Gearboxes, actuators and other systems that employ polymer gears are being used in an ever-increasing number of applications. From the automotive industry, where small actuators make the vehicles more comfortable and aid autonomous driving , to high-performance e-bikes used for mountain biking. The increase in the number of applications is due to the improved performance of the polymers and their inherent properties, such as low weight, ease of manufacture, low cost, low noise, minimal vibrations, suitability for dry lubrication and freedom of design . Thermoplastics, which can be recycled, are the main type of polymers used for gears. However, due to the lower mechanical performance of polymer materials when compared to traditional gear materials, i.e., metals, the lifetime and transmitted power of polymer gears are two of their key disadvantages. Here we discuss some important aspects when evaluating polymer materials for a more reliable and safe design of gears.
Guidelines for current design calculations
Polymer gears can fail in many ways (Figure 1), e.g., flank failure, thermal degradation, melting, extensive tooth deformation, pitting, root fatigue failure, as well as abrasive and adhesive wear, leading to tooth thinning, a lack of mechanical support and deformation. Several of these failures are known from traditional metal gears, which have been the subject of research for 200 years. Therefore, there are also several standards that guide the designer through the metal-gear design process. However, some failures are different or very pronounced, like tooth thinning and deformation, and this is especially so for those related to thermal effects . Since the thermal stability of polymers is much lower than that of metal gears, and the modulus of elasticity for thermoplastics is more than 100-times lower, the existing standards and norms cannot be applied to polymer-gear design. In 1981 there was a VDI guideline established, i.e., VDI 2545, which tried to consider this difference; however, it was soon revoked. In 2014, a new guideline VDI 2736  was published. Along with the design guideline for cylindrical and worm gears, it includes guidelines for selecting characteristic material values of different polymers to design gears for the two prime failure modes (dry running), i.e., fatigue life and wear coefficients.
Accordingly, this guideline is comprehensive, but there are still some drawbacks, especially at the practical level where the data for predictive models are generated, i.e., testing. If the data are not correct, the prediction will also not be correct. So, there needs to be a strong emphasis on obtaining relevant and reliable data. One of these issues is the very limited data on the fatigue life and wear coefficient of polymer gears, including their wide variation. There are many different polymers that can be used for gears today, the molecular structure, crystallinity, mechanical and thermal properties of which vary a lot. And these cannot be predicted without proper validation. Moreover, these materials are often reinforced with different fibers, typically glass or carbon, which means an even greater variety of materials being available. In addition, the wear coefficient of the materials varies a lot, since typically the data are not obtained under gear-meshing conditions, but rather in model tribology tests, which are associated with many parametric details that are often not considered, but can be overcome with an appropriate tribological approach.
The result of all this is that gear design with polymer materials is not fully reliable due to the lack of specific Wöhler curves and the correct wear coefficients, so the calculation of the gear’s lifetime is uncertain. However, it must be stressed that both the prime failure mechanisms, i.e., fatigue and wear, go hand in hand, and both need to be understood and properly considered for a safe and reliable prediction of a polymer gear’s lifetime.
Figure 1: Different failure modes for polymer gears: (a) thermal degradation, (b) root fatigue, (c) flank fatigue, (d) tooth deformation and flank wear.
Root fatigue-life evaluation
To design a cost-efficient polymer gear with sufficient root safety for a specific application the S-N curve of the chosen polymer material needs to be well defined. This means that the S-N curve shouldvbe measured using an appropriate number of different load conditions, typically four or more, in a relevant range, from low to high values, and under different, well-controlled environmental conditions (temperature, humidity, lubrication). Since the polymers are highly temperature dependent, the root fatigue-life evaluations need to be conducted at a constant material temperature, otherwise the mechanical properties change over time and the root fatigue is a consequence of unknown and continuously varying polymer temperatures, which equates to unknown properties . Therefore, such an S-N curve has limited meaning and cannot be used for an accurate gear-design calculation. In addition, the thermal expansion of polymer gears changes the backlash between the gears, and this will affect the results, calling for adjustments in different environmental conditions. This means the test temperature should be constant to keep the backlash constant, which is the only way to achieve a properly predicted fatigue life at various temperatures in an application. Therefore, a well-controlled and constant gear temperature is a pre-condition for a reliable and repeatable fatigue-life testing of polymer gears.
Another parameter to consider in an root-fatigue evaluation is the load, or the torque. Too high a load can cause severe deformation, which, among other obvious issues, leads to a change in the load sharing between the teeth , while too low a load can lead to a high number of cycles at which the wear of the polymer gear flanks can become dominant, shielding the effect of root fatigue. For a reliable performance, these phenomena need to be appropriately analyzed for a broad range of loads and controlling, simultaneously, the fatigue and wear behavior and the separating effects of the two mechanisms.
Evaluation of wear coefficient
VDI 2736  recommends that the wear coefficient (volume loss divided by load and sliding distance) used in the prediction of a gear’s wear life is obtained from pin-on-disc tests. While the wear-coefficient equation is trivial, the data used are far from this, and the methodology to obtain the data is not prescribed. As a result, it is the source of well-known large variations. The key variables start with the materials, i.e., the contacting material pair, which can be polymer/polymer or steel/polymer, or even polymer/steel, which is a different case, and all these dramatically change the thermal conditions at the surfaces. Another major mistake made in the evaluation of polymer materials and their performance is using machined (hobbed) samples instead of injection-molded samples. Especially when pin-on-disc tests are replaced with “real” gear tests to obtain the wear coefficient, sometimes the gears are produced by milling to obtain better tolerances, but molded or machined gears are not comparable in their essence, so machined gears or pin-on-disc samples are broadly irrelevant for any application where molded gears are used.
The second set of variables is contact related: sliding velocity, the roughness of both materials, contact pressure, temperature and moisture, mechanical and thermal material properties, etc. These are broadly recognized, and the differences make results difficult to compare, and sometimes they are not even reported. However, these variables are easily described and when properly reported they can be at least noted as a possible source of variation, and the results somehow understood. However, a larger source of discrepancy and possibly more important for variations is an often entirely neglected fact that contact conditions in pin-on-disc are pure sliding, which is different to a gear-meshing contact that changes from sliding to rolling and back to sliding in a single meshing contact. In addition, here we also need to consider the load relief due to multiple gear contacts and changes to the direction of the relative sliding velocity, which changes the stress conditions completely. These parameters are of great importance, but unfortunately seldomly considered, and so they introduce a major source of uncertainty, errors in the data and poorly understood behavior and discrepancies from predictions.
In accordance with the above, the wear mechanisms acting on a gear vary along the meshing line (Figure 2). For example, at least three different wear mechanisms  can be observed for injection-molded POM gears that meshed with a steel pinion. Near the tip and root area, abrasive sliding wear is present due to the predominant sliding. In the single contact area, deformation ridges were observed due to the higher contact pressure at a lower slide-to-roll ratio (SRR). The third mechanism was observed in the pith-line region, where together with high pressures, only rolling motion is present, causing a welldefined deformation layer with many pit-shaped wear features. For all these reasons, the values of the wear coefficient obtained from the pin-on-disc (pure sliding) tribological tests can vary by up to two or three orders of magnitude from the wear obtained in real gear in operation .
Fortunately, today we can overcome these problems with proper pin-on-disc or ball-on-disc devices with variations of the SRR and tribological methodology, separating effects and understanding the mechanisms and sources of failures and discrepancies, which can lead us to a better understanding of failures and better predictive models. However, at a final stage, real scale tests using gears under properly designed experiments are needed to validate, not only the root fatigue failures, but also the wear mechanisms, which is a well-established methodology in all successful wear and tribology studies for countless applications, apart from gears. Therefore, the wear performance can also be well predicted, even though no obvious empirical or analytical computational model exists.
Figure 2: SEM images of different wear mechanisms from an injection-molded POM gear after meshing with a steel pinion for 10 million cycles .
The recent advances in polymer materials have brought many possibilities for lightweight, polymergearbox design; however, design engineers need to work with reliable data and models to be able to exploit all the design possibilities that polymer materials bring. Therefore, both root fatigue and the wear of the polymer materials, occurring jointly in most applications, and also affecting secondary sources of failure, like tooth thinning, deformation, fractures and thermal degradation, need to be evaluated in properly designed model wear tests and a real-scale gear test rig and with well-thought-out methodologies that must include several fully controlled parameters.
Prof. dr. Mitjan Kalin
Head of the Laboratory for Tribology and Interface Nanotechnology – TINT, University of Ljubljana,
Editor of the Lubrication Science, Wiley, and Deputy-President of the International Tribology Council.
Sebastjan Matkovič, MSc
Researcher and PhD student in the Laboratory for Tribology and Interface Nanotechnology – TINT, University of Ljubljana.
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