Stiffness of bearings

Anyone who has worked on lathes, both old and new, will know that effective turning is not possible if the work-piece in its chuck and mounted on the head stock (the main spindle) is able to jump up and down because the bearings are worn or just badly adjusted. One solution shown in figure 16-38 is used on my lathe. The main bearing is tapered and the lubricated spindle can be moved in or out until it has almost no movement in response cutting loads. What it amounts to is that the clearance is a minimum consistent with the bearing not seizing even at the highest speeds.

Most bearings are not tapered and the shaft can move in the bush. The shaft will move and its movement depends on the magnitude and direction of the load applied to it. If that load is steady, as it might be for an electric motor driving a shaft through a coupling, the shaft will not move erratically but run with an eccentricity that is constant in magnitude and direction. If the bearing is a main bearing for an engine the shaft will be subject to a force that varies cyclically and the shaft will always be changing its eccentricity and the direction of this eccentricity. How much it moves depends on the stiffness of the bearing.

 

The idea of stiffness has its roots in springs where it means the ratio of the force to the extension. Here we have a shaft moving within the limits of its clearance and resisting the forces applied to it by viscous effects and inertia forces in the lubricant. It has stiffness and I have heard lathes with low stiffness being described as “lively”. It seemed very apt.

 

We need to understand stiffness in connection with plain bearings and also with ball bearings.

 

What we do know from the work on wedge action is that for a bearing that is well-designed and well-made the clearance will be very small and small changes in the position of the shaft relative to the bush will lead to very large resisting forces. A good plain bearing is stiff. We also know that the faster that a plain bearing runs the closer will be the axis of the shaft to the axis of the outer race. Such bearings are used up to 20,000 rpm in high performance engines for racing.

 

There are some applications where ball bearings having a high stiffness must be used. Figure 16-39 is of a turbo fan aircraft engine. It is complicated. The front part comprises the fan and the compressor section and the back part is the turbine section. In between is the combustion chamber. The fan and the first stages of the compressor are driven by the last stages of the turbine through a hollow shaft that runs right through the engine and runs in ball bearings mounted in the frame of the engine. The high-pressure section of the compressor is driven by the first stages of the turbine and these two also run on a hollow shaft but this shaft is mounted on ball races that run on the central shaft.

Here we have ball bearings running one inside the other with a requirement to use up the minimum radial space. The pressures in gas turbine engines now exceed those on diesel engines and this is only possible because the compressor blades have the smallest possible clearance in the casing. Now we have bearings that must be stiff to prevent the blades rubbing on the case. The only way is to reduce the clearances to a practical minimum. We have seen that bearing balls are produced by a process that leaves a random element to their size and roundness and the only way to get bearings of the standard required for aircraft engines is to select from a very large batch of balls and match balls for diameter and accuracy of shape and surface finish. Such bearings are very expensive but very stiff.