Orthogonal Cutting Schematic, Rake-Angle Limits, and Chip Breakers: 23-Ind-B2 Manufacturing Processes, May 2018, Q7

Question 7: Orthogonal Cutting Schematic, Rake-Angle Limits, and Chip Breakers (20 marks: 8/6/6)

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) Orthogonal Cutting Schematic

Orthogonal cutting geometry (schematic): the tool bit removes material of uncut thickness $t_0$ (the depth of cut) from the workpiece, separating it along the shear plane (shear angle $\phi$) into a chip of thickness $t_c$ that flows up the tool's rake face (rake angle $\alpha$, measured from the vertical/normal to the cut surface); the relief (clearance) angle is the small angle between the tool's flank face and the newly machined surface, kept just large enough to avoid the flank rubbing against that surface.

The workpiece moves relative to the tool at cutting velocity $v$; ahead of the tool the surface still carries the uncut layer of thickness $t_0$ (the depth of cut), and behind the tool that layer has been removed, leaving the finished (machined) surface. The tool bit itself is bounded by two working faces: the rake face, over which the separated chip flows away (thickened to $t_c>t_0$ by the shearing deformation), and the flank face, which trails just behind the cutting edge over the newly machined surface at the (small) relief angle.

(ii) Why the Rake Angle Cannot Be Increased Very Much

Although a larger rake angle does bring real benefits — it reduces the cutting force and power required, tends to favour a continuous chip over a discontinuous one, and reduces the tendency to form a built-up edge (by lowering contact pressure/friction on the rake face) — it comes at the cost of the tool's own strength. Increasing the rake angle necessarily thins the included wedge of tool material immediately behind the cutting edge, which weakens the edge mechanically and makes it substantially more prone to chipping or outright fracture under the cutting load. A thinner wedge also has less mass of tool material available right at the cutting zone to conduct frictional and shear-zone heat away from the edge, so the tool tip runs hotter and wears faster. Beyond a moderate rake angle, this loss of edge strength and heat dissipation outweighs the force/power and chip-quality benefits, which is why rake angle is chosen as a compromise rather than maximized — the exact practical limit depends on the tool material's own strength/toughness (harder, more brittle tool materials such as ceramics and cemented carbides are given smaller rake angles than tougher high-speed steel).

(iii) Why a Chip-Breaker Is Used

Left uninterrupted, a continuous chip forms one long, thin, sharp, and still-hot ribbon of metal. That ribbon readily curls and can wrap around the cutting tool, the workpiece, or the machine's rotating spindle/chuck — a genuine safety hazard to the operator, and a source of damage to the tool and to the just-machined surface if the trailing chip drags across it or tangles in the setup. A chip-breaker — a groove or step formed into (or clamped onto) the tool's rake face just behind the cutting edge — forces the flowing chip to curl more tightly than its natural radius, which fractures it into short, manageable segments that fall clear of the cutting zone on their own. This also makes unattended or automated machining far more reliable, since chip evacuation and coolant access no longer depend on an operator manually clearing a tangle of continuous chip.

Topic. Orthogonal-cutting geometry (depth of cut, rake/relief/shear angles, chip thickness), the strength-vs-performance trade-off that limits rake angle, and the purpose of a chip-breaker.

Key relations. Chip-thickness ratio $r=t_0/t_c\ (<1)$; shear angle from Ernst & Merchant's relation $\tan\phi=\dfrac{r\cos\alpha}{1-r\sin\alpha}$; larger rake angle $\alpha$ lowers cutting force but also thins the tool wedge (edge strength $\downarrow$, heat dissipation $\downarrow$).

Why this works. Every labelled quantity in the orthogonal-cutting schematic (depth of cut, rake/relief/shear angles, chip thickness) describes one geometric event: a wedge-shaped tool advancing into the workpiece shears a layer of material away from the bulk along the shear plane and diverts it, thickened, up the rake face as the chip. The rake-angle trade-off and the chip-breaker's role both follow directly from that same picture — one concerns the tool's own geometry/strength, the other concerns what happens to the separated chip once it leaves the shear plane.

Common pitfall. Treating rake angle as a free parameter to maximize purely for cutting-force reduction, or describing the relief angle as unimportant — too small a relief angle causes the flank face itself to rub against the freshly machined surface, generating heat and poor surface finish independent of anything happening at the rake face.

Source. Groover, Fundamentals of Modern Manufacturing, 6th ed., Ch. 21 (theory of metal machining: orthogonal cutting model, chip formation, tool geometry).

Question 7 of 7: Orthogonal Cutting Schematic, Rake-Angle Limits, and Chip Breakers

Question 7: Orthogonal Cutting Schematic, Rake-Angle Limits, and Chip Breakers (20 marks: 8/6/6)

(i) Orthogonal Cutting Schematic

(ii) Why the Rake Angle Cannot Be Increased Very Much

(iii) Why a Chip-Breaker Is Used