Is There An Optimum Bearing Design?

Now if we change the geometry of the bearing to make it accommodate a wheel, the modern design looks rather like the bearing on the left side below (the right hand drawing - a two-row bearing - is discussed later). As shown, the modern circular roller bearing has an inner race and an outer race which retain the rolling balls between the races. Call the inner race's outside radius Ri and call the outer race's inner radius Ro. Note that the inner and outer race's circumferences are not the same: Ci = 2*pi*Ri and Co = 2*pi*Ro so the difference in circumference is Ci -Co = 2*pi*(Ro-Ri). Normally, the bearing is tight-fitting so that Ro-Ri=Db where Db is the diameter of the rolling balls. Finally, the circumference difference is:

Bearing Frictional Power Loss

Bearing Heating

Bearing Combined Constraint

Like the spokes of a wagon wheel (left below) the balls in the bearing support the outer and inner circular members and keep the members at a constant radial distance apart. The blue curve at the bottom of the wagon wheel shows a greatly exaggerated deformation of the outer circular member under gravity. Likewise, the balls prevent the outer raceway from deforming at the position of the balls but the strength of the raceway is all that prevents bending between the balls. Unlike the wagon wheel, the balls roll around the races so that any deformation of the races propagates around the outer member at the speed of the balls themselves. To get a clue to the distances that are important in a good bearing look at the figure on the right below. This shows that the outer raceway wear ranges between 10 and 25 microns (micron = meter/1,000,000).The inner raceway wears much more slowly. This sequence of figures is adapted from a paper by H. Aramaki "Roller Bearing Analysis Program Package (BRAIN)", 1997, which is on the net in .pdf format.

It is apparent that any deformation from perfect circles in any rolling member will show up as a drag force or power loss. Consequently there must be enough balls to support the outer raceway adequately and this depends on the thickness and materials properties of the outer raceway. The figure below (left) shows only a few of the forces considered in bearing computer programs: various sliding and rolling friction forces. Other forces which are accounted for in the BRAIN program include contact forces, centrifugal force, gyroscopic moments, and lubrication viscous drag. Much of the analysis of bearing performance builds on the work of A.B. Jones in the 1960's which was picked up and expanded on by NASA. Now it is apparent that finding an optimum bearing is a very much greater chore than I had imagined when I set out to write this page so I will narrow the scope to a description of the factors involved. Any final design will need computer analysis and lab or street testing.

The figure on the lower right appears to show the importance of lubrication viscous drag. The torque required to spin up a bearing to speed increases at first, then levels off, and even drops at very high speed. This is interpreted as a drop in lubricant viscosity at higher temperatures from the higher speed.

For comparison 80mm and 100mm diameter skate wheels are considered in the figure below. Typically the rpm will be in the 2000-3000 range except for downhill where the rpm is much higher.

Some sliding friction results when the spacers between rolling elements contact the raceway. Friction also arises from slippage of the rolling elements. This mainly occurs in the unloaded region of a bearing where clearance between rolling elements and raceway is at a maximum (My interpretation is in an appendix at the bottom of this page). Slippage also increases with decreasing speed because the reduction of centrifugal force on the rolling elements results in greater clearance. Friction can also result from rusting or corrosion of metal surfaces which produces abrasive oxide particles. Needless to say, cleanliness is extremely important for fast bearings as is the requirement that they not be allowed to become wet (rust).

The temperture coefficient of expansion is important because changes in the dimension of any rolling element will result in vibration, slippage, or drag through a compressive contact force which retards rolling. The practical effect of these requirements will be discussed in the Bearing Sizing and Material section.

So far we have assumed that the only forces acting are perpendicular to the axis of the bearing as in an automobile which is gear-driven and gravity loaded. In the skater's case there can be significant force along the bearing's axis when the skater strokes. This axial loading can wear an ordinary bearing out quickly leading to vibration and slippage. There are new bearing designs including the single-row and double-row angular contact bearings. In an ordinary bearing the balls contact the races in a plane perpendicular to the bearing axis whereas in an angular contact bearing the balls are at an angle other than 90 degrees with respect to the bearing axis. The angle is determined by the amount of axial offset in the grooves in the inner and outer races. A double row angular contact bearing has two rows of balls with opposite offset angles so that axial loading can be resisted from both sides. This kind of design extends the bearing lifetime significantly. Here is an example of a double-row angular contact bearing (left) and a single-row angular contact bearing (right):

Skate bearings usually are in a "608" size or a "688" minibearing or microbearing (note: minibearings like Baby Bonts don't fit all frames and may require an adapter to fit wheels designed for larger bearings). Traditionally they have used 7-10 balls with chrome-steel races. Recently the hybrid bearing made it's way into the skating scene. Beware that the term hybrid is used in two different senses which mix the traditional chrome-steel with the new ceramic materials (usually Silicon nitride).

1. Metal raceways with all ceramic balls.
2. Metal raceways with half metal balls and half ceramic balls (alternating)

Now as SINERAMICS indicates, the Silicon Nitride ("SiN") ceramic balls can be made in two different processes and come in three grades. Sineramics (the parent company of the apparently defunct SINSYSTEMS) also shows that SiN balls are available in three grades. Grade A was used in aerospace and Grade B was used in skate bearings. Grade C was even lower quality. So beware that not all SiN balls are equal.

One trend that can be discerned is the downsizing of skate bearings and the increase in number of balls. While 7-8 balls were standard, it is not unusual to find 9-10 now. It seems to me that this is a healthy trend. As the outer raceway diameter drops it becomes less likely to flex so one might expect less vibration and slippage. The old argument for large and heavy balls (large "m") came from the fact that they had more centrifugal force when spinning and so were more likely to make good rolling contact with the outer raceway whereas lighter ones might slip. This argument seems to have fallen away as a smaller diameter outer raceway (small "r") increases centrifugal force (F = mv*v/r) without the need for massive balls. And with the smaller mass comes less stress and longer wear. In addition, the bearing stiffness increases with an increasing number of balls as there are more support points for the raceways. Consequently, I expect this trend to continue toward smaller balls and more of them.

Now as regards the number of rows of balls per bearing, there has been very little exploration in skating. I came across one double-row bearing used in hockey but none for speed. It seems clear that the angular contact bearing has advantages over the old design. Most bearing companies advertise that they produce angular contact hybrid bearings so they are embracing this design. But I have not seen any mention in skate bearing ads that they use angular contact bearings. So either they don't use them or they don't think it's important enough to mention. It appears that the double-angular-contact bearing has advantages wherever sideways (axial) loading occurs. Since this looks very likely in skating it seems that they should be employed. Of course they are wider than ordinary bearings, but since the outer diameter and ball diameter can be reduced it does not look too hard to modify the wheel slightly or come up with an adapter to fit them into existing wheels. In the hockey case the wider double-row bearing meant that the bearing spacer could be eliminated altogether.

Appendix: Ball Speed And Slippage

Consider that the balls in a bearing travel slower than the outer raceway. You can convince yourself of this by measuring the "King Tut" bearing: Get two flat rulers (or yardsticks, meter sticks etc) and a cylinder , perhaps a pill bottle. Lay the first ruler on the ground and place the cylinder on top of it. Finally, the second ruler goes on top of the cylinder. Now as you push the cylinder with the top ruler the top ruler moves twice as far as the center of the cylinder. Consequently, the center of mass of the cylinder moves only half as fast as the top ruler. For our bearing this means that the center of mass of a ball moves at half the speed of the outer raceway when it is firmly gripping the raceway. It is only the outer edge of the ball which moves at the speed of the raceway by virtue of the ball's rotation.