Tool wear, tool life and machinability

Why it matters

In a high-volume automotive machining line, tool changes, scrapped parts from worn tools and the choice of cutting speed decide the cost per crankshaft or gearbox housing. Tool life equations let a process engineer choose a speed that balances productivity against tool cost, and machinability ratings explain why free-cutting steels and grey cast iron are preferred for heavily machined parts. Taylor's equation and its economics are among the most frequently examined manufacturing calculations.

Key ideas

Where tools wear.

• Flank wear – a land worn on the clearance face by rubbing against the newly machined surface; measured as the average land width VB. It changes the part size and finish, and it is the usual tool-life criterion.
• Crater wear – a depression on the rake face where the chip slides, at the hottest region a short distance from the edge; measured by its depth KT. Dominant at high speed with carbide tools on steel.
• Notch wear at the depth-of-cut line (work-hardened surfaces, scale), nose wear, and sudden failures: chipping, thermal (comb) cracking in interrupted cuts such as milling, plastic deformation of the edge when it overheats, and fracture.

Wear mechanisms.

• Abrasion by hard particles (carbides, oxides, sand inclusions) – mainly flank wear, important at all speeds.
• Adhesion – pressure welding of chip or work to the tool and tearing away; linked to the built-up edge (BUE) at low speeds with ductile materials.
• Diffusion – atoms of the tool (e.g. C, W, Co from carbide) diffuse into the chip at high temperature – the main cause of crater wear.
• Oxidation/chemical wear at high temperature. Temperature rises steeply with cutting speed, so diffusion and oxidation make wear speed-sensitive.

The wear curve. Flank wear against time shows three stages: rapid initial break-in, a long, roughly linear steady region, and an accelerating final region that ends in failure. Tool life ends at a chosen criterion – commonly an average flank wear land (a typical criterion for carbide is VB ≈ 0.3 mm; take the exact value from the standard or the shop's practice), a crater depth, a loss of finish or size, or catastrophic failure.

Taylor's tool-life equation. For a given tool–work pair, plotting log V against log T gives a straight line: V·Tⁿ = C. The exponent n is lower for tool materials whose life falls sharply with speed. Typical ranges: HSS about 0.08–0.2, carbides about 0.2–0.5, ceramics higher – use values given in the question. C is the speed for a one-minute tool life. The extended Taylor equation includes feed and depth of cut, whose effects are weaker than speed.

Tool materials (in roughly increasing hot hardness). Carbon tool steel → HSS (W- or Mo-based, tough, for drills, taps, broaches) → cast cobalt alloys → cemented carbides (WC–Co; with TiC/TaC for steel) → coated carbides (TiN, TiCN, Al₂O₃ layers by CVD/PVD) → cermets → ceramics (Al₂O₃, Si₃N₄) → cubic boron nitride (CBN, for hardened steel and cast iron) → polycrystalline diamond (PCD, for aluminium–silicon alloys and non-ferrous metals; not for steel, because carbon diffuses into iron). Harder materials usually trade away toughness.

Machinability is the ease of machining a material, judged by tool life, surface finish, cutting forces/power and chip control. It improves with lower hardness and strength (up to a point – very soft, gummy metals form BUE), free-cutting additions (S, Pb, Bi, Ca form inclusions that break chips and lubricate), suitable microstructure (spheroidised or lamellar pearlite as appropriate, graphite in grey iron) and higher thermal conductivity. A machinability index compares the cutting speed giving a standard tool life (often 60 min) with a reference free-cutting steel rated 100 %.

Machining economics. Higher speed shortens machining time but uses more tools and more tool changes. Minimum cost and maximum production rate each correspond to an optimum tool life; the maximum-production speed is always higher than the minimum-cost speed.

Formulas

V·Tⁿ = C V = cutting speed (m/min), T = tool life (min), n = Taylor exponent (dimensionless), C = constant (m/min, the speed for T = 1 min).

n = ln(V₂ / V₁) / ln(T₁ / T₂) From two test points.

T₂ / T₁ = (V₁ / V₂)^(1/n) Effect of a speed change on tool life.

V·Tⁿ·f^a·d^b = K Extended Taylor equation; f = feed (mm/rev), d = depth of cut (mm); exponents a and b are found experimentally (usually b < a < 1).

T_opt,cost = (1/n − 1)·(t_c + C_t / C_m) Tool life for minimum cost per piece (min); t_c = tool-change time (min), C_t = cost of a tool cutting edge (₹), C_m = machine-and-labour cost rate (₹/min).

T_opt,prod = (1/n − 1)·t_c Tool life for maximum production rate (min).

Machinability index (%) = V₆₀ (material) / V₆₀ (reference) × 100 V₆₀ = cutting speed for 60 min tool life under the same conditions.

Worked examples

Example 1 (standard) – Taylor constants from two tests. A carbide tool lasts 60 min at 100 m/min and 12 min at 150 m/min. Find n, C and the speed for 30 min life.

1. n = ln(V₂/V₁)/ln(T₁/T₂) = ln 1.5/ln 5 = 0.4055/1.6094 = 0.252.
2. C = V₁·T₁ⁿ = 100 × 60^0.252 = 280.5 m/min.
3. V₃₀ = 280.5/30^0.252 = 119 m/min.

Example 2 (GATE level) – economic cutting speed. Given: V·T^0.25 = 300 (V in m/min, T in min), tool-change time 2 min, cost per cutting edge ₹50, machine-and-labour rate ₹5/min.

1. Minimum cost: T_opt = (1/n − 1)(t_c + C_t/C_m) = (4 − 1)(2 + 50/5) = 3 × 12 = 36 min.
2. V_opt = 300/36^0.25 = 300/2.449 = 122.5 m/min.
3. Maximum production: T = (1/n − 1)·t_c = 3 × 2 = 6 min; V = 300/6^0.25 = 191.7 m/min.
4. As expected, the maximum-production speed exceeds the minimum-cost speed.

Example 3 – sensitivity to speed. With n = 0.25, raising speed by 20 % changes tool life by (1/1.2)⁴ = 0.482: tool life falls by about 52 %.

Common mistakes

• Solving V·Tⁿ = C as T = (C/V)·n or T = (C/V)ⁿ; the correct form is T = (C/V)^(1/n).
• Using log₁₀ for one quantity and ln for the other in the two-point method (either works if used consistently).
• Mixing time units (min vs s) in Taylor constants; C is tied to the units in which it was found.
• Thinking crater wear is mainly abrasive – it is mainly diffusion at high temperature.
• Using PCD on steel – carbon dissolves into iron at cutting temperatures.
• Forgetting that the maximum-production tool life ignores tool cost, so it is shorter than the minimum-cost tool life.

For GATE ME

Expect Taylor numericals (n and C from two tests, new life after a speed change, percentage changes, extended Taylor with feed), optimum tool life and speed for minimum cost or maximum production, and conceptual questions on wear types, mechanisms, tool materials and machinability. Practise logarithms quickly and always check that a higher speed gives a shorter life.

Quick check

1. In V·Tⁿ = C, what does C represent?
2. Which wear mechanism mainly causes crater wear?
3. If n = 0.5 and speed doubles, by what factor does tool life change?
4. Which tool material is preferred for machining aluminium–silicon alloys?
5. Which optimum tool life is longer: minimum cost or maximum production?

Answers: 1. The cutting speed for a 1-minute tool life; 2. Diffusion; 3. It falls to one-quarter; 4. Polycrystalline diamond (PCD); 5. Minimum cost.