Gear Technology: Basic Terms Explained Clearly

Gear technology is the foundation of modern mechanical engineering. Gears transmit torques reliably and with high efficiency. However, the large number of technical terms – module, pitch circle, involute gearing, profile shift – can initially seem overwhelming.

This guide explains the fundamental terms and concepts of gear technology in a practice-oriented way. Whether you are selecting a gear, sizing a gearbox, or specifying suppliers – these fundamentals are indispensable.

The Module: m = d/z

The module is a fundamental parameter of every gear. It is defined as the ratio of the pitch circle diameter to the number of teeth:

m = d / z

Where:

• m = module in millimeters
• d = pitch circle diameter in millimeters
• z = number of teeth (dimensionless)

The module literally determines all gear dimensions: tooth height, tooth width, addendum height, and root radius. Standardized modules are defined according to DIN 780: 0.5 | 0.75 | 1.0 | 1.25 | 1.5 | 2.0 | 2.5 | 3.0 | 4.0 | 5.0 | 6.0 | 8.0 | 10.0 | 12.0 | 16.0 | 20.0 mm (and others). The use of standard modules greatly simplifies calculation, manufacturing, and inventory management.

Practical example: A gear with z = 40 teeth and module m = 2.0 mm has a pitch circle diameter of d = m × z = 2.0 × 40 = 80 mm.

Pitch Circle and Tip Circle

To understand a gear geometrically, you must distinguish between two characteristic diameters:

Pitch Circle Diameter (d)

The pitch circle is the theoretical circle on which the tooth flanks roll and where the gears mesh with each other. The diameter is:

d = m × z

Tip Circle Diameter (d_a)

The tip circle is the outer diameter of the gear – where the tooth tips lie. The addendum height equals one module unit (ha = m). The tip circle diameter is:

d_a = (z + 2) × m

There is also the root circle (d_f), on which the tooth root transitions lie:

d_f = (z - 2.5) × m

These three diameters are critical for gear geometry, tooth flank contacts, and strength calculations.

Involute Gearing per DIN 3960

Involute gearing is the standard tooth form in modern mechanical engineering. The tooth flanks follow a mathematical involute – a curve generated when a string is unwound from a circle.

Advantages of involute gearing:

• Constant gear ratio: The contact always follows the same pressure line, so transmission is uniform.
• Tolerance insensitivity: Small manufacturing or assembly deviations have little effect on transmission. This is a major advantage over other tooth forms.
• Long service life: Uniform loading reduces wear and fatigue.
• Simple manufacturing: Involute gears can be produced with standard tools (hob cutters).

Involute gears are standardized according to DIN 3960. There are also older tooth forms (such as cycloidal gears), which are now only used in special applications.

The Pressure Angle

The pressure angle α is the angle between the tooth flank normal (pressure line) and the line of action at the tooth flank contact point. The standard value is α = 20° per DIN 3960.

The pressure angle of 20° was chosen because it offers an optimal compromise:

• Tooth strength: A larger pressure angle leads to wider tooth roots and higher bending strength.
• Wear and friction: A smaller pressure angle reduces sliding velocity and friction losses.
• Contact area: 20° is a practical compromise for moderate bearing stresses.

Other pressure angles such as 14.5° (older standard) or 25° (for special high-load gearboxes) are less common and require specialized manufacturing tools. 20° is the universal standard.

Profile Shift (x-Factor)

The profile shift x is a manufacturing parameter that optimizes the tooth flank contacts and load-carrying capacity of a gear. A shifted profile means that the hobbing tool does not work on the pitch circle but offset from it.

Effects of profile shift:

• Positive shift (x > 0): Strengthens the tooth roots and increases the tooth flank thickness. This is advantageous for small gears (small z), which would otherwise have pointed teeth.
• Negative shift (x < 0): Reduces the tooth root thickness. This is rare and only used for large gears.
• Center distance: Profile shift changes the required center distance, but can be compensated by oppositely shifted gear pairs.

The profile shift factor is calculated per DIN 3960. For standard gears without special requirements, x = 0 (no shift).

Spur Gears vs. Helical Gears

Two basic forms differ in the orientation of the teeth relative to the gear axis:

Spur Gears

The teeth are arranged parallel to the gear axis. Engagement is abrupt (all teeth engage simultaneously). This leads to lower cost but higher noise emissions and lower load capacity. Applications: conveyor technology, non-high-frequency drives, cost optimization.

Helical Gears

The teeth are arranged at an angle (helix angle β = 10–30°) to the axis. Engagement is gradual (teeth engage progressively). This enables higher torque, lower noise emission, and better wear characteristics. Disadvantage: Higher axial forces require stronger bearings. Applications: high-performance gearboxes, automotive transmissions, ring gear drives.

Internal Gearing

An internally toothed gear has teeth on the inside of a ring shape. The counterpart is a smaller externally toothed pinion running inside. Internal gears are often used in planetary gearboxes or ring gear drives.

Advantages of internal gearing:

• Compact design: Since the pinion runs inside, radial installation space is reduced.
• Higher gear ratio: Achievable with fewer teeth.
• Better load capacity: The larger contact area enables higher loading.

Internal gears require specialized manufacturing tools and are therefore more expensive. They are standardized according to DIN 3960 and DIN 3974.

Quality Grades per DIN 3961–3967

The manufacturing precision of gears is classified in quality grades 1–12 per DIN 3961–3967. Grade 1 is the highest precision (laboratory conditions), grade 12 is the lowest tolerance (rough casting state).

Higher quality grades are expensive (grade 6 costs approx. 2–3× more than grade 9), but are indispensable for zero-backlash gearboxes and high-speed drives. The choice of quality grade depends on the application, required service life, and control accuracy.