Calculator Input
Formula Used
Pitch diameter: d = m × z
Gear ratio: i = z2 / z1
Center distance: a = m × (z1 + z2) / 2
Outside diameter: do = d + 2m
Root diameter: dr = d - 2.5m
Circular pitch: p = πm
Pitch line velocity: v = πdn / 60
Torque: T = 9550P / n
Tangential force: Wt = 2000T / d
Radial force: Wr = Wt × tan φ
Lewis form factor: y = 0.154 - 0.912 / z
Bending stress: σb = Wd / (b × m × y)
Contact stress estimate: σH = ZE × √(Wd / (b × d × I))
Geometry factor estimate: I = cos φ × sin φ × i / (2 × (i + 1))
How to Use This Calculator
- Enter pinion teeth and gear teeth.
- Enter module, pressure angle, and face width.
- Add power, pinion speed, and load factors.
- Enter allowable bending and contact stress values.
- Press the calculate button.
- Review dimensions, forces, stress checks, and safety factors.
- Use CSV or PDF export for design records.
Example Data Table
| Case | Pinion Teeth | Gear Teeth | Module | Face Width | Power | Speed |
|---|---|---|---|---|---|---|
| Light conveyor | 20 | 60 | 3 mm | 30 mm | 5 kW | 1450 rpm |
| Workshop drive | 24 | 72 | 4 mm | 45 mm | 12 kW | 960 rpm |
| Slow machine | 18 | 54 | 5 mm | 55 mm | 8 kW | 520 rpm |
Understanding Spur Gear Design
A spur gear transfers rotary motion between parallel shafts. Its teeth are straight and easy to machine. Good design starts with tooth count, module, pressure angle, and face width. These values control size, strength, speed, and contact quality. This calculator turns those inputs into practical dimensions and checks. It gives pitch diameters, outside diameters, root diameters, base circles, center distance, velocity, torque, and forces.
Why Dimensions Matter
The module defines tooth size. A larger module gives thicker teeth and higher load capacity. It also increases gear diameter. The number of teeth sets ratio and pitch diameter. A low tooth count may create undercutting. A high tooth count can give smoother motion. Face width spreads load across the tooth. Designers often begin with eight to twelve times module for face width. Wider faces reduce stress, but they need better alignment.
Strength Checks
Spur gear teeth usually fail by bending fatigue or surface pitting. The bending estimate uses tangential load, face width, module, and a Lewis form factor. The contact estimate uses load, gear geometry, face width, diameter, and material elasticity. These checks are simplified. They are useful during early design. Final gears should follow a recognized standard and real material data.
Using Results Carefully
Use the results to compare options before making drawings. Increase module, face width, or material strength when safety factors are low. Reduce load factors only when the duty is truly smooth. Check bore size, keyway strength, shaft deflection, lubrication, heat, and noise. Confirm backlash and tolerances with manufacturing teams. The calculator is a design aid. It does not replace testing, inspection, or a qualified engineering review.
Practical Workflow
Start with the ratio and available space. Choose the pinion teeth first. Then select the gear teeth. Pick a module that gives a reasonable pitch diameter. Set face width from duty, alignment, and housing limits. Enter power and speed. Review tangential and radial forces. These forces help size shafts, bearings, keys, and fasteners.
Important Limits
Real gears also need standards, drawings, and inspection. Heat treatment can change allowable stress. Lubrication changes wear life. Accuracy grade changes noise and dynamic load. Use conservative factors for shock, dust, poor alignment, or uncertain data before final purchase release.
FAQs
What is a spur gear?
A spur gear has straight teeth parallel to the shaft axis. It transfers motion between parallel shafts with simple geometry.
What does module mean?
Module is the pitch diameter divided by tooth count. A larger module means larger teeth and usually higher strength.
Why is pressure angle important?
Pressure angle affects radial force, tooth shape, contact action, and bearing load. Common values include 20 degrees for many modern gears.
What is face width?
Face width is the gear tooth width across the gear. Wider faces spread load, but they need accurate alignment.
What is tangential force?
Tangential force is the useful force at the pitch circle. It transmits torque from one gear to the other.
What is bending stress?
Bending stress estimates tooth root loading. High bending stress can cause fatigue cracks near the tooth base.
What is contact stress?
Contact stress estimates surface pressure between mating teeth. High contact stress can cause pitting and wear.
Can I use this for final manufacturing?
Use it for preliminary design only. Final gears need standards, drawings, tolerances, material data, lubrication checks, and engineering review.