Cutting Tools

§1The cutting wedge

A cutting tool is a hardened wedge. Driven into the workpiece, it shears a layer of metal ahead of it into a chip that flows up the tool face — cutting is controlled shearing, not scraping.

Three things must be true for it to work: the tool must be much harder than the work (the materials section covers how tool steels and carbides achieve that), it must present the right angles to shear cleanly rather than rub, and it must survive the heat and force of the cut long enough to be economic. Those three — hardness, geometry and life — organise this whole section. This page sets out the geometry and the speed-and-life relationships; the pages that follow apply them to each tool type, from drills to broaches.

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§2Rake and clearance

Two angles define the wedge. The rake angle sets how the chip is sheared; the clearance (relief) angle keeps the tool from rubbing the surface it has just cut.

The rake angle is measured on the face the chip flows over. A large positive rake shears easily, cuts with low force and gives a good finish, but leaves a thin, weak edge that chips under shock — so it suits ductile materials and lighter machines. A negative rake presents a strong, blunt edge that survives interrupted cuts and hard materials, at the cost of higher cutting force; carbide and ceramic tools often run negative rake for exactly this strength. The clearance angle is the small angle (typically 5–10°) beneath the cutting edge that lifts the tool flank clear of the freshly cut surface; too little and the flank rubs, generating heat and wear, too much and the edge is left unsupported and fragile. Every tool geometry in this section is a particular choice of these two angles.

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§3The tool signature

A single-point turning tool is fully specified by a short ordered list of angles — its signature — so that any tool can be described, ground and reproduced unambiguously.

The signature names, in a fixed order, the back rake, side rake, end relief, side relief, end cutting-edge angle, side cutting-edge angle and nose radius. The two rakes control chip flow and force; the two reliefs prevent rubbing; the two cutting-edge angles set how the edge leads into the work and distribute the load along it; and the nose radius rounds the tip, which strengthens it and improves finish (a larger radius gives a smoother surface but raises cutting force and chatter tendency). The signature is to a cutting tool what the four-digit code is to a steel — a compact, complete specification — and the same seven-element idea underlies the more specialised tools that follow.

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§4Cutting speed and spindle speed

Cutting speed is how fast the cutting edge passes the work, in metres per minute — a property of the material and tool. Spindle speed, in rev/min, is what the machine is set to, and one converts to the other through the diameter.

N = 1000 Vπ D — N in rev/min, cutting speed V in m/min, diameter D in mm

Example 1 — setting the lathe

Turning a 50 mm bar at a recommended cutting speed of 30 m/min: N = 1000 × 30/(π × 50) = 191 rev/min. The diameter matters as much as the material — the same 30 m/min on a 100 mm bar needs only half the spindle speed. This is why cutting speed, not spindle speed, is quoted for a material: it is the figure that stays constant as diameters change, and every speed table in this section is in m/min for that reason.

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§5Material removal rate

How fast metal is actually cut away — the material removal rate — is the product of the three cutting parameters, and it sets both productivity and the load on the machine.

MRR = V × f × d — cutting speed × feed per revolution × depth of cut

Raising any of the three lifts the removal rate and the productivity, but each has a cost: more speed shortens tool life sharply (§6), more feed roughens the finish, and more depth raises the cutting force and the power demanded of the machine. Roughing therefore uses heavy feed and depth at modest speed to shift metal; finishing uses light feed and depth for surface quality. The art of setting up a cut is choosing the three to remove metal as fast as the tool life, finish and machine power allow — a balance, not a maximum.

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§6Tool life — the Taylor law

The single most important trade-off in machining: cutting speed and tool life are inversely and steeply related, captured by Taylor’s tool-life equation.

V Tⁿ = C — V cutting speed, T tool life (min), n and C constants of the tool-work pair

Example 2 — how sharply speed costs life

For a tool-work pair with n = 0.25 and C = 150, a cutting speed of 100 m/min gives a life of T = (150/100)⁴ = 5.1 min. Drop the speed by a quarter to 75 m/min and the life becomes (150/75)⁴ = 16 min — over three times as long for a 25 % speed cut (the hero curve). Push up to 150 m/min and the tool lasts barely a minute. The low exponent n is what makes the curve so steep: small speed changes swing tool life enormously, which is why the economic cutting speed sits well below the maximum the tool can briefly survive.

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§7Quick reference

The working core of the page on one card rack.

Two angles

rake → chip & force

clearance → no rubbing (5–10°)

Signature

rakes · reliefs · edge angles · nose R

Spindle speed

N = 1000 V / (π D)

Removal rate

MRR = V × f × d

Tool life

V Tⁿ = C

small speed ↑ → big life ↓

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Handbook application: from concept to controlled practice

Purpose. This expanded section turns the original page into a practical handbook. It preserves the supplied material and adds a repeatable way to apply, check and review Cutting Tools. It does not replace a contract, legislation, a controlled standard, competent engineering judgement or specialist advice.

The operating aim is to carry the subject from function and assumptions through design evidence, verification and controlled release. Read the original explanation first, then use the workflow and checks below to convert knowledge into evidence.

Apply Cutting Tools by beginning with the duty, not the component or software command. Convert the key ideas—cutting, tool, speed, rake, clearance—into measurable requirements and interfaces. Record operating and non-operating environments, duty cycle, expected life, loads, energy sources, human interaction and reasonably foreseeable abnormal conditions. When a value is not a project requirement or verified supplier datum, identify it as an assumption or illustrative value.

Create a calculation and evidence trail that another competent person can audit. Every input should carry a source, unit, revision and uncertainty or tolerance where relevant. Every model should state its boundary conditions and limitations. Keep nominal capacity separate from design capacity, and keep verification margin separate from an arbitrary safety factor. If a code or standard governs the work, confirm the applicable edition and contractual status rather than copying a number from a secondary summary.

Design for manufacture, assembly, inspection, operation and maintenance at the same time. A technically valid geometry can still fail because it cannot be fixtured, measured, cleaned, guarded, reached or replaced. Review process capability, datum or reference strategy, tolerance accumulation, access, error-proofing and changeover. Where people interact with plant, apply the hierarchy of controls and consult those who will operate, clean, maintain and recover the equipment.

Plan verification before release. Define the characteristic, method, equipment, sample or test condition, acceptance criterion, record and responsible person. Validation then asks a different question: whether the resulting system is effective and suitable in the intended use context. A passed drawing check or analysis does not by itself validate usability, maintainability or production performance.

Step-by-step operating method

Define the duty. Capture the required function, interfaces, operating environment, life, loads and unacceptable outcomes.
Establish the model. Identify governing principles, units, material or process data, assumptions and uncertainty.
Develop alternatives. Compare feasible concepts against performance, manufacturability, safety, maintainability and cost.
Verify the design. Use analysis, test, inspection or demonstration with acceptance criteria defined before execution.
Release and learn. Baseline the design, control changes, retain evidence and feed operating results into the next revision.

Illustrative design review record

Illustrative values only. Build a one-page record with the required function, input sources, assumptions, governing load or process condition, failure consequences, selected concept, verification method and acceptance criterion. Mark every numerical input as project requirement, verified supplier data, measured value, calculation output or assumption. Review the weakest evidence first. If an assumption can change safety, compliance, interchangeability or capacity, it must be resolved before release rather than buried in a calculation note.

Evidence class	Question	Release expectation
Requirement	What must the design do and under which conditions?	Approved and traceable
Input	Where did the load, property, tolerance or process limit come from?	Source, unit and revision recorded
Analysis	Which model and assumptions connect input to result?	Checkable calculation or simulation
Verification	How will conformity be demonstrated?	Method and acceptance criterion agreed
Validation	Will the solution work for intended users and conditions?	Representative use evidence

Common failure modes and recovery actions

1. Watch for

Starting detailed design before interfaces and operating limits are agreed.

Recovery: Return to the governing definition or requirement and restate the decision in one sentence.

2. Watch for

Using catalogue or typical values as though they were certified project inputs.

Recovery: Separate evidence from assumption, assign an owner and set a date for validation.

3. Watch for

Checking nominal performance while ignoring tolerances, degradation and foreseeable misuse.

Recovery: Run a small counterexample, boundary test, pilot or independent check before proceeding.

4. Watch for

Confusing verification of requirements with validation of user need.

Recovery: Record the consequence, decision and rationale, then update the controlled baseline.

5. Watch for

Releasing drawings or procedures without configuration, inspection and change controls.

Recovery: Escalate when the issue affects safety, compliance, acceptance, material value or an agreed tolerance.