RotoPrecision Miniature and Instrument Bearings

Bearing Fatigue Life

Even when properly mounted, lubricated, protected from contamination and subjected to theoretically "ideal" operating conditions, all miniature and instrument bearings will eventually fatigue and wear out. The repeated stresses at the point of contact between balls and raceways will eventually become evident through such phenomena as spalling of the raceway surfaces. The fatigue life, therefore, is essentially the maximum useful life of a bearing when subjected to ideal conditions.

More specifically, the fatigue life of a bearing is defined as the number of revolutions (or hours of service at a constant speed) that can be successfully achieved by 90% of a sample of apparently identical bearings before the first signs of fatigue develop.  Fatigue life rating calculations assume the following conditions:   

• Proper mounting, alignment and loading of the bearing
• Correct lubrication type and quantity
• No contamination is present in the bearing or lubricant
• Loads and speeds used in the calculation are accurate

Sample Calculation

What would be the expected bearing life in revolutions and in total number of hours for the bearing
SM-940W25 O7 given the following observed conditions:

• Radial Load (Fr) = 3.15 lbf
• Axial Load (Fa) = 1.35 lbf
• Measured speed: 14,000 rpm

Note: Since the dynamic load rating data provided in the bearing series tables below are expressed in Newtons, we must convert the observed loads in this example from pounds-force (lbf) into Newtons. The conversion factor is: 1 lbf = 4.448 N thus 3.15 lbf = 14N and 1.35 lbf = 6N.


Solution

In order to solve this sample problem, we will need to solve for L10 using the bearing life formula:

Step 1: From the data provided in the RotoPrecision Catalogue (Pg.7) for bearing SM-940W25 O7, we know that this bearing has a Dynamic Load Rating of (Cr) = 294 N.  In order to solve for L10 we still need to determine the value of the Dynamic Equivalent Radial Load Rating (Pr).

Step 2: Calculating Pr can be achieved by using the equivalent load formula:

Currently, we know that Fr = 14 N (given) and Fa = 6 N (also given), but we will need to determine the appropriate values for the X and Y factors. This can be achieved by calculating a value for Fa/Co and "e" and then cross-referencing the X and Y values using Table 1. From the Bearing Series Data Tables, we also know that the bearing SM-940W25 O7 has a Static Load Rating (Co) = 116 N. We can therefore calculate a value for Fa/Co:


Table 1: Values of X and Y for Calculating Load Ratings.

Step 3: Having determined the value for Fa/Co to be 0.0517, we then cross-reference this value with Table 1 and note that the Fa/Co value lies between 0.0355 and 0.0705. Since we are estimating the bearing life, it is acceptable to take the closer of the two numbers (0.0705 in this case) and use the corresponding "e" value for the purposes of this example. The "e" value is therefore 0.26.


Step 4:
The next step is to compare the ratio of Fa/Fr to "e" in order to determine which set of X and Y factors to use. We must first complete the calculation:

Scanning the values from Table 1, we observe in this case that (Fa/Fr) > e since 0.4286 > 0.26 and therefore the X and Y values for our example here are X = 0.56 and Y = 1.71.

Step 5:
Substituting our values into the Dynamic Equivalent Radial Load formula:

Step 6: We now have our Pr value and can substitute it back into the original bearing life formula:

Therefore, the life expectancy in total revolutions for this bearing under the given conditions is approximately 4.28 x 109 revolutions.

Step 7: To convert the life expectancy into expected hours (given the information that the measured speed is 14,000 rpm) we use the following:

Conclusion

Therefore, the expected life for this bearing application is approximately 4.28 x 109 revolutions or roughly 5,095 hours.


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