Page 77 - Fluid Power Engineering

54 Cha pte r T w o

B = Bulk modulus of oil, Pa
B = Equivalent bulk modulus of mixture, Pa
e
c = Radial clearance, m
C = Hydraulic capacitance, m /N
5
D = Orifice diameter, inner pipe diameter, spool diameter, m
F = Force, N
f = Friction coefficient, Ns/m
v
F = Pressure force acting on the fluid element, N
P
F = Shear force acting on the fluid element, N
τ
k = Spring stiffness, N/m
L = Pipe length, length of spool land, length of leakage
path, m
m = Mass of the moving parts, kg
n = Polytropic exponent
P = Pressure, Pa
Q = Leakage flow rate, m /s
3
L
r = Radial distance from the midpoint of the clearance, m
Re = Reynolds number
R = Resistance to leakage, Ns/m 5
L
u = Fluid velocity, m/s
v = Mean fluid velocity m/s
V = Initial oil volume, m 3
V = Volume of oil in chamber A, m 3
A
V = Volume of oil in chamber B, m 3
B
V = Total volume of oil-gas mixture, m 3
T
x = Spool displacement, m
y = Displacement perpendicular to the velocity vector, m
y = Piston displacement, m
α= Ratio of gases volume to mixture volume, at atmospheric
pressure
α= Coefficient of volumetric thermal expansion, K −1
ΔP = Pressure difference across the radial clearance, Pa
ΔT = Temperature variation, °C
ΔV = Variation of oil volume due to oil compressibility, m 3
C
ΔV = Variation of oil volume due to thermal expansion, m 3
T
λ= Friction coefficient
μ= Coefficient of dynamic viscosity, Ns/m 2
ρ= Oil density, kg/m 3
τ= Shear stress, N/m 2
2
ν= Kinematic viscosity, m /s

Appendix 2A Transfer Functions
The transfer function of a linear system is defined as the Laplace
transform of a system output divided by that of its input when the
initial conditions are zero. Conventionally, the symbol G(s) is used for
the transfer function. For evaluating the transfer function of a linear