25-Nav-A6 Advanced Strength of Materials (25-Mec-A6) · May 2016
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Reference texts: Kalpakjian & Schmid, Manufacturing Engineering and Technology, 8th ed.; Groover, Fundamentals of Modern Manufacturing, 7th ed.; Hibbeler, Mechanics of Materials, 10th ed.; Hibbeler, Engineering Mechanics: Statics, 14th ed.; Shigley's Mechanical Engineering Design, 11th ed.
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
(i) Cutting-fluid functions at low speed. At low cutting speeds the two principal functions are lubrication (reducing friction, and hence cutting force and power, at the tool–chip and tool–workpiece interfaces) and reduction of built-up edge (BUE) and adhesion (improving surface finish by keeping chip material from welding to the tool face). Mechanism (1): at low speed, contact time at the tool–chip interface is long enough for the fluid to be drawn in by capillary action along the freshly cut surfaces and the tool's clearance face, forming a thin boundary-lubricant film that lowers the coefficient of friction. Mechanism (2): extreme-pressure (EP) additives (sulfur-, chlorine-, or phosphorus-bearing compounds) react chemically with the nascent, highly reactive metal surface exposed by cutting to form a low-shear-strength surface film (a metal sulfide or chloride), which prevents the chip from adhering to and welding onto the tool rake face.
(ii) Cutting-fluid functions at high speed. At high cutting speeds the two principal functions shift to cooling (removing the much larger heat generated, to control tool temperature and prevent thermal softening/rapid wear, and to limit thermal expansion of the workpiece) and flushing (carrying chips clear of the cutting zone so they are not re-cut, which would damage the finish and the tool). Mechanism (1): at high speed the tool–chip contact time is too short and the interface pressure too high for a lubricant film to penetrate and form effectively, so the fluid's dominant role becomes bulk forced convection — a flood or high-pressure jet carries heat away from the tool, chip, and workpiece far faster than still air could. Mechanism (2): the same flood/jet supplies the hydraulic momentum needed to physically sweep hot chips away from the tool tip and out of the cutting zone.
(iii) Chatter in lathe turning. (a) Manifestations: an audible high-pitched "singing" or rattling noise; a wavy, rippled surface finish with a regular chatter-mark pattern visible on the machined surface; accelerated tool wear or edge chipping; and visible vibration of the tool/toolholder or workpiece. (b) Steps to identify the cause, in a logical diagnostic order: (1) check and improve system rigidity first — reduce tool overhang, shorten the toolholder, add a steady/follower rest, and verify workpiece clamping and tailstock support; (2) run a speed-change test, since chatter is often resonance-driven and shifting spindle speed away from the resonant frequency will suppress it if rigidity is not the root cause; (3) reduce feed and depth of cut, which reduce the exciting cutting force; (4) inspect tool geometry and condition — excessive tool wear, insufficient relief angle, or an oversized nose radius all raise cutting forces and promote chatter; (5) check the machine itself for worn/loose slides, spindle bearing play, or unbalance in the workpiece or chuck.
(iv) Improving surface finish for a 1-mm-nose-radius tool. Theoretical turned-surface roughness scales approximately as $R_t \approx f^2/(8R)$, where $f$ is feed and $R$ is the tool nose radius — so roughness can be reduced by lowering $f$ or raising $R$. (a) Process change: reduce the feed rate $f$. Since roughness scales with $f^2$, even a modest feed reduction gives a large finish improvement. Unintended consequence: material removal rate falls in direct proportion to feed, lengthening cycle time and reducing productivity; if feed is reduced too far relative to the cutting-edge radius, the tool begins to rub rather than shear cleanly, which can paradoxically degrade finish and accelerate flank wear. (b) Tool change: increase the nose radius $R$, which directly lowers the theoretical roughness for the same feed. Unintended consequence: a larger nose radius increases the radial (thrust) component of the cutting force, raising the risk of chatter and deflection — especially on slender or long-overhang workpieces — and demands a stiffer setup to realize the finish benefit in practice.
