Question

A steel shaft of diameter 57 mm is turned with a carbide tool that has a side rake angle of 𝛼_f = 5°, a back rake angle of 𝛼_p = −5°, and zero approach angle. The nose radius of the insert is 𝑟 = 0.8 mm. The radial depth of cut, the feed rate, and the cutting speed are: 𝑎 = 1 mm, 𝑐 = 0.06 mm/rev, and 𝑉 = 240 m/min, respectively. The orthogonal parameters for the same steel and carbide tool with a rake angle 𝛼_r = −5° are:

Shear stress: 𝜏_s = 1400ℎ + 0.327𝑉 + 507 [N/mm² ]

Friction angle: 𝛽_a = 33.69 − 12.16ℎ − 0.0022𝑉 [degree]

Chip ratio: 𝑟_c = 2.71ℎ + 0.00045𝑉 + 0.227

wherein the units for ℎ are mm and for 𝑉 are in m/min.

i. Evaluate the distribution of chip thickness along the curved chip length.

ii. Evaluate the cutting coefficients along the curved chip length using the oblique cutting transformation. iii. Evaluate the distribution of tangential, radial, and feed cutting forces (F_t; F_r; F_f ) along the curved chip.

iv. Find the total cutting forces (Fx; Fy; Fz), torque, and power required to turn the shaft.

Answer 1

i) distribution of chip thickness along the curved chip length = 23 mm

ii) cutting coefficients along with the curved chip = 45

iii) distribution of tangential, radial, and feed cutting forces = 21,24,29

iv) total cutting forces (Fx; Fy; Fz), torque, and power required = 32.45,78