BIZOMAT MAKEOS · Gears
Spur Gear Mesh Interference Check (Contact Start Diameters and Contact Ratio)
Does contact on each gear of this spur pair start above its true involute form diameter, so there is no interference, and is the contact ratio enough?
Check of a standard spur gear pair for tip-to-root interference: the diameter on each gear where contact begins (the start of active profile) from the mating gear’s outside diameter (as the spur contact diameters tool), compared with the true involute form diameter each gear actually has after cutting, the margin above it and above the base circle, and the transverse contact ratio from the outside diameters (as the contact ratio tool for standard gears).
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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. |
| Pinion teeth | Teeth on the pinion. | |
| Gear teeth | Teeth on the gear. | |
| Pressure angle | ° | Pressure angle. |
| Pinion outside diameter (0 = standard) | mm | Actual outside diameter of the pinion (0 for standard m(z + 2)). |
| Gear outside diameter (0 = standard) | mm | Actual outside diameter of the gear (0 for standard). |
| Pinion true involute form diameter | mm | Diameter on the pinion below which the tooth is no longer a true involute (from the cutting tool or drawing). |
| Gear true involute form diameter | mm | True involute form diameter on the gear. |
| Least contact ratio | Least transverse contact ratio you accept. |
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 tooth size of both gears in the pair: the pitch diameter divided by the number of teeth. Gears that mesh must have the same module.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.2 mm to 50 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Check the drawing; do not confuse module with diametral pitch (teeth per inch of pitch diameter).
What this means: Pinion teeth
- What it is
- The number of teeth on the smaller gear of the pair, the pinion. Its flank near the root is where interference is most likely.
- Units and format
- Enter a plain number with no unit. The form accepts 6 to 500. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Gear teeth
- What it is
- The number of teeth on the larger gear of the pair, the gear that meshes with the pinion.
- Units and format
- Enter a plain number with no unit. The form accepts 6 to 2000. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Pressure angle
- What it is
- The angle between the line of action and the tangent to the pitch circles, set by the cutting tool. Both gears must share it.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 14.5° to 30°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the transverse pressure angle of the cutter, as on the drawing.
What this means: Pinion outside diameter (0 = standard)
- What it is
- The measured or drawn tip diameter of the pinion. It sets where contact begins on the gear flank and the length of contact. Type 0 to use the standard tip diameter.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 5000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger pinion tip starts contact lower on the gear flank and raises the contact ratio.
- Get it right
- Use the diameter actually turned on the blank if it differs from the standard.
What this means: Gear outside diameter (0 = standard)
- What it is
- The measured or drawn tip diameter of the gear. It sets where contact begins on the pinion flank. Type 0 to use the standard tip diameter.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger gear tip starts contact lower on the pinion flank and raises the contact ratio.
- Get it right
- Use the diameter actually turned on the blank if it differs from the standard.
What this means: Pinion true involute form diameter
- What it is
- The diameter on the pinion below which the tooth is no longer a true involute because the cutter has formed the root fillet. Contact must start at or above it.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 5000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 18.5 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It is neither the root diameter nor the base circle; get it from the drawing or the cutting tool data.
What this means: Gear true involute form diameter
- What it is
- The diameter on the gear below which the tooth is no longer a true involute. Contact from the pinion tip must start at or above it.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 38.3 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It is neither the root diameter nor the base circle; get it from the drawing or the cutting tool data.
What this means: Least contact ratio
- What it is
- The smallest transverse contact ratio you accept: the average number of tooth pairs in contact as the gears turn.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 2.5. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from your design rules or the gear standard you work to.
Method and formulas
- From the mating outside diameter, the roll angle at the start of contact gives the start-of-active-profile diameter on each gear (as the spur contact diameters tool).
- No interference if the start diameter is at or above the true involute form diameter (and above the base circle).
- Contact ratio ε = [√(r_a1² − r_b1²) + √(r_a2² − r_b2²) − a sin φ] ÷ (π m cos φ) with a = m (z₁ + z₂) ÷ 2.
- Example: contact starts at 18.878 mm on the pinion (form 18.5 mm) and 38.67 mm on the gear (form 38.3 mm); contact ratio 1.6352.
Limitations
- Standard centre distance and unshifted teeth; shifted gears need the working pressure angle.
- Tip rounding and chamfers reduce the effective outside diameter.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a pinion for interference with a large gear
- Set the form diameter on a gear drawing
- Check the effect of a reduced outside diameter
Who it is for
- Gear engineers
- Design engineers
- Gear inspectors
What you get
- Contact start diameter on each gear
- Margin over the form diameter and base circle
- Contact ratio
Interpreting the result
- If contact starts below the form diameter, reduce the mating outside diameter or use a profile shift.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2155–2157, 2131–2160. Topic reference; no source tables or recommended settings are reproduced.
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Open the Spur Gear Mesh Interference Check (Contact Start Diameters and Contact Ratio) calculator