GATE PI key terms

The thin zone ahead of a cutting tool where workpiece material deforms plastically and separates as a chip. Its angle controls cutting force, chip thickness, and heat generation in orthogonal machining.

The ratio of undeformed chip thickness to deformed chip thickness in machining, always less than one. It measures how much the chip thickens and is used to estimate shear plane angle.

A force-circle construction relating cutting force, thrust force, friction force, and shear force on the tool rake face during orthogonal machining. It lets you resolve measured forces into friction and shear components.

The angle between the tool face and a reference plane, measured in the cutting direction. Positive rake reduces cutting force but weakens the edge; negative rake strengthens the edge for hard materials.

Gradual loss of tool material on the clearance face, measured as flank wear land width. It raises cutting forces and dimensional error and sets the practical tool life limit.

An empirical relation VT^n = C linking cutting speed V to tool life T, where n and C depend on tool and workpiece material. It guides selection of economic cutting speeds.

How easily a material can be cut to give acceptable surface finish, tool life, and chip form at practical speeds and forces. It is judged relative to a reference steel under fixed conditions.

Adherent workpiece material welded onto the tool edge during cutting at certain speeds. It can protect the edge but breaks away irregularly, worsening surface finish and causing vibration.

A cutting configuration where the cutting edge is perpendicular to the cutting velocity, producing two-dimensional chip flow. It is the standard model for analyzing forces, shear, and chip formation.

A coded designation giving abrasive type, grit size, grade (hardness), structure (porosity), and bond. These letters and numbers determine wheel behavior for a given workpiece and operation.

Material removal using hard abrasive particles bonded in a wheel or coated on a belt. It achieves fine finish and tight tolerance and is used for hard materials and finishing operations.

The arithmetic average deviation of the surface profile from its mean line over a sampling length. It is the most common numerical indicator of surface finish in manufacturing specifications.

Tolerance is the permissible variation in a dimension; allowance is the intentional difference between mating part sizes. Both control fit, function, and interchangeability in assembly.

A system of maximum and minimum sizes for mating parts, classified as clearance, interference, or transition fits. It defines how loosely or tightly a shaft sits in a hole.

A symbolic language on drawings specifying form, orientation, location, and runout limits relative to datums. It communicates functional requirements that simple size tolerances cannot express.

A riser is a reservoir of molten metal that feeds shrinkage as the casting solidifies. Its size and placement must ensure it freezes after the casting it feeds.

Solidification time is proportional to the square of the volume-to-surface-area ratio of the casting. It is used to size risers and compare freezing times of different sections.

Volume reduction as molten metal cools and freezes, causing cavities unless fed. It is distinct from solid contraction, which occurs after freezing and affects pattern dimensions.

A joining process where electric current passes through overlapping sheets held under pressure, melting a small nugget at the interface. Heat depends on current squared, resistance, and time.

Joining metals by melting the faying surfaces, often with filler metal, to form a solid joint on cooling. Common energy sources are arc, laser, and electron beam.

Heat energy delivered per unit length of weld, calculated as voltage times current divided by travel speed. It controls cooling rate, microstructure, and heat-affected zone width.

The instantaneous stress needed to continue plastic deformation of a material at a given strain and temperature. It determines forming loads and is often represented by a strain-hardening power law.

The reduction in thickness of a workpiece passing between rolls, equal to initial minus final thickness. Draft limits per pass depend on roll radius, friction, and material ductility.

The ratio of the initial billet cross-sectional area to the extruded product area. Higher ratios require greater pressure and are limited by tool strength and billet ductility.

The controller function that computes intermediate tool positions to generate straight lines, arcs, or curves between programmed points. It determines path accuracy and smoothness of motion.

Preparing the sequence of coordinates, feeds, speeds, and auxiliary commands that a numerical control machine executes. It may be manual or generated by computer-aided manufacturing software.

The closeness of machined features to intended dimensions, affected by geometric errors, thermal distortion, and stiffness. It differs from repeatability, which concerns consistency of repeated results.

The order size that minimizes the sum of ordering cost and holding cost for a constant-demand item. It balances fixed cost per order against inventory carrying cost.

The cost of keeping stock, including capital tied up, storage, insurance, obsolescence, and handling. It is usually expressed as a percentage of unit value per period.

The inventory level at which a new order is placed, set to cover expected demand during lead time plus a safety buffer. It links stock policy to replenishment timing.

Extra inventory held to absorb demand variability and lead-time uncertainty. It reduces stockout risk at the cost of higher holding expense.

For a stable queueing system, the average number in the system equals arrival rate times average time spent. It relates work-in-process, throughput, and flow time in production systems.

The fraction of time a server is busy, equal to arrival rate divided by service rate. As utilization approaches one, waiting times rise sharply in single-server queues.

The maximum output rate of the slowest operation in a process, which limits output of the whole line. Improving non-bottleneck stations alone does not raise system throughput.

Every linear program has a dual problem whose optimal objective equals the primal's. Dual variables, or shadow prices, show how much the objective changes per unit increase in a constraint.

A linear program minimizing cost of shipping goods from several sources to several destinations subject to supply and demand limits. It is solved by specialized methods such as Vogel approximation.

A special transportation problem where each job is assigned to exactly one resource at minimum total cost or time. The Hungarian method solves it efficiently.

Network techniques for planning projects. PERT uses probabilistic activity times to estimate completion risk; CPM uses deterministic times and identifies the critical path and float.

The longest-duration sequence of dependent activities through a project network. It determines the shortest possible project duration, and any delay on it delays the project.

Shortening project duration by adding resources to selected critical activities at extra cost. The aim is to reduce time with minimum increase in total cost.

Systematic examination of how work is done to simplify methods and set time standards. It combines method study of the process with work measurement of the time taken.

An analyst's judgment of a worker's pace relative to normal performance, used to convert observed time to normal time. Allowances are then added to obtain standard time.

A set of published time values for basic motions such as reach and grasp, used to build standard times without direct observation. It supports consistent time standards before production.

A ratio comparing specification width to process spread, typically Cp or Cpk. Values below about 1.33 indicate the process may produce out-of-specification output.

A time-ordered plot of a quality statistic with control limits that signal unusual variation. It distinguishes common-cause from assignable-cause variation in a process.

Deciding whether to accept a lot by inspecting a sample and comparing defects to a plan. Producer's and consumer's risks quantify the chance of wrong decisions.

The output level at which total revenue equals total cost, so profit is zero. It equals fixed cost divided by contribution per unit, and shows the sales needed to avoid loss.

Rules for allocating an asset's cost over its useful life, such as straight-line, declining-balance, and sum-of-years-digits. The choice affects book value and annual cost comparisons.

Comparing alternatives by discounting all future cash flows to a common time zero at a stated interest rate. The option with the higher present worth is preferred.

Choosing whether to produce a component in-house or purchase it externally. The comparison should use relevant incremental costs, not allocated fixed overhead.

A ratio compares two quantities of the same kind; a proportion states equality of two ratios. Cross-multiplication solves for an unknown term in proportion problems.

The difference between new and old values expressed as a percentage of the old value. Successive percentage changes do not simply add; they compound multiplicatively.

The average is the sum divided by count; the weighted average multiplies each value by its weight before dividing by total weight. Weights shift the mean toward heavily weighted values.

Permutations count ordered arrangements, while combinations count unordered selections. The distinction matters whenever the order of chosen items is or is not significant.

The probability of an event given that another event has occurred, computed as the joint probability divided by the condition's probability. It underlies Bayes-type updating problems.

A counting rule for unions of sets that adds individual sizes, subtracts pairwise intersections, and adds back higher-order intersections. It prevents double counting of shared elements.

Reading values and trends from tables, bar charts, line graphs, or pie charts and computing derived quantities. Speed comes from estimating before calculating exactly.

Answering questions about a passage's main idea, inference, tone, or vocabulary using only the given text. Correct options must be supported by evidence in the passage.

Drawing conclusions that follow necessarily from stated premises, or identifying which conclusion does not. Validity depends on structure, not on the truth of the premises.