What module do I need for 500 N·m output? The module is the dimensioning DNA of every worm gear pair — and the answer follows a rigorous reverse calculation that takes about 10 minutes when done correctly.
Worm gear module (m) is the basic tooth-size parameter measured in millimetres, defined as m = pitch / π = d₁ / q (worm pitch diameter divided by diameter quotient). Standard modules per ISO 54 are 1, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, and 25 mm — with 1 to 8 covering roughly 90 percent of industrial worm gear demand. Module choice is reverse-calculated from the application output torque: small modules (1 to 2) handle 1 to 50 N·m, medium modules (2.5 to 4) handle 50 to 800 N·m, large modules (5 to 8) handle 800 to 5,000 N·m, very large modules (10+) handle above 5,000 N·m. Worm gear module choice is bound to centre distance and ratio through a = m(q + z₂)/2 — change one and the other two must adjust. The most common procurement mistake is specifying a non-standard module (e.g., m=3.5) when the standard m=3 or m=4 would fit; the correction saves 60 to 80 percent on tooling cost.
Module (m) is the metric basic tooth-size parameter for the worm gear, measured in millimetres. The simplest definition is geometric: module equals the axial pitch divided by pi, or m = pₐ / π. A worm gear pair with axial pitch 12.566 mm has module 4. The relationship is the same as for spur and helical gears, where module defines the linear distance between adjacent teeth in millimetres of pitch circle.
Module is the dimensioning DNA of the entire worm gear pair. From module flow the worm pitch diameter (d₁ = m × q), the wheel pitch diameter (d₂ = m × z₂), the centre distance (a = m × (q + z₂) / 2), the tooth height (h = 2.25 × m), the contact line length, the maximum permissible tangential force, and the load capacity calculations per DIN 3996 and ISO 14521. Get the module right and the rest of the design self-consistently follows. Get it wrong and every subsequent calculation propagates the error.
For Korean and Japanese OEM design teams, worm gear module choice is the first parameter set after deciding application torque and available envelope. Small errors in module selection cascade into oversized housings, undersized wheels, or marginal load capacity that emerges as accelerated wear at 18 to 24 months in service.
ISO 54 (and equivalent DIN 780) defines preferred and secondary worm gear worm gear module values. Preferred modules are 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25 mm. Secondary modules (1.125, 1.375, 1.75, 2.25, 2.75, 3.5, 4.5, 5.5, 7, 9, 11, 14, 18, 22) exist but are rarely stocked.
Each module corresponds to a specific application range based on output torque. The table below aligns module to typical centre distance, output torque, and application class — a working reverse-calculation tool.
| Module m | Typical a (mm) | Output torque (N·m) | Tooth height (mm) | Application class |
|---|---|---|---|---|
| m = 1.0 | 25 | 8 to 15 | 2.25 | Instruments, miniature actuators |
| m = 1.5 | 40 | 25 to 50 | 3.4 | Small servo, indexers |
| m = 2.0 | 50 | 50 to 100 | 4.5 | Light conveyors, packaging |
| m = 2.5 | 63 | 100 to 200 | 5.6 | Standard light industrial |
| m = 3.0 | 80 | 200 to 400 | 6.75 | General industrial |
| m = 4.0 | 100 | 400 to 800 | 9.0 | Heavier industrial, hoists |
| m = 5.0 | 125 | 800 to 1,500 | 11.25 | Heavy industrial |
| m = 6.0 | 160 | 1,500 to 3,000 | 13.5 | Cement, mining |
| m = 8.0 | 200 | 3,000 to 5,000 | 18.0 | Large hoists, ship deck |
| m = 10.0 | 250 | 5,000 to 10,000 | 22.5 | Very large industrial |
The worm gear torque values are typical for phosphor bronze wheel against case-hardened steel worm at standard q value 8-10, ratio 30:1 to 50:1, ZN or ZI tooth profile, with normal duty cycle. Variations of plus or minus 30 to 40 percent occur with material upgrades, accuracy class, and lubricant choice. Use the table for first-pass module selection; refine with strength calculation per DIN 3996 for final specification.
The practical worm gear design problem is reversed from textbook problems: the engineer knows the application output torque and ratio, and needs to find the module that delivers that torque at acceptable cost and envelope. Three steps make the reverse calculation tractable.
Step 1 — Apply service factor to design torque. Multiply the calculated steady output torque by the service factor (typically 1.25 to 2.0 depending on duty cycle and shock load class). A 500 N·m steady load with 1.5 service factor produces 750 N·m design torque.
Step 2 — Look up the table to find the matching module. 750 N·m design torque falls in the m=4.0 range (400-800 N·m) — the table column gives the answer directly. The corresponding centre distance is approximately 100 mm.
Step 3 — Verify centre distance and ratio compatibility. Check that a = m × (q + z₂) / 2 produces a sensible centre distance with reasonable q value. For m=4, target a=100 mm, ratio 50:1 (z₂=50): q = 2(100)/4 − 50 = 0. Infeasible — q must be positive and ideally 8 to 12. The fix is increasing centre distance to 125 mm (m=4 still works, q = 2(125)/4 − 50 = 12.5, feasible) or accepting smaller ratio at 100 mm centre distance.
The three-step process takes about 10 to 15 minutes per design and avoids the most common module specification errors. Skipping verification of centre distance compatibility produces designs that look correct on paper but cannot be manufactured at the chosen module.
A Japanese textile machinery builder once submitted a worm gear specification at module 2.5 for an application calculating to 175 N·m output torque under 1.4 service factor. The choice landed at the upper edge of the m=2.5 capacity envelope (100-200 N·m). Quality engineering review proposed stepping up to module 3.0 — a 20 percent increase in module size, less than 8 percent increase in worm gear unit cost, but moving the operating point from 87 percent of m=2.5 capacity to 44 percent of m=3.0 capacity. The capacity utilisation difference translated to roughly 30 percent longer expected service life because contact stress drops with the square root of module increase. Annual cost difference for the 240-unit production run: 4,300 USD on parts. Annual saving from extended replacement intervals: 18,000 USD against mid-life replacements at the m=2.5 spec. The 0.5 module step was effectively free after the second year. Always check whether the chosen module operates in the upper third of its torque envelope — if so, the next module up is usually better.
Worm gear module does not exist in isolation. It is bound to centre distance (a) and diameter quotient (q) through the equation a = m × (q + z₂) / 2. Three of the four variables (m, a, q, z₂) are typically constrained by the application — the fourth then has to satisfy the equation. The trick is recognising which three are constrained and which one is free.
Constraint scenario 1 — fixed envelope. The application packaging dictates centre distance (e.g., a = 100 mm for the existing housing). Required ratio fixes z₂ (e.g., 50 teeth for 50:1 ratio with single-start worm). Module is then constrained to give acceptable q value: m = 2a / (q + z₂). For typical q = 10, m = 2(100) / (10 + 50) = 3.33 — non-standard. The standard m=3 (q calculates to 16.67) or m=4 (q calculates to 0, infeasible) are the candidates. Choose m=3 with higher q.
Constraint scenario 2 — fixed module from torque requirement. The application output torque dictates module (e.g., m = 4.0 for 600 N·m). Required ratio fixes z₂. Centre distance becomes the derived value: a = m × (q + z₂) / 2. For m=4, q=10, z₂=50, a = 4(10+50)/2 = 120 mm — non-R10 standard. The closest R10 values are 100 mm (q=0, infeasible) or 125 mm (q=12.5, feasible). Choose a = 125 mm with q=12.5.
Constraint scenario 3 — fixed q from supplier capability. Some suppliers stock standard q values (q = 8, 10, 12 are most common). Required ratio fixes z₂. Module and centre distance must satisfy the equation jointly. For q=10 and z₂=50, the relationship a = m × 30 means m=4 gives a=120 mm, m=3 gives a=90 mm, m=5 gives a=150 mm. Only m=3 produces a value close to a standard centre distance (90 mm sits between R10 80 and 100 — see our centre distance calculation methodology for resolving this).
Three tooth-size measurement systems exist globally for worm gear specification. Module (m, mm) dominates Europe, Asia, and most of the world. Circular pitch (CP, inches) was historically used in some imperial specifications. Diametral pitch (DP, teeth per inch) dominates American AGMA usage.
Cross-supplier worm gear sourcing requires fluent conversion between the three. Korean and Japanese OEMs serving North American customers routinely encounter all three on the same project.
Module to circular pitch: CP = π × m. Module 2 corresponds to CP = 6.283 mm (or 0.247 inches). Module 4 corresponds to CP = 12.566 mm.
Module to diametral pitch: DP = 25.4 / m. Module 2 corresponds to DP = 12.7. Module 4 corresponds to DP = 6.35. The conversion is reciprocal — a smaller module gives a larger DP. Common American worm gear sizes are DP 8, 10, 12 — corresponding roughly to module 3.18, 2.54, 2.12 (none are standard ISO module values, which is why imperial and metric worm gears are not directly interchangeable).
Practical implication. ΕΝΑ ατέρμονα κοχλία specified as “10 DP” is approximately equivalent to module 2.54 — non-standard in metric, no direct catalogue match. Cross-system substitution always involves some compromise; the safer path is matching system to system at original specification time.
The three cases below illustrate three different worm gear module selection patterns — choosing the smaller of two adjacent modules at upper capacity edge, choosing for smoothness when capacity is generous, and converting non-standard module to standard via housing modification.
Each pattern is the right answer for its application context — the procurement skill is recognising which pattern applies.
A Korean parts conveyor manufacturer needed a worm gear pair for a new belt conveyor product line. Application output torque calculated 280 N·m steady, 1.5 service factor giving 420 N·m design torque. Required ratio 40:1 to match desired belt speed. Module-table lookup placed 420 N·m near the boundary between m=3 (200-400 N·m) and m=4 (400-800 N·m). Engineering review chose m=3 because the design torque sat at 105 percent of m=3 capacity — marginal but acceptable for the 16-hour-per-day duty cycle, with the cost saving of m=3 vs m=4 being roughly 15 percent on the worm gear pair. Centre distance worked out to 80 mm at q=10, z₂=40 (a = 3 × 50 / 2 = 75 mm — close to R10 standard 80 mm with q=13.3). Decision: m=3, a=80 mm, q=13.3, z₂=40. Field service life over 6 years across 180 units installed: average 5.5 years before bronze wheel replacement, slightly below the 7-year typical target but acceptable for the conveyor application. Lesson: choosing the smaller of two adjacent worm gear modules at the upper edge of capacity is a defensible cost optimisation when duty cycle is moderate.
A Japanese rotary indexer builder specified a high-precision worm gear pair for a 12-station rotary table with positioning repeatability of plus or minus 6 arcseconds. Application output torque was modest at 65 N·m peak; both module 2.0 and module 2.5 were within capacity envelope. Selection criterion: smoothness of motion. Smaller module produces shorter pitch and more teeth in mesh per worm rotation, which translates to smoother angular position output. Calculation: m=2.0 gave 36 percent of capacity utilisation, m=2.5 gave 33 percent, m=3.0 gave 22 percent. Either m=2 or m=2.5 was acceptable on capacity. Decision: m=2.5 for better tooth contact area and longer service life, accepting marginally less smoothness than m=2 would deliver. Final pair: m=2.5, a=63 mm, q=10, z₂=40, ratio 40:1, ZI ground. Indexing repeatability measured at plus or minus 4.2 arcseconds, exceeding the 6 arcsecond requirement. Lesson: when capacity is generous, module choice tilts toward longer service life; when capacity is tight, module choice tilts toward higher torque margin.
A Vietnamese repair shop received a worm gear failure on an imported European machine. Original specification: module 3.5, centre distance 90 mm, ratio 31:1. Both the module and centre distance were non-standard ISO values. Catalogue suppliers in Korea, Japan, and China all returned “non-standard, custom only” quotes at 1,400 USD per pair with 8 to 10 weeks lead time. Engineering review proposed converting to standard module 3 or module 4. Module 3 would shift centre distance to 90 mm with q calculating to 9 — close to original but with reduced torque capacity. Module 4 would shift centre distance to 100 mm with q=10 — modest housing modification needed. Decision: module 4 with new mounting plate to accommodate the 10 mm centre distance shift. Standard catalogue pair at 380 USD per pair, 1 week lead time. Modification of the housing mounting plate took 2 hours machining at the local shop. Total saving against custom: 1,020 USD per pair, plus 7 weeks of project schedule. The customer was running again 4 weeks earlier than the custom path would have allowed. Lesson: non-standard modules often arise from old-design legacy and rarely justify the custom premium; converting to standard module with modest housing modification almost always wins economically. Browse μειωτήρας ατέρμονα κοχλία options that align module to ISO 54 standard values for fast catalogue access.
Axial module (mₐ or mₓ) is the module measured in the worm axial plane — the plane containing the worm axis. Normal module (mₙ) is the module measured perpendicular to the worm thread helix. The two are related by mₙ = mₐ × cos γ, where γ is the worm lead angle. For typical low-lead-angle worms (γ less than 10 degrees), the difference between axial and normal module is small (typically 1 to 2 percent). For high-lead-angle worms (γ greater than 20 degrees), the difference becomes significant. Specification convention: ZA-type worm gear pairs use axial module by default; ZN, ZI, ZK, and ZC use normal module. Always check which convention the supplier uses to avoid confusion at the design review.
Yes, but at a significant cost premium. Non-standard modules require new hob design and tooling, which typically adds 2,000 to 6,000 USD to first-article cost and 4 to 8 weeks to lead time. Custom hobs are then held in storage by the supplier for future reorders, which adds inventory cost. The justification for non-standard module is rare in practice — most “must have non-standard module” requirements turn out, on examination, to be flexible. The few genuinely fixed cases involve replacement parts for legacy equipment where modifying the housing is impractical, or precision indexers where the module choice is bound to the indexing ratio in a way that no standard module satisfies. For these cases, the cost premium is justified; for everything else, the standard module path saves significant money and time.
Three measurement methods. First, count the teeth on the wheel (z₂) and measure the wheel pitch diameter (d₂) — module is then m = d₂ / z₂. The pitch diameter is roughly equal to the wheel outside diameter minus 2 × module, which becomes a self-consistency check. Second, measure the worm axial pitch (pₐ) — distance between adjacent thread crests along the worm axis. Module is then m = pₐ / π. Third, use a gear-tooth-size gauge or wire-and-pin measurement against the worm thread depth. The first method is simplest and most reliable. For a wheel showing d₂ = 160 mm and 40 teeth, module = 160 / 40 = 4.0. Standard ISO 54 module — confirmed.
ISO 54 builds on Renard preferred numbers (R10 series, 1.25 step). Preferred modules: 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25. Secondary modules sit on R20 values for finer steps. For most worm gear procurement, preferred-only is the right approach.
Indirectly yes — module is bound to lead angle (γ) through the equation tan γ = z₁ / q, where z₁ is the number of worm starts and q is the diameter quotient. Smaller modules at the same q produce smaller worm pitch diameters and slightly different lead angles depending on z₁. Lead angle is the primary efficiency driver — higher lead angles produce higher efficiency. The module-to-efficiency relationship is therefore secondary, working through the lead angle. For practical design purposes, optimise the lead angle directly (through z₁ and q) rather than trying to manipulate efficiency through module choice. The efficiency difference between adjacent modules at the same lead angle is typically less than 2 percent.
For industrial applications, module 1.0 is the practical lower limit. Below module 1, production transitions to precision instrument techniques — different tooling, inspection equipment, supplier base. Module 0.5 and 0.75 worm gear pairs exist for precision instruments and laboratory equipment but typically come from specialised suppliers (KHK, SDP-SI) rather than general industrial worm gear catalogues. Output torque at module 0.5 is roughly 1-3 N·m. Catalogue inventory below module 1 is significantly smaller than at module 1 and above.
Not necessarily. The smallest worm gear module that meets capacity gives lowest cost and smallest envelope but operates at high utilisation (often 80-100 percent of rated). High utilisation means service life closer to design minimum and more sensitivity to load excursions. Stepping up one module size typically increases unit cost 8-15 percent but moves utilisation from 80-100 percent to 40-60 percent — translating to 30-80 percent longer service life and more tolerance to load excursions. The economically optimal module is usually one step above the minimum — not the minimum itself. The exception is space-constrained applications where the larger module physically does not fit; for those, the minimum module must be accepted and the shorter service life budgeted in the maintenance plan.
Worm gear module is the dimensioning DNA of the pair — change it and every other parameter responds (pitch diameter, centre distance, tooth height, contact line, load capacity). The 10 standard modules from m=1.0 to m=10.0 cover roughly 90 percent of industrial demand, and the right choice for a given application follows from a three-step reverse calculation: apply service factor to torque, look up the matching module from the table, verify centre distance compatibility with q. Skipping the verification step is the most common cause of designs that look correct on paper but fail manufacturing feasibility. The economically optimal module is typically one step above the minimum that meets capacity — the modest cost premium delivers significantly longer service life and broader tolerance to the inevitable real-world load variation.
Send the application output torque, ratio, duty cycle, and envelope constraints. We will run the three-step module reverse-calculation, recommend the right module from the ISO 54 preferred series, and confirm centre distance compatibility — typically within one Korean working day for standard catalogue specifications.
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