Meisterprüfung Mechatronik cheat sheet

A mechatronic system is the integrated, simultaneous design of mechanical, electrical/electronic, control, and software subsystems; the V-model (VDI 2206) defines requirements, system design, subsystem design, implementation, integration, verification, and validation.

Sensors convert physical quantities into electrical signals; characteristic values are measuring range, sensitivity (output change per input change), resolution, linearity error, hysteresis, and response time.

Actuators convert electrical energy into mechanical work: DC/BLDC motors, stepper motors, piezo actuators, solenoids, and pneumatic/hydraulic cylinders; selection criteria are torque/speed curve, duty cycle, positioning accuracy, and dynamics.

Stepper motor step angle = 360° / (steps per revolution); microstepping reduces step angle but also holding torque per microstep; open-loop operation risks step loss under overload.

Servo drive closed-loop control uses encoder or resolver feedback; key figures are rated torque, peak torque, rotor inertia, and the inertia ratio (load inertia / motor inertia, typically < 10 for good dynamics).

Gear ratio i = n_in / n_out = M_out / M_in (ideal); efficiency η reduces output torque: M_out = M_in · i · η; backlash and torsional stiffness limit positioning accuracy.

Reliability: failure rate λ is the reciprocal of MTBF; for series systems λ_total = Σλ_i, so system reliability R = e^(−λ_total·t) decreases with each added component.

Interfaces between subsystems (mechanical mounting, electrical connectors, fieldbus, software APIs) are the main source of integration faults; interface specifications must be defined before subsystem design.

Ohm's law U = R·I; power P = U·I = I²·R = U²/R; for AC with sinusoidal quantities use RMS values and power factor cos φ: P = U·I·cos φ, Q = U·I·sin φ, S = U·I.

Three-phase systems: line voltage U_L = √3 · U_ph in star connection; total power P = √3 · U_L · I_L · cos φ; neutral conductor carries the sum of phase currents (zero only for balanced loads).

Impedance Z = √(R² + (X_L − X_C)²) with X_L = 2πfL and X_C = 1/(2πfC); at resonance X_L = X_C and Z = R (minimum), current is maximal.

Kirchhoff's laws: ΣI = 0 at a node, ΣU = 0 around a loop; superposition, mesh analysis, and Thévenin/Norton equivalents simplify linear networks.

Diode forward voltage ≈ 0.7 V (Si) / 0.3 V (Ge); bridge rectifier output average U_dc ≈ 0.9·U_rms without capacitor, rising toward √2·U_rms with smoothing capacitor under light load.

Operational amplifier basics: inverting gain = −R_f/R_in, non-inverting gain = 1 + R_f/R_in; input impedance high, output impedance low; negative feedback sets linear operation.

Protective measures per DIN VDE 0100: TN-S/TN-C-S/TT/IT systems; RCD (FI) trips at residual current I_Δn (typically 30 mA for socket circuits); earth resistance and loop impedance must be verified before energizing.

Cable sizing: current-carrying capacity depends on cross-section, installation method, ambient temperature, and bundling; voltage drop ΔU ≈ (2·l·I·cos φ)/(κ·A) for single-phase, with κ ≈ 56 m/(Ω·mm²) for copper.

Static equilibrium: ΣF = 0 and ΣM = 0; free-body diagrams identify all forces and moments; friction force F_R = μ·F_N with static μ_s > kinetic μ_k.

Stress σ = F/A, strain ε = Δl/l, Hooke's law σ = E·ε in the elastic range; E_steel ≈ 210 GPa, E_aluminium ≈ 70 GPa.

Bending: maximum bending stress σ_b = M_b / W with section modulus W; for a rectangular section W = b·h²/6; deflection depends on E·I (area moment of inertia).

Torsion: τ = M_t / W_t; for a solid circular shaft W_t = π·d³/16; allowable shear stress limits shaft diameter.

Bolted joints: preload F_V is set by tightening torque M_A = F_V · (d_2/2 · tan(φ+ρ) + μ_K · d_K/2); approximately M_A ≈ 0.2 · F_V · d for steel/steel with μ ≈ 0.14.

Bearings: basic rating life L_10 = (C/P)^p · 10⁶ revolutions, p = 3 for ball bearings, 10/3 for roller bearings; C = dynamic load rating, P = equivalent dynamic load.

Tolerances and fits per ISO 286: hole basis H, shaft basis h; clearance fit (H/h), interference fit (H/p), transition fit (H/k); ISO tolerance grades IT01–IT18 describe manufacturing accuracy.

Kinematics: v = ω·r, a = α·r; gear pair transmission ratio i = z_2/z_1 = n_1/n_2; belt drive slip reduces actual ratio and must be considered in positioning tasks.

Open-loop transfer function G_o(s) = G_R(s)·G_S(s); closed-loop transfer function G_w(s) = G_o/(1+G_o) for unity feedback; characteristic equation 1 + G_o(s) = 0 determines stability.

PID controller: u(t) = K_p·e + K_i·∫e dt + K_d·de/dt; parallel form G_R(s) = K_p·(1 + 1/(T_n·s) + T_v·s); K_i = K_p/T_n, K_d = K_p·T_v.

Ziegler–Nichols tuning (ultimate gain method): set K_i = K_d = 0, increase K_p until sustained oscillation at K_u with period T_u; then K_p = 0.6·K_u, T_n = 0.5·T_u, T_v = 0.125·T_u.

First-order lag: G(s) = K/(1+T·s); step response reaches 63.2 % after T, 95 % after 3T, 99 % after 5T; time constant T characterizes speed of response.

Second-order system: G(s) = ω_n²/(s² + 2·ζ·ω_n·s + ω_n²); damping ratio ζ < 1 oscillatory, ζ = 1 critically damped; overshoot depends only on ζ (e.g., ≈ 4.3 % at ζ = 0.707).

Stability criteria: necessary condition all coefficients of the characteristic polynomial positive; Routh–Hurwitz array gives exact stability limit; Nyquist criterion counts encirclements of −1 point.

PLC cycle: read inputs → execute program → write outputs (cyclic scan); scan time must be shorter than the shortest process reaction time; watchdog monitors cycle overrun.

Fieldbus/industrial Ethernet: PROFINET, EtherCAT, Modbus TCP; deterministic real-time requires isochronous mode; typical cycle times 1–10 ms for motion control, 10–100 ms for process control.

Maintenance strategies per DIN EN 13306: corrective, preventive (time-based), condition-based, and predictive; selection depends on failure consequence, cost, and detectability.

Key figures: MTBF = total operating time / number of failures; MTTR = total repair time / number of repairs; availability A = MTBF / (MTBF + MTTR).

Condition monitoring methods: vibration analysis (ISO 10816 zones A–D), thermography, oil analysis (particle count, viscosity, water content), ultrasound, and motor current signature analysis.

Vibration diagnosis: unbalance shows 1× rotational frequency; misalignment shows 2×; bearing defects produce characteristic frequencies (BPFO, BPFI) and high-frequency shock pulses (envelope analysis).

Electrical diagnostics: insulation resistance measurement with 500 V DC (minimum values per DIN VDE 0100-600, e.g., ≥ 1 MΩ for 230/400 V circuits); continuity and loop impedance tests.

Five-why and Ishikawa (fishbone) analysis structure root-cause investigation; fault tree analysis (FTA) quantifies probability of the top event from basic event probabilities.

Spare-parts management: ABC/XYZ classification; critical spares identified by failure impact and lead time; safety stock = z · σ_d · √(lead time) for normally distributed demand.

Repair documentation must record fault symptom, root cause, measures, replaced parts, and post-repair test results to feed back into maintenance planning (continuous improvement).

Technical drawings follow ISO 128 (line types), ISO 5457 (sheet sizes), ISO 7200 (title block); first-angle or third-angle projection must be indicated by the projection symbol.

Dimensioning rules per ISO 129: dimensions in millimetres without unit symbol, not redundant, not scaled from drawing, reference dimensions in parentheses.

Geometric tolerancing per ISO 1101: form (straightness, flatness, roundness, cylindricity), orientation (parallelism, perpendicularity, angularity), location (position, concentricity, symmetry), run-out.

Surface roughness per ISO 1302: Ra (arithmetic mean), Rz (maximum height); symbols indicate machining allowance and direction of lay.

Circuit diagrams per IEC 60617 use standardized graphical symbols; reference designators (e.g., K1, M1, Q1) and cross-references link contacts and coils across sheets.

Technical documentation structure per IEC 82045 / IEC 61355: document kinds (e.g., DCC, schematic, parts list), identification codes, revision status, and change history.

Operating instructions per Machinery Directive 2006/42/EC Annex I must contain intended use, residual risks, PPE, commissioning, maintenance, and troubleshooting in the language of the target country.

Version control: unique document ID, revision index, date, author, approver; obsolete documents must be withdrawn from use to avoid confusion on the shop floor.

Machinery Directive 2006/42/EC: manufacturer performs risk assessment (ISO 12100), applies harmonized standards (e.g., EN ISO 13849), issues Declaration of Conformity and affixes CE marking.

EN ISO 13849-1 determines Performance Level PL a–e from categories B, 1, 2, 3, 4, MTTF_d, and DC_avg; required PL follows from risk graph (S, F, P parameters).

Emergency stop per EN ISO 13850: red actuator on yellow background, latching, manual reset, stop category 0 or 1; not a substitute for safeguarding.

Protective measures per DIN VDE 0100: automatic disconnection of supply, RCD, double insulation, SELV/PELV (≤ 50 V AC / 120 V DC ripple-free), equipotential bonding.

Five safety rules for working on electrical installations: disconnect, secure against reconnection, verify absence of voltage, earth and short-circuit, cover adjacent live parts.

Electrical equipment of machines per EN 60204-1: main switch, emergency stop, protective conductor continuity, insulation resistance, and verification tests before handover.

Hazardous areas: ATEX Directive 2014/34/EU and IEC 60079 define zones (0, 1, 2 for gas; 20, 21, 22 for dust) and equipment categories; ignition protection types Ex d, Ex e, Ex i.

Lifting and load handling: DGUV regulations require periodic inspection of cranes and lifting gear; rated capacity must not be exceeded; load charts depend on radius and boom configuration.

Cost accounting: direct costs (materials, direct labour) are allocated directly; overhead costs are allocated via overhead rates (e.g., material overhead rate, production overhead rate, administration overhead rate).

Machine hour rate = (annual fixed costs + annual variable costs) / annual machine hours; used for costing when machines dominate the process.

Break-even point: quantity Q_B = fixed costs / (price per unit − variable cost per unit); contribution margin per unit = price − variable cost.

Depreciation: linear method = (acquisition cost − residual value) / useful life; declining-balance method applies a constant percentage to the book value; choice affects taxable profit.

Investment appraisal: net present value NPV = Σ C_t/(1+i)^t − C_0; accept if NPV > 0; internal rate of return IRR is the discount rate where NPV = 0.

Make-or-buy decision: compare relevant costs (variable manufacturing cost plus avoidable fixed costs) with purchase price plus transaction and quality costs.

Key performance indicators: OEE = availability × performance × quality; productivity = output / input; cost per unit = total cost / units produced.

Quotation and contract: fixed-price, cost-plus, and time-and-material models; payment terms, warranty, and risk allocation must be defined in the offer.

German dual system: Betrieb (company training) and Berufsschule (vocational school) cooperate; the Ausbildungsrahmenplan defines in-company content, the Rahmenlehrplan defines school content.

Training contract (Berufsausbildungsvertrag) must be registered with the competent chamber (IHK/HWK); it specifies training occupation, duration, probation, remuneration, and leave.

Ausbilder-Eignung requires professional competence and pedagogical aptitude (AEVO examination or equivalent); the training plan must be adapted to the apprentice's level.

Training methods: four-step method (prepare, demonstrate/explain, imitate/practise, consolidate), project method, and learning assignments support action-oriented learning.

Assessment: formative feedback during training, intermediate examination (Zwischenprüfung) and final examination (Abschlussprüfung / Gesellenprüfung); grades weighted per examination regulations.

Apprentices under 18 are covered by the Jugendarbeitsschutzgesetz: maximum 8 h/day, 40 h/week, rest breaks, no hazardous work, and medical examination before employment.

Documentation: Ausbildungsnachweis (training record book) must be kept regularly; the trainer reviews and signs it; it is part of the admission requirements for the final examination.

Conflict and drop-out prevention: early feedback talks, clear performance expectations, and involvement of the chamber's training advisers (Ausbildungsberater) when problems arise.

Project planning: work breakdown structure (WBS), milestones, Gantt chart, critical path method; resource leveling avoids overallocation.

Commissioning procedure: safety check, insulation test, functional test of sensors and actuators, parameterization of drives and PLC, documentation update, customer acceptance.

Systematic troubleshooting: observe symptom, gather information from documentation and HMI, form hypotheses, test one variable at a time, verify repair, document root cause.

Measurement practice: use calibrated instruments, select range for best resolution, consider measurement uncertainty, and record ambient conditions.

Customer communication: clarify requirements, document changes in writing, agree acceptance criteria, and provide training and handover documentation.

Occupational safety: risk assessment per ArbSchG and DGUV; PPE, lockout/tagout, and safe working procedures for electrical and mechanical tasks.

Time and cost control: track actual vs. planned hours, analyze deviations, and adjust schedule or resources; change orders must be priced and approved.

Ethical and legal responsibility: only perform work within one's qualification; report safety defects; maintain confidentiality of customer data.

Product liability: EU Product Liability Directive 85/374/EEC and national implementation impose strict liability for defective products; the producer must prove compliance with state of the art.

Contract types: Werkvertrag (work contract, success owed) vs. Dienstvertrag (service contract, activity owed); warranty rights depend on the type and on the defect notice.

Quality management per ISO 9001: process approach, risk-based thinking, PDCA cycle; documented information, internal audits, management review, and corrective actions.

Seven basic quality tools: check sheet, histogram, Pareto chart, cause-and-effect diagram, scatter diagram, control chart, flowchart.

Statistical process control: control charts distinguish common-cause from special-cause variation; process capability C_p = (USL − LSL)/(6σ), C_pk considers centering.

Measurement system analysis: gauge R&R studies quantify repeatability and reproducibility; acceptance often requires < 10 % of tolerance (AIAG guideline).

CE marking process: identify applicable directives, perform conformity assessment, compile technical file, issue EU Declaration of Conformity, affix CE mark.

Document control and traceability: ISO 9001 requires identification, version control, and retention of records; traceability links products to batches, tests, and personnel.