J. -hoon Choi and Bryant, M. D., “Combining Lumped Parameter Bond Graphs with Finite Element Shafts in a Gearbox Model,” Computer Modeling in Engineering and Sciences, vol. 3, pp. 431–446, 2002.
This paper presents an updated bond graph model of a gearbox, which now includes bending of shafts. The gearbox system has an input shaft, layshaft, output shaft, spur gears, bearings, and housing. The bond graph model integrates separate sub-models into a composite model. Sub-modules include tooth-to-tooth contact, rotor dynamics of shafts, global dynamics of the gearbox housing structure, and shaft bending modeled by finite element modeling. The tooth-to-tooth model includes tooth bending; shaft torsion; gear inertia; conversion of gear torque into tooth forces; tooth contact mechanics; and multiple tooth contact. To analyze shaft dynamics more precisely, elementary finite element theory was adopted into the shaft bending module. The complete dynamics model was simulated, combining numerical methods for lumped elements and finite element techniques into a single code.