Rolling bearings

Introduction

When I started to write this section I had various preconceptions that really hinged round my view that it was easy to see the basic principle of the rolling bearing but it was not easy to see why they seemed to be so effortlessly successful. I think that I came to see that, despite the simple principles, the rolling bearing depends for its success on a great deal of well-documented empirical data. I also came to have a better idea of the mechanism of lubrication that made it all look so simple. I also decided that ball and roller bearings were so different that I could deal with only one and I chose the ball bearing.

 

It is hard to see any obvious origin for rolling bearings that corresponds to runners on sledges or wheels on carts. It looks to be an invention. The first patent for a ball bearing was taken out in 1791. However the ball bearing requires ingenuity and adequate means of manufacture. 

 

In figure 16-26 I have drawn the basic features of a ball bearing. It comprises two tracks called the inner and outer races, a set of eight balls (in this case.) and a cage, that is not shown on the diagram, to separate the balls. They form a closely-fitted assembly. The inner race fits snugly on a shaft and the outer race fits snugly in a housing.  Even if the balls are perfect spheres and the races are perfectly cylindrical there must be clearance. If a shaft is at rest and is supported on two such bearings figure 16-26 might represent one of the bearings. In the position shown, the inner race will, in fact, be supported by two of the three lower balls B, C and D in the bearing and be out of contact with the rest. Let us suppose that the inner race is in contact with C and D. As soon as the shaft starts to rotate in the anticlockwise direction balls C and D rotate clockwise and start to move their centres anticlockwise. The shaft and the inner race “topple” about ball C and come into contact with ball B. At the same time D goes out of contact. As the shaft continues to turn balls A, B and C will move to the positions of B, C and D as shown and the switch will take place again. This is repeated over and over again as the inner race rotates.

 

We need to look more closely at surfaces that are separated by balls or rollers.

 

Suppose that you had two flat steel plates with surfaces that had been ground and lapped to the standard of surface plates. Suppose that one plate was set up horizontally and four steel balls set up in a line as shown and the second plate rested on them also as shown. (If you feel perturbed that the top plate may drop sideways, add, mentally, a fifth ball some way behind these four balls to stabilise the plate.) I have shown the arrangement in fig 16-27. Two of the four balls would not be in contact with the top plate because these balls will have been made by some manufacturing process and there will be some variation in diameter from one ball to another. This difference may be very small but, because the error is of the same magnitude as the deformation of the two balls that are in contact under the weight of the top plate, it becomes significant. We need to think more about this simple system.

The balls that move are in contact with both plates and will initially have point contact and this inevitably means that there is a high pressure on the balls at these points of contact. Both plates and the rollers will deform. If the force being supported by the balls is not excessive, the deformation is elastic and, if it is large enough, the top plate may drop enough to allow it to come into contact with one or more of the other two balls. These will not be subject to the same forces as the first two rollers. So the behaviour of these four rollers is critically dependent on the dimensions of the balls and, if the top plate were to start moving and rolling the balls the points of contact would move and the elastic deformation move along the plate with the balls and round the balls.

 

In my supposition above I have described the material as steel. Now I have to be more specific. Steels are alloys of iron and other elements and there are hundreds of useful alloys.

 

All of these alloys can be deformed elastically and, surprisingly, Young’s modulus, that is a measure of the relationship between applied stress and elastic strain, does not vary much at around . What does vary is the stress that can be applied to a given steel before it deforms permanently and the nature of this deformation. The stress when the steel deforms plastically and permanently is often called the yield stress. This is around  for mild steel. However for a hardened steel alloy there is no plastic deformation, only a sudden brittle fracture at about . No one would think of making a rolling bearing from mild steel because the balls would soon develop flats from overload. One of the alloy steels would be used in a hardened condition and then the safe working load would be nearly three times that for a bearing in mild steel. However there is a snag. Where mild steel would acquire flats the hardened steel would chip and pit in brittle failure. The tungsten carbide roller in figure 16-3 is very hard and it has been damaged by excessive stress. Figure 16- 28 shows the damage. There is a feint line on the highly polished surface that is a line of cracks and the black mark is a chip out of the roller, as is the smaller black mark. This roller worked with a second identical roller to squeeze stainless steel wire of about 0.5 mm diameter into a flat ribbon about 2 mm wide that was made into pot-scourers. A very large chip that extended to the edge of the roller fell out of the second roller. My guess is that the stress was close to the limit for this material and one or other or both rollers were turning slightly eccentrically. It is a typical brittle failure and the piece that came from the other roller could be fitted exactly back where it came from. The failure shown in figure 16-28 could have been made by a ball rolling on the surface when the ball would be damaged as well.