Involute profile and pressure angle

Have you ever disassembled a gear after a failure and found the teeth worn unevenly, with oblique streaks on the flanks? In most cases, the problem isn't the chosen material or the transmitted torque: it's the tooth profile. The geometry with which the teeth touch during rotation determines how much load passes from one flank to the other, how much energy is lost to friction, and how long the gear lasts over time.

The involute profile: the industrial standard

The tooth profile defines the geometric shape of the flank, the surface that comes into contact with the tooth of the opposite wheel. The three main profiles are: involute, cycloid and special profiles. Almost all industrial transmissions use the involute profile, for three concrete reasons: it is produced with simple tools (rack cutters or straight-profile cutters), it tolerates small variations in center distance without altering the transmission ratio, and it maintains continuous contact between the teeth that reduces vibration and noise.

The cycloid profile gives better strength at the tooth root, but requires special curved tools and precise center distances: it is used where precision is the main constraint, such as in watchmaking. Special profiles are designed case by case for custom applications, for example in robotics, where the parameters fall outside the standards.

The pressure angle

The pressure angle is the angle between the direction of the contact force between teeth and the tangent to the pitch circle at the contact point. In more direct terms: it determines how much of the force is transmitted usefully (tangential component, which turns the wheel) and how much generates radial thrust on the supports (component that loads bearings and shafts).

The standard values are 14.5° and 20°. The 20° is the most used in modern designs. If you work with high loads, small-module teeth or moderate speeds, consider 25°: it widens the tooth base, increases load capacity, but generates greater radial forces on the supports. Keep this in mind when sizing the bearings.

Why the involute profile works well with technopolymer gears

Technopolymer gears, such as those in PA, POM-C or PK, offer light weight, corrosion resistance and quiet operation. The involute profile pairs well with these materials for a precise geometric reason: the contact point moves along the line of action, a fixed straight line, which concentrates contact in the pitch-circle zone. At that point, sliding between the flanks is minimal and friction is lower.

This is particularly useful with technopolymers, which can deform slightly under load. The involute profile absorbs these deformations better than other profiles, keeping meshing more regular.

When to choose the involute profile

The involute profile is generally the right choice when:

• The application involves dry running, without lubrication
• The environment is chemically aggressive (paired with high chemical-resistance technopolymers)
• Noise is a design constraint (robotics, medical devices, packaging)
• You want a self-centering system with minimal backlash
• Speed is medium-high with moderate loads

Dimensional accuracy and ISO quality

The involute profile works well only if it is made well. Standard ISO 1328-1 classifies gear quality on a scale from 0 to 12, where lower values correspond to greater precision.

For standard industrial mechanisms, ISO 6-7 (equivalent to AGMA Q8-Q9) is the common reference. For precision automation and medical applications, ISO 4-5 is required.

CNC and injection molding cover different needs. CNC allows tight tolerances on the single part, suited to prototypes, small runs and critical profiles, with a direct effect on backlash (the gap between tooth flanks at rest) and meshing quality. Injection molding is more cost-effective on large volumes and, on reinforced materials, orients the fibers along the tooth geometry to the benefit of strength; keep in mind that shrinkage and thermal deformation affect the final tolerances, to be verified after molding with the same instrumentation as CNC.

Key parameters for design

The module is the parameter that defines tooth size. Two gears can mesh only if they have the same module, exactly like screws and nuts: you don't mix different sizes. The fundamental relation is: d = m × Z, where d is the pitch-circle diameter, m the module and Z the number of teeth.

As a starting point for sizing:

• Use a 20° pressure angle as the default
• Switch to 25° for high loads, small teeth or moderate speeds
• For light-to-medium applications, module from 1 to 5 mm; larger modules for industrial loads
• Respect a minimum tooth count of 17 with a 20° pressure angle, to avoid undercut (interference at the tooth base that reduces its strength). If you go below this value, use profile shift

The standard tooth height has an addendum equal to the module and a dedendum equal to 1.25 times the module. The fillet at the tooth root must be sized to avoid stress concentrations, especially in technopolymers where fatigue strength is lower than in steels.

When to modify the standard profile

Modifications to the standard profile become necessary in certain specific cases:

• Tooth count below the minimum (undercut to be avoided with profile shift)
• Elastic deformation of the technopolymer under load that alters meshing
• Non-standard center distance imposed by the mechanical design
• High quietness requirements or contact ratio greater than 1.4

These measures improve the durability, precision and function of technopolymer gears, providing an adequate response even under demanding operating conditions.

If you're designing with CAD, the 3D models of Stagnoli gears are available on TraceParts: you can download the geometry you need directly and integrate it into your project.