Tool wear, tool life and machinability

Why it matters

Every cutting edge wears out, and the rate at which it wears decides how often a CNC machine stops for a tool change, how consistent the part dimensions stay and what each part costs. Taylor's tool life equation lets a process engineer pick a cutting speed that balances tool cost against machine time, and tool-wear monitoring is a classic sensing problem in automated (mechatronic) machining cells.

Key ideas

Wear mechanisms. A tool loses material at the tool–chip and tool–work interfaces through:

• Abrasion – hard particles (carbides, oxides) in the work material plough the tool; dominant at low to moderate speeds.
• Adhesion – welded junctions between tool and chip shear off, carrying tool material away.
• Diffusion – at high interface temperatures atoms (for example carbon and cobalt from a carbide tool) diffuse into the chip, weakening the tool surface; strongly temperature dependent.
• Oxidation / chemical wear – the hot edge reacts with air or coolant. Because diffusion and oxidation are thermally activated, wear rate rises very steeply with cutting temperature, and therefore with cutting speed.

Forms of wear.

• Flank wear – a land of width VB on the clearance (flank) face, caused by rubbing against the newly machined surface. It directly changes the part size and surface finish, so it is the usual tool-life criterion.
• Crater wear – a depression of depth KT on the rake face where the chip slides; it is mainly diffusion-driven and weakens the edge until it breaks.
• Notch wear – localised wear at the depth-of-cut line, often caused by a work-hardened or scaled surface.
• Chipping and fracture – sudden loss of edge material from impact (interrupted cuts) or thermal cracking.
• Built-up edge (BUE) – work material welded onto the edge at low speed with ductile work. It is not wear itself, but it changes the effective geometry, spoils the finish and pulls off tool fragments when it breaks away.

Flank-wear curve. Plotting VB against cutting time shows three zones: a rapid initial (break-in) zone, a long steady uniform-wear zone, and a final accelerating zone in which the edge fails rapidly. A tool should be changed before the third zone.

Tool life is the cutting time to reach an agreed failure criterion. ISO 3685 commonly uses an average flank wear of VB = 0.3 mm (or a maximum of 0.6 mm if wear is uneven) and a crater-depth limit for carbide tools; shop practice also uses surface-finish loss, size drift, a rise in cutting force or power, or volume of metal removed. Always state the criterion – tool life has no meaning without it.

Taylor's equation. For a fixed tool–work pair, feed and depth, tests show that ln V and ln T fall on a straight line, giving V·T^n = C. The exponent n is the (negative) slope on log–log axes: a small n means tool life is very sensitive to speed. Indicative ranges: HSS about 0.08–0.2, cemented carbide about 0.2–0.5, ceramics about 0.5–0.7. C is the cutting speed that gives a tool life of 1 minute (in the same time unit used for T). Actual n and C come from tests or a machining data handbook.

Effect of feed and depth. The extended Taylor equation V·T^n·f^a·d^b = C shows speed has the strongest effect, feed the next and depth of cut the least – which is why roughing uses a large depth and moderate feed rather than high speed.

Tool materials are chosen for hot hardness, toughness and chemical stability: carbon steel → HSS → cast alloys → cemented carbides (often coated with TiN, TiCN, Al₂O₃) → ceramics → cBN → polycrystalline diamond (not for ferrous work, because carbon diffuses into iron).

Machinability is the ease with which a material is machined, judged by tool life, surface finish, cutting forces/power and chip form. A machinability index compares the cutting speed for a fixed tool life with that of a reference free-cutting steel (rated 100 %). Sulphur and lead additions (free-machining steels) improve it; hardness, work-hardening (austenitic stainless steel) and abrasive inclusions reduce it.

Economics. Raising speed shortens machining time but raises tool cost and tool-change time per part. The optimum tool lives below follow from minimising cost per piece or time per piece. Coolant lowers interface temperature and so raises the effective C.

Formulas

V·T^n = C

• V = cutting speed (m/min); T = tool life (min); n = Taylor exponent (dimensionless); C = Taylor constant (m/min, the speed for T = 1 min). Valid for one tool–work pair at fixed feed and depth, within the tested speed range.

n = ln(V₂/V₁) / ln(T₁/T₂)

• Exponent from two tests (V₁, T₁) and (V₂, T₂).

T₂ = T₁·(V₁/V₂)^(1/n)

• Tool life at a new speed with the same n and C.

V·T^n·f^a·d^b = C

• f = feed (mm/rev); d = depth of cut (mm); a, b = empirical exponents (take from test data or a handbook).

T_c = (1/n − 1)·(t_c + C_t/C_m)

• Tool life for minimum cost per piece. t_c = tool-change time (min); C_t = tool cost per cutting edge (Rs); C_m = machine plus operator cost rate (Rs/min).

T_p = (1/n − 1)·t_c

• Tool life for maximum production rate (minimum time per piece).

Machinability index (%) = (V for chosen tool life, test material / V for same tool life, reference material) × 100

Worked examples

Example 1 (standard). A carbide tool gives a life of 60 min at 120 m/min and 12 min at 180 m/min. Find n, C and the tool life at 150 m/min.

1. n = ln(V₂/V₁) / ln(T₁/T₂) = ln(180/120) / ln(60/12) = 0.4055 / 1.6094 = 0.252
2. C = V₁·T₁^n = 120 × 60^0.252 = 120 × 2.805 = 336.6 m/min (check: 180 × 12^0.252 = 336.6 m/min).
3. T = (C/V)^(1/n) = (336.6/150)^(1/0.252) = 2.244^3.97 = 24.7 min Answer: n = 0.252, C = 336.6 m/min, T = 24.7 min at 150 m/min.

Example 2 (GATE level). For a tool–work pair, V·T^0.25 = 300 (V in m/min, T in min). Tool-change time t_c = 2 min, cost of a cutting edge C_t = Rs 60, machine and operator cost C_m = Rs 6/min. Find the cutting speed for minimum cost and for maximum production.

1. Minimum cost: T_c = (1/n − 1)(t_c + C_t/C_m) = (4 − 1)(2 + 60/6) = 3 × 12 = 36 min
2. V_c = C / T_c^n = 300 / 36^0.25 = 300 / 2.449 = 122.5 m/min
3. Maximum production: T_p = (1/n − 1)·t_c = 3 × 2 = 6 min
4. V_p = 300 / 6^0.25 = 300 / 1.565 = 191.7 m/min Answer: 122.5 m/min for minimum cost; 191.7 m/min for maximum production. The maximum-production speed is always higher, because it ignores the cost of the tool.

Common mistakes

• Inverting the exponent: T = (C/V)^(1/n), not (C/V)^n. With n = 0.25, a 2× speed increase cuts life by 2^4 = 16 times, not by 1.19.
• Mixing time units: if C is defined with T in minutes, T in seconds gives a wrong answer.
• Treating C as dimensionless or as a tool life; it is a speed (m/min).
• Calling the built-up edge a type of wear and assuming it appears at high speed – it forms at low speed and disappears as speed rises.
• Forgetting that n is a property of the tool material–work pair; ceramics have larger n, so their life is less sensitive to speed.
• Using (1/n − 1)·t_c for minimum cost; that is the maximum-production tool life – the cost formula also needs C_t/C_m.

For GATE ME

• Numericals on Taylor's equation: find T at a new speed, find n and C from two tests, or find the percentage change in tool life for a given change in speed.
• Extended Taylor equation with feed and depth exponents; which parameter most affects tool life.
• Optimum cutting speed or tool life for minimum cost and maximum production rate.
• Conceptual MCQs on wear mechanisms (diffusion at high temperature), crater versus flank wear, BUE, tool materials and machinability. Practise log manipulation and keep four significant figures in intermediate steps; the answers are very sensitive to rounding of n.

Quick check

1. Which face of the tool carries crater wear?
2. With n = 0.5, if the cutting speed is doubled, by what factor does tool life change?
3. What does the constant C in V·T^n = C physically represent?
4. Which wear mechanism dominates at very high cutting temperatures with carbide tools?
5. Which tool material should not be used for machining steel, and why?

Answers: 1. The rake face. 2. Life becomes 1/4 of the original, since T ∝ V^(−1/n) = 2^(−2). 3. The cutting speed that gives a tool life of 1 minute. 4. Diffusion wear. 5. Diamond (PCD), because carbon diffuses into iron at cutting temperatures.