KEVOS® MAKEOS · Gears
Spur Gear Profile Checker Settings (Significant Diameters, Roll Angles, TIF, HPSTC, Undercut)
For a pair of spur gears at standard centre distance, where are the true involute form, contact, lowest and highest single-tooth-contact diameters on each gear, what roll angles do I set on the involute checker, is the hob tip radius allowed and is any tooth undercut?
Every significant diameter of a spur gear pair at standard centre distance by the handbook’s three-step and two-step formulas: contact diameter (cos A = N cos φ ÷ Do P, tan b = tan φ − (N ÷ n)(tan A − tan φ), dc = n cos φ ÷ P cos b), contact ratio by three formulas, lowest point of single tooth contact (tan c = tan a − 2π ÷ n), highest point (tan d = tan b + 2π ÷ n), the maximum hob tip radius rc = (0.785398 cos φ − b sin φ) ÷ (1 − sin φ), the undercut limit (b − rc) ÷ sin φ + rc ≤ 0.5 n sin φ, the true involute form diameter tan e = tan φ − (4 ÷ n)[(b − rc) ÷ sin 2φ + rc ÷ 2 cos φ], the base radius and the roll angle at each point (tan × 57.2958) for the involute checker.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Module m (25.4 ÷ P) | mm | Module of both gears; for a diametral pitch P it is 25.4 ÷ P. |
| Pressure angle φ | ° | Pressure angle of the gears and the hob. |
| Teeth in pinion n | teeth | Number of teeth in the pinion. |
| Outside diameter of pinion do | mm | Outside diameter of the pinion as made. |
| Teeth in gear N | teeth | Number of teeth in the mating gear. |
| Outside diameter of gear Do | mm | Outside diameter of the gear as made. |
| Tooth system and hob | ||
| Dedendum constant b (dedendum = b ÷ P) | Dedendum constant of the tooth system: 1.25 when the dedendum is 1.25 ÷ P. | |
| Hob tip radius constant rc (radius = rc ÷ P) | Tip radius of the hob or rack as a constant times the module: 0.30 when the radius is 0.30 ÷ P. | |
| Least contact ratio you accept | Least contact ratio you accept for the drive. | |
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 m (25.4 ÷ P)
- What it is
- Module of the pinion and gear, the pitch diameter per tooth in millimetres.
- 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 2.54 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Scales every diameter, tooth thickness and centre distance.
- Get it right
- For an inch diametral pitch P, enter 25.4 ÷ P.
What this means: Pressure angle φ
- What it is
- Pressure angle of the gears and the hob at the standard pitch circle.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 10° to 35°. 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.
- Effect on the result
- Changes the base circles and every involute angle.
- Get it right
- 20° is the usual standard; 14½° and 25° are also used.
What this means: Teeth in pinion n
- What it is
- Number of teeth in the pinion, the smaller gear of the pair.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 5 teeth to 10000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 23 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 pinion diameters and its undercut limit.
- Get it right
- Count the teeth on the drawing or the part.
What this means: Outside diameter of pinion do
- What it is
- Outside (tip) diameter of the pinion as it is made.
- 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 63.5 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets where contact ends on the pinion and starts on the gear.
- Get it right
- Standard is (n + 2) × module; measure it on an odd-tooth gear with care.
What this means: Teeth in gear N
- What it is
- Number of teeth in the mating gear of the pair.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 5 teeth to 10000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 31 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 gear diameters and its undercut limit.
- Get it right
- Count the teeth on the drawing or the part.
What this means: Outside diameter of gear Do
- What it is
- Outside (tip) diameter of the mating gear as it is made.
- 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 83.82 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets where contact starts on the pinion.
- Get it right
- Standard is (N + 2) × module.
Tooth system and hob
What this means: Dedendum constant b (dedendum = b ÷ P)
- What it is
- Dedendum of the tooth system as a multiple of the module.
- Units and format
- Enter a plain number with no unit. The form accepts 0.000001 to 3. 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
- A deeper root lowers the true involute form diameter.
- Get it right
- Enter 1.25 for a dedendum of 1.25 ÷ P (1.25 module); 1.35 for shaved or ground teeth.
What this means: Hob tip radius constant rc (radius = rc ÷ P)
- What it is
- Tip radius of the hob or rack cutter as a multiple of the module.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger radius raises the TIF diameter and reduces undercut.
- Get it right
- Enter 0.30 for a tip radius of 0.30 ÷ P; 0 for a sharp-cornered hob.
What this means: Least contact ratio you accept
- What it is
- Least contact ratio you accept for this drive.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 5. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.4 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 pair when the contact ratio is lower.
- Get it right
- The handbook suggests not less than about 1.4 for power gears, 1.15 at the very least.
Method and formulas
- cos A = N m cos φ ÷ Do; tan b = tan φ − (N ÷ n)(tan A − tan φ); dc = n m cos φ ÷ cos b; the same with the gears swapped gives a, B and Dc.
- mf = N (tan A − tan B) ÷ 2π = n (tan a − tan b) ÷ 2π = (√(Ro² − Rb²) + √(ro² − rb²) − C sin φ) ÷ (π m cos φ).
- LPSTC: tan c = tan a − 2π ÷ n, tan C = tan A − 2π ÷ N; HPSTC: tan d = tan b + 2π ÷ n, tan D = tan B + 2π ÷ N; diameter z m cos φ ÷ cos of the angle.
- rc (max) = (0.785398 cos φ − b sin φ) ÷ (1 − sin φ); no undercut when (b − rc) ÷ sin φ + rc ≤ 0.5 z sin φ.
- tan e = tan φ − (4 ÷ z)[(b − rc) ÷ sin 2φ + rc ÷ (2 cos φ)]; dTIF = z m cos φ ÷ cos e.
- Base radius z m cos φ ÷ 2; roll angle at each point = its tangent × 57.2958°.
- Example: the pinion’s TIF diameter is 55.069 mm below its contact diameter of 55.411 mm, and the contact ratio is 1.6262.
Limitations
- The contact formulas assume the gears run at the standard centre distance (n + N) m ÷ 2.
- The undercut and TIF formulas apply only to standard gears hobbed with the hob rolling on the gear’s pitch diameter.
- Profile tolerances on the checker chart come from the gear’s quality class, not from these settings.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set an involute profile checker to the significant points of a spur gear
- Check that the true involute form diameter lies below the contact diameter
- Check a hob tip radius and whether the teeth will be undercut
Who it is for
- Gear inspectors
- Machinists and gear cutters
- Gear designers
What you get
- Contact diameter on each gear
- Contact ratio by three formulas
- Lowest and highest points of single tooth contact
- True involute form diameter on each gear
- Maximum hob tip radius and the undercut limit
- Base radius and roll angles for the involute checker
Interpreting the result
- The TIF diameter must be smaller than the contact diameter, or the mating tip runs into the fillet.
- Roll angles increase from TIF to outside diameter; set the checker’s base radius first.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2155–2160. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Useful alongside · KEVOS® original book
Centre distance and contact ratio
What it covers: Calculate the standard centre distance and the transverse contact ratio, and see how a centre distance error changes the pressure angle and overlap.
Also in Undercut and profile shift
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