Semi-analytical modelling of a hydraulic free-piston engine

•A semi-analytical method for the HPFE parameter design is proposed.•The HFPE piston oscillation is a hard self-oscillation.•The piston oscillation has an unsymmetrical oscillation characteristic.•Stable running of a single piston HFPE prototype is realised.

The hydraulic free-piston engine is a hybrid of a hydraulic plunger pump and a free-piston engine. This paper presents a semi-analytical method for the hydraulic free-piston engine parameter design. An oscillation function described the piston oscillation were established. The piston oscillation characteristics were analysed. The parameter sensitivity and the limit cycle stability of the piston oscillation were investigated. The results show that the single piston free-piston engine system is a hard self-oscillation with variable damping and stiffness. External energy is required to start the piston oscillation. The piston oscillation has an unsymmetrical oscillation characteristic. The dead centres of the piston motion are determined by the energy balance. The energy supply and the energy consumption are determined by the generalised damping in the piston oscillation function. The piston oscillation frequency should satisfy the minimum compression ratio requirement for the compression ignition. In the steady operation, the piston motion is a self-excitation oscillation. The trajectory stability is mainly determined by the fuel combustion energy supply. The scavenging affected by the BDC should be paid special attention to ensure the trajectory stability.