A pair of spur gears with $${20^ \circ }$$ full-depth involute teeth is used to transmit $$3.5$$ $$kW$$ of power. The pinion rotates at $$700$$ $$rpm$$ and has pitch circle diameter of $$100$$ $$mm.$$ Assuming a single pair of teeth in contact, the total force acting on a gear tooth (in $$kN$$) is

In a machining operation with turning tool, the tool life $$(T)$$ is related to cutting speed $$v$$ $$(m/s),$$ feed $$f(mm)$$ and depth of cut $$d(mm)$$ as $$$T = C\,v{\,^{ - 2.5}}\,{f^{ - 0.9}}\,{d^{ - 0.15}}$$$
where, $$C$$ is a constant. The suggested values for the cutting parameters are: $$V=1.5$$ $$m/s,$$ $$f=0.25$$ $$mm$$ and $$d=3$$ $$mm$$ for normal rough turning. If the operation is performed at twice the cutting speed and the other parameters remain unchanged, the corresponding percentage change in tool life is ______________.

The Merchant circle diagram showing various forces associated with a cutting process using a wedge shaped tool is given in the Figure

The coefficient of friction can be estimated from the ratio

Turning, drilling, boring and milling are commonly used machining operations. Among these, the operation (s) performed by a single point cutting tool is (are)