Handbook of Mechanical Engineering Calculations, Second Edition

Section 25: Hydraulic and Pneumatic Systems Design

DETERMINING RESPONSE TIME OF PILOT-OPERATED SOLENOID-ENERGIZED SPOOL VALVES IN HYDRAULIC SYSTEMS

A pilot-operated solenoid-energized spool control valve in a hydraulic system has the dimensions, operating pressures, and performance given in lable l. Pilot supply pressure is 100 lb/in 2 (689 kPa); main supply pressure is 500 lb/in 2 (3445 kPa). Find the maximum velocity of this valve, its acceleration time, and the total response time. Next, using the same dimensions and main operating pressure, find the same unknowns when the pilot pressure is made equal to the main operating pressure i.e., 500 lb/in 2 (3445 kPa). As a further modification, a small actuating piston is placed at each end of the main spool, Fig. 3, to increase the longitudinal velocity for a given pilot-fluid flow rate. Trial and error would normally be used to calculate the most effective diameter for the actuating piston. In this procedure we will use a diameter d x= 1.4 in (3.56 cm) for this small actuating piston. If the dimensions and operating pressures are unchanged, analyze the valve for the same unknowns as above.


Figure 3: Piston-operated solenoid-energized spool valve.
Table 1: Dimensions and Operating Conditions*
Pilot Spool Main spool

Diameter, in

d = 0.25

D = 2.5

Mass, lb-sec 2/in

m = 0.0002

M = 0.05

Stroke, in

s = 0.375

S = 1.5

Land length, in

L = 6.0

Radial clearance, in

C = 0.0003

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