Contact ratio and dynamic contact ratio: the flexibility of polymers
A plastic gear that distributes load better than a steel one isn't a paradox. It's what happens when the flexibility of the material works in your favor, changing the contact ratio during operation instead of keeping it fixed.
What the contact ratio is
The contact ratio measures how many tooth pairs work simultaneously during meshing. In spur gears it typically ranges between 1.4 and 1.8, which means that between one and two teeth transmit load at the same moment.
It is calculated as the ratio between the length of the line of action and the base pitch of the teeth. The base pitch develops on the base circle of the involute profile, the most widespread profile because it guarantees smooth transmission without sliding.
The value must always stay above 1 and, under normal conditions, between 1.2 and 2.0. Below 1 there is no continuity of contact: each tooth bears the load alone at the moment it passes.
| Parameter | Description |
|---|---|
| Contact ratio | Average number of tooth pairs in simultaneous mesh |
| Typical values | 1.4 – 1.8 for spur gears |
| Calculation | Length of line of action / base pitch of teeth |
| Most used profile | Involute, for smooth transmission without sliding |
| Importance | Load distribution, reduced stress and noise, system stability |
Increasing the number of teeth lengthens the contact line and raises the contact ratio: more teeth share the work, less stress on each one.
What changes with technopolymers: the dynamic contact ratio
POM and PA6 have a markedly lower elastic modulus than steel. This means that, under load, the teeth flex. It isn't a flaw: it's the mechanism that turns the contact ratio from a static value into a dynamic one.
A POM-C gear with a theoretical contact ratio of 1.6 can reach, during operation, a dynamic value close to 2. In practice you're distributing the load over nearly two full teeth instead of one.
The flexibility comes from the molecular structure of the polymer: chains of monomers bonded together so as to absorb deformation. This elasticity doesn't break the tooth, it lets it yield the minimum necessary to spread the peak over more contact points.
The dynamic contact ratio is not a fixed parameter: it varies with the load level, temperature and lubrication conditions. For reliable sizing, calculate it under the most demanding operating conditions, not unloaded.
Advantages over metal gears
This flexibility brings concrete consequences:
- Load distribution. Load distributed over more teeth. Each tooth bears a fraction of the total load instead of the whole peak. Service life increases.
- Reduced noise. The transition from one tooth pair to the next is more gradual: less impact, less noise.
- Tolerance to assembly errors. Small inaccuracies in center distance or profile are compensated by the flexing of the material, without translating into concentrated wear.
- Light weight and chemical resistance. Lower weight than metals, no corrosion problems in humid or chemically aggressive environments.
| Aspect | Technopolymers | Metals |
|---|---|---|
| Elastic modulus | Much lower (flexibility) | High (stiffness) |
| Load distribution | Over more teeth thanks to flexing | Concentrated on few teeth |
| Noise | Low, gradual transition | Generally higher |
| Chemical resistance | Excellent | Variable, subject to corrosion |
| Weight | Light | Heavy |
| Typical applications | Packaging, medical, automotive, aeronautics | Heavy machinery, high precision |
What to keep in mind during design
The dynamic contact ratio explains why technopolymer gears handle impulsive loads well: flexibility spreads the peaks over more teeth before any single one reaches its limit. Components custom-designed with CAD software and produced by injection molding let you optimize weight, strength and stiffness from the drawing stage, opening the way to metal replacement in many applications.
The dynamic contact ratio is not an unlimited safety margin. If you exceed the material's elastic limit, deformation becomes permanent and the tooth breaks. Always size considering maximum loads, operating temperature and system stability under the most demanding conditions.
If you're designing with CAD, the 3D models of Stagnoli gears are available on TraceParts: download the geometry you need directly and integrate it into your project.