Basque PAU Technology & Eng II cheat sheet
Basque PAU Technology & Eng II · Keep the key ideas within reach.
Materials: properties, structure, testing and selection
Density ρ = m/V; specific strength = σy/ρ - key for aerospace and transport selection where mass dominates.
Elastic modulus E is the slope of the linear σ–ε region; Hooke's law σ = E·ε valid up to the proportional limit.
Ductility measured as elongation at break A% = (Lf − L0)/L0 × 100, or reduction of area Z%.
Hardness scales are not interchangeable: Brinell (HB, hard indenters, coarse materials), Vickers (HV, universal, diagonal-based), Rockwell (HRC for hardened steel, HRA/B for thin or soft).
Toughness = energy absorbed before fracture (area under σ–ε curve); ceramics are hard but brittle (low KIC), metals tough.
Crystal structures: BCC (Fe-α, low ductility at low T), FCC (Al, Cu, austenite - ductile, many slip systems), HCP (Mg, Ti - limited slip, anisotropic).
Strengthening mechanisms: grain refinement (Hall–Petch σy = σ0 + k/√d), solid solution, precipitation, cold work (strain hardening), dispersion.
Fe–C diagram: eutectoid at 0.77 %C, 727 °C → pearlite; austenite (FCC) transforms to martensite on fast quench (BCT, hard and brittle); tempering restores toughness.
Selection uses Ashby charts: plot two properties on log axes, performance index lines (e.g. E^(1/2)/ρ for stiff lightweight beams) select the material class.
Mechanical systems and mechanisms: kinematics, dynamics, transmission and transformation
Four-bar Grashof condition: shortest + longest ≤ sum of the other two links ⇒ at least one full rotation possible.
Velocity ratio in gears: i = ω1/ω2 = z2/z1 = d2/d1; module m = d/z must be equal for meshing gears.
Compound gear train: i_total = product of driven teeth / product of driver teeth; sign convention for external/internal meshing.
Belt drive ratio i = n1/n2 = D2/D1; slip reduces real ratio; crossed belt reverses direction.
Screw: torque–force relation F = 2πT·η/p, where p is the lead; efficiency η = tanλ/tan(λ+φ) with friction angle φ.
Power transmitted P = T·ω = F·v; torque T = F·r; efficiency of a transmission η = P_out/P_in.
Inclined plane: force parallel to plane F = W·sinθ + μW·cosθ; on the horizontal base F = W·tan(θ+φ).
Kinetic energy of rotation Ec = ½Iω²; moment of inertia of a solid cylinder about its axis I = ½mr².
Dynamic equilibrium: ΣF = ma and ΣM = Iα; in static equilibrium ΣF = 0 and ΣM = 0 about any point.
Electrical and electronic circuits: DC/AC analysis, components and basic electronics
Ohm's law V = IR; power P = VI = I²R = V²/R; Kirchhoff: ΣI at node = 0, ΣV around loop = 0.
Series: R_eq = ΣR; parallel: 1/R_eq = Σ1/R; voltage divider Vx = V·Rx/R_total.
Thevenin equivalent: V_th = open-circuit voltage, R_th = resistance seen with sources deactivated (V sources shorted, I sources open).
AC: V_rms = V_peak/√2; impedance Z = R + j(XL − XC) with XL = ωL, XC = 1/(ωC); resonance when XL = XC, f0 = 1/(2π√(LC)).
Power in AC: P = V_rms·I_rms·cosφ; power factor correction adds parallel capacitors to raise cosφ toward 1.
Three-phase star: V_line = √3·V_phase, I_line = I_phase; delta: V_line = V_phase, I_line = √3·I_phase.
Diode: forward drop ≈ 0.7 V (Si), 0.3 V (Ge); half-wave rectifier gives V_dc ≈ 0.318·V_peak, bridge full-wave V_dc ≈ 0.637·V_peak.
Transistor as switch: cut-off (V_BE < 0.7 V, no current) or saturation (V_CE ≈ 0.2 V); as amplifier, gain A = −R_C/r_e in common emitter.
Logic gates: AND, OR, NOT, NAND, NOR, XOR; NAND and NOR are functionally complete; Boolean simplification via De Morgan: ¬(A·B) = ¬A + ¬B.
Control and automatic systems: open/closed loop, sensors, actuators and logic control
Open loop: no feedback, output depends only on input; closed loop: sensor feedback compares output to setpoint and the error drives the controller.
Error e(t) = setpoint − measured value; PID output u(t) = Kp·e + Ki∫e dt + Kd·de/dt.
Proportional-only control leaves a steady-state offset; integral action removes it; derivative action damps overshoot but amplifies noise.
Characteristic quantities of a step response: rise time, overshoot, settling time, steady-state error.
Sensors by magnitude: potentiometer/LVDT (position), encoder (angular position), thermistor/thermocouple/RTD (temperature), strain gauge (force), Hall (magnetic field), photodiode (light).
Actuators: DC/stepper/servo motors, solenoids, relays, pneumatic and hydraulic cylinders; a relay isolates a low-power control circuit from a high-power load.
PLC scan cycle: read inputs → execute program → update outputs, repeated cyclically; ladder logic uses contacts (normally open/closed) and coils.
Boolean control design: truth table → Karnaugh map → minimized expression → logic gates or ladder rungs.
Stability: a closed-loop system is stable if all poles of the transfer function have negative real parts; gain too high can cause oscillation.
Pneumatic and hydraulic systems: components, schematics and circuit design
Pneumatics uses compressible air (typical working pressure 6 bar); hydraulics uses incompressible oil (often 100–200 bar) giving high force and stiffness.
Pascal's principle: pressure transmitted undiminished, F1/A1 = F2/A2; hydraulic press multiplies force by the area ratio.
Cylinder force F = p·A; extend force uses full bore area A = πD²/4, retract force uses annulus A = π(D² − d²)/4.
Flow and speed: v = Q/A; hydraulic cylinder speed set by flow rate, pneumatic speed usually by throttle (flow control) valves.
Symbols per ISO 1219: compressor, reservoir, filter, pressure regulator, directional control valve (number of ports/positions, e.g. 5/2), non-return valve, throttle.
Directional valve designation: first digit = number of ports (ways), second = number of positions; centre condition shown by the middle box of a 3-position valve.
Circuit layout: power source → filter/regulator → directional valve → actuator; return lines to tank; exhaust silencers on pneumatic valves.
Meter-in vs meter-out: meter-in controls actuator speed on entry, meter-out is more stable for overrunning loads and prevents runaway.
FRL unit (filter, regulator, lubricator) conditions compressed air; pressure switch and limit switches provide feedback for sequence control.
Manufacturing and production systems: machining, forming, joining and metrology
Turning parameters: cutting speed v = π·D·n/1000 (m/min), feed f (mm/rev), depth of cut a; material removal rate Q ≈ v·f·a.
Drilling: n = 1000·v/(π·D); tapping requires the tap drill diameter ≈ D − pitch.
Milling: feed rate vf = fz·z·n (mm/min), where fz is feed per tooth and z the number of teeth.
Forming: rolling, forging, extrusion, drawing, deep drawing; hot working reduces strength and increases ductility, cold working improves surface finish and strength (strain hardening).
Welding: arc (electrode, MIG/MAG, TIG), resistance spot, oxyacetylene; brazing and soldering join without melting the base metal.
Metrology instruments: vernier caliper (0.02 mm), micrometer (0.01 mm), dial gauge (0.01 mm), gauge blocks for calibration.
Tolerance and fits: ISO system, tolerance = upper − lower deviation; clearance fit (hole > shaft), interference fit (shaft > hole), transition in between.
Surface roughness Ra is the arithmetic mean deviation of the profile; lower Ra = smoother surface, achieved by finishing passes.
Quality control: SPC control charts, Cp/Cpk process capability; a process is capable when Cpk ≥ 1.33.
Energy and power: sources, generation, conversion and environmental impact
Power P = E/t; electrical energy E = P·t, billed in kWh; 1 kWh = 3.6 MJ.
Mechanical power P = F·v = T·ω; hydraulic power P = p·Q.
Thermal machines: η = W_net/Q_in = 1 − Q_out/Q_in; Carnot limit η_max = 1 − T_cold/T_hot (temperatures in K).
Renewables: wind P = ½ρA v³ (power scales with the cube of wind speed); hydro P = ρgQHη; photovoltaic efficiency typically 15–22 %.
Fossil and nuclear plants use a heat source to raise steam that drives a turbine coupled to an alternator (Rankine cycle).
Electrical transmission uses high voltage to reduce line losses (P_loss = I²R); transformers step voltage up/down with negligible loss.
Environmental impact: CO2 per kWh, land use, water use, waste; life-cycle analysis compares technologies from extraction to decommissioning.
Energy efficiency: cogeneration reuses waste heat; heat pumps deliver more heat than electrical input (COP > 1).
Units: 1 cal = 4.18 J; 1 CV ≈ 735.5 W; 1 tep = 41.87 GJ.
Engineering project and technical drawing: representation, dimensioning and design process
Views per first-angle projection (UNE/ISO): front view, top view below it, left-side view to the right.
Scale = drawing dimension / real dimension; standard scales 1:1, 1:2, 1:5, 2:1, 5:1.
Dimension lines show the true size regardless of scale; dimensions are not repeated in multiple views and are placed outside the outline.
Tolerances: general tolerance notes, ISO fits (e.g. H7/g6), geometric tolerances (GD&T: flatness, cylindricity, position) with datum references.
Sections and cuts: hatching at 45° for solid material, half-sections for symmetric parts, broken-out sections for local features.
Design process stages: need → specification → conceptual design → detailed design → prototyping → testing → production → evaluation.
Project documents: memory, budget, Gantt chart, technical specifications (pliego de condiciones), drawings list, bill of materials.
Standard drawing sheet: ISO A series - A4 210×297 mm; each size is half the area of the previous (A0 = 1 m²).
Orthographic rules: hidden lines dashed, centre lines chain-dotted, visible outlines continuous thick.
Technological innovation and digital tools: CAD/CAM, ICT and product development
CAD: parametric modelling uses constraints and dimensions; features (extrude, revolve, fillet) build the solid tree; associativity updates downstream drawings.
CAM workflow: CAD model → toolpath generation → post-processing to machine code (G-code) → CNC machining.
G-code basics: G00 rapid, G01 linear interpolation with feed F, G02/G03 circular interpolation, M03/M05 spindle on/off.
Rapid prototyping: FDM (fused filament), SLA (resin), SLS (powder) - additive manufacturing builds layer by layer from a 3D model (STL).
ICT in product development: PLM, ERP, collaborative cloud tools, digital twin, simulation (FEA, CFD) to validate before manufacture.
Innovation types: incremental vs radical; technology push vs market pull; the innovation process includes idea generation, screening, development, launch.
Intellectual property: patent (novel, inventive, industrial application, 20 years), utility model, trademark, industrial design, copyright.
File formats: DXF/DWG for 2D CAD exchange, STEP/IGES for 3D, STL for additive manufacturing, PDF for drawings.
Automation and Industry 4.0: sensors, IoT, robotics, big data, additive manufacturing and cyber-physical systems integrated in production.
Control and automatic systems: open/closed loop, sensors, actuators and logic control
Open loop: no feedback, output depends only on input; closed loop: sensor feedback compares output to setpoint and the error drives the controller.
Error e(t) = setpoint − measured value; PID output u(t) = Kp·e + Ki∫e dt + Kd·de/dt.
Proportional-only control leaves a steady-state offset; integral action removes it; derivative action damps overshoot but amplifies noise.
Characteristic quantities of a step response: rise time, overshoot, settling time, steady-state error.
Sensors by magnitude: potentiometer/LVDT (position), encoder (angular position), thermistor/thermocouple/RTD (temperature), strain gauge (force), Hall (magnetic field), photodiode (light).
Actuators: DC/stepper/servo motors, solenoids, relays, pneumatic and hydraulic cylinders; a relay isolates a low-power control circuit from a high-power load.
PLC scan cycle: read inputs → execute program → update outputs, repeated cyclically; ladder logic uses contacts (normally open/closed) and coils.
Boolean control design: truth table → Karnaugh map → minimized expression → logic gates or ladder rungs.
Stability: a closed-loop system is stable if all poles of the transfer function have negative real parts; gain too high can cause oscillation.
Pneumatic and hydraulic systems: components, schematics and circuit design
Pneumatics uses compressible air (typical working pressure 6 bar); hydraulics uses incompressible oil (often 100–200 bar) giving high force and stiffness.
Pascal's principle: pressure transmitted undiminished, F1/A1 = F2/A2; hydraulic press multiplies force by the area ratio.
Cylinder force F = p·A; extend force uses full bore area A = πD²/4, retract force uses annulus A = π(D² − d²)/4.
Flow and speed: v = Q/A; hydraulic cylinder speed set by flow rate, pneumatic speed usually by throttle (flow control) valves.
Symbols per ISO 1219: compressor, reservoir, filter, pressure regulator, directional control valve (number of ports/positions, e.g. 5/2), non-return valve, throttle.
Directional valve designation: first digit = number of ports (ways), second = number of positions; centre condition shown by the middle box of a 3-position valve.
Circuit layout: power source → filter/regulator → directional valve → actuator; return lines to tank; exhaust silencers on pneumatic valves.
Meter-in vs meter-out: meter-in controls actuator speed on entry, meter-out is more stable for overrunning loads and prevents runaway.
FRL unit (filter, regulator, lubricator) conditions compressed air; pressure switch and limit switches provide feedback for sequence control.
Manufacturing and production systems: machining, forming, joining and metrology
Turning parameters: cutting speed v = π·D·n/1000 (m/min), feed f (mm/rev), depth of cut a; material removal rate Q ≈ v·f·a.
Drilling: n = 1000·v/(π·D); tapping requires the tap drill diameter ≈ D − pitch.
Milling: feed rate vf = fz·z·n (mm/min), where fz is feed per tooth and z the number of teeth.
Forming: rolling, forging, extrusion, drawing, deep drawing; hot working reduces strength and increases ductility, cold working improves surface finish and strength (strain hardening).
Welding: arc (electrode, MIG/MAG, TIG), resistance spot, oxyacetylene; brazing and soldering join without melting the base metal.
Metrology instruments: vernier caliper (0.02 mm), micrometer (0.01 mm), dial gauge (0.01 mm), gauge blocks for calibration.
Tolerance and fits: ISO system, tolerance = upper − lower deviation; clearance fit (hole > shaft), interference fit (shaft > hole), transition in between.
Surface roughness Ra is the arithmetic mean deviation of the profile; lower Ra = smoother surface, achieved by finishing passes.
Quality control: SPC control charts, Cp/Cpk process capability; a process is capable when Cpk ≥ 1.33.
Energy and power: sources, generation, conversion and environmental impact
Power P = E/t; electrical energy E = P·t, billed in kWh; 1 kWh = 3.6 MJ.
Mechanical power P = F·v = T·ω; hydraulic power P = p·Q.
Thermal machines: η = W_net/Q_in = 1 − Q_out/Q_in; Carnot limit η_max = 1 − T_cold/T_hot (temperatures in K).
Renewables: wind P = ½ρA v³ (power scales with the cube of wind speed); hydro P = ρgQHη; photovoltaic efficiency typically 15–22 %.
Fossil and nuclear plants use a heat source to raise steam that drives a turbine coupled to an alternator (Rankine cycle).
Electrical transmission uses high voltage to reduce line losses (P_loss = I²R); transformers step voltage up/down with negligible loss.
Environmental impact: CO2 per kWh, land use, water use, waste; life-cycle analysis compares technologies from extraction to decommissioning.
Energy efficiency: cogeneration reuses waste heat; heat pumps deliver more heat than electrical input (COP > 1).
Units: 1 cal = 4.18 J; 1 CV ≈ 735.5 W; 1 tep = 41.87 GJ.
Engineering project and technical drawing: representation, dimensioning and design process
Views per first-angle projection (UNE/ISO): front view, top view below it, left-side view to the right.
Scale = drawing dimension / real dimension; standard scales 1:1, 1:2, 1:5, 2:1, 5:1.
Dimension lines show the true size regardless of scale; dimensions are not repeated in multiple views and are placed outside the outline.
Tolerances: general tolerance notes, ISO fits (e.g. H7/g6), geometric tolerances (GD&T: flatness, cylindricity, position) with datum references.
Sections and cuts: hatching at 45° for solid material, half-sections for symmetric parts, broken-out sections for local features.
Design process stages: need → specification → conceptual design → detailed design → prototyping → testing → production → evaluation.
Project documents: memory, budget, Gantt chart, technical specifications (pliego de condiciones), drawings list, bill of materials.
Standard drawing sheet: ISO A series - A4 210×297 mm; each size is half the area of the previous (A0 = 1 m²).
Orthographic rules: hidden lines dashed, centre lines chain-dotted, visible outlines continuous thick.
Technological innovation and digital tools: CAD/CAM, ICT and product development
CAD: parametric modelling uses constraints and dimensions; features (extrude, revolve, fillet) build the solid tree; associativity updates downstream drawings.
CAM workflow: CAD model → toolpath generation → post-processing to machine code (G-code) → CNC machining.
G-code basics: G00 rapid, G01 linear interpolation with feed F, G02/G03 circular interpolation, M03/M05 spindle on/off.
Rapid prototyping: FDM (fused filament), SLA (resin), SLS (powder) - additive manufacturing builds layer by layer from a 3D model (STL).
ICT in product development: PLM, ERP, collaborative cloud tools, digital twin, simulation (FEA, CFD) to validate before manufacture.
Innovation types: incremental vs radical; technology push vs market pull; the innovation process includes idea generation, screening, development, launch.
Intellectual property: patent (novel, inventive, industrial application, 20 years), utility model, trademark, industrial design, copyright.
File formats: DXF/DWG for 2D CAD exchange, STEP/IGES for 3D, STL for additive manufacturing, PDF for drawings.
Automation and Industry 4.0: sensors, IoT, robotics, big data, additive manufacturing and cyber-physical systems integrated in production.
Materials: properties, structure, testing and selection
Density ρ = m/V; specific strength = σy/ρ - key for aerospace and transport selection where mass dominates.
Elastic modulus E is the slope of the linear σ–ε region; Hooke's law σ = E·ε valid up to the proportional limit.
Ductility measured as elongation at break A% = (Lf − L0)/L0 × 100, or reduction of area Z%.
Hardness scales are not interchangeable: Brinell (HB, hard indenters, coarse materials), Vickers (HV, universal, diagonal-based), Rockwell (HRC for hardened steel, HRA/B for thin or soft).
Toughness = energy absorbed before fracture (area under σ–ε curve); ceramics are hard but brittle (low KIC), metals tough.
Crystal structures: BCC (Fe-α, low ductility at low T), FCC (Al, Cu, austenite - ductile, many slip systems), HCP (Mg, Ti - limited slip, anisotropic).
Strengthening mechanisms: grain refinement (Hall–Petch σy = σ0 + k/√d), solid solution, precipitation, cold work (strain hardening), dispersion.
Fe–C diagram: eutectoid at 0.77 %C, 727 °C → pearlite; austenite (FCC) transforms to martensite on fast quench (BCT, hard and brittle); tempering restores toughness.
Selection uses Ashby charts: plot two properties on log axes, performance index lines (e.g. E^(1/2)/ρ for stiff lightweight beams) select the material class.
Mechanical systems and mechanisms: kinematics, dynamics, transmission and transformation
Four-bar Grashof condition: shortest + longest ≤ sum of the other two links ⇒ at least one full rotation possible.
Velocity ratio in gears: i = ω1/ω2 = z2/z1 = d2/d1; module m = d/z must be equal for meshing gears.
Compound gear train: i_total = product of driven teeth / product of driver teeth; sign convention for external/internal meshing.
Belt drive ratio i = n1/n2 = D2/D1; slip reduces real ratio; crossed belt reverses direction.
Screw: torque–force relation F = 2πT·η/p, where p is the lead; efficiency η = tanλ/tan(λ+φ) with friction angle φ.
Power transmitted P = T·ω = F·v; torque T = F·r; efficiency of a transmission η = P_out/P_in.
Inclined plane: force parallel to plane F = W·sinθ + μW·cosθ; on the horizontal base F = W·tan(θ+φ).
Kinetic energy of rotation Ec = ½Iω²; moment of inertia of a solid cylinder about its axis I = ½mr².
Dynamic equilibrium: ΣF = ma and ΣM = Iα; in static equilibrium ΣF = 0 and ΣM = 0 about any point.
Electrical and electronic circuits: DC/AC analysis, components and basic electronics
Ohm's law V = IR; power P = VI = I²R = V²/R; Kirchhoff: ΣI at node = 0, ΣV around loop = 0.
Series: R_eq = ΣR; parallel: 1/R_eq = Σ1/R; voltage divider Vx = V·Rx/R_total.
Thevenin equivalent: V_th = open-circuit voltage, R_th = resistance seen with sources deactivated (V sources shorted, I sources open).
AC: V_rms = V_peak/√2; impedance Z = R + j(XL − XC) with XL = ωL, XC = 1/(ωC); resonance when XL = XC, f0 = 1/(2π√(LC)).
Power in AC: P = V_rms·I_rms·cosφ; power factor correction adds parallel capacitors to raise cosφ toward 1.
Three-phase star: V_line = √3·V_phase, I_line = I_phase; delta: V_line = V_phase, I_line = √3·I_phase.
Diode: forward drop ≈ 0.7 V (Si), 0.3 V (Ge); half-wave rectifier gives V_dc ≈ 0.318·V_peak, bridge full-wave V_dc ≈ 0.637·V_peak.
Transistor as switch: cut-off (V_BE < 0.7 V, no current) or saturation (V_CE ≈ 0.2 V); as amplifier, gain A = −R_C/r_e in common emitter.
Logic gates: AND, OR, NOT, NAND, NOR, XOR; NAND and NOR are functionally complete; Boolean simplification via De Morgan: ¬(A·B) = ¬A + ¬B.