PRESSURE STORES ENERGY. FLOW MAKES MOTION.
Follow a pump, accumulator and position servo through a command, a pump loss and a backup response.
Pressure acting on piston area provides force. Delivered volume determines displacement and speed.
Whole-run summary · live values appear above
CAUSE → RESPONSE → COMPARISON
B · solid turquoise A · dashed amber
Time plots share the playback cursor. Design sweeps and phase plots retain their own axes. A stopped run holds its final resolved state.
| Whole-run quantity | A · saved | B · live | B − A | Unit |
|---|
A snapshot includes parameter values and event times. Export retains both configurations and their calculated traces.
THE PHYSICS BEHIND THE RESPONSE
Follow each balance, then connect it to the response above. Open Symbols & units for the notation. A dot denotes a time derivative unless a non-dimensional time is stated.
Pump flow first supplies valve demand and leakage; any imbalance changes pressure in the compressible fluid and accumulator.
Within the normal stroke, inflow must both fill the moving chamber and compress its fluid. Internal leakage reduces that supply.
The pressure force accelerates the piston against the external load, spring and damping. The soft-stop force is zero inside the 0–0.4 m travel.
Pressure determines available piston force; volume flow determines speed. Their product accounts for mechanical power at the piston, before other losses.
Equations describe this bounded teaching model. Assumptions and source references are retained below. Internal calculations use SI units; controls and plots show their own labelled units.
Single-acting, spring-return teaching servo; 80 kg moving mass, piston area 0.0012 m², 0.4 m stroke, spring 30 kN/m, damping 5 kN s/m, bulk modulus 1.2 GPa. Reservoir is the gauge-pressure reference. Accumulator precharge is 8 MPa absolute. Supply initially 14 MPa gauge. Main flow falls linearly to zero at 18 MPa; relief opens above 16 MPa. Backup supplies 70% of nominal flow. No fluid temperature, cavitation, pipe-wave propagation or certified hydraulic architecture.
FAA · Aircraft systems ↗Numerical checks test the stated equations. They do not establish aircraft certification or experimental accuracy. Schematic flow markers indicate direction; their speed is illustrative. No manufacturer geometry or performance data is reproduced. Version: coupled-labs-v1.1.