Bearing Life Calculations
Capacity and Fatigue Life of Ball Bearings
Aircraft Control Bearings Load Limit Rating
The Limit Load Ratings listed in this catalog were developed to rate bearings that operate in slow speed applications such as those encountered in aircraft control applications. For Bearing Life Calculations, please consult the Schatz Engineering Department.
Basic Dynamic Radial Load Rating Cr
Schatz dynamic radial load ratings are the radial bearing loads that will give a basic rating life
of 1,000,000 revolutions. The basic dynamic load ratings have been determined in accordance
with the methods prescribed by ISO, ABMA, and ANSI.
Bearing Fatigue Life
The fatigue life of a bearing is defined by the number of revolutions the bearing will operate before the first signs of fatigue occur. The L10 life is the basic rating life in hours that 90% of a sufficiently large group of apparently identical bearings will operate before the first signs of fatigue appear.
Basic Rating Life Formula
\[L_{10} = \left ( \frac{C_{r}}{F} \right )^{3}\times 10^{6}\]
\[L_{10,h} = \frac{16667}{S} \times L_{10}\]
𝐿10 = 𝐵𝑎𝑠𝑖𝑐 𝑅𝑎𝑡𝑖𝑛𝑔 𝐿𝑖𝑓𝑒 (𝑟𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠)
𝐿10,ℎ = 𝐵𝑎𝑠𝑖𝑐 𝑅𝑎𝑡𝑖𝑛𝑔 𝐿𝑖𝑓𝑒 (ℎ𝑜𝑢𝑟𝑠)
𝐶𝑟 = 𝐵𝑎𝑠𝑖𝑐 𝐷𝑦𝑛𝑎𝑚𝑖𝑐 𝐿𝑜𝑎𝑑 𝑅𝑎𝑡𝑖𝑛𝑔 (𝑙𝑏𝑓)
𝐹 = 𝐸𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 𝐿𝑜𝑎𝑑 (𝑙𝑏𝑓)
𝑆 = 𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑆𝑝𝑒𝑒𝑑 𝑜𝑓 𝑅𝑜𝑡𝑎𝑡𝑖𝑜𝑛 (𝑟𝑝𝑚)
Equivalent Load Formula for Radial Ball Bearings
\[F = XF_{R}+YF_{A}\]
𝐹𝑅 = 𝑅𝑎𝑑𝑖𝑎𝑙 𝐿𝑜𝑎𝑑 (𝑙𝑏𝑓)
𝐹𝐴 = 𝐴𝑥𝑖𝑎𝑙 𝐿𝑜𝑎𝑑 (𝑙𝑏𝑓)
𝑋 = 𝑠𝑒𝑒 𝑏𝑒𝑙𝑜𝑤
𝑌 = 𝑠𝑒𝑒 𝑏𝑒𝑙𝑜𝑤
For radial contact bearings calculate F with X = 1 and Y = 0. Next, recalculate F with X = 0.56 and Y = (see chart below). Use the larger value of F to determine L10 life.
| \[\frac{F_{A}}{nd^{2}}\] | Y |
|---|---|
| 25 | 2.3 |
| 50 | 1.99 |
| 100 | 1.71 |
| 150 | 1.55 |
| 200 | 1.45 |
| 300 | 1.31 |
| 500 | 1.15 |
| 750 | 1.04 |
| 1000 | 1.0 |
𝑛 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑎𝑙𝑙𝑠
𝑑 = 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑏𝑎𝑙𝑙𝑠
Life Adjustment Factors
Many life adjustment factors can be applied to the calculated bearing life as stated above. These factors are simply multiplied by the bearing life to determine the final adjusted operating life of the bearing.
Adjusted Rating Life Formula
\[L_{nA} = A_{1}\times A_{2}\times A_{3}\times A_{4}\times \left ( \frac{C_{r}}{F} \right )^{3}\times 10^{6}\]
\[L_{nA,h} = \frac{16667}{S}\times L_{nA}\]
𝐿𝑛𝐴 = 𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑅𝑎𝑡𝑖𝑛𝑔 𝐿𝑖𝑓𝑒 𝑟𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠, 𝑛 = 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑓𝑎𝑖𝑙𝑢𝑟𝑒 (%)
𝐿𝑛𝐴,ℎ = 𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑅𝑎𝑡𝑖𝑛𝑔 𝐿𝑖𝑓𝑒 (ℎ𝑜𝑢𝑟𝑠)
𝐴1 = 𝐿𝑖𝑓𝑒 𝐴𝑑𝑗𝑢𝑠𝑡𝑚𝑒𝑛𝑡 𝐹𝑎𝑐𝑡𝑜𝑟 𝑓𝑜𝑟 𝑅𝑒𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑦
𝐴2 = 𝐿𝑖𝑓𝑒 𝐴𝑑𝑗𝑢𝑠𝑡𝑚𝑒𝑛𝑡 𝐹𝑎𝑐𝑡𝑜𝑟 𝑓𝑜𝑟 𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙
𝐴3 = 𝐿𝑖𝑓𝑒 𝐴𝑑𝑗𝑢𝑠𝑡𝑚𝑒𝑛𝑡 𝐹𝑎𝑐𝑡𝑜𝑟 𝑓𝑜𝑟 𝐿𝑢𝑏𝑟𝑖𝑐𝑎𝑡𝑖𝑜𝑛
Reliability (A1)
All formulas are based on an L10 life. If a different life needs to be calculated, use the following table for the adjustment factor:
| Reliability (%) | 90 (L10) | 95 (L5) | 96 (L4) | 97 (L3) | 98 (L2) | 99 (L1) |
|---|---|---|---|---|---|---|
| Factor (A1) | 1.00 | .62 | .53 | .44 | .33 | .21 |
Material (A2)
There are several material options for use with Schatz bearing. The following chart shows the life adjustment factors for the materials offered:
| Material Type | 52100 | 440C | XD15NW |
|---|---|---|---|
| Factor (A2) | 2.2 | .6 | 4.2 |
Lubrication (A3)
Lubrication and the presence of an elastic-hydrodynamic lubrication film is critical to achieving proper bearing life. Please consult the Schatz engineering department for information on determining the lubrication factor for a specific application. While the calculation for the specific lubrication film thickness is complex, in general, choosing a grease with a base oil that has a high viscosity is more suitable for low to moderate speed and high load applications. Alternatively, grease with a low viscosity base is more suitable for high-speed applications with light to moderate loads.
Visit our Lubrication Options page for grease specifications.