Spiral bevel gears are standard components for right-angle power transmission because they combine a high contact ratio with smooth running and high load capacity. In heavy-duty reducers, however, their axial thrust is not a secondary detail. It can be large, it reverses when the direction of rotation reverses, and it directly affects bearing selection and service life. A practical design problem is therefore not only how to make the spiral bevel gear strong enough, but how to arrange the gearbox so that its thrust is partly balanced by another gear on the same shaft.
The B3SH12 mining belt-conveyor reducer provides a useful case. It is a two-stage, modular unit in which a spiral bevel stage drives an intermediate shaft carrying a cylindrical helical pinion. The nominal ratio range discussed for the mining application is 25:1 to 40:1, with additional lower-ratio variants included in the force study. The design lever is the tooth hand of the large bevel gear and the helical second-stage pinion: with the correct combination, their axial forces oppose each other on the intermediate shaft, reducing the net thrust that the bearings must carry.
Force Direction in Spiral Bevel Gears
For the B3SH12 gear set, the spiral bevel stage uses a mean spiral angle \(\beta=35^\circ\) and a pressure angle \(\alpha=20^\circ\). The force directions are defined from the small end toward the large end of the bevel gear. Viewed in that direction, clockwise rotation is treated as right-hand rotation and counterclockwise rotation as left-hand rotation. Axial force is positive when it acts from the small end toward the large end; radial force is positive when it acts toward the shaft axis.
With these conventions, the axial and radial components of a spiral bevel gear can be written in the general form
$$F_a=\frac{K}{\cos\beta}\left(\tan\alpha\sin\delta \pm \sin\beta\cos\delta\right)$$
$$F_r=\frac{K}{\cos\beta}\left(\tan\alpha\cos\delta \pm \sin\beta\sin\delta\right)$$
where \(\delta\) is the pitch-cone angle and \(K\) is a tangential load parameter proportional to torque. The sign is not arbitrary: it depends on the combination of tooth hand and rotation direction. The \(\sin\beta\) term is the source of the strong direction sensitivity. Reversing the rotation reverses the contribution of the spiral angle, so an arrangement that reduces thrust in one direction can increase it in the other.
This is why Gleason-type spiral bevel gears, which can be ground after heat treatment, are common in demanding applications. They offer high load capacity, stable meshing, low noise, and relatively low sensitivity to mounting error and elastic deflection, and they are used at pitch-line speeds above about 5 m/s, at input speeds above about 1000 rpm, and in heavy-duty drives. Equal-clearance spiral bevel designs retain these advantages, but they do not remove the axial-force problem. The force must be managed by the surrounding arrangement.
Two-Stage Arrangement and Thrust Path
In the B3SH12 layout, the input spiral bevel pinion is right-hand, the large spiral bevel gear is left-hand, the second-stage helical pinion on the intermediate shaft is left-hand, and the second-stage wheel on the output shaft is right-hand. The large bevel gear and the second-stage helical pinion share the intermediate shaft. That shared shaft is the critical location: the two axial forces act along the same axis, and their vector sum determines the thrust seen by the intermediate-shaft bearings.
| Component | Hand | Location and role | Design relevance |
|---|---|---|---|
| Input spiral bevel pinion | Right | First stage, input shaft | Sets the first-stage thrust direction together with rotation |
| Large spiral bevel gear | Left | First stage, intermediate shaft | Produces a large axial component on the intermediate shaft |
| Second-stage helical pinion | Left | Second stage, intermediate shaft | Its helical thrust can be made to oppose the large bevel-gear thrust |
| Second-stage wheel | Right | Second stage, output shaft | Reacts the second-stage thrust on the output side |
The modular ratio family changes the second-stage tooth combination and therefore the magnitude of the helical thrust. Typical second-stage tooth-count pairs in the family include 26/33, 23/32, 21/34, and 19/34, giving stage ratios from about 1.26 to 1.78, with additional combinations at the higher nominal ratios. As the nominal ratio rises, the balance between the bevel-stage thrust and the helical-stage thrust changes. In some ratio ranges the two forces oppose each other strongly; in others they add. This is a macroscopic arrangement effect, not a small correction.
Ratio, Rotation, and Cancellation
The direction of the bevel-gear thrust is fixed by the tooth hand and the direction of torque. The direction of the helical-pinion thrust is fixed by its hand and the same rotation. Consequently, the intermediate-shaft thrust cannot be evaluated from one gear alone. It is necessary to compare the magnitudes and signs at each ratio and at each specified operating direction.
For one direction of input rotation, the B3SH12 study shows the intended behavior: the large bevel gear and the second-stage helical pinion produce opposing axial forces, and the net thrust on the intermediate shaft is only the difference between two components that are individually above 10 kN. For the opposite direction, the same tooth hands can make the components additive. The effect is strongly ratio-dependent because the second-stage pinion diameter, helix geometry, and transmitted torque change across the modular family.
This behavior has a direct consequence for gearbox specification. A cancellation scheme designed for a unidirectional belt conveyor is not automatically valid for a reversing drive. If the machine can run in reverse, the bearing arrangement must be checked for the additive case, even if the normal production direction gives a much lower thrust.
Quantified Result at Part Load
The force comparison for the B3SH12 family was carried out at half the reducer’s rated power, using the specified four-pole drive basis. The following values are for the counterclockwise input direction viewed from the small end, where the large bevel gear and the second-stage pinion oppose each other. The net force is the absolute difference between the two axial components on the intermediate shaft.
| Nominal ratio | Large bevel gear axial force \(F_b\) (N) | Second-stage pinion axial force \(F_s\) (N) | Net axial force \(|F_b-F_s|\) (N) |
|---|---|---|---|
| 20 | 12,622 | 15,107 | 2,485 |
| 22.4 | 12,622 | 15,107 | 2,485 |
| 25 | 12,238 | 13,251 | 1,013 |
| 28 | 11,798 | 13,006 | 1,208 |
| 31.5 | 12,174 | 12,304 | 130 |
| 35.5 | 11,728 | 11,633 | 95 |
| 40 | 12,275 | 10,884 | 1,391 |
In this direction, the individual axial components are in the range of roughly 10.9 kN to 15.1 kN, while the net thrust on the intermediate shaft is only 95 N to 2,485 N. The closest balance occurs at nominal ratios of 31.5 and 35.5, where the two components differ by only 130 N and 95 N respectively. At ratio 40 the match deteriorates again, and the net thrust rises to 1,391 N, still an order of magnitude below either individual component.
The opposite rotation direction demonstrates the risk. For the high-ratio group, the two components become additive: the resultant on the intermediate shaft reaches 13.18 kN at 31.5:1, 13.26 kN at 35.5:1, and 14.44 kN at 40:1. At the lower ratios, the resultant is about 11.7 kN to 12.0 kN. Thus the same hardware can move from almost complete cancellation to a thrust larger than either individual component, solely because the input direction has changed.
Design Rules and Limitations
The first design rule is to define the dominant operating direction before fixing tooth hands. For a belt conveyor that runs continuously in one direction, the hand combination can be selected so that the large bevel gear and the second-stage pinion oppose each other over the normal duty range. The second rule is to check the reverse direction explicitly. A bearing selected only for the cancelled case may be under-sized for the additive case.
The third rule is to evaluate the whole shaft system, not only the intermediate shaft. Cancellation at shaft II reduces the thrust carried by its bearings, but the input pinion bearings and the output-shaft bearings still see their own axial loads. The large bevel gear also imposes radial loads and bending moments that are not removed by axial cancellation. Bearing life depends on the combined equivalent load, lubrication, alignment, and load spectrum, not on axial force alone.
The fourth rule is to treat the calculated net force as a static part-load result rather than a full bearing rating. The values above are useful for comparing arrangements and for identifying the ratio ranges where cancellation is effective. They do not replace a full load-spectrum calculation that includes starting torque, overload, reversing duty, thermal effects, housing and shaft deflection, and manufacturing tolerance on tooth hand and helix angle.
Within those limits, the arrangement principle is clear. Equal-clearance spiral bevel gears provide a compact right-angle stage with high load capacity, but their axial thrust must be balanced by the adjacent helical stage. In the B3SH12 family, the intermediate-shaft thrust falls from component levels of about 10.9–15.1 kN to 0.095–2.485 kN in the favourable direction, while the reverse direction can produce 11.7–14.4 kN. The difference is large enough that tooth-hand selection and rotation direction belong in the initial gearbox layout, not in a late bearing check.
Conclusion
Axial-force management in a spiral bevel gear reducer is an arrangement problem as much as a gear-tooth problem. The B3SH12 case shows that a large bevel gear and a coaxial helical pinion can be given opposing thrusts on the intermediate shaft, reducing the net axial load by roughly one order of magnitude over much of the ratio range. The result is strongly dependent on nominal ratio and rotation direction: the best balance occurs near 31.5:1–35.5:1 in the counterclockwise case, while reverse rotation can make the forces additive and raise the net thrust to 14.4 kN. Designing the tooth hands around the actual duty direction, and checking the reversing case, is therefore the key to using spiral bevel gears effectively in heavy-duty modular reducers.