BIZOMAT MAKEOS · Gears
Spur Gear Pitting Resistance Power Rating (AGMA)
How much power can this spur gear pair transmit before pitting governs?
Allowable transmitted power for pitting resistance by the AGMA power rating formula (metric form), with the external or internal spur gear geometry factor I calculated from the pressure angle and ratio, the dynamic, size, load-distribution, surface and application factors, and the allowable contact stress with its life and hardness factors.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Pinion speed | rpm | Speed of the pinion. |
| Net face width | mm | Net face width in contact. |
| Pinion operating pitch diameter | mm | Operating pitch diameter of the pinion. |
| Gear ratio (gear ÷ pinion teeth) | Gear ratio (always 1 or more). | |
| Gearing | choice | External or internal mesh, for the geometry factor. |
| Pressure angle | ° | Operating transverse pressure angle. |
| Geometry factor I | choice | Calculate I for standard spur gears (load sharing ratio 1), or enter it from AGMA 908. |
| Geometry factor I (entered) | Geometry factor for pitting resistance. | |
| Dynamic factor C_v (≤ 1) | Dynamic factor in the older AGMA form (1 or less). | |
| Size factor C_s | Size factor. | |
| Load distribution factor C_m | Load distribution factor. | |
| Surface condition factor C_f | Surface condition factor. | |
| Application factor C_a | Application (overload) factor. | |
| Allowable contact stress number | MPa | Allowable contact stress number for the material and heat treatment (use the lower of pinion and gear). |
| Life factor C_L | Life factor for the number of cycles. | |
| Hardness ratio factor C_H | Hardness ratio factor (gear only). | |
| Elastic coefficient C_p | √MPa | Elastic coefficient (191 √MPa for steel on steel). |
| Temperature factor C_T | Temperature factor. | |
| Reliability factor C_R | Reliability factor. | |
| Power to transmit | kW | Power you need to transmit. |
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: Pinion speed
- What it is
- The rotational speed of the pinion, the smaller gear of the pair.
- 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 1500 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The allowable power is directly proportional to pinion speed in this formula.
- Get it right
- Use the pinion speed, not the gear speed; they differ by the gear ratio.
What this means: Net face width
- What it is
- The net face width of the teeth in contact: the axial length over which the pinion and gear actually mesh.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 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
- The allowable power is directly proportional to the net face width.
- Get it right
- If one gear is wider, use the narrower face; leave out chamfers.
What this means: Pinion operating pitch diameter
- What it is
- The operating pitch diameter of the pinion, set by the actual centre distance of the gear pair.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 5000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The allowable power rises with the square of the pinion pitch diameter.
- Get it right
- At standard centre distance it equals the reference pitch diameter; use the pinion, not the gear.
What this means: Gear ratio (gear ÷ pinion teeth)
- What it is
- The gear ratio: number of teeth on the gear divided by the number on the pinion. Used to calculate the geometry factor I.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 100. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Always 1 or more: divide the larger tooth count by the smaller. Internal sets need a ratio above 1.
What this means: Gearing
- What it is
- Whether the mesh is external, two gears meshing outside each other, or internal, a pinion inside a ring gear. It changes the geometry factor.
- Units and format
- Choose one of 2 options from the list: External; Internal.
- Example
- The form opens with “External” selected as a worked example. Choose the option that matches your case.
- Get it right
- Ignored when you enter the geometry factor I yourself, except that internal sets still need a ratio above 1.
What this means: Pressure angle
- What it is
- The operating transverse pressure angle of the mesh, used to calculate the geometry factor I for standard spur gears.
- 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.
- Get it right
- Use the operating angle, which differs from the cutter angle if the centre distance is not standard. Not used when I is entered.
What this means: Geometry factor I
- What it is
- Whether the tool calculates the geometry factor I for standard spur gears with full load sharing, or uses a value you enter from AGMA 908.
- Units and format
- Choose one of 2 options from the list: Calculate for standard spur gears; Enter I.
- Example
- The form opens with “Calculate for standard spur gears” selected as a worked example. Choose the option that matches your case.
- Get it right
- Enter I for helical gears or non-standard tooth forms; the calculated form suits standard spur gears only.
What this means: Geometry factor I (entered)
- What it is
- The pitting resistance geometry factor I, taken from AGMA 908 or gear design software, used only when you choose to enter it.
- Units and format
- Enter a plain number with no unit. The form accepts 0.01 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The allowable power is directly proportional to I.
- Get it right
- Ignored when the calculate option is selected.
What this means: Dynamic factor C_v (≤ 1)
- What it is
- The dynamic factor in the older AGMA form, 1 or less, that reduces the rating for tooth impact caused by gear accuracy and pitch-line speed.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.8 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The allowable power is directly proportional to Cv.
- Get it right
- In this older form it multiplies the rating; newer AGMA editions use a Kv of 1 or more that divides. Do not mix the two.
What this means: Size factor C_s
- What it is
- The size factor, allowing for non-uniform material properties in large teeth, from the AGMA standard.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 3. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The allowable power is inversely proportional to Cs.
- Get it right
- Take it from the standard you rate to; it divides the rating.
What this means: Load distribution factor C_m
- What it is
- The load distribution factor, allowing for uneven load across the face width from misalignment, deflection and lead errors.
- 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 1.3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The allowable power is inversely proportional to Cm.
- Get it right
- It grows with face width and poor mounting; take it from the AGMA standard for your mounting and accuracy.
What this means: Surface condition factor C_f
- What it is
- The surface condition factor, allowing for surface finish, residual stress and work hardening effects on pitting.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 3. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The allowable power is inversely proportional to Cf.
- Get it right
- Take it from the AGMA standard; it divides the rating.
What this means: Application factor C_a
- What it is
- The application or overload factor, allowing for shock and uneven loading from the driving and driven machines.
- 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 1.25 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The allowable power is inversely proportional to Ca.
- Get it right
- Choose it for both the prime mover and the driven machine from the AGMA standard or gearbox maker.
What this means: Allowable contact stress number
- What it is
- The allowable contact stress number for the gear material and heat treatment, from the AGMA material tables or the supplier.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 5000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The allowable power rises with the square of Sac.
- Get it right
- Rate pinion and gear with their own values and use the lower result, as the guide says.
What this means: Life factor C_L
- What it is
- The life factor, which adjusts the allowable contact stress for the number of load cycles the teeth will see.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 3. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The allowable power rises with the square of CL.
- Get it right
- Take it from the AGMA life curve for the required cycles; it is squared in the rating.
What this means: Hardness ratio factor C_H
- What it is
- The hardness ratio factor, which raises the gear’s capacity when a harder pinion work-hardens it. It applies to the gear only.
- Units and format
- Enter a plain number with no unit. The form accepts 0.5 to 2. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The allowable power rises with the square of CH.
- Get it right
- Use 1 when rating the pinion; take the gear value from the AGMA standard.
What this means: Elastic coefficient C_p
- What it is
- The elastic coefficient, which depends on the elastic modulus and Poisson’s ratio of the pinion and gear materials.
- Units and format
- Enter a number in √MPa: √MPa. The form accepts 0.000001 √MPa to 1000 √MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 191 √MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The allowable power falls with the square of Cp.
- Get it right
- Take it from the AGMA standard for your material pair; the guide quotes the steel-on-steel value.
What this means: Temperature factor C_T
- What it is
- The temperature factor, allowing for operating oil or gear blank temperatures that reduce the material’s capacity.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 3. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The allowable power falls with the square of CT.
- Get it right
- Take it from the AGMA standard for your operating temperature; it is squared in the rating.
What this means: Reliability factor C_R
- What it is
- The reliability factor, which adjusts the rating for the chance of failure you accept.
- Units and format
- Enter a plain number with no unit. The form accepts 0.5 to 3. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The allowable power falls with the square of CR.
- Get it right
- Take it from the AGMA standard for the reliability you need; it is squared in the rating.
What this means: Power to transmit
- What it is
- The power the gear pair must transmit in service, compared with the allowable power for pitting.
- Units and format
- Enter a number in kW: kilowatts. The form accepts 0 kW to 1000000 kW. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 kW as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- It changes only the ratio and verdict, not the allowable power.
- Get it right
- Use the transmitted power at the pinion; overloads are covered by the application factor, not here.
Method and formulas
- Geometry factor (spur, m_N = 1): I = cos φ sin φ ÷ 2 × m_G ÷ (m_G ± 1), + for external, − for internal gears.
- P_ac = n_p F ÷ 1.91 × 10⁷ × I C_v ÷ (C_s C_m C_f C_a) × [d S_ac C_L C_H ÷ (C_p C_T C_R)]² kW, with F and d in mm and S_ac in MPa (handbook formula 5a).
- Example: a 60 mm pinion, 30 mm face at 1500 rpm rates 13.795 kW for pitting.
Limitations
- Spur gears without helix; helical gears need the load sharing ratio in I.
- Rate both pinion and gear with their own S_ac C_L C_H and use the lower.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Rate a spur gear pair for power
- Check a gear set against a motor power
- Compare face width or material options for durability
Who it is for
- Gear designers
- Design engineers
- Maintenance engineers
What you get
- Geometry factor I
- Allowable power for pitting
- Service factor against the required power
Interpreting the result
- Pitting capacity rises with the square of pinion diameter and allowable stress, but only linearly with face width.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3304–3313. Topic reference; no source tables or recommended settings are reproduced.
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Open the Spur Gear Pitting Resistance Power Rating (AGMA) calculator