S. SOVILJ-NIKI] et al.: MODELING OF THE TOOL LIFE FUNCTION OF A HOB MILLING TOOL USING ...
587–593
MODELING OF THE TOOL LIFE FUNCTION OF A HOB MILLING
TOOL USING GENETIC PROGRAMMING
MODELIRANJE FUNKCIONALNE DOBE TRAJANJA REZKARJEV
S POMO^JO GENETSKEGA PROGRAMIRANJA
Sandra Sovilj-Niki}
1*
, Ivan Sovilj-Niki}
2
, Bogdan Sovilj
2
1
University of Novi Sad, Faculty of Education, Podgori~ka 4, Sombor, Serbia
2
University of Novi Sad, Faculty of Technical Sciences, Trg Dositeja Obradovi}a 6, Novi Sad, Serbia
Prejem rokopisa – received: 2023-07-24; sprejem za objavo – accepted for publication: 2023-09-17
doi:10.17222/mit.2023.954
The tool life of a hob milling tool and its cutting parameters have the greatest impact on gear cutting costs. The aim in this re-
search was to model the tool life function of a hob milling tool, taking into account its impact on production costs. Experimental
research of the tool life of a model single-tooth hob milling tool was carried out. On the basis of the obtained measurement re-
sults and by applying genetic programming, the tool life function of the hob milling tool was modelled. The paper presents a
new model of the tool life function of the model single-tooth hob milling tool depending on the input cutting parameters, which
include the cutting speed, axial feed and tangential feed.
Keywords: tool life, gear cutting, hob milling tool, genetic programming
@ivljenjska doba trajanja rezkarja in parametri rezanja imajo velik vpliv na stro{ke izdelave menjalnikov. V tem ~lanku avtorji
predstavljajo modeliranje `ivljenjske dobe oziroma funkcionalne dobe trajanja rezkarja za gredi menjalnikov in njen vpliv na
stro{ke proizvodnje. V ~lanku opisujejo raziskavo pri uporabi modela rezkalnega orodja z enojnim ozobljenjem. Na osnovi
meritev in uporabe genetskega programiranja so avtorji modelirali funkcionalno dobo trajanja izbranega modelnega rezkarja. V
~lanku predstavljajo avtorji nov model funkcije za funkcionalno dobo trajanja rezkarjev za rezkanje gredi menjalnikov v
odvisnosti od izbranih vhodnih parametrov rezkanja v katere so vklju~eni hitrost rezanja ter osni (radialni) in tangencialni
pomik rezkarja.
Klju~ne besede: funkcionalna doba trajanja, rezkar za rezkanje gredi menjalnikov, genetsko programiranje
1 INTRODUCTION
Hob milling, as one of the most complex cutting pro-
cesses, is mostly used in the gear cutting of cylindrical
gears due to the high productivity of the process. The de-
sign of a modern process of gear cutting requires an
analysis of all technical/technological parameters of the
process and an application of appropriate scientific meth-
ods in order to model and optimize the conditions of the
gear cutting process. Hob milling is a multi-parameter
and complex way of processing the toothing of cylindri-
cal gears. It is an efficient machining process for
high-quality gear cutting of cylindrical gears that
achieves the highest productivity.
Hob milling is associated with complicated kinemat-
ics, chip formation and flow, as well as with hard-to-de-
scribe wear mechanisms of the hob milling tool. Other
authors presented results of a study of hob milling mod-
eling including tool wear prediction models and experi-
mental determination of the tool life.
1
The relationship
between the wear and geometric parameters of the
cross-section of a chip was also studied.
2
In this study,
the tangential displacement values of the hob milling
tool during hob milling for a more uniform wear distri-
bution of cutting teeth were recommended. There is no
analytical wear model based on computer modeling of
the geometry of chips. Also, the influence of thermal and
frictional causes of wear is estimated only visually. Ef-
fects of different factors on the wear resistance and tool
life in hob milling were investigated in several studies.
3–5
The methods of these studies are based on a simulation
of hob milling of multi-axis CNC machines, which re-
produce the kinematics of the hob milling tool using
simplified cutting tools – such as a single-tooth linear fly
hob, which simulates hob milling of hob milling ma-
chines and multi-axis CNC machines. However, the main
disadvantage of this approach is that the kinematics of
cutting with this hob milling tool only partially corre-
sponds to the generative type of hob milling.
6
Hob mill-
ing computer simulation and research of kinematics data
were also investigated.
6
In this paper the operation of a
hob milling tool at the level of certain elements – teeth
and edges – was studied. The aim of the research is to
identify the possibility of improving the tool operability
and durability as well as to investigate the wear develop-
ment on the hob milling tool considering shifting kine-
matics.
An investigation of the structure and tribological
characteristics of the material of uncoated and coated
single-tooth hob milling tool was carried out under
Materiali in tehnologije / Materials and technology 57 (2023) 6, 587–593 587
UDK 519.87: 620.169.1 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 57(6)587(2023)
*Corresponding author's e-mail:
sandrasn@eunet.rs (Sandra Sovilj-Niki})

model conditions. The authors examined the friction co-
efficient and wear volume and determined that the high-
est quality of the tested materials for a model sin-
gle-tooth hob milling tool was HS 6-5-2-5 coated with
TiAlN.
7
Other authors have shown that the introduction
of a three-tread coated integral hob milling tool into the
production process of gear cutting of cylindrical gears is
justified because a significantly higher productivity is
achieved and better quality of a machined surface is also
obtained.
8
An analysis of the obtained research results
for real production conditions showed that less axial dis-
placement, a
p1
= 1.1 mm, provides less wear and a more
uniform distribution of wear on all the teeth of a hob
milling tool during gear cutting of cylindrical gears with
oblique teeth.
9
Some authors determined that the tool
material, work-piece material, module, procedure of hob
milling, coolant and lubrication and coating of a tool
have an impact on the hob milling process of gear teeth
and on the tribological characteristics of the coated and
uncoated elements of tribo-mechanical systems in a
model and in real conditions.
10
Experimental research
was carried out in a model and real production condi-
tions and results have shown that hob milling tools with
inserted combs coated with TiN have their tool life
higher by 27.28 % compared to hob milling tools with
inserted uncoated combs. Results have also shown that
hob milling tools with inserted combs coated with TiAlN
have their tool life higher by 60.6 % compared to hob
milling tools with inserted combs coated with TiN.
11
The most significant parameter that characterizes the
operating capacity of a cutting tool is wear. In the last
few years, the development of information technologies
enabled an increasing application of artificial intelli-
gence methods for the prediction and intelligent monitor-
ing of tool wear. Some authors developed an LS-SVM
(least square-support vector machine) based wear model
that enables the prediction of tool wear under specific
cutting conditions.
12
In many studies, various optimiza-
tion methods were applied in order to improve the pre-
dictive performance. The SVM classifier was optimized
with the gray wolf algorithm in order to obtain a more
accurate model with a higher generalization ability.
13
The
least square method was used to optimize the model.
14
The recognition accuracy of the tool wear is higher than
that of traditional neural networks. Particle swarm opti-
mization algorithm was used in the kernel parameter set-
ting of an SVM that resulted in an accuracy of 95 % for
the wear status evaluation.
15
In order to improve the gen-
eralization ability and computing efficiency of the basic
gradient boosting decision tree (GBDT), researchers in-
troduced bagging to form a bagging-GBDT milling cut-
ter wear prediction model.
16
The complicated kinematic
and geometric connections between the hob milling tool
and the workpiece create a series of difficulties and prob-
lems that prevent the optimal use of the tool and ma-
chine. Insufficient scientific knowledge in the field of
gear cutting, as well as the current economic situation,
require further research of this process, primarily the tool
life function as one of the basic functions of the hob
milling process.
There are numerous goals of modeling and optimiza-
tion of the gear cutting process by hob milling, which in-
clude increased productivity, increased product quality,
dimensional accuracy and quality of the machined sur-
face, as well as reduced material consumption, energy,
processing time and costs per product unit. Having in
mind the importance of predicting the wear of a hob
milling tool to achieve increased productivity and prod-
uct quality, the aim of the research in this paper is to de-
termine the functional dependence of the tool life of a
model single-tooth hob milling tool on three input cut-
ting parameters, which include the cutting speed, axial
feed and tangential feed. When modeling the tool life
function, the method of genetic programming was used.
This paper is organized as follows: The Introduction
gives an overview of different researches in the field of
hob milling emphasizing, in particular, the significance
of predicting the wear of a hob milling tool to achieve in-
creased productivity and product quality. The experimen-
tal research of the process of gear cutting of cylindrical
gears by hob milling and obtained results are presented
in Section 2. In Section 3 results of the tool life function
modeling of a single-tooth hob milling tool using the ge-
netic programming algorithm are discussed. Finally, con-
clusions and further research directions are given in last
section.
2 EXPERIMENTAL RESEARCH
When researching the process of gear cutting of cy-
lindrical gears by hob milling, it is necessary to carry out
a long-term experimental research that requires consider-
able financial resources and efforts, and it is extremely
difficult to implement it in a real production process. In
the process of hob milling, compared to other cutting
processes, it is necessary to take into account the high
costs of tools, conditioned by the complex production of
hob milling tools, high accuracy requirements and an ex-
tremely expensive tool material. The biggest influences
on the cost of gear cutting is the tool life of a hob milling
tool and the cutting parameters. The shorter time of gear
cutting reduces skilled worker costs and machine costs.
The high tool life of a hob milling tool has a favorable
effect on the tool maintenance and replacement costs.
The application of a model single-tooth hob milling tool
instead of an integral hob milling tool in the research sig-
nificantly reduces both the tool costs and the testing time
due to the accelerated development of the wear process.
10
Also, the costs for test samples are significantly lower.
Experimental research was carried out in the Labora-
tories of the Department of Production Engineering of
the Faculty of Technical Sciences in Novi Sad under the
following conditions:
S. SOVILJ-NIKI] et al.: MODELING OF THE TOOL LIFE FUNCTION OF A HOB MILLING TOOL USING ...
588 Materiali in tehnologije / Materials and technology 57 (2023) 6, 587–593

Workpiece:
– cylindrical gear with straight teeth: d
T
= 141 mm
– module: m=3mm
– number of teeth: n
t
=45
– length of the gear ring: l=54mm
– profile moving: x=0
– angle of contact:  = 20°
– tooth inclination angle:  =0°
– workpiece material: 20 MnCr 5
Tool
– model single-tooth hob milling tool
– tool diameter: D = 135 mm
– number of threads: z
1
=1
– number of grooves: n
i
=16
– tool material: HS 6-5-2-5
– hardness after heat treatment: 65
±1
(HRC)
– helix angle:   = 1°39’
– direction of the spiral: left
– cutting direction: right
– accuracy class: A
Machine tool: hob milling machine MODUL-ZFWZ-
250x5A, manufacturer VEB STARKSTROM-Anlagen-
bau, Karl Marx, Germany
– engine power: 15.5 kW
– available turnover numbers: 50–400 min
–1
– available feeds: 1) axial: 0.63–6.3 mm/r
2) tangential: 0.315–3.15 mm/r
– maximum modulus: m=5mm
Non-emulsifying cutting oil EPN-46, Modri~a Oil
Refinery, was used as the cooling and lubricating agent.
The measurement of the width of the wear band was per-
formed on a universal measuring instrument for measur-
ing lengths and angles manufactured by Carl Zeiss-Jena.
Investigations of the tool life of a model single-tooth hob
S. SOVILJ-NIKI] et al.: MODELING OF THE TOOL LIFE FUNCTION OF A HOB MILLING TOOL USING ...
Materiali in tehnologije / Materials and technology 57 (2023) 6, 587–593 589
Table 1: Part of experimental results
Measurement number
Cutting speed Axial feed Tangential feed Tool life
v (m/min) fa
(mm/r) f
t
(mm/r) L (mm)
1 68.92 1.0 0.5 38
2 76.30 1.0 0.5 36
3 84.78 1.0 0.5 44
4 94.95 1.0 0.5 45
5 105.98 1.0 0.5 43
6 118.69 1.0 0.5 38
7 133.53 1.0 0.5 35
8 68.92 2.0 0.5 38
9 76.30 2.0 0.5 36
10 84.78 2.0 0.5 43
11 94.95 2.0 0.5 46
12 105.98 2.0 0.5 44
13 118.69 2.0 0.5 38
14 133.53 2.0 0.5 34
15 68.92 2.5 0.5 38
16 76.30 2.5 0.5 36
17 84.78 2.5 0.5 40
18 94.95 2.5 0.5 44
19 105.98 2.5 0.5 46
20 118.69 2.5 0.5 38
21 133.53 2.5 0.5 34
22 68.92 3.15 0.5 35
23 76.30 3.15 0.5 32
24 84.78 3.15 0.5 38
25 94.95 3.15 0.5 37
26 105.98 3.15 0.5 36
27 118.69 3.15 0.5 33
28 133.53 3.15 0.5 31
... … … .... …
78 68.92 3.15 2 25
79 76.30 3.15 2 24
80 84.78 3.15 2 27
81 94.95 3.15 2 29
82 105.98 3.15 2 27
83 118.69 3.15 2 24
84 133.53 3.15 2 22

milling tool were performed for seven different cutting
speeds, four axial feeds and three tangential feeds. Tool
life, L (mm), represents the length of teeth that is reached
at the moment of satisfying the wear criterion
VB = 0.2 mm. Part of the experimental results is shown
in Table 1. The obtained experimental results were used
when modeling the tool life function using genetic pro-
gramming, which is presented in the next section.
3 RESULTS AND DISCUSSION
The GPLAB software tool was used for modeling the
tool life function in this research.
17
GPLAB is a software
tool designed for solving modeling problems using ge-
netic programming in the MATLAB programming envi-
ronment. Thanks to its modular and parameterized struc-
ture, GPLAB can be interesting for different types of
users. GPLAB provides the possibility to solve a corre-
sponding problem by using genetic programming for a
user without any knowledge of the available parameters,
as well as without the need to set them. Also, GPLAB
benefits the users who want the possibility of setting and
testing different parameter values, as well as the possibil-
ity of creating and testing new methods, genetic opera-
tors, functions, etc. In the case that the parameter values
set by the user are outside the allowed range, automatic
correction of the parameter values will be performed and
a warning will be sent to the user. Also, in the case the
user does not set some parameters, they will be set auto-
matically. The only parameters that the user must set are
the maximum number of generations, the size of the pop-
ulation, and the names of the files containing the data
that will be used in the modeling process.
As any other algorithm that implements genetic pro-
gramming, GPLAB also requires the appropriate func-
tions that are needed to create a population. GPLAB can
use all MATLAB functions including addition, subtrac-
tion, multiplication, sin, cos, AND, OR, NOT, XOR, as
well as some protected and logical functions including
division, square root, exponentiation, ln, ld, log,
if-than-else, NAND and NOR. To create a population
within this paper, the functions such as addition, subtrac-
tion, multiplication, division, sin and cos were used.
GPLAB applies different genetic operators to indi-
viduals of the population in order to obtain new individu-
als. Reproduction, crossover and mutation are genetic
operators implemented within GPLAB. The selection of
individuals that will provide their offspring after the ap-
plication of one of the genetic operators is carried out by
applying one of the selection methods. Within GPLAB,
four methods are available for selecting parents: 'rou-
lette', 'tournament', 'lexictour' and 'doubletour'. Within
this research, the 'lexictour' selection method was used.
Similar to the 'tournament' selection method, a random
number of individuals are randomly selected from the
population, from which the best is selected. The main
difference between these two methods is that in the case
two individuals are equally good as the best individual,
the one whose tree has the least number of nodes is
taken. This technique proved to be very effective for con-
trolling different types of problems which is the reason
for choosing this selection method within this research.
17
By applying genetic programming, the tool life func-
tion L (mm) is modelled depending on the input parame-
ters v (m/min), f
a
(mm/r) and f
t
(mm/r). The experimental
values of L, v, f
a
(mm/r) and f
t
(mm/r) are given in Ta-
ble 1 in Section 2. When starting the GPLAB program,
the user should enter the names of the files that contain
the data used during the execution of the algorithm. The
files must be in one of the formats that MATLAB di-
rectly accepts. The csv (comma separated values) file
format was used in this research. The user is required to
enter the names of two files. The first file contains the in-
put data, while the second file contains the expected or
output values. Each individual occupies one species
within the file. Within the GPLAB software tool, there
are three different methods for calculating the fitness
function value of each individual. To determine the value
of the fitness function within this research, the
'regffitness' method was chosen. This method implies
that for each individual in the population, the sum of the
absolute difference between the expected and actual out-
S. SOVILJ-NIKI] et al.: MODELING OF THE TOOL LIFE FUNCTION OF A HOB MILLING TOOL USING ...
590 Materiali in tehnologije / Materials and technology 57 (2023) 6, 587–593
Figure 1: Mean absolute error for 15 civilizations

put values for each input datum is calculated. The best
individual is the one with the smallest difference, i.e., the
individual whose fitness function is the smallest. Mean
absolute error (MAE) represents the difference between
the expected (calculated) and the actual (measured) value
of the tool life function in mm. The best individual also
has the smallest mean absolute error (MAE). As men-
tioned earlier, the parameters that the user is obliged to
enter are the size of the population and the number of
generations. The population size represents the total
number of individuals within one generation, while the
number of generations is actually a criterion for stopping
the execution of the algorithm.
During this research, it was decided that the popula-
tion would contain 2500 individuals, and the total num-
ber of generations would be 100. Figure 1 shows the
MAE for 15 different civilizations generated during the
research. It shows the MAE values for 100 generations
of each civilization. Table 2 shows the values of the tree
depth, number of nodes and MAE of the last (hundredth)
generation for each of the 15 civilizations.
Figures 2, 3 and 4 show the depth of tree, the number
of nodes and the MAE of the last (hundredth) generation
for each of the 15 civilizations. Based on the results
shown in Table 2, as well as in Figures 2, 3 and 4,itcan
be noted that the lowest value of MAE = 0.82702 mm
was achieved in the seventh civilization with a tree depth
of 73 and a total number of nodes of 2048, representing
the largest tree within all 15 civilizations. It can also be
noted that in the 15th civilization MAE = 0.99048 mm,
the depth of tree is 55 and the number of nodes is 1680,
while in the 6th civilization MAE = 0.99166 mm, the
depth of tree is 33 and the number of nodes is 515.
Based on the above, the sixth civilization was chosen as
the optimal one, considering the tree depth, number of
nodes and MAE.
Figure 5 shows the MAE for each generation in the
sixth civilization. It can be seen that the criterion for
stopping the algorithm was well chosen. It would be bad
if 50 generations were chosen as a criterion because it
can be seen that the curve does not yet converge but it is
in a linear decline.
S. SOVILJ-NIKI] et al.: MODELING OF THE TOOL LIFE FUNCTION OF A HOB MILLING TOOL USING ...
Materiali in tehnologije / Materials and technology 57 (2023) 6, 587–593 591
Figure 4: Mean absolute error of the 100th generation in each civili-
zation Figure 2: Depth of tree of the 100th generation in each civilization
Table 2: Depth of tree, number of nodes and mean absolute error for
the 100th generation in each civilization
Civilization Depth of tree
Number of
nodes
MAE (mm)
1 39 463 1.03798
2 32 416 1.49345
3 42 462 1.79012
4 41 627 1.15952
5 43 750 1.03726
6 33 515 0.99166
7 73 2048 0.82702
8 33 364 1.12071
9 35 467 1.11667
10 59 1182 1.40548
11 65 1122 1.62988
12 42 716 1.38036
13 35 537 1.66714
14 28 381 1.35845
15 55 1680 0.99048
Figure 5: Mean absolute error in the sixth civilization
Figure 3: Number of nodes of the 100th generation in each civiliza-
tion

Using the GPLAB software tool and genetic pro-
gramming, the tool life function was obtained:
L=((X2) - (((((((sin((X1) - ((((sin(X1))) + (X1)) *
(((sin(( cos((cos(X1))))))) / (0.89556)))) )) /
((sin(0.23247)))) - (((sin(((X1) * ((sin(X2)))) /
(((sin(0.79233))) * ((0.091343) * ((sin(X2)))))))) +
((cos((X3) / (((0.46818) - (X3)) *
((sin((sin((cos(X2))))))))))))) - (((sin((X3) /
(((sin((0.46818) - (X3)))) * ((0.091343) * (((sin((X1) -
((((sin(X1))) + (X1)) * (((sin((cos((cos(X1))))))) /
(0.89556)))))) / (0.23247))))))) + ((((sin((X1) + (X1))))
+ ((( sin(((X1) * (( sin(X2)))) / ((( sin(0.79233))) *
((sin(X2))))))) + ((((sin(X2))) + ((cos((0.46818) -
(X3))))) * (((cos((X2) / (0.32248)))) + ((sin(((((X3) *
((sin(X3)))) / ((X2) - (((((((sin((X1) - ((((sin(X1))) +
(X1)) * (((sin((cos((cos(X3))))))) / (0.89556)))))) /
((sin(0.23247)))) - (((sin(((X1) * ((sin(X2)))) /
(((sin(0.79233))) * ((0.091343) * ((sin(X2)))))))) +
((cos(((X1) / (X1)) / (((0.46818) - (X3)) *
((sin((sin((cos(X2))))))))))))) - (((sin((X3) /
(((sin((0.46818) - (X3)))) * ((0.091343) * (((sin((X1) -
((((sin(X1))) + (X1)) * (((sin((cos((cos(X1))))))) /
(0.89556)))))) / (0.23247))))))) + ((((sin(((sin(X1))) +
(X1)))) + (((sin(((X1) * ((((X3) - ((cos(X2)))) / (X1)) +
(((((sin(X3))) * ((sin(0.46472)))) + (((X3) * (0.23723))
* (X3))) / (X2)))) / (((sin(0.79233))) * ((sin(X2))))))) +
((((sin(0.75752))) + ((cos(X3)))) * (((cos((X2) /
(0.32248)))) + ((sin(((((sin((cos((cos(X3))))))) / (X1))
+ ((cos((0.91729) / (((0.46818) - (X3)) *
((cos(X1)))))))) / (0.69141)))))))) + ((cos((X3) /
(((0.46818) - (X3)) * ((sin(0.20106)))))))))) -
(((sin((0.46818) - (X3)))) + ((cos(((X2) * (X3)) /
(((0.46818) - (X3)) * ((sin((sin((cos(X1))))))))))))) -
(((X2) - (X3)) + ((cos(((0.90576) / (X3)) / (((0.46818)
- ((sin(0.79233)))) * ((sin(0.20106))))) )))))) +
((cos((0.91729) / (((0.46818) - (X3)) * ((cos(X1))))))))
/ (0.69141)))))))) + ((cos((X3) / (((0.46818) - (X3)) *
((sin(0.20106)))))))))) - (((sin(((X1) * ((sin(X2)))) /
(((sin(0.79233))) * ((0.091343) * ((sin(X2)))))))) +
((cos(((X2) * (X3)) / (((0.46818) - (X3)) * (( sin(( sin((
cos(X1) )) )) )))) )))) - (((sin((X3) / (((sin((0.46818) -
(X3)))) * ((0.091343) * ((sin(X2)))))) )) +
((cos(((sin(X1))) / (((((sin((X1) - ((((sin(X1))) + (X1))
* (((sin((cos((cos(X1))))))) / (0.89556)))))) /
((sin(0.23247)))) - (((sin(((X1) * ((sin(X2)))) /
(((sin(X1))) * ((0.091343) * ((sin(X2)))))))) +
((cos(((X1) / (X1)) / (((0.46818) - (X3)) *
((sin((sin((cos(X2))))))))))))) - ((0.46818) +
((((sin(((sin((((((X1) - (0.45069)) + ((sin(X1)))) *
((cos(X3)))) * (X1)) + ((((sin(X2) )) + ((X1) - ((X1) /
(X2)))) / ((X3) + ((cos(X3)))))) )) + (X1)))) +
(((sin(((X1) * ((sin(X2) ))) / (((sin(0.79233))) *
((sin(X2))))))) + ((((sin((cos((cos(0.67533))))))) +
((cos(X3)))) * (((cos((X2) / (0.32248)))) + ((sin(((((X3)
* (0.46818)) / (X1)) + (((((sin(X2))) + ((cos(X3)))) /
(0.32248)) + (((X3) / (X3)) / (0.1162)))) /
(0.69141)))))))) + ((cos((X3) / (((0.46818) - (X3)) *
((sin(0.20106)))))))))))))))) + ((((((sin(X2) )) +
((cos(X3)))) / (0.32248)) + (((X3) / (X3)) / (0.1162))) /
(0.36442)) (1)
X1 – cutting speed (m/min)
X2 – axial feed (mm/r(
X3 – tangential feed (mm/r)
L – tool life (mm)
The mean absolute error (MAE) obtained by model-
ing is in a range of 2.16–4.15 % in relation to the mea-
sured tool life values.
4 CONCLUSIONS
Based on the obtained results, the following can be
concluded:
• By applying genetic programming and using mea-
surement results, a model of the tool life function of a
single-tooth hob milling tool was obtained.
• The average difference between the expected (calcu-
lated) and actual (measured) value of the tool life
function MAE = 0.99166 mm for the optimal model
where the tree depth is 33 and the number of nodes is
515.
• The mean absolute error (MAE) obtained by model-
ing is less than 5 %, i.e., in a range of 2.16–4.15 % in
relation to the measured tool life values.
• The application of the proposed model of the tool life
function of a single-tooth hob milling tool will enable
gear manufacturers to predict tool life, which is a
novelty in gear cutting that will contribute to a ratio-
nalization of the machining process and technologi-
cal preparation of production, as well as reducing the
costs of gear cutting.
• In further research, the goal will be to optimize the
obtained tool life function of the hob milling tool,
which will enable the selection of optimal cutting pa-
rameters and be of great importance for the produc-
tion of gears.
5 REFERENCES
1
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