### Engineering Reference

## Miniature & Instrument Ball Bearings

## Load Ratings & Bearing Life

Utilize the following load calculations, in conjunction with the life modifiers listed below, to estimate a bearing's operational life. Please contact the Precision Division if you need assistance.

### Static Load Ratings

The static load rating (C_{o}) given in the product listings is the radial load that a non-rotating bearing will support without damage. In evaluating static load conditions, any forces exerted during assembly and test must be considered along with vibration and impact loads sustained during handling, test, shipment and assembly.

### Dynamic Load Ratings

Dynamic loading (C) includes built-in preload, weight supported members, and the effect of any acceleration due to vibration or motion changes. The dynamic load rating (C) for a radial or angular contact ball bearing is a calculated, constant radial load that a group of apparently identical bearings will theoretically endure for a rating life of one million revolutions. The dynamic load rating is a reference value only. A base value rating life of one million revolutions has been chosen for ease of calculation. The dynamic load rating values (C) given in the product engineering tables, found on this website and in our catalogs, include the effects of race-to-ball conformity and are in accordance with ABMA standards #9 and #12.

### Rating Life

The rating life L_{10} of a group of apparently identical ball bearings is the life in millions of revolutions that 90% of the group will complete or exceed. For a single bearing, L_{10} also refers to the life associated with 90% reliability. The rated life (L_{10}) can be computed from the formula:

L_{10} = (C/P_{r})^{3} x 10^{6} revolutions, where:

C = dynamic radial load rating (lb) *The dynamic radial load (C) can be found on the product listing pages.*

P_{r} = dynamic equivalent radial load (lb) *See calculating dynamic equivalent radial load below.*

For a more conservative estimate of life than L_{10}, multiply the above formula by a reliability modifier (a_{2}). Values for a_{2} can be found in the Reliability Material Life Modifier table shown below. The table provides selected modifiers for calculating failure rates down to 1% (L_{1}) for both 440C and 52100 alloys.

#### Rating Life in Hours

To convert the rating to number of hours, multiply the results of the above equation by the following: L_{10}/(rpm x 60).

### Calculating Equivalent Radial Load

More often than not, bearings whose loads are primarily radial are also subjected to some axial forces. When the magnitude of this axial component of the load is greater than a negligible value, it is convenient to interpret this combined radial and thrust load in terms of a simple radial load so that the basic life equation may be used. This simple radial load is referred to as the equivalent load. It is defined as the constant stationary radial load that, if applied to a rotating inner ring, would lead to the same life calculation as the actual conditions of load and rotation. For conventional bearing types other than those with filling notches, the equivalent radial load is given by the maximum of the two values where:

a) P_{r} = VF_{r}

b) P_{r} = XVF_{r} + YF_{a}

V is a rotation factor

X is a radial factor

Y is a thrust factor

F_{r} is the radial load

F_{a} is the thrust load

In calculations for miniature and instrument bearings whose outside diameter is .625 inches and below, the following values are sufficiently accurate: X=0.56, Y=2.10 and e=0.16. With the larger bearing series, consult the following table (see below) for determining values X, Y and e. In all series the rotational factor V is 1.0 for inner ring rotation and 1.2 for outer ring rotation with respect to load.

In the following chart, the factor e represents the ratio of F_{a} /V F_{r} for which the two equations are equal. If the ratio of loads is such that F_{a} /V F_{r} < e, then formula (a) is used; if F_{a} /V F_{r} > e, then formula (b) is used.

#### Table: Factors X, V, and Y

Bearing Type | F_{a}/ZD^{2}Units, lb., in. | In relation to the load The inner ring is: | Single Row Bearings F _{a}/VF_{r}>e | e | ||
---|---|---|---|---|---|---|

Rotating V | Stationary V | X | Y | |||

Radial deep groove ball bearings | 25 50 100 150 200 300 500 750 1,000 | 1 | 1.2 | 0.56 | 2.30 1.99 1.71 1.55 1.45 1.31 1.15 1.04 1.00 | 0.19 0.22 0.26 0.28 0.30 0.34 0.38 0.42 0.44 |

Angular contact ball bearings with contact angle: 5° | 25 50 100 150 200 300 500 750 1,000 | 1 | 1.2 | 0.56 | 2.30 1.99 1.71 1.55 1.45 1.31 1.15 1.04 1.00 | 0.23 0.26 0.30 0.34 0.36 0.40 0.45 0.50 0.52 |

10° | 25 50 100 150 200 300 500 750 1,000 | 1 | 1.2 | 0.46 | 1.88 1.71 1.52 1.41 1.34 1.23 1.10 1.01 1.00 | 0.29 0.32 0.36 0.38 0.40 0.44 0.49 0.54 0.54 |

15° | 25 50 100 150 200 300 500 750 1,000 | 1 | 1.2 | 0.44 | 1.47 1.40 1.30 1.23 1.19 1.12 1.02 1.00 1.00 | 0.38 0.40 0.43 0.46 0.47 0.50 0.55 0.56 0.56 |

20° 25° 30° 35° 40° | 1 1 1 1 1 | 1.2 1.2 1.2 1.2 1.2 | 0.43 0.41 0.39 0.37 0.35 | 1.00 0.87 0.76 0.66 0.57 | 0.57 0.68 0.80 0.95 1.14 |

### Bearing Life Under Varying Loads

In many applications, bearings operate at different loads and speeds for extended periods of time. If the data for loads, speeds and their time periods are available, the following formula can be used to calculate life:

L_{n} = 1/ (p_{1}/L_{n1}) + (p_{2}/L_{n2}) + … + (p_{n}/L_{nn})

Note: p_{1} + p_{2} + … + p_{n} = 1.0

### Life Modifiers

For most cases, the L_{10} life obtained from the basic rating life formula described earlier will provide a satisfactory criteria for bearing performance. For particular applications, however, it may be desirable to consider life calculations for different reliabilities and special bearing properties and operating conditions.

#### Bearing Material

For 440C, NHBB recommends reducing the load rating published for 52100 by 20%. This is a conservative approach to ensure that the bearing capacity is not exceeded under the most adverse conditions. This is incorporated in the reliability modifier (a_{2}) as shown:

#### Table of Reliability - Material Life Modifier

Required Reliability—% | L_{n} | Value of a_{2} | |
---|---|---|---|

52100 | 440C | ||

90 | L_{10} | 1.00 | 0.50 |

95 | L_{5} | 0.62 | 0.31 |

96 | L_{4} | 0.53 | 0.27 |

97 | L_{3} | 0.44 | 0.22 |

98 | L_{2} | 0.33 | 0.17 |

99 | L_{1} | 0.21 | 0.11 |

#### Elastohydrodynamics (EHD Effect)

The presence of a thin film of oil at the mutually contacting ball-to-raceway interface enhances the load capacity of a ball bearing.

#### Lubricant Life

A bearing's effective life is often governed by the lubricant's life. This is usually the case for applications involving very light loads and/or very slow speeds. In such instances, the conventional fatigue life calculated will be unrealistically high. The lubricant's ability to provide sufficient film strength is affected by:

- Quantity and condition of the lubricant in the bearing
- Environmental conditions (e.g. ambient temperature, area cleanliness)
- The load-speed cycle

Specialized oils and greases which exhibit favorable performance characteristics over an extended period, are available.

#### Other Life Adjustments

Loads are seldom applied ideally. Often, the conventional rating life has to be modified due to application abnormalities, intentional or unknown. The following conditions have the practical effect of modifying the ideal, theoretical rating life (L_{10}):

- Vibration and/or shock-impact loads
- Angular misalignment
- Oscillatory duty
- High-speed effects
- Operation at elevated temperatures
- Fits
- Internal design

While it is difficult to provide the exact effect upon life under any of these conditions, NHBB can provide bearing life estimates based on empirical data to help you forecast bearing life for your application.