Catalonia PAU Technology and Engineering II cheat sheet
Catalonia PAU Technology and Engineering II · Keep the key ideas within reach.
Materials: properties, structure, selection and environmental criteria
Mechanical properties: hardness (resistance to indentation, Mohs/Rockwell/Brinell), toughness (energy absorbed before fracture), ductility (% elongation at break), stiffness (Young's modulus E = σ/ε in the elastic region).
Density ρ = m/V; specific strength = σ/ρ and specific stiffness = E/ρ decide selection where mass matters (aerospace, transport).
Crystalline defects: point (vacancy, interstitial), line (edge and screw dislocations), planar (grain boundary). Plastic deformation proceeds by dislocation slip; grain refinement raises yield strength (Hall–Petch).
Fe–C equilibrium: ferrite (soft, low C), austenite (FCC, high T), cementite Fe3C (hard, brittle), pearlite (lamellar ferrite+cementite). Eutectoid at 0.77 % C, ~727 °C.
Heat treatments: annealing (soften, relieve stress), normalizing, quenching (martensite, hard and brittle), tempering (restore toughness). Surface hardening: carburizing, nitriding, induction.
Corrosion is an electrochemical cell (anode oxidizes, cathode reduces); prevention by cathodic protection, sacrificial anodes (Zn on steel), coatings, alloying (Cr in stainless steel forms passive Cr2O3 layer).
Environmental selection criteria: recyclability, embodied energy, toxicity, biodegradability, energy recovery (LCA thinking). Thermoplastics are recyclable; thermosets and composites are hard to recycle.
Material families and typical values: metals (E ≈ 70–210 GPa), ceramics (high hardness, brittle, E ≈ 300 GPa), polymers (E ≈ 1–4 GPa, low T resistance), composites (anisotropic, high specific properties).
Mechanical systems and machine elements: transmission, support, union and motion conversion
Gear ratio i = z2/z1 = n1/n2 = ω1/ω2 = M2/M1 (ideal); with efficiency η, M2 = M1·i·η. Module m = d/z; center distance a = m(z1+z2)/2.
Belt and chain drives: i = n1/n2 = D2/D1 (pulleys); belt slip lowers efficiency, chain drives keep a fixed ratio. Crossed belt reverses rotation direction.
Screws: torque to raise load M = F·p/(2π·η) for a square thread with pitch p; self-locking when friction angle exceeds lead angle.
Bearings: radial (deep-groove ball), axial/thrust, tapered roller (combined loads), needle (compact). Plain bearings rely on hydrodynamic lubrication.
Couplings and clutches transmit torque; a clutch allows engagement/disengagement, a coupling is permanent or flexible (absorbs misalignment).
Unions: bolted (removable), riveted (permanent, shear load), welded (permanent, continuous), adhesive, keyed and splined shafts (transmit torque, allow axial sliding for splines).
Motion conversion: crank–slider (rotation ↔ translation, stroke = 2·crank radius), cam–follower (profile defines displacement law), four-bar linkage (Grashof condition for full rotation), rack and pinion (rotation ↔ linear).
Mechanical advantage and efficiency: η = P_out/P_in = (F_out·v_out)/(F_in·v_in); losses from friction, slip and deformation.
Springs: Hooke's law F = k·x; series 1/k = 1/k1 + 1/k2, parallel k = k1 + k2.
Electrical and electronic circuits: DC and AC, components, analysis and measurement
Ohm's law V = I·R; power P = V·I = I²R = V²/R. Kirchhoff: ΣI at node = 0, ΣV around loop = 0.
Series: R_eq = ΣR, same current. Parallel: 1/R_eq = Σ1/R, same voltage. Voltage divider V_out = V·R2/(R1+R2).
Capacitor i = C·dV/dt, energy ½CV²; series 1/C = Σ1/C, parallel C = ΣC. Inductor v = L·di/dt, energy ½LI².
AC: V_rms = V_peak/√2; impedance Z = √(R² + (X_L − X_C)²); X_L = 2πfL, X_C = 1/(2πfC); resonance f = 1/(2π√(LC)).
Three-phase: line voltage V_L = √3·V_phase in star connection; P = √3·V_L·I_L·cos φ. Power factor correction raises cos φ with parallel capacitors.
Diodes: forward drop ~0.7 V (Si); half-wave and bridge rectifiers; Zener for voltage regulation; LED needs a series resistor R = (V_s − V_f)/I_f.
Transistor as switch: cutoff (no base current) and saturation (V_CE ≈ 0.2 V); relay and optocoupler isolate control from power.
Measurement: voltmeter in parallel (high impedance), ammeter in series (low impedance), ohmmeter on de-energized circuit. Multimeter errors: loading effect, tolerance, resolution.
Safety and protection: fuses and circuit breakers (overcurrent), ground/earth connection, differential (RCD) protection against leakage.
Control systems and automation: open/closed loop, sensors, actuators, logic and block diagrams
Open loop: no feedback, output not compared with reference. Closed loop: sensor feedback, error e = r − b, controller acts on e.
Block diagram algebra: series G1·G2; parallel G1+G2; feedback transfer function G/(1+G·H) for negative feedback.
PID: u = Kp·e + Ki∫e dt + Kd·de/dt. P reduces steady error, I eliminates it, D damps oscillation and speeds response.
Stability and response: gain too high causes oscillation; dead band, hysteresis and transport delay degrade accuracy.
Sensors: potentiometer (position), LDR (light), NTC/PTC thermistor and thermocouple (temperature), strain gauge (force), Hall/reed (magnetic), inductive/capacitive/ultrasonic (proximity), encoder (angular position and speed).
Actuators: DC/stepper/servo motor, solenoid, pneumatic cylinder, relay, contactor; a stepper moves in discrete steps per pulse.
Boolean logic: AND, OR, NOT, NAND, NOR, XOR; truth tables; De Morgan: ¬(A·B) = ¬A + ¬B. Karnaugh maps simplify expressions.
Sequential control: GRAFCET/stage diagram with steps, transitions and actions; PLC ladder logic implements the same sequences.
Safety in automation: emergency stop hardwired, limit switches as end-of-travel, guards and interlocks.
Pneumatic and hydraulic systems: components, schematics and circuit design
Pressure p = F/A; flow Q = v·A (continuity); hydraulic power P = p·Q. Pascal's principle: pressure transmits equally in a confined fluid.
Pneumatics uses compressible air (fast, clean, low force, ~6 bar typical); hydraulics uses incompressible oil (high force, precise, high pressure).
Cylinder force: extension F = p·A_piston; retraction F = p·(A_piston − A_rod). Speed controlled by flow-control valve (meter-in or meter-out).
Components: compressor/pump, reservoir, filter, pressure regulator, accumulator, directional valve, non-return valve, flow-control valve, actuator.
Directional valves designated by ports and positions (e.g. 5/2, 3/2); actuation types: manual, lever, pedal, solenoid, pilot, spring return.
Circuit symbols: ISO 1219 conventions; lines for working lines, dashed for pilot, dotted for drain. Numbering of valves and actuators in the schematic.
Speed control: meter-out gives better control of a pneumatic cylinder under overrunning load; meter-in is simpler.
Maintenance and safety: air treatment (filter–regulator–lubricator), avoiding leaks, pressure relief valve, safe venting before disassembly.
Manufacturing and production: processes, machining, forming, joining and quality
Machining by chip removal: turning (lathe, rotational), milling (fracture/face), drilling, grinding (finishing). Cutting speed v = π·D·n; feed and depth of cut set productivity and finish.
Forming: forging (hot, grain flow), rolling, extrusion, drawing, stamping and bending (sheet metal), with springback compensation and bend allowance.
Casting: sand casting (complex shapes, rough finish), die casting (non-ferrous, high volume), investment casting (precision). Shrinkage allowance and draft angle required.
Joining: welding (arc, MIG/MAG, TIG, resistance spot), soldering (electronics), brazing, riveting, bolting, adhesive bonding.
Non-conventional and additive: laser/water-jet cutting, EDM, FDM/SLA/SLS 3D printing (layer-based, minimal tooling, good for prototypes).
Metrology: caliper (0.02–0.05 mm), micrometer (0.01 mm), dial gauge, gauge blocks; measurement uncertainty and calibration.
Quality: tolerances and fits (hole-basis H7/g6), surface roughness Ra, control charts, sampling, ISO 9001 quality management.
Production organization: lean manufacturing, just-in-time, 5S, kanban, and automation (CNC, robots) for repeatability.
Technical drawing and graphical expression: views, dimensioning, sections and CAD conventions
First-angle (European) projection: the object is between observer and plane; the view from the left is placed on the right. Third-angle (ISO/ASME US) is the mirror arrangement.
Standard views: front (elevation), top (plan), side (profile). Hidden edges shown dashed; center lines for axes of symmetry and holes.
Dimensioning rules: dimension lines parallel to the measured edge, extension lines from the object, arrows at intersections, dimensions in mm without unit, never duplicated.
Sections: cutting plane indicated by a chain line with arrows and letters; hatch lines at 45° for the cut material; half sections and offset sections for symmetric parts.
Scale: 1:1, 1:2 (reduction), 2:1 (enlargement); title block with scale, projection method, material and tolerance class.
Tolerances and fits on drawings: nominal size, upper/lower deviation, geometric tolerancing (GD&T: flatness, concentricity, position).
CAD conventions: layers for lines, dimensions and hidden edges; parametric modeling (sketch → constraints → features); orthographic views generated from a 3D model.
Surface finish symbols and welding symbols follow ISO 1302 and ISO 2553; note general roughness in the title block.
Energy, resources and sustainability: sources, conversion, efficiency and environmental impact
Energy units: 1 kWh = 3.6 MJ; power P = E/t; efficiency η = useful energy out/energy in, always < 1.
Renewables: solar PV (η ≈ 15–22 %), solar thermal, wind (P ∝ v³, Betz limit 16/27), hydro, biomass, geothermal, tidal.
Non-renewables: coal, oil, natural gas (fossil, CO2), nuclear fission (no CO2 but radioactive waste).
Conversion chain: primary source → conversion (turbine, generator, motor, fuel cell) → transport/distribution → end use; each stage has losses.
Environmental impact: greenhouse gases, acid rain (SO2, NOx), particulates, thermal pollution, land use, water use; life-cycle assessment (LCA) from extraction to disposal.
Energy efficiency measures: insulation, LED lighting, variable-speed drives, heat recovery, cogeneration (CHP), demand management.
Sustainability: circular economy (reduce, reuse, recycle), renewable share, carbon footprint, energy payback time of a system.
Electricity grid: base load vs peak load, storage (pumped hydro, batteries), distributed generation and smart grids.
Product design, projects and technological innovation: methods, documentation and evaluation
Design process: need identification → specifications → conceptual design → detailed design → prototyping → testing → production. Iterative, with feedback loops.
Specifications (PDS): functions, constraints, target values, standards, cost, safety, ergonomics and environmental requirements.
Creativity methods: brainstorming, morphological analysis, TRIZ, functional analysis, benchmarking; evaluation matrices (weighted criteria) to select solutions.
Documentation: technical report, drawings, bill of materials (BOM), user manual, maintenance plan, budget and schedule (Gantt).
Project management: work breakdown structure (WBS), critical path, milestones, risk analysis, quality control at each phase.
Prototyping and testing: virtual (CAD/CAE simulation) and physical (3D printing, mock-ups); design of experiments and validation against specifications.
Innovation and IP: incremental vs disruptive innovation, patents and utility models, technology readiness level (TRL).
Evaluation criteria: technical feasibility, economic viability (cost, payback), safety, environmental impact, usability and maintainability.