A prediction of the machining defects in flank milling
11 Jun 2003-The International Journal of Advanced Manufacturing Technology (Springer-Verlag)-Vol. 24, Iss: 1, pp 102-111
TL;DR: In this paper, the authors present a prediction method of the tool deflection on every ruled surface using the cutting pressure notion, which is applicable on all ruled surfaces and can be applied to any ruled surface.
Abstract: In peripheral milling with great axial engagements, the tool deflections generate some geometrical defects on the machined surface. This article present a prediction method of these defects which is applicable on every ruled surface. The cutting forces are estimate with the cutting pressure notion. The parameters of the tool/workpiece material couple are identified by a test part. The prediction of the tool deflections requires controlling the tool immersion angle for each angular position of the tool. The deflections can be significant. An original procedure which is based on an engagement cards avoids an iterative calculation of the radial engagement. The experimental checking of the method of prediction is presented in a test.
Summary (1 min read)
Jump to: [3.1 Introduction] – [3.2 The prediction algorithm in steady mode] – [3.4 The tool input in the workpiece material] – [5.3 The engagement line] and [5.4 Verification]
- By misnomer, the authors call the ''rough'' surface of the part the part surface before the tool passes.
- This raw part can be described by a CAD model or by a raw management dynamical system according to the tool paths during the preceding operations (NCSIMUL software  , Vericut software  and Delmia software  ).
3.2 The prediction algorithm in steady mode
- The tool crosses a transition zone (the zone where the engagement conditions rapidly vary), also known as Case 1.
- The tool enters the workpiece material (the initialisation of the calculation), also known as Case 2.
3.4 The tool input in the workpiece material
- Generally, in this first section, the tool is out of the workpiece material and there is no deformation.
- Criterion 5 is thus checked before passing to the following step.
5.3 The engagement line
- The maximum engagement card (Fig. 20 ) shows that on a section extracted from the steady mode phase the maximum immersion angle clearly increases then decreases when the generating point moves away from the embedding position.
- The authors see that the more significant the deformation is, the less the tool engages in the workpiece material as was described in paragraph 4.2.
- The method of prediction of peripheral milling defects proposed in this article is based on the estimation of the real tool engagement conditions.
- Several milling tests on different forms were carried out and made it possible to validate this method.
- The method rests on the precise analysis of the tool generating points kinematics.
- The authors research tasks now tend to exploit the concept of an engagement card within the framework of the machined tool paths generation by respecting a constant tool engagement in the workpiece material.
- Another objective is the direct compensation of the defects estimated by the model previously described, the objective being to machine a part by respecting the functional constraints which were initially defined.
Did you find this useful? Give us your feedback
HAL Id: hal-00098361
Submitted on 16 Feb 2018
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entic research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diusion de documents
scientiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
Prediction of the machining defects in ank milling
Arnaud Larue, Bernard Anselmetti
To cite this version:
Arnaud Larue, Bernard Anselmetti. Prediction of the machining defects in ank milling. International
Journal of Advanced Manufacturing Technology, Springer Verlag, 2004, Vol. 24/1-2 (1), pp. 102-111.
A. Larue, B. Anselmetti
A prediction of the machining defects in ﬂank milling
Abstract In peripheral milling with great axial engage-
ments, the tool deﬂections generate some geometrical
defects on the machined surface. This article present a
prediction method of these defects which is applicable
on every ruled surface. The cutting forces are estimate
with the cutting pressure notion. The parameters of the
tool/workpiece material couple are identiﬁed by a test
part. The prediction of the tool deﬂections requires
controlling the tool immersion angle for each angular
position of the tool. The deﬂections can be signiﬁcant.
An original procedure which is based on an engagement
cards avoids an iterative calculation of the radial
engagement. The experimental checking of the method
of prediction is presented in a test.
Keywords Peripheral milling Æ Tool deﬂections Æ
Identiﬁcation of a tool workpiece material couple Æ
1.1 Prese ntation
The present stud y is about ﬂank milling using the long
cutters of free forms. This free forms are made up of
ruled surfaces. This very powerful process, from a pro-
ductivity and surface quality point of view, is very
popular in aeronautics and mould manufacturing.
The magnitude of the defect induced by the deﬂection
of a long HSS cutter with a diameter of 20 mm can reach
0.7 mm for a radial engagement of 3 mm. Such geo-
metrical variations induce the nonrespective of the part
The purpose of this article is to establish a prediction
method of ﬂank milling defects at low speeds which can
be integrated in a computer aided sesign and manufac-
turing software (CAD/CAM).
The characterisation of the tool deﬂections is based
on a cutting pressure model. The model parameters are
gauged by milling a test part on the production machine
tool. When the tool workpiece coupl e is identiﬁed, the
inﬂuence of the tool deﬂection on the part geometrical
defects can be predicted.
1.2 The problem
To predict tool deﬂection, it is necessary to control the
engagement of the cutting edges into the workpiece
material at every moment.
At high cutting speed, chatter vibration phenomena
appears [1, 2]. To model that phenomena, lots of re-
search took the mass, the damping and the acceleration
of the milling structure into account [3, 4, 5, 6]. These
studies allow the prediction of the vibratory behaviour
of the structure. First ly, they result in long calculations
which are diﬃcult to implement in a CAD/CAM system
on all the surfaces to machine. Secondly, such studies
require a dynamical protocol to identify the dynamical
structure characteristics and the force model parameters.
Our objective at low speed milling was to predict the
surface defects and to compensate for the tool paths. We
also needed a model whic h was easy to identify and fast
to use. We showed that a satisfying result can already be
obtained without taking the vibratory behaviour into
account . That’s why the calculation of surface defects
thus passes by the motion study of the generating point
of each cutting edges in catch in the workpiece material.
In fact, the surface is generated by the cutter sweep-
ing. Each rule of the surface is obtained by the gener-
ating point displacement along the helicoidal cutting
edge during the rotation of the cutter.
A. Larue (&)
LURPA Ecole Normale Supe
rieure de Cachan,
61 Av Pt Wilson, 94235 Cachan Cedex, France
Institut Universitaire de Technologie de CACHAN,
9 avenue de la division, Leclerc 94234 Cedex, France
The tool deﬂection can be calculated at every moment
using a model resulting from the materials resistance
The cutting forces applied to the tool thus depend on
the number of teeth in catch and on the length of the
cutting edge engaged in the workpiece material at every
It is thus necessary to calculate the immersion angles
for each cutting edge starting from the ﬁnished surface
and from the rough surface deﬁned by the CAD model.
This calculation must be carried out for each rule and
for each angular position of the cutt er.
During our tests, we have showed that the deﬂections
are so signiﬁcant that it is absolutely necessary to take
the deﬂection into account to calculate the cutting edge
engagement. In the ﬁrst approach, this analysis requires
considering an iterative calculation process which is very
expensive in terms of computation times. The article’s
purpose is to establish a precise process, which avoids
this iterative calculat ion in the majority of the cases. It
presents the engagement card concept which represents
the tool load during the milling.
2 The modelisation of surface defects
2.1 The surface generation
The problem studied is the peripheral milling of a ruled
surface. Our interest is focused on the down milling case.
At ﬁrst approximation, the tool path is generated so that
during that time, the cutter generatrix is combined with
the various rules of the surface. However, the surface
concavity is not constant along the rule. Various tech-
niques of the cutter axis shifting make it possible to
improve the milling quality by limiting the undercut and
the overcut [8, 9, 10, 11].
This work thus considers that the CAM system
constructs the tool path generation and gives the tool
axis (axis ~z position A
and the normal to the machined
y at every moment, which makes it possible to
deﬁne the cutting section S
at the curvilinear abscissa
along the directrix (Fig. 1).
x completes the trihedral
y, ~z in the feed direction.
In this section, we will suppose that the generatrix to
machine is the line D
. Our objective is thus to determine
the variations of the machined surface position com-
pared with the theoretical line D
. These variations are
added to the undercut and overcut defects. The diﬀerent
sections will be studied with a ‘‘normal’’ step and a
‘‘reduced’’ step. The reduced step will be used when
some engagement discontinuities are detected on the
machined surface or on the rough surface.
The generating point of a tool is mobile on the line
. At moment t, the generating point is in P at distance
z of the tool holder which is supposed to provide a
perfect embedding. It is thus necessary to know the tool
deﬂection in P which will be equal to the surface position
variation in this point.
At moment t+dt, the generating point is in P’ at the
distance z’ (Fig. 2).
The deﬂection varies according to the generating
point P, which generates a deformed proﬁle on the
2.2 The deﬂection model
Our deﬂection model correspond to an extension of the
Kline and DeVor model , which has involved lots of
semi static models [13, 14, 15].
At a given moment, the generating point is in P. Each
elementary length of the cutting edges in catch in the
workpiece generates an elementary tool deﬂection in
P. The sum of these deﬂections gives the variation of the
surface in P.
At point Q located along the cutting edge, the
angular position is b. The force applied in Q on a part of
the cutting edge, whose elementary length is dz, consists
Fig. 1 The place of the generating points
Fig. 2 The evolution of the generating point of a tool
of a tangential compone nt dFt and a radial component
The cutting forces are obtained with the following
dFr ¼ Kr ep dz ¼ Kr
fz sin bðÞdz
fz sin bðÞðÞ
ep is the depth of cut given by: ep ¼ fz sin bðÞ.
fz is the feedrate per tooth.
Kr ¼ Kr
and Kt ¼ Kt
The cutting pressures Kr
of the tool workpiece material couple. They are deter-
mined by an identiﬁcation test.
Only the normal component dN of the cutting force
acts on the mac hined surface deformation (Fig. 3):
dN bðÞ¼dFr bðÞcos bðÞþdFt bðÞsin bðÞ
In P, the resulting deﬂection dy induced by the force
dN appl ied to point Q is given by a simple model of a
ﬁxed beam of the constant quadratic moment of inertia:
z L bðÞðÞ
z L bðÞðÞ
where L bðÞ
2pðÞis the distance between P and
Q for the tooth which leaves its trace on the part, h being
the helicoidal milling cutter step.
A similar relation is deﬁned for the points Q which
belong to the following cutting edge in catch (when Q
is on the left of P).
For each point P, the theoretical total deﬂection is the
sum of the elementary deﬂections generated by all the
points Q of the cutting edges simultaneously engaged in
the workpiece material.
where Nc is the number of cutting edges in catch.
The diﬃculty of the calculation lies in the deﬁnition
of the maximal and minimal immersion tool angles
). The se angles are deﬁned by the inter-
section of the screw which characteri ses the tool cutting
edge when the generating point is in P. b
sponds to the intersection with the rough surface. b
corresponds either to the intersection with the ﬁnished
=0), or to the intersection with the side
of the part 06b
ðÞ. This calculation will be
developed in pa ragraph 4, because it should take the
tool deﬂection into account. Figure 4 shows the calcu-
lation of the resulting deﬂection dy at point P.
2.3 The identiﬁcation of the coeﬃcients
To determine the coeﬃcients Kr
, an identiﬁ-
cation protocol on an unspeciﬁed industrial milling
machine was proposed [7, 16, 17]. The identiﬁcation
procedure consists in the down peripheral milling of a
plan starting from the test part deﬁned in Fig. 5. The
width of the part is slightly higher than
where h is the
dal pitch and Z is the total number of teeth.
The radial depth of cut varies gradually from 0.5 to
3 mm (Fig. 5). The tool end is left free so as to make it
possible to stud y only the inﬂuence of the helicoidal
cutting edge on the part defect.
From an operational point of view, the identiﬁcation
procedure consists in milling the test part and measuring
the defects of the machined surface.
The immersion angles can be calculated by taking the
tool deﬂection which is estimated starting from the
measured dots into account.
The coeﬃcients Kr
are calculated by mini-
mising the sum of the squares of the diﬀerences between
the dots measured and the dots simulated.
Fig. 3 The deﬂection model deﬁnition Fig. 4 The calculation of the resulting deﬂection dy at point P
2.4 The identiﬁcation of the tool workpiece material
For our application, the conditions of the identiﬁcation
test are the following:
HSS tool of diameter 20 mm, whose active length is
88 mm—4 teeth:
– Machined workpiece material: C48
– Milling on a vertical milling centre
– Vc=25 m/min
– fz=0.2 mm/tooth
, the coeﬃcients calculated are:
The simu lated machine surface is illustrated in Fig. 6.
Several tests showed that these coeﬃcients are almost
independent from the cutting speed.
Figure 7 shows that the diﬀerence between the sim-
ulated and the cloud of theoretical dots lie for 95 percent
of the surface between ±0.05 mm.
3 The prediction of the milling defects in CAM
3.1 Introdu ction
The work objective is to predict the form and the posi-
tion variations of the ﬂank machined surfaces. These
variations are due to the too l deﬂections generated by
the variable cutting forces. The part deformations and
the machine deformations are not taken into account.
These cutting forces are depending on the cutter
immersion angle at every moment which also consider-
ably depends on the tool deﬂection, which makes the
calculation diﬃcult (Fig. 8).
In front of this problem, we propose a defects pre-
diction method which is applicable in a CAD environ-
ment for the milling of an unspeciﬁed ruled surface. The
ﬁnal geometry to obtain is thus deﬁned by a CAD
model. The tool paths are initially given by the CAD for
example with the use of tool laying techniques on a
surface, suggested by Rubio , To
nshoﬀ  and
By misnomer, we call the ‘‘rough’’ surface of the part
the part surface before the tool passes. This raw part can
be described by a CAD model or by a raw management
dynamical system according to the tool paths during the
preceding operations (NCSIMUL software , Vericut
software  and Delmia software ). In all cases, the
radial engagement is supposed to be lower than the
cutter diameter: ap £ 2·R, in order to exclude the mill-
ing in full matter.
3.2 The prediction algorithm in steady mode
An iterative solution would ﬁrstly consist in calculating
the cutter deﬂection by considering the theoretical angle
Fig. 5 The part for the calibration of the tool workpiece material
Fig. 6 A simulation of the machined surface
Fig. 7 A comparison of the simulated and machined surfaces
TL;DR: In this paper, the role of surface defects on static flat seal efficiency is investigated on synthetic "turned-like" surfaces generated by combinations of the first 50 vibrational eigen modes determined from modal discrete decomposition.
Abstract: We report on the role of the modal content of surface defects on static flat seal efficiency. The configuration under consideration is an annular contact between two surfaces, one holding all the defects, the other being assumed flat and infinitely rigid. The analysis is carried out on synthetic "turned-like" surfaces generated by combinations of the first 50 vibrational eigen modes determined from modal discrete decomposition. The transmissivity of the contact, that fully characterizes the seal efficiency, is computed on the basis of a Reynolds model for incompressible flow. The dependence of the transmissivity upon the modal content of the surface defects is analyzed on a contact pressure range of common use employing a simplified deformation algorithm. Impact of the defects modal content is investigated statistically through a pair of experimental designs. It is shown that, i) the uncertainty on transmissivity, while considering a series of parts, can be drastically reduced if defect modes are well selected; ii) the transmissivity itself can be very significantly decreased when the defects modal content is conveniently controlled. While clearly indicating that the common surface roughness specification is generally not a relevant one to ensure a required seal performance, this work opens wide perspectives on the seal improvement by surface defects optimization only.
TL;DR: In this paper, a geometrical model of an end mill is developed based on the CAD/CAM integration via modeling its grinding processes, and the cutting coefficients and distributed cutting forces along the tool axis are obtained via finite element analysis of cutting simulation.
Abstract: Tool deflection of end mills caused by cutting forces has a great effect on the machining quality and efficiency. Cylindrical cantilever beam model with 80 % of tool radius is generally used to predict the tool deflection roughly. But that ignored the complex geometrical structure of end mills, which is manufactured with a set of grinding operations. In this study, the geometrical model of end mill is developed based on the CAD/CAM integration via modeling its grinding processes. Using the developed CAD model, the cutting coefficients and distributed cutting forces along the tool axis are obtained via finite element analysis of cutting simulation. Besides, the moment of inertia along the tool axis is also precisely measured based on the CAD model. Finally, with the measured inertia and distributed cutting forces, the tool defection can be predicted accurately with the unit loading algorithm for the cantilever beam. This study provides an accurate approach to predicting tool deflection of end mills based on the CAD/CAM/CAE integration.
TL;DR: In this article, a model-based approach for monitoring of shape deviations for milling operations is presented, which can be monitored against geometric tolerances, providing a quality monitoring of manufacturing processes.
Abstract: This paper presents a model-based approach for monitoring of shape deviations for milling operations. In order to detect occurring shape deviations of the machined workpiece during the milling process, different kinds of process models are presented and discussed for their application on manufacturing quality monitoring. Thereby, a model-based system was presented for the monitoring of shape deviations based on measured cutting forces. For the transformation of cutting forces into shape deviations, a tool deflection model and material removal model were designed and applied to a monitoring system. The presented model-based monitoring approach delivers accurate quality information, like geometric shape deviations, which can be monitored against geometric tolerances, providing a quality monitoring of manufacturing processes. The reconstruction of shape deviations from measured cutting forces is verified experimentally by comparing measured and reconstructed shape contours.
10 Sep 2014
TL;DR: In this paper, a CAD/CAM/CAE integration approach for the end-mill was carried out to predict the cutting forces and tool deflection, and also the prediction results with various methods were verified to demonstrate the advantage of proposed approach.
Abstract: Milling is used widely as an efficient machining process in a variety of industrial applications, such as the complex surface machining and removing large amounts of material. Flutes make up the main part of the solid end-mill, which can significantly affect the tool’s life and machining quality in milling processes. The traditional method for end-mill flutes design is using try-errors based on cutting experiments with various flute parameters which is time- and resources-consuming. Hence, modeling the flutes of end-mill and simulating the cutting processes are crucial to improve the efficiency of end-mill design. Generally, in industry, the flutes are ground by CNC grinding machines via setting the position and orientation of grinding wheel to guarantee the designed flute parameters including rake angle, relief angle, flute angle and core radius. However, in previous researches, the designed flute profile was ground via building a specific grinding wheel with a free-form profile in in the grinding processes. And the free-form grinding wheel will greatly increase the manufacturing cost, which is too complicated to implement in practice. In this research, the flute-grinding processes were developed with standard grinding wheel via 2-axis or 5-axis CNC grinding operations. For the 2-axis CNC flute-grinding processes, the flute was modelled via calculating the contact line between the grinding wheel and cutters. The flute parameters in terms of the dimension and configuration of grinding wheel were expressed explicitly, which can be used to planning the CNC programming. For the 5-axis CNC flute-grinding processes, the flute was obtained with a cylinder grinding wheel via setting the wheel’s position and orientation rather than dressing the dimension of grinding wheel. In this processes, optimization method was used to determine the wheel’s position and orientation and evaluating the machined flute parameters. Beside, based on the proposed flute model, various conditions for grinding wheel’s setting were discussed to avoid interference of flute profile. A free-form flute profile is consequently generated in its grinding processes. However, in the end-mill design, the flute profile is simplified with some arcs and lines to approximate the CAD model of end-mills, which would introduce errors in the simulation of cutting processes. Based on the proposed flute-grinding methods, a solid flute CAD model was built and a CAD/CAM/CAE integration approach for the end-mill was carried out to predict the cutting forces and tool deflection. And also, the prediction results with various methods are verified to demonstrate the advantage of proposed approach. This work lays a foundation of integration of CAD/CAM/CAE for the end-mill design and would benefit the industry efficiently.
TL;DR: In this article, a new method for the analytical prediction of stability lobes in milling is presented, which requires transfer functions of the structure at the cutter -workpiece contact zone, static cutting force coefficients, radial immersion and the number of teeth on the cutter.
Abstract: A new method for the analytical prediction of stability lobes in milling is presented. The stability model requires transfer functions of the structure at the cutter - workpiece contact zone, static cutting force coefficients, radial immersion and the number of teeth on the cutter. Time varying dynamic cutting force coefficients are approximated by their Fourier series components, and the chatter free axial depth of cuts and spindle speeds are calculated directly from the proposed set of linear analytic expressions without any digital iteration. Analytically predicted stability lobes are compared with the lobes generated by time domain and other numerical methods available in the literature.
TL;DR: In this article, the authors present a mechanistic model for the force system in end milling, which is based on chip load, cut geometry, and the relationship between cutting forces and chip load.
Abstract: This paper presents the development, verification, and implementation of a mechanistic model for the force system in end milling. This model is based on chip load, cut geometry, and the relationship between cutting forces and chip load. A model building procedure based on experimentally obtained average forces is presented and both instantaneous and average force system characteristics are described as a function of cut geometry and feed rate. A computer program developed to implement the mechanistic model provides tabular and graphical outputs which show force distributions as functions of the axial depth of cut and rotation of the cutter. Force characteristics during concerning cuts are predicted by the model and verified via a set of cornering cut experiments typical of aerospace machining operations. Force characteristics in cornering are examined as a function of axial depth of cut and feedrate.
TL;DR: In this paper, the dynamic stability of the milling process is investigated through a single degree of freedom mechanical model and two alternative analytical methods are introduced, both based on finite dimensional discrete map representations of the governing time periodic delay differential equation.
Abstract: The dynamic stability of the milling process is investigated through a single degree of freedom mechanical model. Two alternative analytical methods are introduced, both based on finite dimensional discrete map representations of the governing time periodic delay-differential equation. Stability charts and chatter frequencies are determined for partial immersion up- and down-milling, and for full immersion milling operations. A special duality property of stability regions for up- and down-milling is shown and explained.