Page 75 - Fluid Power Engineering

52 Cha pte r T w o

Recalculate for different values of clearance, up to c = 100 μm, and plot the
relation Q (c).
L

14. (a) Derive the transfer function relating the spool displacement to the
applied pressure difference, X(s)/ΔP(s), where ΔP = P − P .
2
1
(b) Calculate and plot the transient response if ΔP is a step of magnitude
4 bars, given
Spool mass m = 0.07 kg Spool diameter D = 8 mm
Spring stiffness k = 20 kN/m Radial clearance c = 4 μm
Spool land length L = 10 mm Oil density ρ= 860 kg/m 3
Oil dynamic viscosity μ= 0.02 Ns/m 2

15. Calculate the pressure upstream of the throttle valve, A , assume laminar
t
flow in the lines, and then check this assumption, given
Pump flow Q = 14 L/min Oil density ρ= 866 kg/m 3
Dynamic viscosity Throttling valve Area A = 3 mm 2
μ= 0.0185 Ns/m 2 Dimensions of lines D = 14 mm,
1
Discharge coefficient D = 8 mm, D = 10 mm
2 3
C = 0.611 L = 1.3 m, L = 2 m, L = 1.5 m
D 1 2 3

A t 2
1
3