BIZOMAT MAKEOS · Gears
Helical Gear Milling Set-up (Lead, Change Gears, Cutter, Indexing)
How do I set up a universal milling machine to cut this helical gear: lead and change gears, table swivel, cutter number and index setting?
Set-up for milling a helical gear with a form cutter on a universal dividing head: pitch diameter from the normal module, the lead of the helix and the change gears from the table lead screw to the dividing head with the lead error (as the helical milling tool), table swivel, the cutter number from the formative number of teeth (as the gear cutter number tool for helical gears), the simple indexing setting (as the simple indexing tool), blank diameter and depth of cut.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Normal module | mm | Normal module of the gear. |
| Number of teeth | Number of teeth. | |
| Helix angle | ° | Helix angle at the pitch diameter. |
| Lead of the machine | mm | Lead of the machine: table travel for one turn of the dividing head spindle with equal gears. |
| Change gears available | choice | Change gears you have. |
| Dividing head worm ratio | :1 | Worm ratio of the dividing head. |
| Index plates available | choice | Index plates you have. |
| Dedendum factor (dedendum ÷ module) | Dedendum as a multiple of the normal module. | |
| Largest lead error | % | Largest lead error you accept from the gear train. |
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.
What this means: Normal module
- What it is
- The module of the gear measured in the plane normal to the teeth, which is the module of the form cutter you use. Pitch diameter is normal module times teeth divided by the cosine of the helix angle.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.3 mm to 50 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Pitch diameter, lead, blank diameter and depth of cut all rise in proportion to the module.
- Get it right
- Do not use the transverse module (measured across the gear face); a helical gear cut with a standard cutter is specified by its normal module.
What this means: Number of teeth
- What it is
- The number of teeth on the helical gear to be cut. It sets the pitch diameter, the formative tooth count that picks the cutter number, and the indexing.
- Units and format
- Enter a plain number with no unit. The form accepts 6 to 1000. Use a whole number. 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
- More teeth give a larger pitch diameter and lead, and change the index setting.
What this means: Helix angle
- What it is
- The helix angle of the teeth measured at the pitch diameter, between a tooth and the gear axis. The table is swivelled by this angle.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 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 angle increases the formative tooth count and shortens the lead.
- Get it right
- Use the angle at the pitch diameter, not at the outside diameter, and note the hand of helix separately; it sets the swivel direction.
What this means: Lead of the machine
- What it is
- The lead of the milling machine: how far the table travels for one full turn of the dividing head spindle when the change gears are equal. It depends on the table lead screw and the dividing head worm ratio.
- 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 254 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The gear ratio needed is the helix lead divided by this machine lead.
- Get it right
- Check it on your own machine or its manual; it differs between machines and between inch and metric lead screws.
What this means: Change gears available
- What it is
- Which set of change gears you have for the train between the table lead screw and the dividing head; the tool searches this set for the four-gear train closest to the ratio needed.
- Units and format
- Choose one of 2 options from the list: Standard set: 24, 24, 28, 32, 40, 44, 48, 56, 64, 72, 86, 100; 24 to 100 in steps of 4.
- Example
- The form opens with “Standard set: 24, 24, 28, 32, 40, 44, 48, 56, 64, 72, 86, 100” selected as a worked example. Choose the option that matches your case.
- Get it right
- Pick the set that matches the gears actually in the cupboard; the search uses each listed gear once.
What this means: Dividing head worm ratio
- What it is
- The number of crank turns needed for one turn of the dividing head spindle, set by the worm and worm wheel in the head. It is used to work out the simple indexing setting.
- Units and format
- Enter a number in :1: a ratio to one (type 3 for 3:1). The form accepts 1 :1 to 200 :1. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 :1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Read it from the head’s nameplate or manual; most heads are marked, and the setting is wrong if this ratio is wrong.
What this means: Index plates available
- What it is
- Which index plates you have on the dividing head. The tool looks for a hole circle on these plates that gives the simple indexing for the tooth count.
- Units and format
- Choose one of 2 options from the list: Brown & Sharpe plates 1–3; Cincinnati standard plate (both sides).
- Example
- The form opens with “Brown & Sharpe plates 1–3” selected as a worked example. Choose the option that matches your case.
- Get it right
- If no circle suits the tooth count, the result points you to differential or angular indexing.
What this means: Dedendum factor (dedendum ÷ module)
- What it is
- The dedendum (depth of tooth below the pitch circle) divided by the module, from your gear standard or drawing. With an addendum of one module, it sets the depth of cut.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 1.6. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.25 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Depth of cut = normal module × (1 + this factor).
- Get it right
- This is a ratio, not a length in millimetres.
What this means: Largest lead error
- What it is
- The largest difference you accept between the lead the chosen change gears give and the lead the gear needs, as a percentage of the needed lead, from the gear drawing or your quality requirement.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0.001% to 10%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.5% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Type the percentage itself, not a fraction.
Method and formulas
- Pitch diameter D = m_n z ÷ cos β; lead = π D ÷ tan β; ratio driven ÷ driver = lead ÷ machine lead, best four-gear train from the set (as the helical milling tool).
- Formative teeth = z ÷ cos³ β → cutter number (as the gear cutter number tool); index setting from ratio ÷ z (as the simple indexing tool).
- Blank diameter = D + 2m_n; depth = m_n (1 + dedendum factor); swivel the table by the helix angle.
- Example: lead 376.99 mm with drivers 24 and 44, driven 28 and 56 (error 0.042547%); cutter No. 3; index 1 turns and 5 holes in the 15-hole circle.
Limitations
- Form cutters give approximate profiles; the formative tooth count only picks the nearest cutter.
- Gear fit on the quadrant and the hand of helix (swivel direction) must be checked on the machine.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set up a universal mill to cut a replacement helical gear
- Check the lead error of the best gear train
- Choose the form cutter for a helical gear
Who it is for
- Machinists
- Toolroom staff
- Maintenance fitters
What you get
- Pitch diameter, lead and change gears
- Cutter number and indexing
- Blank diameter and depth
Interpreting the result
- If the lead error is too large, try the other gear set or a compound train with an idler change.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2060–2062, 2205, 2107–2121, 2148–2150. Topic reference; no source tables or recommended settings are reproduced.
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