Asking gas spring model

Hello all,

I'm newb here.

I have no idea how to make the fomula of Gas Spring model.

Hope you guys can give me ideas.

Gas spring model (sqrt = square root, ddt = double dot, dt = single dot)

△T =0, T1=T2

Costant Numbers

K=0.5229sqrt(ºR) /sec

γ=1.4 (ratio of specific heat)

R=661.9 in/ºR

Pcr = 0.5283 (critical pressure)

Cd = 0.7 (drag coefficient)

ρ = P/RT

ºR=460+ºF

ºF = 32+0.18 ºC

Variable Numbers

P0 : initial pressure

x0 : Original piston position

Fμ : Frition of piston

A0 : orifice setion-area

Pi,Vi,Ai : Pressure, Volume, Section-area of piston compartment

F : Force on piston load.

Equation of Motion (ddt = double dot, dt = single dot)

Mxddt = (P2A2-P1A1) - Fμ -F

where, P1dt = (-m12dt + ρA1xdt)*γRT1/V1

P2dt = (m12dt - ρA1xdt)*γRT1/V1

if P1≥P2, m12dt = (Cd*A0*K*P1*N12)/sqrt(T1)

N12 = [((P2/P1)^2/γ - (P2/P1)^γ+1/γ) / (((γ-1)/2)*(2/(γ+1))^(γ+1)/(γ-1))]^1/2 for P2/P1 > Pcr

N12 =1 for P2/P1 ≤ Pcr

if P1≤P2, m12dt = -(Cd*A0*K*P1*N12)/sqrt(T1)

N12 = [((P1/P2)^2/γ - (P1/P2)^γ+1/γ) / (((γ-1)/2)*(2/(γ+1))^(γ+1)/(γ-1))]^1/2 for P1/P2 > Pcr

N12 =1 for P1/P2 ≤ Pcr

V1 = A1(L-x-x0-pt)

V2 = A2*x

*Foe adiabatic process : ρ2/ρ1 = (P2/P1)^(1/γ), T2/T1 = (P2/P1)^((γ-1)/γ)

initial temperature : T0

Temp. of chamber 1 : T1 = T0(P1/P0)^((γ-1)/γ)

Temp. of chamber 2 : T2 = T0(P2/P0)^((γ-1)/γ)

ρ1 = P1/RT1 = P1/(R*T0*(P1/P0)^((γ-1)/γ) = (P0/(RT0)) * (P1/P0)^((γ-1)/γ)

ρ1 = P2/RT2 = P2/(R*T0*(P2/P0)^((γ-1)/γ) = (P0/(RT0)) * (P2/P0)^((γ-1)/γ)

continuity equation:

P1dt = (-m12dt + ρA1xdt)*γRT1/V1

P2dt = (m12dt - ρA1xdt)*γRT1/V1

[Vijay]

Do you want to model your equations?

if yes then please refer Model Differential Algebraic Equations - MATLAB & Simulink - MathWorks India