Balearic PAU Technology & Engineering II cheat sheet

Crystal structures: BCC (Fe-α, low packing factor 0.68), FCC (Fe-γ, Cu, Al, packing factor 0.74), HCP (Zn, Mg, Ti). Allotropic metals change structure with temperature; steel's austenite-martensite transformation underlies hardening.

Mechanical properties from the tensile test: elastic modulus E = σ/ε (Hooke's law, elastic zone), yield strength σy at 0.2% offset, ultimate strength σu, elongation A% = (Lf−L0)/L0 × 100, toughness = area under σ-ε curve.

Hardness scales: Brinell (HB, hard indenter, rough parts), Vickers (HV, diamond pyramid, all hardnesses), Rockwell C (HRC, hardened steels). Approximate conversion: HV ≈ HB for non-austenitic steels; HRC 20–65 spans roughly 240–800 HV.

Fe-C diagram: eutectoid at 0.77% C and 727 °C gives pearlite; <0.8% C hypoeutectoid (ferrite + pearlite), >0.8% hypereutectoid (cementite + pearlite); >2.1% C is cast iron. Quenching forms martensite; tempering restores toughness.

Non-ferrous: Al alloys (density 2.7 g/cm³, corrosion-resistant, low melting), Cu alloys (brass Cu-Zn, bronze Cu-Sn, high conductivity), Ti alloys (high strength/weight, biocompatible, costly machining).

Selection criteria ranked by function: strength/stiffness/stress state, density (specific strength σ/ρ), thermal and electrical conductivity, corrosion and wear resistance, machinability/weldability, cost and availability, recyclability.

Material index minimisation: tie-rod in tension → maximise σy/ρ; beam in bending → maximise σy^(2/3)/ρ; stiff panel → maximise E^(1/3)/ρ. Use Ashby charts to compare families.

Environmental impact: embodied energy (MJ/kg) and carbon footprint (kg CO2e/kg) are largest for Al primary (~170 MJ/kg) and smallest for recycled Al and timber; recycling Al saves ~95% of the energy versus primary production.

Static equilibrium: ΣF = 0 and ΣM = 0 about any point. For a simply supported beam with point load P at distance a from left support of span L: RA = P(L−a)/L, RB = Pa/L; maximum bending moment M = Pa(L−a)/L.

Friction on an incline: block stays at rest if tan θ ≤ μs; sliding acceleration a = g(sin θ − μk cos θ). Belt friction: T1/T2 = e^(μθ) with θ in radians.

Kinematics: uniform acceleration v = v0 + at, s = v0t + ½at², v² = v0² + 2as. Circular motion: v = ωr, an = ω²r = v²/r, at = αr.

Dynamics: Newton's second law ΣF = ma; work W = F·d·cos θ; power P = F·v = M·ω; kinetic energy ½mv²; rotational inertia I and torque M = Iα.

Gear trains: velocity ratio i = ωin/ωout = Zout/Zin (external gears reverse direction). Compound train i = product of driven teeth / product of driver teeth. Module m = d/Z; centre distance a = m(Z1+Z2)/2.

Four-bar linkage Grashof condition: shortest + longest ≤ sum of the other two links → at least one full rotation (crank-rocker). Quick-return ratio = time of working stroke / time of return stroke.

Power transmission: pulley ratio n1D1 = n2D2 (flat belt, no slip); chain drives keep exact ratio; lead screw advance per turn = pitch × number of starts. Efficiency η = Pout/Pin < 1 due to friction.

Cams and followers: base circle radius, lift, dwell, pressure angle; uniform velocity, simple harmonic and cycloidal profiles trade acceleration peaks against vibration.

Ohm's law V = IR; series Req = ΣR; parallel 1/Req = Σ1/R. Kirchhoff: ΣI at node = 0, ΣV around loop = 0. Voltage divider Vx = V·Rx/Req; current divider Ix = I·(Req/Rx).

Power: P = VI = I²R = V²/R. Energy in kWh = P(kW) × t(h). Thevenin equivalent: Vth = open-circuit voltage, Rth = resistance seen with sources deactivated (voltage sources shorted, current sources opened).

Capacitors: C = Q/V, series/parallel opposite to resistors; time constant τ = RC; charge q(t) = CV(1 − e^(−t/τ)). Inductors: L, τ = L/R; energy ½LI².

AC: Vrms = Vpeak/√2; f = 1/T; ω = 2πf. Impedance Z = √(R² + (XL − XC)²), XL = ωL, XC = 1/(ωC); at resonance XL = XC, Z = R, f0 = 1/(2π√(LC)). Power factor cos φ = P/S; P = VrmsIrms cos φ.

Three-phase: line voltage VL = √3·Vphase in star (Y); power P = √3·VL·IL·cos φ. Star delivers 230 V phase from 400 V line in the standard low-voltage distribution.

Electromagnetism: Faraday's law emf = −N·dΦ/dt; Lenz's law opposes the change; force on conductor F = BIL sin θ; transformer V1/V2 = N1/N2 = I2/I1 (ideal, no losses).

Diodes: forward drop ~0.7 V (Si), ~0.3 V (Ge); half-wave rectifier gives Vdc = Vpeak/π, full-wave bridge Vdc = 2Vpeak/π; Zener regulates in reverse breakdown; LED needs a series resistor R = (V − Vf)/I.

Transistors and op-amps: BJT in saturation acts as a switch (VCE ≈ 0.2 V), in active region as amplifier; β = IC/IB. Ideal op-amp: virtual short V+ = V−, infinite input impedance; inverting gain −Rf/Rin, non-inverting 1 + Rf/Rin.

Open loop: no feedback, output depends only on input; fails if disturbances appear. Closed loop: sensor measures output, comparator forms error e = setpoint − measured, controller acts to reduce e.

Transfer function G = Y/X; closed-loop gain = G/(1 + GH) for negative feedback; steady-state error decreases as loop gain increases; stability requires all poles in the left half-plane.

PID control: u = Kp·e + Ki∫e dt + Kd·de/dt. Kp speeds response and reduces error; Ki removes steady-state error but adds overshoot; Kd damps and anticipates but amplifies noise.

Sensors by magnitude: potentiometer (position), LDR (light), NTC thermistor (temperature, R falls with T), strain gauge (force, via Wheatstone bridge), Hall effect (magnetic field, current), ultrasonic/infrared (distance), encoder (angular position and speed).

Actuators: DC motor with H-bridge for bidirectional drive, stepper motor (discrete steps, open-loop positioning), servo motor (closed-loop with encoder), pneumatic/hydraulic cylinders, solenoids, relays.

PLC cycle: read inputs → execute program → update outputs, repeated in scan time. Ladder logic elements: contacts (NO/NC), coils, timers TON/TOF, counters, set/reset.

Robot classification: Cartesian, cylindrical, spherical, SCARA, articulated (6 axes), delta. Degrees of freedom, workspace, payload and repeatability define capability; articulated robots reach the widest workspace.

Boolean algebra: De Morgan (A+B)' = A'·B', (A·B)' = A'+B'; Karnaugh maps minimise combinational logic before implementation in gates or PLC logic.

Pascal's principle: pressure transmitted undiminished; F1/A1 = F2/A2. Hydraulic press force multiplication equals the area ratio; the smaller piston must travel proportionally further (volume conserved).

Flow and speed: Q = A·v, so cylinder extension speed v = Q/Apiston, retraction v = Q/(Apiston − Arod). Pressure p = F/A; hydraulic systems use oil at 50–300 bar, pneumatics air at 4–8 bar.

Cylinder force: extension F = p·A (full bore), retraction F = p·(A − Arod). Single-acting uses one port and a spring return; double-acting uses two ports for both strokes.

Circuit symbols: compressor/pump (circle with triangle), filter/regulator/lubricator (FRL unit), 5/2 directional valve (five ports, two positions, two actuators), non-return valve, throttle, pressure relief, accumulator, reservoir.

Directional valve notation: number of positions drawn as squares, ports labelled A, B, P, R/S, T; centre condition determines pump unloading and cylinder locking.

Speed control: meter-in throttles supply, meter-out throttles exhaust (more stable for overrunning loads); flow control valves set actuator speed, pressure relief valves set maximum system pressure.

Pneumatic advantages: clean, fast, cheap, overload-safe; limits: compressibility gives imprecise positioning, low force, noise. Hydraulics: high force density, rigid control, but leaks and higher cost.

Circuit design sequence: define actuators and sequence, choose valves and pressure rating, size pipes for velocity limits (air 10–20 m/s, oil 2–5 m/s), add relief, filtration and safety interlocks.

Machining parameters: cutting speed vc = π·D·n/1000 (m/min), feed f (mm/rev), depth of cut a. Material removal rate Q ≈ vc·f·a. Turning uses a lathe, milling uses a rotating cutter, drilling uses a bit.

Forming processes: rolling (plates/profiles), forging (grain flow, high strength), extrusion (constant cross-section), drawing (wire), stamping and deep drawing (sheet), bending. Cold working raises strength but lowers ductility.

Casting: sand casting for complex shapes, die casting for non-ferrous high-volume, investment casting for precision. Shrinkage allowance and draft angle are design requirements.

Joining: arc and MIG/TIG welding, spot welding for sheet, brazing/soldering (below base-metal melting), adhesive bonding, riveting, threaded fasteners. Welding heat-affected zone weakens some alloys.

Non-traditional and additive: laser cutting, waterjet, EDM for hard conductive materials, 3D printing (FDM, SLA, SLS) for prototypes and low-volume parts.

Production organisation: job shop (low volume, flexible), batch, mass/line production (high volume, specialised), lean manufacturing (just-in-time, kanban, poka-yoke, 5S, continuous improvement).

Costs: total cost = fixed + variable × units; break-even point Q = fixed cost / (unit price − unit variable cost). Automation lowers unit cost at high volume but raises fixed cost.

Quality and metrology: tolerance, dimensional inspection with calliper/micrometer, SPC control charts, ISO 9001 quality management; six sigma targets 3.4 defects per million.

Project phases: needs identification → feasibility study → preliminary design → detailed design → prototyping and testing → production → marketing and disposal. Iteration loops back through phases.

Design methodology: problem statement, functional analysis, specifications (constraints and requirements), brainstorming, selection matrices, detailed design, verification. Concurrent engineering integrates design and manufacturing.

Technical drawing standards: ISO/UNE first-angle projection (European) versus third-angle (US); views, sections, auxiliary views, scale, dimensioning rules; never duplicate a dimension.

Tolerances and fits: ISO 286 hole basis H, shaft letters a–zc; clearance fit, transition fit, interference fit. Geometric tolerancing (GD&T): straightness, flatness, concentricity, perpendicularity, position.

Representation: lines (continuous for visible, dashed for hidden, chain for centre lines), surface roughness Ra (µm), welding symbols, thread notation M10×1.5, chamfers and fillets.

Budget: direct costs (materials, labour, machinery), indirect costs (overhead, administration), amortisation, contingency (typically 5–15%), VAT applied to the final price.

Planning tools: Gantt chart (time schedule), PERT/CPM network (critical path = longest path, zero slack), resource levelling; earned value tracks cost and schedule deviation.

Documentation: technical report, bill of materials, assembly and exploded drawings, user manual, maintenance plan, CE marking and applicable EU/Balearic safety regulations.

Innovation types: product, process, organisational and marketing. Technology push versus market pull; the linear model versus the chain-linked model of innovation.

Technology transfer channels: patents and licences, spin-offs, university-industry contracts, joint ventures, open innovation. Patent grants exclusivity for 20 years; utility models have shorter terms.

R&D indicators: investment as % of GDP (Spain ~1.4%, EU target 3%), patents per million inhabitants, researchers per thousand employed. Balearic economy is service-dominated (tourism), so innovation policy targets diversification.

Life-cycle analysis (LCA) phases per ISO 14040: goal and scope → inventory (LCI) → impact assessment (LCIA) → interpretation. Functional unit is the reference for all comparisons.

Impact categories: global warming potential (kg CO2e), eutrophication, acidification, water use, resource depletion, land use. Carbon footprint is a single-indicator subset of LCA.

Circular economy strategies ranked by value: refuse, reduce, reuse, repair, remanufacture, recycle, recover energy, dispose. Design for disassembly and modularity enable repair and recycling.

Sustainability: Brundtland definition (meeting present needs without compromising future generations); triple bottom line (economic, social, environmental); UN Sustainable Development Goals, Agenda 2030.

Environmental management and regulation: ISO 14001, EMAS, eco-labels, extended producer responsibility, WEEE for electronic waste, REACH for chemicals, Ecodesign directive for energy-related products.