Reciprocating compressor

Investigation of the kinematics of the crank mechanism: piston travel, speed and acceleration depending on the crank angle. Interactive derivation of the path function s(φ) on the moving model; all parameters correspond to the real laboratory test rig (GUNT ET-513).

Analysis of the operating cycle of a single-stage reciprocating compressor in the p–V diagram: compression, discharge, re-expansion and intake. A polytropic cycle model is compared with real indicator measurements from the test rig, and the compression work is determined.

DC network analysis using an installed test-rig component: the piezoresistive Kulite pressure sensor that supplies the raw cylinder-pressure data for the indicator diagram is essentially a Wheatstone full bridge made from four strain-sensitive resistors — a purely resistive DC network. The module covers voltage division and bridge balancing, Kirchhoff's voltage law, pressure-induced imbalance (ΔR/R → U_out), and the loaded bridge as a two-terminal network. The load current is determined step by step using Thévenin/Norton equivalents and the current-divider rule; series/parallel reduction, mesh-current analysis and nodal analysis converge on the same result, while maximum power transfer reconnects the theory to the test rig's measurement chain.

RLC resonant circuits in the real drive: the test-rig motor's stator winding combines inductance with copper-winding resistance; together with a compensation capacitor at the motor terminals, it forms a resonant circuit supplied by the variable-frequency drive. The component laws (capacitor i = C·du/dt, inductor u = L·di/dt) lead to free oscillation and natural frequency, the differential equation for damped oscillation (underdamped, critically damped and overdamped cases), and resonance with quality factor and bandwidth. The relationship to the drive remains visible throughout, including compensation resonance that can endanger the motor. Inductance, capacitance, resistance and excitation frequency are freely adjustable; an animated energy pendulum and oscilloscope make the behaviour visible.

Analysis of the installed compressor drive (Siemens SIMOTICS three-phase induction motor with variable-frequency drive): rotating field and synchronous speed, slip, the Kloss torque characteristic and the operating point on the compressor load characteristic. Frequency, pole count, breakdown torque, breakdown slip and back pressure are freely adjustable; the test-rig motor's data-sheet values can be loaded at the touch of a button.

Pressure control for a reciprocating compressor: The variable-frequency drive and compressed-air receiver form a plant comprising two first-order lag elements. The module uses the Laplace transform and inverse transform to develop a closed-loop PID controller; an interactive controller demonstrates setpoint tracking and disturbance rejection.

Numerical determination of the speed maximum of the piston using difference quotient and bisection method. Both methods are implemented in Python directly in the browser; The calculated results are immediately displayed in the v(φ) diagram of the crank mechanism.