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2.2 Convex optimization

2.2.3 Algorithms

The gear wheels are generally ar-ranged between the bearings for design reasons. This is also true for the bevel/spur gearboxes.

For shaft diameters up to approx-imately 90 mm, two taper roller bear-ings mounted back-to-back (➔ fig ) provide a technically advantageous and cost-favourable arrangement. With larger dimensions, the casings are often inadequately stiff with regard to the axial forces (tooth force + internal axial force of the bearings). This makes adjustment of the bearings difficult and shaft guidance is generally not suffi-ciently accurate. The bearing arrange-ment with cross location is then not altogether suitable.

The axial force from the gear wheel always acts in one direction. As the axial force from the pinion dominates, it is possible that the direction of the resultant axial force will change. This must be taken into consideration when adjusting the mesh.

When adjusting the taper roller bear-ings, the shim at the gear wheel side determines the position of the wheel in the gearbox. The shim at the pinion side is used to set the axial clearance of the taper roller bearings.

Oil from the collecting pockets above the bearings runs down at the cover side of each bearing. From there the oil must pass through the bearing and thus lubricate it. Oil retaining plates en-sure that there is an adequate supply of oil available even when starting up.

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Bearing arrange-ment for a bevel wheel shaft with two taper roller bearings arranged face-to-face Bearing

arrange-ment for a bevel pinion shaft with one taper roller bearing as a thrust bearing and one taper roller bear-ing as a radial bearing (locating position) and one cylindrical roller bearing (non-locating position)

Shafts in bevel gearboxes

The locating/non-locating bearing arrangement shown in fig has the advantage, compared with that shown in fig , that no bearing adjustment is required. The bearings are also in-sensitive to axial deformation of the casing. This will only be subjected to the tooth forces and not to the internal bearing forces, so that there will be less deformation.

A double row angular contact ball bearing is used as the locating bearing.

Alternatively, single row angular con-tact ball bearings in matched sets having the same diameters as the double row bearing and being margin-ally wider can be used for higher load carrying capacity.

To determine the position of the gear wheel in the gearbox and to adjust the mesh, a split washer is inserted between the bearing outer ring and the retaining ring. When doing this the bearing can remain on the shaft. A cylindrical roller bearing of the NU design is used as the non-locating bearing at the other side where the radial load is heavier.

The locating/non-locating bearing arrangement shown in fig is similar in design and function to that shown in fig . At the locating side, two single row taper roller bearings are arranged face-to-face. Compared with the double row angular contact ball bearing, the taper roller bearings provide higher load carrying capacity and greater stiffness.

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Adjustment of the bevel gear wheel is simplified using a special (hook-shaped) sleeve. In order to prevent the thin-walled intermediate ring of the paired taper roller bearings from being deformed as the cover screws are tightened, the length of the spigot in the cover should be chosen to give a preload corresponding to approxim-ately 0,01 mm.

Oil should be supplied to the taper roller bearings via the lubrication groove and holes in the intermediate ring. To allow an even distribution over the two bearings, an oil drain should be provided at the cover side.

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Bearing arrange-ment for a bevel wheel shaft with two matched single row taper roller bearings (locating position) and one cylindrical roller bearing (non-locating position) Bearing

arrange-ment for a bevel wheel shaft with a double row angular contact ball bearing (locating position) and a cylindrical roller bearing (non-locating position)

Shafts in bevel gearboxes

Demands on the bearings

Modern bevel gearboxes usually have hardened gear wheels with ground helical teeth. This enables high power transmission to be achieved with little friction and little noise generation. A prerequisite for this good performance is the use of high-performance ball and roller bearings which should have the properties listed in Table .

In addition to these general require-ments for bearings for high-perform-ance gearboxes, there are additional requirements which are specific to the actual bearing position.

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Bearings for the pinion shaft High radial and axial forces act simul-taneously on the pinion shaft. There-fore high radial load carrying capacity is required of the non-locating bearing and high axial load carrying capacity of the locating bearing. Because of the high speed, bearings having low friction should be used. These two require-ments are in part contradictory.

Experience shows that pinion bear-ings do not fail from fatigue but are en-dangered by other influences. From this it is possible to derive the require-ments and actions listed in Table 7.

Demands on rolling bearings for bevel gears

Demands on bevel pinion shaft bearings

Shafts in bevel gearboxes

Demand Required bearing design feature

High load carrying capacity Optimised rolling element size and number.

Logarithmic roller/raceway contact.

Good lubricant film formation through low friction and low raceway surface roughness.

High stiffness Optimised rolling element size and number.

Logarithmic roller/raceway contact.

High dimensional and running accuracy Particularly the inner ring running accuracy should preferably be to tolerance class P6 or better.

Low friction Low friction in roller end/flange contact for taper roller bearings.

Low friction in roller/raceway contact.

Low raceway surface roughness.

Low running noise High precision of all bearing components.

Most frequent reason for How to alleviate problem/demands

pinion bearing damage on bearings

Lubrication breakdown Guarantee lubrication when starting up in the cold state.

Overloading because of too When selecting bearing size, check the temperature differential heavy a preload between shaft and casing. C3 internal clearance often required.

Inadequate lubricant film generation be- Use low friction bearings.

cause of too high operating temperatures Avoid over-dimensioning.

Improve cooling.

Smearing on rollers and Avoid over-dimensioning.

raceways caused by roller Spherical roller bearings are more favourable than cylindrical slip or sliding roller bearings in larger size range (d > 150 mm).

When using cylindrical roller bearings aim for small roller diameters; use a full complement bearing.

Wear caused by contaminants Avoid contaminating the gearbox during production, assembly and in operation.

Table 6

Table 7

To obtain good meshing it is neces-sary among other things to have a bearing arrangement with high radial and axial stiffness. The locating bear-ing should therefore have a large contact angle and as small an axial clearance as possible.

Bearings for the output shaft These bearings are predominantly radially loaded so that high radial load carrying capacity is also required of the locating bearing. Because of the slow speeds the risks in respect of thermal behaviour and over-dimension-ing compared with the pinion shaft are negligible. The requirements for axial and radial stiffness, for minimum axial clearance and for bearing accuracy correspond to those for the pinion shaft bearings.

Bearing selection

When selecting the bearings it is use-ful to refer to the cheklist given below.

Adjusted basic rating life

Permissible speed

Axial and radial stiffness

Sufficient bearing clearance in the mounted but cold state to avoid inad-missible preload under conditions of maximum temperature differentials

Minimum load

A preliminary selection can be made using the overview of the bearing series commonly used; see Table 8.

Bearing selection

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Shafts in bevel gearboxes

Bearing Bearing series normally used arrangement

Bevel pinion shaft Bevel gear wheel/Bevel/spur gear wheel Input side Pinion side Gear wheel side Opposite side or

spur pinion side

Cross location 72 BE 72 BE 72 BE 72 BE

73 BE 73 BE 73 BE 73 BE

313 323 B 322 322

323 B 323 B 332 332

303 303

323 323

Locating bearing(s) (2×) 72 BECB 33

(2×) 73 BECB (2×) 72 BECB

313/DF (2×) 73 BECB

322 + 293 E 320 X/DF

322/DF 303 + 294

Table 8

Shafts in worm