OpenSpecEngineering

Finds the basic rating life L₁₀ of a ball or roller bearing from its dynamic load rating, the load it carries and its speed, in millions of revolutions and in hours. It can work out the equivalent load from radial and axial loads, and adjust the life for a reliability above 90 %. Designers use it to choose a bearing from a catalog or to check how long one will last. The results update as you type or drag a slider; there is no Solve button.

Equations

L₁₀ = (C/P)^k     L_10h = L₁₀·10⁶/(60·n)     L_nm = a₁·L₁₀

L₁₀ is the life in millions of revolutions that 90 % of a large group of identical bearings reach or exceed [1]. C is the dynamic load rating from the bearing maker’s catalog, P (F_EQ on the page) the equivalent radial load, k = 3 for ball bearings and 10/3 for roller bearings, and n the speed in rpm. L_10h is the same life in hours. a₁ is the ISO 281 reliability factor, for example 0.64 at 95 % and 0.25 at 99 % [1]. The page takes the lubrication and contamination factor a_ISO as 1.

P = X·F_r + Y·F_a

F_r and F_a are the radial and axial loads, and X and Y their load factors. For a deep-groove ball bearing the page reads them from Table 11-1 of [2] by F_a/C₀, where C₀ is the static load rating. When F_a/F_r is at most e, X = 1 and Y = 0; above e, X = 0.56 and Y comes from the table, interpolated between rows. For other bearings, enter the maker’s X and Y.

Limits and common mistakes

• L₁₀ is a statistical life: one bearing in ten fails sooner. Raise the reliability when a failure is costly.
• Poor lubrication or dirt can cut the life far below L₁₀, and the page doesn’t model either.
• Table 11-1 is for single-row deep-groove ball bearings, and it ends at F_a/C₀ = 0.56.
• Use C and C₀ for the exact bearing from its maker’s catalog. Ratings for the same size differ between makers.

Worked example

A pump shaft runs at 1,450 rpm on a 6205 deep-groove ball bearing (C = 14.8 kN, C₀ = 7.8 kN from the catalog). It carries 2.5 kN radial and 1 kN axial load. The duty calls for 1,000 hours at 95 % reliability.

1. Choose Bearing Type Ball (k = 3) and enter Dynamic Load Rating 14.8 kN.
2. Choose Equivalent Load Source Compute from radial & axial loads, and enter Radial Load 2.5 kN and Axial Load 1 kN.
3. Choose Load Factors X and Y Deep-groove ball bearing — from Fa/C0 (Shigley Table 11-1), and enter Static Load Rating 7.8 kN.
4. Enter Rotational Speed 1450 rpm and choose Reliability 95 % (a1 = 0.64). The Solution shows: From Shigley Table 11-1: Fa/C0 = 0.128205, e = 0.312137, X = 0.56, Y = 1.40752
   Equivalent Load (FEQ) = 2.80752 kN
   L10 Life: 146.493 million revolutions / 1,683.82 hours
   Life at 95 % reliability (a1 = 0.64): 93.7553 million revolutions / 1,077.65 hours

Check: F_a/F_r = 0.4 is above e, so P = 0.56 × 2.5 + 1.4075 × 1 = 2.808 kN, and (14.8/2.808)³ = 146.5 million revolutions. The bearing just meets the 1,000 hours.