A Split Spur Gear is a spur gear cut into two thin co-axial halves that rotate slightly relative to each other under spring preload, so the two halves grip opposite flanks of the mating pinion tooth at the same time. Unlike a single solid spur gear, which always carries a finite backlash gap on one flank, the split design loads both flanks continuously. We use it where positional reversal must happen with zero lost motion — servo-driven rotary axes, optical mounts, telescope drives, and indexing tables. Typical residual backlash drops from 15-30 arc-minutes to under 1 arc-minute.
Split Spur Gear Interactive Calculator
Vary peak pinion torque, preload percentage, and centre-distance error to see the recommended split-gear spring preload range and mesh tolerance margin.
Equation Used
The spring preload torque is set as a percentage of peak working torque at the pinion. The article recommends roughly 10% to 15%: too little can allow a flank skip on reversal, while too much wastes motor torque and increases wear.
FIRGELLI Automations - Interactive Mechanism Calculators.
- Peak torque is the peak working torque at the pinion.
- The article rule of thumb sets split gear spring preload at 10% to 15% of peak working torque.
- Centre-distance tolerance is based on the article value of +/-0.02 mm for a typical Module 1 gear set.
- The default peak torque is a normalized 100 N*m design value because the article gives the preload ratio but no numeric peak torque.
The Split Spur Gear in Action
The principle is simple. You take a normal spur gear, slice it through the face into two equal-thickness halves, then mount the halves on the same hub with a torsion spring or a stack of Belleville washers between them. Before you mesh it with the pinion, you rotate one half against the other by a tooth-or-so worth of angle and lock it. When you release the lock after meshing, the spring forces the two halves apart in the rotational sense — one half pushes hard against the leading flank of every pinion tooth, the other half pushes hard against the trailing flank. There is no gap left for the pinion to rattle into when the drive direction reverses. That is gear backlash elimination in its mechanical form.
The preload torque has to be set carefully. Too little and a sudden reversal under load lets the loaded half skip a flank — you hear a click and your encoder reads a step. Too much and you waste motor torque fighting your own gear, and tooth wear accelerates on both flanks instead of one. A common rule of thumb on a servo drive gearing application: set the spring preload to roughly 10-15% of the peak working torque at the pinion. The two halves should still be free to creep relative to each other as the teeth wear in — that is the whole point of the scissor gear design, the spring takes up wear automatically over the life of the gearset.
Gear mesh tolerance still matters. Centre distance between pinion and split gear must hold to within ±0.02 mm on a typical Module 1 set, otherwise the spring runs out of travel at one extreme of the rotation and you lose preload on a portion of the cycle. We have seen a Module 0.8 split spur on an indexing table fail to hold position at one specific angle because the operator had shimmed the pinion bracket 0.1 mm off-centre — the preload torque collapsed at that mesh point and the load drove the gear backwards by 8 arc-minutes.
Key Components
- Front gear half: Carries roughly half the face width of the original solid gear. Profile and module match the rear half exactly — both halves are usually cut as one solid blank, then parted off, so tooth-to-tooth indexing error between the two halves stays under 5 µm.
- Rear gear half: Identical geometry to the front half but free to rotate on the shared hub through a small angle, typically ±2-4°. The rear half is the one that takes the spring force and pushes against the opposite flank of every pinion tooth.
- Preload spring: Either a coil torsion spring around the hub or a stack of 2-4 Belleville washers acting on a pin-and-slot. Sets the constant separating torque between the two halves — typical preload 10-15% of working torque, often 0.2-2 N·m on a small servo drive gearset.
- Common hub: Holds both halves co-axial to within 0.01 mm TIR. Any axial runout here directly becomes mesh wobble and shows up as periodic torque ripple in the servo current trace.
- Locking pin or shipping screw: Compresses the two halves into alignment for installation, then gets removed once the gear is meshed. Forget to remove it and you are running an ordinary spur gear with all its backlash intact — a surprisingly common mistake on first builds.
Who Uses the Split Spur Gear
Anywhere a drive has to reverse under positional control without losing a count, the split spur gear earns its keep. The cost is real — you are buying two gears, a spring, and tighter tolerances — so you only see it where backlash directly hurts the application. Optical and instrument drives, machine-tool indexing, and small servo gearheads are the obvious territory. You would be amazed how many precision instruments quietly rely on a scissor gear inside.
- Astronomy / Optical instruments: Right-ascension and declination drives on Celestron CGX-L and Software Bisque Paramount ME II equatorial mounts use split spur or split worm-wheel pairs to keep guiding error under 1 arc-second during long-exposure imaging.
- Machine tool indexing: Haas HRT210 rotary indexers use a split-gear preload arrangement on the worm-driven main wheel so that climb-cut and conventional-cut moves both register against zero lost motion at the spindle.
- Robotics / Servo gearheads: Harmonic Drive's CSG-series and several Maxon GP-series planetary heads ship with split output stages in their 'low-backlash' variants, holding output backlash under 3 arc-minutes.
- Aerospace actuation: Trim-tab and flap position drives on Bombardier Global series business jets use split spur stages in the position-feedback path so that reversal hysteresis stays inside the certified ±0.1° band.
- Semiconductor metrology: Wafer-stage rotary axes on KLA and Applied Materials inspection tools use split spur reducers between the brushless servo and the chuck so reversal at the edge of a die does not show up as a stitching error in the inspection image.
- Defence / Targeting systems: Azimuth and elevation drives on the Kongsberg PROTECTOR remote weapon station run split spur preloaded gearing to hold pointing within 0.5 mrad through fire-induced reversal shock.
The Formula Behind the Split Spur Gear
The number you actually care about on a split spur gear is the preload torque required to keep both halves locked against the mating pinion under the worst-case reversal load. Set it too low and the gear loses contact on one flank during a fast reverse — you get an audible click and a position-feedback step. Set it too high and the motor wastes current dragging the spring around forever. The sweet spot lies between roughly 10% and 20% of the peak working torque seen at the pinion. Below 5% you are essentially running an ordinary spur gear; above 25% wear and motor heating dominate and you may as well have specified a tighter solid gear.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| Tpreload | Spring preload torque between the two gear halves | N·m | lbf·in |
| k | Preload coefficient, typically 0.10 to 0.20 | dimensionless | dimensionless |
| Tpeak | Peak reversing torque at the pinion under worst-case load | N·m | lbf·in |
| Dgear | Pitch diameter of the split spur gear | mm | in |
| Dpinion | Pitch diameter of the mating pinion | mm | in |
Worked Example: Split Spur Gear in a planetarium projector tilt drive
You are specifying the preload spring on a split spur output stage for the dome-tilt drive of a refurbished Goto Chronos Space planetarium projector at a university observatory in Christchurch, New Zealand. The mating pinion is Module 1.5, 20 teeth, pitch diameter 30 mm. The split spur output is 120 teeth, pitch diameter 180 mm. Peak reversing torque at the pinion under worst-case dome inertia is 4.0 N·m. The drive must reverse smoothly during fade-in scene transitions where audience-visible jerk above 0.5°/s² ruins the immersion.
Given
- Tpeak = 4.0 N·m
- Dpinion = 30 mm
- Dgear = 180 mm
- knominal = 0.15 dimensionless
Solution
Step 1 — compute the gear ratio factor that scales pinion torque up to the split-gear hub:
Step 2 — at the nominal preload coefficient k = 0.15, compute the spring preload torque the two gear halves must exert against each other:
That is the design point. Now check the low end of the typical operating range, k = 0.10:
At 2.4 N·m the spring is just barely holding the flanks loaded. On a fast tilt-down reversal, the dome's 200 kg moving mass momentarily exceeds the preload and you will hear a faint tick from the gearbox — the audience will not see it but the encoder will log a 0.5 arc-minute step. Acceptable for slow scenic moves, marginal for star-tracking demos.
Now the high end, k = 0.20:
At 4.8 N·m the servo is constantly fighting 4.8 N·m of static drag even when the dome is not moving. On the projector's 80 W brushless servo this eats roughly 12% of continuous current as pure heat, and tooth wear on both flanks doubles compared with the nominal setting. You would only push to 0.20 if the dome had to survive a seismic transient — relevant in Christchurch, actually, given the 2011 quake history.
Result
Specify a torsion spring delivering 3. 6 N·m of preload between the two split gear halves at the installed angle. That value gives roughly 0.7 arc-minute residual backlash at the pinion shaft, which feels like a perfectly stiff drive to the audience and lets the servo loop close cleanly without buzzing. The full sweep of the operating range tells the story: at k = 0.10 (2.4 N·m) the gear ticks audibly on hard reversals, at k = 0.15 (3.6 N·m) it sits in the sweet spot, at k = 0.20 (4.8 N·m) the motor cooks itself to no benefit. If you measure 5+ arc-minutes of residual backlash after assembly instead of the predicted 0.7, the three suspects in order are: (1) the shipping pin was never removed and one half is locked solid, (2) centre distance is off by more than 0.05 mm so the spring has bottomed out at one extreme of the dome's travel, or (3) tooth-indexing error between the two gear halves exceeds 10 µm — usually because the halves were re-cut separately rather than parted from a single blank.
Split Spur Gear vs Alternatives
The split spur gear is one of three common ways to fight backlash in a spur or worm drive. The other two are precision-ground solid gears with very tight centre-distance control, and harmonic (strain-wave) drives. Each occupies a different cost and performance band, and the right pick depends on how much backlash your application actually tolerates and what you can spend.
| Property | Split Spur Gear | Precision Solid Spur Gear | Harmonic Drive |
|---|---|---|---|
| Residual backlash at output | < 1 arc-min | 5-15 arc-min | < 0.5 arc-min (zero-backlash by design) |
| Typical input speed range | 0-3,000 RPM | 0-6,000 RPM | 0-3,500 RPM |
| Peak torque capacity | Limited by spring preload, typically up to 50 N·m at output | Up to several kN·m at output | Up to 800 N·m on standard CSG sizes |
| Cost per stage (qty 1, Module 1, ~100 mm) | $80-200 | $30-90 | $600-2,500 |
| Service life before re-preload required | 10,000+ hours, spring takes up wear automatically | Re-shim every 2,000-5,000 hours as flanks wear | 20,000+ hours, no preload adjustment |
| Reversal hysteresis under load | Negligible up to spring preload | Always present, scales with wear | Negligible, but flexspline windup adds compliance |
| Mounting tolerance on centre distance | ±0.02 mm on Module 1 | ±0.05 mm acceptable | Fixed by housing, no mesh adjustment |
Frequently Asked Questions About Split Spur Gear
The most common cause is tooth-indexing error between the two halves. If the halves were not parted from a single hobbed blank — say someone replaced one half with a spare cut on a different machine — the relative tooth pitch can drift by 10-20 µm, and the spring runs out of travel before both halves contact opposite flanks at the same mesh point. Pull the gear, lay both halves on a surface plate, and check tooth-tip alignment with a 10x loupe. If the tips do not line up to within roughly 5 µm when the spring is removed, the halves are not a matched pair.
The second possibility is that the pinion itself has runout. A 0.05 mm pitch-diameter runout on the pinion looks identical to backlash at the encoder because the mesh point shifts in and out as the pinion rotates.
Size for the 95th-percentile reversal event, not the absolute peak and not the mean. Log a few hours of motor current during real operation, convert to torque, and pick the value that 5% of reversals exceed. Setting preload to 15% of that figure keeps the gear loaded during normal operation and lets the rare extreme event briefly unload one flank — a momentary tick is acceptable once a shift, not once a minute.
If you size for the absolute peak you will sit at 25-30% preload all day, which doubles tooth wear and roasts your motor for an event that happens twice a week.
Decide on torque density and shock tolerance, not on backlash spec alone. Both solutions deliver sub-arc-minute backlash, but a harmonic drive carries 5-10x the torque in the same envelope and survives shock loads that would skip a flank on a split spur. Conversely, a harmonic drive has flexspline compliance — the output windup under load can hit several arc-minutes even though the static backlash is zero, and that compliance shows up as ringing in a stiff servo loop.
Rule of thumb: continuous low-shock precision (telescope tracking, optical scanning) — split spur wins on cost and stiffness. High-torque jerky duty (robot joints, weapon stations) — harmonic drive wins on durability.
Almost always a centre-distance problem in the host frame. Bench fixtures hold the two shafts rigidly; production frames flex under operating load. If the gearbox housing deflects 0.05 mm under peak motor torque, the mesh opens up at exactly the moment the preload is needed most, and the unloaded half snaps across to the other flank — that is the tick you hear.
Mount a dial indicator on the pinion shaft pointing at the gear shaft and run the machine through a peak-torque cycle. If you see more than 0.03 mm of relative motion, stiffen the housing before blaming the gear.
Output stage almost always. Backlash multiplies down the gear train but reduces back up it — backlash on the input pinion of a 50:1 reducer divides by 50 at the output, so the input stage barely affects positioning accuracy. Putting a split gear on the input wastes the preload coefficient on a stage where backlash does not matter, while the loaded output stage still has its full backlash gap.
The exception is a 1:1 or low-ratio (<5:1) drive where every stage contributes meaningfully to the output error budget. There, splitting the input is worth the cost.
Tighter, because both flanks are loaded continuously and any roughness gets ground in equally on both sides. Aim for Ra under 0.8 µm on the working flanks — about one AGMA grade better than the equivalent solid gear. A standard hobbed-and-shaved spur gear at Ra 1.6 µm will work, but the spring preload measurably decays over the first 50 hours as the asperities get knocked down, and you end up re-tensioning. Ground or honed flanks settle in within the first 5 hours and hold preload for the life of the gearset.
References & Further Reading
- Wikipedia contributors. Backlash (engineering). Wikipedia
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