KEVOS® MAKEOS · Gears
Fine-Pitch Worm and Wormgear Design (ANSI B6.9 Proportions, Centre Distance, Face Width, Thread Length)
For a fine-pitch worm and wormgear, what are the diameters, tooth proportions, centre distance, face width and threaded length, how many threads or what lead angle hits my centre distance, and is the worm diameter in range?
Proportions of a fine-pitch worm and wormgear by the American Standard (ANSI B6.9-1977) formulas the handbook gives: lead, worm and wormgear pitch diameters and centre distance from the axial pitch, lead angle, threads and teeth; normal pitch, addendum, whole and working depth, clearance and tooth thickness from the normal pitch; worm and wormgear outside diameters, minimum wormgear face width and the safe minimum threaded length of the worm; the approximate number of threads and the lead angle that give your target centre distance; and checks of the centre distance and worm pitch diameter against your limits.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Worm and wormgear | ||
| Axial pitch of the worm | mm | Axial pitch of the worm, equal to the circular pitch of the wormgear in the central plane; the standard is built on axial pitch. |
| Lead angle | ° | Lead angle of the worm thread, normally one of the standard series of fifteen angles from 0.5° to 30°. |
| Threads (starts) on the worm | Number of threads or starts on the worm; most fine-pitch worms have one or two. | |
| Teeth on the wormgear | Number of teeth on the wormgear; the ratio is teeth ÷ threads. | |
| Targets and limits | ||
| Target centre distance | mm | Centre distance the housing or mechanism needs. |
| Accepted centre distance difference | mm | Largest difference from the target centre distance you can accept or take up in the housing. |
| Smallest worm pitch diameter accepted | mm | Smallest worm pitch diameter you accept; the handbook gives 0.250 in (6.35 mm) as the minimum recommended. |
| Largest worm pitch diameter accepted | mm | Largest worm pitch diameter you accept; the handbook gives 2.000 in (50.8 mm) as the maximum recommended. |
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 and wormgear
What this means: Axial pitch of the worm
- What it is
- Axial pitch of the worm: distance between adjacent threads along the worm axis, equal to the wormgear circular pitch.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.01 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4.064 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 dimension of the worm and wormgear.
- Get it right
- Fine-pitch standard pitches are given in inches; 0.160 in is 4.064 mm.
What this means: Lead angle
- What it is
- Lead angle of the worm thread, measured from a plane square to the worm axis.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0.1° to 45°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger lead angle gives a smaller worm diameter for the same lead and a more efficient drive.
- Get it right
- Choose from the standard series (0.5° to 30°) to keep tooling standard.
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 20. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More threads multiply the lead and lower the ratio for the same wormgear.
- Get it right
- Most fine-pitch worms have one or two threads; more threads give a larger lead.
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 4 to 1000. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More teeth enlarge the wormgear and the centre distance.
- Get it right
- Ratio = teeth ÷ threads; choose a count with no common factor with the threads for a hunting tooth.
Targets and limits
What this means: Target centre distance
- What it is
- The centre distance between the worm and wormgear axes that the design must meet.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 76.2 mm 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 target check and the threads or lead angle suggested to meet it.
- Get it right
- Take it from the housing or mechanism layout.
What this means: Accepted centre distance difference
- What it is
- How far the calculated centre distance may differ from the target.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.5 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A tighter allowance may force another thread count or lead angle.
- Get it right
- Use what the housing can take up, for example by shims or an adjustable mounting.
What this means: Smallest worm pitch diameter accepted
- What it is
- Smallest worm pitch diameter you accept.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6.35 mm 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 diameter check.
- Get it right
- The handbook gives 0.250 in (6.35 mm) as the minimum recommended for fine-pitch worms.
What this means: Largest worm pitch diameter accepted
- What it is
- Largest worm pitch diameter you accept.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50.8 mm 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 diameter check.
- Get it right
- The handbook gives 2.000 in (50.8 mm) as the maximum recommended for fine-pitch worms.
Method and formulas
- Lead l = n P_x; worm pitch diameter d = l ÷ (π tan λ); wormgear pitch diameter D = N P_x ÷ π; centre distance C = 0.5(d + D).
- Normal pitch P_n = P_x cos λ; addendum a = 0.3183 P_n; whole depth h_t = 0.7003 P_n + 0.002 in (0.0508 mm); working depth h_k = 0.6366 P_n; clearance c = h_t − h_k; tooth thickness t_n = 0.5 P_n.
- Worm outside diameter d_o = d + 2a; wormgear outside diameter D_o = 2C − d + 2a.
- Minimum wormgear face width F_G = 1.125 √((d_o + 2c)² − (d_o − 4a)²); safe minimum worm threaded length F_W = √(D_o² − D²).
- Threads for a target centre distance ≈ 2πC ÷ (P_x (cot λ + m_G)); lead angle for the target with these threads from cot λ = 2πC ÷ (n P_x) − m_G.
- Example: 10 threads at 30° and 100 teeth give d = 22.406 mm, D = 129.36 mm and C = 75.884 mm against 76.2 mm, with a 16.995 mm minimum face width.
Limitations
- Fine-pitch worm gearing with axes at right angles and non-throated wormgear blanks, as the standard assumes; coarse-pitch power worms follow other proportions.
- The 20° cutter gives a slightly larger normal pressure angle on the worm, depending on the worm diameter, lead angle and cutter size; that change is not calculated.
- Strength, wear and efficiency are not checked.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Lay out a fine-pitch worm drive for an instrument or small gearbox
- Choose threads or lead angle to suit a centre distance
- Check worm blank, wormgear blank and threaded length sizes
Who it is for
- Instrument and mechanism designers
- Gear designers
- Toolmakers
What you get
- Lead, ratio and worm and wormgear pitch diameters
- Centre distance against the target
- Normal pitch, addendum, depths, clearance and tooth thickness
- Worm and wormgear outside diameters
- Minimum wormgear face width and worm threaded length
- Threads and lead angle for the target centre distance
Interpreting the result
- The lead angle sets the worm diameter for a given lead: a small lead angle gives a large worm, a large one a slender worm.
- More threads raise the lead angle and efficiency for the same ratio, but need more wormgear teeth.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3321–3325. Topic reference; no source tables or recommended settings are reproduced.
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