4.2 Support Vector Regression
4.3.1 Primal gradient methods
Single row angular contact bearings (angular contact ball bearings, taper roller bearings) are adjusted axially on mounting. The adjustment values (axial clearance or preload) are based on the operating conditions when the bearing is under load and has reached its operating temperature. Light pre-load is recommended for gearbox bearings and provides the following advantages compared with clearance:
● accurate shaft guidance,
● increased stiffness,
● extended calculated and service lives,
● quiet running, and
● compensation for settling move-ments in operation.
As the bearings have to be adjusted on mounting, i.e. in an unloaded con-dition at ambient temperature, the changes produced when the bearings are in operation must be considered when determining the adjustment values. The main influences are those of temperature and deformations.
Influence of temperature on the adjustment of angular contact bearings
The inner rings of bearings mounted on gearbox shafts are generally hotter than the outer rings. This will reduce the set clearance or increase the set preload. The influence of temperature on the adjustment can be calculated using the following equation provided both shaft and casing are of steel or a material with the same thermal behaviour
∆a = 11 × 10−6[0,5 (dmAT∆AcotαA
+ dmBT∆BcotαB) ± T∆mL]
where
Da = reduction in axial internal clearance caused by tem-perature differential, mm dm = mean bearing diameter
= 0,5 (d + D), mm L = mean distance between
bearings (➔ fig ), mm α = contact angle of bearing,
degrees (cotα = 1,5/e;
for values of bearing-dependent factor e see SKF General Catalogue) T∆A, T∆B= temperature differential from
inner to outer ring across bearings A and B, °C T∆m = temperature differential
from shaft to casing, °C The plus sign is used for bearings arranged face-to-face, the minus sign for bearings arranged back-to-back.
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4
Dimensioning the bearing arrangement
Table 9
Fig 15
δa1
F01
Ka
δ1
If the value of the temperature dif-ferential T∆is not known from experi-ence or measurements, the following guideline values can be used:
T∆= 5 to 10 °C for slowly rotating gear-box shafts
T∆= 10 to 20 °C for intermediate shafts and moderate speeds T∆= 20 to 30 °C for slim high-speed
shafts
T∆= 30 to 40 °C for high-speed input shafts and well-cooled gearboxes
Influence of deformations on the adjustment of angular contact bearings
When considering deformations it should be remembered that the total resilience is influenced not only by the resilience of the bearings but also by the elasticity of the associated compo-nents, the fits and the elastic deforma-tions of all other components through which the forces pass, including the gearbox support. The effects of the different stiffnesses of the associated components can be represented in preload force/preload path diagrams.
The three preload force/preload path diagrams shown in Diagrams to show the influence of casing stiffness
3 1
Preload force/pre-load “path” dia-grams for a bear-ing arrangement (Design 1)
Preload force/pre-load “path” dia-grams for a bear-ing arrangement (Design 2)
Dimensioning the bearing arrangement
Diagram 1 Preload force F0
Bearing A Bearing B
Bearing position B total
Bearing position A total
Axial displace-mentδa
Preload force F0
Bearing A Bearing B
Bearing position B total
Bearing position A total
Axial displace-mentδa
Ka
Dimensioning the bearing arrangement
Diagram 3
Fig 16
Preload force/pre-load “path” dia-grams for a bear-ing arrangement (Design 3)
Pinion shaft bearing arrange-ment
Preload force F0
Bearing A Bearing B
Bearing position B total
Bearing position A total
Axial dis-placementδa
on the axial displacement δafor the pinion shaft shown in fig as a re-sult of the external force Ka.
In all three cases, the bearing stiff-ness and the external force Kaare the same. The casing in case 1 is very stiff whereas the casings in cases 2 and 3 are less stiff. Cases 2 and 3 differ only in the preload. Whereas in case 2 the preload path d is kept constant with respect to case 1, for case 3, the pre-load force F0is the same as for case 1.
Irrespectively of whether the preload path or the preload force is kept con-stant, the axial displacement δawill change depending on the casing stiff-ness. Thus it is imperative that the total resilience at the bearing positions is taken into account when determining
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the preload in order to limit the axial displacement.
Using the application example shown in fig (a bevel/spur gear) the choice of adjustment (axial clear-ance, zero clearance or preload) will be discussed.
The locating bearings for the bevel pinion shaft have axial clearance because the temperature differential from shaft to casing is relatively large as the speed is high and the pinion shaft has a small mass. Also the bear-ings are arranged in the (hook-shaped) sleeve and this arrangement is relatve-ly stiff in the axial direction.
The intermediate shaft bearings and those on the output (power take-off) shaft can be either clearance-free or –
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depending on casing stiffness – even be adjusted to preload. The reason for this is that the speeds are low (less frictional heat), the masses of the shafts are relatively large, and the axial stiff-ness of the casing is lower. In fact, because of the axial forces generated in the bearings, the casing tends to deform (bulge).
Influence of adjustment on bearing life
The adjustment has different effects on the life of the two bearings shown in
fig . Whereas the life of bearing A which is subjected to the external force Kaimmediately drops with increasing preload, bearing B will achieve its maximum life when it has a slight preload.
Diagram shows qualitatively the dependence of bearing life on preload and clearance. From this it will be seen that the stiffness does not increase very much with increasing preload whereas there is a risk that bearing life will be shortened and there will be inc-reased friction and heat. Thus it is advisable to choose the adjustment so that when under load and at the operat-ing temperature the bearoperat-ing arrange-ment will have virtually zero clearance.
An adjustment to give a distinct pre-load should only be chosen if the oper-ating conditions (loads, temperatures, deformations) are accurately known, so that the preload force can be deter-mined using sophisticated computer programs.
4 16
Influence on bear-ing life of preload and clearance Bevel/spur gear-box bearing arrangements
Dimensioning the bearing arrangement
Diagram 4
Life
Bearing A
Bearing B
Preload Clearance
When selecting the bearings there-fore, not only must the complete bear-ing designation (cage design, bearbear-ing clearance) be established, but informa-tion regarding adjustment values, oil flow rates and minimum load must also be given to production and assembly as well as to the end user, so that proper bearing performance can be guaranteed.
4
Dimensioning the bearing arrangement
Grease lubrication . . . 92 Oil lubrication . . . 95 Maintenance . . . 98