An experimental method to determine the minimum uncut chip thickness (Hmin) in orthogonal cutting

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DOI: 10.1016/j.promfg.2017.07.047

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Peer-review under responsibility of the organizing committee of the 45th SME North American Manufacturing Research Conference doi: 10.1016/j.promfg.2017.07.047

Procedia Manufacturing 10 ( 2017 ) 194 – 207 Available online at www.sciencedirect.com

ScienceDirect

45th SME North American Manufacturing Research Conference, NAMRC 45, LA, USA

An Experimental Method to Determine the Minimum Uncut Chip

Thickness (h

min

) in Orthogonal Cutting

Reginaldo T. Coelho

a

* , Anselmo E. Diniz

b

and Tatiany M. da Silva

b

a_{School of Engineering at Sao Carlos, University of Sao Paulo, SP, Brazil} b_{Mechanical Engineering School, University of Campinas, SP, Brazil}

Abstract

Chip formation has been studied for more than a century using, initially, process description followed by experimental procedures and mathematical models. At first, cutting edges were modelled as perfectly sharp, but real cutting tools contain small radius. Some of them are as low as few micrometers. Micro-machining operations often need uncut chip thickness (h) lower than edge radius. In such conditions a minimum value (hmin) may be found, under which material may not be properly removed. There

is an extensive range of values for hminin literature, as a percentage only of the edge radius (re). The criterion for establishing

hminalso extensively varies as well as the cutting conditions used. The present work proposes an innovative method to study hmin

with realistic values of cutting and feed speed (vcand vf) in orthogonal cutting. Using the proposed method several edges were

tested and two of them, one sharp (re= 6 Pm) and one blunt (re= 120 Pm), are here presented in 3 different conditions. Values

of hminwere detected for each of the cutting conditions. They were found to depend on the cutting conditions, on the maximum

hmax established and on the way it grows during the interaction between edge radius and workpiece material. It was also

suspected that BUE can be formed in front of the tool, depending on the way the uncut chip thickness increases during the interaction. The method also proved to be capable of detecting hmin and several other associations with the main parameters

affecting that minimum value.

Peer-review under responsibility of the Scientific Committee of NAMRI/SME.

Keywords: minimum chip thickness, edge radius, cutting edge, chip, machining

* Corresponding author. Tel.: +55 16 3373 8235; fax: +55 16 3373 9214. E-mail address: rtcoelho@sc.usp.br

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1. Introduction

Chip formation has been studied and described as early as the 30´s of last century [1, 2]. Those process descriptions and mathematical modelling started using an ideally sharp cutting edge, which creates a line as it contacts the workpiece. Uncut chip thickness (h) was usually significantly higher than edge radius (re) in most cases,

at that time. The action of such edge establishes a state of stress, which leads the material into first flowing followed, by plastic deformation and failure. The state of stress at the contact between edge and workpiece is three-dimensional and stresses increase very rapidly, due to the speed of interaction. Experimentally, flowing of metals and, subsequently failure, occurs due to a state of stress involving the second and third invariants (Tresca) or only the second one (VonMises). Both criteria disregard the hydrostatic stress and conclude that metals fail due to a state of stress capable of distorting the shape, i.e. predominantly by shear. That mechanism of failure occurs independently of the cutting edge shape.

In micromachining operations, feeds or uncut chip thickness (h) can be typically as low as 0.25 to 1 Pm [3], and can very often become of the same size as the edge radius. Carbide tools with radius around 30-50 Pm are commonly found in the market [4]. In special cases 1.0-2.0 Pm are mentioned in literature [5, 6], which seem to be a lower limit for such radius because of grain size. Although carbide grain size as low as 0.3 Pm [4] can be found, such low radius would increase the difficulties with grain anchorage and alignment. Special edges made with single crystal diamonds can achieve lower values, but they are often applied to even lower feed rate values, changing only the scale of the same problem.

Theoretical models of chip formation involving edge radius have been developed, in general, using slip line theory. Materials are considered perfectly rigid-plastic and elastic contributions are ignored, which become important to micro-machining operations. Normal slip line applications consider 3 deformation zones, but when radius is added that number grows up to 27 zones [7] and material is admitted to flow around the cutting edge radius. Those aspects add significant complexity to the problem. In addition, when feed, or uncut chip thickness, is lower than edge radius, shear-plane angle becomes very low and the chip formation process results quite different. Experimental and theoretical analyses demonstrated the existence of a minimum uncut chip thickness (hmin), below

which it is believed that no chip is formed, since part of the material is subjected to an elastic-plastic deformation (ploughing) without effective material removal [8].

A large range of values for hmincan be found in literature, ranging from 0.05 to 0.43 of the edge radius (re) [3, 9].

Vogler et al. [10] used the Finite Element Method (FEM) developed by Chuzhoy et al. [11] to determine the hminof

ferrite–pearlite steels, finding hminĬ0.14-0.43re. Using an analytical model based on molecular-mechanical theory,

Liu et al. [12] determined that hmin=0.20̢0.35 and 0.35̢0.40re for AISI 1040 steel and Al6082-T6, respectively.

Malekian et al. [13] found hmin=0.23re for Al6061 aluminum by applying an analytical method developed when

using the minimum energy principle and infinite shear strain. FEM simulations performed by Lai et al. [14] in oxygen-free high-conductivity copper yields chips when cutting thickness reaches 0.25re. Experimentally Cuba

Ramos et al. [15] determined that hmin was on average 0.295re using 100 m/min of cutting speed cutting in AISI

1045. Micro-milling tests confirmed the existence of size effect if specific cutting force was lower than 20 GPa for fz> hmin and close to 40GPa if fz< hmin. Kang et al. [16] assert that hmin is 0.30re when micro-milling AISI 1045.

Their finding was based on constant cutting force whenever h < hmin. There is also a variety of criteria to establish

the limit for hmin, and it depends on several parameters, such as, workpiece and tool material, workpiece hardness,

etc. [14]. Only normal machining operations (turning and milling, for example) have been used to predict or detect hmin values. As a consequence, a wide variation on the values has been found. The present work introduces a novel

method intended to experimentally determine the minimum uncut chip thickness (hmin) using orthogonal cutting

operation in a machining center. Nomenclature

a The width of contact (mm) according to [17] D Specimen diameter (mm) = 2r0

f Feed (mm/rev)

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Fc Cutting force (N)

Fn Normal force (N)

h Uncut chip thickness (mm)

hmin Minimum uncut chip thickness (mm)

hmax Maximum uncut chip thickness (mm)

n Rotation speed (RPM – Rotation per minute)

t Time (s)

tIR Time of interaction between specimen and cutting edge (s)

vc Cutting speed (m/min)

vf Feed speed (mm/min)

ro Specimen radius (mm)

w Specimen rotation speed (rot/s) Y Material yielding (MPa) [17]

TT Total interaction angle (°)

2. Experimental Method and Theoretical Development The proposed experimental method is capable of:

- Increasing the uncut chip thickness (h) progressively, in a well know and controlled proportion, - Executing just one cut at a time and with the possibility to replicating it;

- Measuring normal and cutting force at realistic conditions of feed rate (f) and cutting speed (vc);

- Detecting the first and last contact between cutting edge and specimen; - Measuring the actual h values after cutting.

To achieve that in an orthogonal cutting operation a machining center is used holding the specimen in the spindle and rotating it at realistic cutting speed (vc), moving it simultaneously according to a specified feed speed (vf). The

cutting edge is positioned on a dynamometer clamped on the machine table. Figure 1 shows a schematic of the setup, together with a photograph of the real arrangement. The specimen used for the orthogonal cut has a useful part, 2 mm thick, and the clamping part, which is shown in Figure 2.

One additional cutting edge turning is clamped on the table and the experiment starts with a finishing turning and facing operation on the specimen to guarantee its concentricity. Then, it is positioned at least 200 mm from the cutting edge on the Y axis of the machine (Figure 3). At this point the rotation is set to the required vcas well as the

hmaxon the X axis. The specimen feeds towards the prepared edge on the Y direction with the specified vf. During

the interaction the specimen will make the initial touch at the edge with zero thickness and due to the combination of rotation and feed speed h increases to hmax and decreases to zero again at the last touch. Figure 3 shows

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Author name / Procedia Manufacturing 00 (2017) 000 000 5

Fig.2. Specimen used in the experiments.

Fig. 3. Schematic of the experiment to determine the minimum uncut chip thickness (hmin).

During the interaction h increases and decreases according to Eq. (1) as a function of time t (s):

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where, rois the initial specimen radius (mm), w is the specimen rotation speed (rot/s), TT (°) is the interaction

angle left on the specimen after the test and hmax(mm) is the maximum uncut thickness. Equation (1) is valid only if:

1 2

-3 - , being tIRthe interaction time calculated by:

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where is the diameter (mm), vcis the cutting speed (m/min), vf is the feed speed (mm/min) calculated

by:

(3) Figure 4 shows a typical graph obtained during the experiment.

Fig. 4: Typical graph obtained during the experiment to assess hmin.

Together with the cutting and normal force (Fcand Fn) signals there is an electrical contact signal (“Contact” in

Figure 4) used to detect the first and last touch between the specimen and the cutting edge (see Figure 2). In addition, an inductive sensor (Sense model PS1,5-8GI45-E2-V1) was used to check the spindle rotation speed (“Rot ck” in Figure 4) during the interaction. The sensor captures 6 pulses per rotation (each at 60°). A standard square wave 1,2 kHz (“Sq Wave” in Figure 4) was used to check the acquisition frequency. Acquisition was set in LabView routine for 50,000 pts/s with a DaQ 6062E National Instruments board connected with a BNC2110 connector block. Later the calibrated square wave served to confirm the acquisition frequency. Force was measured with a Kystler model 92678A dynamometer using the amplifier model 5233A1. The feed (vf) and rotation (n) speed were measured

using the Siemens internal diagnosis system (CNC Siemens 840D), which measured them in real time. Differences were below 0.03% during all the interactions.

After each experiment the specimen was submitted to a circularity measurement using the Taylor Hobson 131 and Ultra Contour Software. The circularity data were extracted in intervals of 0.1° and processed by a MatLab routine giving typical profiles, as shown in Figure 5.

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(a) Typical circularity profile after the experiment. (b) Typical data treatment after submitted to MatLab routine and linearized.

Fig. 5: Roundness data treatment

The roundness profile and the acquired data were, initially, submitted to a smooth routine using a window of approximately 1°, and then synchronized centring the removed material angle (by the roundness) with the contact angle (by electric contact signal).

3. Experimental Planning

Although several others edges have been used for testing the whole system, only two of them are presented here, with average edge radius, re of 6 and 120 Pm, respectively. Figure 6 shows their profiles obtained by a

confocal Olympus Microscope model OS4100.

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Fig. 6: Profile of the 2 edges used for testing the whole system.

Other tests used intermediate edge radius, but only the most significant are presented here. The specimens were made of AISI 1045, with 25 mm of initial diameter and electrically isolated from the collet system. The whole machining parameters are shown in Table 1.

Table 1:Machining parameters used in the experiments.

Parameter rg P Pm vc m/min n rpm vf mm/min hmax P Pm b mm TTT degree ro mm JJrake) degree Test 1 6 120 1571 14,669 100 2 120 12,155 6 Test 2 120 120 1547 14,556 100 2 120 12,345 6 Test 3 120 120 1571 14,669 200 2 180 12,500 6

4. Results and Discussions

Figure 7 shows the results from Test 1. The data were cut at the exact angle within which there was electrical contact during the interaction.

(a) For the whole interaction (b) Detail at the first contact

Fig. 7: Result from Test 1 (hmax= 100 Pm, vc= 120 m/min, re= 6 Pm).

Since the very first contact at 0º the uncut chip thickness (h) started to change after aprox. 0.5º at a theoretical h = 0.0014 mm indicating initial material removal. Forces were Fn = 0.351 N and Fc = 0.781 N at that point. The

beginning of removal was at very early stage and it was difficult to exactly determine the first change in h. The force values were also within the uncertainty of the dynamometer. After approx. 4.8º h reached the re value and the

removal follows the usual pattern of normal cutting operation since it was higher than re. During that period h did

increase until its maximum value, which was 85 Pm, although the machine was set to 100 Pm. The difference of 15 Pm can be accounted to the system lack of stiffness (spindle, collet, workpiece, dynamometer, tool shank, insert clamping, etc.). At the end of the contact there was still some remaining force at the dynamometer due to the dynamical return of the whole mechanical system. To contrast with those conditions the other edge with 120 Pm radius (blunt) was used with the same cutting conditions. Figure 8 shows the result for such experiment named as Test 2.

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(a) For the whole interaction (b) Detail at the first contact Fig. 8: Graphs obtained from Test 2 (hmax= 100 Pm, vc= 120 m/min, re= 120 Pm).

Using an edge radius larger than hmax, it can be noticed that h started to change after 10.5º at a theoretical h = 0.037

mm. Forces were Fn= 63.978 N and Fc= 28.110 N at that point. The actual hmaxwas around 27 Pm, much lower

than that in Figure 7. Contrasting with Figure 7, the force component Fn was always higher than Fc similar to

operations with very negative rake angle [18]. An additional test was performed this time with hmaxset to 200 Pm,

above the edge radius, whose result is shown in Figure 9 named as Test 3.

(a) For the whole interaction (b) Detail at the first contact

Fig. 9: Graphs obtained from Test 3 (hmax= 200 Pm, vc= 120 m/min, re= 120 Pm).

The value of h started to change after 6.3º at a theoretical h = 0.0285 mm. Forces were Fn= 39.070 N and Fc=

25.522 N at that point. The maximum achieved h value was around 72 Pm. The behaviour of force components

during the interaction starts to be similar to that in Figure 8 and there is a short period in which reminds Figure 7, but it returns to behave like Figure 8 again. Comparing the results of those 3 experiments and using some concepts developed by the Contact Mechanics [17] some of that results can be explained.

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At the first contact, the cutting edge radius touched the specimen establishing a contact line, electrical signal went to zero (short circuit) and all the other variables started at zero values (rotation angle, h, Fn and Fc). As the

interaction continues the rotation angle increases, the whole mechanical system starts to elastically complain, force values begin to grow and the contact changes from a line to a strip. Depending on dynamometer sensitivity no reading can appear during this time. Assuming the cutting edge radius as a cylinder acting upon a flat surface subjected to normal and tangential forces (Fnand Fc) moving with the cutting speed (vc), material flow first occurs

below the surface at depths around 0.7-0.78a and reaching 1.79Y-1.67Y stress, depending on yielding criterion (VonMises or Tresca), according to Johnson [17]. Being a the width of the contact strip and Y the material tension flow stress. If the time period of the interaction bearing such conditions allows, temperature may increase facilitating the process of material flow, plastically deforming and may even failing below the surface. Such condition also depends on how steep, or gentle, h grows during the interaction and material mechanical properties play a decisive role too. If material failure occurs during this stage, there might be removal, but not with chips flowing up through edge radius, but underneath it, after the edge passes. No significant increase in real h values may be noticed because those failures tend to be concentrated and not extensively on the contact length. Material also tends to slightly grows in front and behind the edge radius. If that occurs, contact area slight increases, so does forces.

Such stage was very brief during Test 1, but could be well observed in Test 2 and 3 because of the differences in

reand hmax. Before detecting any change in actual h, it took about 0.5 º for Test 1, reaching theoretical h = 0.0014

mm, i.e. 0.230re. For Test 2 those numbers were 10.5º, 0.0370 mm, i.e. 0.308reand for Test 3, 6.3º, 0.0285 mm, i.e.

0.237re. When the edge radius was moving on the specimen material before reaching those values there was no

detectable increase in h and they can be defined as hmin for the present experimental method. That does not mean

material has not been removed before hmin. Some failure could have occurred below the surface, as explained above

[17].

In Test 1, after hmin there was an extremely short period of rotation, from 0.5 to 2º during which chips were

formed under the edge radius, similarly to machining with highly negative rake angles [18]. Normal force (Fn) higher than cutting force (Fc) should be recorded, but that difference was probably below dynamometer sensitivity.

After reaching actual values of h equal and above rethe process ran just like a conventional chip formation with 6º

rake angle.

The equivalent stage for Test 2 was significantly different, since actual h was always below re. Between hmin

and hmax, between 10º and 61º, the whole experiment ran with a highly negative rake angle and that is evident

looking at the relation between Fc and Fn recorded in Figure 8 [18]. With hmax(26 Pm), chip is being formed at

0.21re, or at an equivalent rake angle of -48º.

When looking at the equivalent point for the Test 3, hmaxwas 72 Pm, 0.60re, with an equivalent rake angle of

-16º. The difference in Test 3 was the steepness of h between hmin and hmax, which was much higher than Test 2.

Actual h was higher than Test 2 and combined with a low negative rake angle may have created conditions for the build-up (BUE) of a stationary point, in front of the edge radius, changing the shear plane angle and affecting the resultant force direction and, consequently, the proportion between Fnand Fc[19, 20, 21]. Figure 10 shows some

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Fig. 10: Some adhered material after Test 3.

The occurrence of such stable built up edge (BUE) makes the real shear plane angle to move towards a neutral or positive value. Such behaviour starts around 0.5re, i.e. at an equivalent rake angle of about -45º [22]. Immediately

after -45º there was some vibration on the forces due to instabilities caused by losing the BUE. Figure 11 shows some chips acquired after the experiments.

(a) Chip from Test 1 (b) Chip from Test 3

Fig. 11: Chips formed during Test 1 and Test 2.

The chip formed with re = 6 Pm is like a spiral and its thickness follows approximately the pattern of the

theoretical uncut thickness. In contrast, when using re = 120 Pm the shape resulted like a ribbon with almost no

significant variation on its thickness. When h rapidly becomes higher than re the chip flows on the rake face and

continues like that for most of the interaction period. If h grows gently and never overcome the radius, such as in Test 2 and 3 the chip is formed under the radius similarly to situations where rake angle is highly negative and tends to result like a ribbon with low variations on its thickness.

Initially, any chip formation process initiates like an extrusion, or a cold drawing process, when material flows under the edge radius with h slightly above zero and rake angle almost -90°. As h increases, material flows under the edge radius still similarly to those forming processes, which have been extensively described and modelled [23]. Until that point no material has been removed as chip flowing towards the rake face. After the edge passing, the result is material permanently deformed with some spring back return. Very small amount of dimensional reduction occurs and residual stresses are left. Depending on re value, the time extension and, consequently the temperature

reached, the state of stress may cause localized failure underneath the surface [17]. If those failure occur and the material properties favour, a micro-crack occurs and reaches the surface, resulting in some removed material, usually in concentrated points along the contact strip length. Normally, at this condition material rises in front and behind the edge radius.

If the actual h continues to increase the higher stress point moves from underneath to the interface workpiece-edge and slightly in front of workpiece-edge radius [17]. When that happens, the magnitude of the actual h, with the additional raised material in front of the edge radius, make the rake angle “less negative” and reaches the conditions for rupture in a shear plane [1, 18]. The shear angle tends to be very low because it has to occur between the rake face and the vc direction. When that situation happens the operation reminds a fault extrusion process failing due to shaving

caused by a very high die angle [23]. Then, material starts to be removed like chips being sheared, and now flowing on the edge radius similarly to a rake face (still very negative). That happens because the actual uncut chip thickness cannot pass under the edge radius. Rupture occurs on a shear plan, material is removed and at that point, the present

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work experimentally establishes the value of hmin. Besides the material strength and re, it was also found that hmin

depends on some other parameters, such as the variation of h and the interaction time.

As the actual h continues to rise its height can reach a point where there may be conditions for a BUE in front of the radius. That will change significantly the shear plane angle and, consequently direction of the resultant force, perceived on the relation between its components Fn and Fc. Because the BUE will eventually break, force

components tend to oscillate and so does the direction of the resultant.

If the actual h value reaches and exceed re, then the process will behave like a normal macro-machining

operation. With the proposed method many other variables will be studied, especially vc, vf, temperature and

material strength.

After these first tests here presented and many others performed, it could be seen two limitations. First, the relation between hmin and forces depend on the resolution of the dynamometer. Early stages could be better

understood using a MiniDyn™, for example. Second, it is difficult to prepare edges with specifically targeted radius. Usually, processes aim at a range and all edges have to be measured before testing. Above all, the machine and acquisition systems must be of good quality because the speeds and synchronization between them are key factors.

Conclusions

From these first experiments using the proposed method to study minimum uncut chip thickness (hmin) it was

possible to conclude that:

x In agreement with several previous works the present one found an uncut chip thickness below which no material was actually removed in an orthogonal cutting operation;

x Comparing a relatively sharp edge with re= 6 Pm with a blunt one with re= 120 Pm, it was found that hmin

can vary from 0.230 to 0.308re, depending on the theoretical value set for hmax into the machine and the

edge sharpness.

x It seems that the steepness by which h increases can influence hmin, besides some other parameters (vc, vf,

material strength, etc.). It was also found possible the existence of a BUE in front of the edge radius. Its appearance may depend on the actual value of h, compared to re, and on the extension time that particular

condition is kept during the interaction. At the present work BUE seemed to have appeared around h = 0.5reand only when the interaction was increased in time and length for about 1.5 times;

x The proposed method demonstrated to be able to study the relationship between hmin and several other

machining parameters in realistic cutting conditions for macro- and micro-machining, which seems to be important to a comprehensive understanding of the phenomena.

x The method is fast executed and allows expressively large variations on the parameters around realistic values, which will create new possibilities of studying and comparing results for further understanding the chip formation when h is below re, especially in micro-machining.

Acknowledgements

The authors would like to thank FAPESP for the financial support for the present work as well as UNICAMP and EESC-USP for the equipment, facilities and personnel.

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