Almost every printed drive train on the internet turns in the same direction. The motor spins, a spur gear spins, a belt goes round, and the output is parallel to the input. That works until the thing you are building needs the motion turned ninety degrees, or slowed down by a factor of thirty in one stage, or held in position without a brake. Then you need a worm, or a helix, or a bevel, and the advice you find stops being about printing and starts being about machining centres.
The gap matters because worm drives and helical gears break in ways that spur gears do not. A worm drive generates an axial thrust that has to go somewhere, and on a printed housing it usually goes into a bearing boss that tears off. A helical gear pair pushes its shafts apart along the axis, which is invisible until the shoulder wears. A worm written in the wrong hand turns the wrong way, and no amount of slicer tuning fixes chirality. And the classic print orientation for a spur gear — flat on the bed — is almost exactly wrong for a worm, whose whole load path runs along the helix.
This is the settled companion to the spur gear guide and the belt and pulley guide. Everything below assumes you already know what module is, why backlash has to be cut into the tooth rather than dialled in by moving the centres, and why a tooth root wants a fillet. What is new here is what happens when the teeth are not perpendicular to the axis: the ratio arithmetic, the thrust, the hand, the helix angle, and the four ways a printed right-angle stage fails even when the teeth themselves are perfect.
The ratio stops being a division and becomes a multiplication of starts
A spur gear ratio is a tooth count over a tooth count. A worm drive ratio is a thread count over a tooth count, and the thread count is almost always one. That single sentence is the whole mechanical appeal: a single-start worm driving a 30-tooth wheel gives you 30:1 in one stage, in a package the size of your thumb, with no idler and no compound gear.
The cost is efficiency, and it is not a small cost. A spur pair at these speeds is around 97% per mesh. A worm drive is dramatically worse because the contact between a worm thread and a wheel tooth is dominated by sliding, not rolling. The worm thread sweeps across the wheel tooth like a plough. Published figures for well-lubricated steel worms running on bronze wheels sit near 90% at a generous lead angle and fall toward 50–60% as the lead angle gets shallow and the ratio gets high. Change both members to printed polymer and you land somewhere in the 40–70% band depending on lead angle, surface finish and load. That energy does not disappear; it becomes heat at the contact line.
Two consequences follow immediately, and they should be written down before any geometry is drawn. First, the motor has to be sized for the input torque, not the output torque divided by the ratio. Second, the wheel tooth has to survive a contact temperature that a spur gear never sees. If your design cannot afford to throw away half the motor's work as frictional heat, a worm is the wrong answer and two spur stages are the right one.
A single start is not a slow compromise, it is the self-locking design
The most useful property of a single-start worm is not the ratio. It is that a shallow-lead worm cannot be driven backwards by the load. Push on the wheel and friction in the thread interface holds the assembly still, which means your mechanism stays where you put it with the motor de-energised. For a camera slider, a tilt head, a lifting column or an adjustable desk, that is worth more than any efficiency number.
The self-locking condition is set by the thread's lead angle and the friction coefficient between the two materials. A rough working rule: a single-start worm stays self-locking while the lead angle stays comfortably below roughly five degrees, and it stops being reliable as the angle climbs past about five or six degrees. Printed polymer pairs, which have higher friction than steel on bronze, self-lock at somewhat larger angles — which is helpful here and harmful everywhere else.
| Starts | Wheel teeth | Ratio | Lead angle (approx.) | Self-locking | Behaviour |
|---|---|---|---|---|---|
| 1 | 20 | 20:1 | low (~3°) | yes, reliably | Holds position, low efficiency, runs hot |
| 1 | 30 | 30:1 | very low (~2°) | yes, strongly | Slowest output, highest self-locking margin |
| 2 | 20 | 10:1 | moderate (~6°) | marginal | Back-drives under shock, efficient enough to motor |
| 2 | 30 | 15:1 | moderate (~4°) | usually | The practical middle for printed drives |
| 3 | 30 | 10:1 | high (~6–7°) | no | Back-drivable, viable for motor-driven axes |
| 4 | 40 | 10:1 | high | no | Back-drivable; needs a real brake or a detent |
Read the table as a design decision, not a menu. Every start you add buys efficiency and back-drivability and costs you holding torque. If the mechanism must hold when power is cut, choose one start and accept the loss. If the mechanism is driven in both directions under control, choose two or three and plan for the load to run the motor backwards the moment it stops.
The thrust is real, and it is the failure nobody plans for
Here is the number that changes the housing. A worm thread at lead angle λ pushes the wheel not just tangentially but axially, and the axial force on the wheel is roughly the tangential force multiplied by the tangent of the lead angle. For a shallow worm the axial component is small — that is why self-locking works. But the reaction on the worm itself is the full tangential force, and it acts along the worm's own axis, pushing the worm shaft endwise with everything the motor is delivering.
Printed housings are not built for this. The typical printed worm stage has the worm shaft carried in two printed wall bosses with a plain bore, and the endwise load is taken by whatever plastic shoulder happens to be there. Three things then happen in sequence:
- The shoulder face, which was printed as a horizontal top surface, wears against the rotating end of the shaft and loses a tenth of a millimetre a week.
- The freed play lets the worm walk axially, so the contact pattern on the wheel moves from the middle of the tooth toward one edge.
- The edge-loaded tooth then fails in bending at its root, and the whole stage is diagnosed as “poor layer adhesion” when it was a shoulder wear problem.
The fix is mechanical, not a slicer setting. Give the worm shaft a hard axial stop on the loaded side. The cheapest version is a thrust washer of metal, or a captive steel ball in a printed cup, or a short piece of PTFE sheet with a hole punched in it. Better still, put a small ball bearing at the loaded end and let the bearing take the thrust — a 608 with a printed seat is more accurate than any printed shoulder you will produce. This is the same reasoning as the pivot guide, applied along the axis instead of across it: a rotating joint needs a deliberate bearing surface, and plastic on plastic is not one.
On the wheel side the axial force is small by comparison but not zero, and it appears as a side load on the wheel's own shaft. If the wheel is carried on a cantilevered printed pin, that side load becomes a bending moment at the root of the pin, which is exactly the failure mode a straight-on load would not have produced. Support the wheel on both sides of the mesh if the ratio or the load is serious.
Hand, and the one mistake that cannot be corrected afterwards
A worm can be right-handed or left-handed, and the direction it drives depends on both the hand and which side of the wheel the worm sits on. Rotate the worm clockwise with the worm above the wheel and the wheel turns one way; move the worm below the wheel and the same rotation turns it the other way. None of this is tuneable in software. If you model the wrong hand you will print a gearbox that runs backwards, and the only fixes are to mirror the part in CAD or to invert the motor in firmware.
Two practical rules make this a non-issue. First, decide the hand by drawing the motion path rather than the gear: an arrow on the input, an arrow on the output, then work back. Second, print a single-start check ring before the real part — a 10 mm length of worm thread with a raised centre line, held against a scrap wheel tooth. A wrong hand is obvious in five seconds on a check ring and invisible in a rendered assembly.
The same chirality problem arrives as a subtler defect on helical gears. A left-hand pinion meshes correctly only with a right-hand wheel, and a printed pair with the same hand will look right, sit together, and refuse to run. If you generate both gears from one CAD feature, make sure the generator is applying opposite hands rather than cloning the first part.
Helix angle: the trade you make for smoothness and quiet
Helical gears exist because a straight tooth engages all at once and a slanted tooth engages gradually. That gradual engagement is why a helical pair is quieter and carries load more smoothly than a spur pair of identical size, and why it is worth the trouble on any drive where you can hear it. The price is a permanent axial thrust on both shafts, proportional to the tangential load times the tangent of the helix angle.
For printed parts the useful window is narrow. Below about 15° the overlap benefit is small and you have added thrust for nothing. Much above 30° the thrust component grows fast and the tooth starts to behave like a worm contact — more sliding, more heat, more wear. A 20–25° helix is the practical band: enough overlap to smooth the mesh, not so much that a printed housing has to fight a large end load.
| Helix angle | Axial thrust (as fraction of tangential load) | Contact overlap | Where it belongs |
|---|---|---|---|
| 10° | 0.18 | low | Almost a spur gear; only worth it for noise in a light drive |
| 15° | 0.27 | moderate | Quiet light drives, cosmetic mechanisms, low load |
| 20° | 0.36 | good | General purpose: the default recommendation for printed pairs |
| 25° | 0.47 | very good | Smooth, quiet, load-bearing; housing must take the thrust |
| 30° | 0.58 | excellent | Only with a real thrust bearing and a stiff frame |
| 35° | 0.70 | excessive | Approaching worm behaviour in a gear that has no worm's ratio |
There is a second, purely additive option that solves the thrust problem by cancelling it: the herringbone. Two opposite hands cut into one tooth, meeting at the centre. Axial force from the left half cancels the right half, so the shaft sees essentially no net thrust, while keeping the smooth engagement. The catch on a printed part is the meeting point in the middle, which is exactly where a seam or a small step lands if the model is assembled from two mirrored halves. If you print a herringbone, model it as one continuous tooth, not as two halves butted together.
Print orientation decides the tooth, and the answer is not the obvious one
For a spur gear the accepted answer is to print flat, so the tooth's bending load runs across the layers rather than peeling them apart. That reasoning comes from how layer bonding actually fails, and it is correct for a straight tooth.
A worm is a different animal. Its thread is a helical ramp that wraps the shaft, and the load on that ramp runs almost entirely along the thread. Print the worm standing on end, with its axis vertical, and every layer is a flat disc: the thread is built as a stack of complete rings, and there is no layer boundary crossing the load path at all. This is the one case where standing a round part upright is the right call for strength, and it is also the case where the part is most likely to topple, so add a brim and reduce speed for the first twenty layers.
Print the worm lying down and the opposite happens: the helix is sliced into successive arcs, every one of which ends on a layer boundary somewhere along its length. The thread becomes a chain of short segments glued end to end, which is precisely the weakest arrangement possible under the tangential load the worm carries.
For the wheel, flat on the bed is still correct for a spur-toothed wheel, and for a helical wheel it is a genuine compromise: the slanted tooth is no longer perpendicular to the layer plane, so bending introduces a small peeling component. A 20° helix printed flat loses noticeably less than a 40° helix printed flat. Above 30°, consider printing the wheel on its side with the tooth axis vertical, accepting support marks on the flanks in exchange for a load path that no longer crosses layers. Those support scars are then a wear surface, which is its own problem — see what grit does to a sliding face.
Layer height is a helix angle, and the printer decides which one you get
This is the part of the design that most people never look at, and it is the single most useful number in this article.
A printed helical flank is not a smooth surface. It is a staircase of layers, and the size of each step depends on the layer height divided by the flank's slope. On a 20° helix, a 0.20 mm layer produces a step that is measurably larger than the one a 30° helix would produce at the same layer height. Fewer, bigger steps mean the load lands on the protruding corners of a handful of layers instead of being shared.
There is a second, less obvious constraint. The surface of a worm thread has an inherent slope that varies around the thread: the flank angle at the root is steep, and it shallows toward the tip. Where the surface becomes shallower than the layer height allows, the slicer stops producing a proper wall and starts producing a series of nearly-flat top surfaces. At that point the thread's outer edge is no longer a continuous extrusion but a set of stacked terraces, and those terraces are what the wheel tooth rubs against.
The practical consequence is that a worm wants a finer layer height than the rest of the part, and it wants a small nozzle. A 0.4 mm nozzle at 0.20 mm layers produces a usable 60-tooth wheel and a coarse worm; a 0.4 mm nozzle at 0.12–0.16 mm layers produces a worm that runs noticeably more smoothly and generates less heat. If you are printing filled material, a hardened or tungsten nozzle keeps the thread geometry stable over a long run instead of widening with wear, and a high-flow nozzle helps when the fine layer height is costing you too much time.
The contact is a smear, so pressure limits are the real design constraint
A worm thread contacts a wheel tooth over a small area that moves as the mesh rotates. The relevant load measure is not tooth bending stress — it is contact pressure, and it is where printed worm drives die. Polymer has poor resistance to high surface pressure combined with sliding; it does not gall and seize the way metal does, but it does deform, warm, deform further, and then wear quickly.
Three levers control the pressure, and they are available to you at the modelling stage. The first is the projected contact area, which grows with face width and with the wheel's tooth count: a wider wheel spreads the same load over more length. The second is the wheel material's hardness and the stiffness behind it. The third is the surface finish of the worm thread, which you control with layer height.
The pressure estimates below are order-of-magnitude bands for printed polymer meshes running at low speed with sensible clearance, and they are here to tell you when to expect trouble rather than to certify a design.
| Surface pressure | Speed and duty | Expected outcome on a printed pair |
|---|---|---|
| Under ~3 MPa | continuous, fast | Stable running; wear limited to the rubbed band |
| 3–5 MPa | continuous, moderate | Acceptable with a good dry film; expect gradual thread polish |
| 5–8 MPa | intermittent | Short runs only; watch for local melting and material transfer |
| Over ~8 MPa | any | Local welding and tearing; redesign the tooth, do not add lubricant |
The fastest diagnostic is a paper test: run the stage for ten minutes under its real load, then touch the wheel tooth with the back of a finger through a gap. A pair running near its limit will be noticeably warm on the wheel, not the motor. If it is, the pressure is too high or the lead angle too shallow. Warming that appears only when the ambient is warm points back to the material's heat deflection temperature rather than to the mesh.
Clearance is cut into the worm, not into the wheel
The backlash logic from spur gears transfers directly, but the place you apply it moves. On a spur pair you offset each tooth flank inward by the same amount and both gears are correct. On a worm drive, the practical intervention is on the worm: reduce its effective thread thickness. That produces clearance all along the mesh, and it is far easier to control because the worm is a single part turned from a cylinder profile.
Printed materials need more clearance than metal, and the amount depends on which side of the pair you are asking to be accurate. A sensible starting point for a 0.4 mm nozzle at 0.20 mm layers is 0.15 mm of thread thinning on the worm for PETG-class materials, and 0.25 mm for ABS or ASA inside an enclosure where shrinkage runs high. Add roughly 0.05 mm per side at 0.30 mm layers. If the housing is a single printed piece holding both axes, add the manufacturing tolerance rules on top, and check the stack-up if more than two parts locate each axis.
Materials: the ranking is decided by heat, not by strength
A spur gear's material question is about tooth strength. A worm drive's material question is about heat and friction, and the answer is different enough to be worth a table. The failure signature is not a broken tooth; it is a polished, flattened thread and a wheel with its teeth worn into trapezoids.
| Material | Contact temperature behaviour | Friction and wear | Verdict for a printed worm stage |
|---|---|---|---|
| PLA+ | Softens near 55–60 °C | Acceptable when cold | Light duty only; softened by its own friction in continuous running |
| PETG | Usable to roughly 70 °C | Slightly sticky, self-limiting | The default for low-load worm stages; runs well with a dry film |
| PETG-CF | Similar to PETG | Lower wear, harder surface | Better thread stability on the worm; brittle at the tooth root on the wheel |
| PA12-CF10 | Well above PETG | Low friction, dimensionally stable | Strong all-round choice for the worm; must be printed bone dry |
| PA6-CF20 | Highest of this list | Very low wear, but abrasive to itself | Best on the wheel if the worm is a different material |
| PA612-CF15 | High, and the least moisture-sensitive nylon here | Low wear, less abrasive than PA6-CF | The stable nylon choice for a wheel that must hold position |
| ePA-CF | High | Tough and low friction | Good wheel material where shock load is expected |
| PA6-GF25 | High | Moderate wear, less abrasive than CF | Compromise where cost and printability matter |
| PET-CF17 | High stiffness, low creep | Very low wear | Worm only; stiff enough that thrust actually goes into the bearing |
| ABS / ASA | Reasonable in an enclosure | Moderate friction | Workable, but shrinks the housing around the mesh |
| PETG Matte | Same as PETG | Surface additive raises friction | Avoid on the contact face; it rubs rather than slides |
One rule from the sliding-surface side carries over unchanged and is worth repeating: never run the same fibre-filled material against itself in a sliding contact. Two PA6-CF20 surfaces facing each other behave like a lap, and the wear rate is worse than either material against plain polymer. Pair a filled worm with an unfilled wheel, or a filled wheel with an unfilled worm, and keep the pair dissimilar. The reasoning is in the mechanisms that move on purpose.
The housing is the gearbox, and most failures are housing failures
Once the teeth are correct, the remaining failures are structural, and they cluster in the housing. Four appear often enough to name.
Bearing bosses that tear off. The worm's radial load and the wheel's tangential load both end up as a pull on the boss that holds each shaft. A boss printed as a thin cylinder attached to a flat wall has a fillet at one end and a sharp transition at the other. The failure starts at the sharp one. Fillet both, and make the boss wall thicker than the shaft radius.
Housings that flex the mesh open. A printed housing with the worm and wheel mounted on opposite ends of a long open frame will bend under load, and the axis spacing grows. That opens the mesh, increases backlash, and makes the contact land on the tooth tips — which is where a helical tooth is thinnest. Close the frame into a box, or add a rib between the two bearing seats. Motor mount stiffness is the same problem seen from the other end.
Creep under a standing load. A self-locking worm holds a static load through friction, and the wheel tooth feels that load continuously. Printed polymer creeps under continuous load, slowly and at room temperature. A wheel that held position perfectly in the first week may have moved two degrees by the third month. If position retention matters, oversize the contact or use a higher-stiffness material rather than relying on friction holding indefinitely. Load paths explains the mechanism.
Seats that are not square to the axis. A worm only works if its axis is parallel to the wheel's tangent plane within a fraction of a degree. A printed bearing seat that is off by 0.3 mm across a 20 mm seat is off by nearly a degree, which is enough to move the contact band to one end of the thread. Print a gauge, check the seat, and do not assume it — the discipline is the one in the shop tooling guide.
A build sequence that keeps the variables separate
- Draw the motion path first, then the hand, then the ratio. Confirm the output turns the right way on a paper sketch before touching CAD.
- Pick the ratio from the starts. One start if it must hold position; two if it must be driven both ways. Write the decision down; it drives everything after.
- Size the wheel for contact area, not for tooth strength. Wide and fine-toothed beats narrow and coarse for a worm.
- Engineer the axial stop on the worm before modelling the housing. Metal washer, ball, PTFE disc or a real bearing — decide now, not after the third failure.
- Cut the clearance into the worm thread, not the wheel. Start at 0.15 mm for PETG.
- Print the worm upright with a brim, and at the finest layer height you can afford. Print a check ring first to confirm the hand.
- Print the housing with fillets at every boss transition and a rib between the bearing seats.
- Assemble dry, run by hand, and look for a contact band that sits in the middle of the wheel tooth. If it sits at an edge, fix alignment before adding power.
- Run ten minutes under load, then check the wheel for warmth. Warm means pressure; silent and cool means the design is in range.
Diagnosing what comes out of that sequence is the subject of the field guide to failed parts, and the same evidence rules apply: a polished thread and a worn wheel are a pressure-and-heat story, while a tooth lying on the bench is a bending story, and the two have completely different fixes.
When a printed worm is the wrong answer
Be specific about the envelope, because the failure mode is expensive. A printed worm drive is a poor choice when the gearbox has to hold a load at high ambient temperature, when efficiency matters because the motor is small, when the duty cycle is continuous at high contact pressure, when backlash has to be under a few hundredths, and when the assembly has to be quiet and stay quiet after a thousand hours. In each of those cases the honest answer is a steel worm on a bronze wheel, bought rather than printed, and a printed housing that holds them.
The realistic role for printed right-angle stages is the one where the alternatives are worse: low-speed positioning, light lifting, adjustment mechanisms, prototype axes, and anything where the 30:1 ratio in one stage is what lets a small stepper do a real job. Those are good jobs, and printing them well is mostly a matter of respecting the thrust, the hand, the helix and the layer steps rather than chasing a perfectly modelled involute.
Ten rules, in the order they matter
- Choose starts before geometry. One for holding, two for driving both ways.
- Put a hard axial stop on the worm's loaded end. A printed shoulder will wear into a slot.
- Confirm the hand on a check ring before printing the gearbox.
- Keep the helix at 20–25° for printed pairs; above 30° you are building a thrust problem.
- Print the worm upright. Its load runs along the thread, so layers should run across it.
- Use the finest layer height you can afford on the worm; more, smaller steps share the load.
- Thin the worm thread for clearance, and cut the clearance into one part only.
- Never pair a fibre-filled material with itself as a sliding contact.
- Judge the stage by contact pressure and wheel temperature, not by tooth strength.
- Fillet every boss transition and rib the frame between bearing seats; housings fail before teeth do.
The rest of the drive train around this stage is already covered: getting the torque into the shaft, thread forms that survive real loads for the fastener side, heat-set inserts for anything that must be opened again, shaping a part so it breaks where you want for the arms around the housing, keeping a drive from shaking itself apart once it runs, and managing the heat that friction creates inside a closed case. Start with the ratio, finish with the thrust stop, and a printed right-angle stage will do real work for years.