World Academy of Science, Engineering and Technology
Published March 22, 2009 | Version 8754
Journal article Open

Bond Graph Modeling of Mechanical Dynamics of an Excavator for Hydraulic System Analysis and Design

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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.

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References

  • J. Denavit, and R. S. Hartenberg, "A kinematic notation for lower-pair mechanisms based on matrices," Journal of Applied Mechanics, pp. 215- 221., 1955.
  • K.S. Fu, R. C. Gonzalez, and C. S. Lee, Robotics: Control, Sensing, Vision and Intelligence. McGraw Hill Book Publishing Company, 1987.
  • J. J. Craig, Introduction to Robotics: Mechanics and Control. Addison- Wesley Publishers, USA, 1986.
  • V. Anand, H. Kansal, and A. Singla, "Some aspects in bond graph modeling of robotic manipulators: Angular velocities from symbolic manipulation of rotation matrices," Technical Report, Department of Mechanical Engineering, Sant Longowal Institute of Engineering and Technology, 2003.
  • H. M. Paynter, Analysis and Design of Engineering Systems. MIT Press Publishers, Cambridge, 1961.
  • D. C. Karnopp, D. L Margolis, and R. C. Rosenberg, System Dynamics: Modelling and Simulation of Mechatronic Systems. John Wiley and Sons Publishers, Newyork, 2000.
  • D. C. Karnopp, D. L. Margolis, and R. C. Rosenberg, System Dynamics; A Unified Approach. John Wiley and Sons Publishers, Newyork, 2nd ed., 1990.
  • D .C. Karnopp and R. C. Rosenberg, Introduction to Physical System Dynamics. McGraw Hill Publishers, Newyork, 1983.
  • P. Breedveld, "Bond graphs," in Encyclopedia of Life Support Systems, Modeling and Simulation, 2003. [10] P. Gawthrop and L. Smith, Metamodeling: Bond Graphs and Dynamic Systems. Prentice Hall International Publishers, UK Limited, 1996. [11] F. Fakri, A. Rocaries, and A. Carrierre, "A simple method for conversion of bond graph models in representation by block diagrams," in 1997 Proc. International Conference on Bond Graph Modeling and Simulation. [12] J. F. Broenink, "Introduction to Physical Systems Modeling with Bond Graphs," Technical Report, Department of Electrical Engineering, University of Twente, Netherlands, 1996. [13] O. M. Muvengei, "Design of an excavating mechanism to be used with juja diesel tractor jk01," Design Innovation, Department of Mechanical Engineering, J.K.U.A.T, 2006. [14] A. Koivo, "Kinematics of excavator (back hoe) for transfering surface materials," Journal of Aerospace Engineering, vol. 7(1), pp. 7-31, 1994. [15] J. Y. Luh, M. W. Walker, and R. P. Paul, "On-line computational scheme for mechanical manipulators," Journal of Dynamic Systems, Measurement and Control, vol. 120, pp. 69-76, 1980. [16] H. N. Cannon, "Extended earthmoving with an autonomous excavator," MSc. thesis, Robotics Institute, Carnegie Mellon University, Pittsburgh, 1999. [17] H. Q. Nguyen, "Robust low level control of robotic excavation". PhD. thesis, Australian Centre for Field Robotics, The University of Sydney, 2000. [18] S. Sarkar, "Dynamic modeling of an articulated forestry machine for simulation and control," MSc. thesis, Department of Mechanical Engineering, McGill University, Canada, 1996. [19] O. M. Muvengei, "Simulation of the dynamic behavior of an excavator due to interacting mechanical and hydraulic dynamics," MSc. thesis, Department of Mechanical Engineering, JKUAT, Kenya, 2008.