequences for the bearing life.” - ‘The SKF formula for rolling bearing life’
In order to keep up with bearing innovations the Lundberg and Palmgren theory has gone through various alterations, but each manifestation of a ball bearing life formula has had its basis in the Lundberg and Palmgren equation which is a testament to the brilliance of the original mathematical and engineering prowess which first brought it into fruition.