Page 579 - Mechatronics with Experiments

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JWST499-Cetinkunt
JWST499-c07
ELECTROHYDRAULIC MOTION CONTROL SYSTEMS 565
% Piston and load inertia dynamics
zdot(7) = z(8);
zdot(8) = (1/(m_p+m_l))∗(-c_p ∗ z(8) + p_a ∗ A_a - p_b ∗ A_b - F_load) ;
return;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Example: One Degree of Freedom Hydraulic Motion Control System
with Flexible Base and Load Contact Consider a single-acting hydraulic cylin-
der which is connected to a non-rigid base as well as a load (Figure 7.105). The base of
the cylinder is not connected to a rigid ground, but to a flexible and moving base. This
is the case in mobile work equipment where the hydraulic cylinder is connected to the
machine frame and the machine frame rides on tires which are highly flexible. In addition,
the rod-end is connected to the load through a non-rigid tool mechanism or the the load is
not rigid, such as a pile of soil. The interaction between the cylinder and the load is modeled
as an inertia, a spring, and a damper. The machine frame, tires, and the cylinder outer shell
inertia are modeled as mass 1, m , and spring and damper constants k and c . The piston
1
1
1
and rod are modeled as moving inertia (mass) 2, m . The load contact and load inertia
2
are modeled as mass 3, spring and damper constants, m , k , c , respectively. The same
3
3
3
dynamic model principle is used in modeling hydraulically powered roll-thickness control
systems in steel mills and other web-thickness control applications. In the roll-thickness
F
load
Load
m 3
k c
Tool 3 3 y 3
fixture
Cylinder
P re
A re
m
2
P A y 2
Frame he he

Tire m 1
k 1 c 1
y 1
y 0

FIGURE 7.105: One degree of freedom hydraulic motion system with flexible base and load
connection. A hydraulic cylinder is connected to a frame which rides on tires. The contact
between the load and cylinder is a non-rigid tool fixture. The base frame and tire, as well as the
tool fixture, are modeled as inertia with stiffness and damping. Cylinder inertia is included in
the base inertia and modeled as mass 1, and piston and rod inertia is included as the mass 2,
and load inertia is modeled as mass 3. This type of dynamic condition exists in many
applications such as mobile equipment riding on tires, hydraulically controlled thickness
control mechanisms in steel mill rolls. In steel mill roll thickness control systems, the base
motion would be stationary (y (t) = 0.0).
0