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SELECTION OF BEARING SIZE

5.3 Calculation of Bearing Loads 5.3.2 Bearing Loads in Belt or Chain Transmission 5.3.3 Bearing Loads in Gear Transmission 5.3.4 Load Distribution on Bearings
Applications Applications
The loads applied on bearings generally include the In the simple examples shown in Figs. 5.5 and 5.6.
weight of the body to be supported by the bearings, The force acting on the pulley or sprocket wheel when The loads imposed on gears in gear transmissions vary
the weight of the revolving elements themselves, the power is transmitted by a belt or chain is calculated according to the type of gears used. In the simplest The radial loads on bearings1and 2 can be calculated
transmission power of gears and belting, the load using the following equations. case of spur gears, the load is calculated as follows: using the following equations:
produced by the operation of the machine in which the
bearings are used, etc. These loads can be theoretically }M = 9 550 000H / n ....( N ⋅ m m ) FC1 = b K ...............................................(5.16)
calculated, but some of them are difficult to estimate. = 0 974 000H / n ....{kgf ⋅ mm} .............(5.9) c
Therefore, it becomes necessary to correct the }M = 9 550 000H / n ....( N ⋅ m m )
estimated using empirically derived data. Pk = M / r .............................................(5.10) = 0 974 000H / n ....{kgf ⋅ mm} ...........(5.12) FC2 = a K ..............................................(5.17)
c
5.3.1 Load Factor where M : Torque acting on pulley or sprocket
wheel (N ⋅ mm), {kgf⋅ mm} Pk = M / r .............................................(5.13) where FC1 : Radial load applied on bearing1
When a radial or axial load has been mathematically (N), {kgf}
calculated, the actual load on the bearing may be Pk : Effective force transmitted by belt or Sk = P√k⎯Ptka2n+⎯Sθk.2.=...P..k..s..e.c...θ.....................................................((55..1145))
greater than the calculated load because of vibration chain (N), {kgf} Kc = FC2 : Radial load applied on bearing 2
and shock present during operation of the machine. (N), {kgf}
The actual load may be calculated using the following H : Power transmitted(kW) where M : Torque applied to gear
equation: (N . mm),{kgf . mm} K : Shaft load (N), {kgf}
n : Speed (min–1)
}Fr = fw ⋅ Frc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (5.8) Pk : Tangential force on gear (N), {kgf} When these loads are applied simultaneously, first the
r : Effective radius of pulley or sprocket Sk : Radial force on gear (N), {kgf} radial load for each should be obtained, and then, the
Fa = fw ⋅ Fac wheel (mm) Kc : Combined force imposed on gear sum of the vectors may be calculated according to the
load direction.
where Fr, Fa : Loads applied on bearing (N), {kgf} When calculating the load on a pulley shaft, the belt (N), {kgf}
tension must be included. Thus, to calculate the actual
Frc, Fac : Theoretically calculated load (N), load Kb in the case of a belt transmission, the effective H : Power transmitted (kW)
{kgf}
transmitting power is multiplied by the belt factor fb, n : Speed (min–1) c a
fw : Load factor ab cb
which represents the belt tension. The values of the r : Pitch circle radius of drive gear (mm)
The values given in Table 5.5 are usually used for the
belt factor fb for different types of belts are shown in θ : Pressure angle
load factor fw.
Table 5.6. In addition to the theoretical load calculated above, FC1 FC2 FC1

Kb = fb ⋅ Pk .........................................(5.11) vibration and shock (which depend on how accurately Bearing1 K Bearing 2 K
Bearing1 FC2 Bearing 2
In the case of a chain transmission, the values the gear is finished) should be included using the gear Fig. 5.6 Radial Load

corresponding to fb should be 1.25 to 1.5. factor fg by multiplying the theoretically calculated load Distribution (2)

by this factor. Fig. 5.5 Radial Load
Distribution (1)
The values of fg should generally be those in Table 5.7.

When vibration from other sources accompanies gear

operation, the actual load is obtained by multiplying

the load factor by this gear factor.

Table 5. 5 Values of Load Factor fw Table 5. 6 Belt Factor f b 5.3.5 Average of Fluctuating Load

Operating Conditions Typical Applications fw Type of Belt fb Table 5. 7 Values of Gear Factor fg When the load applied on bearings fluctuates, an
average load which will yield the same bearing life as
Smooth operation Electric motors, 1.0 to 1.2 Toothed belts 1.3 to 2.0 Gear Finish Accuracy fg the fluctuating load should be calculated.
free from shocks Machine tools, 1.2 to 1.5 V belts 2.0 to 2.5
Air conditioners Flat belts with tension pulley 2.5 to 3.0 (1) When the relation between load and rotating speed
1.5 to 3.0 Flat belts 4.0 to 5.0 is divided into the following steps (Fig. 5.7)
Precision ground gears 1.0~1.1
Load F1 : Speed n1 ; Operating time t1
Normal operation Air blowers, Load F2 : Speed n2 ; Operating time t2
Compressors,
Elevators, Cranes, …
Paper making
machines …
…

Ordinary machined gears 1.1~1.3 Load Fn : Speed nn ; Operating time tn

Then, the average load Fm may be calculated using the

Operation Construction following equation:
accompanied by equipment, Crushers, ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯p
shock and vibration Vibrating screens, √Fm =
Rolling mills F1pn1t1+ F2pn2t2+ ... + Fnpnntn
n1t1+ n2t2+ .........+ nntn

..........................(5.18)

where Fm : Average fluctuating load (N), {kgf}
p = 3 for ball bearings
p = 10/3 for roller bearings

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