Influence of the Geometric Module on the Tribological Behaviour of Technopolymer Gears
30 June 2026
In mechanical design, we often carry forward the knowledge acquired while working with steel. When a transmission must withstand sudden torque peaks or when one wants to increase the tooth root safety factor, the instinctive reaction is almost always the same: increase the module to enlarge the tooth and make it more robust.
However, when entering the world of technopolymers, this strategy can turn into a dangerous paradox: an oversized tooth is by no means synonymous with a longer service life. The concrete technical risk is finding a transmission that 'holds up' perfectly under the static load on paper, but fails rapidly in the field due to the loss of the profile geometry.
The reason lies in the kinematics of meshing. If we increase the module while keeping the centre distance or the number of teeth unchanged, the geometric dimensions of the tooth grow. This results in longer moment arms and, above all, a much higher sliding velocity (v_s) at the start and end contact points (critical points A and E of the line of action).
In plastic materials, wear is linked to the product p × v (contact pressure multiplied by sliding velocity) and to the heat generated by friction and hysteresis. Consequently, an excessive module can cause localised surface overheating that accelerates profile deterioration, completely nullifying the structural mechanical strength of the tooth itself.
Comparative Analysis: Small Module vs Large Module in POM-C Transmissions
To understand the impact of this choice, we can compare the stress behaviour of a pair of gears made of POM-C (Polyoxymethylene copolymer), keeping both the material and the applied torque constant. Unlike metals, where the module is chosen almost exclusively based on fracture resistance, with polymers the parameter to monitor is thermal deformation.
The international reference standard for calculating the load-bearing capacity of plastic gears is VDI 2736. A larger module undoubtedly offers a greater resistant cross-section at the root, reducing the bending stress (σ_F), but simultaneously extends the arc of action and increases specific sliding.
The following table clearly illustrates this practical correlation:
Technical Parameter | Small Module (e.g. 1.0) | Large Module (e.g. 2.5) | Operational Impact |
Bending Stress (σ_F) | Lower (reduced cross-section) | Higher (+150% approx.) | Resistance to impact loads |
Sliding Velocity (v_s) | Contained | High | Local heat generation |
Contact Ratio (ε_α) | High (more teeth in mesh) | Lower | Smoothness and quietness |
Thermal Efficiency | Better (less friction) | Critical (heat build-up) | Profile service life |
According to calculations derived from DIN 3990 adapted for polymers, the contact stress (Hertz pressure) p_H follows the well-known relationship:
p_H = Z_H · Z_E · √( F_t / (d₁ · b · u) · (u+1) )
On paper, a larger module allows for larger pitch diameters (d₁) or wider face widths (b), which could theoretically lower the contact pressure. In practice, however, the increase in sliding velocity (v_s) often pushes the surface temperature beyond the glass transition temperature (T_g) of the polymer, cancelling out the benefits of reduced pressure.
TCO Optimisation Through Geometric Balancing
Choosing the correct module is not merely a theoretical exercise, but directly influences the Total Cost of Ownership (TCO) of the production plant. An optimised module (generally in the range between 0.5 and 3.0) allows operation in a fully self-lubricating regime without ever reaching the critical surface melting point of the tooth.
The operational advantages of this balancing are clearly measured in three directions:
- Reduction of machine downtime: A gear with an excessive module tends to 'smear' material on the tooth flanks due to the extreme heat induced by sliding. Conversely, a correct module keeps the working temperature below 60–80°C (the limit value for POM-C), guaranteeing dimensional stability for thousands of service hours.
- Energy efficiency: Smaller modules exhibit considerably lower friction losses. In complex systems with multiple stages, this approach reduces the total resistant torque, resulting in lower electrical consumption of the motors.
- Elimination of external lubrication: Modern technopolymers such as PA6 + MoS₂ or POM are specifically chosen to operate dry. A balanced module minimises heat dissipation, allowing the material to operate within its native tribological limits, eliminating the need for greases or oils that could contaminate the products.
Physical Limits and Operating Envelope: When a Large Module Becomes Mandatory
Despite the great advantages of using small modules, there are insurmountable physical limits dictated by the intrinsic properties of the plastic.
If the tangential stress at the tooth root exceeds the yield strength of the technopolymer (which for PA6 is approximately 60–80 MPa at 23°C, and drops drastically as temperature increases), increasing the module becomes a structural obligation, irrespective of subsequent wear problems.
On the other hand, the use of high modules (m > 3.0) is strongly discouraged in transmissions operating at high speed (peripheral velocity > 3–4 m/s). The reason lies in the poor ability of polymers to dissipate heat by conduction: their thermal conductivity λ is only 0.2–0.4 W/mK, compared to 50 W/mK for steel. In these high-speed scenarios, if the load requires a high module but the heat generated is excessive, the 'bare' technopolymer shows its limits: it is necessary to switch to reinforced solutions or use metal inserts to facilitate heat dissipation.
At the opposite extreme, the adoption of very small modules (m < 0.5) introduces severe criticalities in mounting tolerances: even a minimal centre distance error can compromise meshing far more seriously than would occur with larger modules.
Frequently Asked Questions (FAQ)
Can increasing the module compensate for the absence of lubrication?
In practice, the opposite often occurs. A larger module increases sliding and, consequently, the heat generated. If no lubrication system is present to remove this heat, a large module risks degrading much more rapidly than a small one, which, although operating at slightly higher specific pressures, works at decidedly lower operating temperatures.
How does the module affect transmission noise?
In general, smaller modules allow more teeth to be inserted for a given gear diameter, increasing the so-called contact ratio (ε_α). This ensures that there is always at least one pair of teeth simultaneously in mesh, making the transmission considerably smoother and quieter. Large modules, conversely, tend to generate more vibrations due to the greater impact forces occurring at tooth entry.
Is it possible to produce gears with non-standard custom modules?
Certainly. When components are manufactured by injection moulding or CNC machining from bar stock, it is possible to optimise the module to non-standard values (for example, module 1.15). This flexibility allows for the correction of fixed centre distances or finding the perfect balance point between mechanical strength and wear, although the ISO standard remains always preferable to guarantee maximum interchangeability.
Technical Glossary
Module (m): The ratio between the pitch diameter of the gear and its number of teeth; it represents the fundamental parameter defining the geometric size of the tooth.
Sliding velocity (v_s): The relative velocity between tooth profiles during the meshing phase; maximum values occur at the extremities of the contact zone.
Contact ratio (ε_α): The average number of teeth simultaneously in contact and sharing the load during meshing.
Hertz pressure (p_H): The localised compressive stress generated in the narrow contact zone when two bodies with curved surfaces are pressed against each other.
Thermal hysteresis: The heat generated internally within the polymer material due to the continuous and cyclic mechanical deformations undergone during load application.