*Corr. Author’s Address: National Aviation University, Lubomyr Huzar 1, 03680 Kyiv, Ukraine, anatoliykor80@gmail.com 713
Strojniški vestnik - Journal of Mechanical Engineering 68(2022)11, 713-721 Received for review: 2022-06-20
© 2022 The Authors. CC BY 4.0 Int. Licensee: SV-JME Received revised form: 2022-09-03
DOI:10.5545/sv-jme.2022.242 Original Scientific Paper Accepted for publication: 2022-11-04
Comparison of Load-Carrying Capacity, Wear, and Resource of 
Metal-Polymer Corrected Spur Gears with a Gear  
Made of Polyamides РА6 or PA6+30CF
Chernets, M. – Opielak, M. – Kornienko, A.
Myron Chernets
1
 – Marek Opielak
2
 – Anatolii Kornienko
1,*
1 
National Aviation University, Aerospace Faculty, Ukraine 
2 
Lublin University of Technology, Poland
Based on the developed calculation research method of metal-polymer gears the analysis of the influence of height and angular correction 
of engagement of spur gears on load-carrying capacity, linear teeth wear, and resources is carried out. Gears with a pinion made of carbon 
steel 0.45%C and a gear made of basic polyamide PA6 or carbon fibre composite PA6 + 30CF were investigated. Quantitative and qualitative 
patterns of influence of both types of correction, changes in the initial teeth profile due to wear, mating conditions on the load carrying 
capacity, teeth linear wear, and service life of investigated metal-polymer gears have been established. Profile correction causes a decrease in 
the contact pressure in the engagement by different amounts during the meshing cycle. They are most significantly reduced in the input area 
of two-pair engagement. It was found that when using PA6 + 30CF, the maximum contact pressures are about 1.29 times higher than with 
PA6 at all values of the shift coefficients, regardless of its type. The tooth linear wear has different values during the meshing cycle depending 
on the shift coefficients and parity of engagement. The resource first increases with increasing the shift coefficients, reaching their optimum, 
and then decreases again. Regularities of this influence for each type of correction of engagement are established. Metal-polymer gears with 
a gear made of PA6 + 30CF will have a significantly higher service life than with a gear made of PA6.
Keywords: metal-polymer spur gear, height and angular correction of engagement, polyamides PA6 and PA6 + 30CF, maximum contact 
pressures, linear teeth wear, resource
Highlights
• 	 Calculation of contact pressures, wear, and resources of corrected MP spur gears is performed.
• 	 The influence of height and angular teeth correction on these service characteristics of gears is investigated.
• 	 Quantitative and qualitative patterns of the effect of correction on these characteristics are given.
• 	 The optimal values of the shift coefficients providing maximum gears resource are determined.
• 	 A comparative evaluation of service characteristics of gears made of PA6 and PA6 + 30CF was performed.
0  INTRODUCTION
Metal-polymer (MP) gears are common in various 
fields of human activity, in a variety of technical 
devices, mechanisms, and machines. As with metal 
gears in MP gears for the purpose of increasing 
their loading carrying capacity, resources, and wear 
resistance, profile shifting is used. However, effective 
methods for calculating tribotechnical parameters, 
i.e., the tooth wear and resource of both uncorrected 
and corrected MP have not been developed. There 
are standardized calculation methods [1] and [2] and 
numerical methods [3] to [5] for studying uncorrected 
gears with metal-toothed wheels. In [3] to [5], the 
modelling of the tooth wear of spur and screw gears 
by numerical methods with Archard’s linear law of 
abrasion wear was carried out. They were used to 
assess the load-carrying capacity of MP gears in [6] to 
[10], where the contact and bending teeth strength was 
studied. In [6] and [7], the MP gears with a gear made 
of polyamide PA6 were investigated for these stresses. 
In [8], the load capacity of spur gears with PA66 
was studied. In contrast, virtually no computational 
methods exist for studying the wear and resources 
of MP gears in the literature. [9] presents simplified 
and [10] presents improved methods for calculating 
the wear resistance of an MP spur gears with a gear 
made of PA6 + 30GF, PA6 + 30CF with dispersed 
glass and carbon fibres. Dry friction using Archard’s 
law of abrasive wear is considered, by which the wear 
is directly proportional to the contact pressure and 
depends linearly on the path of sliding friction. This 
wear mechanism is not inherent, much less dominant 
for MP gears.
Regarding the study of the effect of correction 
(height or angle) on the load-carrying capacity, wear, 
and resources of MP gears, such methods and relevant 
calculations are not available in the literature. There 
are some results in the literature of studies of metal 
gears with corrected teeth [11] to [16] for their load-
carrying capacity and efficiency. Accordingly, in [11], 
on the basis of the wear model of screw gears, the 
influence of different types of profile shifting on wear 
according to Acrhard’s law was investigated; in [12], 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)11, 713-721
714 Chernets, M. – Opielak, M. – Kornienko, A.
the influence of the angular correction of spur gears on 
the contact and bending stresses was investigated; in 
[13] and [14], the analysis of influence of geometrical 
parameters of gears, including teeth correction to the 
specified stresses was given; in [15], the optimization 
algorithm for spur gears with height correction of 
engagement is presented; in [16], the influence of 
height correction on normal Mises stresses, bending 
stresses, and teeth deformation was studied.
Also, [17] provides an overview of various types 
of metal spur and helical gears with non-involute 
teeth, found in various applications. The comparison 
of involute and non-involute gears was carried out on 
the basis of the following criteria: Hertzian pressure, 
oil film thickness, bending stress at the root of the 
tooth, contact temperature, and gear noise.
Given the urgency of these scientific and technical 
problems, a modified method of calculating MP gears 
with correction of engagement was developed [18] and 
[19] based on the author’s multicriteria generalized 
method of studying metal gears, including correction 
of engagement [21] to [25]. These calculation methods 
are based on the phenomenological methodology of 
research of wear resistance at sliding friction [20] and 
[21] by friction-fatigue mechanism. This approach is 
fundamentally different from the wear mechanism of 
metal-polymer tribocouples according to the adhesive-
abrasive wear Archard’s law.
The solution of the wear-contact problem is 
given in the article and the tribological behaviour of 
MP spur gears with a steel pinion and gears made 
of two polyamides: unreinforced PA6 or reinforced 
with short carbon fibres PA6 + 30CF composite is 
investigated. The study considered such real factors 
as the conditions of tooth engagement, height and 
angular correction of engagement, and the impact of 
tooth wear on contact pressures and resource.
1  CALCULATION METHODS
The calculation method aspects for the study of 
uncorrected MP spur gears are thoroughly presented in 
authors’ previous works [18] and [19]. Therefore, the 
following are the basic design relationships for gears 
with height and angular correction of engagement.
The teeth contact strength of the MP gears 
is determined using the known Hertz formula for 
different gear materials. Respectively 
 pN
jj max
./ () ,   0 564  (1)
where p
j max
 is initial maximum contact pressures at 
the j
th
 point, which occur under the action of nominal 
torque; j = 0, 1, 2, …, s the points of contact on the 
teeth profiles; N′ = N / (bw); N = T
nom
 K
g
 / (r
1
 cos α) force 
in engagement; T
nom
 = 9550P / n
1
 rated torque; P power on 
the driving shaft; n
1
 pinion rotational speed; K
g
 dynamic 
coefficient; r
1
 = z
1
m pitch circle diameter of the pinion; 
m module; α = 20° pressure angle; z
1
, z
2
 numbers of 
teeth;     



11
1
2
12
2
2
// EE ; E, ν Young’s 
modules and Poisson’s ratios; b face width; w the number 
of teeth pairs in engagement; ρ
j
 reduced radius of curvature 
of the tooth profiles at the j
th
 point. 
Respectively,
 


j
jj
jj
js 


12
12
0123 ,, ,,,, ,  (2)
where ρ
1j
, ρ
2j
 are the radii of curvature of the teeth 
profiles of the spur pinion and gear at j
th
 point [19] and 
[25], j = 0 and j = s correspond to the first and last point 
of the teeth engagement.
The linear teeth wear h′
2j
 of the polymer gear 2 
at any point j of their profiles during a single time of 
their contact t′
j
 in a one-pair engagement at maximum 
contact pressure p
j max
 is calculated as follows [18], 
[21], [22] and [24].
 
( )
( )
( )
( )
max max
0.5
kk
kk
mm
jj j jj j
kj
mm
k m kS
vt f p vt
h
CR C
τ
τ
′′
′ = = , (3)
where ν
j
 = ω
1
 r
b1
(tgα
1j
 – tgα
2j
) [21] and [22] sliding 
speed in the engagement; t′
j
 = 2b
j
 / ν
0
 time of 
teeth contact at movement of j
th
 contact point 
on a tooth profile to hertz contact patch width  
22 256 bN
jj
  .  ; ν
0
 = ω
1
 r
1
 sinα the speed of 
contact point movement on the tooth profile; ω
1
 
pinion angular velocity; f sliding friction coefficient; 
τ
j max
 = fp
j max
 specific force of friction according to 
Coulomb’s law; R
m
 tensile strength of polymeric 
material under tension (compression); τ
S 2
 the shear 
strength of the gear polymer material; C
k
, m
k
 wear 
resistance characteristics of gear materials; k = 1, 2,  
toothed wheels numbering (1 – pinion, 2 – gear).
In spur gears two - one - two-pair teeth 
engagement is realized. The angle Δφ
1F
2
 of exit from 
the two-pair and at the same time the entrance to the 
one-pair engagement and the angle Δφ
1F
1
 of exit from 
it is determined according to the author’s method
During the gears operation due to the teeth 
slippage in the engagement, their wear inevitably 
occurs. Its variable value during each subsequent act 
of their tribocontact is calculated as follows [19], [21], 
[22], and [25]: 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)11, 713-721
715 Co m pariso n	o f	Lo ad-Carr ying	Capacity ,	W ear ,	and	R eso urce	o f	Me tal-Po lymer	Co rrect ed	Spur	Gear s	with	a	Gear	Made	o f	Po lyamid es	Р А6	o r	P A6+30CF	
  



h
vt fp
CR
kjn
jj hj h
m
km
m
k
k
max
. 05
, (4)
where t′
jh
 = 2b
jh
 / ν
0
 = var time of teeth wear during 
movement of j that point of their contact along a tooth 
contour to a variable due to wear width of a contact patch
 
2b
jh
; p
jh max
 variable maximum contact pressure at the j
th
 
point of teeth interaction during wear. 
As a result of tooth profiles wear their initial radii of 
curvature increase ρ
1j
, ρ
2j
. Consequently, the maximum 
contact pressures p
j max
 are reduced and the width of the 
contact patch 2b
j
 at j
th
 points is increased. Accordingly, 
their current values of p
jh max
 and 2b
jh
 are calculated 
according to modified Hertz formulas [19] and [25]:
pN bN
jh jh jh jh max
./ () ,. ,     0 564 22 256   (5)
where ρ
jh
 = (ρ
1jh
 ρ
12h
) / (ρ
1jh
 + ρ
12h
) is the reduced radius 
of curvature of the gear profile, changeable in the 
result of wear, ρ
1jh
, ρ
2jh
 changeable curvature radii of 
pinion and wheel tooth profiles.
The variable radii of curvature ρ
kjh
 are calculated 
according to the method given in [18], [19], and [25]. 
For the numerical solution, a block calculation 
procedure is used, in which, during a randomly 
selected number of teeth interactions (blocks of 
interactions B), the single wear is calculated according 
to Eq. (2) followed by linear summation [18] and [25]. 
In each subsequent block, the single wear of the teeth 
is calculated by Eq. (4).
For the number of revolutions of the pinion n
1s
 
and the gear n
2s
 corresponding to a certain number 
of the accepted size of the interaction blocks B with 
constant contact conditions, their total wear h
1jn
 and 
h
2jn
 at j
th
 points of contact is determined as follows:
 hh hh
jn jB
n
jn jB
n
ss
11
1
22
1
12


,, (6)
where n
2s
 = n
1s
 / u; h
kjB
 = Σ h′
kj
 teeth wear in each block 
of their interaction.
Then, considering the change in initial contact 
pressures p
j max
 due to tooth wear, the gears resource 
t
В
 at the calculated number of revolutions n
1s
 or n
2s
 is 
expressed as follows:
 t
n
n
n
n
B
ss
= =
1
1
2
2
60 60
. (7)
The above method of calculating the uncorrected 
MP gears is also used [22], [24] and [26]. For gears 
with height and angular correction (Fig. 1).
a) 
b) 
Fig. 1. a) Spur gears with height, and  
b) correction and angular correction
In gears with height correction, the shift 
coefficients are assumed to be the same x
1
 = – x
2
 and 
the total shift coefficient is x
Σ
 = x
1
 + x
2
 = 0. Accordingly , 
the centre distance a = r
1
 + r
2
 remains the same as 
in the gears without offset. Only the addendum and 
dedendum radii will be variable
 rr xm rr xm
aa 11 12 22
11   () ,( ), (8)
 rr xm rr xm
ff 11 12 22
12 51 25    (. ), (. ), (9)
where r
2
 = mz
2
 is a pitch radius.
All formulas for calculating other parameters 
have the same structure as for uncorrected gears [22].
In gears with angular correction, the shift 
coefficients x
1
 ≠ x
2
 (usually x
1
 > 0, x
2
 > 0); total shift 
coefficient x
Σ
 > 0; the corrected centre distance 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)11, 713-721
716 Chernets, M. – Opielak, M. – Kornienko, A.
a
w
 = (r
w1
 + r
w2
) > a; the corrected pressure angle α
w
 > α 
on the initial pitch circle. Accordingly, the pitch radii 
of the pinion and the gear, radii of the addendum and 
dedendum are expressed as follows
 rr rr
w
w
w
w
11 22

cos
cos
,
cos
cos
,




 (10)
rr xK mr rx Km
aa 11 12 22
11   () ,( ),
 (11)
 
rr xK m
rr xK m
f
f
11 1
22 2
12 5
12 5
 
 
(. ),
(. ), (12)
where K = [(a – a
w
) / m] + x
Σ
 is the reduction coefficient 
of the addendum heights.
At this type of correction due to changes in 
values of a
w
, α
w
, r
w1
, r
w2
, r
a1
, r
a2
, some formulas 
for calculation of geometrical parameters will have 
a changed structure [21] and [22], compared to 
uncorrected gears.
In practice, for a positive correction x
Σ
 > 0 the 
inversely proportional method of resolution of x
Σ
 is 
often used [22]:
 x
z
zz
xxxx
1
2
12
21




,. (13)
At height correction, the centre distance will not 
change, unlike the angular correction.
2  RESULTS OF THE SOLUTION, DISCUSSION
Data for calculation: Т
nom
 = 4000 Nmm, n
1
 = 700 rpm; 
В = 420000 revolutions (10 hours of operation) the size 
of the block with constant conditions of tribocontact; 
K
g
 = 1.2; m = 4 mm, u = 3 gear ratio, z
1
 = 20, z
2 
= 60, 
b = 50 mm, h
2*
 = 0.5 mm acceptable teeth wear of the 
polymer gear.
Hight correction: x
1
 = – x
2
 = 0, 0.1, 0.2, 0.3; 
а = 160 mm; α = 20°. Angular correction:x
Σ
 = 0.3; 
x
1
 = 0, x
2
 = 0.3; x
1
 = 0.05, x
2
 = 0.25; x
1
 = 0.1, x
2
 = 0.2; 
x
1
 = 0.2, x
2
 = 0.1; x
1
 = 0.25, x
2
 = 0.05; а
w
 = 161.169 mm; 
α
w
 = 21.11°. The recommended values of the shift 
coefficients for the specified number of teeth in the 
case of angular correction are x
1
 = 0.225, x
2
 = 0.075.
The characteristics of materials of MP gears: 
• Pinion: carbon steel 0.45%C, normalizing, 
grinding, Е
1
 = 2.1·10
5 
MPa, ν
1
 = 0.3; С
1
 = 10
9
, 
m
1
 = 2, τ
S1
 = 365 MPa. 
• Gear: polyamide Р А6, Е
2
 = 2300
 
MPa, ν
2
 = 0.4; 
С
2
 = 1.34·10
6
, m
2
 = 1.15, τ
S2
 = 40 MPa; f = 0.23; 
polyamide composite Р А6+30CF, filled with 30 
% fine carbon fiber, Е
2
 = 3300
 
MPa, ν
2
 = 0.41; 
С
2
 = 3.67·10
6
, m
2
 = 1.15, τ
S2
 = 40 MPa; f = 0.25.
The wear resistance of materials of metal-
polymer tribocouples was established according to the 
pin-on-disk scheme in the conditions of dry friction 
according to the ISO 7148-2 standard (T = 23 ± 1 °C, 
relative humidity of air 50 ± 5 %) [27].
The results of research of height and angular 
correction influence on initial maximum contact p
j max
 
and wear contact p
jh max
 pressures in engagement, 
linear wear h
2j
 of gear teeth, minimum gears resource 
t
Вmin
 are given in Figs. 2 to 6. Figs. 2 and 3 show the 
pressure level p
j max
 in the meshing cycle for both 
types of correction. To the left and right are the areas 
of two-pair engagement (input and output), and in the 
centre, the area of one-pair engagement. Here Δφ
 
is 
the angle of rotation of the pinion tooth from the point 
of the entry of the teeth into the engagement (p.0) to 
the next points with the selected step. 
a) 
b) 
Fig. 2.  Maximum contact pressures in engagement (PA6):  
a) height correction [x
1
 (–x
2
) 	≡	(x
1
 = –x
2
)], b) angular correction

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)11, 713-721
717 Co m pariso n	o f	Lo ad-Carr ying	Capacity ,	W ear ,	and	R eso urce	o f	Me tal-Po lymer	Co rrect ed	Spur	Gear s	with	a	Gear	Made	o f	Po lyamid es	Р А6	o r	P A6+30CF	
а)	
b) 
Fig. 3.  Maximum	co ntact	pressures	in	engagement	(Р А6+30CF):	
a) height correction, b) angular correction
The obtained results of calculations show that at 
the entrance to the one-pair engagement, the initial 
contact pressures p
j max
 reach the highest value. When 
the teeth are corrected, the contact pressures will 
decrease in different ways during the meshing process. 
At the entrance to the two-pair engagement up to 1.23 
times for the height correction and up to 1.17 times 
for the angular correction, and then up to 1.14 times. 
In the area of one-pair engagement, the pressure drop 
due to tooth correction will be smaller. Instead, in the 
initial area of two-pair engagement, the pressure drop 
will be much less noticeable. The specified qualitative 
regularities of reduction of the initial maximum 
contact pressures in engagement of MP gears at both 
types of correction are close irrespective of a type 
of polymeric materials. In terms of quantification, 
the pressures will be about 1.29 times higher in the 
gears with a gear made of PA6 + 30CF than with a 
gear made of PA6 at different values of the shift 
coefficients. When the engagement is corrected, the 
angle of entry into the one-pair engagement and the 
pitch point are shifted to the left. With both types of 
correction, the pressure level in the pitch point will 
not change.
The wear of the gear teeth of the corrected gears 
leads to a certain differentiated reduction of pressures 
p
j max
 in the engagement. For the example of the 
gears with height correction trends of these changes 
are shown in Fig. 4. The figure shows the trends of 
these changes on the example of the gears with height 
correction.
а)	
b) 
Fig. 4.  Maximum	w ear	co ntact	pressures:	а)	Р А6,	b)	Р А6+30CF
The smallest decrease in p
j max
 (up to 1.053 times) 
is observed in the input area of engagement and in the 
transition to the central region. In contrast, at the exit 
from the central region the duction will be up to 1.15 
times and much more up to 1.24 times at the exit from 
its right region. Wear-contact pressures at angular 
correction have similar quantitative and qualitative 
laws, as in case of height correction.
Correction of the engagement affects the course 
of linear wear h
2j
 of the gear polymer teeth in different 
ways at selected points of their profile. The research 
results are shown in Fig. 5.

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)11, 713-721
718 Chernets, M. – Opielak, M. – Kornienko, A.
а)	
b) 
Fig. 5.  Linear wear of the teeth profile of the polymer gears during 
engagement: a) height correction, b) angular correction
Correction of engagement leads to changes in 
tooth wear at characteristic points: at the entrance to 
the left area of two-pair engagement, at the entrance 
to the area of one-pair engagement, at the exit from 
it, and at the exit from the right area of two-pair 
engagement. In all cases of height correction, the 
acceptable wear is achieved at the exit of the teeth 
from the area of one-pair engagement. For angular 
correction, the acceptable wear is achieved at the point 
of entrance of the teeth into one-pair engagement at  
x
1
 = 0, 0.05, 0.1, and at x
1
 = 0.2, 0.25 the acceptable 
wear is achieved at the exit from this engagement. 
As already noted, the correction leads to a shift of 
the pitch point to the left, which is clearly seen in the 
figures because here the wear of the teeth is close to 
zero. This is because the slippage speed at the pitch 
point is almost zero.
The estimated minimum resource t
B min
 of MP 
gears for both types of correction and the studied gear 
materials is shown in Fig. 6. Of the gears resource 
determined at all characteristic points of engagement, 
the minimum will be that where the accepted 
allowable wear of the gear teeth is achieved (Fig. 5). 
а)	
b) 
Fig. 6.  Influence of the teeth correction on the minimum resource 
t
B min
 of MP gears at a teeth inclination:  
a) height correction, b) angular correction
The gears with a gear made of PA6 + 30CF will 
have a significantly higher resource t
B min
 than a gears 
with a gear made of PA6 in the whole range of shift 
coefficients. It is 2.4 times larger at the optimal values 
of the shift coefficients of height correction x
1
 = –x
2
 = 
0.1 and angular correction x
1
 = 0.1, x
2
 = 0.2. Therefore, 
the results show that the correction of the engagement 
in relation to the gears resource will be most effective 
at these coefficients. It should be noted that with 
these optimal shift coefficients, the gears resource 
with height correction increases about 1.05 times, 
and with angular correction in 1.1 times (gear made 
of PA6) and in 1.22 times (gear made of PA6+30CF. 
A comparison of the effectiveness of engagement 
correction by both methods shows that at height 
correction at x
1
 = –x
2
 = 0.126 the gears resource will be 
lower than at x
1
 = –x
2
 = 0. That is, in the future such 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)11, 713-721
719 Co m pariso n	o f	Lo ad-Carr ying	Capacity ,	W ear ,	and	R eso urce	o f	Me tal-Po lymer	Co rrect ed	Spur	Gear s	with	a	Gear	Made	o f	Po lyamid es	Р А6	o r	P A6+30CF	
correction will not make sense given the reduction 
of gears resource. Instead, with angular correction 
in the gears at x
1
 = 0.3, x
2
 = 0, its resource will be 
the same as the uncorrected gears. For the angular 
correction in the case of normative distribution of 
coefficients x
1
 = 0.225, x
2
 = 0.075, the gears resource 
will be somewhat higher, as at x
1
 = 0, x
2
 = 0.3, but 
less in 1.13 times than at the optimal values of the 
coefficients x
1
 = 0.1, x
2
 = 0.2. Presented in Fig. 6, the 
nature of the hange in the gears resource indicates that 
the pre-optimal shift coefficients are better for height 
correction, and the post-optimal are better for angular 
correction.
The results of this type of analytical research 
realize the possible optimization of gears by three 
criteria:
1)  The load carrying capacity of the gears by p
max
 or 
p
h max
.
 This confirms the well-known trend that the 
correction of engagement leads to a decrease in 
the level of p
max
, and the above also shows their 
change during tooth wear. Contact pressures 
will be lowest at the highest values of the shift 
coefficients.
2)  Linear wear h
2j
 of the tooth profile 
 Given this criterion, larger coefficients are more 
rational for height correction x
1
 = –x
2
 or angular 
correction x
1
. Then the acceptable wear will not 
be at the entrance to the two-pair engagement, as 
is the case of uncorrected gears, but at the exit of 
the teeth from the one-pair engagement or at the 
entrance to it.
3)  Gears resource t
B min
 As established, the longest life of corrected 
gears will be achieved with the specified optimal 
shift coefficients. Since the service life of the 
gears is its most important characteristic from a 
practical point of view, the other two criteria will 
be subordinate. It should be noted that with the 
specified optimal shift coefficients, the second 
criterion will actually be provided as well.
3  CONCLUSIONS
1.  The initial maximum contact pressures p
j max
 in 
the studied MP gears with height and angular 
correction have converged quantitative and 
qualitative patterns of change during the cycles 
of two-one-two-pair engagement. Correction 
of teeth has the most significant effect on their 
reduction in the entrance area of two-pair 
engagement, and less in one-pair engagement. 
The contact pressure in the gears with a gear 
made of PA6 + 30CF will be 29 % higher than 
with a gear made of PA6 regardless of the shift 
coefficients. Due to the wear of the polymer gear 
teeth, there is no noticeable effect on the change 
of initial pressures p
j max
 in the first and second 
areas of engagement. Instead, such a change in 
pressure is more significant in the initial region of 
two-pair engagement. Quantitative and qualitative 
patterns of changes in wear and contact pressures 
are similar in both types of tooth correction.
2.  The linear wear h
2j
 of the polymer gear teeth 
profiles depends not only on the specific friction 
force (nonlinear) and sliding speed (linear), which 
are variable at each point of contact, but also 
on the number of pairs of teeth simultaneously 
engaged. Therefore, it systematically changes 
with successive contact of the teeth during their 
rotation, reaching the acceptable value of h
2*
 
at any of the three characteristic points: at the 
entrance to the two-pair engagement, at the 
entrance or exit of the one-pair engagement. 
This fact depends on the combination of the shift 
coefficients. In fact, for both types of correction, 
the maximum wear h
2*
 will be achieved at the 
edges of one-pair engagement
3.  Along with the contact teeth strength, which must 
be ensured when designing uncorrected gears 
according to ISO 6336: 2006-10, DIN 3990: 1987-
12 [1] and [2] for calculating the load capacity 
of gears with metal toothed wheels or also the 
recommendations of VDI 2736 Blatt 2:2014-06: 
2014 [28] for thermoplastic gears, from a practical 
point of view, the most desirable tribotechnical 
parameter is their forecast resources. According 
to the developed calculation method of research 
of MP gears, such estimation of resources was 
carried out both for uncorrected, and for corrected 
gears. Accordingly, both quantitative and 
qualitative patterns of the impact of height and 
angular correction of engagement on the resource 
are established above. It is shown that there are 
optimal shift coefficients that provide a higher 
gears life compared to uncorrected gears. Also, 
expedient areas of shift coefficients values at 
height and angular correction are established. In 
fact, this method can be a reasonable basis for the 
rational choice of shift coefficients, both metal 
and metal-polymer gears.
4.  It should be noted that it is known from practice 
that, as a result of the increased bending of the 
teeth of polymer composite gears, a positive 
effect arises, which consists in an increased area 
of two-pair engagement, that is, in an increase 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)11, 713-721
720 Chernets, M. – Opielak, M. – Kornienko, A.
disperse-reinforced composites: Part 1. Journal of Friction and 
Wear, vol. 34, p. 65-69, DOI:10.3103/S1068366613010133.
[11] Kahraman, A., Bajpai, P., Anderson, N.Е. (2005). Influence 
of tooth profile deviations on helical gear wear. Journal 
of Mechanical Design, vol. 127, no. 4, p. 656-663, 
DOI:10.1115/1.1899688.
[12] Pasta, A., Mariotti Virzi, G. (2007). Finite element method 
analysis of a spur gear with a corrected profile. The Journal of 
Strain Analysis for Engineering Design, vol. 42, no. 5, p. 281-
292, DOI:10.1243/03093247JSA284.
[13] Zwolak, J., Martyna, М. (2011). Analysis of contact stress and 
bending stress occuring in tooths of gear transmission power 
shifts. Tribologia, vol. 42, no. 3, p. 155-165. (in Polish)
[14] Zwolak, J., Wittek, M. (2011). Optimization of the geometrical 
parameters of toothed gears in the aspect of contact stress 
minimization. Tribologia, vol. 45, no. 6, p. 283-291. (in Polish)
[15] Miler, D., Loncar, A., Žeželj, D., Domitran, Z. (2017). Influence 
of profile shift on the spur gear pair optimization. Mechanism 
and Machine Theory, vol. 117, p. 189-197, DOI:10.1016/j.
mechmachtheory.2017.07.001.
[16] Bodzás, S. (2019). Analysis of the effect of the addendum 
modification coefficient for contact surfaces of spur gear. 
Journal of Mechanical Engineering, vol. 69, no. 1, p. 5-16, 
DOI:10.2478/scjme-2019-0001.
[17] Okorn, I., Nagode, M., Klemenc, J. (2021). Operating 
Performance of External Non-Involute Spur and Helical 
Gears: A Review. Strojniški vestnik - Journal of Mechanical 
Engineering, vol. 67, no. 5, p. 256-271, DOI:10.5545/sv-
jme.2020.7094.
[18] Chernets, M. (2019). Method of calculation of tribotechnical 
characteristics of the metal-polymer gear, reinforced with glass 
fiber, taking into account the correction of tooth. Maintenance 
and Reliability, vol. 21, no. 4, p. 546-552, DOI:10.17531/
ein.2019.4.2.
[19] Czerniec, M., Kornienko, A. (2020). Prediction of the 
service life of metal-polymer gears made of glass and 
carbon fibre-reinforced polyamide, considering the 
impact of height correction. Advances in Science and 
Technology Research Journal, vol. 14, no. 3, p. 15-21, 
DOI:10.12913/22998624/124553.
[20] Chernets, M.V., Kelbinski, J. (2004). Computional evaluation of 
the wear and service life of helical involute cylindrical gears. 
Problems of Tribology, no. 3, p. 104-112.
[21] Chernets, M.V., Kelbinski, J., Yarema, R.Ya. (2011). 
Generalized method for the evaluation of cylindrical involute 
gears. Materials Science, vol. 47, p. 45-51, DOI:10.1007/
s11003-011-9366-9.
[22] Chernets, M.V., Yarema, R.Y., Chernets, Y.M. (2012). A method 
for the evaluation of the influence of correction and wear of 
the teeth of a cylindrical gear on its durability and strength. 
Part 1. Service life and wear. Materials Science, vol. 48, р. 
289-300, DOI:10.1007%2Fs11003-012-9505-y.
[23] Chernets, M.V., Yarema, R.Y., Chernets, Y.M. (2013). A method 
for the evaluation of the influence of correction and wear of 
the teeth of a cylindrical gear on its durability and strength. 
Part 2. Contact strength. Materials Science, vol. 48, p. 752-
756, DOI:10.1007/s11003-013-9565-7.
in the overlap coefficient. Moreover, this should 
lead to some reduction of the contact pressures 
at the entrance to the one-pair engagement. 
Perhaps they will then have values close to or 
lower than the pressures at the entrance to the 
two-pair engagement (Figs. 1 and 2). Due to the 
reduction of the maximum contact pressures, 
the gears resources will increase. The method 
of calculating MP gears developed by us does 
not take into account the influence of tooth 
deflection on the studied contact and tribocontact 
parameters. However, based on it, it is possible 
to carry out their full-scale quantitative and 
qualitative analysis, which has not yet been 
carried out by other researchers. Its results should 
be interpreted as reflecting worse conditions of 
contact and wear-contact interaction of teeth in 
engagement. The deflection of the teeth in the 
actual state of engagement of MP gears even 
improves in view of the above-mentioned typical 
geometric condition.
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721 Co m pariso n	o f	Lo ad-Carr ying	Capacity ,	W ear ,	and	R eso urce	o f	Me tal-Po lymer	Co rrect ed	Spur	Gear s	with	a	Gear	Made	o f	Po lyamid es	Р А6	o r	P A6+30CF	
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