Andalusia PAU Technology and Engineering II cheat sheet

Stress σ = F/A₀ (Pa); engineering strain ε = (L−L₀)/L₀ (dimensionless); Young's modulus E = σ/ε in the elastic (linear) region, measured as the slope of the σ–ε curve.

Hardness scales are not interchangeable: Brinell (HB) uses a 10 mm ball for coarse/grey cast iron and steel; Vickers (HV) uses a 136° diamond pyramid and suits thin or hardened layers; Rockwell uses defined scales (e.g. HRC for hardened steel, HRB for soft metals).

Ductile fracture shows necking and cup-and-cone morphology; brittle fracture is flat and cleavage-like with little deformation. Charpy impact tests measure absorbed energy (J) and reveal the ductile–brittle transition temperature.

Crystal defects: point (vacancies, interstitials), line (edge and screw dislocations), planar (grain boundaries, twins). Plastic deformation occurs mainly by dislocation glide; grain refinement raises yield strength (Hall–Petch).

Steels: carbon content up to ~2.1 %; low-carbon (<0.25 %) is weldable and ductile, medium-carbon (0.25–0.6 %) is heat-treatable, high-carbon (>0.6 %) is for springs and tools. Alloying elements: Cr for corrosion resistance, Ni for toughness, Mn for hardenability.

Heat treatments: annealing (soften, relieve stresses), normalizing (refine grain), quenching (form martensite), tempering (restore toughness after quench). Case hardening (carburizing, nitriding) hardens only the surface layer.

Non-ferrous: aluminium alloys (2xxx Al–Cu, 7xxx Al–Zn) give high strength-to-weight ratio; copper alloys (brass Cu–Zn, bronze Cu–Sn) give conductivity and wear resistance; titanium offers high strength with low density and corrosion resistance.

Selection criteria: density, strength, stiffness, toughness, thermal/electrical conductivity, corrosion resistance, machinability, weldability, cost and recyclability. Ashby-style charts plot one property against another to identify candidate materials.

Static equilibrium: ΣF = 0 and ΣM = 0. For a simply supported beam with point load P at mid-span L: R = P/2, Mmax = PL/4. For a uniformly distributed load q: Mmax = qL²/8.

Axial stress σ = N/A; shear stress τ = V/A; bending stress σ = M·y/I with y the distance from the neutral axis; maximum at the outer fibre (y = c).

Deflection of a simply supported beam under central load: δ = PL³/(48EI); under uniform load: δ = 5qL⁴/(384EI). Cantilever with end load: δ = PL³/(3EI).

Torsion of a circular shaft: τmax = T·r/J (J = πd⁴/32), angle of twist θ = TL/(GJ). Solid shaft transmits torque T = P/ω, with ω in rad/s.

Mechanisms: degrees of freedom (Grübler) M = 3(n−1) − 2j₁ − j₂ for planar linkages. Four-bar linkage, slider-crank and cam mechanisms are the standard building blocks.

Gear trains: velocity ratio i = ω₁/ω₂ = z₂/z₁ for a simple pair; compound trains multiply ratios. Module m = d/z (mm); circular pitch p = πm.

Bearings: rolling bearings (deep-groove ball, tapered roller, needle) for low friction and easy maintenance; sliding bearings for high loads and quiet operation. Selection uses dynamic load rating C and equivalent load P.

Failure criteria: Tresca (maximum shear stress) and von Mises (distortion energy) for combined loading; fatigue design uses S–N curves and the endurance limit, with stress concentration factors Kt applied to nominal stress.

Ohm's law V = I·R; power P = V·I = I²R = V²/R. Series resistors add (R = ΣRi); parallel resistors add reciprocally (1/R = Σ1/Ri).

DC circuits: Kirchhoff's current law (sum of currents at a node = 0) and voltage law (sum of voltages around a loop = 0). Thévenin and Norton equivalents simplify linear networks.

Capacitors: C = Q/V, energy W = ½CV², time constant τ = RC. Inductors: V = L·di/dt, energy W = ½LI², time constant τ = L/R. Impedance: Z_R = R, Z_C = 1/(jωC), Z_L = jωL.

AC: RMS value = peak/√2; power factor cos φ = P/S; reactive power Q = S·sin φ. Three-phase systems: line voltage = √3 × phase voltage in star connection; total power P = √3·V_L·I_L·cos φ.

Transformers: V₁/V₂ = N₁/N₂ = I₂/I₁; ideal transformer conserves apparent power. Losses: copper (I²R) and iron (hysteresis + eddy currents).

DC machines: shunt, series and compound excitation; EMF E = k·Φ·ω. Induction motors: slip s = (ns − n)/ns with ns = 60f/p; synchronous speed depends on frequency and pole pairs.

Semiconductors: diode forward drop ≈ 0.7 V (Si); Zener for voltage regulation; BJT as switch in saturation/cut-off; MOSFET as voltage-controlled switch. Rectifiers: half-wave and full-wave bridge.

Digital electronics: logic gates (AND, OR, NOT, NAND, NOR, XOR), truth tables, Karnaugh maps for simplification, combinational vs sequential circuits (flip-flops, counters, registers).

Sensors and signal conditioning: Wheatstone bridge for resistive sensors, operational amplifier configurations (inverting, non-inverting, differential), instrumentation amplifier for low-level signals.

Open-loop control acts without feedback; closed-loop control measures the output and compares it with the setpoint to compute an error. Feedback reduces sensitivity to disturbances but can cause instability.

PID controller: u(t) = Kp·e + Ki·∫e dt + Kd·de/dt. Proportional reduces rise time, integral eliminates steady-state error, derivative reduces overshoot but amplifies noise.

Transfer function G(s) = Y(s)/X(s) for LTI systems. First-order response: time constant τ, reaches 63 % of final value in τ, 95 % in 3τ. Second-order: damping ratio ζ and natural frequency ωn.

Stability: a linear system is stable if all poles of the closed-loop transfer function have negative real parts. Routh–Hurwitz criterion and Bode/Nyquist plots are standard tools.

Sensors: inductive/capacitive proximity, photoelectric, ultrasonic, encoders (incremental and absolute), thermocouples, strain gauges, LVDT. Selection depends on range, resolution, response time and environment.

Actuators: DC and stepper motors, servomotors, solenoids, piezoelectric actuators. Stepper motors move in discrete steps (e.g. 1.8° per step); microstepping improves resolution.

PLCs: cyclic scan (input read → program execution → output write). Ladder logic uses contacts (XIC, XIO), coils (OTE), timers (TON, TOF) and counters (CTU).

Robotics: degrees of freedom, workspace, end-effector, joints (revolute, prismatic). Forward kinematics computes end-effector pose from joint variables; inverse kinematics does the reverse.

Industrial communication: fieldbus and Ethernet-based protocols (PROFIBUS, PROFINET, Modbus, EtherCAT) connect PLCs, sensors and drives; safety functions use dedicated safety relays or safety PLCs.

Pascal's law: pressure applied to a confined fluid is transmitted undiminished in all directions. Force multiplication: F₁/A₁ = F₂/A₂; hydraulic press gives large force from small input.

Flow rate Q = A·v (continuity). Hydraulic power P = p·Q. Pressure drop across a restriction depends on flow and orifice area; valves control flow and direction.

Hydraulic components: pump (gear, vane, piston), reservoir, filter, pressure relief valve, directional control valve, flow-control valve, accumulator, actuator (cylinder or motor).

Pneumatic components: compressor, air receiver, dryer, filter-regulator-lubricator (FRL), directional valves, flow regulators, cylinders. Air is compressible, so positioning is less precise than hydraulics.

Cylinder force: F = p·A (extend) and F = p·(A − A_rod) (retract). Cylinder speed v = Q/A. Cushioning and end-of-stroke damping protect the cylinder.

Valve designation: number of ports and positions (e.g. 5/2 valve = 5 ports, 2 positions). Solenoid, pilot, manual and spring-return actuation are common.

Circuit symbols: ISO 1219 symbols for pumps, cylinders, valves, filters and accumulators. Lines represent flow; dashed lines indicate pilot or drain connections.

Safety: pressure relief valves protect against overpressure; lockout/tagout before maintenance; air is not a lubricant and moisture must be removed by dryers and filters.

Efficiency: hydraulic systems have high power density but pressure losses in pipes and valves reduce efficiency; pneumatic systems are simple and clean but have low efficiency due to compression heat losses.

Machining: turning (lathe, cylindrical surfaces), milling (rotating cutter, flat surfaces), drilling, grinding (fine finish). Cutting speed v = π·D·n; feed and depth of cut determine material removal rate.

Forming: rolling, forging, extrusion, drawing, stamping. Hot working reduces strength and allows large deformation; cold working improves surface finish and strength (strain hardening).

Joining: welding (arc, MIG/MAG, TIG, resistance), soldering/brazing, adhesive bonding, riveting, bolting. Weldability depends on material composition and heat input.

Casting: sand casting, die casting, investment casting, continuous casting. Shrinkage allowance compensates for solidification contraction; draft angles ease pattern removal.

Metrology: vernier caliper (0.02 or 0.05 mm resolution), micrometer (0.01 mm), dial gauge, gauge blocks. Measurement uncertainty and calibration are essential for quality.

Tolerances and fits: ISO system uses holes (H) and shafts (h); clearance, transition and interference fits. Surface roughness Ra is expressed in micrometres.

Production organization: job shop, batch, mass and lean production. Just-in-time (JIT), kanban, 5S and total quality management (TQM) reduce waste and inventory.

CNC and CAM: G-code and M-code programming, tool offsets, work coordinate systems. CAD/CAM integration generates toolpaths from 3D models.

Automation: robots, conveyors, AGVs and automated inspection. Flexible manufacturing systems (FMS) combine CNC machines, material handling and control software.

Energy units: 1 kWh = 3.6 MJ; 1 tep ≈ 41.87 GJ. Power P = E/t; efficiency η = useful energy output / energy input × 100 %.

Renewable sources: solar photovoltaic (irradiance ~1000 W/m² at standard test conditions), solar thermal, wind (P ∝ v³), hydro, biomass, geothermal. Intermittency requires storage or backup.

Fossil fuels and nuclear: combustion releases CO₂; nuclear fission releases large energy per mass but produces radioactive waste. Life-cycle assessment (LCA) compares environmental impact.

Energy efficiency: insulation, heat recovery, high-efficiency motors (IE3/IE4), LED lighting, variable-speed drives. Energy audits identify savings.

Environmental impact: greenhouse gases, acid rain (SO₂, NOx), particulate matter, water use. Carbon footprint quantifies CO₂-equivalent emissions.

Project methodology: phases (initiation, planning, execution, monitoring, closure), work breakdown structure (WBS), Gantt chart, critical path method (CPM), budget and risk analysis.

Technical documentation: specifications, technical reports, bill of materials, user manuals, maintenance plans. Standards and regulations (e.g. CE marking, ISO 14001) apply.

Sustainability: circular economy (reduce, reuse, recycle), eco-design, end-of-life management, renewable integration, energy storage (batteries, pumped hydro, hydrogen).

Standard views (first-angle projection, ISO): front, top and side views aligned. In first-angle projection the top view is placed below the front view; in third-angle (ISO/ANSI) it is placed above.

Scale: drawing scale = drawing dimension / real dimension. Standard scales: 1:1, 1:2, 1:5, 1:10, 2:1, 5:1. Always state the scale on the drawing.

Dimensioning: dimension lines with arrows, extension lines, numerical value in the unit stated (mm by default). Avoid duplicate dimensions; place dimensions outside the outline where possible.

Tolerances: general tolerances (ISO 2768), fit designation (e.g. H7/g6), geometric tolerancing (GD&T) with symbols for flatness, perpendicularity, concentricity and position.

Section views: cutting plane line, hatching at 45°, half sections and offset sections. Sections reveal internal features that hidden lines would obscure.

Line types: continuous thick for visible edges, dashed for hidden edges, chain line for centre lines, thin continuous for dimension and hatching lines.

Standard parts: threads (M for metric, e.g. M10), keys, pins, bearings, springs. Thread representation uses simplified or schematic conventions.

CAD: parametric modelling with constraints, sketches, extrusions, revolutions, assemblies and drawings. Layers, blocks and templates organize drawings; file formats include DXF, DWG, STEP and IGES.

Drawing standards: ISO, UNE (Spanish), ANSI and DIN. Title block contains drawing number, scale, projection method, tolerances and approval signatures.