In this article is proposed optimization, gradientless algorithm in forming cutting conditions for high-speed milling with single flute mill cutters of elements from aluminium sheets, high presssure laminate (HPL) panels and aluminium composite panels on machining centers. Used optimization parameters (criteria) - production cost and production rate. The analysis requires, a finding such values of variable factors – cutting speed and feed, satisfactory set of technical requirements, under which the criteria are unique optimum.

1. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 11, November (2014), pp. 01-09 © IAEME
1
OPTIMIZATION OF MACHINING CONDITIONS FOR HIGH-
SPEED MILLING WITH SINGLE FLUTE END MILL CUTTERS
OF ELEMENTS FROM ALUMINIUM SHEETS, HPL PANELS
AND ALUMINIUM COMPOSITE PANELS
V. Dimitrov1
, V. Dimitrova2
1, 2
Department MEMETE, Engineering Pedagogical Faculty –
Sliven Technical University of Sofia, Bulgaria, European Union
ABSTRACT
In this article is proposed optimization, gradientless algorithm in forming cutting conditions
for high-speed milling with single flute mill cutters of elements from aluminium sheets, high
presssure laminate (HPL) panels and aluminium composite panels on machining centers. Used
optimization parameters (criteria) - production cost and production rate. The analysis requires, a
finding such values of variable factors – cutting speed and feed, satisfactory set of technical
requirements, under which the criteria are unique optimum.
Keywords: Optimization of Machining Conditions, Cutting of Materials; Cutting Tools; Single Flute
Mill Cutters, Machining Centers, High-Speed Milling, High Presssure Laminate (HPL) Panels,
Aluminium Composite Panels.
1. INTRODUCTION
Determination of cutting conditions, in the presence of multiple variables factors is complex
variation techno - economic problem, allowing multiple technically justified solutions
[1, 3, 4, 10, 12, 16, 18]. It is especially relevant in the design of innovative technological processes
for machining. The staging of the optimization includes gradientless scanning of the factor space
with a consistent calculation of investigated parameters, based on the selected optimization model
[4]. Problem is reduced to calculating the extreme nonlinear criterion test function (objective
function), in fulfilment of a set of technical constraints (factors). They have a service-kinematic and
technological nature and for each process of cutting and high-speed milling in particular, have
specific features and should be specified. Set of combinations of variables formed the area of
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2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
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feasible solutions of the problem, it is solvable in compatible constraints and limited area of possible
solutions [1, 14, 15].
2. EXPOSE AND AIMS
In this work is proposed a classical algorithm for parallel solving two multifactorial,
iteratives, single parameters optimizations with factorial scaning using the method of nonlinear
mathematical programming, fully validated according to the theory of cutting materials methods
[1,3,12]. Designed models serve quasi-dry maschining high-speed milling with single flute mill
cutters on machining centers. Variables are the elements of the system of cutting - speed Vc[m/min]
and minute feed fm[mm/min]. The machining of the elements of aluminium sheets, HPL panels and
aluminium composite panels runs under intensive cutting conditions with a full penetration into the
material of the cutting tool, i.e. here is a single pass cutting with a constant cutting depth ap[mm],
equal to the maximum:
ap = amax = 4mm (1)
Optimization tasks in this case are constructed according to assumptions for ensuring rational
cutting conditions in the study of parameters - minimum production cost and maximum production
rate, i.e here are valid production cost criterion and production rate criterion. Tools are single flute
mill cutters with a diameter D=8mm, made of high speed steel HSS Co8 hardness 63-68HRc
(without inflicted multilayer coating) [2,5,6].
The resulting feasible solutions of parallel performed multifactorial, iteratives, single
parameters optimizations in effect are compared and evaluated. On cutting speed would be more
favorable to lower values regime to meet the reliability tools requirements – fastness and
storage capability. While feeding, on the light conditions for maximum relative gain, in guaranteed
quality of machined surface, by appropriate would be the selection of a more intensive feeding
regimes.
3. MATHEMATICAL MODEL FOR OPTIMIZATION IN PRODUCTION COST
CRITERION
Although, when using this type of objective function, production rate is lower than the
optimum, the theory of cutting of materials ensure its appropriateness, as it provides maximum
performance values are close to the theoretically derived extreme ones.
Production cost, at a set depth of cut, is determined by the dependence [1,3,5-10,12]:
11
2
11
11 .... −−−−
+=+= TT y
m
n
cmcu fVCfVCKKK [€] (2)
where:
- K1, Ku – equations of asymptotic planes,
- nТ = 1/m – coefficient of relative durability(tool life),
- m – indicator of relative durability (tool life),
- yT=yv.nT – exponent, taking into account the impact of feeding in determining the
durability,
- yv – exponent, taking into account the impact of feeding in determining the cutting speed
[17],

3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 11, November (2014), pp. 01-09 © IAEME
3
For its part, the coefficients C1 and C2 are defined as:
EKLC ac ..1 = (3)






+=
E
S
tE
k
aKL
C ad
tc
x
pac
T
.
..
2 (4)
where:
- Lc = 6000[mm] – length of stroke (maximum during the working table for machining
centers),
- Ка = 1 – correction factor, wherein the influence of cutting depth, at ap = const, is assumed
to be one,
- Е – costs for 1 min operation, defined by [17]:
79,319,06,3 =+=+= ma EEE €/d (5)
- Еа – depreciation charges:
6,3
95,0.322
110000
.322
===
π
rP
E €/d (6)
- Pr =110 000 € - approximate cost of machining center of its type,
- η = 0,95 – efficiency,
- Еm – cost for rehabilitation,
19,0
100
8.47,112.66,0
100
47,1.66,0
=
+
=
+
=
pcEP
E €/d (7)
- P =12[kW] - power of the machine,
- Еpc = 8 – factor determining the complexity of the machine,
- tad =1,5[min] – time for change of tool,
- ktc
m
= kT.Cvc [m/min] – constrant, derived under determinate cutting, taking into account the
type of machined materials (kT = 0,7) [11],
- CVc – constant, derived under determinate cutting, taking into account the type of cutting
speed [1,12,17],
- S = 40€ – cost tool to reach MTBF(technical resources),
- xT=xv.nT – exponent, taking into account the impact of depth of cut feeding in determining
the tool life (durability) [1,3,16,17].
The values of the variables in the dependencies for different types of machined materials are
shown in Table 1. Threshold levels of factors cutting speed Vc[m/min] and minute feed fm[mm/min],
form factor space reaches maximum values:
- where n = 0÷30000 min-1
, D=8mm - Vc = 0÷754 [m/min]
- fm = 0÷5000 [mm/min].
Based on the results obtained are built graph – Fig.1,a,b,c interpreting models of production cost in a
coordinate system lgK-lgVc-lgf in different types of workpieces, together with the patterns of
production rate lgQ-lgVc-lgf.

4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 11, November (2014), pp. 01-09 © IAEME
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Table 1
4. MATHEMATICAL MODEL FOR OPTIMIZATION IN PRODUCTION RATE
CRITERION
The use of such a objective function, inevitably leads to an increase of the cost, over the
unambiguous optimum function defined in (1). But in turn this allows to intensify the cutting
conditions.
Fig.1: Effect of production cost – К (lgK-lgVc-lgf) and production rate - Q (lgQ-lgVc-lgf) on
cutting speed Vc and minute feed f by:
a) aluminium sheets, b) HPL panels, c) aluminium composite panels

5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 11, November (2014), pp. 01-09 © IAEME
5
Production rate is obtained by equation [1,3,12,17]:






















+





=
+
=
fV
KL
k
afVt
fV
KLt
T
t
t
Q
c
ac
ct
x
p
yn
cad
c
acm
ad
m
TTT
.
.
.
...
.
.
1
.
1
(8)
Based on the results - Table 1 are constructed graph – Fig.1,a,b,c, interpreting models of
production rate in a coordinate system lgQ-lgVc-lgf in different types of workpieces.
5. TECHNICAL REQUIREMENTS
The design of the formed surfaces on the plane lgVc-lgf presents family izolines expressing
the production cost and production rate. The decision of the optimization problem is reduced to
finding the intersections of the area bounded by the input technical requirements and contours of cost
and rate - Figure 2,a,b,c. Conduct adequate optimization requires introduction of four technological
constraints that in high-speed milling are expressed in [1,3]:
5.1 Lower bounds of feed
30min),max(min 1minmin1 =≥⇒=≥ ffffff mTMm mm/min (9)
where:
- fM min = 0 – lowers kinematic bounds of feed for machining centers,
- fТ min = 30mm/min – lowers technological bounds of minute feed for high-speed milling
with single flute mill cutters.
5.2 Min permissible economical cutting speed [1, 3, 12, 17]
T
T
n
y
mT
cQ
fnC
C
V
/1
2
1
).1( 







−
= (10)
5.3 Upper bounds of feed [1, 3, 12, 17], the maximum values of the main cutting force Fc[N]:
F
FF
FF y
FcT
ux
p
zn
cc
m
KnzBa
DVF
f
1
max
2
....
..








≤ (11)
where:
- Fcmax = Кc1.hmax [N] – maximum values of the main cutting force Fc[N],
- Кc1 [N/mm2
]– specific cutting force [7,8,9,13],
- hmax [mm] – maximum thickness of cut [13],
- Ка = 1 – correction factor, wherein the influence of cutting depth, at ap = const, is assumed
to be one,
- D = 8 mm – tool diameter,
- zF=xF=uF = nF =1 – exponents,

6. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 11, November (2014), pp. 01-09 © IAEME
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- B=8[mm] – width of cut,
- z = 1 – number of flute,
- КFc – correction factor taking into account the type of machined material [17].
5.4 Max cutting speed allowed by the power of the machine [1,3,12,17]:
F
FF
F n
FcT
ux
p
z
c
KnzBa
DP
V
−








≤
1
1
3
2
....
...10.60 η
(12)
For different categories of machined materials - results that satisfy the system are presented
in Table 2 and graphically - Figure 2,a,b,c.
Depending on (10) gives too high values for Vc2, which is explained by the fact that the
permissible power of the machine is significant as it is designed for devices with higher strength
characteristics. In this case for Vc2 = 754m/min, taken the speed that is achieved at maximum spindle
speed n = 30 000 min-1
.
Table 2
Fig.2: Optimization model in the machining of:
a) aluminium sheets , b) HPL panels, c) aluminium composite panels

7. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 11, November (2014), pp. 01-09 © IAEME
7
Intersections, determine the optimum cutting conditions.
As seen in the aluminium sheets values of the factors speed and minute feed are lower than
those in the HPL panels and aluminium composite panels, which is mainly due to the higher
hardness of the first.
On fig.3 is shown a summary according to the K,Q=f(Vc), which fully confirms the
previously expressed expectations that the permitted speed on the criterion production cost is
significantly lower than that obtained under criterion production rate.
Fig. 3: Influence of cutting speed on the production cost and production rate
After final processing and analysis of results, on the cutting speed to meet the tools reliability
requirements for tool life (durability) and storage capability, as optimal values are chosen for the
individual categories of materials shown in Table 3. While the giving in order conditions for a
maximum relative cost in guaranteed quality of the machined surface for optimal choose those listed
in Table 4.
Table 3
Table 4

8. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 11, November (2014), pp. 01-09 © IAEME
8
6. RESULT AND DISCUSSIONS
The results and analysis allow the following principal conclusions:
6.1. Based on the parallel solution of two multifactorial, iteratives, single parameters optimizations
with factorial scaning are displayed optimal values for the elements of cutting conditions – cutting
speed Vc[m/min] and minute feed fm [mm/min] when machining elements from aluminium sheet,
HPL panels and aluminium composite panels.
6.2. Parameters are the lowest in aluminum sheets, increasing in HPL panels, especially in composite
panels. Which is mainly explained by the higher hardness of the first.
6.3. Exposed is a balanced approach for the selection of optimal values of the cutting conditions,
satisfaction of reliability and production rate requirements.
7. CONCLUSIONS
Development and its results have scientific and applied nature. Based on numerical
optimization here are drawn cutting conditions for high-speed milling with single flute end mill
cutters of elements from aluminium sheets, HPL panels and aluminium composite panels on
machining centres. The results are useful for companies whose main activity is the manufacture and
assembly of products from these materials through processes based on high-precision milling
strategies. Data presented in the literature of this type are basically catalogue offered by
manufacturers of tools and largely recommendatory in character. While returnees in the development
claim to comprehensiveness and veracity, as due to a strictly scientific character, in which the results
are received and on the basis of their approbation in production companies, "Preciz Al"Ltd Rousse,
"Alex glas"Ltd Sliven and "Difoat"Ltd Sliven. Where are proven their advantages in accordance with
the comparative tools life analysis, taking into account the condition of the cutting edges.
The application of multilayer coatings on tools, intensify the cutting conditions, in proportion
to the increase in hardness. In subsequent levels of experimental research that could be reported, by
introducing a correction factor reflecting changes in physical-mechanical indicators about individual
groups of machined materials.
8. ACKNOWLEDGMENTS
Studies were carried out in accordance with the research project №02 / 07.08 / 2014, entitled
"Determination of cutting conditions in high-speed milling with single flute end mill cutters"
funded by the company "Difoat" Ltd Sliven.
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