BIZOMAT MAKEOS · Gears
Inch Spur Gear Pair Check (Diametral Pitch Proportions, Pinion Bending)
For this diametral-pitch spur gear pair, what are the pitch and outside diameters and centre distance, and is the pinion strong enough for the horsepower?
Check of a spur gear pair made to inch diametral-pitch proportions: pitch and outside diameters and centre distance for the tooth system (as the spur gear dimensions by diametral pitch tool), the ratio and gear speed, pinion torque and tangential force from the horsepower, and the Lewis bending stress with the velocity factor for the way the teeth are made (as the Lewis bending stress tool, worked in metric with module = 25.4 ÷ P), against your allowable.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Diametral pitch | 1/in | Diametral pitch (teeth per inch of pitch diameter). |
| Pinion teeth | Teeth on the pinion. | |
| Gear teeth | Teeth on the gear. | |
| Tooth system | choice | Tooth system of the pair. |
| Load | ||
| Power | hp | Power transmitted in horsepower. |
| Pinion speed | rpm | Speed of the pinion. |
| Face width | in | Face width in mesh, in inches. |
| Lewis form factor of the pinion | Lewis form factor for the pinion tooth count and system (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: Diametral pitch
- What it is
- The diametral pitch of both gears: the number of teeth per inch of pitch diameter. A higher diametral pitch means smaller teeth.
- Units and format
- Enter a number in 1/in: threads per inch. The form accepts 0.000001 1/in to 200 1/in. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 1/in as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher diametral pitch gives smaller gears and smaller teeth, raising the bending stress.
- Get it right
- Diametral pitch is not circular pitch; module in millimetres = 25.4 ÷ diametral pitch.
What this means: Pinion teeth
- What it is
- The number of teeth on the pinion, the smaller driving gear.
- Units and format
- Enter a plain number with no unit. The form accepts 5 to 1000. 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.
- Effect on the result
- More pinion teeth give a larger pinion pitch diameter and a lower tangential force.
What this means: Gear teeth
- What it is
- The number of teeth on the larger driven gear.
- Units and format
- Enter a plain number with no unit. The form accepts 5 to 5000. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 45 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the ratio, gear speed and centre distance; it does not change pinion stress.
What this means: Tooth system
- What it is
- The tooth system both gears are cut to. It sets the addendum used for the outside diameters.
- Units and format
- Choose one of 3 options from the list: 20° full depth; 14½° full depth; 20° stub.
- Example
- The form opens with “20° full depth” selected as a worked example. Choose the option that matches your case.
- Get it right
- Both gears must be cut to the same system; the Lewis factor must also be for this system.
Load
What this means: Power
- What it is
- The power the pinion transmits, in horsepower, from the motor rating or the driven load.
- Units and format
- Enter a number in hp: hp. The form accepts 0.000001 hp to 100000 hp. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 hp 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.
- Get it right
- This is mechanical horsepower (745.7 W), not metric horsepower; kW must be converted.
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 1200 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, higher speed lowers torque and tangential force but raises the velocity factor.
- Get it right
- Pinion speed, not gear speed.
What this means: Face width
- What it is
- The width of the teeth in mesh, measured along the gear axis, in inches.
- Units and format
- Enter a number in in: inches. The form accepts 0.000001 in to 100 in. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.25 in 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 gears differ in width, 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 system, 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 0.32 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 tooth 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.
- Get it right
- Enter megapascals even though the gear dimensions are in inches.
Method and formulas
- Pitch diameter = N ÷ P; outside diameter = pitch diameter + 2 × addendum; centre distance = (N₁ + N₂) ÷ 2P (as the spur gear dimensions by diametral pitch tool).
- Torque = hp × 745.7 ÷ ω; tangential force = 2T ÷ pitch diameter.
- Module = 25.4 ÷ P; σ = K_v F_t ÷ (b m Y) (as the Lewis bending stress tool).
- Example: pitch diameters 2 and 4.5 in, centre distance 3.25 in; pinion bending 67.981 MPa.
Limitations
- Lewis bending only; check surface durability separately.
- Standard addendum proportions for the tooth system.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a replacement inch gear pair
- Rate an existing DP gear set for a new motor
- Work out blank sizes for inch gears
Who it is for
- Maintenance engineers
- Gear cutters
- Design engineers
What you get
- Pitch and outside diameters and centre distance
- Ratio, torque and tangential force
- Pinion bending stress
Interpreting the result
- If the pinion is overstressed, a wider face or a coarser pitch (smaller P) lowers the bending stress.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2131–2160, 2249–2251. Topic reference; no source tables or recommended settings are reproduced.
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Open the Inch Spur Gear Pair Check (Diametral Pitch Proportions, Pinion Bending) calculator