Valencian Community PAU Technology & Engineering II cheat sheet

Crystal structures: BCC (α-Fe, ferrite), FCC (γ-Fe, austenite, Al, Cu), HCP (Mg, Zn, Ti). FCC metals are ductile because 12 slip systems exist; HCP metals are brittle with only 3.

Allotropic transformation of pure iron: BCC ferrite below 912 °C, FCC austenite between 912 and 1394 °C, BCC delta above 1394 °C up to 1538 °C melting.

Tensile test gives the stress-strain curve: elastic zone obeys Hooke's law σ = E·ε; the yield strength is measured at 0.2 % permanent strain; UTS is the maximum stress; ductility is the elongation at break.

Hardness scales: Brinell (10 mm ball, HBW), Vickers (pyramid, HV, valid for any material), Rockwell C (120° cone, HRC, used for hardened steels). Empirical relation: tensile strength (MPa) ≈ 3.45 × HBW.

Heat treatments of steel: tempering relieves stresses after quenching; annealing softens and refines grain; normalising gives uniform fine pearlite; quenching in water or oil produces martensite (hard, brittle).

Jominy test measures hardenability (depth of hardening); a steel with high hardenability needs slower cooling and resists cracking in thick sections.

Selection criteria: density (aerospace → Al, Ti, composites), specific stiffness, corrosion resistance (stainless steel needs ≥ 10.5–12 % Cr), electrical conductivity (Cu, Al), cost per kg and recyclability.

Non-destructive testing: ultrasound detects internal defects, X-rays reveal porosity and inclusions, dye penetrant and magnetic particles detect surface cracks (magnetic only on ferromagnetic materials).

Mechanical advantage of a lever: MA = effort arm / load arm; three classes defined by the position of the fulcrum relative to load and effort.

Gear trains: velocity ratio i = ω_in/ω_out = Z_out/Z_in; compound trains multiply the ratios; power is conserved minus losses, so torque ratio equals the velocity ratio.

Pulley systems: a movable pulley halves the effort; in a block and tackle the effort is the load divided by the number of supporting rope strands.

Inclined plane and wedge: F = P·sin α for a frictionless plane; the screw converts torque into axial force, F = 2π·T/(p·η), where p is the pitch.

Friction: F_r = μ·N; static friction coefficient is larger than kinetic; efficiency η = useful work / input work.

Structural equilibrium: ΣF = 0 and ΣM = 0; a bar in tension is verified with σ = F/A ≤ σ_adm; Euler buckling load P_cr = π²·E·I/L² for a pinned strut.

Beams: simply supported beam with central point load P gives M_max = P·L/4 and maximum deflection δ = P·L³/(48·E·I); bending stress σ = M·y/I.

Triangulation gives rigidity to trusses; joints are assumed pinned, and only axial forces act on the bars (tension or compression).

Ohm's law V = I·R; series resistors add (R_eq = ΣR), parallel resistors satisfy 1/R_eq = Σ(1/R); voltage dividers give V_out = V·R2/(R1+R2).

Power and energy: P = V·I = I²·R = V²/R; energy in kWh = P(kW)·t(h); domestic supply in Spain is 230 V, 50 Hz single phase.

Three-phase systems: line voltage 400 V, phase voltage 230 V, relation V_L = √3·V_ph; star connection shares the neutral, delta connection has no neutral.

Alternating current: X_L = 2πf·L, X_C = 1/(2πf·C); impedance Z = √(R² + (X_L − X_C)²); resonance occurs when X_L = X_C.

Transformers: V1/V2 = N1/N2 = I2/I1; ideal transformer conserves apparent power; real efficiency is 95–99 % for large units.

Diode: conducts in forward bias above ≈ 0.7 V (Si) or 0.3 V (Ge); rectifier bridge converts AC to pulsating DC; a Zener diode regulates voltage in reverse breakdown.

Operational amplifier: ideal model has infinite gain and input impedance; inverting gain = −R_f/R_in, non-inverting gain = 1 + R_f/R_in.

Digital logic: truth tables for AND, OR, NOT, NAND, NOR, XOR; Karnaugh maps simplify Boolean expressions; De Morgan's laws: ¬(A·B) = ¬A + ¬B.

Open-loop control has no feedback and cannot correct disturbances; closed-loop control measures the output with a sensor and compares it with the setpoint.

Block diagram elements: setpoint (reference), comparator, controller, actuator, process, sensor and feedback loop; error e = setpoint − measured value.

PID controller: proportional action responds to present error, integral action removes steady-state offset, derivative action damps oscillations and anticipates change.

Stability: a system oscillates when the loop gain is too high; the transient response is described by rise time, overshoot, settling time and steady-state error.

On/off (two-position) control switches the actuator between two states with hysteresis to avoid chattering; used in thermostats and level controls.

Sensors and transducers: thermocouple, thermistor (NTC/PTC), LDR, strain gauge, inductive and capacitive proximity sensors, encoders for position and speed.

Pneumatic and hydraulic actuators: force F = p·A; hydraulic systems work at high pressure with incompressible oil; pneumatic systems are fast and clean but less precise.

Programmable logic controllers execute a cyclic scan: read inputs, execute the program, update outputs; ladder logic uses contacts and coils, and GRAFCET models sequential automation.

Energy units: 1 kWh = 3.6·10⁶ J; 1 tep = 41.87 GJ; power is energy per unit time, P = E/t.

Thermal machines: Carnot efficiency η = 1 − T_f/T_c with absolute temperatures; real efficiency is always lower; a heat pump has COP = Q_c/W.

Fossil fuels (coal, oil, gas) dominate primary energy but emit CO₂; nuclear fission releases about 8·10¹³ J per kg of U-235 and produces long-lived radioactive waste.

Renewables: photovoltaic efficiency of commercial panels is 18–22 %; wind power P = ½·ρ·A·v³ depends on the cube of wind speed; hydropower P = ρ·g·Q·H·η.

Electric power transmission uses high voltage to reduce I²R losses; step-up and step-down transformers link generation, transport and distribution.

Environmental impact: greenhouse effect, acid rain (SO₂, NOₓ), ozone depletion (CFCs), eutrophication; the ecological footprint measures land needed per capita.

Energy efficiency measures: LED lighting, cogeneration, heat recovery, building insulation; the energy label rates appliances from A to G in the current EU scale.

Sustainable development balances economic growth, social equity and environmental protection; life-cycle analysis evaluates impact from raw material to disposal.

Project phases: identification of the need, feasibility study, preliminary design, detailed design, construction, testing and final report with budget.

Project documents: memory (objectives, calculations, annexes), plans (drawings), specifications (technical conditions) and budget (measurements, unit prices, totals).

Orthographic projection (first-angle, ISO E) places the top view below the front view and the left view to the right; the third-angle system (ANSI) places them differently.

Scale = drawing dimension / real dimension; common scales are 1:1, 1:2, 1:5, 1:10, 1:100; dimension lines carry the real measurement regardless of scale.

Isometric perspective uses axes at 120° and natural or reduced lengths along them; cavalier and cabinet perspectives keep the front face true to shape.

Tolerances and fits: ISO system with holes H and shafts h; clearance fit, interference fit and transition fit; surface roughness is given by Ra in micrometres.

CAD/CAM/CAE: CAD creates geometry, CAE performs simulation (FEA, CFD), CAM generates toolpaths for CNC machines; parametric modelling uses constraints and parameters.

ICT in engineering: spreadsheets for calculations and budgets, databases for inventories, project management software (Gantt, PERT) for scheduling.