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Imagine I have an important axle in the gearbox of a motor. I want to support it with ordinary ball bearings at several places along its length. I need both the outer and inner races to stay at fixed diameters at a fixed distance from each other.

However, I can change the number of balls in between the races. I can choose any number of different bearings (though each one has to have a certain diameter, so there's actually a limit). I could squeeze an arbitrary number in, so long as that number is below the maximum and can still support the inner and outer rings.

What determines the optimal number of balls used?

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  • $\begingroup$ Is this an exercise or an actual application? Because if that's your real plan, my next question is "Why are you assembling the bearings yourself?" $\endgroup$ – Trevor Archibald Feb 20 '15 at 0:22
  • $\begingroup$ @TrevorArchibald It's a hypothetical situation I've come up with. I'm asking about the rationale behind a bearing manufacturer choosing a specific number of balls. $\endgroup$ – HDE 226868 Feb 20 '15 at 0:31
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    $\begingroup$ Wouldn't the answer also be dependent on the size & strength of the individual balls to be used in the bearings? $\endgroup$ – Fred Feb 20 '15 at 0:38
  • $\begingroup$ @Fred I suppose it would. I'm no expert on bearings. Like I said, the situation is hypothetical. $\endgroup$ – HDE 226868 Feb 20 '15 at 0:44
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    $\begingroup$ I'm a little tired to type this into a full answer, but the answer is really "as many as you can get based on the necessary bearing size and assembly method." Bigger bearings>more contact area>lower stress, but how you assemble it limits how many bearings and what size they can be. You might get a more complete answer from me in the coming days. $\endgroup$ – Trevor Archibald Feb 20 '15 at 1:48
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The number of balls in a bearing affects a couple of different properties of the bearing:

  • Bearing Speed
  • Bearing Strength
  • Bearing Life
  • Bearing Cost

A Full Complement bearing means that the bearing has as many ball as can physically fit. Having the maximum number of balls means that there isn't enough space left for a cage. The cage keeps the balls from touching each other. When the balls are allowed to touch and rub, the maximum speed of the bearing is reduced. A full complement of balls increases the load capacity by 30% over a bearing with fewer balls in a cage. (Reference page 16)

The Number of Balls affects the load on each individual ball. The equation for the force per length unit of bearing diameter is:

$\frac{F}{ZD^2}$

where: $Z=\text{Number of balls}$

The number of balls directly affects the load on each bearing and thence the life of the bearing. (reference page 46)

Bearing Life is controlled by a number of factors. These factors are:

  • Type
  • Race material
  • Ball material
  • Load
  • Speed
  • Lubrication
  • Cleanliness

All of these are factors that affect the number on cause of bearing failure: Fatigue. (Reference page 45)

The final consideration is Cost. Using standard, off-the-shelf bearings are the cheapest. If one of these bearings can be used in your project, it is quite possible that this the best solution. This is even if the project has to be redesigned slightly to accommodate the bearing. Anything that makes your bearing special is likely to cost a lot more.

So in the end, there may not be a definable optimum number of balls. The best bearing will likely be the one that meets your speed, load and life requirements while being available for a reasonable price.

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  • $\begingroup$ Wow, thanks. I didn't think this would ever be answered. $\endgroup$ – HDE 226868 Mar 13 '15 at 21:06

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