KEVOS® MAKEOS · Gears
Gear Pitting Geometry Factor I (Spur and Helical, Contact Ratios, Load Sharing)
For my external spur or helical gear pair, what pitting resistance geometry factor I does the AGMA method give, with the contact ratios and load sharing behind it, and does it support the value used in my rating?
Pitting resistance geometry factor I for an external spur or helical gear pair by the AGMA 908-B89 equations the handbook gives: standard and operating transverse pressure angles, base radii and base pitches, the distances along the line of action to the lowest and highest points of single tooth contact, the transverse and axial contact ratios, the minimum length of the lines of contact and the load sharing ratio for helical gears, the helical overlap factor for low axial contact ratio helicals, the radii of curvature of the profiles at the stress point and the factor I, compared with the value used in your rating.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Gear pair | ||
| Normal module | mm | Normal module of the pair (the transverse module for spur gears), from the gear drawing. |
| Pinion teeth | Number of teeth on the smaller gear of the pair. | |
| Gear teeth | Number of teeth on the larger gear; the method is for external gears only. | |
| Normal pressure angle | ° | Standard normal pressure angle of the cutting tool, from the drawing. |
| Helix angle (0 for spur) | ° | Standard helix angle at the reference diameter; enter 0 for spur gears. |
| Effective face width | mm | Face width over which the teeth are in contact, the narrower of the two gears less any end chamfers. |
| As made | ||
| Operating centre distance | mm | Centre distance at which the gears actually run, from the housing drawing. |
| Pinion outside diameter | mm | Outside (tip) diameter of the pinion as made, from the drawing or a measurement. |
| Gear outside diameter | mm | Outside (tip) diameter of the gear as made. |
| Rating | ||
| Geometry factor I used in the rating | Geometry factor I assumed in your pitting resistance rating, so this tool can confirm it. | |
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.
Gear pair
What this means: Normal module
- What it is
- The normal module: reference diameter ÷ teeth, measured normal to the teeth; for spur gears it is the ordinary module.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.1 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 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 length; I itself does not change with module for the same tooth numbers and proportions.
- Get it right
- Take it from the drawing or the cutter; for helical gears do not use the transverse module.
What this means: Pinion teeth
- What it is
- Teeth on the pinion, the smaller gear of the pair.
- 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 21 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 flatten the profile curvature and usually raise I.
- Get it right
- Count the teeth on the driving or smaller gear; the larger gear goes in the next box.
What this means: Gear teeth
- What it is
- Teeth on the gear, the larger member of an external pair.
- Units and format
- Enter a plain number with no unit. The form accepts 6 to 10000. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 55 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher ratio raises I towards the value for a rack.
- Get it right
- Count the teeth; it must be at least the pinion's count.
What this means: Normal pressure angle
- What it is
- Normal pressure angle of the cutting tool, at the reference diameter.
- 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 25° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger pressure angle gives larger radii of curvature and a higher I.
- Get it right
- Common values are 20° and 25°; take it from the drawing, not from a measurement.
What this means: Helix angle (0 for spur)
- What it is
- Helix angle at the reference diameter; zero for spur gears.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 45°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A helix angle adds axial overlap and load sharing, which can raise I considerably.
- Get it right
- Enter 0 for spur gears; for helicals use the drawing value, not the base helix angle.
What this means: Effective face width
- What it is
- Face width over which the teeth actually mesh, the narrower of the two gears less end chamfers.
- 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 40 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Matters for helical gears: more face width raises the axial contact ratio and load sharing.
- Get it right
- Do not use the wider gear's face width; only the overlapping width carries load.
As made
What this means: Operating centre distance
- What it is
- The centre distance at which the pair runs in its housing.
- 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 152 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 centre distance raises the operating pressure angle and shortens the contact.
- Get it right
- Use the housing's centre distance; for standard gears it is (n₁ + n₂) mₙ ÷ (2 cos ψ).
What this means: Pinion outside diameter
- What it is
- Outside (tip) diameter of the pinion as made.
- 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 92 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 tip extends the contact and moves the lowest point of single tooth contact.
- Get it right
- Measure it or take it from the drawing, including any addendum modification.
What this means: Gear outside diameter
- What it is
- Outside (tip) diameter of the gear as made.
- 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 228 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes where contact begins on the pinion flank and the contact ratio.
- Get it right
- Measure it or take it from the drawing; a short-addendum gear has a smaller tip.
Rating
What this means: Geometry factor I used in the rating
- What it is
- The geometry factor I assumed in your pitting resistance rating.
- Units and format
- Enter a plain number with no unit. The form accepts 0.001 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.12 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the pass or fail line; it does not change the calculated I.
- Get it right
- Read it from the rating calculation or the supplier's data sheet.
Method and formulas
- All lengths are divided by the normal module (unity normal module), as the method requires.
- Gear ratio m_G = n₂ ÷ n₁; R₁ = n₁ ÷ (2 cos ψ); transverse pressure angle φ = arctan(tan φn ÷ cos ψ); base radii R_b1 = R₁ cos φ, R_b2 = R_b1 m_G.
- Operating pressure angle φr = arccos((R_b2 + R_b1) ÷ C_r); base pitch p_b = 2π R_b1 ÷ n₁; normal base pitch p_N = π cos φn; base helix angle ψ_b = arccos(p_N ÷ p_b).
- C₆ = C_r sin φr; C₁ = C₆ − √(R_o2² − R_b2²); C₅ = √(R_o1² − R_b1²); C₂ = C₅ − p_b; C₄ = C₁ + p_b; Z = C₅ − C₁.
- Transverse contact ratio m_p = Z ÷ p_b; axial pitch p_x = π ÷ sin ψ; axial contact ratio m_F = F ÷ p_x (0 for spur).
- For helicals with m_F > 1: L_min from the fractional parts n_r of m_p and n_a of m_F (case I or II), m_N = F ÷ L_min, radii of curvature at the mean radius R_m1 = ½[R_o1 + (C_r − R_o2)], C_ψ = 1.
- For spur gears and helicals with m_F ≤ 1: m_N = 1, radii at the lowest point of single tooth contact ρ₁ = C₂, ρ₂ = C₆ − ρ₁, and C_ψ = [1 − m_F(1 − ρ_m1 ρ_m2 Z ÷ (ρ₁ ρ₂ p_N))]^0.5.
- Operating pinion pitch diameter d = 2 C_r ÷ (m_G + 1); I = cos φr C_ψ² ÷ [(1 ÷ ρ₁ + 1 ÷ ρ₂) d m_N].
- Example: a 21/55 spur pair at 25° has a contact ratio of 1.4822 and I = 0.12077, against 0.12 used in the rating.
Limitations
- External gears only: the handbook prints the curvature sum for external pairs; internal gears need the AGMA standard itself.
- Spur gears with a transverse contact ratio above 2 (high contact ratio) are outside this method.
- The bending strength geometry factor J is not calculated; the handbook refers to AGMA 908-B89 for it.
- Undercut pinions and tip relief change the active profile; check them with the gear maker.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Calculate I for a gear pair instead of reading a chart
- Check the I used in a pitting rating for a helical or profile-shifted pair
- See how face width and helix angle change load sharing
Who it is for
- Gear designers
- Mechanical design engineers
- Gearbox reviewers
What you get
- Gear ratio, transverse and operating pressure angles
- Line-of-action distances C1 to C6 and the active length
- Transverse and axial contact ratios
- Minimum length of contact lines and load sharing ratio
- Helical overlap factor and radii of curvature
- Pitting resistance geometry factor I against the value used
Interpreting the result
- I scales the contact stress: a larger I means a lower contact stress for the same load, so overestimating I overstates the pitting rating.
- For helical gears, longer face width (more axial overlap) raises load sharing and usually raises I.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3286–3289, 3295–3300. 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
Surface contact stress
What it covers: Estimate Hertzian contact stress between gear teeth, see how face width and size change it, and connect it to materials, hardening and lubrication.
Also in Helical gears and axial thrust, Centre distance and contact ratio
KEVOS® tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Gear Pitting Geometry Factor I (Spur and Helical, Contact Ratios, Load Sharing) calculator