Bearing Life Calculation - Bearing Loads & Speeds | American Roller Bearings

## Bearing Selection

In many cases involving bearing selection during the initial design of a machine, obtaining a satisfactory rating life is the prime consideration. The shaft size is usually decided first, based on allowable working stress and deflection. This establishes the bearing bores. Fortunately for the equipment designer, standard bearings can be found with different O.D.s and widths for a given bore size. As the bearing envelope volume increases with O.D. and width, dynamic capacity increases accordingly, yielding increased rating life.

Once the loads and speeds have been determined, the question now becomes, “How many hours of rating life are needed for a well-designed machine?” Sometimes, this is spelled out either by specific industry standards or company policy based on the industry and customer expectations. It may be perfectly acceptable in one industry for the end user to overhaul their equipment, replacing bearings, seals, etc. once every year. In another industry, it may be expected that the bearings last ten years minimum. Also to be taken into consideration when determining the value of the minimum desired rating life is how often the equipment is in use. Does it run intermittently or full time during a work shift? How many shifts per day and how many days per week?

## Table I

Table I below shows suggested minimum bearing rating lives for various operating and reliability conditions.

Operating ConditionMinimum L10 Life (Hours)
Intermittent operation during day, service interruptions acceptable 8,000
Intermittent operation during day, reliability important 12,000
Continuous 1 shift operation 20,000
Continuous 2 shift operation 40,000
Continuous 24 hour operation 60,000
Continuous 24 hour operation reliability important 100,000

## Bearing Dynamic Capacity – C

The bearing Dynamic Capacity, C, is defined as the constant stationary radial load which a rolling bearing can theoretically endure for a basic rating life of one million revolutions. Values for this important bearing parameter, C, are shown in each bearing table except Crane Hook bearings.  Bearing dynamic capacity is used to predict a rating life for each bearing at its anticipated loading and rotational speed.  Generally, a bearing should only be subject to a maximum operating load equal to half its Bearing dynamic capacity. The method of calculating bearing dynamic capacity has been defined by associations such as the American Bearing Manufacturers Association (ABMA) and the International Organization for Standardization (ISO). The formulas use the internal dimensions of the bearing raceways and its rolling elements.

## Static Capacity - Co

The Bearing Static Capacity, Co, is the maximum load that can safely be applied to a non-rotating bearing that will not cause subsequent bearing operation to be impaired. It is based on  calculated contact stress at the center of the most heavily loaded rolling element where it contacts the Inner Race. These stress levels for three types of bearings are:

• - 4600 MPa (667,000 psi) for self-aligning ball bearings
• - 4200 MPa (609,000 psi) for all other ball bearings
• - 4000 MPa (580,000 psi) for all roller bearings

## Bearing Rating Life Calculation

“Rating life” is the bearing life calculated for 90% reliability.  This is the amount of time that a group of apparently identical bearings will complete or exceed before the formation of a fatigue spall. The basic formula for calculating bearing L10 rating life is:

where:

• C = Dynamic Capacity (dN or Lbs)
• P = Equivalent Bearing Load (N or Lbs)
• N = Rotating speed in RPM
• e = 3.0 for ball bearings, 10/3 for roller bearings

Radial cylindrical roller bearings that have opposing flanges on their inner and outer races have a limited capability of taking a thrust load though the length of the rollers. It is so limited that we do not recommend users intentionally do this.  Acceptable thrust loading is using roller ends and flanges for intermittent thrust and locating purposes. Since any thrust load would be perpendicular to the radial load and would use different bearing contact surfaces, it is not a factor in the bearing’s life calculation.

Many applications do not operate at a constant load or speed, and to select bearings for a certain rating life in hours based on the worst operating condition might prove uneconomical.  Often, a duty cycle can be defined for the various operating conditions (load and speed) and the percentage of time at each.  A related situation also occurs in some machines that create a reciprocating motion.  In such instances, a complete duty cycle occurs within one revolution of the bearing.  Furthermore, the two examples could be combined for several anticipated operating conditions with reciprocating motion and different peak loads and speeds. Calculating the rating life when loads and speeds vary involves first calculating the L10 rating life at each operating condition of the duty cycle.  Next, the formula below is used to combine the individual L10 lives to a rating life for the complete duty cycle.

T1, T2, Tn = percentage of time at different conditions, expressed as a decimal

T1 + T2 + … Tn = 1

Lp1, Lp2, Lpn = Life in hours for each period of constant load and speed

When a bearing does not make a complete rotation, but oscillates back and forth in operation, a lower equivalent radial load can be calculated using the formula below:

Pe = Po x (β/90)1/e

where:

• β = angle of oscillation, in degrees
• e = 10/3 (Roller Bearings) 3.0(Ball Brgs)

Life adjustment factors allow the original equipment manufacturer to better predict the actual service lives and reliability of bearings that you selects and install in your equipment.  An adjusted calculated L10 rating life is calculated by using the following formula:

Lna = a1 x a2 x a3 x L10

where:

• Lna = adjusted rating life
• a1 = life adjustment factor for reliability
• a2 = life adjustment factor for special bearing properties, such as material
• a3 = life adjustment factor for operating conditions, lubrication, cleanliness, etc.
• Life adjustment factors, a1, a2 and a3, can theoretically be greater or less than 1.0, depending on their evaluation.

## Life Adjustment for Reliability - a1

In the OEM’s process of predicting the service reliability of his/her equipment, it is sometimes necessary to increase the reliability of the selected bearings to predict a longer mean time between failures. The a1 factors shown below are for increased values of reliability.  If a lower value for L10 is calculated with an a1 factor, and it is not acceptable, then a bearing with greater Dynamic Capacity needs to be chosen.

Reliability - % Ln a1 factor
90 L10 1.00
95 L5 0.64
96L4 0.55
97 L6 0.47
98 L2 0.37
99 L1 0.25

## Life Adjustment Factor for Special Bearing Properties - a2

There have been many improvements in bearing design and manufacture over the years that have been proven in life tests that result in improved L10 rating life. Some of these improvements are:

• Improved surface finishes
• Improved materials and heat treating
• Contoured Rollers and Raceways

## Life Adjustment Factor for Operating Conditions - a3

The Bearing Dynamic Capacity formula was empirically determined through carefully controlled laboratory life testing. Many bearing applications are far from laboratory conditions. Therefore it can be difficult to justify an a3 factor greater than 1.0. Conditions such as high temperature, contamination, exterior vibration, etc. will lead to an a3 factor less than 1. If the lubrication is supior and the operating speed high enough, a significant improved lube film can develop between the bearing’s internal contact surfaces justifying an a3 factor greater than 1.0.  To safely use this benefit for design or commercial reasons requires a thorough analysis and either test data or previous experience.

## System Life

Most machines employ two or more bearings on a shaft, and often there are two or more shafts. All of the bearings in a machine are then considered to be a bearing system.  For business purposes, it is important for the manufacturer to know the reliability or system life of their machine.  This evaluation process considers the importance of combining the L10 lives of all the bearings in the system to answer the question, “How long will the machine perform with 90 percent reliability?” In simpler terms, the system L10 reliability will be less than the lowest individual L10 rating life. The following formula is used to calculate the System Rating Life:

L10sys = (L1-w + L2-w + … Ln-w)-1/w

where

• L10sys = rating life for the system of bearings
• L1, L2, Ln = rating life for the individual bearings in the system
• w = 10/9 for ball bearings and
• w = 9/8 for roller bearings

It has been learned from experience that bearings require a minimum applied load to insure traction for the rolling elements so they roll as the shaft starts to rotate. If the balls or rollers do not roll, they will skid on the moving raceway, wiping away the lubricating oil, and causing damage to the rolling element O.D.s and raceway surfaces. This is called “skidding” and the resultant damage is referred to as “smearing”, which will shorten bearing life.

A good approximation of the minimum load for each is:,

Pmin = 0.02 x C

where:

C = Bearing Dynamic Capacity

In most applications, the existing weight of the shaft, gears, couplings, etc. is sufficient to exceed the Minimum Bearing Load.  However, during startup, the angular acceleration of the shaft should be monitored and limited to insure that the bearings immediately start rolling as the shaft starts to rotate.

## High Temperature Capacity

Bearing Dynamic and Static Capacities are reduced at high operating temperatures. The basic reason is the reduction of raceway and rolling element hardness at high temperatures. Bearing Dynamic Capacity should be reduced by multiplying  the reduction factors as shown below. The temperatures shown are those of the bearing components themselves, which are usually higher than the ambient temperature of the application.

For temperature factors between the values shown, linear interpolation may be applied.

## Misalignment

Misalignment of a bearing typically happens for two reasons:

1. Housings are statically misaligned
2. Shaft deflects or bends under load

Generally, misalignment is not a good thing for rolling element bearings that are not specifically designed to accommodate misalignment. Ball, tapered and cylindrical roller bearing capacity is based on the assumption that the misalignment will not exceed 0.0005 radians (0.03°).  Misalignment greater than this will lead to L10 lives less than that calculated.

Spherical roller bearings and self-aligning thrust bearings are specifically designed to accommodate misalignment.   Self-aligning cylindrical roller bearings can also accommodate some misalignment these bearings. This type of bearing is found in the "Custom" bearings section. These special bearing types can accommodate misalignments from 1.0° to 1.5°.

## Distortions

A review of the standard bearing tables will reveal that for a given bore diameter, several bearings are available with increasing O.D.s and widths. Section heights and capacities increase accordingly. Section height is simply the radial dimension between a bearing’s bore and its outside diameter, into which must be fitted an inner race, balls or rollers, and an outer race. A properly designed bearing balances the thicknesses of the two races with the rolling element diameter in order to optimize Dynamic Capacity without significantly reducing the structural strength of the races. Bearings with thinner races are more subject to distortion than those with thicker cross sections and thicker races.

In general, for a bearing to properly operate, the inner and outer races must be properly supported by the shaft and housing. However, the nature of the design of some types of equipment does not always allow this. As discussed in the misalignment section, sometimes significant shaft deflection can occur causing misalignment. Housings can distort under relatively heavy loads and allow the bearing’s outer race to distort in the same manner. All of these effects tend to reduce the theoretical life of the bearing, but with proper analysis and a special internal design, this reduction can be minimized.

Employing Finite Element Analysis (FEA) of the shaft and housing under load can predict the amount of distortion that will occur. A computer analysis of the internal workings of the bearing can show the stress distribution. Next, optimized roller crowning can be applied to minimize the reduction in bearing life. Consult American’s sales department if the effect of distortion needs to be included in the calculation of bearing life.

## Axial Displacement

Most bearing systems employ two or three bearings in order to support a shaft under radial and thrust loads. The number of bearings depends on whether one bearing is also capable of taking a thrust load. In cases where the thrust load is negligible, one bearing should be a considered a “locating” bearing that positively positions the shaft. When there is a significant distance between two support bearings, differences in thermal growth between the shaft and the housing require that one bearing be the locating or thrust bearing and the other be a “float” bearing. Also, a stack up of axial tolerances between the two bearing locations needs to have one bearing “float” axially so that a parasitic thrust load is not created.

The best bearing for a float location is a cylindrical roller bearing with one straight race. Axial float is easily accommodated by the lubricated rollers sliding on the straight roller path. If another type of bearing is used, such as a deep groove ball bearing, double row angular contact bearing, TDO tapered roller bearing or spherical roller bearing, the typical practice is to allow the outer races of these bearings to slide in the housing bore.