Transmission ratio in technopolymer gears: calculation and choice of tooth count
What the transmission ratio is
The transmission ratio is the ratio between the rotational speed of the input gear and that of the output gear. For two meshing wheels, it's calculated by dividing the number of teeth of the driven wheel by that of the driving one:
Where $n_1$ is the speed of the driving wheel, $n_2$ that of the driven one, $Z_1$ and $Z_2$ the respective tooth counts, $d_1$ and $d_2$ the pitch diameters.
If the ratio is greater than 1, you get a speed reduction and an increase in output torque. If it's less than 1, speed increases and torque decreases. You can express it as a fraction, a decimal number or a colon-separated pair: a 20-tooth pinion with a 60-tooth driven wheel gives a 3:1 ratio, that is, the output speed is one third of the input.
Some catalogs and software use the inverse convention, dividing the driving teeth by the driven ones. Always specify whether the ratio indicates reduction, multiplication or inverse kinematic ratio, to avoid interpretation errors.
Why in technopolymers the calculation isn't enough
With metal gears, once you've calculated the geometric ratio, the system behaves predictably. With technopolymers you can't stop there.
The effective ratio can vary based on temperature, thermal expansion, moisture absorption, applied load and wear over time. The transmission ratio is also a ratio between pitch diameters: any dimensional change, even small, alters the real behavior of the system.
On top of that, friction generates heat that polymers dissipate less quickly than metals. This affects durability and behavior under continuous load, especially at high peripheral speed:
Where v is the peripheral speed, d the pitch diameter and n the rotational speed in rpm.
In technopolymers, underestimating the dimensional change with temperature leads to insufficient clearances and a risk of seizing. Always calculate the nominal ratio, then check under the real operating conditions.
Torque, speed and power
The relation between angular speed and torque is direct: at equal power, reducing speed increases the transmitted torque. Torque depends on the tangential force and the pitch radius:
In technopolymers these values aren't static. Elastic deformation under load, thermal variations and progressive wear make them fluctuate during operation. Keep this in mind when you size the system.
Willis's rule for epicyclic systems
In epicyclic (or planetary) reducers, the wheels don't rotate around fixed axes: part of the system is carried by the planet carrier. In these cases, Willis's rule lets you calculate the ratio in the various operating configurations:
Where ωA and ωB are the angular speeds of two wheels, ωC the planet-carrier speed, ZA and ZB the respective tooth counts.
In technopolymer systems, Willis's rule describes the ideal behavior. The real system can deviate from it due to deformation, backlash, wear and thermal variations: this deviation is called ratio error, and it's the difference between the theoretical position and the actual position of the driven gear.
To limit it: size the tooth backlash as a function of material, temperature and moisture; evaluate reinforced materials such as PA6+GF for greater dimensional stability; check dimensions and clearances after environmental conditioning.
How many teeth to choose
The number of teeth affects strength, quietness, durability, precision and the risk of interference (the abnormal contact between teeth that leads to seizing or accelerated wear).
With a 20° pressure angle, the minimum number to avoid undercut is about 17 teeth. You can go down to 14-17 teeth using shifted profiles, but it requires accurate case-by-case verification.
A pinion with few teeth increases the risk of interference, reduces the resistant section and accelerates wear. In technopolymers this aspect is more critical than in metals: the lower stiffness of the material can cause additional deformation under load. If you need a small pinion, consider increasing the module, using shifted profiles or switching to a stiffer material.
The module and the face width are chosen together. A small module allows more teeth but reduces the robustness of the single tooth. A large module increases robustness but also the footprint and the inertia. A wide face distributes the load, but in technopolymer it can retain heat and generate non-uniform pressure along the tooth.
Which material for which application
The choice of material changes the bending strength and the tribological behavior of the tooth:
- PA6+GF (glass-fiber reinforced polyamide): highest mechanical strength, good for high loads.
- POM-C (polyoxymethylene): preferable when dimensional stability is the priority and loads are moderate.
- PK (polyketone): suited to chemically aggressive or high-humidity environments.
All three offer light weight, corrosion resistance and the option to run without lubrication: characteristics that make them suited to sectors such as food, chemical and medical.
The optimal module for a pair of technopolymer gears isn't derived from geometric calculation alone. Load, speed, lubrication, temperature and expected service life all come into play. In many cases experimental tests show critical pairings different from the estimated ones, even among materials with similar nominal characteristics. Use simulations to orient yourself, but always verify in the field.
If you're sizing a technopolymer transmission and aren't sure of the tooth count or the right module for your case, write to the technical office: we assess load, material and operating conditions together.