When designing plastic gears, engineers mostly rely on the VDI 2736 guideline. It is a very helpful document for the plastic gear calculation, but it has some shortcomings. That is understandable, since it was written almost 10 years ago and knowledge about certain relevant effects was not available at that time.
The research and development of plastic gears has increased significantly in the last years, focusing on different fields like strength calculation, gear temperatures, wear, and manufacturing, to name just a few. It would be important to update the new guideline or standard with the latest findings from the field of plastic gears.
This paper gives a short overview of the topics, which are very important for the plastic gear design, however they are currently not considered in the VDI 2736.
Contact ratio under load
Plastic materials have much smaller elasticity modulus versus strength ratio compared to steel, which results in higher tooth deflection under load. Because of bigger deflection of the teeth, the path of contact is prolonged at the beginning and end of meshing. This can cause higher load capacity, however, can also cause higher noise and vibrations.
The VDI 2736-2 is currently considering only the unloaded contact length for the strength calculation. It would make sense to consider the actual contact ratio under load also in the strength calculation of plastic gears. Some research in this area was performed by the FZG . The authors proposed an improved equation for the calculation of the contact ratio factor. With a modified equation, the tooth root stress calculation seems more accurate compared to the one currently used in the VDI 2736-2.
Availability of SN (Woehler) curves for plastic materials
VDI 2736-2 contains 6 materials with measured SN curves for the tooth root or/and flank strength calculation. The SN curves are based on the VDI 2545 and were measured prior to 1981. There is an evident lack of up-to-date plastic gear fatigue data. Currently, the largest public database of SN curves for plastic materials is in available in the commercial software package KISSsoft (total of 82 materials, 44 with measured root SN curve and 10 with measured flank SN curve) .
There are numerous testing facilities (Bochum, Erlangen, Ljubljana, Munich, Padova, …) capable of measuring the SN curves according to procedures described in the VDI 2736-4. It would be important to include additional fatigue data in the future guideline or standard for plastic gears. This would give the gear engineers a bigger material database to work with. Beside just measuring the root and/or flank fatigue data, the influence of reinforced materials and internally lubricated materials could also be evaluated.
The VDI 2736-2 contains equations to calculate root and flank temperature of plastic gears. However, the calculation method is not well accepted by the engineers, as it can give unreliable results . The temperature calculation factors are only available for a few material combinations, further limiting its use. Since plastic gears are very sensitive to temperature, a reliable gear temperature model is required. The existing model would have to be improved and generalized (if possible). There are research results available in the scientific community regarding the temperature of plastic gears [4, 5].
Measuring the wear factor
Wear of plastic gears is an important topic, especially for dry-running gears. The most influential parameter for the calculation is the wear factor, which depends on the material combination, loading conditions, temperature, roughness, … Until now, the recommended wear factors in the VDI 2736 are based on pin-on-disc measurements. But recent studies have shown that the difference between the wear factor measured on pin-on-disc and the one measured on gears can be quite significant . It would be important to establish a more precise methodology to reliably measure wear factors, also creating a wear factor database within a new guideline or standard.
Effect of lubricant on the tooth root fatigue failure
The effect of a lubricant on the tooth root strength of plastic gears is not included in the VDI 2736-2. The root SN curves from the VDI 2736-2 are assumed to be valid for all lubrication regimes (oil, grease, dry running). Theoretically, if the temperature of the gears is the same and there is no substantial wear, the root strength of the plastic gears should be similar in all lubrication cases (the difference being the coefficient of friction). However, there can be a significant difference in cycles to failure between dry running and oil lubricated gears – for a factor of 2x (at the same loading conditions and at the same temperature). The effect of lubricant on the tooth root strength of the gears is very important and must be considered more precisely in future formulae for strength assessment.
Swelling of plastic material
Especially for PA based materials, water/humidity absorption is an important factor. It causes 2 different effects: decrease of the mechanical properties as well as an increase in size. As described in the DIN 3967, the relative water/humidity absorption can be considered in the operating backlash calculation through the following relations: the increase in size of the unreinforced plastic gears is 1/3 (for reinforced 1/12) of the relative water absorption in vol %. For a new guideline or a standard, it would be important to document the expansion factors for different materials and different environmental conditions, thus enabling the users a more precise methodology for the calculation of operating backlash.
There are further interesting research topics in the field of plastic gears. To name just a few: the effect of fiber alignment in the root area of the gears, the effect of cold line on the strength of the gears, the effect of injection moulding parameters on the quality of the gears, difference in strength between cut and injection moulded gears, ageing of plastic materials and its effect on the strengths. Some of the topics are currently under research and could be included in the future plastic gear guideline or standard.
The research of plastic gears is in full swing, with a variety of topics under research at different institutes around Europe and elsewhere. The new scientific results, which are giving us a more in depth understanding of plastic gears, could be included in the future plastic gear guideline or standard. There is no doubt that a new guideline or standard on plastic gears can be created, but it would require a big effort from all the involved parties. A new guideline or standard would be a great achievement, helping to bring the field of plastic gears forward. To conclude with the words of Lao Tzu: “A journey of a thousand miles begins with a single step”.
This topic will be presented in detail at the International Conference on High Performance Plastic Gears 2021, which will be held on 15-17 September 2021 in Garching, near Munich.
Dr. A. Pogačnik, Bauhar s.p., Bled, Slovenia
Dr. Pogačnik is a mechanical engineer with 10+ years of experience in the field of plastic gears.
Dr. U. Kissling, KISSsoft AG, Bubikon, Switzerland
Dr. Kissling is the CEO of KISSsoft AG, Switzerland. He was also a member of the VDI 2736 committee.
 Hasl, C. et al.: Zur Zahnfußtragfähigkeit von Kunststoffstirnrädern, PhD thesis, 2018.
 KISSsoft internal information, 2021.
 Tavčar J., Pogačnik A.: Accelerated testing method for polymer gears, High Performance Plastic Gears, 2017.
 Mao K. et al.: Polymer gear surface thermal wear and its performance prediction, Tribiology Int., vol. 43, no. 1-2, 2010.
 Černe B. et al.: Thermo-mechanical modeling of polymer spur gears with experimental validation using high-speed infrared thermography, Mech. Mach. Th., vol. 146, 2020.
 Matkovič, S. et al. Wear-coefficient analyses for polymer-gear life-time predictions: A critical appraisal of methodologies. Wear, 2021.