Medical, Pharma, Engineering, Science, Technology and Business

**Kouadri S ^{1*}, Bensari A^{2} and Tirenifi M^{2}**

^{1} Superior School of Material, BP 188 Beau-lieu, Algiers, Algeria

^{2}University of Mascara, BP 29 Route de Mascara , Mascara, Algeria

- *Corresponding Author:
- Kouadri S

Superior School of Material

BP 188 Beaulieu, Algiers, Algeria

**Tel:**+213 (45) 804169

**E-mail:**[email protected]

**Received Date:** April 17, 2017 **Accepted Date:** June 02, 2017 **Published Date:** June 06, 2017

**Citation: **Kouadri S, Bensari A, Tirenifi M (2017) Experimental and Theoretical Analysis of the Chip Flow Direction in Turning using Flatted and Grooved Inserts – Impact of the Tool Rake Face Geometry, the Work Material and Cutting Conditions. J Appl Mech Eng 6: 269. doi: 10.4172/2168-9873.1000269

**Copyright:** © 2017 Kouadri S, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

**Visit for more related articles at** Journal of Applied Mechanical Engineering

This paper deals mainly with an experimental and theoretical analysis of the Chip Flow Direction (CFD) in turning process using flatted and grooved inserts. Turning tests have been performed to determine the CFD from measured cutting force components. Different cutting conditions have been considered by varying the cutting speed, the feed rate and the depth of cut. From a theoretical point of view, two models have been applied. The first one is an analytical model based on the discretization of the undeformed chip area. The second one is a purely geometrical model which assumes the CFD normal to the major axis of the projected cutting area on the rake face. The effect of cutting conditions on the CFD was clearly highlighted experimentally and by adopted models. It has been shown that the CFD depends strongly on the depth of cut in the browsed range of cutting parameters, while cutting speed has a little effect. One of main discussed results concerns the impact of the tool rake face geometry (flatted and grooved) on the CFD. Finally, it has been shown that the CFD is independent on machined materials.

Turning; Chip flow direction; Cutting force; Tool geometry; Grooved insert; Cutting condition

*V _{c}* Cutting speed

*f* Feed rate

*d* Depth of cut

*d´ *Projected depth of cut on the rake face plane

*r* Tool nose radius

*K _{r}* Approach angle

*C _{e}* End cutting edge angle

*C _{s}* Side cutting edge angle

Projected angle of Cs on rake face plane

*i *Inclination angle of tool

α_{n} Normal rake angle

P_{r}, P_{p}, P_{f}, P_{n}, P_{s}, P’_{s} Planes used for the definition of tool angles

*F _{c}, F_{f}, F_{p}* Force components (cutting, feed and depth of cut forces)

F_{0} Friction force at tool-chip interface

*dF _{0}, dF_{0x}, dF_{0y}* Friction force acting on a chip element and its components

*F _{0}, F_{0x}, F_{0y}*

*u *Friction force intensity

A, B, S Area of undeformed chip section

*dA* Area of undeformed section of chip element

*ds* Differential length of cutting edge

*t(s)* Varying undeformed chip thickness

θ Angle made by positive X axis with the undeformed chip element

θ_{0}, θ_{1}, θ_{2}, θ_{3}, Limit angles of integration

Ω_{0} Angle made by elemental undeformed chip or dF_{0} with the positive Y axis

Angle made by the friction force F_{0} with the positive Y axis

*η _{c}* Chip flow angle measured from the normal to the side cutting edge

COF Coefficient of friction

The control of chips formation and chips flow in machining pro cesses are important to facilitate their evacuation and to avoid interaction during cutting between chips and the machined part. In such situation, chips may alter the workpiece surface quality if it is badly directed. Jared and Dow [1] stated that under some cutting conditions, contact between chips and the machined workpiece can result in superficial damage to the finished surface. Therefore, estimating the chip flow direction allows improving the machining operation by choosing adequate cutting conditions as well as geometrical characteristics of cutting tools. It is important to distinguish between the local chip flow direction, at the exit of the cutting zone (immediate vicinity of the active or engaged cutting edge), and the global chip flow direction (far from the cutting zone). The chip flow direction analysed in this work corresponds to the local one, and is frequently characterised by the angle between the normal to the side (main) cutting edge and the direction of chip flow on rake face of the cutting tool.

To estimate the chip flow direction, several models are proposed in literature. The earliest model is attributed to Stabler [2], who was considered that in oblique cutting configuration the chip flow angle is equal to the inclination angle of the insert (i.e. *η _{c} = i*). This rule has been found to be only as a first approximation (Stabler [3]; Armarego and Brown, [4]. In later work, Stabler (1964) proposed another law by introducing a correction factor (

Physical models, which include workmaterial behaviour, were developed for oblique cutting configuration to predict the chip flow angle. For example, Moufki et al. [10] have been proposed a thermomechanical modelling to predict cutting forces, shear angle, cutting temperature as well as the orientation of the chip flow. Their approach was based on the discretization of the cutting edge and assumes a flat cutting face. As input data of the model, they use thermomechanical parameters of the tool and workpiece materials. Strenkowski et al. [11] proposed a combined analytical-numerical model, based on Usui’s energy model (Usui et al., [12]; Usui and Hirota, [13]) for the analytical calculation and Eulerian finite element model for the numerical calculation. Usui’s energy model is based on the minimisation of shear and friction energies to find the chip flow angle. The proposed hybrid model predicts well the CFD and cutting forces. Other models are proposed based on energy minimisation. Seethaler and Yellowley [14] have proposed a so called “Upper-bound model” based on the minimisation of the cutting power (sum of shear and friction energies) to predict chip flow angle. This approach was extended later by Adibi- Sedeh et al. [15] and recently improved by Zou et al. [16]. Fang [17] has developed a similar approach to determine the chip flow angle and also the chip flow speed.

Physical models, which include workmaterial behaviour, were developed for oblique cutting configuration to predict the chip flow angle. For example, Moufki et al. [10] have been proposed a thermomechanical modelling to predict cutting forces, shear angle, cutting temperature as well as the orientation of the chip flow. Their approach was based on the discretization of the cutting edge and assumes a flat cutting face. As input data of the model, they use thermomechanical parameters of the tool and workpiece materials. Strenkowski et al. [11] proposed a combined analytical-numerical model, based on Usui’s energy model (Usui et al., [12]; Usui and Hirota, [13]) for the analytical calculation and Eulerian finite element model for the numerical calculation. Usui’s energy model is based on the minimisation of shear and friction energies to find the chip flow angle. The proposed hybrid model predicts well the CFD and cutting forces. Other models are proposed based on energy minimisation. Seethaler and Yellowley [14] have proposed a so called “Upper-bound model” based on the minimisation of the cutting power (sum of shear and friction energies) to predict chip flow angle. This approach was extended later by Adibi- Sedeh et al. [15] and recently improved by Zou et al. [16]. Fang [17] has developed a similar approach to determine the chip flow angle and also the chip flow speed.

Nowadays, in machining processes the major cutting inserts present a grooved (non-flatted) rake face. Hence to control the chip flow it is interest to know the CFD in such cases with respect to cutting parameters variation. For this purpose, two turning cases have been analysed; one with flatted rake face insert and the other with grooved rake face insert. Experimental tests have been performed with varying the cutting speed, the feed rate and the depth of cut, and the measurement of cutting force components for each cutting condition. For the analysis purpose, two models are considered: the Wang and Mathew analytical model Wang and Mathew [18] based on the discretization of undeformed chip area (considered as flat), and the Colwell model (Colwell, 1954), based on purely geometrical considerations. The predicted chip flow angles with these two models are compared to the experimental ones. The analysis highlights the effect of the rake face geometry and cutting parameters on the CFD, and gives an indication about the validity of assumptions of adopted models.

Two separate turning tests have been performed, one using flatted inserts and the other using grooved inserts, to analyse the CFD. Cutting tests were performed on CNC lathe which allows the variation of cutting conditions in a large range. The machine is instrumented with a dynamometer system for the measurement of cutting force components (*F _{0}, F_{f} and F_{p},*). The machining device is shown in

Uncoated triangular flatted inserts, designated by TCMW16T304 (**Figure 2(a)**), and AISI 1045 (a ferrite-perlite steel) as a workmaterial were chosen for the first turning tests. The selected cutting conditions are reported in **Table 1**. While coated triangular grooved inserts, designated by TCMT16T308 (**Figure 2(b)**), and AISI 304L as a workmaterial (a stainless steel) were chosen for the second turning tests. The selected cutting conditions are reported in **Table 2**. The browsed range of each cutting parameter, for the two cases, has been chosen from recommendations of tools manufacturers for considered tool/work material couples.

f = 0.1 mm/tr, d = 1.1 mm |
|||||||||||||||||||||||||||

50 | 100 | 150 | 180 | 200 | 250 | 300 | 350 | 400 | 450 | 500 | 600 | 700 | |||||||||||||||

Vc = 250 m/min, d = 1.1 mm |
|||||||||||||||||||||||||||

0.10 | 0.125 | 0.15 | 0.175 | 0.20 | 0.225 | 0.275 | 0.30 | ||||||||||||||||||||

Vc = 250 m/min, f = 0.26 mm/tr |
|||||||||||||||||||||||||||

0.70 | 0.80 | 0.90 | 1.00 | 1.10 | 1.20 | 1.30 | 1.40 |

**Table 1:** Cutting conditions used for machining AISI 1045 with flatted insert TCMW16T304.

f = 0.2 mm/tr, d = 1 mm |
||||||||||||||

20 | 50 | 100 | 150 | 200 | 250 | 300 | 400 | 500 | ||||||

Vc = 100 m/min, d = 1 mm |
||||||||||||||

0.05 | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 | 0.35 | ||||||||

Vc = 100 m/min, f = 0.15 mm/tr |
||||||||||||||

0.20 | 0.50 | 1.00 | 1.50 | 2.00 | 2.50 | 3.00 |

**Table 2:** Cutting conditions used for machining AISI 304L with grooved insert TCMT16T308, from Kagnaya.

In order to analyse the CFD in turning with flatted and grooved inserts, two models were selected among those proposed in the literature: Colwell model (Colwell, 1954) and Wang and Mathew model (Wang and Mathew, 1995). Wang (2001) and Kishawya et al. [19] adopted later similar approach as Wang and Mathew. These models were chosen to account for the nose radius effect. Colwell model is purely geometrical while the Wang and Mathew model is developed under the assumption that the tool rake face is flat. This allows showing their ability to predict the CFD when machining with complex tool geometries, and therefore highlighting the effect of rake face geometry on the CFD. **Figure 3** illustrates tool angles, defined on nose radius insert, used in analytical formulations described in following sections **Figure 4**.

To estimate the CFD from experimental data, the assumption that the CFD is collinear with the tangential (frictional) force applied on the rake face is made [20,21]. The same assumption was considered by Moufki et al. (2000) in their thermomechanical model. Although using experimental data, Yegneswaran [22] has shown that the CFD may slightly deviate from the frictional force direction. In considered cutting configuration (α_{n}=i=0), for both cases (machining with flatted and grooved inserts) the CFD corresponds to the direction of the resultant feed force and depth of cut components (i.e. *CFD//F _{fp}*). The obtained CFD is taken as the experimental flow direction, given for α

(1)

Colwell model is purely geometrical, assuming the CFD normal to the major axis of the projected area of cut on the rake face. In case of nose radius inserts, this axis corresponds to the segment joining the extreme points of the engaged cutting edge, as illustrated in **Figure 5**. Four cases can be defined, as reported e.g. by Wang and Mathew (1995). Here only two cases are considered, corresponding to the engagement of the main cutting edge and/or nose radius edge. It includes all undeformed chip areas obtained with cutting conditions of **Table 1** and **Table 2**, used in experiments. The two other cases correspond in addition to the engagement of the end cutting edge.

**Case 1:** engaged side cutting and nose radius edges: and* f ≤ 2r *sinCe

Where *d´* is the projection of depth of cut, *d*, in the rake face, given by

(2)

To derive the chip flow angle, the slope of the segment [P_{1},P_{2}] is to define. First, the coordinates of points P_{1} and P_{2} (see Fig. 5(a)) are given by:

(3)

With α_{1}= cos^{-1} *(f /2r)*.

The slope of the segment [P_{1},P_{2}] can be defined by the angle between the X axis and this segment, given as

(4)

According to Colwell model, the CFD is the normal to this segment.

Thus chip flow angle is obtained by the relation

(5)

**Case 2: **engaged nose radius edge: and *f ≤ 2r* sinCe

For this case, coordinates of points P_{10} and P_{2} in **Figure 5(b)** are

(6)

With

The slope of the segment [P_{1},P_{2}] is

(7)

Chip flow angle is then deduced from relation .

**CFD predicted by the Analytical Wang and Mathew Model**

The model of Wang and Mathew (1995) is based on some assumptions suggested by Young et al. (1987). The main assumption is that only friction force acting at the tool-rake face has an effect on the CFD. In the model, the chip is considered as a series of infinitesimal elements. As shown in **Figure 6**, each element has its thickness and orientation. The friction force was assumed linearly proportional to the undeformed chip thickness and the direction for each element coincided with the local chip velocity. Based on these assumptions, the magnitude of the friction force *dF _{0}*, shown in

( 8)

Where *u* is the friction force intensity, *dA* is the area of the small chip element, ds is the width of the element, and *t(s) *is the varying undeformed chip thickness in the rake face plane. *dF _{0}* can be decomposed on two components in the reference defined in

(9)

Where Ω_{0} is the angle made by *dF _{0}* with the positive Y axis and given by

(10)

where θ is the angle made between the positive X axis and the direction of elementary friction force. Expressing Eq. in an integral form gives

(11)

As the chip velocity is assumed to be coincident with the friction force vector, the angle made by the resultant friction force F_{0} and the positive Y axis can be found from

(12)

Since friction force intensity u is eliminated in the above equation, the evaluation of can be made from the tool and cut geometry only.

The chip flow angle *η _{c}*, which is measured from the normal to the straight major cutting edge of the tool in the rake face plane, is deduced from

(13)

As reported in Wang and Mathew (1995), four configurations can be defined to evaluate the CFD. Two cases are treated in **Figure 7**, which include all undeformed chip areas obtained with cutting conditions of **Table 1** and **Table 2**, used in experiments.

Case 1: engaged side cutting and nose radius edges: in this case *d > k _{s}r* and

(14)

with *k _{s}=cos i* for particular case C

(15)

and is found from equation

(16)

To integrate Eq., undeformed chip area is decomposed into three regions, as shown in **Figure 7**. Regions A and B correspond to the nose radius edge and S to the straight part of the major cutting edge. In regions A and B, the undeformed chip thickness is given by the two following equations, respectively

(17)

where or region A, and for region B.

The limit angles are

Note that θ is measured counter-clockwise form the positive X axis to the elemental chip. S_{0}, in both regions A and B, the angle Ω_{0} in Eq. is given by

Ωo (θ )=θ -π /2 (18)

For region S, the small thickness segments, which have the same orientation with the corresponding friction force components, act in the same direction in their respective region. Thus, the orientation angle Ω_{0s} for region S can be found from

(19)

Factors containing Ω_{0} can be taken out from the integrals when evaluating Eq. for region S. The area of this region can be determined from the associated cut geometry and given by

(20)

where *d´* is the projection of depth of cut, d, in the rake face:

(21)

The integral in Eq. are taken over the entire area of the undeformed chip section. Taking into account the relationship *dA=t(θ) ds ≈ t(θ) rdθ* for regions A and B, Eq. can be expressed as

(22)

**Case 2: **engaged nose radius edge:

In this case is evaluated by only considering regions A and B, thus:

(23)

The evaluation of Eq. or can be performed analytically, as done by Wang and Mathew (1995). In the present study, numerical integration, using adaptive Simpson’s rule, is performed in MATLAB^{®} software. Knowing the CFD in the cutting plane is then deduced from the relationship .

**Analysis of measured cutting force components**

The evolution of measured cutting force components (*F _{c}, F_{f} and F_{p}*) with respect to cutting parameters (

For machining the AISI 1045 steel with flatted uncoated insert, as shown in **Figure 8(a)**, up to about 200 m/min cutting force components increase and beyond decrease. This is due to the increase of the COF at low cutting speed, as shown in **Figure 8(a)**. The COF increases because cutting inserts are uncoated and sliding velocity at the toolchip interface, which is proportional to the cutting speed, is not high enough to promote sliding. As reported in Kagnaya (2009) a builtup -edge effect with adhesion of the workmaterial on the rake face of inserts is observed in this range, sign that sticking by sliding area ratio is higher, while beyond about 200 m/min the sliding is more promoted. In addition, at higher cutting speed the softening effect due to heat generated by plastic deformation in removed layer of the workmaterial, which results in temperature raise in the cutting zone, has an impact on the decease of the flow stress of the workmaterial, and therefore on cutting force components. The increase of the feed rate and depth of cut, as shown in **Figure 8(b) and (c) Figure 8(c)** respectively, results in the increase of all cutting force components . Their evolution is quasi linear. In the same time the COF decreases nonlinearly.

In the other hand, this is not the case when machining the AISI 304L steel with grooved coated inserts, as shown in **Figure 9(a)**, where cutting force components decreases rapidly with the increase of the cutting speed up to 100 m/min, and tends to stagnate beyond.Observations of cutting inserts did not reveal any apparent adhesion of the workmaterial on the rake face of inserts. The COF, as shown in **Figure 9(a)**, follows the same evolution tendency with respect to the cutting speed evolution. The increase of the feed rate and depth of cut, as shown in **Figure 9 (b) and (c) Figure 9 (c)** respectively, results in the increase of all cutting force components . Their evolution is quasi linear. In the same time the COF decreases nonlinearly.

**Analysis of the chip flow direction**

To analyse the CFD in turning with flatted and grooved inserts, measured cutting force components F_{f }and F_{p}, reported in **Figure 8 and Figure 9**, are used to estimate the experimental value of the CFD with Eq. , considered as reference value. The described Colwell and Wang and Mathew models, described in Section 3.2 and Section 3.3 respectively, are then used to predict the CFD. Comparison between predicted and experimental CFD in cases of using flatted and grooved inserts are given in **Figure 10 and Figure 11**, respectively. A global overview of these figures shows that experimental chip flow angles are close to the predicted values with the two models. In all cases, Wang and Mathew model gives lower values of the chip flow angle, while Colwell model gives higher values. The Colwell model and Wang and Mathew model can be considered, respectively, as a lower and upper bounds models.

For turning tests with flatted inserts, the experimental CFD is slightly sensitive to cutting speed (**Figure 10(a)**). The average value of the chip flow angle is about 18°, which is between 13° obtained with the Colwell model and 22° obtained with the Wang and Mathew model. It can be noted that these models are a velocity independent; experimental values of the CFD confirm the model assumptions in case of flatted rake face. At high cutting speed (**Figure 10(a)**), the experimental CFD is close to the Colwell’s CFD. The effect of feed rate in the range of 0.1 to 0.3 mm/tr, for fixed cutting speed (250 m/min) and depth of cut (1.1 mm), is shown in **Figure 10(b)**. Increasing the feed rate increases slightly the chip flow angle in the browsed range. The experimental flow angle tends to that predicted by the Colwell model. The chip flow angle gap in the range 0.1 to 0.3 mm/tr is about 9.7° (experimental), 5.3° (Colwell ) and 4.8 (Wang and Mathew). The effect of depth of cut in the tested range 0.7 to 1.4 mm, for fixed cutting speed (250 m/min) and feed rate (0.26 mm/tr), is shown in **Figure 10(c)**. The chip flow angle decreases when increasing the depth of cut, and experimental chip flow angles are very close to that predicted by the Colwell model over the tested range, especially for high depth of cut values.

For turning tests with grooved inserts, as shown in **Figure 11**, it can be concluded that although the two models ignore the cutting face geometry, however globally same tendencies are observed as for turning tests with flatted inserts. When varying the cutting speed, as shown in **Figure 11(a)**, for fixed feed rate (0.2 tr/m) and depth of cut (1 mm), the experimental CFD evolves as power with saturation law curve, with tendency to stagnate at high cutting speed. The experimental chip flow angle at low cutting speed is close to the one predicted by the Wang and Mathew model, and with increasing cutting speed it tends to the predicted one by the Colwell model. Such evolution tendency was also observed by Zorev (1966), who proposed an empirical power law as function of inclination angle and cutting speed The effect of feed rate on the CFD in the range of 0.05 to 0 .35 mm/tr, for fixed cutting speed (100 m/min) and depth of cut (1 mm), is shown in **Figure 11(b)**. The experimental chip flow angle gap is about 12°. This effect is less pronounced compared to the effect of depth of cut (**Figure 11(c)**), since the feed rate modifies slightly the engaged part of the nose radius edge, and the engaged part of the side cutting edge remains the same when depth of cut is fixed. For low feeds, the experimental chip flow angle is slightly close to the predicted one by the Wang and Mathew model, while for high feeds it tends to the predicted values by the Colwell model. When varying the depth of cut over a large range (0.2 to 3 mm), the CFD strongly varies from 70° to 15°, as shown in **Figure 11(c)**. In the first half range (from 0.2 to 1.5 mm), the chip flow angle decreases drastically from 70° to 23° (gap of 47°), while in the second half range (from 1.5 to 3 mm), the chip flow angle decreases slightly from 23° to 14° (gap of 9°). Indeed, for small depths of cut the effect of nose radius on the CFD is very pronounced, since elemental engaged cutting edges of the nose radius edge act in different directions and this part of the engaged cutting edge is the higher. While for high depths of cut the CFD tends to stagnate, since the effect of engaged side cutting edge tends to predominate, and elemental edges in this part act in the same direction. Experimental chip flow angles are close to that predicted by the Colwell model for the highest values of depth of cut.

Globally, predicted chip flow angles are in the order of the experimental ones. The tool rake face geometry of the grooved insert has a low impact on the CFD under used cutting conditions, since the two adopted models did not take into account the rake face geometry and predicts well the CFD. It is important to note assumption that the experimental CFD corresponds to the direction of the friction force on the rake face is relatively true. As reported by Yegneswaran (2001), using CCD camera for the CFD measurement and dynamometer system for the friction force measurement, these two directions may differ slightly under same cutting conditions. This may also have an impact on the difference between the real CFD and the determined one from measured cutting force components. However, this is coherent with the main assumption of the Wang and Mathew model that assumes the CFD collinear with the resultant of elemental frictional forces. Finally it can be noted that the workmaterial has no effect on the CFD, since although different materials are machined, the two models, which are workmaterial independent, predict well the CFD with upper and lower bounds.

Experimental and theoretical analysis of the chip flow direction in turning process using flatted and grooved inserts has been performed in this study. From the experimental CFD, assessed with measured cutting force components, based on assumption that CFD is collinear with the frictional force on the rake face, it has been shown that the CFD is little sensitive to the cutting speed in the two cases. However, for turning tests with grooved insert tendency to stabilisation of CFD is observed at high cutting speed. It has been shown that the CFD is highly sensitive to the depth of cut, followed, by the feed rate and then much lower by the cutting speed. The strong effect of the depth of cut on the CFD is due to the fact that the effect of the nose radius on CFD is predominant for small depths of cut, since elemental engaged cutting edges of the nose radius edge act in different directions. While for high depths of cut the CFD tends to stagnate, since the effect of the engaged side cutting edge tends to predominate and elemental edges in this part act in the same direction.

It can be concluded that the tool rake face geometry, under used cutting conditions, has a little impact on the CFD, since the two adopted models did not take into account the rake face geometry and predict well the CFD. Using the assumption of flat tool rake face may be sufficient to determine the CFD with acceptable accuracy when machining metallic materials. In this study two different steel materials have been machined (AISI 1045 with flatted inserts and AISI 304L with grooved inserts), since the models are material independent and predict well the CFD, it can be concluded that metallic materials has a little effect on the CFD. Finally, inclination and normal rake angles are considered equal to zero in this study, so as a future work the effect of these angles on the CFD will be investigated when machining with other grooved inserts.

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- Simulation
- Social Robots
- Soil Physics
- Solid State Plasmas
- Space
- Space Plasmas
- Spark Ignition
- Splitting Method
- Stellar Spectroscopy
- Stochastic control
- Supply Chain Management
- Suprnova Remnants
- Surface Physics
- Technologies Management
- Telerobotics
- Thermodynamics Methods
- Unmanned-Vehicles
- swarm intelligence and robotics

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Peer Reviewed Journals

International Conferences 2017-18