BIZOMAT MAKEOS · Gears
Internal Gear Drive Check (Proportions, Tooth Difference, Pinion Bending)
Will this pinion and internal gear mesh without interference, what are their proportions and centre distance, and is the pinion strong enough for the power?
Check of a spur pinion driving an internal (ring) gear: pitch diameters, centre distance, enlarged and conventional internal and outside diameters and the tooth-number difference against the minimum for the tooth form (as the internal gear proportions tool), the ratio and output speed, pinion torque and tangential force from the power, and the Lewis bending stress with the velocity factor (as the Lewis bending stress tool) against your allowable.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Module | mm | Module of both gears. |
| Internal gear teeth | Teeth on the internal gear. | |
| Pinion teeth | Teeth on the pinion. | |
| Tooth form | choice | Tooth form of the pair. |
| Load | ||
| Power | kW | Power transmitted. |
| Pinion speed | rpm | Speed of the pinion. |
| Face width | mm | Face width in mesh. |
| Lewis form factor of the pinion | Lewis form factor for the pinion tooth count and form (from your gear data). | |
| Tooth manufacture | choice | How the teeth are made (sets the velocity factor). |
| Allowable bending stress | MPa | Allowable bending stress of the pinion material. |
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: Module
- What it is
- The module shared by the pinion and the internal gear: pitch diameter divided by the number of 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 3 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Diameters and centre distance rise in proportion; bending stress falls as the module grows.
What this means: Internal gear teeth
- What it is
- The number of teeth on the internal (ring) gear, the gear with teeth cut on its inside.
- Units and format
- Enter a plain number with no unit. The form accepts 20 to 1000. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 72 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More ring teeth raise the ratio and the tooth-number difference, and lower the ring speed.
What this means: Pinion teeth
- What it is
- The number of teeth on the external pinion that drives the ring gear.
- Units and format
- Enter a plain number with no unit. The form accepts 8 to 1000. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 18 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More pinion teeth give a larger pinion pitch diameter and a lower tangential force.
What this means: Tooth form
- What it is
- The tooth form of the pair. It sets the minimum difference in tooth numbers between ring and pinion used in the interference check.
- Units and format
- Choose one of 3 options from the list: 20° full depth; 20° stub; 14½° full depth.
- Example
- The form opens with “20° full depth” selected as a worked example. Choose the option that matches your case.
- Get it right
- Use the form both gears are cut to; pinion and ring must match.
Load
What this means: Power
- What it is
- The power the pinion transmits to the ring gear, from the motor rating or the driven load.
- Units and format
- Enter a number in kW: kilowatts. The form accepts 0.000001 kW to 100000 kW. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 kW as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Torque, tangential force and bending stress rise in proportion to power.
What this means: Pinion speed
- What it is
- The rotational speed of the pinion.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 100000 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
- For the same power, a higher speed lowers torque and tangential force but raises the velocity factor.
- Get it right
- Pinion speed, not ring gear speed.
What this means: Face width
- What it is
- The width of the teeth that are actually in mesh, measured along the gear axis.
- 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 30 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Bending stress is inversely proportional to face width.
- Get it right
- If the ring is wider than the pinion, use the narrower width in contact.
What this means: Lewis form factor of the pinion
- What it is
- The Lewis form factor for the pinion, a dimensionless tooth-strength factor that depends on its tooth count and tooth form, from your gear data tables.
- Units and format
- Enter a plain number with no unit. The form accepts 0.05 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.31 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Bending stress is inversely proportional to it.
- Get it right
- Use the capital-Y Lewis factor (Y = π × y), not the lower-case y; mixing the two gives a stress π times too large or too small.
What this means: Tooth manufacture
- What it is
- How the teeth are made. The choice selects the velocity factor that increases the load for dynamic effects at the pitch-line speed.
- Units and format
- Choose one of 4 options from the list: Cast teeth; Cut or milled; Hobbed or shaped; Shaved or ground.
- Example
- The form opens with “Hobbed or shaped” selected as a worked example. Choose the option that matches your case.
What this means: Allowable bending stress
- What it is
- The bending stress you accept in the pinion teeth, from the material supplier, a gear standard or your design rules.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 100000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 150 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- Pitch diameters m Z; centre distance = m (Z_g − Z_p) ÷ 2; enlarged and conventional diameters and the tooth-difference rule (as the internal gear proportions tool).
- Torque = 9549 P ÷ n; tangential force = 2T ÷ pinion pitch diameter; output speed = n Z_p ÷ Z_g.
- σ = K_v F_t ÷ (b m Y) with the velocity factor for the manufacture (as the Lewis bending stress tool).
- Example: centre distance 81 mm; ring turns at 362.5 rpm; pinion bending 41.145 MPa.
Limitations
- Lewis bending only; surface durability (pitting) needs a separate check.
- Proportions follow the handbook rules for internal gearing; tip relief may still be needed.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check an internal gear drive for a turntable or slewing ring
- Size the pinion of a ring gear drive
- Avoid interference in internal gearing
Who it is for
- Gear designers
- Machine designers
- Design engineers
What you get
- Diameters, centre distance and tooth difference
- Ratio, torque and tangential force
- Pinion bending stress
Interpreting the result
- Internal gears share load over more teeth than external pairs, so the Lewis check is conservative.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2170–2171, 2131–2160. Topic reference; no source tables or recommended settings are reproduced.
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Open the Internal Gear Drive Check (Proportions, Tooth Difference, Pinion Bending) calculator