Abstract: In this paper, a bond graph dynamic model for a valvecontrolled
hydraulic cylinder has been developed. A simplified bond
graph model of the inter-actuator interactions in a multi-cylinder
hydraulic system has also been presented. The overall bond graph
model of a valve-controlled hydraulic cylinder was developed by
combining the bond graph sub-models of the pump, spool valve and
the actuator using junction structures. Causality was then assigned
in order to obtain a computational model which could be simulated.
The causal bond graph model of the hydraulic cylinder was verified
by comparing the open loop state responses to those of an ODE
model which had been developed in literature based on the same
assumptions. The results were found to correlate very well both
in the shape of the curves, magnitude and the response times,
thus indicating that the developed model represents the hydraulic
dynamics of a valve-controlled cylinder. A simplified model for interactuator
interaction was presented by connecting an effort source with
constant pump pressure to the zero-junction from which the cylinders
in a multi-cylinder system are supplied with a constant pressure from
the pump. On simulating the state responses of the developed model
under different situations of cylinder operations, indicated that such
a simple model can be used to predict the inter-actuator interactions.
Abstract: This paper focuses on the development of bond graph
dynamic model of the mechanical dynamics of an excavating mechanism
previously designed to be used with small tractors, which are
fabricated in the Engineering Workshops of Jomo Kenyatta University
of Agriculture and Technology. To develop a mechanical dynamics
model of the manipulator, forward recursive equations similar to
those applied in iterative Newton-Euler method were used to obtain
kinematic relationships between the time rates of joint variables
and the generalized cartesian velocities for the centroids of the
links. Representing the obtained kinematic relationships in bondgraphic
form, while considering the link weights and momenta as
the elements led to a detailed bond graph model of the manipulator.
The bond graph method was found to reduce significantly the number
of recursive computations performed on a 3 DOF manipulator for a
mechanical dynamic model to result, hence indicating that bond graph
method is more computationally efficient than the Newton-Euler
method in developing dynamic models of 3 DOF planar manipulators.
The model was verified by comparing the joint torque expressions
of a two link planar manipulator to those obtained using Newton-
Euler and Lagrangian methods as analyzed in robotic textbooks. The
expressions were found to agree indicating that the model captures
the aspects of rigid body dynamics of the manipulator. Based on
the model developed, actuator sizing and valve sizing methodologies
were developed and used to obtain the optimal sizes of the pistons
and spool valve ports respectively. It was found that using the pump
with the sized flow rate capacity, the engine of the tractor is able to
power the excavating mechanism in digging a sandy-loom soil.