KEVOS® MAKEOS · Gears
Industrial Worm Gearing Proportions (Coarse Pitch: Diameters, Lead Angle, Face Width, Thread Length, Efficiency)
For a coarse-pitch power worm and wormgear, what diameters, lead angle, tooth depths, face width and worm thread length do the handbook rules give at my pitch, ratio and centre distance, and what efficiency, rubbing speed and hunting-tooth action follow?
Proportions of industrial (coarse-pitch) worm gearing by the rules and formulas of the handbook’s Table 4 and the AGMA proportions it gives: ratio and lead, wormgear pitch diameter from teeth and axial pitch, worm pitch diameter from the centre distance (or the centre distance from a chosen worm), lead angle, normal pitch, addendum, whole depth, dedendum and clearance, worm outside diameter, wormgear throat diameter and throat radius, wormgear outside diameter by the lead-angle and thread-count rules, face width for shell or integral worms, worm thread length, rubbing speed, efficiency with the worm or the wormgear driving by the friction-angle formulas and the empirical rules, the hunting-tooth check, the teeth-plus-threads total and the pressure angle the handbook relates to the lead angle.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Worm set | ||
| Axial pitch of the worm (circular pitch of the wormgear) | mm | Axial pitch of the worm, which equals the circular pitch of the wormgear in its central plane; the handbook example uses 0.5 in (12.7 mm). |
| Threads (starts) on the worm | Number of threads or starts on the worm; multi-thread worms with lead angles of 25° to 45° are the efficient choice for power. | |
| Teeth on the wormgear | Number of teeth on the wormgear; the ratio is teeth ÷ threads. | |
| Pressure angle chosen | ° | Pressure angle you intend to use (half the included thread angle), checked against the handbook’s guide by lead angle. |
| Size | ||
| Size the worm from | choice | With the centre distance fixed the worm takes what is left after the wormgear; otherwise the centre distance follows from the worm you choose. |
| Centre distance (used when it is fixed) | mm | Centre distance between the worm and wormgear axes, from the housing. |
| Worm pitch diameter (used when chosen) | mm | Worm pitch diameter you have chosen for strength and stiffness. |
| Tooth proportions from | choice | The handbook’s depth rules are written in axial pitch; for lead angles over 15° to 20° it says the normal pitch is commonly used instead, giving shallower teeth. |
| Worm construction | choice | A shell worm is bored and fitted on a shaft; a worm with threads cut on the shaft uses the face width rule from the centre distance. |
| Running | ||
| Worm speed | rpm | Speed of the worm shaft, for the rubbing speed. |
| Coefficient of friction (worm on wormgear) | Coefficient of friction between the worm and wormgear for your materials, finish and lubricant, from test data or the gear maker. | |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
Worm set
What this means: Axial pitch of the worm (circular pitch of the…
- What it is
- Axial pitch of the worm, equal to the circular pitch of the wormgear.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.5 mm to 200 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12.7 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Scales every tooth proportion and the wormgear diameter.
- Get it right
- Measure from one thread to the next along the worm axis, not along the thread.
What this means: Threads (starts) on the worm
- What it is
- Number of threads or starts on the worm.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 12. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More threads raise the lead angle and efficiency for the same worm diameter.
- Get it right
- Count the thread starts at the worm end.
What this means: Teeth on the wormgear
- What it is
- Number of teeth on the wormgear.
- Units and format
- Enter a plain number with no unit. The form accepts 10 to 400. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 36 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the ratio and the wormgear diameter.
- Get it right
- Choose it with the threads to give the ratio; avoid a common factor for hunting-tooth action.
What this means: Pressure angle chosen
- What it is
- Pressure angle you intend to use, half the included thread angle.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 10° to 35°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the pressure angle check.
- Get it right
- The handbook relates it to the lead angle: 14½° for small leads up to 30° for leads over 35°.
Size
What this means: Size the worm from
- What it is
- Whether the centre distance is fixed or the worm diameter is chosen.
- Units and format
- Choose one of 2 options from the list: The centre distance (fixed); A chosen worm pitch diameter.
- Example
- The form opens with “The centre distance (fixed)” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Decides which of the two size inputs the tool uses.
- Get it right
- Fix the centre distance when the housing is given; choose the worm when strength sets it.
What this means: Centre distance (used when it is fixed)
- What it is
- Centre distance between the worm and wormgear axes.
- Units and format
- Enter a number in mm: millimetres. The form accepts 5 mm to 5000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 91.44 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- With a fixed centre distance the worm gets 2C − D, so it sets the lead angle.
- Get it right
- Take it from the housing bores.
What this means: Worm pitch diameter (used when chosen)
- What it is
- Worm pitch diameter you have chosen.
- Units and format
- Enter a number in mm: millimetres. The form accepts 2 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 37.36 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A smaller worm raises the lead angle and efficiency but lowers stiffness.
- Get it right
- Size it for bending and torsion; the handbook gives empirical ranges by centre distance.
What this means: Tooth proportions from
- What it is
- Whether the tooth depths are worked from the axial or the normal pitch.
- Units and format
- Choose one of 2 options from the list: Axial pitch (Table 4 rules); Normal pitch (lead angles over 15–20°).
- Example
- The form opens with “Normal pitch (lead angles over 15–20°)” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Normal pitch gives shallower teeth at steep leads.
- Get it right
- For lead angles over 15° to 20° the handbook says the normal pitch is commonly used.
What this means: Worm construction
- What it is
- Whether the worm is a shell fitted on a shaft or cut integral with the shaft.
- Units and format
- Choose one of 2 options from the list: Shell worm (bored, fitted on a shaft); Threads integral with the shaft.
- Example
- The form opens with “Shell worm (bored, fitted on a shaft)” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Changes the face width rule.
- Get it right
- Integral worms are usual for case-hardened alloy steel worms.
Running
What this means: Worm speed
- What it is
- Rotational speed of the worm (input) shaft.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 1 rpm to 20000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1450 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the rubbing speed, which drives heat and lubrication needs.
- Get it right
- Use the motor or input speed after any first reduction.
What this means: Coefficient of friction (worm on wormgear)
- What it is
- Coefficient of friction between the worm thread and the wormgear teeth.
- Units and format
- Enter a plain number with no unit. The form accepts 0.001 to 0.5. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.05 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Higher friction lowers efficiency and makes self-locking more likely.
- Get it right
- Take it from test data or the gear maker for your materials, finish, lubricant and rubbing speed.
Method and formulas
- Ratio R = T ÷ t; lead L = t P; wormgear pitch diameter D = T P ÷ π (rule 22).
- Fixed centre distance: worm pitch diameter d = 2C − D (rule 18); otherwise C = (D + d) ÷ 2 (rule 2).
- Lead angle tan λ = L ÷ (π d) (rule 12); normal pitch P_n = P cos λ (rule 17).
- AGMA proportions: single and double thread a = 0.318 p, W = 0.686 p; triple and quadruple a = 0.286 p, W = 0.623 p, with p the axial pitch or, for steep leads, the normal pitch; dedendum b = W − a; clearance c = W − 2a.
- Worm outside d_o = d + 2a (rule 13); throat diameter D_t = D + 2a (rule 28); throat radius U = d_o ÷ 2 − 2a (rule 29).
- Wormgear outside diameter: D + 3 × 0.3183 P up to 20° lead angle, D + 3 × 0.3183 P cos λ above; or D_t + 0.4775 P (one or two threads), D_t + 0.3183 P (three or more).
- Face width: shell worms 2.38 P + 0.25 in (one or two threads) or 2.15 P + 0.20 in (three or four); integral worms C^0.875 ÷ 3 with C in inches. Thread length G = P (4.5 + 0.02 T) (rule 31).
- Rubbing speed V = π d n ÷ cos λ (0.262 d n sec λ ft/min, rule 27).
- Friction angle φ_f = arctan f; worm driving E = 100 tan λ ÷ tan(λ + φ_f) and empirically 100 − R ÷ 2; wormgear driving E = 100 tan(λ − φ_f) ÷ tan λ and empirically 100 − 2R.
- Example: 36/6 at 12.7 mm pitch on a 91.44 mm centre distance gives D = 145.53 mm, d = 37.349 mm and a 33.001° lead angle, with 89.836 % efficiency with the worm driving.
Limitations
- The handbook gives the AGMA depth rules and face width rules for one to four threads; for more threads the triple-and-quadruple rules are used here and should be confirmed with the gear maker.
- Efficiency excludes bearing and oil-churning losses, as the handbook notes; the empirical rules and the friction formulas differ somewhat.
- Load and thermal ratings are not calculated; check them with the gear maker or a rating standard.
- The handbook’s pressure angle guide by lead angle is a general guide with overlapping bands.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Lay out a power worm drive at a fixed centre distance and ratio
- Choose threads and teeth for a hunting-tooth ratio
- Get blank sizes, face width and thread length for drawings
Who it is for
- Gearbox designers
- Mechanical design engineers
- Machine builders
What you get
- Ratio, lead and lead angle
- Wormgear and worm pitch diameters and centre distance
- Normal pitch, addendum, whole depth, dedendum and clearance
- Worm outside diameter, wormgear throat diameter, throat radius and outside diameter
- Face width and worm thread length
- Rubbing speed and efficiency with the worm or the wormgear driving
- Hunting tooth, teeth-plus-threads total and pressure angle checks
Interpreting the result
- A lead angle of 25° to 45° keeps efficiency high; single-thread worms with small lead angles are inefficient but give large ratios and may self-lock.
- Teeth and threads with no common factor give hunting-tooth action, which spreads hob errors over all teeth; if the worm threads are not accurately indexed, the handbook prefers to avoid it.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3331–3338, 3344. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Useful alongside · Library collection
Gears and gearboxes: choosing reducers and geared motors that last
In Machine Elements and Mechanical Design
What it covers: A gearbox chosen on ratio and price alone can overheat, waste energy or let a load run back. How gear types differ and how to select, install and maintain reducers and geared motors.
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