In this article we will discuss about the mechanics of machining operation. And also learn about:- 1. Mechanism of Chip Formation 2. Mechanics of Chip Formation 3. Heat Generation and Cutting Tool Temperature 4. Failure of Cutting Tool and Tool Wear 5. Cutting Tool Materials 6. Tool Life and Machinability and 7. Cutting Fluids.

Before we start our discussion on the mechanics of the machining operation, it is advisable that we study the basic similarity in the nature of material removal during the different types of machining operations (Fig. 4.7). The sectional view XX of the actual cutting zone in Figs. 4.7a, 4.7b, and 4.7c and an enlarged view of the cutting zone in Fig. 4.7d show that the basic nature of material removal in each of these operations is similar and can be represented as in Fig. 4.8.

The important parameters involved are – (i) the thickness of the uncut layer (t1), (ii) the thickness of the chips produced (t2), (iii) the inclination of the chip-tool interface with respect to the cutting velocity (the face of the tool in contact with the chip is commonly known as the rake face), i.e., the rake angle (α), and (iv) the relative velocity of the work piece and the tool (v). To make cutting possible, a clearance angle between the job and the flank surfaces is also provided.


It should be noted that the machining operation can be represented by a two-dimensional figure (see Fig. 4.8) only when all the work and chip material particles move in the planes parallel to the plane of the paper. There is no component of velocity or motion in the direction perpendicular to the plane of the paper. Such a situation is realized when the cutting edge is straight and the relative velocity of the work and the tool is perpendicular to the cutting edge. Figure 4.9a shows such an idealized case. This type of machining is known as orthogonal machining.

On the other hand, when the relative velocity of the work and the tool is not perpendicular to the cutting edge (Fig. 4.9b), all the work and chip material particles do not move in parallel planes, and thus a two dimensional representation of the operation is not possible. Such a machining is termed as an oblique machining. It is obvious that the study and analysis of the orthogonal machining operation is much simpler.


We shall therefore discuss examples from this category when dealing with the basic mechanics of the machining operation. However, in a large number of situations, the conditions for orthogonal machining are not satisfied, but to get an approximate result, the orthogonal analysis may be sufficient. For an analysis of the oblique machining, the interested reader may consult any standard book on metal cutting.

Mechanism of Chip Formation:

When the zone under the cutting action is carefully examined, the following observations can be made. The uncut layer deforms into a chip after it goes through a severe plastic deformation in the primary shear zone (Fig. 4.10a). Just after its formation, the chip flows over the rake surface of the tool and the strong adhesion between the tool and the newly formed chip surface results in some sticking.

Thus, the chip material at this surface (and the adjacent layers) undergoes a further plastic deformation since, despite the sticking, it flows. This zone is referred to as the secondary shear zone. Under suitable conditions, the machining operation is smooth and stable and produces continuous ribbon-like chips. As a result, the surface produced is smooth and the power consumption is not unnecessarily high.

At a somewhat high speed, the temperature increases and the tendency of the plastically deformed material to adhere to the rake face increases and a lump is formed at the cutting edge (Fig. 4.10b). This is called a Built-Up Edge (BUE); it grows up to a certain size but ultimately breaks due to the increased force exerted on it by the adjacent flowing material.


After it breaks, the broken fragments adhere to the finished surface and the chip surface results in a rough finish. With a further increase in the cutting speed or when a cutting fluid is used, the built-up edge disappears.

When the machining is performed at a very low speed or the work material is brittle, the shearing operation on the work material does not continue without causing a fracture. The ruptures occur intermittently, producing discontinuous chips. Figure 4.11 shows the progress of the formation of discontinuous chips. The resulting surface is rough.

We shall now summarize the conditions for the various types of chips:


(i) Continuous Chips without BUE:

(a) Ductile material

(b) Small uncut thickness


(c) High cutting speed

(d) Large rake angle

(e) Suitable cutting fluid

(ii) Continuous Chips with BUE:

(a) Stronger adhesion between chips and tool face

(b) Low rake angle

(c) Large uncut thickness

(iii) Discontinuous Chips:

(a) Low cutting speed

(b) Brittle work material

(c) Small rake angle

(d) Large uncut thickness

It is obvious that continuous chips without BUE are most desirable, and the machining is steady.

An analysis of the actual machining operation, schematically shown in Fig. 4.10a, is very difficult. But it is observed that under normal machining conditions at moderate and high speeds the thickness of the shear zone is very small and it can be idealized as a plane (Fig. 4.12a). The plane OS where the shear occurs is known as the shear plane and its inclination with the machined surface (ɸ) is called the shear angle.

A direct determination of the shear angle ɸ is quite difficult but t1 and t2 can be easily measured. To establish a relation among t1, t2, α, and ɸ, let us drop two perpendiculars SM and SN from S on the extension of the machined surface and the rake face of the tool. Further, SP is drawn parallel to OM and Q is the intersection of SP with the normal drawn at O to OM.

Considering the two right-angled triangles Δ SNO and Δ QPO, we get –

Mechanics of Chip Formation:

The first scientific treatment of the problem was proposed by Ernst and Merchant. They considered the idealized case of a single shear plane. Later, more accurate and exhaustive analyses were carried out by various researchers. However, the simple theory, based on the idealized single shear plane model, is good enough to predict the approximate values of power consumption, and this will be enough for our purposes.

If the chip above the shear plane is considered as a rigid body moving with a constant velocity, the resultant of the forces acting on it from the rake surface of the tool R and the work surface along the shear plane (R’) must be zero (Fig. 4.13a). The total force R can be resolved into two components N and F normal to and along the rake surface, respectively.

Since F must be the friction force due to the existence of the normal load N, we have, according to the usual convention,

Where μ is the average coefficient of friction between the chip and the tool, The coefficient of friction can be expressed also as-

Where λ is the friction angle (Fig. 4.13a). Similarly, R’ can also be resolved into the components along the directions normal and parallel to the shear plane, and let these components be FN and Fs (Fig. 4.13a).

Now, since the inclinations of the shear plane and the rake surface vary, they do not suffice to provide some standard invariant directions. For this purpose, the directions along and perpendicular to the cutting motion are quite suitable. So, the force acting on the tool (which is equal to R in magnitude and opposite to the direction of R) can be resolved into two components FC and FT along and normal to the direction of the cutting velocity v.

FC and FT are normally called the cutting and thrust components, respectively. Obviously, FC is the component responsible for the energy consumption since it is along the direction of motion.

The relationship among the different components and the resultant cutting force can be best understood with the help of a diagram, first proposed by Merchant and commonly known as Merchant’s circle diagram (Fig. 4.13b). Since the resultants of FC, FT and FN, Fs are the same and those of F and N are the same in magnitude, the tips of all these force vectors must lie on an imaginary circle of diameter R, as shown in Fig. 4.13b.

Using Fig. 4.13b, the relations that we can write are –

However, we should try to find out a method for determining the components FC and FT theoretically when the material properties and the other necessary data are given.

Merchant attempted to do this in the following way:

If τs is the ultimate shear stress of the work material, then the shear force FS along the shear plane can be written as –

Merchant found that this theory yields quite agreeable results when cutting synthetic plastics but agrees poorly with the results of machining metals. It was realized that τs is not completely independent of the normal stress.

P. W. Bridgman showed that τs can be expressed as –

Where Cm = cot-1 k1 and is a constant for the work material. Cm is sometimes also called the machining constant.

This modified theory of Merchant agrees better with the experiments. It is seen (Fig. 4.14) that the plots of ɸ versus (λ – α) yield different straight lines of the same slope (obtained theoretically from Merchant’s original theory) and can match the experimental results in the case of mild steel, copper, and lead.

From equation (4.19), it is clear that when α increases, ɸ also increases, and when μ (and so λ) increases, ɸ decreases. Further, when the machining speed increases, the coefficient of friction μ decreases.

Figure 4.15 shows the variations of FC, r with v, α. It has been experimentally observed that the nature of variation of FC with the cutting speed v and the rake angle α tallies with that indicated in Fig. 4.15.

Heat Generation and Cutting Tool Temperature:

When a material is deformed elastically, some energy is spent to increase its strain energy which is returned during unloading. But in plastic deformation, most of the energy thus spent is converted into heat. During machining, the plastic deformation is large and takes place at a very high rate, and under such conditions, almost 99% of the energy is converted into heat. For cutting a low strength material, heat generation and the consequent increase in temperature of the tool at the cutting zone is not a big problem.

However, when ferrous and other high strength materials are machined, the temperature rises with the speed and the tool strength decreases, leading to a faster wear and failure. So, though machining at a high speed is desirable, for higher productivity, the faster tool wear due to the high temperature puts a limit to the cutting speed. Thus, an understanding of the phenomena of heat generation and temperature rise during machining is very important.

The sources of heat generation during machining are as shown in Fig. 4.16.

The major plastic deformation takes place in the shear zone and this heat source is the primary heat source. A large fraction of this heat goes to the chip. The sliding motion of the chip on the rake surface of the tool also generates heat, and this is the secondary heat source. From this source also, the chip takes away the major portion of the heat. There is another source of heat where the job rubs against the flank surface of the tool. But with sharp tools, the contribution of this source to the heating phenomenon is insignificant.

Now, the total power consumption (= total rate of heat generation) during machining is W = Fcv. If the rates of heat generation in the primary and the secondary deformation zones are Wp and Ws, respectively, then –

Hence, if ɸ is known or determined, A can be calculated using equation (4.29), and so θP can be estimated with the help of equation (4.27).

The maximum temperature rise θS when the material particle passes through the secondary deformation zone along the rake face of the tool can be approximately expressed as –

Failure of Cutting Tool and Tool Wear:

It is not very difficult to realize that the success of a machining process depends on the sharpness of the tool. Even common sense tells us that the use of a blunt tool results in a large power consumption and deteriorated surface finish. When a cutting tool is unable to cut, consuming reasonable energy, and cannot produce an acceptable finish, it is considered to have failed.

The failure of a cutting tool may be due to one or a combination of the following modes:

(i) Plastic deformation of the tool due to high temperature and large stress (Fig. 4.18a).

(ii) Mechanical breakage of the tool due to large force and insufficient strength and toughness (Fig. 4.18b).

(iii) Blunting of the cutting edge of the tool through a process of gradual wear (Fig. 4.18c).

By a proper selection of the cutting tool material, tool geometry, and cutting conditions, plastic deformation and mechanical failure can be prevented. However, the gradual wearing process cannot be totally stopped and ultimately the tool failure through wearing cannot be avoided. This makes the study of wear so very important.

It is clear that the wearing action takes place on those surfaces along which there is a relative sliding with other surfaces. Thus, the wear takes place on the rake surface where the chip flows over the tool, and on the flank surface where rubbing between the work and the tool occurs (Fig. 4.19a). These wears are called the crater and the flank wears, respectively.

In Fig. 4.19b, we see that the width hf can be taken as the measure of the flank wear. But the measure of a crater wear is not so simple. Quite often a non-dimensional quantity hk given by –

is taken as a measure of the crater wear.

There are various mechanisms of wear, e.g., abrasion wear, adhesion wear, and diffusion wear. Though all these mechanisms are normally active during a wear process, one or more mechanisms may play a predominant role depending on the various conditions. Thus, abrasion and adhesion are primarily responsible for the flank wear, whereas diffusion may play an important role in the development of crater wear at a high speed since then the temperature in the rake face is much higher than that in the flank surface.

The typical nature of growth of flank wear is shown in Fig. 4.20a for various cutting speeds. Here, we see that, initially, there is a break in the wear region where the wear grows quickly. Then, the wear rate stabilizes and remains constant for a considerable period; this region is again followed by a rapid growth of wear. The uniform wear zone constitutes the major portion of the period of usability of a cutting tool.

The growth of a crater wear is a more complex phenomenon. The typical nature of variation of l, ƒ, and e is shown in Fig. 4.20b.

Cutting Tool Materials:

Since the machining operation is basically a deformation process of the work material through the application of a force by the cutting tool, the stability of the geometric form (or form stability) of the tool is a key factor. Obviously, the cutting tool must provide the maximum resistance to any tendency of alteration of its geometric shape. To achieve this, the cutting tool material must be properly selected.

One basic point is that the tool must be harder than the work material. But it has been shown that the tool material must be at least 35% to 50% harder than the work material. The high strain rate of deformation and elevated temperature of the work material further complicate the situation. The apparent strength (or resistance to plastic deformation) increases as the rate of deformation increases, whereas it becomes easier to deform a material at a high temperature.

Thus, when the speed of machining increases, the temperature of both the tool and the work material increases, resulting in a lowered effective hardness of the tool. Unfortunately, the expected fall in the hardness of the work material is neutralized by the higher rate of deformation. Moreover, the rate of deformation during a hardness test is orders of magnitude lower than that during machining.

So, the condition of hardness ratio, proposed by T.N. Loladze, has to be applied after finding out the modified hardness value, taking care of the elevated temperature and high strain rate of the work material. This condition can be stated as –

Table 4.5 lists a number of cutting operations for various combinations of tool and work material with a cutting speed of 0.5 m/min, an uncut thickness of 0.2 mm, and an average depth of cut of 6 mm (the rake angle of each of the tools is 10°). It is clear from this table that, though the apparent hardness ratio indicates the possibility of successful machining, in all the cases the modified hardness ratio reveals the correct situation.

The properties of an ideal tool material can be summarized as follows:

(i) As far as possible, it should maintain its hardness which is appreciably higher than that of the work at the elevated temperature.

(ii) It should be tough enough to withstand shocks.

(iii) It should provide a large resistance to the wearing action so that excessive wear does not occur.

(iv) The coefficient of friction between the work and the tool should be low.

(v) Its thermal conductivity and specific heat should be high.

The materials commonly used for making the cutting tools are – (i) high carbon steel, (ii) High Speed Steel (HSS), (iii) cemented carbide, and (iv) ceramic. Of course, for grinding and other machining processes, abrasive minerals, e.g., silicon carbide, aluminium oxide, and diamond, are used. Figure 4.21 shows the variation of hardness with temperature for various tool materials.

Cemented carbide is produced by the powder metallurgy technique. For this, powders of several carbide compounds are pressed and bonded together in a matrix to form the cemented material. The matrix is always Co. When machining a steel, TaC and TiC are added to avoid large scale diffusion. Table 4.7 shows some typical carbide compositions.

Also, coated carbides have been developed where the cemented carbide is coated with a thin (≈5 μm) layer of a ceramic, e.g., TiC, TiN, Al2O3, and carbon boron nitride. The coated carbides are used for machining super alloys.

Ceramics, For example- AI2O3, may be directly used as cutting tools. Though they are highly temperature and wear-resistant, a fracture may be caused by shock. Therefore, such tools are used for very high speeds but only for light and smooth, continuous cuts.

The maximum possible speed at which mild steel can be cut with various tool materials is indicated in Table 4.8.

Tool Life and Machinability:

A comparative evaluation of the machining operations has always remained an interesting but a difficult problem. The term “machinability”, which loosely means the ease of machining, is used quite commonly. However, the criteria for judging this ease may be different, depending on the point of view or the objective.

For example- machining a lead piece with an HSS tool may be quite easy so far as the force requirement is concerned, but a good surface is extremely difficult to achieve. Thus, for a given operation, the machinability may be considered to be good or bad depending on the criterion.

To tackle the problem in a more meaningful manner, we shall first identify the major criteria for judging machinability:

(i) Machining forces and power consumption – A machining requiring a large force indicates low machinability and vice versa. When the strength of the tool is a matter to worry about, this is the criterion to be considered.

(ii) Surface finish – In some situations, the major concern can be over the quality of finish and, depending on the severity of this problem, the machinability may be low or high.

(iii) Tool life – The length of the period for which a tool can be used is defined as the tool life. This criterion is also linked up with the productivity and economics and can be a very good index for an overall judgement of a machining operation.

As long as the available power is enough and does not pose any problem on the machining and we are not concerned with a very special precision machining operation requiring a high quality of finish, the tool life may be considered the index for judging the machinability. In cases where the major objective is to remove a large amount of material quickly and cheaply, the tool life is used as a direct measure of machinability.

A precise definition of tool life is also not a simple problem. As a machining operation progresses, the wear on the flank and rake surfaces keeps on increasing. So, limits on these wears have to be chosen for defining the tool life. The commonly recommended criteria for HSS and carbide tools are given in Table 4.9.

In a very large number of cases, the criterion of the average flank wear hf serves well. Figure 4.22 shows the growth of flank wear for different speeds. Using hf = 0.3 mm as the tool life criterion, we note that the tool lives are T1, T2, and T3, as shown in the figure. Also, it is obvious that a higher speed of cutting leads to a lower tool life. It has been experimentally established that the tool life equation is –

where C and n are constants depending on the tool and work material, tool geometry, and cutting conditions (except speed).

Figure 4.23 shows the typical variation of tool life with speed for HSS, WC, and ceramic tools, keeping the other conditions the same. It is clear that the tool life for a given speed is normally much higher with WC than that with HSS. A ceramic tool performs better at a high cutting speed.

Though cutting speed is the most dominant variable, the other cutting parameters, e.g., the uncut thickness and width of cut, also affect the tool life. When machining is through the production of continuous chips without a built-up edge, the generalized Taylor equation can be written as –

The units of v, T, t, and w are m / min, min, mm, and mm, respectively. It is observed that q is smaller than p, and this indicates that the tool life is more sensitive to the uncut thickness than to the width of cut.

The two most important geometric parameters of a tool, viz., the rake and the clearance angles, also affect the tool life and the typical characteristics are indicated in Fig. 4.24. When the rake angle increases, the tool life starts improving because the cutting force reduces.

A further increase in the rake angle results in a larger temperature since the tool becomes thinner and the area available (Fig. 4.25a) for heat conduction reduces. Similarly, when the clearance angle increases, the tool life increases at first. This is due to the fact that for the same volume of flank wear, hf reduces (Fig. 4.25b).

However, with a further increase in the clearance angle, the tool becomes thinner and the tool life decreases due to the higher temperature.

The formation of a built-up edge is another factor which must be seriously considered when investigating the machinability. This is particularly so when the surface finish is of great importance. In Fig. 4.10b, we showed the formation of a built-up edge. When the temperature at the rake surface is below the recrystallization temperature, a seizure of the deformed work material by the tool surface occurs.

This is due to the fact that, because of the large plastic deformation (which is maximum at the layers adjacent to the rake surface), the hardness of the chip material increases and the bonding between the tool and the chip breaks along a path not at the interface but inside the chip which is softer. Figure 4.26a shows a typical hardness distribution in the cutting zone. It is clear that such a path (Fig. 4.26b) consumes lesser energy.

Thus, the highly deformed and strain hardened lump sticks to the tool edge and gradually grows in size till the force on the lump is so large that it breaks and the fragments are carried away by the finished surface and the chip. When the temperature is large enough to cross the recrystallization temperature, strain hardening is not very effective and the bonding breaks along the path B (Fig. 4.26b), preventing the formation of a built-up edge.

Since the built-up edge effectively increases the rake angle, the cutting force and the power consumption reduce. If the built-up edge is stable, it improves the tool life. But when the hard fragments are carried away after the BUE breaks, they can cause a large abrasion wear on the tool, resulting in a lowered tool life. However, for machining a hard material such as cast iron, the formation of a stable built-up edge is welcome since it protects the tool. In general, the effect of BUE on the tool life is erratic.

Apart from the effect through abrasion wear, a BUE can lead to tool failure by other mechanisms. For example- when using a carbide tool, a sudden disengagement of the tool from the work may lead to the tearing off of the BUE along with a fragment of the tool material. Again, when the tool cools down after a cut, cracks may develop in the tool due to the higher contraction rate of the welded BUE (Fig. 4.27). The coefficient of thermal expansion of steel is almost twice that of carbide.

The effects of the major cutting conditions, i.e., cutting speed and uncut thickness, can be represented by the machining chart introduced by E.M. Trent. Figure 4.28 shows such a chart for machining Ni-Cr-Mo steel with cemented carbide. In the case of ferrous metals, the microstructure is one of the most important factors controlling the machinability. Thus, here, a consideration of only the hardness of the work material is not enough.

Figure 4.29 shows the generalized behaviour of tool life-cutting speed characteristics for different microstructures when machining steel using a carbide tool. It should be noted that the tool life has been represented not by time but by the volume of material removed. The main structural constituents of cast iron are pearlite and free graphite. The finer the pearlite structure, the lower the machinability. Graphite acts as an internal lubricating agent and prevents the formation of BUE.

Cutting Fluids:

Though in a large number of cases machining can be conducted in a dry condition, quite often the use of a cutting fluid is very effective for improving the overall machinability. It is not difficult to realize that a suitably chosen fluid may reduce the coefficient of friction at the interfaces. This may be achieved either through lubrication or by lowering the strength of the welded junctions between the tool and the chip by forming a weaker solid (Fig. 4.30). A cutting fluid also prevents the formation of BUE.

For example- if a cutting fluid containing chlorine is used while machining steel, iron chloride is formed at the interface. It is a weak material and seizure is prevented as shearing takes place only at the interface.

The ways in which a cutting fluid affects machining can be summarized and classified as follows:

(i) Cooling down of the chip-tool-work zone by carrying away some of the generated heat.

(ii) Reducing the coefficient of friction at the chip-tool interface due to the formation of a weaker compound at the interface.

(iii) Reducing the thermal distortion caused by temperature gradients generated during machining.

(iv) Washing away the chips and clearing the machining zone.

(v) Protecting the finished surface from corrosion.

Cooling down obviously increases the tool life and reduces the thermal distortion. A reduction in the coefficient of friction lowers the machining force and power consumption. This also prevents the formation of BUE, and the surface finish improves greatly. Washing away of the chips is very helpful in cases where chips are very small as in grinding and milling.

An ideal cutting fluid should:

(i) Have a large specific heat and thermal conductivity,

(ii) Have a low viscosity and small molecular size (to help rapid penetration to the chip-tool interface),

(iii) Contain a suitable reactive constituent (for forming a low strength compound after reacting with the work material),

(iv) Be nonpoisonous and noncorrosive,

(v) Be inexpensive and easily available.

Since the action of a cutting fluid takes some minimum time, it is expected that at a high cutting speed the effectiveness of the cutting fluid decreases. Moreover, at a high cutting speed, a large fraction of the generated heat is carried away by the chip (Fig. 4.31a). Figure 4.31b shows how the coefficient of friction changes with speed when copper is machined using carbon tetrachloride as the cutting fluid.

Figure 4.32 illustrates a case where 0.15% carbon steel is machined with a tool with +18° rake angle and 0.125 mm uncut thickness, and compares three conditions for cutting.

The cutting fluids are mainly of two types, namely – (i) water based fluids, and (ii) mineral oil based fluids. Additives are used in conjunction with each of these types to accomplish different objectives. Table 4.11 lists the common cutting fluids.

The effectiveness of a cutting fluid also depends on the technique of application. It has been found that when the cutting zone is flooded, the coolant faces some resistance to enter the chip-tool interface; the effectiveness thus is not high. But if the coolant is forcibly injected into the interface, the fluid acts in a much more efficient manner.