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Spur vs helical gears

Turning the teeth through a helix angle changes how they meet: the contact sweeps across the face instead of arriving all at once, more teeth share the load, and the bearings get an axial force. This guide compares the two on one pair designed both ways in the same housing - same centre distance, same diameters, same face width - so the difference is the helix and nothing else.

A fair comparison

A helical gear with the same normal module and tooth numbers as a spur gear is larger: its reference diameter is d = z m_n / cos β. A 20/40 pair of module 3 at 15° has a centre distance of 93.17 mm instead of 90, and it rates better partly because it is bigger. So the helical pair here keeps the spur pair's envelope instead: 19 and 38 teeth at β 18.195°, which puts the diameters back at 60 and 120 mm and the centre distance at 90 mm. Both carry 100 Nm at 1 450 min^-1, case hardened, ISO 1328-1 class 6, face width 30 mm.

Contact: how many teeth carry the load

A spur pair alternates between one and two pairs of teeth in contact; with ε_γ 1.635 it spends about a third of each engagement on a single pair, and the change from two to one is a step in stiffness every time a tooth comes in. The helical pair adds the overlap ratio ε_β = b sin β / (π m_n) (ISO 21771): contact lines run diagonally across the flank, so a tooth takes up the load gradually, and two to three pairs share it. This is why helical gears run quieter. At ε_β of 1 or more a full helix pitch is always in mesh; this pair is just short of it - 31 mm of face would make it 1.027.

Forces on the bearings

The axial force is the price of the helix: a third of the tangential force here, taken by a bearing that can carry thrust, and it grows with tan β. Its direction follows the hand of the helix and the sense of rotation, so the same pair pushes its shafts the other way when it reverses. A double helical (herringbone) gear cancels it inside the gear.

Load capacity

In the same envelope the helix gave the root 17 % more margin and the flank almost nothing. The contact ratio, helix and overlap factors of ISO 6336-2 and -3 all favour the helical pair; what takes the flank's share back is the transverse load factor K_Hα, which ISO 6336-1 raises with the total contact ratio and with the pitch error: the more pairs share the load, the more a pitch deviation of a few micrometres decides how unevenly they share it.

Why accuracy decides it

The better the gears are made, the more the helix is worth. At class 5 the helical pair is ahead on both counts; at class 7 its flank is no better than the spur pair's. A helical pair earns its capacity with accuracy - which is also what makes it quiet.

Making and checking them

Both are generated by the same hob or shaper, the helical one with the machine's differential set for the lead. Inspection is the same list - pitch, profile, helix and tooth thickness to ISO 1328-1 - and the span measurement W_k needs a face wide enough for the calipers to sit on a helical flank, which the designer checks (b_Fmin, ISO 21771 A.7). A shaper needs a helical guide for every lead it cuts, which is one reason internal and shouldered gears are so often spur.

Which to choose

• Spur when the axial force cannot be taken, the speed and the noise limit are modest, the gear slides on a shaft (a gearbox's shift gear) or the shop is simple.
• Helical when the pair runs fast or must be quiet, when the root is the limit, or when the gears can be made at class 6 or better - and the bearings can take the thrust.

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