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SCHATZ 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 guide wheel 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 = π΅π‘Žπ‘ π‘–π‘ π‘…π‘Žπ‘‘π‘–π‘›π‘” 𝐿𝑖𝑓𝑒 (π‘Ÿπ‘’π‘£π‘œπ‘™π‘’π‘‘π‘–π‘œπ‘›π‘ )
𝐿10,β„Ž = π΅π‘Žπ‘ π‘–π‘ π‘…π‘Žπ‘‘π‘–π‘›π‘” 𝐿𝑖𝑓𝑒 (β„Žπ‘œπ‘’π‘Ÿπ‘ )
πΆπ‘Ÿ = π΅π‘Žπ‘ π‘–π‘ π·π‘¦π‘›π‘Žπ‘šπ‘–π‘ πΏπ‘œπ‘Žπ‘‘ π‘…π‘Žπ‘‘π‘–π‘›π‘” (𝑙𝑏𝑓)
𝐹 = πΈπ‘žπ‘’π‘–π‘£π‘Žπ‘™π‘’π‘›π‘‘ πΏπ‘œπ‘Žπ‘‘ (𝑙𝑏𝑓)
𝑆 = π‘‚π‘π‘’π‘Ÿπ‘Žπ‘‘π‘–π‘›π‘” 𝑆𝑝𝑒𝑒𝑑 π‘œπ‘“ π‘…π‘œπ‘‘π‘Žπ‘‘π‘–π‘œπ‘› (π‘Ÿπ‘π‘š)

Equivalent Load Formula for Radial Ball Bearings

\[F = XF_{R}+YF_{A}\]

𝐹𝑅 = π‘…π‘Žπ‘‘π‘–π‘Žπ‘™ πΏπ‘œπ‘Žπ‘‘ (𝑙𝑏𝑓)
𝐹𝐴 = 𝐴π‘₯π‘–π‘Žπ‘™ πΏπ‘œπ‘Žπ‘‘ (𝑙𝑏𝑓)
𝑋 = 𝑠𝑒𝑒 π‘π‘’π‘™π‘œπ‘€
π‘Œ = 𝑠𝑒𝑒 π‘π‘’π‘™π‘œπ‘€

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 = π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘Žπ‘™π‘™π‘ 
𝑑 = π‘‘π‘–π‘Žπ‘šπ‘’π‘‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘Žπ‘™π‘™π‘ 

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 = 𝐴𝑑𝑗𝑒𝑠𝑑𝑒𝑑 π‘…π‘Žπ‘‘π‘–π‘›π‘” 𝐿𝑖𝑓𝑒 π‘Ÿπ‘’π‘£π‘œπ‘™π‘’π‘‘π‘–π‘œπ‘›π‘ , 𝑛 = π‘π‘Ÿπ‘œπ‘π‘Žπ‘π‘–π‘™π‘–π‘‘π‘¦ π‘œπ‘“ π‘“π‘Žπ‘–π‘™π‘’π‘Ÿπ‘’ (%)
𝐿𝑛𝐴,β„Ž = 𝐴𝑑𝑗𝑒𝑠𝑑𝑒𝑑 π‘…π‘Žπ‘‘π‘–π‘›π‘” 𝐿𝑖𝑓𝑒 (β„Žπ‘œπ‘’π‘Ÿπ‘ )
𝐴1 = 𝐿𝑖𝑓𝑒 π΄π‘‘π‘—π‘’π‘ π‘‘π‘šπ‘’π‘›π‘‘ πΉπ‘Žπ‘π‘‘π‘œπ‘Ÿ π‘“π‘œπ‘Ÿ π‘…π‘’π‘™π‘–π‘Žπ‘π‘–π‘™π‘–π‘‘π‘¦
𝐴2 = 𝐿𝑖𝑓𝑒 π΄π‘‘π‘—π‘’π‘ π‘‘π‘šπ‘’π‘›π‘‘ πΉπ‘Žπ‘π‘‘π‘œπ‘Ÿ π‘“π‘œπ‘Ÿ π‘€π‘Žπ‘‘π‘’π‘Ÿπ‘–π‘Žπ‘™
𝐴3 = 𝐿𝑖𝑓𝑒 π΄π‘‘π‘—π‘’π‘ π‘‘π‘šπ‘’π‘›π‘‘ πΉπ‘Žπ‘π‘‘π‘œπ‘Ÿ π‘“π‘œπ‘Ÿ πΏπ‘’π‘π‘Ÿπ‘–π‘π‘Žπ‘‘π‘–π‘œπ‘›

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.

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