Pressure Dependent Damper $—$ Translational damper through pressure dependent forces

Non-linear damper model: hydrodynamic friction in a cylinder. The damping coefficient shall be smaller than the piston area at port A.

 Equations $f=\left({p}_{A}-{p}_{B}\right){k}_{p}$ $\mathrm{flange_b.f}=f$ ${m}_{\mathrm{flow}\left(A\right)}=0$ ${m}_{\mathrm{flow}\left(B\right)}=0$ ${s}_{\mathrm{rel}}=\mathrm{flange_b.s}-\mathrm{flange_a.s}$ ${v}_{\mathrm{rel}}={\partial }_{t}\left({s}_{\mathrm{rel}}\right)$ $\mathrm{flange_a.f}+\mathrm{flange_b.f}=0$

Variables

 Name Value Units Description Modelica ID ${s}_{\mathrm{rel}}$ $m$ Relative distance s_rel ${v}_{\mathrm{rel}}$ $\frac{m}{s}$ Relative viscosity v_rel $f$ $N$ Force between flanges f ${p}_{A\left(\mathrm{summary}\right)}$ ${p}_{A}$ $\mathrm{Pa}$ Pressure at port A summary_pA ${p}_{B\left(\mathrm{summary}\right)}$ ${p}_{B}$ $\mathrm{Pa}$ Pressure at port B summary_pB ${f}_{a\left(\mathrm{summary}\right)}$ $\mathrm{flange_a.f}$ $N$ Force acting on flange a summary_fa ${f}_{b\left(\mathrm{summary}\right)}$ $\mathrm{flange_b.f}$ $N$ Force acting on flange b summary_fb

Connections

 Name Description Modelica ID ${\mathrm{flange}}_{a}$ Cylinder mounting point flange_a ${\mathrm{flange}}_{b}$ Piston mounting point flange_b ${\mathrm{port}}_{A}$ Pressure in chamber A port_A ${\mathrm{port}}_{B}$ Pressure in chamber B port_B

Parameters

 Name Default Units Description Modelica ID ${k}_{p}$ $0$ Pressure damping coefficient kp