Why model and simulate? Types of models
A model is a simpler copy of a product that keeps what matters for a question ("Will it break?"). A simulation uses the model to predict how the product behaves.
- Physical models: sketch models, scale models, prototypes (e.g. a 1:10 bridge in a wind tunnel).
- Mathematical models: equations, such as stress = force / area or V = I × R.
- Digital models: a CAD model that software can test (stress, heat, flow, motion).
Why? Simulation is cheaper, faster and safer than building and breaking many real parts. It lets you try many ideas and see inside a part, where no sensor can go.
Rapid prototyping (3D printing, laser cutting) turns the best digital model into a real part quickly for the final checks.
Model variables: effort and flow
Many simulation tools describe every kind of system with the same pair of variables:
| Domain | Effort (pushes) | Flow (moves) | Power |
|---|---|---|---|
| Mechanical (straight line) | force F (N) | speed v (m/s) | F × v |
| Mechanical (turning) | torque (N·m) | angular speed (rad/s) | torque × ω |
| Electrical | voltage U (V) | current I (A) | U × I |
| Fluid (hydraulic) | pressure p (Pa) | flow rate Q (m³/s) | p × Q |
| Thermal | temperature (K) | heat flow | - |
Because effort × flow = power in each domain, a tool can join an electric motor, a gearbox and a pump in one model and follow the energy through it.
How the software solves: mesh, solver and time step
Finite elements
A real part has a complicated shape. The software cuts it into many small, simple pieces: elements (little bricks or triangles) joined at nodes. This net is the mesh. For each element it writes simple equations; together they make thousands of equations.
The solver
The solver is the part of the program that solves all the equations at once and gives values at each node: displacement, stress, temperature.
Time step
For moving or changing systems (a motor starting, a tank filling), the solver goes forward in small time steps Δt. A smaller step follows fast changes better but needs more steps.
Choosing software
Pick the tool by the question: CAD-based FEA for stress and bending, multi-physics / block-diagram tools for motors, circuits and control, CFD for air and water flow, motion tools for mechanisms. Check the cost, the licence (free student versions exist), and whether it can import your CAD file.
Reading results and accuracy versus computing time
Results are shown as colour maps (blue low, red high), exaggerated shapes (the bend is drawn bigger than real) and graphs over time.
- Stress σ (Pa or MPa) = how hard the material is being pulled or pushed inside.
- Deflection (mm) = how far a point moves.
- Safety factor = strength of the material / highest stress. Designers usually want 1.5 to 3 or more.
Accuracy vs time
| Mesh | Accuracy | Computing time |
|---|---|---|
| coarse (few elements) | rough; can miss the peak stress | seconds |
| fine (many elements) | close to the true value | minutes to hours |
Doubling the elements roughly halves the error here but can multiply the time by 4 or more. Engineers refine the mesh until the answer stops changing much (a convergence check) and use fine elements only where stress is high.
Formulas behind our bracket
For a beam fixed at one end with load F at the tip: highest stress σ = 6FL / (b h²) at the wall; tip bend δ = FL³ / (3EI) with I = b h³ / 12. E is stiffness (Young's modulus).
Experiment and simulate: checking with real tests
A simulation is only trusted after it is compared with a real experiment.
- Sensors: load cell (force), strain gauge (stretch), displacement sensor (mm), thermocouple (temperature), ammeter and voltmeter. Each gives a signal (often a voltage) with a range, a resolution (smallest step) and a sampling rate.
- Measurement errors: every reading has an uncertainty, e.g. 3.6 ± 0.1 mm. Random errors scatter the readings; systematic errors shift them all (a badly zeroed scale). Repeat and average; calibrate.
- Test protocol: a written plan: aim, set-up, steps, loads, safety rules (goggles, guards, limits), what to record.
If simulation and test differ by more than the measurement uncertainty, find out why: wrong material data, wrong fixing, too coarse a mesh. Then improve the model. This loop is called validation.
Try it: a ruler bracket
- Clamp a 30 cm plastic ruler to a table so 25 cm sticks out.
- Hang 1, 2 then 3 coins (or small bags of rice) from the tip. Measure the tip drop with another ruler each time.
- Predict: if one load gives 5 mm, what will twice the load give? (The formula says double.)
- Now use 20 cm overhang. The formula says the bend falls by (20/25)³ ≈ 0.5. Check it.
- Open the last 3D step and compare steel, aluminium and plastic with the same load.
Key formulas and definitions
- Power = effort × flow (F·v, U·I, p·Q)
- Stress σ = F / A; beam at the wall: σ = 6FL / (b h²)
- Tip bend δ = F L³ / (3 E I), I = b h³ / 12
- Safety factor = material strength / highest stress
- Finer mesh or smaller Δt → more accurate, more computing time
Worked examples
1. A motor gives a force of 50 N while moving a load at 2 m/s. What is the power? Name the effort and flow.
Effort = force 50 N, flow = speed 2 m/s. Power = 50 × 2 = 100 W.
2. A pump makes a pressure of 200 000 Pa with a flow rate of 0.001 m³/s. Find the power.
P = p × Q = 200 000 × 0.001 = 200 W.
3. A steel bracket (strength 250 MPa) has a highest stress of 120 MPa. Find the safety factor. Is it acceptable if the rule is at least 2?
SF = 250 / 120 ≈ 2.08. It is just above 2, so it passes.
4. Our bracket: L = 0.3 m, b = 0.03 m, h = 0.01 m, F = 200 N. Find the highest stress.
σ = 6FL / (b h²) = 6 × 200 × 0.3 / (0.03 × 0.0001) = 360 / 0.000003 = 120 000 000 Pa = 120 MPa.
5. A mesh of 8 elements gives 112 MPa, 16 gives 116 MPa, 32 gives 118 MPa. Which would you use and why?
The answer changes by only about 2 MPa (under 2%) from 16 to 32, so it has nearly converged. 16 or 32 elements is good enough; 32 if computing time is not a problem, because peak stress matters for safety.
6. A test with a displacement sensor gives 3.9 ± 0.2 mm; the simulation says 3.6 mm. Is the model validated?
The difference is 0.3 mm, bigger than the 0.2 mm uncertainty, so not quite. Check the fixing (a real clamp is never perfectly rigid) and the material data, then rerun.
Common mistakes
- Trusting colourful results without checking. A simulation must be validated against a real test or a hand calculation.
- Thinking the exaggerated bend is real size. Software usually draws deflection many times bigger.
- Using a very coarse mesh: it can miss the highest stress and make a part look safer than it is.
- Choosing the finest mesh and tiniest time step everywhere: the run may take hours for almost no gain.