The short answer is that a gearbox shaft almost never fails because it is too weak in torsion - it fails or misbehaves because it is too flexible, because a keyway concentrates stress where the drawing did not expect it, or because the drive train passes through a torsional resonance at some speed nobody calculated. Two numbers describe the same shaft: the shear stress at the surface, which decides whether it breaks, and the angle of twist per metre, which decides whether the machine it drives can still do its job. For a long shaft the twist limit is usually reached long before the stress limit, and that is the part most catalogue selections skip.

This guide works through torsion in the order a drive engineer meets it: what the shaft actually carries, how stress and stiffness diverge, the arithmetic for both, how hollow shafts and keyways change the answer, where critical speed enters, and what can be measured on site when a drive feels soft or rings at a particular speed.

What Torsion Actually Does to a Gearbox Shaft

Torque enters a gearbox shaft at one end and leaves at the other. Between those two points the shaft winds up: the input end rotates slightly ahead of the output end, and the difference is the angle of twist. In a single-stage unit with a short, stiff shaft the twist is a fraction of a degree and nobody notices. In a long input shaft between a motor coupling and the first bearing, in a hollow output shaft clamped onto a conveyor pulley shaft, or in an extended shaft on a right-angle unit, the same fraction of a degree becomes visible as lost motion at the load.

Three consequences follow. The winding-up stores energy, released when the load drops away - the reason a drive with a soft shaft overshoots on a reversing or positioning duty. The twist adds to backlash, so a gearbox with a healthy 8 to 12 arcmin at the output can show far more at the load flange once torsion is included. And every start or jam applies torque as a step, which a flexible shaft turns into an oscillation the gear mesh has to survive.

The torque the shaft sees is not nameplate torque. A standard induction motor started direct-on-line delivers roughly 1.8 to 2.5 times rated torque at pull-up, and a reversing hoist or a conveyor restarted against a jam can double that again for a few hundred milliseconds. Gearbox shafts are therefore rated with a nominal torque and a separate peak or acceleration torque, and the two are not interchangeable.

Stress and Twist Are Two Separate Limits

Shear stress is a strength question. It scales with torque divided by the polar section modulus, so for a solid round shaft it rises with the cube of nothing and falls with the cube of diameter - doubling the diameter cuts the surface stress by a factor of eight. The allowable value depends on the material and the duty: a quenched and tempered alloy steel shaft in steady industrial service is usually designed in the 25 to 45 MPa range for continuous torque, and is allowed to climb toward 70 MPa or more for short-duration peaks, with the exact figure set by fatigue analysis rather than by a single yield number.

Angle of twist is a stiffness question, and it scales differently: it depends on torque, length, and torsional rigidity (shear modulus times polar moment of inertia). Because both stress and twist depend on torque, the two limits can be compared directly for a given shaft - twist per metre is proportional to shear stress divided by diameter. A large shaft therefore reaches a generous stress long before its twist becomes noticeable, while a small or long shaft reaches an unacceptable twist at a stress that looks almost trivial.

Typical practice limits are worth keeping in mind, because they explain why gearbox shafts look over-dimensioned next to a plain transmission shaft.

The Arithmetic for a Real Shaft

Start with the torque. Torque in Nm is 9550 multiplied by power in kW divided by speed in rpm. A 22 kW motor at 1470 rpm gives about 143 Nm; add the service factor of the driven machine - 1.5 for a uniform conveyor, 2.0 for a mixer with lumpy product - and the shaft must carry roughly 215 to 285 Nm continuously, with peaks above that.

For a solid shaft, the surface shear stress is 16 times the torque divided by pi times the diameter cubed. In the units that matter on a drawing: a 50 mm shaft carrying 700 Nm sits at about 28 MPa, and the same shaft at 1400 Nm reaches 57 MPa, which is a peak-only condition for most steels. A 40 mm shaft at the same 700 Nm is already at 56 MPa, which is why one size of shaft changes the verdict completely.

The angle of twist then follows from the same numbers: twist in radians equals torque times length divided by the product of shear modulus (about 80 GPa for steel) and polar moment of inertia, which is pi times diameter to the fourth power divided by 32. Rather than work the two steps separately, use the combined relation - twist per metre in radians equals twice the shear stress divided by the product of shear modulus and diameter. That single line is the whole argument: a 50 mm shaft at 30 MPa twists about 0.85° per metre, which is inside a general drive limit but already outside a positioning limit, while a 100 mm shaft at the same stress twists only 0.43° per metre.

Two practical notes. Length matters as much as diameter, so a shaft that is stiff inside the housing can still be soft across a 600 mm exposed extension. And gearbox ratings are quoted at the output shaft, where torque is highest but speed lowest; check torsion at the shaft with the long span, which is often the input.

Why Hollow Shafts Are Not Simply Weaker

A hollow shaft looks like a compromise, and in pure strength terms it is: at the same outside diameter, a shaft with a bore of 60 percent of the diameter carries about 87 percent of the solid shaft's torque at the same stress. What it gains is the ability to be clamped directly onto the driven machine's shaft, which removes a coupling, shortens the drive train, and in a shaft-mounted unit lets the gearbox hang on the machine shaft instead of on its own foundation.

Stiffness falls a little faster than strength - the polar moment drops by the same 13 percent, so twist rises by about 15 percent for the same torque. That is rarely decisive. What is decisive is the fit: a hollow output shaft transmits torque through a shrink disc or a keyed clamp, and any slip at that interface converts shaft torsion into fretting, wear and eventually a loose drive. The mounting procedure matters more than the section modulus. For the layout side of this, the note on shaft-mounted gearbox mounting covers the fit and abutment details that decide whether the clamp holds.

Keyways, Shrink Discs and Where Cracks Start

A keyway removes material exactly where the stress is highest and adds a sharp corner. The combined effect is a stress concentration factor of roughly 1.6 to 2.0 at the keyway end for a normal end-milled key, and if the key is a loose fit the shaft also carries impact as the key rocks in the slot. This is why a keyed shaft that calculates at 40 MPa nominal should be treated as 65 to 80 MPa at the corner, and why almost every torsional fatigue failure in a gearbox starts at the end of a keyway rather than in the middle of a shaft.

Shrink discs and clamp rings avoid the keyway entirely by generating torque capacity through friction on a plain cylindrical surface. Capacity is the friction coefficient (about 0.15 for dry steel on steel) times the radial contact pressure times the contact area times the radius, so the connection is honest about what it needs: a clean, correctly toleranced, oil-free bore, and the specified bolt torque. Under-torque the bolts and the connection slips; slip once under load and the friction capacity drops further, which is why a slipping shrink disc rarely recovers on its own.

Torsional Vibration and Critical Speed

Every drive train is a torsional spring with inertias at each end, so it has a natural frequency. If an excitation lands on that frequency - once-per-revolution imbalance, gear mesh frequency and its harmonics, blade passing in a fan, or the pulse rate of a reciprocating load - the torque oscillates far above the mean value even though nothing has changed in the load. The rule of thumb is to keep the lowest torsional natural frequency at least three times the highest steady excitation frequency, and for variable-speed drives to check that no operating speed sweeps slowly through a resonance.

Bending critical speed is the separate, more familiar limit. For a steel shaft supported at both ends the first critical speed in rpm is close to 1.19 × 10⁸ times the diameter in millimetres divided by the square of the span in millimetres: a 50 mm shaft across a 1000 mm span comes out near 6000 rpm, and the same shaft across 1500 mm falls to about 2650 rpm. Long exposed shafts, cardan spacers and extended input shafts are where this bites, and the fix is a shorter span, a larger diameter, or an intermediate support - not a stronger material.

FAQ

Does a larger gearbox always give a stiffer shaft?

Not in proportion. Torque capacity rises with the cube of shaft diameter, but the shaft inside a larger unit is also longer, and a long span can cancel the gain in diameter. Ask for the shaft diameter and the bearing span rather than assuming the bigger frame is stiffer.

My drive overshoots on stop - is that shaft torsion?

It can be, particularly on a positioning duty with a long input shaft or a spacer coupling. Separate the causes by measuring twist: mark both ends, lock the output, apply a known torque, and read the angle. If the measured twist matches the calculated value, the shaft is behaving as designed and the overshoot is a tuning or inertia problem.

Can I increase torque capacity by changing the shaft material?

Only within limits. Moving from a plain carbon steel to a quenched and tempered alloy steel raises the allowable shear stress substantially, but the twist stays essentially the same because stiffness depends on geometry and shear modulus, not strength. If the problem is lost motion rather than breakage, material will not fix it.

Why does the shaft fail at the keyway and not at the gear?

Because the keyway is a notch with a stress concentration of roughly 1.6 to 2.0, and a fatigue crack starts where local stress is highest. A keyed connection designed at 35 MPa nominal may run at 60 MPa or more at the corner, which is why keyed shafts are usually specified one size up from the pure torsion calculation.

How much twist is acceptable at the load?

It depends on what the load does with lost motion. A conveyor or fan tolerates a degree or more across the drive train; a positioning axis, a printing register or a synchronised line may need the whole train inside a few arc minutes. Define the number before sizing, and check it at the shaft with the longest span. The online selection tool will narrow the frame size on torque and speed; the twist check still has to be done against your own tolerance.

Next Step

If a drive feels soft, rings at one speed, or shows fretting at a clamp, the shaft is usually the first place to look and the cheapest place to correct. Send the motor power, output speed, duty description and the span between bearings, and we will come back with the shaft diameter, the calculated twist and the critical speed for the frame you are considering - or run the first pass yourself in the selection system and bring the shortlist to us for the torsion check.