A backlash figure is measured with the input locked and almost no torque on the output. The machine it goes into reverses direction while carrying a load. Those are not the same measurement, and the difference is often larger than the figure itself. Engineers who specify backlash precisely and then find the axis missing position are usually not looking at a bad gearbox. They are looking at one number where the machine responds to three.

Backlash Is Measured With Almost Nothing on the Output

Torsional backlash is the angular movement at the output when the input is held rigid and the output is rocked back and forth. What it measures is clearance: the gap between the loaded flank of one tooth and the unloaded flank of the next, converted to an angle at the output shaft. Some manufacturers quote it at zero load, some at a stated fraction of rated torque, and the two figures differ because the gear train is already deflecting at the second one. A catalogue that prints a number without saying which convention it used has printed something that cannot be compared with anything.

Clearance is necessary. Without it the teeth would bind as they warm up, lubrication would have nowhere to sit, and manufacturing tolerance would have to be tighter than the price allows. So the figure is not a defect. It is a clearance, and what the axis experiences is clearance plus deflection.

The Error Your Machine Reverses Into Has Four Terms

Total lost motion on a reversal is the sum of four things: the gearbox backlash, the gearbox wind-up, the coupling backlash, and the coupling wind-up. Wind-up is simply the applied torque divided by torsional stiffness, so it scales with load while backlash does not.

The principle is easiest to see at a scale where the numbers get published. A servo gearbox rated at three arcminutes of backlash and twenty newton metres per arcminute of stiffness, running at two hundred newton metres, deflects ten arcminutes under load. The axis therefore sees thirteen arcminutes of reversal error, and the backlash figure describes less than a quarter of it.

At the torques a small gearmotor runs at, the two terms are usually the same order of magnitude rather than one dominating the other. Which is exactly why quoting only the clearance term misleads: the customer sizes a mechanism around the number he was given, and the mechanism then has more play than that.

Convert to Millimetres, and Watch the Units

An angular figure means nothing until it meets a radius. The conversion is the angle in arcminutes multiplied by the radius and divided by 3437.75, which gives the tangential movement at that radius in the same unit. One arcminute at 50 mm is 0.015 mm. Thirty arcminutes at the same radius is 0.44 mm, which is a visible gap in a small mechanism and enough to fail a sensor alignment.

The unit is where most comparisons go wrong. Small gearboxes are commonly quoted in whole or partial degrees, precision gearboxes in arcminutes, and one degree is sixty arcminutes. A small planetary gearbox at half a degree of backlash is carrying thirty arcminutes, which is worse than the standard grade of a servo reducer quoted at eight to fifteen. Those two numbers look similar in a catalogue and are not similar at all. Convert both to arcminutes, or both to millimetres at the radius that matters, before deciding which unit is tighter.

Half the Play Is Usually Outside the Gearbox

A gearbox can meet its backlash specification and still leave an axis with more play than expected, because the connection to the load introduces its own. A hub with a D-flat and a set screw has rotational clearance around the flat. A keyed hub has clearance in the keyway. A coupling with a flexible element adds both clearance and compliance. Each of these is a term in the same sum, and on a short output shaft with a small hub the coupling term can exceed the gearbox term.

There is a measurement consequence that catches people out. An encoder mounted on the motor shaft reads position before the gearbox, before the coupling, and before any of the play. A closed loop built on it will report a position the machine does not have. If position at the load matters, the sensor belongs near the load, or the play has to be accounted for in the control rather than assumed away.

What to Put on the Drawing

Four things turn a backlash figure into a specification. State the angle at the output shaft, in arcminutes rather than degrees, because that is the unit that can be compared. State the torque at which it was measured, since a figure taken at zero load is a clearance and a figure taken at working torque is closer to what the axis sees. State whether it applies before or after run-in, because backlash grows as the teeth wear. And state the temperature, since a plastic-and-metal train changes clearance as it warms.

Then add the number that actually governs the mechanism: the permitted lost motion at the working torque, including the coupling. Where the axis never reverses under load, backlash barely matters and torsional stiffness is the figure worth arguing about. Where it reverses constantly, both matter, and the gearbox is only part of the answer.

What to Send

Three items let this be settled before a drawing is released. The output torque and the radius at which position matters, which together convert any angular figure into a real displacement. Whether the axis reverses direction under load, and how often. And how the load is attached, since a clamp collar, a keyed hub and a set screw each contribute differently. With those, a backlash figure can be quoted in the form the machine needs, rather than as a clearance measured on a bench with nothing attached to the shaft.