BIZOMAT MAKEOS · Gears
Spur Gear Set Design Check
Will this spur gear set carry the power for bending and pitting, and what face width does it really need?
One-pass design check of an external spur gear pair: geometry, pitch-line speed, torque and tangential load, contact ratio, undercut check, tooth bending stress (AGMA form with geometry factor J) and contact stress (Hertz with elastic and zone factors) against your allowables, with the face width each criterion requires.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Duty | ||
| Power | kW | Power transmitted. |
| Pinion speed | rpm | Pinion speed. |
| Overload factor | Overload (application) factor for the driver and load. | |
| Load distribution factor | Face load distribution factor for alignment and face width. | |
| Dynamic factor (0 = Barth for cut gears) | Dynamic factor; 0 uses the Barth factor (6.1 + v) ÷ 6.1 for cut gears. | |
| Geometry | ||
| Pinion teeth | Pinion tooth count. | |
| Gear teeth | Gear tooth count. | |
| Module | mm | Module. |
| Face width | mm | Face width in mesh. |
| Pressure angle | ° | Pressure angle. |
| Bending geometry factor J | Bending geometry factor for the pinion (AGMA 908 or software). | |
| Materials | ||
| Elastic modulus (both gears) | GPa | Elastic modulus of the gear materials. |
| Poisson’s ratio | Poisson’s ratio. | |
| Allowable bending stress | MPa | Allowable bending stress adjusted for life and reliability. |
| Allowable contact stress | MPa | Allowable contact stress adjusted for life and reliability. |
| Required bending safety factor | Safety factor required on bending. | |
| Required contact safety factor | Safety factor required on contact. | |
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.
Duty
What this means: Power
- What it is
- The power the gear pair must transmit through this mesh in normal running, taken at the pinion.
- Units and format
- Enter a number in kW: kilowatts. The form accepts 0.000001 kW to 100000 kW. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7.5 kW as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Tangential load, bending stress and the face width needed for bending all rise in proportion to power.
- Get it right
- Allow for shocks and overloads with the overload factor, not by raising the power as well.
What this means: Pinion speed
- What it is
- The rotational speed of the pinion, the smaller gear, while it transmits the power entered.
- 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 1450 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 a higher speed lowers torque and tooth load, but raises the Barth dynamic factor when that is used.
- Get it right
- Pinion speed, not gear speed; the gear turns slower by the tooth ratio.
What this means: Overload factor
- What it is
- A multiplier on the tooth load for shocks and overloads from the driving machine and the driven load, from the application tables of AGMA 2001 or ISO 6336.
- 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
- Bending stress rises in proportion to it and contact stress with its square root.
- Get it right
- This factor multiplies the load; do not also add the overload into the power.
What this means: Load distribution factor
- What it is
- A multiplier for uneven load sharing across the face width, caused by misalignment, shaft deflection and wide faces, from the gear standard.
- 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
- Bending stress rises in proportion to it and contact stress with its square root.
What this means: Dynamic factor (0 = Barth for cut gears)
- What it is
- A multiplier for the extra dynamic tooth load caused by tooth spacing errors and pitch-line speed, from the gear standard for your accuracy grade.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 5. 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
- Bending stress rises in proportion to it and contact stress with its square root.
- Get it right
- 0 uses the Barth factor (6.1 + v) ÷ 6.1 for cut gears; enter your own value for ground or high-accuracy gears.
Geometry
What this means: Pinion teeth
- What it is
- The number of teeth on the pinion, the smaller gear of the pair.
- Units and format
- Enter a plain number with no unit. The form accepts 8 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.
- Effect on the result
- At the same module more pinion teeth give a larger pinion, a lower tooth load and lower stresses.
- Get it right
- Too few teeth cause undercut: the tool warns when z₁ is below 2 ÷ sin² φ.
What this means: Gear teeth
- What it is
- The number of teeth on the larger gear; with the pinion teeth it fixes the ratio u = z₂ ÷ z₁ and the centre distance.
- Units and format
- Enter a plain number with no unit. The form accepts 8 to 2000. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 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 raises the ratio and centre distance; contact stress falls slightly as the ratio rises.
What this means: Module
- What it is
- The module of the gear pair: pitch diameter divided by number of teeth, which sets the size of the teeth.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 50 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 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 module enlarges the gears and teeth and lowers both bending and contact stress.
- Get it right
- Both gears must share one module; a diametral pitch gear has m = 25.4 ÷ P.
What this means: Face width
- What it is
- The face width in mesh: the length of tooth contact measured along the gear axis.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 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
- Bending stress falls in proportion to face width and contact stress with its square root.
- Get it right
- Use the width actually in contact, which is the narrower of the two gears.
What this means: Pressure angle
- What it is
- The pressure angle of the tooth profile, between the line of action and the tangent to the pitch circle, common to both gears.
- 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 pressure angle of the hob or cutter standard the gears are cut with.
What this means: Bending geometry factor J
- What it is
- The AGMA bending geometry factor for the pinion teeth, which accounts for tooth shape, load position and stress concentration at the root.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 0.7. 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 J.
- Get it right
- Take it from AGMA 908 or gear software for your tooth numbers and pressure angle; it is not the Lewis form factor.
Materials
What this means: Elastic modulus (both gears)
- What it is
- The elastic modulus of the gear material, taken as the same for pinion and gear, used in the elastic coefficient for contact stress.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 1000 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 206 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Contact stress rises with the square root of the modulus; bending stress does not use it.
- Get it right
- In GPa, not MPa; take it from the material data sheet.
What this means: Poisson’s ratio
- What it is
- Poisson’s ratio of the gear material, the lateral contraction per unit axial strain, used in the elastic coefficient.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 0.5. 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.
What this means: Allowable bending stress
- What it is
- The bending stress the gear material can carry at the tooth root, adjusted for the required life and reliability, from AGMA 2001 or ISO 6336 data for the material and heat treatment.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 3000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The bending safety factor is directly proportional to it.
What this means: Allowable contact stress
- What it is
- The surface contact (pitting) stress the gear material can carry, adjusted for life and reliability, from the gear standard for the material and hardness.
- 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 1100 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The contact safety factor is directly proportional to it; the face width needed for contact falls with its square.
What this means: Required bending safety factor
- What it is
- The minimum safety factor you require against tooth bending fatigue, set by your design code, customer or company practice.
- 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 1.5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- It does not change the stresses; a higher requirement raises the face width needed for bending in proportion.
What this means: Required contact safety factor
- What it is
- The minimum safety factor you require against surface pitting of the tooth flanks.
- 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 1.2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The face width needed for contact rises with the square of this factor.
Method and formulas
- d = m z; a = (d₁ + d₂) ÷ 2; v = π d₁ n₁ ÷ 60,000; F_t = 2 T₁ ÷ d₁.
- Contact ratio = [√(r_a1² − r_b1²) + √(r_a2² − r_b2²) − a sin φ] ÷ (π m cos φ); undercut-free pinion needs z₁ ≥ 2 ÷ sin² φ.
- Bending σ_F = F_t K_o K_v K_H ÷ (b m J).
- Contact σ_H = Z_E Z_H √[F_t K_o K_v K_H (u + 1) ÷ (b d₁ u)], with Z_E = √[E ÷ 2π(1 − ν²)] and Z_H = √[2 ÷ (sin φ cos φ)].
- Face width needed: bending ∝ 1 ÷ b, contact ∝ 1 ÷ √b.
- Example: 7.5 kW at 1450 rpm on a module 3, 20/60 pair needs 27.71 mm of face width.
Limitations
- External spur gears of the same material; helical and internal gears need their own factors.
- Factors and allowables come from AGMA 2001 or ISO 6336 for your gears.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a new spur gear pair for a motor and ratio
- Check an existing pair against a power increase
- Decide whether module or face width must grow
Who it is for
- Gear designers
- Design engineers
- Mechanical engineers
What you get
- Geometry, speed, torque and tangential load
- Bending and contact stresses with safety factors
- Face width needed for each criterion
Interpreting the result
- If contact governs, a harder material or larger pinion helps most; if bending governs, a larger module does.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2131–2156, 3304–3320. Topic reference; no source tables or recommended settings are reproduced.
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