A helical gear with involute tooth profile has been machined with a disc-type form gear milling cutter. The helical gear has $$30$$ teeth and a helix angle of $${30^ \circ }$$. The module of the gear milling cutter is $$2.$$ The pitch circle diameter (in $$mm$$) of the helical gear is _______.

A cylindrical bar of $$100$$ $$mm$$ diameter is orthogonally straight turned with cutting velocity, feed and depth of cut of $$120$$ $$m/min$$, $$0.25$$ $$mm/rev$$ and $$4$$ $$mm,$$ respectively. The specific cutting energy of the work material is $$1 \times {10^9}\,\,J/{m^3}.$$ Neglect the contribution of feed force towards cutting power. The main or tangential cutting force (in $$N$$) is __________________

A single point right handed turning tool is used for straight turning. The feed is $$0.25$$ $$mm/rev$$ and the uncut chip thickness is found to be $$0.25$$ $$mm.$$ The inclination angle of the main cutting edge is $${10^ \circ }.$$ The back rake angle (in degrees) is ________________

A $$60$$ $$mm$$ wide block of low carbon steel is face milled at a cutting speed of $$120$$ $$m/min,$$ feed of $$0.1$$ $$mm$$/tooth and axial depth of cut of $$4$$ $$mm.$$ A schematic representation of the face milling process is shown below. The diameter of the cutter is $$120$$ $$mm$$ and it has $$12$$ cutting edges. The material removal rate (in $$m{m^3}/s)$$ is __________