Six Steps from Specifications to Decision
A gear is selected systematically in six steps—type of gearing → gear ratio/number of teeth → module → material → gear quality → standard or custom:
- Select gear type – parallel shafts → spur gear (straight/helical); shafts at an angle → bevel gear; high reduction ratio, self-locking if necessary → worm gear; rotation → linear motion → rack and pinion.
- Determine the gear ratio and number of teeth—i = z₂/z₁ is derived from the speeds; below the limit number of teeth z ≈ 17 (20°), undercut is a risk; remedy: profile shift.
- Determine the module—m = d/z—based on torque, material strength, and center distance; give preference to standard modules from DIN 780 Series 1.
- Select a material—determine the load, environment, and quantity: steel, plastic, sintered metal, or bronze (see the previous unit).
- Specify gear quality—in accordance with DIN 3961/ISO 1328—as precisely as necessary, but no more.
- Standard or custom-made? – Catalog part if the module, number of teeth, bore, and material are suitable; custom-made if the center distance is precisely specified or special materials are required.
Special case: rack and pinion
A rack-and-pinion drive converts the rotation of the pinion into linear motion. The reference circle diameter of the pinion is calculated, as usual, from the module and the number of teeth, and for each revolution of the pinion, the carriage travels exactly the circumference of this reference circle:
d₀ = m · z
s = π · d₀ = π · m · z
d₀ = pitch diameter of the pinion (mm) · s = feed per revolution (mm) · m = module · z = number of teeth on the pinion
Standard or custom-made?
A catalog part is the most cost-effective choice when the module, number of teeth, bore, and material from the standard product line are a good fit—immediately available, proven, and with no tooling costs. A custom-made part, on the other hand, is worthwhile if the center distance is precisely specified and no standard combination fits, if special materials or surface treatments are required, if the quantity justifies an optimized geometry, or if the gear must be integrated into an existing machine.
Mnemonic
Worked example
Given
A rack with a module of m = 2.5 mm is driven by a pinion with z = 16 teeth.
Calculation
- Pitch diameter: d₀ = m · z = 2.5 · 16 = 40 mm
- Feed per revolution: s = π · d₀ = π · 40 ≈ 125.7 mm
The actual feed force required also includes acceleration, slope loss, guide friction, and any process forces—the rack-and-pinion calculator is available to calculate these.
Knowledge check
Answer all three questions, then click "Check". From 2 of 3 correct answers, the unit counts as completed. You can retry at any time.
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