The loads acting on the bearing can be calculated if the external forces are known. When calculating the load components for a single bearing, the shaft is considered as being a beam supported on rigid, moment-free supports. Elastic deformations in the bearing, the housing or the machine frame are ignored and so are the moments produced in the bearing as a result of shaft deflection. These simplifications are necessary if a bearing arrangement is to be calculated by hand. The standardized methods for calculating basic load ratings and equivalent bearing loads are based on similar assumptions.
3.5.1 Gear trains
With a gear train, the theoretical tooth forces can be calculated from the power transmitted and the design characteristics of the gear teeth. Additional dynamic forces may be present, produced either in the gear itself or by the input drive or power take-off. Other dynamic forces in gears result from errors of shape of the teeth and unbalance of the rotating components.
Because of the requirements for quiet running, gears are made to accommodate high standards of accuracy to ensure that the forces are generally so small that they can be neglected when making bearing calculations. Additional forces arising from the type and mode of operation of the machines coupled to the gear can only be determined when the operating conditions are known. Their influence on the rating lives of the bearings is considered using an "operation"
factor.
3.5.2 Belt drives
For belt drives it is necessary to take into account the effective belt pull (circumferential force) which is dependent on the transmitted torque, when calculating bearing loads. The belt pull must be multiplied by a factor that is dependent on the type of belt, its preload, belt tension and any additional dynamic forces. Values are usually published by belt manufacturers.
3.5.3 Equivalent dynamic bearing load
If the calculated bearing load F obtained when using the above information is found to fulfil the requirements for the basic dynamic load rating C, i.e. the load is constant in magnitude and direction and acts radially on a radial bearing or axially and centrically on a thrust bearing, then P F and the load may be inserted directly in the life equations.
In all other cases it is necessary to calculate the equivalent dynamic bearing load. This is defined as that equivalent load, constant in magnitude and direction, acting radially on radial bearings or axially and centrically on a thrust bearing which, if applied, would have the same influence on bearing life as the actual loads to which the bearing is subjected.
3.5.4 Constant bearing load
Radial bearings are often subjected to simultaneously acting radial and axial loads. If the resultant load is constant in magnitude and direction, the equivalent dynamic bearing load P can be obtained from the general equation
P = XFr + YFa (3.16)
where P is the equivalent dynamic bearing load in N, Fr is the actual radial bearing load in N, Fa is the actual axial bearing load in N, X is the radial load factor for the bearing and Y is the axial load factor for the bearing.
An additional axial load only influences the equivalent dynamic load P for a single row radial bearing if the ratio Fa/Fr exceeds a certain limiting factor e. With double row bearings even light axial loads are generally significant.
The same general equation is also applied for thrust bearings that can take both axial and radial loads, e.g. spherical roller thrust bearings. For thrust bearings that can carry only purely axial loads, i.e. thrust ball bearings and cylindrical, needle and taper roller thrust bearings, the equation can be simplified provided the load acts centrically.
Notice that the detailed procedure for finding the equivalent load differs from type to type of the bearings.
3.5.5 Fluctuating bearing load
In many cases the magnitude of the load fluctuates. If the load can be divided into a number of forces which are constant for a given number of revolutions, but which are different in magnitude from each other, we use "Miners rule" to determine the lifetime. F1, F2... are the constant loads during U1 U2, life fraction intervals. The sum of all life fraction intervals is
U = U1 + U2 + ... ≤ 1 (3.17)
See Figure 3.17. Denoting the number of revolutions required under load F1 by N1, under load F2 by N2 etc., and the total number of revolutions required by N we can write Miners rule as
where L10m1 L10m2, L10m3,… are the rating lives under loads F1,F2, ... and L10m is the total rating life in the combined load situation. Rearranging gives
and
If bearing speed is constant and the bearing load direction is constant, but the magnitude of the load constantly fluctuates between a minimum value Fmin and a maximum value Fmax , see Figure 3.17, the mean load can be obtained from
If, as illustrated in Figure 3.17, the load on the bearing consists of a load F1 which is constant in magnitude and direction (e.g. the weight of a rotor) and a rotating constant load F2 (e.g. an unbalance load), the mean load can be obtained from
Fm = fm (F1 + F2) (3.22) values for the factor fm can be obtained from Figure 3.17.
If the fluctuating load acts in a purely radial direction for radial bearings and in a purely axial direction for thrust bearings, then the equivalent dynamic bearing load P = Fm. However if the load acts in any other direction, the general equation for the equivalent dynamic bearing load must be used and Fr and Fa are replaced by the radial and axial components of the mean load Fm respectively.
[billedtekst start]Figure 3.17: Types of load combinations [4],[billedtekst slut]
3.5.6 Requisite minimum load
If a rolling bearing is to operate satisfactorily it must be subjected to a given minimum load.
As a general "rule of thumb" a load corresponding to 0.02C should be imposed on roller bearings and a load corresponding to 0.01C on ball bearings. The importance of applying this minimum load increases where accelerations in the bearing are high, and where speeds are higher than 75% of the speed ratings given in the product tables.
More detailed recommendations for calculating the requisite minimum loads for the different bearing types may be given by the bearing manufacturer.