The mathematical model is established according to the physical model of the single-degree-of-freedom oil-gas spring as shown in 2. The initial position of the hydraulic cylinder piston is the equilibrium position of the oil and gas spring under a certain preload. Assume that under the action of the excitation signal x, the pressure in the cylinder chamber is p1; the pressure at the junction of the damping valve and the pipeline is p2; the pressure at the outlet of the accumulator is p3; the oil pressure and gas pressure in the accumulator are respectively For p4 and pg; the initial pressure of the oil is p0. The temperature of the oil and gas spring does not change during the movement.
The compressibility of the oil is in the actual hydraulic system, a small amount of gas is inevitably mixed into the oil, so the characteristics of the compressibility of the oil and the low-pressure nonlinearity must be considered. According to the fluid theory, the instantaneous density Q of the oil can be expressed as <2>Q=Q01+1B0(p-p0)(1) where: Q0 is the density in the standard state of the oil; B0 is the bulk modulus of the oil ;p is the instantaneous pressure of the oil.
According to the fluid theory, the fluid flow rate m (the product of the volume flow rate Q of the fluid and the fluid density Q) remains unchanged, ie m=QQ(2) piston rod force oil and gas spring in the working process The force acting on the piston rod includes the pressure in the hydraulic cylinder and the friction between the piston and the cylinder wall (including the static friction force Fsta and the dynamic friction force Fdyn). Since the static friction force to the dynamic friction force has a transition process, the dynamic friction force It can be shown as Fdyn=1-LDmin(x,utr)utrFsta(3) where: LD=Fsta-FdynFsta; x is the speed of the excitation signal (the stretching stroke is positive, the compression stroke is negative); utr is the full dynamic friction Set speed when force. Therefore, the total force of the oil and gas spring is F = p1Aeff - Fdynsign (x) (4) where: Aeff is the effective area of ​​the piston; sign (x) is a sign function.
The mass flow rate of the oil in the hydraulic cylinder is m=Q1Q1 (5) where: Q1 is the volume flow of the oil in the hydraulic cylinder, which is equal to the product of the moving speed of the piston rod and the effective area of ​​the piston, ie Q1=xAeff; Q1 is the oil in the hydraulic cylinder. The density of the liquid. Where: Q3 is the density of the oil in the pipeline; Dp is the diameter of the pipeline; lp is the length of the pipeline; Q3 is the volumetric flow of the oil in the pipeline; Ap is the cross-sectional area of ​​the pipeline; K is the resistance coefficient along the path, For 1K=2lg(ReK)-0.8(9)2.4 accumulator performance analysis, since the accumulator outlet is connected to the oil pipeline, there is partial pressure loss at the outlet, and the pressure relationship can be shown as p4-p3=12Q4NQ4Aa2sign( x) (10) where: Q4 is the density of the oil at the outlet of the accumulator; N is the partial pressure loss coefficient; Q4 is the accumulator outlet volume flow; Aa is the accumulator outlet cross-sectional area.
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