An investigation on the potential of bio-based polymers for use in polymer gear transmissions

Abstract

The potential for replacing the fossil-based Polyoxymethylene (POM) and Polyamide 66 (PA 66) in polymer gear applications with a bio-based Polyamide 6.10 (PA 6.10) was studied and is presented in the article. The use of bio-based plastics is increasing but mostly in undemanding applications like packaging. High-performance plastics are needed in polymer gear transmissions since their operational conditions are far more severe. The potential of bio-based PA 6.10 was studied by means of gear lifespan testing. Additional insights into the process of polymer gear meshing were garnered by simulating all the tested cases with a FEM model of meshing gears. Test gears were manufactured from commercially available materials, making the results useful for gear designers. Encouraging results were observed since the PA 6.10 gears exhibited a 3.5-times longer lifespan than POM gears and a 10-times longer lifespan than PA 66 gears when tested under identical test conditions. The results indicate great potential for replacing fossil-based plastics in polymer gear applications with bio-based polymer materials. The fatigue strength, coefficient of friction, and wear coefficient were determined and compared for the tested materials, facilitating the reliable design of polymer gears.

Full text

Polymer Testing xxx (xxxx) xxx
Please cite this article as: Damijan Zorko, Polymer Testing, https://doi.org/10.1016/j.polymertesting.2020.106994
Available online 30 November 2020
0142-9418/© 2020 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
An investigation on the potential of bio-based polymers for use in polymer
gear transmissions
Damijan Zorko
*
, Ivan Demˇ
sar, Joˇ
ze Tavˇ
car
*
University of Ljubljana, Faculty of Mechanical Engineering, Aˇ
skerˇ
ceva 6, 1000, Ljubljana, Slovenia
ARTICLE INFO
Keywords:
Biopolymers
Gears
Testing
Simulations
Wear
Fatigue
ABSTRACT
The potential for replacing the fossil-based Polyoxymethylene (POM) and Polyamide 66 (PA 66) in polymer gear
applications with a bio-based Polyamide 6.10 (PA 6.10) was studied and is presented in the article. The use of
bio-based plastics is increasing but mostly in undemanding applications like packaging. High-performance
plastics are needed in polymer gear transmissions since their operational conditions are far more severe. The
potential of bio-based PA 6.10 was studied by means of gear lifespan testing. Additional insights into the process
of polymer gear meshing were garnered by simulating all the tested cases with a FEM model of meshing gears.
Test gears were manufactured from commercially available materials, making the results useful for gear de-
signers. Encouraging results were observed since the PA 6.10 gears exhibited a 3.5-times longer lifespan than
POM gears and a 10-times longer lifespan than PA 66 gears when tested under identical test conditions. The
results indicate great potential for replacing fossil-based plastics in polymer gear applications with bio-based
polymer materials. The fatigue strength, coefcient of friction, and wear coefcient were determined and
compared for the tested materials, facilitating the reliable design of polymer gears.
1. Introduction
In recent decades the use of polymer gears has rapidly increased due
to some of their advantages over metal gears. Mass production is
cheaper if gears are made with injection molding. They can operate
without additional lubrication, which makes them interesting for ap-
plications where lubricant is not desired (e.g. printers, household ap-
pliances, and medicine). Polymer gears dampen vibrations better and
exhibit better response to noise, vibration, and environmental harshness
[1]. Polymers are mostly resistant to corrosion and other chemical in-
uences, so polymer gears can also operate in environments where
corrosive substances are present. Compared to metal gears, they also
have some disadvantages, the main ones being worse mechanical
properties, poorer thermal conductivity, poorer temperature resistance,
and lower manufacturing precision. Polymer gears are mostly produced
through injection molding, while smaller series and gears with larger
modules are made by cutting. Injection molding enables the production
of gears with special tooth geometries and higher load capacities,
leading to lower consumption of polymer materials [2].
Sustainable manufacturing methods have been studied for the pro-
duction of metal gears [3]; lubricant has been identied as one of the
major problems, wherefore dry milling [4] and dry grinding [5] were
proposed. Polymer gears are mainly produced with injection molding,
where clean manufacturing methods can be employed for the tool-
making [6–8]. Besides sustainable toolmaking, there is an additional
design opportunity in terms of materials, since bio-based polymer ma-
terials could be used for gear production in the future.
Currently there are many fossil-based polymer materials with a range
of properties allowing for several material pairs to be used in gear ap-
plications. Mostly semi-crystalline engineering polymers are used, e.g.
POM, PA 66, and PBT. Polymer gears are also being increasingly used in
demanding operating conditions where the use of high-performance
engineering polymers, such as PEEK, is required [9,10]. Various rein-
forcing bers and llers can be added to the base materials to increase
their performance in terms of increased wear resistance and reduced
friction [11]. The material cost rises in proportion to performance. A
positive trade balance of more than 15 billion euros was reached by the
European plastics industry itself in 2018 [12]. A large proportion of
polymer gears are used in the automotive industry. There are more than
twenty gear drives with polymer gears in a modern car. Other important
applications of polymer gears include household appliances, hand tools,
robotics, and medicine. The use of polymer materials in gear trans-
missions is steadily increasing. The cost of manufacturing polymer gears
* Corresponding authors.
E-mail addresses: damijan.zorko@lecad.fs.uni-lj.si (D. Zorko), ivan.demsar@lecad.fs.uni-lj.si (I. Demˇ
sar), joze.tavcar@lecad.fs.uni-lj.si (J. Tavˇ
car).
Contents lists available at ScienceDirect
Polymer Testing
journal homepage: http://www.elsevier.com/locate/polytest
https://doi.org/10.1016/j.polymertesting.2020.106994
Received 2 June 2020; Received in revised form 25 September 2020; Accepted 23 November 2020

Polymer Testing xxx (xxxx) xxx
2
is lower than for metal gears. However, along with the increasing use of
polymers the environmental impact must be considered, wherefore it
would be best to consider the use of bio-based and bio-degradable
polymers [13].
Currently, bioplastics comprise 1% of the more than 359 million tons
of annually produced plastic materials [14]. The most commonly known
bio-based and bio-degradable plastics like PLA, PHA, PBS, and cellulose
are mainly used for simple products that are not subjected to heavy
mechanical loads. Many new biopolymer materials are being developed,
mainly for non-demanding working conditions, mostly for packaging
(53% of the total bioplastics market in 2019) [14]. Other elds of
application include electronics, agriculture, and the automotive in-
dustry. Bio-based or partially bio-based plastics such as PE, PET, and
PVC have identical properties to plastics produced on a fossil-fuel basis
[14]. Thus, the production of such materials reduces carbon footprints
[15], and existing recycling methods can also be used. Biodegradable
plastics such as PLA and PHA, however, offer additional recycling op-
tions, e.g. composting. The main advantage of bio-plastics is that they
are produced from renewable sources and do not require the use of
non-renewable fossil resources for their production. An additional
advantage of some bioplastics is that they are biodegradable, i.e. they
degrade into water, carbon dioxide, and compost in the presence of
environmental microorganisms. PLA and PHA are bio-based and
biodegradable, while PP, PE, PET, and PA are bio-based but not biode-
gradable [15]. A total of 0.02% of the total land suitable for agricultural
land is used for the production of crops intended for bioplastics pro-
duction. Despite the growth of the bioplastics market, no more signi-
cant land use is expected so as not to encroach upon land used for food
production [14].
There are many bio-based materials available today; however, only
few studies can be found on the application of such materials for gears.
Chen et al. [16] studied gears made of POM with added particles of rice
hull carbon powder. Bravo et al. [17] studied the behavior of a
bio-composite material based on a natural polyethylene matrix. Com-
pounds with different percentages of short birch bers with and without
a coupling agent were made and mechanically tested using tensile and
3-point bending tests. In a following study Bravo et al. [18] studied fa-
tigue life and thermomechanical behavior of gears made of
bio-composites with HDPE and NHDPE matrices to which short birch
bers were added.
The properties of basic bioplastics can be improved with additives,
such as nanoclay [19] and cellulose ber [20]. Battegazzore et al. [21]
improved the mechanical properties (elastic modulus and tensile
strength) of PA 6.10 and PA 10.10 bio-polyamides by adding rice husk
ash and nanoclay. High performance bio-polymers are required to
replace fossil-based polymers in demanding applications. Many plastics
manufacturers started developing blends with various bio-based poly-
amides years ago. An appropriate bio-based polymer could replace
fossil-based plastics, thus contributing to a reduction in plastics’ envi-
ronmental impacts. Also, because the impact of bio-based plastics on
environmental sustainability has not yet been fully explored, there are
only few products made from bioplastics in practice [22].
Specimen-based tests are required for basic research into material
properties, and the next step is to study the material’s appropriateness in
a real application. Several studies can be found that address the topic of
polymer gear testing. Mao et al. [23–25] studied wear on gears made of
POM and PA. They have found that in terms of wear the best combi-
nation is when the drive gear is made of the POM and the driven gear of
PA. Senthilvelan and Gnanamoorthy [26] studied the failure mecha-
nisms of polymer gears and the effect of reinforcing bers on the
properties of polymer gears. Letzelter et al. [27] developed a dedicated
gear test rig where the heating sources of polymer gears can be accu-
rately analyzed. Testing the lifespan of polymer gears is
time-consuming, so Pogaˇ
cnik and Tavˇ
car [11,28] developed a new
accelerated method of testing polymer gears, which can determine the
critical load of a gear pair that will result in a thermal failure. The
Nomenclature
σ
F MPa root stress
KF factor for tooth root load
KA application factor for fatigue load
Kv dynamic factor
KF
α
face factor for tooth root load
KFβ width factor for tooth root load
YFa form factor
YSa stress correction factor (notch effect)
Y
ε
contact ratio factor for root stress
Yβ helix angle factor for root stress
Ft N nominal tangential force
b mm face width
mn mm normal module
Wm mm average linear wear
Mt Nm tested torque
N number of load cycles
HV degree of tooth loss
kW 10
−6
mm
3
/(Nm) wear coefcient
VW mm
3
wear volume
zi number of teeth (i =1 for pinion, i =2 for gear)
ϑRoot ◦C root temperature
ϑ0 ◦C ambient temperature
P W nominal output power
μ
coefcient of friction
kϑ,Root
K⋅m
s0,75
⋅mm1,75
Wheat-transfer coefcient of the polymer gear
vt m/s tangential velocity
Rλ,G K⋅ m
2
/W heat transfer resistance of the mechanism housing
AG m
2
heat-dissipating surface of the mechanism housing
ED relative tooth-engagement time with respect to 10 min
T
g
glass transition temperature
A initial point of tooth contact
B lowest point of single tooth contact (LPSTC) for the drive
gear and highest point of single tooth contact (HPSTC) for
the driven gear
C pitch point (kinematic point)
D highest point of single tooth contact (HPSTC) for the drive
gear and lowest point of single tooth contact (LPSTC) for
the driven gear
E end point of tooth contact
SD standard deviation
POM Polyoxymethylene
PA Polyamide
PBT Polybutylene terephthalate
PEEK Polyether ether ketone
PLA Polylactic acid
PHA Polyhydroxyalkanoates
PBS Polybutylene succinate
PE Polyethylene
PET Polyethylene terephthalate
PVC Polyvinyl chloride
PP Polypropylene
HDPE High-density polyethylene
NHDPE Natural high-density polyethylene
D. Zorko et al.

Polymer Testing xxx (xxxx) xxx
3
method is also effective for determining the adequacy of the material
combination used. To obtain reliable fatigue data traditional gear testing
must be conducted up to gear failure. Such tests are very time
consuming, since one test can run for more than a month and several
tests are needed to determine a stress-number of cycles curve. Therefore,
only a few studies [9,18,29] of such gear testing can be found, since
material manufacturers tend to hold this information in-house. There
are even less studies where gears would be tested in a high cycle fatigue
regime (over 10
7
cycles), which in many cases is the required lifetime of
gears in real applications.
Polymer gears heat up during operation; the operating temperature
depends on hysteretic losses in the material and frictional losses between
the meshing tooth anks. Letzelter et al. [27] found that the portion of
the heat generated as a consequence of hysteresis losses is negligible
compared to that generated by friction. The fatigue strength of polymer
materials depends strongly on the temperature. In order to fully char-
acterize the polymer material’s fatigue strength so as to yield data that
are useful for the gear’s root strength control, it is necessary to measure
the gear temperature during testing. The polymer gear’s operating
temperature depends on the load, gear geometry, material, and lubri-
cation conditions. Thus, to characterize the material at the same stress
state and at different temperatures, a test rig is required that allows for
active control of the gear’s temperature. This can be done in several
ways, e.g. by air cooling or using some other medium. It is also possible
to submerge the gears in oil and control the oil temperature, indirectly
controlling the gear temperature. In this case, there is a risk of pitting
[10,30] and gear failure due to another failure type. Evaluation of the
gear bending fatigue strength requires failure due to the root cracking.
There are also other inuences in the operation of the gear pair that
can affect the failure type. Characterizing a polymer gear’s bending fa-
tigue strength requires testing in pair with a steel gear, so that the
polymer gear certainly fails and the desired information for the tested
material is provided. The test must always be carried out until failure;
otherwise, not all of the information on the material’s performance is
obtained. The high cycle fatigue limit, set to 3⋅106 cycles for steel gears
[31], does not exist for polymer materials. The tested gear pair is also
subject to other inuences in conventional gear pair tests, e.g. wear on
the polymer gear will always occur while meshing with a steel pinion.
Wear can become signicant over many test cycles and affect the
polymer gear’s stress state. Wear also increases vibration, which has an
additional impact. In addition, the stress condition in the test gear is also
affected by the geometric tolerances of the gear, and the test stand
(bearings, shafts). Thus, the stress state in the test gear is inuenced by
many parameters other than the load itself. Gear lifespan testing is a
rather complex testing method, but in order to determine whether a
promising polymer material really is appropriate for gear application,
this must be conducted.
Polymer gears usually fail due to temperature, wear, or fatigue [2,32,
33]. To perform well in gear applications the material must exhibit a low
coefcient of friction, good wear resistance, and high fatigue strength.
Bio-based polymer PA 6.10 has been studied in this research with means
of an experimental and numerical approach. The material’s performance
was compared to fossil-based POM and PA 66 materials, which are the
most commonly used materials for polymer gear applications. The study
was focused on exploring the potential for the application of a bio-based
material in applications where a high-performance polymer is needed.
2. Materials and methods
A systematic combination of numerical and experimental methods
was used to investigate the potential of bio-based polymers for use in
applications with a polymer gear and a steel pinion. Test gears were
manufactured and tested on a special in-house developed test rig. All
tested cases were also simulated using numerical methods with FEM,
providing additional insight into the gear meshing process. While life-
span and gear surface temperature were measured using a test, it is
difcult to accurately measure the stress state in the gear during oper-
ation [34], wherefore numerical models were used to determine the
stress.
2.1. Materials
Gears made out of bio-based PA 6.10 were tested and their perfor-
mance was compared to gears made out of fossil-based POM and PA 66.
Commercial grades of the material were tested, making the results of this
research quickly applicable in practice. The PA 6.10 tested is a semi-
crystalline material obtained from the oil of castor seed. The propor-
tion of renewable raw materials is over 60%. Material properties are
presented in Table 1 and were provided from the material manufacturer
datasheets [35–37].
Hardness measurements according to Shore D were conducted for all
three tested polymers. A Hildebrand Shore D durometer (Hildebrand
Prüf-und Messtechnik GmbH, Germany) with a 4000 g weight was used.
Twelve measurements were conducted for each material and the
average values are presented in Table 1.
The data sheet for PA 66 shows the properties for dry conditions of
PA 66. The PA 66 tends to absorb moisture, which negatively affects the
material’s mechanical properties [38]. Therefore all test gears were
stored together with silica moisture absorbing bags to prevent the
moisture uptake. The moisture content in the used PA 66 was also
evaluated during the project, namely at 0.25% for 20 ◦C, and below
0.1% at elevated temperatures in the range from 45 ◦C to 90 ◦C. The
temperature of the polymer gears increased rapidly during testing. The
measured bulk temperature when testing PA 66 gears was in the range
between 50 ◦C and 80 ◦C. The ash temperature on the contacting
surfaces is expected to be even higher. Therefore, any additional mois-
ture was removed from the material quite quickly and it was assumed
that the effect of moisture uptake was not signicant during life testing
of PA 66 gears.
2.2. Sample preparation
Test gears were machine cut from extruded bars using a gear hobbing
process. The test gear parameters are presented in Table 2. The hobbing
tool quality grade was AA according to the DIN 3968 [39]. The geometry
of gears was measured after manufacturing on the LH54 (Wenzel
Table 1
Material properties of the tested materials.
Parameter Standard TECAFORM AH natural TECAMID 66 natural ECO-Gehr PA 6.10
Abbreviation POM-C PA 66 PA 6.10
Elastic modulus (23 ◦C) ISO 527 2800 MPa 3500 MPa 2400 MPa
Tensile strength (23 ◦C) ISO 527 67 MPa 85 MPa 65 MPa
Flexural strength (23 ◦C) ISO 178 91 MPa 110 MPa 85 MPa
Melting temperature ISO 11357 166 ◦C 258 ◦C 220 ◦C
Glass transition temperature DIN53765 −60 ◦C 47 ◦C 50 ◦C
Density ISO 1183 1.41 g/cm
3
1.15 g/cm
3
1.08 g/cm
3
Hardness (Shore D) ISO 868 76.33 76.75 78.17
D. Zorko et al.

Polymer Testing xxx (xxxx) xxx
4
Messtechnik GmbH, Germany) gear-measuring machine. The prole
quality of gears was grade 10, while the lead, pitch, and runout quality
were grade 6–8 according DIN 3961/62 [40].
2.3. Testing procedure
Gears were tested on an in-house developed testing rig, presented in
Fig. 1. A detailed description of the test rig can be found in some of the
previous works [2,9]. The rig is positioned inside a temperature cham-
ber, where the ambient temperature and humidity can be controlled.
Tests were performed at the ambient temperature 20 ±2 ◦C and hu-
midity of 40% ±5%. FY02 (Forsentek Co., Limited, China) torque sen-
sors were mounted on the drive and driven shaft, and, after calibration,
were used for the torque measurement and control during testing. Gears
were tested at torques 0.8 Nm, 1.0 Nm and 1.2 Nm, and rotational speed
was 1400 rpm. Five tests were conducted on each load level and for each
polymer material. All tests were run until gear failure.
The gear surface temperature was measured during testing with
thermal camera FLIR T 420 (Flir Systems, Inc, U. S.). The temperature
was measured in an area size of 3 ×3 pixels in the root area of the tested
polymer gear (Fig. 2). After the camera was calibrated, the emissivity
was set to
ε
=0.95 for all tested materials. Similar emissivity values were
reported in the relevant studies [27,28] where gears made of POM and
PA materials were tested. The used emissivity value was conrmed
before the thermographic measurements. Emissivity stickers with a
known emissivity value of
ε
=0.95 were layered on samples of all three
materials. These samples were put on a heating plate and heated up to
80 ◦C, and then cooled down to ambient room temperature. During the
heating and cooling sequence the sample temperature was measured
with a thermographic camera. No difference was observed in the
measured temperatures in the region where the emissivity sticker was
layered and the region without the sticker, for either of the materials and
in the tested temperature range. Therefore, it was conrmed that the
emissivity value of
ε
=0.95 is appropriate for thermographic mea-
surements of the tested polymer materials.
The polymer gears were tested in pair with a steel pinion, which was
manufactured with hobbing and additionally treated with a supernish
to remove sharp edges (increased tip rounding) and obtain a smoother
surface [9]. The surface roughness of the steel pinion was Ra =
0.689
μ
m. Roughness was measured with the TESA Rogusurf 90G (TESA
Technology, Switzerland) measuring machine, with the measuring di-
rection along the ank prole. A detailed failure analysis was performed
on tested gears using a Keyence VHX-200 (Keyence, Japan) digital
microscope.
Table 2
Parameters of tested gears.
Parameter value
Prole ISO 53 C
Module - m [mm] 1
Number of teeth – z
1, 2
20
Pressure angle -
α
[◦] 20
Face width – b
1, 2
[mm] 6
Center distance [mm] 20.00
Prole shift - x
1
0
Prole shift - x
2
0
Contact ratio -
ε
α
1.557
Fig. 1. Testing rig, front view (left) and top view (right).
Fig. 2. a) Thermographic measurement of a tested gear pair, b) Root temperature during operation.
D. Zorko et al.

Polymer Testing xxx (xxxx) xxx
5
3. Calculation
Stress in the tested gears was calculated using a numerical model for
the gear meshing simulation (Fig. 3). Simulations were performed in the
Ansys Workbench 17.2 (Ansys, Inc., U. S.) computer software. A 2D
numerical model was set up, taking into account the planar stress state.
Quadratic PLANE183 nite elements were used for the geometry dis-
cretization, while contact conditions were simulated with CONTA172
and TARGE169 elements. The drive gear 1 was attached with a support
to a xed point A placed in the center of the drive gear’s hole. With the
used support, the movement of the selected gear hole edge was pre-
vented in the X and Y directions, while rotation of the edge around the Z
axis was allowed. Similarly, a support was used to prop up the driven
gear 2 to prevent displacement of the driven gear’s hole and to allow
rotation of the edge around xed point B placed in the center of the
gear’s hole.
Torque load was prescribed on the driven gear acting in the opposite
direction of the rotation, which was prescribed on the drive gear. Stress
analysis was performed on the middle tooth, which underwent all the
characteristic meshing points. The prescribed torque size on the driven
gear was the same as in gear tests. Three simulations were performed for
each polymer material, with simulated torque at 0.8 Nm, 1.0 Nm, and
1.2 Nm. Mesh was rened in the region of interest in the root and contact
area of the teeth. A convergence test using the h-renement method was
performed to approve the mesh density. The average element quality
was 0.96. Material properties were modelled as linearly elastic, using
the material properties from the manufacturer’s datasheets presented in
Table 1. When simulating a single meshing cycle under the considered
loads, the non-linear material properties do not inuence the material
response noticeably, since in that short time period viscous properties do
not become evident. The assumption of linear elastic behavior is
generally used when calculating the stress in polymer gear design, where
the calculated strains are below the polymer material’s yield point [41,
42]. A comparison with a viscoplastic model was conducted by ˇ
Cerne
et al. [43], where it was conrmed that the presumption of linear elastic
mechanical behavior yields a sufciently accurate approximation of the
material’s behavior for practical thermo-mechanical modeling purposes
in gear design applications.
A frictional contact according to Coulomb’s law was modelled and
the Augmented Lagrange method was used for contact formulation. The
values of the coefcient of friction required for frictional contact
modeling were experimentally determined by using the Pogaˇ
cnik-
Tavˇ
car [28] method, which is explained in more detail in Section 4.2.
Von Misses stress calculated in the root region was considered as the
nominal root stress. Therefore, the compression due to the radial force
acting on the tooth was taken into account, along with the effect of
frictional force. The region of interest (ROI) where the von Mises stress
was evaluated was determined with the 30◦tangent method (Fig. 4).
FEM calculations were conducted to gain better understanding of the
meshing process and to make comparison with stress level calculated
according to the VDI 2736 guideline [44].
4. Results
4.1. Lifespan testing
Lifespan test results are presented in Fig. 5. The average lifespan of
ve test gears at each load is presented, and the error bars represent the
size of one standard deviation between test results. The average lifespan
for POM gears tested at 0.8 Nm is 5.99⋅106 cycles, at 1.0 Nm the average
lifespan is 1.73⋅106 cycles, and for 1.2 Nm at 0.68⋅106 cycles. The
average lifespan for the PA 66 gears was 2.91⋅106 cycles for the gears
tested at load 0.8 Nm, 0.50⋅106 cycles at 1.0 Nm, and 0.19⋅106 for the
PA66 gears loaded with 1.2 Nm. The PA 6.10 gears exhibited the longest
Fig. 3. Numerical model; 1 – drive steel gear, 2 – driven polymer gear.
Fig. 4. Mesh renement in the region of interest.
D. Zorko et al.

Polymer Testing xxx (xxxx) xxx
6
lifespan, despite having the lowest tensile and exural strength reported
in the material datasheet [37]. The average lifespan for the PA 6.10
gears loaded with 0.8 Nm was 26.09⋅106 cycles, at the load 1.0 Nm it
was 6.65⋅106 cycles and 1.49⋅106 for the PA 6.10 gears loaded with 1.2
Nm. In the steel/PA 66 tests at torque 1.2 Nm, three gears failed due to
thermal failure, so the standard deviation is larger there. When tested at
the exact same test conditions a much longer lifespan was observed for
the PA 6.10 gears comparing to POM and PA 66 gears. Relative com-
parison of the lifespan at each tested load is presented in Table 3. When
averaged over the all load cases, the PA 6.10 gears exhibited a lifespan
that was 3.46 times longer than that of POM gears and 10 times longer
than for PA 66 gears.
Loads tested were chosen in such a way as to obtain fatigue failure
due to a root fracture. After reaching the steady state, the temperature
measured in the root area was constant during all tests (except the three
steel/PA 66 tests at 1.2 Nm). The root stress in all the tested cases was
calculated using the presented numerical model and, for comparison,
also with the standard analytical model, which is used in the VDI 2736
[44] polymer gear design guideline:
σ
F=KF⋅YFa⋅YSa ⋅Y
ε
⋅Yβ⋅Ft
b⋅mn
(1)
where the following factor values were used for the tested gear geom-
etry: KF=KA⋅Kv⋅KFβ⋅KF
α
=1.0, YFa =3.13, YSa =1.56, Y
ε
=0.732,
Yβ=1. The analytical model does not take into account the increase of
contact ratio due to tooth deection, whereas, when using a FEM model,
this is taken into account. Therefore, identical root stress is calculated
for all the tested material combinations when using the VDI model, and
small differences can be observed when calculating the root stress with a
numerical model. Transforming the results from Fig. 5 into a stress-
number of cycles (S–N) curve diagram (Fig. 6), it can be observed that
the PA 6.10 gears operated with the lowest root stress at a certain load
level. The difference in root stress is due to load-induced teeth deection
and the corresponding increase in the contact ratio. A lower elastic
modulus leads to a larger teeth deection, and a corresponding reduc-
tion in root stress. The simulation-calculated root stress and average
measured root temperature for each tested load are presented in Table 4.
It was observed that PA 6.10 gears loaded with 1.0 Nm, which corre-
sponds to 48 MPa of root stress and a root temperature of 55 ◦C, survived
a larger number of cycles than POM gears loaded with 0.8 Nm, which
corresponds to 43 MPa of root stress and root temperature of 44 ◦C.
Something similar was observed also when comparing PA 6.10 gears
loaded with 1.0 Nm to PA 66 gears loaded with 0.8 Nm, which corre-
sponds to 45 MPa of root stress and a root temperature of 53.5 ◦C. This
led to the conclusion that the fatigue strength of PA 6.10 is higher than
that of POM and PA 66.
4.2. Temperature measurements
The operating temperature is an important factor when designing a
polymer gear pair, since polymer material properties depend highly on
the temperature. If the applied load is too high, the polymer gear heats
above the acceptable temperature for continuous operation, which leads
to instant thermal failure. Therefore, a temperature control calculation
must be conducted when designing a new gear pair with polymer gears.
Several numerical [42,45,46] and analytical methods [47–50] were
proposed for the temperature calculation of polymer gears; unfortu-
nately the vast majority of them is limited to special cases or is rather
complex to be used in practice by gear designers. A simple-to-use
analytical model developed by Hachmann and Strickle [47] and later
supplemented by Ehrenstein et al. [51] is proposed for temperature
calculation in the VDI 2736 guideline:
ϑRoot =ϑ0+P⋅
μ
⋅HV⋅kϑ,Root
b⋅z⋅(v⋅mn)0,75 +Rλ,G
AG⋅ED0,64 (2)
where ϑ0 is the ambient temperature, P is the rated power transmitted
through a gear pair,
μ
is the coefcient of friction, HV is the degree of
tooth loss, kϑ,Root is the heat-transfer coefcient of the polymer gear, b is
the facewidth, z is the number of polymer gear teeth, v is the tangential
velocity, mn is the normal module, Rλ,G is the heat-transfer resistance of
the housing, AG is the housing surface through which heat dissipates,
and ED is the relative contact time. To calculate temperature for the
desired operating conditions of a polymer gear pair the gear designer
needs the value of the coefcient of friction for the case under consid-
eration. The coefcient of friction between two meshing tooth anks is,
Fig. 5. Lifespan testing results.
Table 3
Relative comparison of the lifespan of tested PA6.10 gears.
in comparison with 0.8 Nm 1.0 Nm 1.2 Nm average
POM 4.35 3.84 2.19 3.46
PA 66 8.97 13.30 7.84 10
Fig. 6. S–N curves for the tested polymer materials.
Table 4
Simulation-calculated root stress and average measured root temperature in
tested cases.
0.8 Nm 1.0 Nm 1.2 Nm
POM 43.48 MPa, ϑRoot =
44.0 ◦C
51.03 MPa, ϑRoot =
48.8 ◦C
58.06 MPa, ϑRoot =
54.4 ◦C
PA66 45.40 MPa, ϑRoot =
53.5 ◦C
52.56 MPa, ϑRoot =
70.8 ◦C
60.01 MPa, ϑRoot =
83.0 ◦C
PA6.10 40.79 MPa, ϑRoot =
46.5 ◦C
47.89 MPa, ϑRoot =
54.7 ◦C
55.66 MPa, ϑRoot =
67.6 ◦C
D. Zorko et al.

Polymer Testing xxx (xxxx) xxx
7
according to its physical behavior, not a constant value, but is rather
dependent on load, sliding velocity, curvature, and temperature [52]. In
addition, the coefcient of friction is not a property of a single material
but it is a property of a material pair in contact. However, when tem-
perature control calculation is done by using Eq. (2), a scalar value of the
coefcient of friction is needed.
The values of the coefcient of friction for some most commonly
used material pairs are very generally suggested in the VDI guideline.
Pogaˇ
cnik and Tavˇ
car [28] proposed an approach to determine the so
called calculated coefcient of friction. In their approach the VDI 2736
temperature equation is used and, based on the measured root temper-
ature (ϑRoot), the coefcient of friction is calculated (Eq. (3)).
Employing the temperature measurements obtained in this study, the
calculated coefcient of friction was determined using the Pogaˇ
cnik-
Tavˇ
car (P.T.) method. This was calculated for each temperature mea-
surement separately, and then the average calculated coefcient of
friction and the standard deviation were determined based on all
calculated values. The calculated values for the coefcient of friction for
the tested material combinations are presented in Table 5. The deter-
mined values of the coefcients of friction were also used to run nu-
merical simulations where the frictional contact was modelled.
μ
≈ϑRoot −ϑ0
P⋅HV⋅kϑ,Root
b⋅z⋅(v⋅mn)0,75 +Rλ,G
AG⋅ED0,64
(3)
A comparison between the measured and the calculated tempera-
tures was made. For the steel/POM material pair it is presented in Fig. 7,
for the steel/PA 66 in Fig. 8, and for steel/PA 6.10 in Fig. 9. The tem-
peratures were calculated using the values of those coefcients of fric-
tion given in the VDI guideline (Calc. T - VDI) and with the new
calculated coefcients of friction determined according the P.T. method
(Calc. T -
μ
P.T.). The calculated temperatures were compared with the
average temperature of all temperature measurements at a given load
and for a given material combination. The average temperature was
calculated on the basis of at least ve individual tests. Calculating the
temperature using Eq. (2) the following values were used:
ϑ0=23◦C,b=6 mm
P=M⋅2⋅
π
⋅n
60,z=20
μ
=0.2, this value is proposed for all non-lubricated steel/polymer
contacts in the VDI 2736 guideline, v=1.466 m/s , mn=1 mm,
HV=0.206 [9],Rλ,G=0
kϑ,Root =900
K⋅m
s0,75
⋅mm1,75
WED =1
To calculate the temperature using the P.T. approach Eq. (2) was
used and the values of the coefcient of friction were selected from
Table 5 as they were calculated for the tested material combinations.
The average discrepancy between the measured temperature and the
VDI-calculated temperature was 9.2% (SD =6.14%) for the steel/POM
gear pairs, 24.3% (SD =12%) for the steel/PA 66, and 14.5% (SD =
16%) for the steel/PA 6.10 combination. It was observed that the
discrepancy between the VDI-calculated and measured temperatures is
load-dependent. With increasing load, the difference between the
measured and calculated temperature also increases. When calculating
the temperature using the P.T. approach to determine the coefcient of
friction (Table 5), a small discrepancy was observed in all analyzed
cases. The average discrepancy between the measured temperature and
the P.T.-calculated temperature was 5.5% (SD =3.64%) for the steel/
POM combination, 7.6% (SD =5.4%) for the steel/PA 66, and 13.6%
(SD =7.25%) for the steel/PA 6.10 gear pairs. It was observed that for
the steel/PA 6.10 combination the temperature increase is not linear
with the increase of tested load, as it can be seen for POM and PA 66 test
cases. The non-linear temperature rise can be accounted to the changed
contact conditions during meshing due to large teeth deections, ma-
terial softening (temperature above T
g
), and worse contact conditions, e.
g. more specic sliding. If the temperature measurements for the load
1.2 Nm are not taken into account, the calculated coefcient of friction
for the material combination steel/PA 6.10 is
μ
=0.2 and the deviations
between calculation and measurement are only 1.5% for loads of 0.8 Nm
and 1.0 Nm.
Table 5
Calculated coefcient of friction.
material pair average
μ
standard deviation
steel/POM 0.17 0.02
steel/PA66 0.28 0.04
steel/PA6.10 0.24 (0.2) 0.05
Fig. 7. Comparison of the calculated and measured temperature for the Steel/
POM material pair.
Fig. 8. Comparison of the calculated and measured temperature for the Steel/
PA 66 material pair.
D. Zorko et al.

Polymer Testing xxx (xxxx) xxx
8
4.3. Failure analysis
A detailed failure analysis was conducted on tested gears. The tested
loads were chosen to impose fatigue failure, but other damage mecha-
nisms were also inevitable. For the POM and PA 6.10 gears the observed
failure mode at each tested load was the result of tooth bending fatigue,
which led to root cracks and nal failure due to teeth breakage. The
same failure mode was also observed for PA 66 gears tested at 0.8 Nm
and 1.0 Nm. A combination of thermal and fatigue failure was observed
for PA 66 gears tested at torque 1.2 Nm where relatively high operating
temperatures were measured (Fig. 10). Severe plastic teeth deformation
can be observed, and several root cracks are also visible as a result of
tooth bending fatigue. After analysis it was found that the location of
root cracks corresponds very well with the critical section location
determined by the 30◦tangent method [34].
Since polymer gears were run in mesh with a steel gear, wear was
also observed on several gears. The amount of wear depended also on
the duration of the test. Therefore, the most prominent wear was
observed on the gears made of PA 6.10 tested at the lowest load (0.8
Nm), since these gears operated for the highest number of load cycles. At
higher loads, i.e. 1.0 Nm and 1.2 Nm, the fatigue root crack failure came
earlier and the wear was not as evident. The damage mechanisms of a PA
6.10 gear tested at 0.8 Nm torque are presented in Fig. 11. After more
than 30 million load cycles a substantial amount of the tooth ank is
worn away, nonetheless the nal failure of the gear was due to root
cracking. The crack location corresponds very well with the 30◦tangent
method (Fig. 12), as was also already observed for the PA 66 gear pre-
sented in Fig. 10; however, the crack path is different. Two different
crack paths were observed for the tested gears, which are schematically
presented in Fig. 13.
Root fracture and the thermal induced failure, which led to a severe
plastic deformation of teeth, were the observed damage modes resulting
in nal failures of the tested gear. While severe plastic deformation was
a failure mode only for PA 66 gears tested at the 1.2 Nm torque, some
deection of teeth, when compared with a theoretic gear prole, was
found also for POM and PA 6.10 gears tested at the 1.2 Nm load. The
same was observed also for PA 66 gears tested at 0.8 Nm and 1.0 Nm
torque. Therefore it can be assumed that some amount of plastic
deformation occurred also in those cases, however it did not lead to a
nal failure of the tested polymer gear.
This observations correlate well with the measured operating tem-
peratures. The PA 66 gears were operating above the material’s glass
transition temperature at all tested loads, therefore the material’s elastic
modulus was reduced which led to larger teeth deection and plastic
deformation. Similar was observed also for PA 6.10 gears tested at 1.2
Nm torque, where the operating temperature surpassed the T
g
of PA 6.10
used in the study. While the glass transition temperature of POM is at
−60 ◦C the material does not exhibit a steep reduction of mechanical
properties in the tested temperature range. However, some plastic
deformation of teeth was observed also for POM gears tested at 1.2 Nm.
4.4. Wear measurement
Wear measurements were conducted using a Keyence VHX-200
(Keyence, Japan) digital microscope. Magnied images of worn gears
were compared with a theoretical gear prole using 3D modeling soft-
ware Siemens NX 12.0 (Siemens Digital Industries Software, U. S.)
(Fig. 14). The wear measurements were conducted on the undeformed
teeth so that the wear could be appropriately measured. At lower loads
of 0.8 Nm, wear was easier to characterize, since the teeth were not
deected as they were at higher loads; where the gears were also
operating at a higher temperature, severe teeth deection was observed.
There was a combination of teeth deection and wear, making it dif-
cult to characterize only the wear part of tooth shape change; several
root cracks were also observed (Fig. 15).
No wear measurements could be done on the PA 66 gears tested at
the torque of 1.2 Nm since the teeth were severely deformed. Deection
from the theoretical gear prole was observed also for PA 6.10 gears
tested at 1.2 Nm torque wherefore wear measurements on PA 66 and PA
6.10 gears were done only for gears tested at 0.8 Nm and 1.0 Nm torque.
Wear was measured on ve PA 6.10 gears tested at 0.8 Nm and 1.0 Nm
torque each. The same was done for POM gears, where three additional
wear measurements could be done also for gears tested at 1.2 Nm torque.
Fig. 9. Comparison of the calculated and measured temperature for the Steel/
PA 6.10 material pair.
Fig. 10. Failure mode of a PA 66 gear tested at 1.2 Nm torque, gear failed after 3.50⋅10
5 load cycles due to thermal softening of the material; also several root cracks
can be observed.
D. Zorko et al.

Polymer Testing xxx (xxxx) xxx
9
The other two POM gears tested at 1.2 Nm had the teeth too much
deected as to wear to be properly measured. As for PA 66 gears wear
was determined on three gears tested at torque 0.8 Nm and two gears
tested at torque of 1.0 Nm.
Based on the observed failure modes it can be concluded that tem-
perature, fatigue, and wear control calculations must be conducted in
order to reliably design steel/polymer gear pairs. A polymer gear wear
control model was proposed by Feulner [53] and is implemented in the
VDI guideline [44]. The value of the wear coefcient is needed for a
reliable wear calculation. This can either be determined with
specimen-based tribological tests, e.g. pin-on-disc or disc-on-disc, but
for a more accurate evaluation the wear coefcient should be deter-
mined via reference gear pair testing [54]. The wear volume of a single
tooth ank during one meshing cycle can be calculated as [44]:
VW=
t=x
t=0
kW⋅Fn⋅vg⋅dt (4)
It can be shown that the wear volume of one tooth is proportional to
the frictional losses:
Fig. 11. Failure mode of a PA 6.10 gear tested at 0.8 Nm torque, gear failed after 30.25⋅10
6 load cycles due to root crack failure.
Fig. 12. Failure mode of a PA 6.10 gear tested at 0.8 Nm the gear failed after
30.25⋅10
6 cycles due to root fracture, and severe wear is present.
Fig. 13. Schematic representation of the crack paths observed in tested polymer gears.
Fig. 14. Wear measurement on worn anks of a PA 6.10 gear, tested at 0.8 Nm
for 28.90⋅10
6 cycles.
Fig. 15. Combination of teeth deection, wear, and root cracking on a PA 66
gear tested at 1.2 Nm.
D. Zorko et al.

Polymer Testing xxx (xxxx) xxx
10
VW=
t=x
t=0
kW⋅Fn⋅vg⋅dt =kW
μ
⋅
t=x
t=0
μ
⋅Fn⋅vg⋅dt =kW
μ
⋅Ploss (5)
The energy loss of a meshing gear pair in one meshing cycle can be
calculated as:
Ploss =Mt⋅2⋅
π
⋅HV⋅
μ
(6)
Frictional losses of a single tooth pair can be determined by dividing
Eq. (5) by the number of teeth. Therefore, the averaged wear volume of a
single tooth during N test cycles can be expressed as:
VW=
kW
μ
Ploss
z=Mt⋅2⋅
π
⋅HV⋅N⋅kW
z(7)
Based on the measured wear volume the wear coefcients for the
tested polymer gears could be determined:
kW=VW⋅z
Mt⋅2⋅
π
⋅N⋅HV
(8)
The average values of the evaluated wear coefcients are presented
in Table 6. Wear volume was determined based on the measured worn
area as presented in Fig. 14. The average wear volume of a single gear
was then determined based on the wear volume measurements of
several worn teeth on each analyzed gear. Measured were only the un-
deformed teeth, where the wear could be appropriately measured. Wear
coefcients were calculated for the known values of the parameters in
Eq. (8) and the lifespan test results: Mt =tested torque (Fig. 5), z =20, N
=lifespan test result (Fig. 5), HV =0.206.
5. Discussion
A systematic combination of experimental and numerical methods
was employed to investigate the potential of the PA 6.10 biopolymer to
be used in polymer gear applications. The performance of PA 6.10 was
compared with the testing results of the two most commonly used en-
gineering polymers in gear applications, e.g. POM and PA 66. Fatigue
strength, coefcients of friction, and wear coefcients, which are the key
parameters that determine the performance of polymer gears, were
studied and compared. Knowing the exact values of these parameters is
necessary for reliable design calculations of polymer gears. Data ob-
tained in this study enable design calculations of new polymer gear
pairs, bearing in mind that the results were obtained by testing a
reference test gear geometry in laboratory conditions. The development
of a new drive with polymer gears still requires prototype testing, but the
development time, the required number of prototypes, and the associ-
ated costs can be signicantly reduced. For the product to be sustainable
the relation between price and performance must also be taken into
account; for now the cost of PA6.10 tested in this study is approximately
3 times higher than that of POM and PA 66. The individual effects on the
results are discussed in more detail separately below.
5.1. Effects on the fatigue strength
The fatigue strength of polymers is temperature-dependent. All tests
were performed at controlled ambient temperatures. Due to the different
coefcient of friction of each tested polymer material in contact with the
steel gear, the gears’ operating temperatures were different at the same
load. Therefore, it should be kept in mind that the fatigue strengths
presented are valid and can only be used for strength controls of gears
operating at the same or a lower temperature than that at which the
fatigue strength was determined. In a conservative approach, the whole
S–N curve can be used for design calculations at the temperature
reached at the lowest tested load. Gears tested at higher loads operated
at higher temperatures and therefore the material’s fatigue strength was
reduced.
The rotational speed was kept constant during gear testing. Testing at
different rotational speeds would result in two effects; the rst is the
effect of the dynamic forces due to vibrations. In the VDI equation for the
root stress calculation (Eq. (1)), the K
F
factor (K
F
=K
A
∙ K
v
∙ K
Fβ
∙ K
F
α
)
value is usually in the range between 1 and 1.25. The effect of the
rotational speed on the tooth root stress, which for steel gears is taken
into account with the factor K
v
, has not been sufciently studied for
polymer gears. The general assumption is that polymer gears dampen
vibrations better and the stress increase due to vibration-related dy-
namic forces is much lower than for steel gears. A study was conducted
by Hasl et al. [55] where the dynamic factor K
v
was evaluated for the
POM gears. It was found that when POM gears were operating in the
near resonance area, failure occurred signicantly earlier than for gears
tested in the subcritical and supercritical ranges. Therefore a value of K
v
=1.2 was proposed for POM gears that operate in the range of ±40% of
the gear resonance speed. For gears operating at the subcritical and
supercritical rotational speeds the value of K
v
=1.0 was reported.
Besides the effect on the dynamic forces due to vibrations, the
rotational speed also determines the sliding velocity. Higher rotational
speed results in a higher sliding velocity and increased frictional losses,
leading to higher operating temperatures (Sentihlvelan et al. [56],
Pogaˇ
cnik and Tavˇ
car [28]). With different operating temperatures the
obtained fatigue strength results would be different in the same manner,
i.e. lower operating temperatures lead to higher bending fatigue
strength and vice versa.
5.2. Effect of the coefcient of friction
When testing a new material for the use in polymer gear applications,
it is necessary to perform gear pair testing. The material’s fatigue
strength can also be determined by pulsator testing [57] or
specimen-based tests [58]. However, in many cases, merely having in-
formation on the material’s fatigue strength is insufcient. Knowledge
of the coefcient of friction is also required, as this is one of the main
factors determining the gear pair’s operating temperature. For polymer
materials the coefcient of friction by its physical denition is a function
of temperature, load, and sliding velocity [52]. In this work, the
Pogaˇ
cnik-Tavˇ
car [28] method was used to determine the so-called
calculated coefcient of friction. According to the results presented in
Figs. 7–9, it can be seen that the temperature calculation with the
calculated friction coefcient is closer to the measured temperature. The
VDI 2736 guideline species the same value of the coefcient of friction
for all polymer materials paired with a steel gear. For the rst iteration
of the gear design, the proposed values are sufciently exact, but a more
precise value of the friction coefcient is needed for more accurate
design calculations.
Employing gear testing it was observed that the bio-polymer PA 6.10
gears exhibited the best results in terms of lifespan, followed by the
POM, and then the PA 66 gears, which exhibited the worst results. If
pulsator tests at a controlled gear temperature were to be performed, the
result would be different, since the effect of the lower efciency (higher
coefcient of friction) of the material combination steel/PA 66 would
Table 6
The evaluated wear coefcient values.
material pair torque
[Nm]
ϑRoot [◦C] kW [10
−6
mm
3
/
(Nm)]
steel (Ra =0.689
μ
m) – POM 0.8 44.0 ◦C 4.54
steel (Ra =0.689
μ
m) – PA 66 0.8 53.5 ◦C 6.22
steel (Ra =0.689
μ
m) – PA
6.10
0.8 46.5 ◦C 1.57
steel (Ra =0.689
μ
m) – POM 1.0 48.8 ◦C 6.15
steel (Ra =0.689
μ
m) – PA 66 1.0 70.8 ◦C 29.24
steel (Ra =0.689
μ
m) – PA
6.10
1.0 54.7 ◦C 4.54
steel (Ra =0.689
μ
m) – POM 1.2 54.4 ◦C 8.32
D. Zorko et al.

Polymer Testing xxx (xxxx) xxx
11
not be taken into account. Thus, the testing of new materials must be
undertaken with great care, as using awed methodology can produce
misleading results.
5.3. Effects on the wear performance
Wear coefcients were determined in a manner as to be useful for
wear control calculations using the existing models [53]. The wear rate
is dependent on specic sliding between the meshing teeth; the larger
the specic sliding, the faster the wear rate will be and vice versa. The
proposed wear coefcients have been determined directly on the basis of
gear pair testing, taking into account the specic conditions that occur in
the contact of the meshing teeth. There is both sliding and rolling motion
present in the contact of meshing teeth, which is taken into account in
the determined wear coefcients. When conducting wear calculations of
a new gear pair, if the new gear pair has a signicantly larger specic
sliding comparing to the reference test gears, then a proportionally
higher wear rate is to be expected. As the study’s primary objective was
to determine the fatigue strength of the polymer gears tested, the steel
gears used were, of course, modied to minimize wear. The super-
nishing process enlarged the steel gears’ tip radius, which led to a
contact pressure reduction in the regions where the steel gear’s tip
meshed with the plastic gear. This effect was described in the authors’
previous work [9], where it was found that enlarging the tip radius led to
a signicant reduction in wear rate.
However, in the event of a steel/polymer contact and a large number
of operating cycles, wear cannot be completely avoided. The wear rate is
certainly also inuenced by the temperature, so the wear coefcients
determined in this work are suitable for controlling gear pairs, which
will operate at the same or lower temperatures than those at which the
reference gear pairs were tested. Some benchmark values on the wear
coefcient can be found in the VDI 2736 [44] guideline, where the wear
coefcient for a steel/POM material pair is given. A wear coefcient of
kW =3.4∙10
−6
mm
3
/(Nm) is given for a POM gear when in contact with
a steel gear of surface roughness Rz =1.5
μ
m. Steel gears with a surface
roughness of Ra =0.689
μ
m were used in this study. Converting the
roughness from Rz to Ra at the upper boundary of the spread gives Ra =
0.4
μ
m and on the lower value of the spread Ra =0.055
μ
m, where the
actual value is probably somewhere in between. In any case, the surface
roughness of the steel gear in the VDI guideline is much smaller than that
of steel gears used in this study. Therefore, also a higher value of the
wear coefcient was obtained (kW =5.86 ∙10
−6
mm
3
/(Nm)).
5.4. Effect of the contact ratio increase
The PA 6.10 gears exhibited a longer lifespan than the gears made
from POM and PA 66, despite the poorer mechanical properties pro-
vided by the material’s manufacturer. Using the numerical model, the
simulation of gear pairs under the tested conditions was simulated. The
coefcient of friction determined according to the Pogaˇ
cnik-Tavˇ
car
method was used when modeling a frictional contact between the
meshing teeth. Due to the small elastic modulus, the polymer teeth
deform under the inuence of load, which leads to an increase in the
contact ratio and reduction of root stress (Fig. 16). Similar observations
were also made by Hasl et al. [41,59]. In Fig. 16b the load-induced teeth
deection (determined at the tooth’s tip) and the corresponding actual
contact ratio of the tested gear pairs are presented. A good correlation
between the teeth deection and the contact ratio increase can be
observed. As the load increases, the actual contact ratio rate increases,
whereas the theoretical contact ratio is only geometry-dependent and
therefore constant. The contact ratio increase is 16–24.5% depending on
the load and the polymer material in gear pair. The relative difference
between the actual contact ratios of tested polymer gears is relatively
small due to the small differences in elastic modulus. The largest relative
difference was observed between the PA 6.10 and PA 66 gear pair loaded
with 1.2 Nm, where the relative difference is 3.7%. Due to having the
smallest elastic modulus the highest contact ratio was calculated for the
gear pair steel/PA 6.10. Corresponding to some differences in actual
contact ratio, there was also some difference in the root stress observed
(Fig. 16a), where the PA 6.10 gears exhibited the lowest root stress due
to the largest contact ratio.
5.5. Effect of the manufacturing technology
The test gears were manufactured by a gear hobbing process.
Extruded circular proles were cut into slices and used as the bases for
gear hobbing. With the exception of smaller series and larger modules,
polymer gears are in practice mostly manufactured with injection
molding. A comparison of wear rates between the injection-molded and
machine-cut POM gears was conducted by Mao et al. [23]. The authors
state that no differences between the observed failure modes of
injection-molded and machine-cut gears were observed. The wear rate
reported was independent of the manufacturing technology; unfortu-
nately, no results were reported on the fatigue behavior.
The material structure of the injection-molded gears is different from
that of hobbed gears. The gear surface where the melt comes into contact
with the mold is of amorphous structure, followed by a crystalline
structure towards the inside of the gear, where the crystals grow toward
the inside, since cooling there is slower and the material has more time
to form crystalline structures [60]. The material’s structure can be
improved with a proper design of gating system and the appropriately
chosen injection-molding process parameters (injection pressure,
Fig. 16. a) Simulation-calculated root stress in the polymer gear tested at torque 1.2 Nm, b) Simulation-calculated contact ratio of the tested gear pairs.
D. Zorko et al.

Polymer Testing xxx (xxxx) xxx
12
packing pressure, mold temperature, melt temperature, melt ow rate).
The effects of different processing parameters on the monotonic prop-
erties of injection molded POM samples were studied by Viana [61] and
Wright et al. [62]. It was observed that small changes in processing
conditions can cause pronounced changes in morphology, while having
numerically small effects on the crystallinity. Samples with a dense
structure of small spherulites were found to exhibit higher strength. In
some of the more recent studies Berer et al. [63] presented a compre-
hensive research on the fatigue behavior of two POM resins processed by
injection molding and compression molding under moderate conditions.
A signicant effect of processing conditions on the fatigue behavior of
simply shaped standard samples was reported. It was found that the
fatigue performance is not dependent only on the polymer material’s
crystallinity and morphology; rather it is also dependent on residual
stresses. Higher residual stresses correlate with lower mold tempera-
tures [64]. It can be expected that for parts of more complex shapes,
such as gears, the effects of processing conditions become even more
evident.
Injection molding gears also gives rise to the possibility of forming
voids [65], which is much less likely when hobbing gears from extruded
proles. If the injection-molding process is poorly executed, the result-
ing gears will not exhibit the same performance as the ones produced by
cutting. Furthermore, the same tolerances as for hobbed gears will be
difcult to achieve when using an injection molding process. Large tooth
deviations lead to stress concentration and higher heat generation [42],
and consequently shorter lifespan [66].
6. Conclusions
Based on the results it can be concluded that the design of polymer
gears is rather more complex than that of steel ones. Despite having the
lowest tensile and exural strength, the PA 6.10 gears exhibited the
longest lifespan when tested at identical test conditions. When
compared to POM gears, the average lifespan was 3.5 times longer, and
when comparing with PA 66 gears, the average lifespan was 10 times
longer. The bio-based material PA6.10 outperformed the most
commonly used fossil-based materials in polymer gear transmissions.
The results indicate that the fatigue strength of the PA 6.10 is higher,
leading to a longer service life of the gear when compared to POM and
PA 66 gears. The PA 6.10 exhibited also a lower coefcient of friction
than PA 66, leading to a lower operating temperature. Nevertheless, the
coefcient of friction for the steel/PA 6.10 was still higher than for the
steel/POM material pair. Based on the failure analysis, the predominant
failure type in all tested cases was root fatigue, though substantial wear
was also observed on gears operating for a higher number of cycles.
Based on the wear measurements, the wear coefcients of tested mate-
rial pairs were determined, leading to a conclusion that PA 6.10 exhibits
the lowest wear rate. The presented study conrms the potential for
using bio-based PA 6.10 in gear applications. The obtained results
enable design calculations for new polymer gear pairs made from the
tested polymer materials. The presented data should be used with great
care, since the results are based on the temperature and load range
tested in this study.
Author agreement
1) The authors have obtained the necessary authority for publication.
2) The paper has not been published previously, that it is not under
consideration for publication elsewhere, and that if accepted it will
not be published elsewhere in the same form, in English or in any
other language, without the written consent of the publisher.
3) The paper does not contain original material which has been pub-
lished previously, by the current authors or by others, of which the
source is not explicitly cited in the paper.
Data availability
The raw data required to reproduce these ndings cannot be shared
at this time due to technical or time limitations. The processed data
required to reproduce these ndings cannot be shared at this time due to
technical or time limitations.
Declaration of competing interest
The authors declare that they have no known competing nancial
interests or personal relationships that could have appeared to inuence
the work reported in this paper.
Acknowledgement
This research was nanced partly by the MAPgears project (the
project is co-nanced by the Republic of Slovenia and the European
Union under the European Regional Development Fund, contract no.
C3330-18-952014) and partly by the Slovenian Research Agency (con-
tract no. 630–33/2019-1).
Appendix A. Supplementary data
Supplementary data to this article can be found online at https://doi.
org/10.1016/j.polymertesting.2020.106994.
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