## 6115 Preloading ball and taper roller bearings

An understanding of the significance of bearing preloading may be best visualized by considering a final drive bevel pinion supported between a pair of taper roller bearings (Fig. 6.24). Since the steel of which the rollers, cone and cup are made to obey Hooke's

20 30

Fig. 6.26 Comparison of bearing load-deflection graph with and without preload law, whereby strain is directly proportional to the stress producing it within the elastic limit of the material, the whole bearing assembly can be given the spring analogy treatment (Fig. 6.25). The major controlling factor for shaft rigidity is then the stiffness (elastic rate) of the bearing which may be defined as the magnitude of the force exerted per unit of distortion, i.e. S = W/x (N/m) where S = (N/m)

Let the bevel pinion nut be tightened so that each roller bearing is squeezed together axially 0.04 mm when subjected to a preload of 15 kN. Each bearing will have a stiffness of

Now if an external force (crownwheel tooth load) exerts an outward axial thrust to the right of magnitude 15 kN, the left hand bearing (1), will be compressed a further 0.04 mm whereas the preloaded right hand bearing (2) will be released 0.04 mm, just to its unloaded free position. Thus the preloaded assembly has increased its bearing 30

stiffness to-= 750 kN/mm, which is twice the

stiffness of the individual bearings before they were preloaded.

Fig. 6.26 shows the relationship between axial load and deflection for bearings with and without preload. With the preloaded bearing assembly, the steepness of the straight line (O-a-c-b) for the left hand bearing and shaft is only half of the unpreloaded assembly (O-d-e) and its stiffness is 750 kN/mm (double that of the unpreloaded case). Once the outer right hand bearing has been relieved of all load, the stiffness of the whole bearing assembly reverts back to the nil preload assembly stiffness of 375 kN/mm. The slope now becomes parallel to the without preload deflection load line. The deflection of the bearing assembly for an external axial force of 10 kN when imposed on the pinion shaft in the direction towards the right hand side can be read off the graph vertically between the preload and working load points (a and c) giving a resultant deflection of 0.012 mm.

For the designer to make full use of bearing preload to raise the rigidity of the pinion shaft bearing assembly, the relieving load (outer bearing just unloaded) should exceed the working load (external force) applied to the shaft and bearing assembly.

The technique of reducing bearing axial deflection against an applied end thrust so that the bearing assembly in effect becomes stiffer can be appreciated another way by studying Fig. 6.27.

Suppose a pair of taper bearings (Fig. 6.24) are subjected to a preload of 15 kN. The corresponding axial deflection will be 0.04 mm according to the linear deflection-load relationship shown. If an external axial load of 10 kN is now applied to the pinion shaft so that it pushes the shaft towards the bearings, the load on the left hand bearing (1) will instantaneously increase to 25 kN. The increased deflection of bearing (1) accompanying the increase in load will cause the right hand bearing (2) to lose some of its preload and hence some of its deflection. Simultaneously the change of preload on bearing (2) will influence the load acting on bearing (1) and hence the deflection of this bearing. Once

LoadkN

A = Preload

B = ExternaHoad (working load) C = Total load on left hand bearing D = Total load on right hand bearing E = Deflection with preload F =s Deflection without preload G = Preload relief {relieving load I

Fig. 6.27 Bearing load-deflection graph using inverted preload curve to obtain working load deflection equilibrium between the two bearings has been established, the rollers of bearing (1) will support a load of less than 25 kN and those of bearing (2) will carry a load of less than 15 kN.

The distribution of the applied load between the two bearings at equilibrium may be determined by inverting the deflection-load curve from zero to preload deflection, a-b. This represents the reduction in preload of the right hand bearing (2) as the external axial load forces the pinion shaft towards the left hand bearing. The inverted right hand bearing preload curve can be shifted horizontally from its original position a-b where it intersects the full curve at point a to a new position a'-b', the distance a to a' being equal to the external load applied to the pinion shaft (working load). Note that point a' is the instantaneous load on bearing (1) before equilibrium is established. The intersection of the shifted inverted curve with the full curve point c represents the point of equilibrium for bearing (1), the total left hand bearing load. The axial deflection of the pinion shaft under the applied load of 10 kN is thus equal to the vertical reading between point a and c, that is 0.012 mm. The equilibrium point for bearing (2) can be found by drawing a horizontal line from point c to intersect at point d on the original inverted curve, so that point (d) becomes the total right hand bearing load.

6.1.16 Relationship between bearing tightness and life expectancy (Fig. 6.28) Taper roller and angular contact ball bearing life is considerably influenced by the slackness or tightness

Optimum preload / 1 > |
t |
redlcted earing fe |

1 |

Fig. 6.28 Effect of bearing tightness or slackness on life expectancy

Fig. 6.28 Effect of bearing tightness or slackness on life expectancy to which the bearings are originally set (Fig. 6.28). The graph shows that if the bearings are heavily preloaded the excessive elastic distortion, and possibly the breakdown in lubrication, will cause the bearings to wear rapidly. Likewise excessive end float causes roller to track misalignment and end to end shock loading with much reduced service life. However it has been found that a small degree of bearing preload which has taken up all the free play when stationary loosens off under working conditions so that the rollers will have light positive contact with their tracks. This results in pure rolling and hence optimum bearing life.

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