BIZOMAT MAKEOS · Gears
Helical Gear Hobbing Change Gears (Machine Without Differential, Feed Correction, Lead Error)
On a gear hobbing machine without a differential, what index gear ratio does a helical gear need, how do I adjust the feed to make up for the error in the index gears I can fit, and what lead do I actually get?
Index and feed change gears for hobbing helical gears on a machine without a differential by the handbook formulas: index gear ratio R = L ÷ (L ∓ F) × K T ÷ N (minus when gear and hob are the same hand, plus when opposite, reversed for climb hobbing), the error of the obtainable index ratio, the feed that compensates for it F = L (N R − K T) ÷ (N R), the feed gear ratio F ÷ M, the feed from the feed gears fitted, and the lead obtained L = F N R ÷ (N R − K T) with its error.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Teeth on gear N | teeth | Number of teeth on the helical gear being hobbed. |
| Lead of gear L | mm | Lead of the gear helix; L = π D cot α for pitch diameter D and helix angle α. |
| Feed per gear revolution F (nominal) | mm | Nominal feed of the hob per revolution of the gear. |
| Machine constant K | Index constant of the hobbing machine, from its maker. | |
| Threads on hob T | threads | Number of threads (starts) on the hob. |
| Feed gear constant M | mm | Feed gear constant of the machine, from its maker. |
| Hands of gear and hob | choice | Whether gear and hob have the same or opposite hand of helix. |
| Hobbing direction | choice | Conventional or climb hobbing; climb hobbing reverses the sign rule. |
| Index gears fitted | ||
| Index driving gear 1 | teeth | First driving index gear. |
| Index driving gear 2 | teeth | Second driving index gear; for a simple pair use equal gears in the second positions. |
| Index driven gear 1 | teeth | First driven index gear. |
| Index driven gear 2 | teeth | Second driven index gear. |
| Feed gears fitted | ||
| Feed driving gear 1 | teeth | First driving feed gear. |
| Feed driving gear 2 | teeth | Second driving feed gear. |
| Feed driven gear 1 | teeth | First driven feed gear. |
| Feed driven gear 2 | teeth | Second driven feed gear. |
| Largest lead error you accept per 100 mm of lead | mm | Largest lead error you accept per 100 mm of lead, from the gear’s lead tolerance. |
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: Teeth on gear N
- What it is
- Number of teeth on the helical gear being hobbed.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 1 teeth to 10000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 48 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the index ratio required.
- Get it right
- Count from the gear drawing.
What this means: Lead of gear L
- What it is
- Lead of the helix on the gear being hobbed.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1119.87076 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 index ratio and the feed correction.
- Get it right
- L = π × pitch diameter ÷ tan helix angle.
What this means: Feed per gear revolution F (nominal)
- What it is
- Nominal feed of the hob per revolution of the gear blank.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 50 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.889 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the index ratio required a little.
- Get it right
- The tool corrects it slightly to offset the index gear error.
What this means: Machine constant K
- What it is
- Index constant of the hobbing machine without a differential.
- Units and format
- Enter a plain number with no unit. The form accepts 0.000001 to 100000. 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
- The index ratio rises in proportion.
- Get it right
- Take it from the machine maker’s manual or index plate.
What this means: Threads on hob T
- What it is
- Number of threads (starts) on the hob.
- Units and format
- Enter a number in threads: threads. The form accepts 1 threads to 20 threads. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 threads as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The index ratio rises in proportion.
- Get it right
- Single-thread hobs are usual; double threads are used for roughing.
What this means: Feed gear constant M
- What it is
- Feed gear constant of the hobbing machine.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.905 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 feed gear ratio for the feed required.
- Get it right
- Take it from the machine maker’s manual.
What this means: Hands of gear and hob
- What it is
- Whether the gear and hob helices are of the same or opposite hand.
- Units and format
- Choose one of 2 options from the list: Same hand; Opposite hand.
- Example
- The form opens with “Same hand” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Changes the sign in the index ratio and feed formulas.
- Get it right
- Same hand uses the minus sign in the handbook formulas.
What this means: Hobbing direction
- What it is
- Whether the hob cuts conventionally or by climb hobbing.
- Units and format
- Choose one of 2 options from the list: Conventional hobbing; Climb hobbing.
- Example
- The form opens with “Conventional hobbing” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Changes the sign in the index ratio and feed formulas.
- Get it right
- Climb hobbing reverses the sign rule for the hands.
Index gears fitted
What this means: Index driving gear 1
- What it is
- First driving gear in the index change-gear train, as fitted on the hobbing machine.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 1 teeth to 1000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 34 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the index ratio obtained and so the feed correction.
- Get it right
- Enter its number of teeth; for a simple pair repeat equal gears in the second positions.
What this means: Index driving gear 2
- What it is
- Second driving gear in the index change-gear train, as fitted on the hobbing machine.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 1 teeth to 1000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 53 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the index ratio obtained and so the feed correction.
- Get it right
- Enter its number of teeth; for a simple pair repeat equal gears in the second positions.
What this means: Index driven gear 1
- What it is
- First driven gear in the index change-gear train, as fitted on the hobbing machine.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 1 teeth to 1000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 43 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the index ratio obtained and so the feed correction.
- Get it right
- Enter its number of teeth; for a simple pair repeat equal gears in the second positions.
What this means: Index driven gear 2
- What it is
- Second driven gear in the index change-gear train, as fitted on the hobbing machine.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 1 teeth to 1000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 67 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the index ratio obtained and so the feed correction.
- Get it right
- Enter its number of teeth; for a simple pair repeat equal gears in the second positions.
Feed gears fitted
What this means: Feed driving gear 1
- What it is
- First driving gear in the feed change-gear train, as fitted on the hobbing machine.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 1 teeth to 1000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 71 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the feed obtained and so the lead.
- Get it right
- Enter its number of teeth; for a simple pair repeat equal gears in the second positions.
What this means: Feed driving gear 2
- What it is
- Second driving gear in the feed change-gear train, as fitted on the hobbing machine.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 1 teeth to 1000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 75 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the feed obtained and so the lead.
- Get it right
- Enter its number of teeth; for a simple pair repeat equal gears in the second positions.
What this means: Feed driven gear 1
- What it is
- First driven gear in the feed change-gear train, as fitted on the hobbing machine.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 1 teeth to 1000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 106 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the feed obtained and so the lead.
- Get it right
- Enter its number of teeth; for a simple pair repeat equal gears in the second positions.
What this means: Feed driven gear 2
- What it is
- Second driven gear in the feed change-gear train, as fitted on the hobbing machine.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 1 teeth to 1000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 112 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the feed obtained and so the lead.
- Get it right
- Enter its number of teeth; for a simple pair repeat equal gears in the second positions.
What this means: Largest lead error you accept per 100 mm of lead
- What it is
- Largest lead error you accept for every 100 mm of lead.
- 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 0.01 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Fails the gear set-up when the lead error is larger.
- Get it right
- Take it from the lead (helix) tolerance on the gear drawing.
Method and formulas
- R = L ÷ (L − F) × K T ÷ N for gear and hob of the same hand (L + F for opposite hand; the rule reverses for climb hobbing).
- Obtainable index ratio Ri = (i1 i2) ÷ (i3 i4); error R − Ri.
- F = L (N Ri − K T) ÷ (N Ri); feed gear ratio F ÷ M (use K T − N Ri for opposite hand or climb hobbing).
- Feed fitted = M (f1 f2) ÷ (f3 f4); lead obtained L = F N Ri ÷ (N Ri − K T); error against the lead required.
- Example: the index ratio required is 0.6255; with the gears fitted the feed becomes 0.85446 mm and the lead 1,119.8 mm, 0.0057822 mm per 100 mm off.
Limitations
- For machines without a differential only; with a differential follow the machine maker’s lead gear formula.
- Machine constants K and M and the sign rule depend on the machine: check them against its manual.
- Find gear combinations close to the ratio with conjugate fractions or a ratio table.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Work out the index ratio for hobbing a helical gear
- Correct the feed to make up for the index gear error
- Check the lead obtained with the gears available
Who it is for
- Machinists and gear cutters
- Toolmakers
- Gear designers
What you get
- Index gear ratio required
- Index ratio obtained and its error
- Feed that compensates for the index error and its feed gear ratio
- Feed from the feed gears fitted
- Lead obtained and its error, with and without the feed correction
Interpreting the result
- Without the feed correction even a tiny index ratio error gives a large lead error.
- The feed correction is small; keep the feed gears close to the ratio required.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2208–2209. Topic reference; no source tables or recommended settings are reproduced.
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