1

Boothroyd Chapter-2 Problems 1-13, page 104-107:

1. In an orthogonal cutting test on mild steel, the following results were obtained:Cutting force Fc

= 900 N

Thrust force Ft

= 450 N

Uncut chip thickness ac

= 0.25 mm

Chip thickness a0

= 0.75 mm

Width of cut aw

= 2.50 mm

Length of contact between chip and tool lf= 0.5 mm

Working normal rake ne

= 0 deg.

a. Calculate the mean angle of friction on the tool face .b. Calculate the mean shear strength of the work material s.c. Calculate the mean frictional stress f.2. In an orthogonal cutting test the following conditions were noted:

Width of chip (width of cut) = 2.5 mm

Undeformed chip thickness = 0.25 mm

Chip thickness

= 1.0 mm

Working normal rake

= -5 deg

Cutting force

= 900 N

Thrust force

= 900 N

a. Calculate the shear angle b. Calculate the mean shear strength of the work material.3. In an experimental turning operation where low-carbon steel was being machined using a carbide tool, the following data were obtained:

Cutting force Fc

= 1 kN

Thrust force Ft

= 0.5 kN

Working normal rake ne

= 20 deg.

Feed f

= 0.141 mm

Working major cutting-edge angle r= 45 deg.

Depth of cut (back engagement) ap= 5 mm

Cutting speed v

= 2 m/s

Cutting ratio rc

= 0.2

Workpiece diameter dw

= 100 mm

Workpiece machined length lw= 300 mm.

Estimate from the above date:

a.The specific cutting energy of the work material ps.

b.The power required for machining Pm.

c.The undeformed chip thickness ac.

d.The width of cut aw.

e.The shear angle .

f.The mean angle of friction on the tool face .

g.The time taken to complete the machining operation.

4. Show that in metal cutting when the working normal rake is zero, the ratio of the shear strength of the work material s to the specific cutting energy ps is given by

5. In an orthogonal machining operation with a rake angle of 5 deg. and an undeformed chip thickness of 1 mm, the chip thickness is found to be 3 mm. What will the chip thickness be if the rake angle is increased to 15 deg assuming Ernst and Merchants first theory holds, that is, 2 + - ne = /2. Assume the friction coefficient is not influenced by changes in rake angle.6. Derive an expression for the specific cutting energy ps in terms of the shear angle and the mean shear strength of the work material s in orthogonal cutting. Assume that the shear-angle relationship of Ernst and Merchant applies, that is 2 + - ne = /27. Assuming that the shear angle theory of Lee and Shaffer applies, namely + - ne = /4, show that the specific cutting energy ps will be given by

ps = s (1+cot )

where s is the mean shear strength of the work material.

8. For the orthogonal cutting of a particular work material, it is found that the length of chip-tool contact is always equal to the chip thickness ac and that the mean shear stress at the chip-tool interface is equal to the mean shear stress on the shear plane. Show that, under these circumstances, the mean co-efficient of friction on the tool face must be equal to or less than 4/3 and that when it is equal to unity, the shear angle is equal to the working normal rake ne.9. In the cutting experiments using a sharp tool with zero rake, it was found that the chip-tool contact length was equal to the chip thickness a0. It was also found that the shear stress along the tool face was constant and was a constant proportion R of the shear strength of the work material on the shear plane. a. Derive an expression for the cutting force Fc in terms of ac, aw, s, R and .

b. Differentiate the expression to obtain the value of to give minimum Fc. 10. Assume that in an orthogonal cutting operation, the frictional force Ff on the tool face is given by KsA0 where K is a constant, s is the apparent shear strength of the work material, and A0 is the cross-sectional area of the chip. Show that the following relationship exists between the mean coefficient of friction on the tool face, the shear angle , and the working normal rake ne

11. For the machining of a particular work material, it is found that the shear angle is always equal to working normal rake ne. Assuming that the shear strength of the work material in the sticking friction region on the tool face is the same as the shear strength s of the material on the shear plane and that the length of the sticking region is equal to the chip thickness a0, derive expressions for the cutting force Fc and the thrust force Ft in terms of s, ne and the cross-sectional area of the uncut chip Ac. Also calculate the value of ne for which Ft = 0. Neglect the forces in the sliding-region on the tool face.12. In machining test it was found that for a particular material the following relation applied: 2 + - ne = /2. Also, when the rack angle ne was 20 deg, the coefficient of friction was 1.2.

a. What would the chip thickness be if in a turning operation, the feed was 0.55 mm and the major cutting angle was 60 deg?

b. If the cutting force is limited to 3 kN and the specific cutting energy of the material 2 GJ/m3, what maximum depth of cut can be taken?13. Assuming the in an orthogonal machining the distribution along the normal stress is along tool rake face is linear, becoming maximum at the cutting edge and reducing to zero at the end of chip tool contact length, drive an expression for the mean coefficient of friction between the tool and the chip and tool in terms of: the maximum normal stress m, normal stress 0 at which real and apparent areas of contact become equal, and the coefficient of friction region s.Solved Examples from Ghosh and Mallik (chapter 4; page no. 195 onwards)

1. During orthogonal machining with a cutting tool having a rake angle, the chip thickness is measured to be 0.4mm, the uncut chip thickness being 0.15mm. Determine the shear plane angle and also the magnitude of the shear strain.2. During an orthogonal machining operation on mild steel, the results obtained are t1= 0.25mm, t2= 0.75mm, w= 2.5mm,, FC= 950N, FT=475N. (i)Determine the coefficient of friction between the tool and the chip. (ii)Determine the ultimate shear stress S of the work material.3. Mild steel is being machined at a cutting speed of 200 m/min with a tool of rake angle. The width of cut and the uncut thickness are 2mm and 0.2mm, respectively. If the average value of the coefficient of friction between the tool and the chip is 0.5 and the shear stress S of the work material is 400 N/mm2, determine (i) the shear angle and (ii) the cutting and the thrust components of the machining forces.4. Find out the order of magnitude of the cutting component of the machining force during orthogonal machining of machining of mild steel with an uncut thickness of 0.25mm, the width of cut being 2.5mm.

Unsolved Examples from Ghosh and Mallik (chapter 4; page no. 282 onwards)

1. The chips from an orthogonal cutting operation with an uncut thickness of 0.2mm for various rake angles are

t20.450.50.631.13

Calculate, for each chip, the corresponding shear angle and shear strain and plot them against.

2. The cutting and the thrust components of the machining force during orthogonal machining of aluminum with a rake angle of are found to be 312N and 185N, respectively. (i) Estimate the coefficient of friction between the tool and the chip (ii) If the rake angle is reduced to, keeping all the other parameters the same, and if the coefficient of friction also remains unchanged, estimate the new values of FC and FT, using Merchants first solution.3. During orthogonal machining with a rake angle and an uncut thickness 0.125mm, the values of FC and FT are found to be 517N and 217N, respectively. The average is also measure and found to be 0.43mm. Evaluate the machining constant for the work material.4. When the rake angle is zero during orthogonal cutting, show that

5. During an orthogonal cutting test, the observations made aret1 = 0.25 mm t2 = 1.2 mm w = 2.5 mm = Fc = 900 N Fr = 810 NCalculate the mean shear strength of the work material.

6. Estimate the cutting component of the machining force during the orthogonal machining of aluminum alloy with an uncut thickness of 0.15mm, the width of cut being 2.5mm.

7. A metal is being cut orthogonally with a tool with zero rake angle. Show that the rate of heat generation in the shear plane can be expressed as.

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