Galicia PAU Technology and Engineering II cheat sheet
Galicia PAU Technology and Engineering II · Keep the key ideas within reach.
Materials Science and Technology
Density ρ = m/V; specific strength = σy/ρ (MPa·cm³/g) ranks materials for weight-critical parts.
Hooke's law σ = E·ε applies up to the yield strength; E for steel ≈ 210 GPa, aluminium ≈ 70 GPa, copper ≈ 110 GPa.
Ductility measured as elongation at break A% or reduction of area Z%; brittle fracture shows A% < 5.
Hardness scales are not interchangeable: Brinell (HB) for coarse/grey cast iron, Vickers (HV) for thin or hardened layers, Rockwell C (HRC) for hardened steel.
Tensile test gives Re (yield), Rm (ultimate), A% and Z%; Charpy impact test quantifies toughness vs temperature and reveals the ductile-brittle transition.
Fe-C diagram: eutectoid at 0.77 %C and 727 °C; pearlite = ferrite + cementite lamellae; martensite forms by fast quench and is hard but brittle, tempered to raise toughness.
Alloys: steel ≤ 2 %C, cast iron 2-4 %C; austenitic stainless 18/8 (Cr/Ni) is austenitic and non-magnetic; brass = Cu-Zn, bronze = Cu-Sn.
Selection criteria ranked: service requirements (mechanical, thermal, corrosion) → manufacturing process compatibility → cost and availability; Ashby charts plot two properties to screen candidates.
Non-destructive testing: ultrasound for internal flaws, dye penetrant for surface cracks in non-porous solids, magnetic particles only for ferromagnetic parts, radiography for internal density changes.
Mechanical Systems: Statics, Strength of Materials, Mechanisms
Static equilibrium: ΣF = 0 and ΣM = 0; free-body diagram first, then reactions from supports (pin = 2 unknowns, roller = 1, fixed = 3).
Normal stress σ = N/A; shear τ = V/A; bearing pressure σb = F/(d·t); allowable stress design uses σ ≤ σy/n with safety factor n > 1.
Bending: σ = M·y/I with maximum at y = c; rectangular section I = b·h³/12, circular I = π·d⁴/64.
Deflection and stiffness scale with E·I (flexural rigidity); beam max deflection formulas depend on load case (point load centre: δ = F·L³/48EI).
Torsion in circular shafts: τ = T·r/Ip with Ip = π·d⁴/32; angle of twist θ = T·L/(G·Ip).
Euler buckling critical load Pcr = π²·E·I/(k·L)²; k = 1 pinned-pinned, 0.5 fixed-fixed, 2 cantilever.
Four-bar linkage Grashof condition: shortest + longest ≤ sum of the other two → at least one link fully rotates; otherwise it is a double-rocker.
Gear train ratio i = ωin/ωout = zout/zin (external gears); belt and chain drives transmit torque with ratio = driven pulley diameter / driver diameter.
Power relations: P = M·ω (ω in rad/s), P = F·v for linear motion; efficiency η = Pout/Pin < 1.
Electrical and Electronic Systems
Ohm's law V = I·R; series resistances add, parallel 1/RT = Σ1/Ri; power P = V·I = I²R = V²/R.
DC circuits solved by Kirchhoff: KCL ΣI at node = 0, KVL ΣV around loop = 0; superposition and Thévenin equivalent simplify networks.
AC: impedance Z = R + j(XL − XC), XL = 2πfL, XC = 1/(2πfC); resonance when XL = XC at f = 1/(2π√(LC)).
Three-phase: line voltage VL = √3·Vphase in star connection; power P = √3·VL·IL·cos φ.
Transformers: V1/V2 = N1/N2 = I2/I1; ideal transformer conserves apparent power.
DC machines: shunt, series and compound excitation; counter-EMF E = k·Φ·ω governs speed; DC motor speed falls with load in shunt connection.
Power electronics: diode rectifies, thyristor (SCR) switches on gate and turns off at zero current, MOSFET/IGBT for high-frequency switching, chopper varies DC voltage.
Logic gates: AND, OR, NOT, NAND, NOR, XOR; Boolean algebra De Morgan: ¬(A·B) = ¬A + ¬B; Karnaugh maps minimise combinational functions.
Sensors and signals: LDR, thermistor (NTC resistance falls with temperature), strain gauge in Wheatstone bridge, encoder for position; ADC converts analogue to digital.
Control Systems and Automation
Open loop: no feedback, output not compared with setpoint; closed loop compares setpoint and measured output to generate error e = r − y.
PID controller: u = Kp·e + Ki∫e dt + Kd·de/dt; Kp reduces steady error, Ki removes offset, Kd damps overshoot and speeds response.
Step response metrics: rise time, overshoot, settling time, steady-state error; first-order system has time constant τ (63.2 % of final value).
Stability: a closed-loop system is stable if all poles of the transfer function have negative real part; Bode gain margin and phase margin > 0 dB / > 0° indicate stability.
Sensors: inductive/capacitive proximity, photoelectric, limit switches, thermocouples, pressure transducers; digital sensors give on/off, analogue give proportional signals.
Actuators: DC/stepper/servo motors, solenoids, pneumatic and hydraulic cylinders; servo uses encoder feedback for closed-loop positioning.
PLC scan cycle: read inputs → execute program (ladder, FBD, SFC) → update outputs; ladder rungs use contacts (X) and coils (Y).
Robotics: degrees of freedom, articulated, SCARA, Cartesian and delta configurations; repeatability is tighter than accuracy; end effector and teach pendant programming.
Pneumatics and Hydraulics
Pascal's principle: pressure transmitted undiminished in a confined fluid; F = p·A, so force multiplication follows area ratio A2/A1.
Flow continuity Q = A·v; hydraulic power P = p·Q (p in Pa, Q in m³/s); efficiency η = output power/input power.
Pneumatic working pressure typically 6 bar (600 kPa); hydraulics commonly 100-350 bar for high force density.
Components: compressor/pump, reservoir, filter, pressure regulator, directional control valve, flow control valve, non-return valve, actuator.
Valve designation 5/2 = five ports, two positions; 3/2 for single-acting cylinder; centre position closed/ open/ tandem determines exhaust and blocking behaviour.
Speed control: meter-in (throttle before cylinder) for resistive loads, meter-out (throttle on exhaust) for overrunning loads, bleed-off for both directions.
Circuit symbols: cylinder single-acting (one port) vs double-acting (two ports); spring return and pilot actuation shown on valve ends.
Air is compressible so pneumatics gives fast, clean but less precise motion; hydraulics gives high force and stiffness but needs oil, filtration and cooling.
Manufacturing and Production Systems
Machining: turning (lathe, cylindrical), milling (planar), drilling, grinding (finishing); cutting speed vc = π·D·n, feed per revolution f.
Machining time for turning t = L/(f·n); material removal rate Q = vc·f·ap (depth of cut).
Forming: rolling, forging, extrusion, drawing; hot working reduces strength and improves ductility, cold working gives better surface finish and work hardening.
Joining: welding (arc, MIG/MAG, TIG, resistance), soldering/brazing, adhesive bonding, riveting, bolting; welded joint types butt, lap, T, corner.
Metrology: vernier caliper (0.02 mm), micrometer (0.01 mm), dial gauge, gauge blocks; tolerance = upper − lower limit; IT grades define tolerance magnitude.
Fits: clearance, interference and transition; shaft basis and hole basis systems; ISO designation H7/g6 indicates a clearance fit.
Quality: statistical process control with control charts (x̄, R), process capability Cp = (USL − LSL)/(6σ), Cpk accounts for centring.
Lean production: just-in-time, kanban, 5S, value stream mapping, poka-yoke (error proofing), total productive maintenance.
CNC programming uses G-codes (G01 linear interpolation, G02/G03 circular) and M-codes (M03 spindle on, M05 stop); zero offsets and tool length compensation.
Energy and Environmental Technology
Energy units: 1 kWh = 3.6 MJ; 1 tep ≈ 41.87 GJ; power P = E/t and efficiency η = useful energy/input energy.
Renewables: solar PV (cell efficiency 15-22 %), wind (P = ½ρAv³, power scales with cube of wind speed), hydro (P = ρgQHη), biomass, geothermal, tidal.
Thermal machines: Carnot limit η = 1 − Tc/Th (absolute temperatures); real cycles (Rankine, Brayton, Otto, Diesel) always below Carnot.
Fossil and nuclear plants convert heat to steam then to mechanical and electrical energy; combined cycle raises efficiency above 55 %.
Environmental impact: CO2, SO2, NOx, particulates; greenhouse effect, acid rain, ozone depletion; mitigation by efficiency, filtering, renewables.
Energy storage and transport: batteries (specific energy Wh/kg), hydrogen fuel cells (efficiency 50-60 %), pumped hydro, flywheels.
Sustainability: life-cycle analysis, carbon footprint, circular economy (reduce, reuse, recycle), energy payback time of a system.
Buildings and industry: insulation reduces heat loss Q = U·A·ΔT; heat pumps COP = Qh/W typically 3-4, greater than resistive heating.
Materials Science and Technology
Density ρ = m/V; specific strength = σy/ρ (MPa·cm³/g) ranks materials for weight-critical parts.
Hooke's law σ = E·ε applies up to the yield strength; E for steel ≈ 210 GPa, aluminium ≈ 70 GPa, copper ≈ 110 GPa.
Ductility measured as elongation at break A% or reduction of area Z%; brittle fracture shows A% < 5.
Hardness scales are not interchangeable: Brinell (HB) for coarse/grey cast iron, Vickers (HV) for thin or hardened layers, Rockwell C (HRC) for hardened steel.
Tensile test gives Re (yield), Rm (ultimate), A% and Z%; Charpy impact test quantifies toughness vs temperature and reveals the ductile-brittle transition.
Fe-C diagram: eutectoid at 0.77 %C and 727 °C; pearlite = ferrite + cementite lamellae; martensite forms by fast quench and is hard but brittle, tempered to raise toughness.
Alloys: steel ≤ 2 %C, cast iron 2-4 %C; austenitic stainless 18/8 (Cr/Ni) is austenitic and non-magnetic; brass = Cu-Zn, bronze = Cu-Sn.
Selection criteria ranked: service requirements (mechanical, thermal, corrosion) → manufacturing process compatibility → cost and availability; Ashby charts plot two properties to screen candidates.
Non-destructive testing: ultrasound for internal flaws, dye penetrant for surface cracks in non-porous solids, magnetic particles only for ferromagnetic parts, radiography for internal density changes.
Mechanical Systems: Statics, Strength of Materials, Mechanisms
Static equilibrium: ΣF = 0 and ΣM = 0; free-body diagram first, then reactions from supports (pin = 2 unknowns, roller = 1, fixed = 3).
Normal stress σ = N/A; shear τ = V/A; bearing pressure σb = F/(d·t); allowable stress design uses σ ≤ σy/n with safety factor n > 1.
Bending: σ = M·y/I with maximum at y = c; rectangular section I = b·h³/12, circular I = π·d⁴/64.
Deflection and stiffness scale with E·I (flexural rigidity); beam max deflection formulas depend on load case (point load centre: δ = F·L³/48EI).
Torsion in circular shafts: τ = T·r/Ip with Ip = π·d⁴/32; angle of twist θ = T·L/(G·Ip).
Euler buckling critical load Pcr = π²·E·I/(k·L)²; k = 1 pinned-pinned, 0.5 fixed-fixed, 2 cantilever.
Four-bar linkage Grashof condition: shortest + longest ≤ sum of the other two → at least one link fully rotates; otherwise it is a double-rocker.
Gear train ratio i = ωin/ωout = zout/zin (external gears); belt and chain drives transmit torque with ratio = driven pulley diameter / driver diameter.
Power relations: P = M·ω (ω in rad/s), P = F·v for linear motion; efficiency η = Pout/Pin < 1.
Electrical and Electronic Systems
Ohm's law V = I·R; series resistances add, parallel 1/RT = Σ1/Ri; power P = V·I = I²R = V²/R.
DC circuits solved by Kirchhoff: KCL ΣI at node = 0, KVL ΣV around loop = 0; superposition and Thévenin equivalent simplify networks.
AC: impedance Z = R + j(XL − XC), XL = 2πfL, XC = 1/(2πfC); resonance when XL = XC at f = 1/(2π√(LC)).
Three-phase: line voltage VL = √3·Vphase in star connection; power P = √3·VL·IL·cos φ.
Transformers: V1/V2 = N1/N2 = I2/I1; ideal transformer conserves apparent power.
DC machines: shunt, series and compound excitation; counter-EMF E = k·Φ·ω governs speed; DC motor speed falls with load in shunt connection.
Power electronics: diode rectifies, thyristor (SCR) switches on gate and turns off at zero current, MOSFET/IGBT for high-frequency switching, chopper varies DC voltage.
Logic gates: AND, OR, NOT, NAND, NOR, XOR; Boolean algebra De Morgan: ¬(A·B) = ¬A + ¬B; Karnaugh maps minimise combinational functions.
Sensors and signals: LDR, thermistor (NTC resistance falls with temperature), strain gauge in Wheatstone bridge, encoder for position; ADC converts analogue to digital.
Control Systems and Automation
Open loop: no feedback, output not compared with setpoint; closed loop compares setpoint and measured output to generate error e = r − y.
PID controller: u = Kp·e + Ki∫e dt + Kd·de/dt; Kp reduces steady error, Ki removes offset, Kd damps overshoot and speeds response.
Step response metrics: rise time, overshoot, settling time, steady-state error; first-order system has time constant τ (63.2 % of final value).
Stability: a closed-loop system is stable if all poles of the transfer function have negative real part; Bode gain margin and phase margin > 0 dB / > 0° indicate stability.
Sensors: inductive/capacitive proximity, photoelectric, limit switches, thermocouples, pressure transducers; digital sensors give on/off, analogue give proportional signals.
Actuators: DC/stepper/servo motors, solenoids, pneumatic and hydraulic cylinders; servo uses encoder feedback for closed-loop positioning.
PLC scan cycle: read inputs → execute program (ladder, FBD, SFC) → update outputs; ladder rungs use contacts (X) and coils (Y).
Robotics: degrees of freedom, articulated, SCARA, Cartesian and delta configurations; repeatability is tighter than accuracy; end effector and teach pendant programming.
Pneumatics and Hydraulics
Pascal's principle: pressure transmitted undiminished in a confined fluid; F = p·A, so force multiplication follows area ratio A2/A1.
Flow continuity Q = A·v; hydraulic power P = p·Q (p in Pa, Q in m³/s); efficiency η = output power/input power.
Pneumatic working pressure typically 6 bar (600 kPa); hydraulics commonly 100-350 bar for high force density.
Components: compressor/pump, reservoir, filter, pressure regulator, directional control valve, flow control valve, non-return valve, actuator.
Valve designation 5/2 = five ports, two positions; 3/2 for single-acting cylinder; centre position closed/ open/ tandem determines exhaust and blocking behaviour.
Speed control: meter-in (throttle before cylinder) for resistive loads, meter-out (throttle on exhaust) for overrunning loads, bleed-off for both directions.
Circuit symbols: cylinder single-acting (one port) vs double-acting (two ports); spring return and pilot actuation shown on valve ends.
Air is compressible so pneumatics gives fast, clean but less precise motion; hydraulics gives high force and stiffness but needs oil, filtration and cooling.
Manufacturing and Production Systems
Machining: turning (lathe, cylindrical), milling (planar), drilling, grinding (finishing); cutting speed vc = π·D·n, feed per revolution f.
Machining time for turning t = L/(f·n); material removal rate Q = vc·f·ap (depth of cut).
Forming: rolling, forging, extrusion, drawing; hot working reduces strength and improves ductility, cold working gives better surface finish and work hardening.
Joining: welding (arc, MIG/MAG, TIG, resistance), soldering/brazing, adhesive bonding, riveting, bolting; welded joint types butt, lap, T, corner.
Metrology: vernier caliper (0.02 mm), micrometer (0.01 mm), dial gauge, gauge blocks; tolerance = upper − lower limit; IT grades define tolerance magnitude.
Fits: clearance, interference and transition; shaft basis and hole basis systems; ISO designation H7/g6 indicates a clearance fit.
Quality: statistical process control with control charts (x̄, R), process capability Cp = (USL − LSL)/(6σ), Cpk accounts for centring.
Lean production: just-in-time, kanban, 5S, value stream mapping, poka-yoke (error proofing), total productive maintenance.
CNC programming uses G-codes (G01 linear interpolation, G02/G03 circular) and M-codes (M03 spindle on, M05 stop); zero offsets and tool length compensation.
Energy and Environmental Technology
Energy units: 1 kWh = 3.6 MJ; 1 tep ≈ 41.87 GJ; power P = E/t and efficiency η = useful energy/input energy.
Renewables: solar PV (cell efficiency 15-22 %), wind (P = ½ρAv³, power scales with cube of wind speed), hydro (P = ρgQHη), biomass, geothermal, tidal.
Thermal machines: Carnot limit η = 1 − Tc/Th (absolute temperatures); real cycles (Rankine, Brayton, Otto, Diesel) always below Carnot.
Fossil and nuclear plants convert heat to steam then to mechanical and electrical energy; combined cycle raises efficiency above 55 %.
Environmental impact: CO2, SO2, NOx, particulates; greenhouse effect, acid rain, ozone depletion; mitigation by efficiency, filtering, renewables.
Energy storage and transport: batteries (specific energy Wh/kg), hydrogen fuel cells (efficiency 50-60 %), pumped hydro, flywheels.
Sustainability: life-cycle analysis, carbon footprint, circular economy (reduce, reuse, recycle), energy payback time of a system.
Buildings and industry: insulation reduces heat loss Q = U·A·ΔT; heat pumps COP = Qh/W typically 3-4, greater than resistive heating.