A bearing's rated life is not how long it lasts. It is the life that nine bearings in ten exceed — the tenth fails earlier, by design, and the spread is wide. A calculated 20 000 hours means half of them are still running at about 100 000 and one in ten has failed before 20 000.
This is a deep-groove ball bearing on a fan shaft: 4 kN of radial load at 1500 rev/min, wanted for five years of continuous duty.
Four significant figures. A life figure with six would be a claim nobody can support — see the opening paragraph.
The basic dynamic load rating comes from the manufacturer's catalogue for the bearing being considered — it is a measured property of that part, not something a calculation can produce. This is a 6208.
The exponent is 3 for ball bearings and 10/3 for roller bearings, and it is the whole character of the calculation: life goes as the cube of the load margin, so a 25% overload costs half the life.
The check above fails, so the question becomes which bearing to fit. The load rating required for a wanted life inverts the same relation — and this is the number to take back to the catalogue.
A rating half again as large is one or two sizes up in the same bore, or the same bearing in a heavier series. It is also worth asking whether the load is really 4 kN: the cube means a 20% overestimate of the load costs 40% of the calculated life, and bearing loads are usually estimated rather than measured.
The cube is the reason this curve falls away so fast, and the reason a bearing that is comfortable at its design load is not comfortable at 30% more.
The basic rating life, and nothing else. It assumes a radial load only — an axial component turns P into an equivalent load with two catalogue factors in it — and it takes no account of lubrication, contamination or temperature, which the modified rating life handles with a factor that can move the answer by an order of magnitude in either direction.