Bearing Loads

:: Bearing Loads ::

Bearing loads due to side thrust on a wheel in semi-floating axle is shown in Fig. 26.55.

Let F = lateral force at the rim of the wheel

r = radius of the wheel

L = distance between the centres of wheel bearings

R1 and R2 = radial reactions of the wheel bearing on the wheel hub

P = the thrust reaction of the bearing In practice,

the radio rIL ~ 0.6.

Considering the forces in the horizontal and vertical directions,

P = F and R\=R2

Fig. 26.55. Bearing loads due to side thrust on semi-floating axle.



Therefore, for semi-floating type axles, P is equal to F, and Ri and R2 each approximately equal to three fifth ofF.Ri adds to the normal static load on the bearing, whereas R2 opposes it.

Axle Shaft

Shafts for semi-floating type axles are subjected to both bending and torsion. Hence, the diameter, of the shaft should vary with the bending moment along the length. Accordingly, the diameter is minimum near the differential end where the shaft is subjected to nearly total torsion alfcd is maximum at the outboard bearing, where bending moment is maximum. The maximum stress in shaft occurs when the wheels slip or lock due respectively to a sudden application of power or braking on dry, hard pavement.

Using torsion formula, the minimum diameter can be calculated and at the bearing the equations for combined stresses can be used, assuming a diameter proportionately larger than the minimum and thus, both the allowable tensile and shear stresses in the shaft at the outboard bearing can be compared with the calculated values.

Axle Housing

Semi-floating axle housing, like axle shafts, is subjected to both bending and torsion. The static load on the ourboard bearing depends on the driving force and the retarding force, and attains its maximum value when the wheel is either spun by the engine or locked by the brake. The bearing load produces a bending moment on the axle housing, which is zero at the centre of the bearing and increases uniformly to a maximum value at the centre of the spring seats and thereafter remains constant. As discussed in the case of axle shafts, the

Three-quarter-floating Axle-hub.

The road-wheel, in this case also, is bolted to the hub forming part of the axle-shaft. The outer end of the shaft and hub is supported by a bearing located over the axle-casing. The bearing in this case is positioned between the hub and the casing unlike between the axle and the casing as in the semifloating layout. The inner end of the half-shaft is splined to the final-drive assembly, same as the semi-floating half-shaft (Fig. 26.52B).

In the three-quarter-floating axle and hub arrangement, the driving torque is transmitted by the shaft, but the shear force and bending moment are absorbed by the tubular axle-casing through the hub bearing, only if the road-wheel and the hub bearing lie in the same vertical plane. Practically, a slight offset of wheel and bearing centres exist so that the hub is tilted relative to the axle-casing. This is resisted by the bearing, but incase this offset is large, the half-shaft provides the additional resistance. Horizontal loads, which create end-thrust, are opposed by the hub bearing and casing. However, the side-forces create a bending moment, which tends to twist the wheel relative to the axle-casing. This tilting tendency is resisted mostly by the hub bearing and partly by the axle-shaft. A large tilting force therefore tends to overload the bearing if it is not adequately sized.

A three-quarter-floating axle shown in Fig. 26.56 was once very popular for cars and light commercial vehicles when semi-floating half-shafts frequently failed due to fracture, specifically in cold weather. However, due to availability of the compact, cheap and reliable semi-floating axle, the three-quarter-floating arrangement is rarely used today.

The half-shaft uses an upset-forged flange at the outer end, which is clamped to the bearing hub by the wheel studs. Either a large-diameter single-row or a double-row ball-race bearing is used (Fig. 26.56), depending upon light- or heavy-duty ap­plications. This bearing is located on the axle-casing and is secured in position by a large nut. The outer bearing track supports the hub. An oil-seal is placed at the back of the hub to prevent excess oil, coming from the final drive, to escape to the brakes from the hub.

Fully Floating Axle-hub

This axle-hub arrangement incorporates a flanged sleeve, which is positioned over the axle casing. The flange is provided to accommodate the road-wheel or wheels. Two bearings widely

Fig. 26.56. Three-quarter-floating axle

spaced are installed between the hub and the casing to support the hub assembly (Fig 2652C) This provides am improvement on the first two types of hub support. The axle-shaft in this case takes only the turning-effort or torque. Both the vertical and horizontal load reactions are resisted by a pair of widely spaced taper-roller bearings installed on the axle-casing. The axle half-shaft, therefore, is free from all the loads except the torsional drive to the wheel.

Figure 26.57 illustrates a fully floating axle-hub, based on a concept of the three-quarter-floating axle. The construction is such that the two hubs on their bearing rotate independently of the half-shaft. Studs connecting the shaft to the hub transmit the drive and when the nuts on these studs are removed, the shaft may be removed without jacking up the vehicle and without interfering with the load-supporting role of the hub. This layout, therefore, allows the vehicle to be towed with a broken half shaft. This is a larger and more expensive construction than both the other layouts. This is specifically suitable for all truck and heavy-duty vehicles employing live axles and for trailers using dead axles where torque and axle loads are greater. Depending upon the application, single or twin road-wheels are used.

Fig. 26.57. Fully floating axle.

Bearing Loads

The diagram showing the bearing loads due to side thrust on a full floating axle is presented in Fig. 26.58. In the figure,

F = lateral force at the rim of the wheel

r = radius of the wheel

L = distance between the centres of wheel bearing

Rl and R2 = radial reactions of the wheel bearing on the wheel hub

P = the thrust reaction of the bearing

In practice, the ratio r/L = 4.

Considering the force in the horizontal and vertical direc­tions,

P = F andRi=R2 Taking moment, Fr = R\L and Fr = R%L

Hence, Ri=R2 = ^F = 4F

Rl adds to the normal static load on the bearing, whereas R2 opposes it. The thrust load on the bearing is equal to the shock load, F on the wheel, whereas radial shock loads, Rl and R2 on the bearing are each ap­proximately four times F.

Fig. 26.58. Bearing loads due to side thrust on full-floating axle.

Axle Shaft

In this case the axle shafts are subjected to torsional stresses only. The shaft is also of constant cross-section. Thus, the formula for the torsional strength of shafts can be applied to calculate the diameter of the shaft.

For better grades of alloy steel that are generally used for axle shafts, shear stress averages to 295 to 325 MPa.

Axle Housing

The housing for full-floating axle transfers the load to the road wheels. This acts as a simply-supported beam at the ends with distributed loads. But for the sake of simplicity in calculations without appreciable error, it can be considered as a beam with concentrated loading at the centre of the spring seats.

Let W = the maximum load on one wheel

I = The distance between the centre planes of the wheel and the spring seat.

Then the bending moment produced by the reaction of the ground on the housing at the centre of the spring seat = Wl