KEVOS® MAKEOS · Gears
Wormgear Hob Design (Over-Size Diameters, Sharpening Allowance, Setting Angle, Flutes)
For a hob to cut my wormgear, what outside, root and pitch diameters should it have with the AGMA sharpening allowance, at what angle should it be set, how many flutes should it have, and what flute lead lets me relieve a helical-fluted hob?
Wormgear hob proportions by the handbook’s formulas and AGMA practice: the over-size sharpening allowance from the normal pitch and the helix angles at the outside and pitch diameters (solved together with the diameters it changes), the hob outside, root and pitch diameters, the hob lead angle and the extra setting angle that makes up for the smaller lead angle of an over-size hob, the approximate number of flutes by the handbook rule with a count that has no common factor with the threads, the common-factor check between hob threads and wormgear teeth, flute pitch and gash width at the periphery, and for helical flutes at right angles to the thread, the teeth per turn along the thread and the modified flute lead and angle that suit the relieving attachment.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Worm and wormgear | ||
| Pitch diameter of the worm | mm | Pitch diameter of the worm the hob copies. |
| Axial pitch of the worm | mm | Axial pitch of the worm; the hob has the same lead and threads as the worm. |
| Threads (starts) on the worm and hob | Number of threads on the worm, which the hob must also have. | |
| Teeth on the wormgear | Number of teeth on the wormgear to be hobbed, for the common-factor check. | |
| Addendum of the worm and wormgear | mm | Addendum of the worm and wormgear teeth, from the worm proportions. |
| Clearance between worm and wormgear | mm | Clearance between the worm and wormgear teeth at the root, from the worm proportions. |
| Flutes | ||
| Number of flutes (gashes) on the hob | Number of flutes or gashes you intend to cut; compare it with the handbook rule and the common-factor check. | |
| Flute direction | choice | Hobs are usually fluted parallel to the axis; flutes at right angles to the thread cut better but need a flute lead the relieving attachment can follow. |
| Teeth per turn along the thread the relieving gears suit (helical flutes) | Number of teeth in one turn along the thread helix for which you can gear the relieving attachment, for example a whole or half number close to the exact value this tool reports. | |
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: Pitch diameter of the worm
- What it is
- Pitch diameter of the worm the hob must reproduce.
- 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 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
- The hob pitch diameter is this plus the sharpening allowance.
- Get it right
- Take it from the worm drawing.
What this means: Axial pitch of the worm
- What it is
- Axial pitch of the worm, the linear pitch of the hob.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.2 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
- Sets the lead, the normal pitch and the flute rule.
- Get it right
- Measure along the axis from thread to thread.
What this means: Threads (starts) on the worm and hob
- What it is
- Number of threads on the worm, which the hob must also have.
- 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 2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the lead and the common-factor checks.
- Get it right
- Count the worm thread starts.
What this means: Teeth on the wormgear
- What it is
- Number of teeth on the wormgear to be cut.
- Units and format
- Enter a plain number with no unit. The form accepts 10 to 1000. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 41 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Checked for a common factor with the hob threads.
- Get it right
- Take it from the wormgear drawing.
What this means: Addendum of the worm and wormgear
- What it is
- Addendum of the worm and wormgear teeth.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4.04 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the hob outside and root diameters.
- Get it right
- Take it from the worm proportions.
What this means: Clearance between worm and wormgear
- What it is
- Clearance between the worm and wormgear teeth.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 50 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.84 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Adds to the hob outside diameter.
- Get it right
- Take it from the worm proportions; the hob cuts the wormgear root this much deeper.
Flutes
What this means: Number of flutes (gashes) on the hob
- What it is
- Number of flutes or gashes you intend to cut in the hob.
- Units and format
- Enter a plain number with no unit. The form accepts 3 to 60. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 9 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the flute pitch, gash width and the common-factor check.
- Get it right
- Start from the rule’s suggestion and avoid a common factor with the threads.
What this means: Flute direction
- What it is
- Whether the flutes are parallel to the axis or helical at right angles to the thread.
- Units and format
- Choose one of 2 options from the list: Straight, parallel to the axis; Helical, at about right angles to the thread.
- Example
- The form opens with “Straight, parallel to the axis” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Helical flutes add the flute lead and angle to the results.
- Get it right
- Straight flutes are easier to relieve; helical flutes cut better.
What this means: Teeth per turn along the thread the relieving g…
- What it is
- Teeth per turn along the thread helix that the relieving attachment can be geared for.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 200. 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
- Sets the modified flute lead; it must be more than the number of flutes.
- Get it right
- Pick a whole or half number near the exact value the tool reports.
Method and formulas
- Lead L = t P; worm lead angle λ = arctan(L ÷ (π D)); normal pitch P_n = P cos λ.
- Outside diameter O = D + 2A + 2C + S; root diameter = D − 2A; hob pitch diameter D_h = O − (2A + 2C) = D + S.
- Helix angles from the axis: H = arctan(π D_h ÷ L) at the pitch diameter, h = arctan(π O ÷ L) at the outside diameter.
- Sharpening allowance S = 0.075 P_n [16 − (h − H)] ÷ 16 + 0.010 in (0.254 mm), with angles in degrees; S and the diameters are solved together by repeated substitution.
- Hob lead angle λ_h = arctan(L ÷ (π D_h)); the hob axis is set at 90° plus λ − λ_h to the wormgear axis.
- Approximate flutes = 3 × hob diameter ÷ (2 × linear pitch); choose a number with no common factor with the threads, and threads with no common factor with the wormgear teeth.
- Flute pitch at the periphery = π O ÷ flutes; gash width ≈ 0.4 × flute pitch.
- Helical flutes: teeth per turn along the thread N = F ÷ cos² α with α the hob lead angle; for a chosen N the flute lead = L F ÷ (N − F), and its angle from the axis at the pitch diameter is arctan(π D_h ÷ flute lead).
- Example: a 2-thread hob for a 50.8 mm worm gets a 1.1133 mm sharpening allowance, 61.673 mm outside diameter and a 0.19083° extra setting angle; the rule gives about 7.2842 flutes.
Limitations
- The sharpening allowance is the AGMA practice for ordinary commercial hobs that the handbook gives; precision hobs may differ.
- Gashing cutter thickness and depth below the thread root are given by the handbook in inches as ranges; they are not calculated.
- For helical flutes the relieving gearing itself is not worked out; choose a value of N you can gear for.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Specify hob diameters for a wormgear
- Choose the number of gashes for a multi-thread hob
- Work out the flute lead for a helical-fluted hob to suit the relieving gears
Who it is for
- Hob and cutter makers
- Gear cutting shops
- Gear designers
What you get
- Lead, worm lead angle and normal pitch
- Sharpening allowance by the AGMA formula
- Hob outside, root and pitch diameters
- Hob lead angle and setting angle correction
- Flutes by the handbook rule and the common-factor checks
- Flute pitch and gash width at the periphery
- Teeth per turn along the thread, flute lead and flute angle for helical flutes
Interpreting the result
- An over-size hob has a larger pitch diameter and a smaller lead angle than the worm; resharpening slowly brings it back, and the setting angle makes up the difference meanwhile.
- A common factor between threads and flutes, or between threads and wormgear teeth, repeats errors on the same teeth; avoid it.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3345–3346. Topic reference; no source tables or recommended settings are reproduced.
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