Why can doubling bearing load reduce calculated life by much more than half?

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Compare life ratios before making a capacity claim

The basic rating-life relationship is proportional to (C/P)^p, with p = 3 for ball bearings and p = 10/3 for roller bearings in this framework.

If the same bearing is evaluated with twice the equivalent load and all other assumptions remain unchanged, the calculated life ratio becomes (1/2)^p. That gives one eighth for the ball-bearing case and approximately 9.9% for the roller-bearing case. These are mathematical sensitivities, not test results. They explain why a modest-looking load-estimation error can materially change a life calculation. The relationship still needs a valid load model and must stay within the manufacturer's stated range of application.

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Use the sensitivity to review the uncertain input

Make two calculation columns: the original equivalent load and a justified higher-load scenario.

Keep the bearing, speed and life method the same so the comparison isolates load sensitivity. If belt tension or a process force is poorly known, state that uncertainty instead of reporting a highly precise life figure. Do not use the ratio to claim that a bearing experiencing an overload will always fail at an exact fraction of its previous lifetime; contamination, lubrication and other failure mechanisms are not controlled by this thought experiment. The value of the exercise is to show which input needs better evidence before the design conclusion is accepted.