Simulation of the Dynamic Behavior of an Excavator due to Interacting Mechanical and Hydraulic Dynamics

Abstract

This research project primarily describes the modeling of mechanical and hydraulicdynamics of an excavating mechanism previously designed to be used with smalltractors, which are fabricated in the Engineering Workshops of Jomo Kenyatta Universityof Agriculture and Technology. The developed models were then used tooptimize the hydraulic system design, and also to simulate the open loop transientand steady state responses of the system.In this study, bond graph method was chosen as the modeling method because,firstly, it is a domain-independent graphical method of representing the dynamics ofphysical systems. Therefore, systems from different engineering disciplines can bedescribed in the same way. Secondly, the available literature shows that the methodbeing relatively new, has not been thoroughly applied to model the dynamics ofnonlinear systems such as excavators. The bond graph method was first reviewed,and then used to develop a complete dynamic model of the excavator by modeling thehydraulic actuation system and the manipulator linkage separately. The two modelsrepresenting different domain dynamics were coupled to a complete model usingappropriate manipulator jacobians which were treated as Modulated TransformerElements. The bond graph method was found to reduce significantly the number ofrecursive computations performed on a manipulator for a mechanical dynamic modelto result. This indicated, that bond graph method is more computationally efficientthan the Newton-Euler method in developing dynamic models of manipulators.The mechanical bond graph model of the manipulator was verified by comparingthe joint torque expressions of a two link planar manipulator to those obtained byusing Newton-Euler and Lagrangian methods as analyzed in robotic textbooks. Theexpressions were found to agree indicating that the model captures the aspects ofxxiiirigid body dynamics of the manipulator. Also the bond graph model of the hydraulicsystem was verified by comparing the open loop state responses to those of an ODEmodel which has been developed in literature based on the same assumptions. Theresults were found to correlate very well both in the shape of the curves, magnitudeand the response times, thus indicating that the developed model represents thehydraulic dynamics of a valve controlled cylinder.Based on the model developed, actuator sizing and valve sizing methodologies weredeveloped and used to obtain the optimal sizes of the pistons and spool valve portsrespectively. It was found that using the pump with the sized flow rate capacity, theengine of the tractor is able to power the excavating mechanism in digging a sandyloomsoil. The causal bond graph model of the excavator was expanded into blockdiagrams and simulated on MATLAB/SIMULINK to determine the transient andsteady state responses of the system. From the responses obtained, the model developedwas found to capture the inter-component interactions and also the interactionbetween the hydraulic and mechanical dynamics. Therefore it can be concluded thatthe model developed can be used to design control laws necessary for controlling thedynamics and motions of the excavating manipulator.