Chartered Membership of IMechE (CEng MIMechE) Core Mechanical Engineering Knowledge Flashcards

24 sample cards from the Core Mechanical Engineering Knowledge deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. Define the drag force equation and the dynamic viscosity (Newton's law of viscosity).

   Drag: $F_D = \frac{1}{2}\rho v^{2} C_D A$. Newton's law of viscosity: $\tau = \mu\frac{du}{dy}$, where $\mu$ is dynamic viscosity and $\frac{du}{dy}$ the velocity gradient.

2. Compare the Otto and Diesel cycles by their heat-addition process.

   The Otto (spark-ignition) cycle adds heat at constant volume; the Diesel (compression-ignition) cycle adds heat at constant pressure. Both reject heat at constant volume.

3. Give the thermal efficiency of the ideal Otto cycle in terms of compression ratio.

   $\eta_{Otto} = 1 - \frac{1}{r^{\gamma-1}}$, where $r$ is the compression ratio and $\gamma$ the specific heat ratio.

4. Name the four components of an ideal vapour-compression refrigeration cycle and define the COP.

   Evaporator, compressor, condenser, expansion valve. $COP_{ref} = \frac{Q_{cold}}{W_{in}} = \frac{\text{refrigeration effect}}{\text{compressor work}}$.

5. List the typical stages of the engineering design process.

   1) Identify need/requirements, 2) define specification (PDS), 3) concept generation, 4) concept evaluation/selection, 5) detailed/embodiment design, 6) prototyping & testing, 7) manufacture & implementation, with iteration throughout.

6. What is a Product Design Specification (PDS) and what is the purpose of a FMEA?

   A PDS is the controlling document listing all design requirements/constraints (performance, environment, cost, standards). A Failure Mode and Effects Analysis (FMEA) systematically identifies potential failure modes, their effects, and prioritises them by a risk priority number.

7. Define the factor of safety and write its basic form.

   The factor of safety is the margin between a material's capacity and the applied/working condition: $FoS = \frac{\text{material strength}}{\text{working (applied) stress}}$ (e.g. $\frac{\sigma_y}{\sigma_{working}}$).

8. Name common machine elements used to transmit power and to join components.

   Power transmission: gears, belts/pulleys, chains, shafts, couplings, bearings. Fasteners/joints: bolts and nuts, screws, rivets, keys, pins, welds, splines.

9. For a pair of meshing spur gears, write the gear (velocity) ratio in terms of teeth and speeds.

   $\frac{\omega_1}{\omega_2} = \frac{N_2}{N_1} = \frac{d_2}{d_1}$, where $N$ is the number of teeth and $d$ the pitch diameter; the larger gear runs slower.

10. Distinguish CAD, CAE, and CAM in the design/manufacture workflow.

    CAD (Computer-Aided Design): geometric modelling and drawings. CAE (Computer-Aided Engineering): analysis/simulation such as FEA/CFD. CAM (Computer-Aided Manufacturing): generating tool paths and machine instructions from the CAD model.

11. Classify the main categories of manufacturing processes.

    Casting (e.g. sand, die), forming/deformation (forging, rolling, extrusion, sheet forming), machining/material removal (turning, milling, drilling, grinding), joining (welding, brazing, adhesives, fasteners), and additive manufacturing (3D printing).

12. Compare additive and subtractive manufacturing.

    Additive builds parts layer by layer adding material (e.g. SLS, FDM), enabling complex geometry with little waste. Subtractive removes material from a blank (e.g. milling, turning), giving high accuracy/finish but more waste and geometric limits.

13. What is a closed-loop (feedback) control system, and what does the transfer function of a system represent?

    A closed-loop system uses feedback to compare output with a reference (error) and adjust the input to reduce that error. The transfer function $G(s) = \frac{Y(s)}{X(s)}$ is the ratio of output to input in the Laplace domain, characterising system dynamics.

14. Write the standard PID controller equation and state the role of each term.

    $u(t) = K_p e(t) + K_i \int e(t)\,dt + K_d \frac{de(t)}{dt}$. Proportional reduces error, integral eliminates steady-state offset, derivative improves damping/transient response.

15. For a single-degree-of-freedom undamped vibrating system, give the natural frequency.

    $\omega_n = \sqrt{\frac{k}{m}}$ (rad/s), so $f_n = \frac{1}{2\pi}\sqrt{\frac{k}{m}}$ (Hz), where $k$ is stiffness and $m$ mass.

16. Define the damping ratio and the condition for critical damping.

    $\zeta = \frac{c}{c_c}$ where $c_c = 2\sqrt{km} = 2m\omega_n$. $\zeta<1$ underdamped (oscillatory), $\zeta=1$ critically damped (fastest non-oscillatory return), $\zeta>1$ overdamped.

17. What is resonance, and how is the decibel level of sound defined?

    Resonance occurs when the forcing frequency approaches the natural frequency, causing large amplitude response (limited only by damping). Sound level: $L = 10\log_{10}\left(\frac{I}{I_0}\right)$ dB, with reference intensity $I_0 = 10^{-12}\,\text{W m}^{-2}$.

18. What is the Finite Element Method (FEM) and what is mesh convergence?

    FEM discretises a continuous domain into small elements with nodes, solving governing equations approximately over each element and assembling them. Mesh convergence is refining the mesh until the result no longer changes significantly, indicating a reliable solution.

19. In probability/statistics, write the mean and standard deviation of a sample, and state the empirical rule for a normal distribution.

    Mean $\bar{x} = \frac{1}{n}\sum x_i$; standard deviation $s = \sqrt{\frac{1}{n-1}\sum (x_i-\bar{x})^{2}}$. For a normal distribution about 68%, 95%, and 99.7% of data lie within $\pm1\sigma$, $\pm2\sigma$, $\pm3\sigma$.

20. Define reliability $R(t)$ and its relationship with failure probability and the exponential model.

    $R(t) = 1 - F(t)$, the probability of surviving to time $t$. For a constant failure rate $\lambda$ (exponential model), $R(t) = e^{-\lambda t}$ and $MTBF = \frac{1}{\lambda}$.

21. For components in series and in parallel, how do reliabilities combine?

    Series (all must work): $R_{sys} = \prod_i R_i$. Parallel/redundant (at least one works): $R_{sys} = 1 - \prod_i (1 - R_i)$.

22. What does the bathtub curve describe in reliability engineering?

    It describes how failure rate varies over a product's life: a decreasing infant-mortality (early-failure) region, a low constant useful-life region (random failures), and an increasing wear-out region.

23. What is a digital twin in modern mechanical engineering?

    A digital twin is a dynamic virtual model of a physical asset or system, continuously updated with sensor/operational data, used to monitor, simulate, predict performance, and optimise maintenance in real time.

24. What is life cycle assessment (LCA) and name a key principle of sustainable/design-for-environment engineering.

    LCA quantifies the environmental impacts of a product across its whole life (raw materials, manufacture, use, end-of-life). A key sustainable-design principle is the waste hierarchy / circular economy: reduce, reuse, recycle (and design for disassembly and material efficiency).

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