Page 523 - Mechatronics with Experiments

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JWST499-Cetinkunt
JWST499-c07
ELECTROHYDRAULIC MOTION CONTROL SYSTEMS 509
Estimating the friction force, F , is rather difficult. One common way to take it into account
f
is to use a safety factor, SF, as follows,
F = F = SF ⋅ (m ⋅ ̈ x + F ) (7.262)
ext
L
where SF is the safety factor (i.e., SF = 1.2). For rotary actuators, analogous relation-
ships hold,
̈
T = T = SF ⋅ (J ⋅ + T ) (7.263)
L ext
̈
where J is the total mass moment of inertia of rotary load, is angular acceleration, T ext is
the torque to be delivered to the load. The flow–current–pressure differential relation for a
proportional or servo valve which is positioned between the pump supply line and load line,
√
Q∕Q = (i∕i ) 1 − (ΔP ∕P ) (7.264)
nl max L S
√
= (i∕i ) (ΔP ∕P ) (7.265)
max v S
where ΔP is the load pressure (i.e., in the case of a linear cylinder this is the pressure
L
difference between the two sides of the cylinder, and in the case of a rotary hydraulic motor
this is the inport and outport pressure differential). In other words, ΔP is the pressure
L
differential between the A and B ports of the valve. ΔP = P −ΔP − P is the pressure
v S L T
drop across the valve, P is supply pressure from pump, P tank return line pressure. Quite
S T
often, P is taken as zero pressure. Q is the flow through the valve when it is fully open
T nl
(i = i ) and the pressure drop across the valve is P . When there is no-load, all of the
max S
supply pressure is dropped across the valve. In order to determine the flow rate (Q )ofa
r
valve at a particular pressure drop (P −ΔP ) when it is fully open, we set i = i in the
S L max
above equation,
√
Q ∕Q = 1 − (ΔP ∕P ) (7.266)
nl
r
L
S
√
= (ΔP ∕P ) (7.267)
v
S
A proportional valve is rated in terms of its flow rate capacity in catalogs for a pressure
drop of ΔP = 150 psi across the valve. A servo valve is rated for ΔP = 1000 psi.
v v
Component Sizing Algorithm 1
Step 1: Determine the performance specifications based on load requirements:
{w ,(w , T )} or {V ,(V , F )}
nl
r
r
r
nl
r
Step 2: Pick either displacement per unit stroke for the actuator (D or A ) or the supply
m c
pressure, P . Let us assume we pick the displacement (D or A ). This selection
s m c
specifies the actuator size (hydraulic motor or cylinder).
Step 3: Calculate Q , Q , ΔP using Equations 7.259 and 7.260 for the specifications.
nl r L
Q = D ⋅ w nl Q = A ⋅ V nl (7.268)
c
m
nl
nl
Q = D ⋅ w r Q = A ⋅ V r (7.269)
r
m
r
c
ΔP = T ∕D ΔP = F ∕A (7.270)
L r m L r c
Step 4: Assume i = i max , calculate the P from Equation 7.266. Add 10–20% to the P as
s
s
a safety factor.
√
Q ∕Q = 1 − (ΔP ∕P ) (7.271)
L
r
S
nl
Step 5: Given the calculated value of Q , and given the operating input shaft speed of the
nl
pump w which is determined by the mechanical power source device driving the
in