Note that the groove is a partial torus, and has a minor and a major radius. ... except for 'four point contact' bearings, where the minor radius is more ogival.
Stick to 'radial' bearings for now; it will be less confusing.
Often they speak of a Conformity Radius as a percentage to the Ball Diameter. Typical would be 52 percent and 51 percent. If you double these numbers they would equal
104 percent and 102 percent times the ball radius.
They are offset to form a gothic arch for angular type bearings. Often there will then be a relief groove to reduce the grinding time as well as being a grease or oil groove. It can be a singular radius for a pure thrust or radial bearing. In Europe they use another standard, and I think theirs' is more in line with ball radius divided by the conformity radius.
As dinjin noted, most radial or angular contact ball bearings use an "osculation" radius value of around .52 to .53 times the ball diameter. A lower value around .52 improves load capacity, but at the expense of efficiency. Conversely, an osculation radius of >.53 would give better efficiency but would have less load capacity.
Well designed ball bearings normally use different values for the inner and outer races, since most typical bearing installations produce different stress levels at the inner and outer race surfaces. Usually, the inner race contact stresses tend to be higher due to the race surface being convex and having a smaller radius of curvature. So a smaller osculation value is used for the inner race to improve load capacity, while the more lightly stressed outer race uses a slightly larger value to help equalize fatigue life and improve efficiency.
I hope that's what you meant by "groove radius".
Regards,
Terry
Tedric Harris, Palmgren, Jones, Erwin V. Zaretsky and other authors have written extensively about this.
There is a good NASA paper by Zarentsky on Palmgren that is worth reading.
A short understanding of how the static capacity varies with the different Conformity Radius is to subtract 50 from the percentage and use this value to divide into the conformity radius percentage and then squareroot it.
For example (51/1)^.5 (52/2)^.5 (53/3)^.5 (54/4)^.5 etc.
gives you the values 7.141 5.099 4.203 3.674
You can make a quick excel spread sheet and check out how important it is to make the radius conform to the ball radius to reduce the contact stresses.
Efficiency in ball bearings can be a very complex issue. So no, there is not a quick and dirty evaluation of the trade-off of varying osculation.
If the bearing is operating with light loads and a low dN value, then the osculation value is not so important. But if the bearing is highly loaded, has some shaft bending, and is subject to a high dN, then osculation can have a big effect on efficiency, scoring and fatigue life.
With a highly loaded, high dN ball bearing, the important thing with regards to efficiency is the operating contact angle between the inner and outer races. If these points are off-axis to the ball's rotation, then some skidding or spin loss will occur at the hydrodynamic oil films supporting the ball's contacts. A larger osculation radius results in less of this off-axis effect as the ball contact geometry changes under load.
If skidding or spin loss at the ball contact becomes severe enough, the heat generated will cause a flash failure of the oil film and the contact will degrade from hydrodynamic to boundary conditions. The friction will increase causing more heat generation, and the bearing will suffer a rapid scoring failure.
