2212-8271 © 2013 The Authors. Published by Elsevier B.V.
Selection and peer-review under responsibility of The International Scientifi c Committee of the “14th CIRP Conference on Modeling of Machining Operations” in the person of the Conference Chair Prof. Luca Settineri
doi: 10.1016/j.procir.2013.06.150
Procedia CIRP 8 ( 2013 ) 558 – 563
14
thCIRP Conference on Modeling of Machining Operations (CIRP CMMO)
Microcutting force prediction by means of a slip-line field force
model
M. Annoni
a, G. Biella
a, L. Rebaioli
a,*, Q. Semeraro
a aDipartimento di Meccanica, Politecnico di Milano, via G. la Masa 1, 20156 Milan, Italy* Corresponding author. Tel.: +39-02-23998592; fax: +39-02-23998585.E-mail address: [email protected]. Abstract
Mechanical micromachining is a very flexible and widely exploited process, but its knowledge should still be improved since several typical phenomena play a role on the microscale chip removal (e.g. “minimum chip thickness effect”, microstructure influence on cutting forces, stable built-up edge, etc. ). Several models have been developed to describe the machining process, but only some of them take into account a rounded-edge tool, which is a typical condition in micromachining. Among these models, the slip-line field model developed by Waldorf for the macroscale allows to separately evaluate shearing and ploughing force components in orthogonal cutting conditions, therefore it is suitable to predict the cutting forces when a large ploughing action occurs, as in micromachining. The present work aims at objectively verifying the cutting and feed force prediction performance of the Waldorf model within typical microscale cutting conditions (uncut chip thickness lower than 50 μm and comparable in size to cutting edge radius) in its original version and in a modified version considering the partial effective rake angle. A suitable set-up, especially designed for microturning conditions, has been used in this research to measure forces and chip thickness. Tests have been carried out on C38500 brass (CuZn39Pb3) with different cutting speeds and different ratios between uncut chip thickness and cutting edge radius.
© 2013 The Authors. Published by Elsevier B.V.
Selection and/or peer-review under responsibility of The International Scientific Committee of the 14th CIRP Conference on Modeling of Machining Operations" in the person of the Conference Chair Prof. Luca Settineri
Keywords: micromachining, chip formation, stable built-up edge, cutting forces
f feed
Fc cutting force
Ft thrust force
k shear flow stress m friction factor
t chip thickness
tc uncut chip thickness
Vc cutting speed
w width of cut rake angle
shear angle prow angle
“W” for the Waldorf model or “WE” for the Waldorf model considering the effective rake angle “c” for cutting force or “t” for thrust force
1.Introduction
Mechanical micromachining is one of the most flexible and widely exploited processes. However, basic knowledge about the physical phenomena [1-3] could still be improved: in particular, the following scale-effects need further study:
tools cannot be considered sharp because the edge radius tends to be comparable in size to the uncut chip thickness; for this reason, effective rake angle gets highly negative, ploughing forces become more relevant than shearing forces and the cutting specific energy gets higher [3-5];
a minimum uncut chip thickness exists under which no material can be removed from the workpiece (“minimum chip thickness effect”); this fact produces discontinuous chip removal [4-7];
© 2013 The Authors. Published by Elsevier B.V.
Selection and peer-review under responsibility of The International Scientifi c Committee of the “14th CIRP Conference on Modeling of Machining Operations” in the person of the Conference Chair Prof. Luca Settineri
Open access under CC BY-NC-ND license.
material microstructure has a strong effect on cutting forces and make them vary in function of the grain orientation [8-9];
a stable built-up edge (called “dead metal cap”) is claimed by some researchers to always occur [10-12].
1.1.State of the art
Many models have been developed to describe the chip removal process; among them, models based on the so-called “slip-line field” theory, firstly introduced with the Lee and Shaffer model [13], are the present paper focus since they potentially can take into account ploughing effects.
Slip-line field models have been developed accounting for different tool shapes, such as:
sharp ([14, 16, 17-22]); worn ([15, 22]);
rounded ([10-11, 23-31]); chamfered ([32-33]).
A rounded tool shape allows to better reproduce the typical microscale conditions, i.e. uncut chip thickness lower than the tool edge radius; such a radius cannot be reduced under a certain value due to tool fabrication technological limitations. All specific microscale models published in recent years [10-11, 23-31] are slip-line field models taking into account a rounded tool edge.
These models can be classified in two groups according to the applied modeling approach: the models by Waldorf et al. [10-11], Jun et al. [25-27], Karpat et al. [28], Yoon et al. [29] and Ozturk et al. [31] assume that a stable build up edge always occurs (according to experimental findings of [12]) while Fang et al. [23-24] and Jin et al. [30] state that the material flow is diverted by a separation point on the tool edge.
As concerning the first family, Waldorf et al. [10-11] developed a slip-line field consisting of three shear zones, which allows to predict also the ploughing force components. The authors assume that the friction factor is constant and the shear flow stress only depends on the machined material but not on strain, strain rate or temperature (rigid perfectly plastic material hypotesis). This model was experimentally validated by means of orthogonal turning tests on Al 6061-T6 [10].
Jun et al. [25-27] state that their proposed field is similar to the Fang model [23-24] but considers only the slip-lines which are needed for cutting force calculations, adds a dead metal cap and takes into account an effective rake angle, which varies with the uncut chip thickness [35].
The study by Karpat et al. [28] presents a model derived from Waldorf’s one: orthogonal turning experiments were carried out on AISI 4340 steel and the friction factor was calculated basing on forces and chip
geometry. Also a finite elements analysis was performed, applying the Johnson-Cook model to evaluate the shear flow stress.
Yoon et al. [29] proposed a slip-line field which takes into account the minimum chip thickness effect and the effective rake angle; the friction factor was supposed to be constant. The authors validated their model by performing micro-turning tests on 260 brass alloy (CuZn30).
In their paper, Ozturk et al. [31] show a slip-line field model composed by eight shear regions and including a dead metal cap, under the assumptions of constant friction factor and perfectly plastic material. The authors carried out validation experiments on 260 brass alloy (CuZn30) and obtained chip micrographs by freezing the cutting action through a quick stop device.
As regarding the second family, Fang et al. [23-24] designed a model which is composed by twenty seven slip-line subregions and whose mathematical formulation with non-unique solution is based on Dewhurst and Collins matrix technique [17, 34]. The Fang model is able to estimate the ploughing force components. The authors compared their results with experimental observations from past works by other authors.
The model developed by Jin et al. [30] is similar to the Fang model, but the Johnson-Cook constitutive model is applied in this study to obtain the shear flow stress and the hydrostatic pressure as functions of strain, strain-rate, and temperature. This model was validated by means of turning tests on 260 brass alloy (CuZn30).
As stated above, some of these studies [10-11, 28-29, 31] provide an experimental validation of their models but only [31] shows some micrographs which confirm, for example, the stable built up edge presence and the angle values. However, these micrographs were obtained at very low cutting speeds in order to avoid thermal effects.
The slip-line field proposed by Waldorf [10] is simple but allows to evaluate the cutting forces when a strong ploughing occurs, which is typical when machining with an uncut chip thickness lower than the tool edge radius. Moreover, [11] points out how models including a dead metal cap describe the experimental observations better than models considering a material separation point. It should also be noticed that the chip micrographs obtained by Kountanya et al. [12] and Ozturk et al. [31] on CuZn30 brass prove the presence of a dead metal cap when machining with a ratio between uncut chip thickness and cutting edge radius lower than unity.
Therefore, the present study focuses on the Waldorf slip-line field model [10] and proposes to modify it, as already done in literature [25-27, 29], accounting for the effective rake angle eff [5] which plays an important
aims at objectively verifying the cutting and feed force prediction performance of the Waldorf model within typical microscale cutting conditions (uncut chip
thickness lower than 50 μm and comparable in size to
cutting edge radius) in both its original and modified versions.
2.The selected slip-line field model
Figure 1: Slip-line field proposed by Waldorf (adapted from [10])
The slip-line field model developed by Waldorf for the orthogonal cutting condition [10-11] predicts the cutting and the thrust force components. This model considers three regions of rigid material motion:
the first region (I in Figure 1) is a pre-flow zone where the prow angle ( in Figure 1) accounts for the material raising up due to compressive stresses;
the second region (II in Figure 1) is the traditional shear zone, i.e. the “primary shear zone”, and is identified by the shear angle ( in Figure 1);
the third region (III in Figure 1), i.e. the so-called “tertiary shear zone”, is close to the dead-metal cap and its dimensions are determined by the friction conditions at the tool-chip interface.
It should be noticed how the “secondary shear zone”, where the tool rake face – chip contact takes place, is not considered.
Figure 2: Effective partial rake angle (adapted from [5])
As stated in Section 1.1, the partial effective rake
angle eff (Figure 2) has been introduced in the Waldorf
slip-line field model to account for the typical effects of low uncut chip thickness machining.
The height ht of the tangent point between the tool
rake surface and the arc of the cutting edge radius re is defined as:
t e 1 sen
h r (1)
As stated in [5], when the uncut chip thickness tc is
lower than ht the effective rake angle can be obtained as
follows: 1 cos 1 2 c eff e t r (2) 3.Experiment description
Figure 3: Microturning set-up [A = workpiece, B = tool holder, C = load cell]
An empirical investigation of the relationship among process forces, cutting speed and normalized feed (i.e.
the ratio between the uncut chip thickness tc and the
cutting edge radius) has been carried out.
The Kern EVO ultra precision 5-axis machining centre available at the “MI_crolab” of Dipartimento di Meccanica of Politecnico di Milano (nominal positioning tolerance = ± 1 m, precision on the workpiece = ± 2 m) has been used to perform orthogonal cutting tests. A Kistler 9257BA triaxial piezoelectric load cell (C in Figure 3) has been employed to measure cutting forces during each test.
The orthogonal cutting condition has been reproduced by turning a thin-walled tubular workpiece (diameter = 15 mm, nominal wall thickness = 0.7 mm), mounted on the machine spindle (A in Figure 3) and
moving at the cutting speed Vc by means of a turning
(B in Figure 3). Each workpiece has been pre-machined rr on a traditional lathe and then measured on the Kern EVO by means of Blum Micro Compact NT laser presetting system (accuracy: 1 m) in order to measure possible errors. Diameter measurements on different workpiece – tool holder couples at different heights showed a maximum standard deviation = 7 m including dimensional, fixturing and run-out errors. Such a deviation is acceptable for the presented experimentation.
Microturning operations have been performed by means of a suitable set-up designed to be used on the Kern EVO machining centre table and to allow on-line force acquisitions.
The turning tests were performed by means of a Sandvik DCGX 070202–ALH10 carbide insert, whose main characteristics are listed in Table 1.
The tested target material is the free-cutting brass C38500 (CuZn39Pb3), whose measured hardness is 81.5 HRB. This material has been selected due to its high machinability.
Table 1. Experimental plan constant parameters
Insert
Codex DCGX 070202–ALH10 Nominal rake angle
( ) 20°
Clearance angle 7°
Cutting edge radius
(re) measured value = 9 μm Target material C38500 brass
The cutting edge radius and the rake angle have been checked by an Alicona Infinite Focus optical 3D measuring system (10x magnification, exposure time = 40.1 ms, polarized light).
The radius mean value (Figure 4) has been calculated in three different zones of the insert cutting edge over a 1.5 mm length.
Figure 4: Tool edge radius measurement by Alicona Infinite Focus
Alicona Infinite Focus was also used to measure the chip thicknessttdirectly on chips produced during each
turning test, as shown in the example of Figure 5 (5x magnification, exposure time = 15.3 ms, polarized light).
Figure 5: Chip thickness measurement by Alicona Infinite Focus
3.1. Experimental design
A factorial experiment (Table 2) has been designed in order to investigate the effect of cutting speed and normalized feed on the Waldorf model prediction performance in case of both the original model version [10] and the partial effective rake angle one.
The experimental plan consists of 24 runs (4 replicates for each factors combination), which have been completely randomized.
Table 2. Experimental plan factors
Factor Symbol Levels
Cutting speed VVVc 250 – 300 m/min Normalized feed tc/re 0.66 – 1 – 2
The ”cutting speed” factor varies on two levels: 250 - 300 m/min, while the considered “normalized feed” levels are three: 0.66, 1 and 2, corresponding, respectively, to a feed of 6, 9, 18 μm/rev. Such feed values have been selected in order to stay immediately above the commonly accepted value of minimum chip thickness (0.3-0.4re [5]) which is necessary for a regular
chip formation.VVVc values have been selected in a range
where good cutting conditions (no vibrations, no burrs, good surface finish) take place according to preliminary tests.
Both the cutting and the thrust force components (respectivelyFFF and Fx FFz) have been calculated according
to both versions of the Waldorf model.
The following values have been used as model input:
m (friction factor) = 0.99, as stated by Waldorf [10];
tc
t (uncut chip thickness) equal to the feed since orthogonal cutting conditions have been applied;
t (chip thickness) as measured by Alicona for each
t
test;
w (width of cut) = 0.73 mm, obtained by measurements made on the workpiece by a Zeiss
Prismo 5 VAST MPS HTG Coordinate Measuring Machine;
(prow angle ) = 23°, as the value which minimizes prediction errors for both the model versions;
k (shear flow stress) = 411 N/mm2, calculated by
means of the Johnson-Cook model (coefficients: A = 112 MPa, B = 505 MPa, C = 0.009, n = 0.42, m = 1.68, Tm = 916°C [36].
The mean values of both the cutting and the thrust force components have been calculated for each experimental test, and the percentage errors between the predicted values and the measured mean values have been obtained as follows:
,pred ,meas _ ,meas 100 F F err F # # (3)
where stands for x or z and stands for “W” (Waldorf model) or “WE” (Waldorf model modified with the effective rake angle).
Percentage errors have been the experimental plan responses.
4.Experimental results
The results of the Analysis Of Variance (ANOVA) on errors are summarized in Table 3.
Table 3. ANOVA p-values (bold = significant factor, = 5%). Factors Cutting speed (Vc) Normalized feed (tc/re) Interaction Vc*(tc/re) Resposnes Cutting force Fx _ W x err 0.661 0.352 0.759 _ WE x err err 0.647 0.183 0.839 Thrust force Fz _ W z 0.086 0.000 0.770 _ WE z err 0.228 0.257 0.388
The ANOVA p-values (Table 3) point out how only
errz_W is influenced by the normalized feed. This fact
means that the prediction performance of Waldorf model including the effective rake angle does not depend on process parameters while the original Waldorf model (W) performance varies with the feed for the thrust force component. Figure 6 shows how both the model performances do not vary with tc/re and Vc, while Figure
7 highlights that the W performance is worse for low feeds.
The data plots in Figure 6-7 and the values listed in Table 4 point out how errx_W anderrx_WE are almost equal
for both models while errz_W anderrz_WE get lower when
using Waldorf model including the partial effective rake angle (it should be noticed that error values do not change for tc/re = 2 sincein this case the effective rake
angle corresponds to the nominal one). Therefore, the prediction performance concerning the cutting force Fx
does not change with the applied model but it is improved for the thrust force Fz with the Waldorf model
including the partial effective rake angle.
Table 4. Percentage error means and standard deviations
mean standard deviation
Cutting force Fx _ W x err 6.33 5.22 _ WE x err 6.02 4.64 Thrust force Fz _ W z err 27.9 15.1 _ WE z err 9.65 7.61
Figure 6: Prediction errors for cutting force component (Fx).
Figure 7: Prediction errors for thrust force component (Fz).
5.Conclusions
The present paper bases on a proper microturning experimental set-up and a suitable experimental plan, whose factors have been varied in typical microcutting ranges, to objectively verify the cutting and feed force prediction performance of the Waldorf model in its original version and in a modified version considering the partial effective rake angle. Results show how the
partial effective rake angle introduction allows to better fit microturning data, while original Waldorf model thrust force prediction performance depends on feed values. Further studies are needed to validate the modified model performance in terms of ploughing and shear forces also considering other target materials, other tool geometries and other process parameters.
Acknowledgements
This study has been partly founded by Regione Lombardia within the project “REMS: Rete Lombarda di Eccellenza per la Meccanica Strumentale e Laboratorio Esteso / Excellence Network for Instrumental Mechanics and Extended Laboratory” (Fondo per la promozione di Accordi istituzionali, d.reg. n°4779 del 14/5/2009).
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