Sensitivity of Colding tool life equation on the dimensions of experimental dataset
In this work, 22 sets of cutting data and tool life for longitudinal turning of steel are analyzed using the Colding equation. When modeling tool life with a limited number of tool performance data points, the model error may be low for these points. Evaluating the model for test points not used whe...
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Інститут надтвердих матеріалів ім. В.М. Бакуля НАН України
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| Zitieren: | Sensitivity of Colding tool life equation on the dimensions of experimental dataset / D. Johansson, S. Hägglund, V. Bushlya, J.-E. Ståhl // Сверхтвердые материалы. — 2017. — № 4. — С. 67-79. — Бібліогр.: 14 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860075092929675264 |
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| author | Johansson, D. Hägglund, S. Bushlya, V. Ståhl, J.-E. |
| author_facet | Johansson, D. Hägglund, S. Bushlya, V. Ståhl, J.-E. |
| citation_txt | Sensitivity of Colding tool life equation on the dimensions of experimental dataset / D. Johansson, S. Hägglund, V. Bushlya, J.-E. Ståhl // Сверхтвердые материалы. — 2017. — № 4. — С. 67-79. — Бібліогр.: 14 назв. — англ. |
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| description | In this work, 22 sets of cutting data and tool life for longitudinal turning of steel are analyzed using the Colding equation. When modeling tool life with a limited number of tool performance data points, the model error may be low for these points. Evaluating the model for test points not used when computing the model coefficients may give larger errors for these points. This work proves that the Colding model also provides sufficient precision when modelling data points not being used to create the model, and is therefore a well-functioning instrument for tool life modelling. The results also prove that for the selected data, the precision of the model can be greatly improved when the dimension of the data set is increased from 5 to 10 data points. Above 13 data points the precision improvements are negligible.
Проаналізовано 22 набору режимів різання і стійкість інструменту при поздовжньому точінні стали при застосуванні моделі Колдінга. При моделюванні стійкості інструменту при обмеженій кількості даних про робочі характеристики помилка моделі може бути незначною в заданих точках. Оцінка моделі для тестових точок, які не використовуються при обчисленні коефіцієнтів моделі, може показати більші помилки в цих точках. Доведено, що модель Колдінга забезпечує достатню точність при моделюванні даних, що не використовуються для створення моделі, і тому може бути застосована для моделювання періоду стійкості інструменту. Результати також доводять, що для даних, що використовуються, точність моделі може бути значно поліпшена при збільшенні набору точок з 5 до 10, а при збільшенні понад 13 точок поліпшення точності моделювання незначні.
Проанализированы 22 набора режимов резания и стойкость инструмента при продольном точении стали с применением модели Колдинга. При моделировании стойкости инструмента при ограниченном количестве данных о рабочих характеристиках ошибка модели может быть незначительной в заданных точках. Оценка модели для тестовых точек, не используемых при вычислении коэффициентов модели, может показать бóльшие ошибки в этих точках. Доказано, что модель Колдинга обеспечивает достаточную точность при моделировании данных, не используемых для создания модели, и поэтому может быть применена для моделирования периода стойкости инструмента. Результаты также доказывают, что для используемых данных точность модели может быть значительно улучшена при увеличении набора точек с 5 до 10, а при увеличении более 13 точек улучшения точности моделирования незначительны.
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| first_indexed | 2025-12-07T17:13:39Z |
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ISSN 0203-3119. Сверхтвердые материалы, 2017, № 4 67
UDC 621.9.02.001.57
D. Johansson1, *, S. Hägglund2, V. Bushlya1, J.-E. Ståhl1
1Division of Production and Materials Enigneering, Lund University,
Lund, Sweden
2Seco Tools AB, Fagersta, Sweden
*daniel.johansson@iprod.lth.se
Sensitivity of Colding tool life equation
on the dimensions of experimental dataset
In this work, 22 sets of cutting data and tool life for longitudinal
turning of steel are analyzed using the Colding equation. When modeling tool life with
a limited number of tool performance data points, the model error may be low for these
points. Evaluating the model for test points not used when computing the model
coefficients may give larger errors for these points. This work proves that the Colding
model also provides sufficient precision when modelling data points not being used to
create the model, and is therefore a well-functioning instrument for tool life modelling.
The results also prove that for the selected data, the precision of the model can be
greatly improved when the dimension of the data set is increased from 5 to 10 data
points. Above 13 data points the precision improvements are negligible.
Keywords: machining, tool life, turning, the Colding equation.
INTRODUCTION
It is well known that a prediction of tool life is of great importance
in modern industrial production involving machining operations. The time it takes
for one tool to be considered worn out and the number of parts it can produce in
combination with the tool change time for one or more tools engaged in the process
plays a big role in the production costs. The life of the tool is governed by the
combination of machinability of a workpiece material, tool properties, and the
applied cutting data: cutting speed, vc, feed, f, and depth of cut, ap. A tool life
normally decreases with an increase of cutting data, and the goal for any
production is to find optimum cutting data either in regard to the minimum cost or
in regard to highest production efficiency.
As an aid in finding optimal cutting data, many tool manufactures offer
catalogue data or software applications to match the right tool to a specific
workpiece material and operation in combination with cutting data suggestions.
These recommendations are made through accumulation of the data on the tool
performance for different combinations of the tool and work materials while
applying different cutting data, and accounting for the tool geometry and chip
cross-section window of operation. This is a costly and time consuming process
and little is known of the amount of data needed to allow for high quality cutting
data recommendations.
The pioneering work of tool life modeling was made by Taylor [1]. A tool life
equation is based on two constants and calculates the tool life for a chosen cutting
speed or vice versa. Applying this equation the optimal economic life of a tool can
be determined. The Taylor equation has proven to work very well in a limited
© D. JOHANSSON, S. HÄGGLUND, V. BUSHLYA, J.-E. STÅHL, 2017
www.ism.kiev.ua/stm 68
range of cutting data, as shown in [2], because it does not include the data on chip
cross-sectional parameters like feed, depth of cut, nose radius, etc. When creating
cutting data recommendations for a larger range of cutting data normally used in
machining practice, the chip thickness parameters need to be taken into
consideration, and therefore there is a need for more complex tool life models.
The Colding equation, introduced by Bertil Colding [3, 4] and further
developed by Lindström [5], has proven to adequately perform in predicting tool
life in cases of such extended cutting data range, as previously shown, among
others, by the authors of [6, 7]. The Colding model, as well as the Taylor model, is
based on a curve fitting algorithm operating with five separate constants and has no
direct link between the physical mechanisms of a tool wear in the cutting process
and the chosen constants. To create a Colding model for one specific combination
of a tool and workpiece material, a minimum of five tests is needed to be
performed. Once the model and constants are established, the model error can then
be calculated for these five or more data points.
OBJECTIVE AND PROBLEM DESCRIPTION
The Colding model represents a function in three dimensional spaces of tool
life, cutting speed, and chip thickness. The function is established on a limited set
of tool performance points from a selected range and interpolates tool life
behaviour within this range. The question of accuracy of interpolation remains
open. The aim of this work is to investigate the number of tool performance tests
needed to create a Colding model that will model the cutting data and tool life with
an acceptably small model error for a wide range of cutting data and tool life. To
limit the cost of testing and minimize the needs for updating cutting data it is of
great importance that the correct amount of data is collected from the start. With a
limited number of tests there may be a risk of creating a tool life model that
provides poor quality cutting data recommendations as a result of the interpolation
or even frequently used extrapolation. The acquisition of the tool performance
information leads to such expenses as workpiece material, tools, and operator time,
and this pushes the tool manufacturers to limit the number of the tests performed.
In this work, a large amount of cutting data and tool life obtained in machining
tests has been used to create a Colding model. The model stability, its sensitivity
and statistical variations are evaluated and presented by excluding selected data
from the overall dataset.
BACKGROUND
The Colding equation with five constants published by B. Colding in 1981 [4]
is, as the pioneering work by Taylor, essentially based on empirical curve fitting
made between a tool life and cutting data:
−−
−
−
=
ThLN
M
Hh
K
ev
lnln0
4
)(ln
c
e
2
e
. (1)
The equations can be regarded as an extension of the Taylor equation which can
be clearly observed in studies of Lindström’s reformulation of the Colding equa-
tion [5].
The Colding equation is based on five constants K, H, M, N0, and L where
cutting speed vc is a function of the tool life, T, and equivalent chip thickness, he.
Equivalent chip thicknesses, he, as defined by R. Woxén [8], is a function of feed,
f, depth of cut, ap, major cutting angle, κ, and the nose radius of the tool, rm:
ISSN 0203-3119. Сверхтвердые материалы, 2017, № 4 69
.
2sin
)cos1(
m
p
p
e f
r
ra
fa
h
+κ+
κ
κ−−= (2)
To create a set of Colding constants, the tool performance needs to be evaluated
in at least five cutting data points. By varying cutting speed, vc, feed, f, and depth
of cut, ap a window of cutting data can be created and tool life accordingly
modelled. Extrapolation of the modelling results outside the cutting data test
window is algorithmically incorrect, but is frequently practiced in the industry and
therefore, extra care needs to be taken. A wear criterion, such as flank wear VBmax
= 0.3 mm or maximum crater wear KTmax = 0.5 mm, is selected. The model does
not take into account how this wear is developed, it only states the total en-
gagement time before a specific wear criterion is met for the selected cutting data.
It is possible to combine the Archad wear model [9] with the Colding model to
allow for different wear criterion, as suggested by Ståhl et al. [10], although this is
not discussed further in this work. Figure 1 shows how the Colding equation
connects cutting data with the tool life.
Colding’s equation
Cutting speed
Equivalent chip thickness
(Woxén)
Work material machinability Tool material and tool design
5 constants
K, H, M, N0 and L
Wear criterion,
e.g. flank wear VB = 0.3 mm
Process data Estimated tool life
Tolerance requirements Surface requirements Process stability
Major cutting angle κ
Depth of cut a
p
Feed f
Nose radius r
m
Fig. 1. The schematic of the Colding model design and its connection to cutting data, tool life
and wear criterion.
B. Colding [11] and B. Hallert [12] used an ASEA automatic computer (Mod.
FACIT EDB) to identify the number of tool life measurements needed to create a
reliable tool life model. Eight different polynomial tool life models were tested
with a range of two to nine model-constants. The Colding model with five
constants (Eq. (1)) was yet not developed when this work was performed. It was
concluded that for the polynomial relationship with 9 constants:
0222 =+++−+++++ hxzgyzfxyzezdycybxaxk , (3)
where x = ln he, y = ln vc, and z = ln T.
The number of tests should be at least about 25.
The ratio between the largest and smallest equivalent chip thickness should be
about 10.
www.ism.kiev.ua/stm 70
The test should be run using at least three equivalent chip thickness data while
varying the cutting speed for the full cutting range where the tool life is linear for a
specific equivalent chip thickness in the log T–log vc plane.
It was also noted that the cost of conducting this testing would be significant
and that a wear model with fewer constants is needed in order to limit the number
and costs of testing.
EXPERIMENTAL SETUP
In this work, a total of 22 tool performance data points were evaluated when
machining C45 E (SS 1672) in longitudinal turning according to ISO 3685:1993
using industry standard coated cemented carbide inserts. The Colding constants
were calculated using the least squares method through the built-in feature Solver
in the MS Excel® software with curve fitting and the minimization of deviation
concerning the obtained measurement points for five or more tool performance
data points. Also, the Matlab environment was used for calculations for which
1000 combinations of tool performance data points were randomly selected and
Colding constants calculated using the least squares method through a built-in
software feature based on an algorithm for data fitting developed by Levenberg-
Marquardt [13, 14]. The full data set used to evaluate the Colding model is
presented in Table 1.
Table 1. Measured tool performance data points when machining C45 E
with cemented carbide inserts used to evaluate the Colding model
Test No.
Depth of cut,
mm
Feed,
mm/rev
Cutting speed,
m/min
Chip thickness,
mm
Tool life,
min
1 3.5 0.50 260 0.416 7.65
2 3.5 0.50 245 0.416 9.51
3 3.5 0.50 230 0.416 13.17
4 3.5 0.50 215 0.416 17.55
5 3.5 0.50 200 0.416 20.34
6 3.5 0.50 185 0.416 30.24
7 3.5 0.50 170 0.416 33.85
8 3.5 0.50 150 0.416 71.03
9 2.0 0.35 355 0.266 10.05
10 2.0 0.15 490 0.119 12.24
11 2.0 0.25 410 0.194 14.34
12 1.5 0.20 455 0.146 14.17
13 3.0 0.20 430 0.169 18.70
14 2.0 0.25 420 0.194 9.06
15 2.0 0.35 365 0.266 7.00
16 1.5 0.30 405 0.214 11.20
17 2.5 0.40 330 0.317 4.64
18 2.0 0.25 420 0.194 9.66
19 2.0 0.35 365 0.266 10.65
20 1.5 0.30 405 0.214 13.45
21 2.5 0.35 330 0.279 13.29
22 2.5 0.40 330 0.317 10.74
ISSN 0203-3119. Сверхтвердые материалы, 2017, № 4 71
The equivalent chip thicknesses (Eq. 2) in Table 1 range from 0.119 mm to
0.416 mm giving a ratio of approximately 3.5 between the smallest and the largest
equivalent chip thickness. The cutting speed ranges from 150 m/min to 490 m/min,
Fig. 2. All tests were performed with the major cutting angle κ = 95° and nose
radius rm = 0.8 mm with no coolant applied.
100
150
200
250
300
350
400
450
500
0.10 0.15 0.20 0.25 0.30 0.35 0.40
v
c
, m/min
h
e
, mm
Fig. 2. The cutting data points plotted in the vc–he plane.
The created models based on different measured tool performance data points
were then evaluated based on the mean error εerr in % between experimentally at-
tained vc, exp and modeled cutting speed vc, mod for each model:
−=
==ε
ji
jiji
c
ccnj
j v
vv
n exp
modexp
1err
100
. (4)
All models were created with the same set of starting values, as shown in Table 2.
The Colding singularity has been discussed by the authors in previous
publications [6, 7] and in this work there have been no limitations set to the
Colding constants when modeling, allowing for the singularity to enter the he area
for applicable cutting data.
Table 2. Starting values applied when modelling the Colding constants
Index Value
K 6.0
H –3.0
M 2.0
N0 0.3
L –0.05
RESULTS AND DISCUSSION
The Colding model created with the curve fitting and no limitations to the
Colding constants and the singularity for all 22 measured tool performance data
www.ism.kiev.ua/stm 72
points is presented in the vc–he plane (Fig. 3) and in the T–vc plane in Fig. 4. The
rather high singularity can be noted in Fig. 3 at he ≈ 0.190 mm.
0.2 0.4 0.6 0.8
100
1000
C
ut
ti
ng
s
pe
ed
, m
/m
in
1
2
3
v
c
, m/min
h
e
, mm
Fig. 3. The Colding model based on all 22 tool performance data points plotted in vc–he plane
with no limitations on the constants: tool life – 5 (1), 15 (2), 40 (3) min.
200 400 600 800 1000
10
100
123 T, min
v
c
, m/min
Fig. 4. The Colding model based on all 22 tool performance data points plotted in T–vc plane
with no limitations on the constants: chip thickness – 0.2 (1), 0.3 (2), 0.4 (3) mm.
Initially five measured tool performance data points, representing applicable
cutting data, were selected according to a normal tool wear testing procedure.
Additional tool performance data points were then selected and added to expand
the cutting data window and verify data points within the cutting data window. The
result is presented in Fig. 5, where all data are normalized to the results obtained
with the largest dataset of all 22 tool performance data points, which is further on
considered as best possible solution. It should be noted that this is a very practical
approach and that the data in Fig. 5 are dependent on the order in which the chosen
data points are added. The order of added data is presented in Table 3, where points
1, 6, 9, 11, and 22 make up the five initial tool performance data points used for
creation of the initial Colding model. Thereafter one more point is added, in this
case data point 2, and a new model is computed based on all previous data points
(initial dataset) including the added point 2 and the error is then calculated.
ISSN 0203-3119. Сверхтвердые материалы, 2017, № 4 73
Sequentially, all 22 tool performance data points are included in the model,
following the order presented in Table 3. This test shows the importance of which
tool performance data points are measured and included in the model. Each model
is then tested on all data including tool performance data points not used to create
the model. The mean error and the maximum error that can be found in the 22 tool
performance data points are presented and normalized to the best possible model.
6 8 10 12 14 16 18 20 22
0
0.5
1.0
1.5
2.0
2.5
R
el
at
iv
e
of
f�
se
t
No. of data points
1
2
6
7
5
3
4
Fig. 5. The Colding constants and errors when sequentially increasing the number of measured
tool performance data points included in the tool life model: Knorm (1), Hnorm (2), Mnorm (3),
N0norm (4), Lnorm (5), mean error (6), max error (7).
Table 4 presents the final set of the Colding constants when all data are in-
cluded. It also presents the mean error and the maximum error found in the set of
data when modeling. The model mean error when using 7 tool performance data
points to create the Colding model was calculated to 4.0% showing the risk of not
including enough data. The largest error found for an individual tool performance
data point for this model was 18.2 %. The identical error, but for the model created
with all 22 tool performance data points was 2.5 times smaller. The best possible
model including all 22 tool performance data points has a mean error of 2.11 %
and the maximum error found in the set of data points is 7.0 %.
When the number of tool performance data points is limited one could probably
reduce the risk of creating a poor model by limiting the constants, controlling the
singularity and in some cases extrapolate data to the left of the maximum point of
the Colding curve, also known as the h-line.
In order to further evaluate the amount of data needed to create a well-
functioning tool life model 1000 randomly created datasets with tool performance
data points was subjected to Colding modelling. No limitations were set on the
selection criteria thus covering both larger and smaller windows of cutting data and
investigating the related accuracy for cases of interpolation and extrapolation. Tests
were performed using 7, 9 and 13 tool performance data points to create 1000
unique data sets for each test. Figure 6 presents the variation of the K constant
dependent on the selected data. The K constant was chosen because it gives the
value of vc=eK at the extreme point of the Colding plot corresponding to a tool life
of 1 min. The corresponding mean error when testing each model on all 22 meas-
ured tool performance data points is presented in Fig. 7. The highest mean error for
7 tool performance data points found was 13.0 %, 10 data sets 10.5 % and 13 data
sets 6.5 %.
www.ism.kiev.ua/stm 74
Table 3. The order of added data points. The error presented
is the mean average error when the model is tested on all 22 tool
performance data points
Test No.
Equivalent chip thickness,
mm
Cutting speed,
m/min
Measured tool life,
min
Error,
%
1 0.416 260 7.65
6 0.416 185 30.24
9 0.266 355 10.05
11 0.194 410 14.34
22 0.317 330 10.74 3.68
2 0.416 245 9.51 3.72
7 0.416 170 33.85 4.01
16 0.214 405 11.20 4.07
12 0.146 455 14.17 3.60
17 0.317 330 4.64 3.13
21 0.279 330 13.29 2.92
3 0.416 230 13.17 2.83
8 0.416 150 71.03 2.75
18 0.194 420 9.66 2.66
13 0.169 430 18.70 2.49
20 0.214 405 13.45 2.53
4 0.416 215 17.55 2.46
5 0.416 200 20.34 2.46
10 0.119 490 12.24 2.13
14 0.194 420 9.06 2.13
15 0.266 365 7.00 2.14
19 0.266 365 10.65 2.11
Table 4. The Colding constants for all measured data and the mean error
and maximum errors presented
Index Value
K 6.136
H –1.331
M 0.610
N0 0.499
L –0.289
Mean error, % 2.11
Max error, % 7.02
The evaluation of the number of tool performance data points needed to create
accurate Colding constants was further investigated by creating 1000 random com-
binations of data sets with number of tool performance data points included from 5
to 17. The errors for these models are presented in Fig. 8. Line 1 represents the
ISSN 0203-3119. Сверхтвердые материалы, 2017, № 4 75
fraction, given in %, of the number of models for which the randomly selected
dataset generates a model error of 5.11%, i.e. additional 3 % to the best possible
2.11 % created on all 22 tool performance data points (see Table 3). It can be noted
that the accuracy increases drastically from 5 to 9 tool performance data points
included and for a set of 11 tool performance data points only 5 % of the Colding
models will have a model error of 5.11 % or larger. Line 2 represents the averaged
maximum error found for all 1000 combinations and the line 3 represents the
average model error for all 1000 combinations. All errors presented are errors
when testing the models on all 22 available tool performance data points, also
those excluded when creating each model.
5.8 6.0 6.2 6.4 6.6 6.8 7.0 7.2
0
50
100
150
200
250
300
F
re
gu
en
cy
K value
1
2
3
K = 6.136
Fig. 6. A histogram plot of the K constant for 1000 combinations of data sets randomly selected
using 7 (1), 10 (2), and 13 (3) tool performance data points in the tool life model.
2 4 6 8 10 12 14
0
200
400
F
re
qu
en
cy
Error, %
1
2
3
Fig. 7. A histogram plot of the mean error for 1000 combinations of data sets randomly selected
using 7 (1), 10 (2), and 13 (3) tool performance data points.
Figure 9 plots the absolute largest error found in one single tool performance
data point among the given 1000 combinations of data sets. This plot illustrates
that more than 1000 combinations are needed as the error is not strictly decreasing
for an increase of tool performance data points. The total number of combinations
www.ism.kiev.ua/stm 76
when operating with 5 data points out of 22 is 26334 and 705432 when operating
with 11 out of 22.
4 6 8 10 12 14 16 18
0
10
20
30
40
50
No. of data points
Error, %
1
2
3
Fig. 8. Model errors for data set dimensions of 5 to 17 points; line 1 represents the ratio of models
with an error over 5.11 %, line 2 represents the averaged max error found in 1000 combinations
and the line 3 represents the mean model error.
6 8 10 12 14 16
0
20
40
60
80
100
120
140
M
ax
im
um
e
rr
or
, %
No. of data points
Fig. 9. A largest error found in an individual data point within 1000 combinations of datasets and
Colding constants.
The cutting speed for a machining operation can be evaluated by selecting,
Fig. 1, targeted tool life and chip thickness (T = 15 min and he = 0.25 mm for the
example given below) and respective calculation via Colding equation (Eq. 1). A
histogram of the cutting speed for 1000 randomly selected combinations of cutting
data points creating the Colding constants when using 7, 10 and 13 tool
performance points in the tool life model is presented in Fig. 10. Table 5 presents
the mean value of the suggested cutting speed as well as the standard deviation.
When operating with 7 tool performance data points, 95 % of the models will esti-
mate the cutting speed within 362±27.9 m/min and when operating with 13 tool
performance data points, the model provides the cutting speed of 358±14.3 m/min
for 95 % of the models. The variation can be recalculated into relative possible
error given in percent. For 7, 10, and 13 tool performance data points used in the
ISSN 0203-3119. Сверхтвердые материалы, 2017, № 4 77
model, the relative variation will be ±7.7, ±5.7 and ±4.0 % respectively. This can
alternatively be equated to the case where 13 randomly selected tool performance
data points will provide accuracy of no less than 4 % with the probability of 95 %.
320 340 360 380 400
0
50
100
150
200
250
300
F
re
qu
en
cy
v
c
, m/min
1
2
3
Fig. 10. The distribution of the modelled cutting speed for a turning operation (he = 0.25 mm and
T = 15 min) for 1000 sets of Colding constants when using 7 (1), 10 (2), and 13 (3) tool perform-
ance data points.
Table 5. Statistical analysis of calculated cutting speed vc for a turning
operation (he = 0.25 and T = 15 min) for 7, 10 and 13 tool performance
data points
No. of data points 7 10 13
Mean value, m/min 362 360 358
Standard deviation, m/min 13.9 10.3 7.2
95 % of the models, m/min ±27.9 ±20.5 ±14.3
95 % of the models, % ±7.7 ±5.7 ±4.0
Table 6 presents the ratio of models in % that have a mean model error larger
than 4 % and alternatively larger than 10 % when tested on the 22 measured data
points.
CONCLUSIONS
For this extended data set of experimentally measured tool performance in
longitudinal turning, modeled with the Colding tool life equation, a number of
conclusions can be made:
– for a randomly selected 1000 combinations of model constants the computed
model error does not exceed 10 % if 10 tool performance data points or more are
employed;
– when selecting 13 tool performance data points, only 2.3 % out of 1000 ran-
domized models have an error exceeding 4 %. The largest error for an individual
tool performance data point error is however approx. 35 % with the mean max
error below 10 %.
The model is improving dramatically when enlarging the dimension of the data-
set from 5 to 10 experimental tool performance data points. Above 13 data points
the model improvement is only marginal.
www.ism.kiev.ua/stm 78
Table 6. The fraction of models resulting in error exceeding 4 %
and alternatively 10 %
The fraction of models, %, for the error, %
No. of data points
> 4 > 10
5 72.9 8.4
6 59.3 3.4
7 42.1 2.1
8 30.9 0.8
9 19.0 0.4
10 15.5 0
11 8.8 0
12 5.4 0
13 2.3 0
14 1.4 0
15 0.6 0
16 0.1 0
17 0.1 0
When using 13 randomly picked tool performance data points we will be 95 %
sure to not add a model error of more than 4 % as a result of poor selection of
modeled tool performance data points.
It should be noted that all 1000 data sets in each test have been randomly
selected. With a more careful selection of tool performance data points, as
suggested by Colding and Hägglund [11, 6], the authors of this work believe that
the result can be greatly improved. Figure 5 shows how a real selection of data
points could be made and one can note that already when selecting 10 data point
the mean error and max error is decreased significantly.
This work has proven that the Colding equation is a well-functioning tool life
model also when tested on data not being used to create the model.
This work is solely based on analyzing one set of data with 22 measured cutting
data points and tool lives. Further statistical analysis is needed with a more general
perspective to create a greater understanding of the Colding tool life model and its
use and limitations.
This work was co-funded from the European Union’s Horizon 2020 Research
and Innovation Programme under Flintstone 2020 project (grant agreement No
689279) and is also a part of the Sustainable Production Initiative cooperation be-
tween Lund University and Chalmers. The authors wish to acknowledge the
valuable contributions made by the Seco Tools AB and would like to thank MSc.
Ville Akujärvi for helping with software programming and PhD Oleksandr
Gutnichenko for interesting discussions.
Проаналізовано 22 набору режимів різання і стійкість інструменту
при поздовжньому точінні стали при застосуванні моделі Колдінга. При моделюванні
стійкості інструменту при обмеженій кількості даних про робочі характеристики помилка
моделі може бути незначною в заданих точках. Оцінка моделі для тестових точок, які не
використовуються при обчисленні коефіцієнтів моделі, може показати більші помилки в
цих точках. Доведено, що модель Колдінга забезпечує достатню точність при моделю-
ванні даних, що не використовуються для створення моделі, і тому може бути застосо-
ISSN 0203-3119. Сверхтвердые материалы, 2017, № 4 79
вана для моделювання періоду стійкості інструменту. Результати також доводять, що
для даних, що використовуються, точність моделі може бути значно поліпшена при
збільшенні набору точок з 5 до 10, а при збільшенні понад 13 точок поліпшення точності
моделювання незначні.
Ключові слова: обробка, стійкість інструменту, точіння, рівняння
Колдінга.
Проанализированы 22 набора режимов резания и стойкость инстру-
мента при продольном точении стали с применением модели Колдинга. При моделирова-
нии стойкости инструмента при ограниченном количестве данных о рабочих характери-
стиках ошибка модели может быть незначительной в заданных точках. Оценка модели
для тестовых точек, не используемых при вычислении коэффициентов модели, может
показать бóльшие ошибки в этих точках. Доказано, что модель Колдинга обеспечивает
достаточную точность при моделировании данных, не используемых для создания моде-
ли, и поэтому может быть применена для моделирования периода стойкости инстру-
мента. Результаты также доказывают, что для используемых данных точность модели
может быть значительно улучшена при увеличении набора точек с 5 до 10, а при увели-
чении более 13 точек улучшения точности моделирования незначительны.
Ключевые слова: обработка, стойкость инструмента, точение, урав-
нение Колдинга.
1. Taylor F. W. On the art of cutting metals. – New York, USA: The American Society of Me-
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Received 06.03.17
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| id | nasplib_isofts_kiev_ua-123456789-160146 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0203-3119 |
| language | Ukrainian |
| last_indexed | 2025-12-07T17:13:39Z |
| publishDate | 2017 |
| publisher | Інститут надтвердих матеріалів ім. В.М. Бакуля НАН України |
| record_format | dspace |
| spelling | Johansson, D. Hägglund, S. Bushlya, V. Ståhl, J.-E. 2019-10-24T17:19:34Z 2019-10-24T17:19:34Z 2017 Sensitivity of Colding tool life equation on the dimensions of experimental dataset / D. Johansson, S. Hägglund, V. Bushlya, J.-E. Ståhl // Сверхтвердые материалы. — 2017. — № 4. — С. 67-79. — Бібліогр.: 14 назв. — англ. 0203-3119 https://nasplib.isofts.kiev.ua/handle/123456789/160146 621.9.02.001.57 In this work, 22 sets of cutting data and tool life for longitudinal turning of steel are analyzed using the Colding equation. When modeling tool life with a limited number of tool performance data points, the model error may be low for these points. Evaluating the model for test points not used when computing the model coefficients may give larger errors for these points. This work proves that the Colding model also provides sufficient precision when modelling data points not being used to create the model, and is therefore a well-functioning instrument for tool life modelling. The results also prove that for the selected data, the precision of the model can be greatly improved when the dimension of the data set is increased from 5 to 10 data points. Above 13 data points the precision improvements are negligible. Проаналізовано 22 набору режимів різання і стійкість інструменту при поздовжньому точінні стали при застосуванні моделі Колдінга. При моделюванні стійкості інструменту при обмеженій кількості даних про робочі характеристики помилка моделі може бути незначною в заданих точках. Оцінка моделі для тестових точок, які не використовуються при обчисленні коефіцієнтів моделі, може показати більші помилки в цих точках. Доведено, що модель Колдінга забезпечує достатню точність при моделюванні даних, що не використовуються для створення моделі, і тому може бути застосована для моделювання періоду стійкості інструменту. Результати також доводять, що для даних, що використовуються, точність моделі може бути значно поліпшена при збільшенні набору точок з 5 до 10, а при збільшенні понад 13 точок поліпшення точності моделювання незначні. Проанализированы 22 набора режимов резания и стойкость инструмента при продольном точении стали с применением модели Колдинга. При моделировании стойкости инструмента при ограниченном количестве данных о рабочих характеристиках ошибка модели может быть незначительной в заданных точках. Оценка модели для тестовых точек, не используемых при вычислении коэффициентов модели, может показать бóльшие ошибки в этих точках. Доказано, что модель Колдинга обеспечивает достаточную точность при моделировании данных, не используемых для создания модели, и поэтому может быть применена для моделирования периода стойкости инструмента. Результаты также доказывают, что для используемых данных точность модели может быть значительно улучшена при увеличении набора точек с 5 до 10, а при увеличении более 13 точек улучшения точности моделирования незначительны. This work was co-funded from the European Union’s Horizon 2020 Research and Innovation Programme under Flintstone 2020 project (grant agreement No 689279) and is also a part of the Sustainable Production Initiative cooperation between Lund University and Chalmers. The authors wish to acknowledge the valuable contributions made by the Seco Tools AB and would like to thank MSc. Ville Akujärvi for helping with software programming and PhD Oleksandr Gutnichenko for interesting discussions. uk Інститут надтвердих матеріалів ім. В.М. Бакуля НАН України Сверхтвердые материалы Исследование процессов обработки Sensitivity of Colding tool life equation on the dimensions of experimental dataset Article published earlier |
| spellingShingle | Sensitivity of Colding tool life equation on the dimensions of experimental dataset Johansson, D. Hägglund, S. Bushlya, V. Ståhl, J.-E. Исследование процессов обработки |
| title | Sensitivity of Colding tool life equation on the dimensions of experimental dataset |
| title_full | Sensitivity of Colding tool life equation on the dimensions of experimental dataset |
| title_fullStr | Sensitivity of Colding tool life equation on the dimensions of experimental dataset |
| title_full_unstemmed | Sensitivity of Colding tool life equation on the dimensions of experimental dataset |
| title_short | Sensitivity of Colding tool life equation on the dimensions of experimental dataset |
| title_sort | sensitivity of colding tool life equation on the dimensions of experimental dataset |
| topic | Исследование процессов обработки |
| topic_facet | Исследование процессов обработки |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/160146 |
| work_keys_str_mv | AT johanssond sensitivityofcoldingtoollifeequationonthedimensionsofexperimentaldataset AT hagglunds sensitivityofcoldingtoollifeequationonthedimensionsofexperimentaldataset AT bushlyav sensitivityofcoldingtoollifeequationonthedimensionsofexperimentaldataset AT stahlje sensitivityofcoldingtoollifeequationonthedimensionsofexperimentaldataset |