Davim J. Paulo (editor). Machining. Fundamentals and Recent Advances

Подождите немного. Документ загружается.

150 A. Pramanik et al.

While the tool moves in the direction of cutting, the hard particles in the

ploughing zone are fractured or displaced. Thus the cutting edge of the tool can be

considered to be responsible for particle fracture/displacement which, therefore,

occurs along the cutting edge of the tool. Pramanik et al. [29] calculated the total

energy for particle fracture during orthogonal cutting of MMC as

El (5.11)

where μ

is the average fracture energy per unit cutting edge length in orthogonal

cutting. If the force in the cutting direction due to particle fracture and displace-

ment is F

, then

cf ft g

LE l, where L is the cutting distance. F

is then

determined by

(5.12)

In order to determine the force due to particle fracture/displacement in the

thrust direction, the direction of the resultant force must be determined. It was

assumed that the reinforcement particles are uniformly distributed and spherical

with uniform average diameter, and that the interaction of particles with the

cutting edge could be represented by a particle placed at the middle of the

ploughing zone, as shown in Figure 5.20. Neglecting the frictional effects during

the interaction, the direction of the resultant force was determined from the

relation

sin

(5.13)

where δ is the angle of resultant force measured from the cutting direction, d

the average diameter of particles and H is the width of the ploughing zone, which

is given by

r( sin ) (5.14)

Then the component of the force due to particle fracture and displacement act-

ing in the thrust direction is

tf cf

Ftan (5.15)

The forces F

and F

can be determined from the above equations when μ

known. The total forces acting on the tool in the cutting and thrust directions F

and F

are therefore given by

ccccpcf

ttctptf

FF F F

=++

⎫

⎬

=++

⎭

(5.16)

Machining of Particulate-Reinforced Metal Matrix Composites 151

Figure 5.20. Interaction of a particle with cutting edge (from Pramanik et al. [29])

In order to determine the forces due to particle fracture and displacement using

Equations (5.11)–(5.15), the value of μ

is required. In order to determine μ

, the

following approach was adopted.

It was noted that Yan and Zhang [65] calculated the specific energy for particle

fracture during scratching of aluminium-alloy-based MMCs. In [66] Griffith’s

theory

was applied to estimate the energy for particle fracture under a pyramid

indenter. The specific energy for particle fracture was determined by subtracting

the scratching energy of the corresponding aluminium matrix material from the

total specific energy of the composites reinforced with SiC (10 and 20 wt%) and

(10 and 20 wt%) particles. Pramanik et al. [29] used the results in [65] to

determine μ

because in deriving Equation (5.11), the tool edge was considered

responsible for particle fracture.

For a given groove depth h, the specific particle fracture energy µ

can be ob-

tained from the results given in [65]. The total energy of particle fracture E

for

scratching is

μθ

ff f

EALhtan L (5.17)

where A is the cross-sectional area of groove,

is the indenter apex angle be-

tween opposite faces and L is the length of scratch. Note that the volume of mate-

rial removed is

Lhtan L. The effective indenter edge length L

causing

particle fracture is given by

cos

(5.18)

Hence, the energy of particle fracture per unit cutting edge length L

()

μθ

h sin L

(5.19)

According to this theory, the energy required to propagate a crack is equal to the surface

energy of the crack surface created.

152 A. Pramanik et al.

The value of

was interpolated from a range of data available in [65], the ob-

tained value of

was 0.01 J/mm for SiC (20 vol%). Using the given data and

Equations (5.11)–(5.15), the cutting and thrust force components due to particle

fracture and displacement can be determined for different cutting conditions.

The predicted forces for chip formation, ploughing and particle fracture and

displacement were first determined. These forces were then summed to determine

the total forces in the cutting and thrust directions (Equation (5.16)), which were

then compared with experimental forces

obtained under identical conditions.

Additionally, for the same conditions, cutting forces

were calculated using the

model described by Kishawy et al. [45]. Predictions made from this model to-

gether with those from the model in Pramanik et al. [29] and experimental results

are given in Figures 5.21–5.23. Based on the information in [66], the maximum

tensile stress of SiC was taken to be 245 MPa.

Figure 5.21 compares the predicted and experimental forces with varying feed.

In this figure, the experimental force results are represented by symbols and the

predicted results by lines. The solid lines represent predictions made using the

model in [29] while the dashed line represents those obtain using the energy based

model in [45]. As expected, the experimental cutting and thrust forces can be seen

In line with the equivalent cutting edge concept used in predicting the forces, the experi-

mental thrust force was taken as the resultant force of experimental feed and radial forces.

Note that the model in [45] allows the determination of the cutting force only.

Predicted lines for model

Experimen-

tal symbol

Ref. [29] Ref. [45]

Cutting force □ 1 3

Thrust force × 2 Unable to predict

Figure 5.21. Comparison of predicted and experimental forces with varying feed (from

Pramanik et al. [29])

100

150

200

250

0 0.05 0.1 0.15 0.2 0.25 0.3

Feed (mm/rev)

Forces (N)

Machining of Particulate-Reinforced Metal Matrix Composites 153

to increase approximately linearly with the increase in feed. The rate of increase in

cutting force is higher than that of the thrust force. The predicted results from the

model in [29] show the same trends as the experimental ones with excellent quan-

titative agreement. On the other hand, the model in [45] can be seen to underesti-

mate the cutting force considerably.

The comparison between the predicted and experimental force results with

varying depths of cut is presented in Figure 5.22. Similar to the force variations

seen in Figure 5.21, the experimental and predicted force results increase ap-

proximately linearly with depth of cut. Once again, a greater rate of increase in

cutting force than thrust force as well as excellent qualitative and quantitative

agreement between predicted (from the model in Pramanik et al. [29]) and ex-

perimental results has been obtained. However, the model in [45] underestimates

the cutting force within the tested range of depths.

The comparison between the predicted and experimental force results for

varying cutting speed is presented in Figure 5.23. Unlike the variations of forces

with feed and depth discussed above, in this case cutting and thrust forces can be

seen to decrease approximately linearly with increasing speed with somewhat

similar rates of decrease. Once again, excellent qualitative and quantitative

agreement between predicted (from the model in Pramanik et al. [29]) and ex-

perimental results seems to exist. On the other hand, the predictions from the

energy-based model [45] are not influenced by the cutting speed (hence the hori-

zontal line) and the measured cutting forces are higher than the predictions for

all speeds.

100

150

200

250

300

00.511.5

Depth of cut (mm)

Force (N)

Predicted lines for model

Experimen-

tal symbol

Ref. [29] Ref. [45]

Cutting force □ 1 3

Thrust force × 2 Unable to predict

Figure 5.22. Comparison of predicted and experimental forces with varying depth of cut

(from Pramanik et al. [29])

154 A. Pramanik et al.

100

150

200

250

300

0 200 400 600 800

Speed (m/min)

Force (N)

Predicted lines for model

Experimen-

tal symbol

Ref. [29] Ref. [45]

Cutting force □ 1 3

Thrust force × 2 Unable to predict

Figure 5.23. Comparison of predicted and experimental forces with varying cutting speed

(from Pramanik et al. [29])

From the above comparisons between predictions (from the model in [29]

and that in [45]) and experimental results, it is clear that the predictions made

from the model in [29] show excellent quantitative/qualitative agreement with

experimental results. However, the model in [45] can be seen to underestimate

the predicted cutting force considerably. This underestimation is possibly due to

the consideration of only the matrix alloy when estimating the specific energies

due to plastic deformation in the primary and secondary shear zones. The influ-

ence of reinforcement particles was accounted for by considering the specific

energy due to particle debonding. For more accurate predictions from this

model, it may be necessary to consider the MMC (instead of the matrix alloy)

when estimating the specific energies due to plastic deformation in the pri-

mary/secondary shear zones.

In an attempt to further verify their predictive method, Pramanik et al. [29]

compared their predictions with the experimental results published in the litera-

ture. It was found that few experimental force results were available. Notably,

Davim et al. [7], Chambers [6] and El-Gallab et al. [46] measured the forces when

machining MMCs with PCD tools for a range of cutting speeds. However, none of

these papers gave data in sufficient detail for comparison. The parameters used or

applicable for the studies in [7,

46] that were used for further verifying the

model are listed in Table 5.1. Note that some of the parameters, which were not

given in the above papers, have been assumed in accordance with general machin-

ing practice or taken from [29].

For the experimental conditions of Davim et al., Chambers and El-Gallab et al.,

all the components of cutting and thrust forces for different mechanisms were cal-

culated and added according to the procedure described in the forgoing sections.

Machining of Particulate-Reinforced Metal Matrix Composites 155

Figure 5.24 compares the predicted cutting and thrust force results with ex-

perimental results obtained from [7,

46]. The number on the abscissa shows the

force component and reference from which the experimental forces were obtained.

The model predictions are shown by bars while the experimental measurements

are denoted by circles with variation ranges.

It can be seen that the agreement between the predicted and experimental cut-

ting/thrust forces is very good for the conditions used by Davim et al. [7] and

Chambers [6]. However, the model seems to have largely overestimated the cut-

ting force for the conditions used by El-Gallab et al. [46]. This is most surprising

when one considers the excellent agreement seen between the experimental and

predicted results for the experimental conditions in [29] and those in [7,

6]. It is

likely that there is an error either in the equipment used by El-Gallab et al. or in

the experimental conditions or force results given in [46]. Attempts made to con-

firm this with the authors of [46] were not successful.

In spite of the simplifications made in developing the model in [29], the good

agreement seen between the predictions and experimental results indicates that

chip formation, ploughing and particle fracture and displacement are indeed the

main factors that contribute to the cutting force generation. To investigate the

variations of the force components (due to these factors) with feed and speed,

cutting/thrust forces due to chip formation, particle fracture/debonding and

ploughing were calculated for the MMC using the force data in Figure 5.16. The

percentages of these forces in the cutting and thrust directions are presented

against the feed and speed in Figures 5.25 and 5.26, respectively. It is found that

the percentage of chip formation force is much higher (80–97%) compared to

particle fracture/debonding (1.5–20%) and ploughing (0.25–2%) forces. The per-

Table 5.1. Machining parameters used in the investigations in [7, 6, 46] (from Pramanik

et al. [29])

Parameters Davim et al. [7] Chambers [6] El-Gallab et al. [46]

Tool material

PCD PCD PCD

Nose radius, r

(mm)

0.8 1.6 (assumed) 1.6

Rake angle, γ (degrees)

0 0 0

Approach angle (degrees)

85 (assumed) 85 (assumed) 85

Cutting speeds (m/min)

250–700 50–300 670, 894

Feed, f (mm/rev)

0.1 0.2 0.25

Depth of cut, a (mm)

1 1 1.5

Workpiece material

A356-20%SiC-T6 A356-15%SiC A356-20%SiC- T71

Yield strength

of matrix (MPa)

138 138 124

Average particle

diameter,d

(μm)

20 22.5 12

156 A. Pramanik et al.

180

270

360

450

1234

Cutting/thrust force (N)

Number on Force Reference

abscissa

[Davim et al., ]

[Chambers]

[El-Gallab et al.,]

[Davim et al.,]

Figure 5.24. Comparison between predicted and experimentally measured forces from

literature (from Pramanik et al. [29])

centages of the particle fracture/debonding and ploughing forces in the cutting

direction decrease and the chip formation force increases with increasing feed

(Figure 5.25(a)). The percentages of the particle fracture/debonding and ploughing

forces are lower and higher, respectively, in the thrust direction compared to those

in the cutting direction (Figure 5.25(b)). No significant change of the percentages

of forces is noted with variations of the feed in the thrust direction. With variation

of the speed, the percentages of the different forces in the cutting and thrust direc-

tions do not appear to vary (Figures 5.26(a and b)). The percentages of the particle

fracture/debonding forces in the thrust direction are low compared to those in the

cutting direction.

Figure 5.25. Effect of feed on the percentages of different force components in (a) the

cutting and (b) the thrust directions (at a speed of 400 m/min and a depth of cut of 1 mm)

Machining of Particulate-Reinforced Metal Matrix Composites 157

0 200 400 600 800

Speed (m/min)

Percentages of cutting force

Chip formation

Particle fracture

Ploughing

(a)

0 200 400 600 800

Speed (m/min)

Percentages of thrust force

Chip formation

Particle fracture

Ploughing

(b)

Figure 5.26. Effect of speed on the percentages of different force components in (a) the

cutting and (b) the thrust directions (at a feed of 0.1 mm/rev and a depth of cut of 1 mm)

5.3.2 Tool–Particle Interaction

A detailed investigation of tool–particle interactions and their consequences are very

important for a deeper understanding of process outcomes such as tool wear, surface

finish, residual stresses, cutting forces, etc. Since analytical and/or experimental

methods cannot be used for this type of investigation, Pramanik et al. [16] used the

finite element method to simulate machining of an MMC. In this work, the develop-

ment of stress/strain fields was explored for various tool–particle orientations and

analysed for possible particle fracture, debonding, etc., to provide an insight into the

mechanism of MMC machining. Their finite element model is given in Figure 5.27.

Figure 5.27. Workpiece and tool for MMC machining simulation (from Pramanik et al. [16])

158 A. Pramanik et al.

This investigation revealed that the magnitude and distribution of stres-

ses/strains in the MMC material and the interaction of particles with the cutting

tool are the main reasons for particle fracture and debonding during machining of

MMC (Figure 5.28). Additionally, the newly generated surfaces were found to be

under compressive residual stress. These surfaces were damaged due to cavities

left by the pull-out of particles. These cavities were formed when particles located

at the lower part of the cutting edge interacted with the cutting tool. The indenta-

tion of particles (located immediately below the cutting edge) due to their interac-

tion with the tool caused localized hardening of machined MMC surface. In these

regions, the matrix was seen to deform plastically to a greater depth. High tool

wear during machining of MMCs was considered to be due to the sliding of

debonded particles over the cutting edge and tool faces that will scratch these

contact surfaces (Figure 5.29).

As discussed in this section, during machining of MMCs, the resultant cutting

force can be considered to consist of components due to chip formation, ploughing

and particle fracture, and displacement. The calculation of these force components

based on Merchant’s shear plane analysis, slip-line field theory and Griffith the-

ory, respectively, gave excellent predictions. They revealed that, the force due to

chip formation is much higher than those due to ploughing and particle fracture.

For both the MMC and the aluminium alloy matrix material, forces in turning

increased with increasing feed. However, the speed did not affect the forces sig-

nificantly for the MMC. On the other hand, forces for the matrix material initially

Figure 5.28. Evolution of stress fields for particles along the cutting path during machining

of MMC. Compressive and tensile stresses are represented by >−< and <−−> symbols,

respectively. Their lengths represent comparative magnitudes (from Pramanik et al. [16])

Machining of Particulate-Reinforced Metal Matrix Composites 159

increased with speed but after a certain speed started to decrease. An FEM inves-

tigation revealed that the magnitude and distribution of stresses/strains in the

MMC material and interaction of particles with the cutting tool are the main rea-

sons for particle fracture and debonding during machining. The indentation of

particles (located immediately below the cutting edge) due to their interaction with

the tool causes localized hardening of the machined MMC surface. In these re-

gions, the matrix can be seen to deform plastically to a greater depth.

5.4 Tool Wear

Comparatively high tool wear is one of the major concerns during processing of

MMCs. Interaction of MMCs’ very hard ceramic reinforcement particles with tool

appears to be the major contributor to tool wear. High tool wear makes MMC

processing very expensive and less efficient.

5.4.1 Performance of Cutting Tools

Performance of cutting tools depends on a number of factors such as tool material,

tool geometry, machining conditions and workpiece material. Hence, choosing the

Figure 5.29. Distribution of von Mises strain during machining of MMC (from Pramanik

et al. [16])