Simulating Coupled Longitudinal, Pitch and Bounce Dynamics of Trucks with Flexible Frames

Simulating the dynamic response of trucks requires that a model be constructed and subjected to road inputs. Inclusion or omission of flexible frame effects is often based on intuition or assumption. If frame vibration is assumed to be significant, it is typically incorporated in one of two ways. Either a complex finite element model of the frame is used, or a simplified linear modal expansion model (which assumes small motions) is employed. The typical low-order modal expansion model, while computationally efficient and easier to use, is limited by the fact that 1) large rigid body motions and road grade changes are not supported, and 2) longitudinal dynamics are not coupled to vertical and bounce dynamics. In this paper, a bond graph model is presented which includes coupled pitch and bounce motions, longitudinal dynamics, and transverse frame vibration. Large rigid body motions are allowed, onto which small flexible vibrations are superimposed. Frame flexibility is incorporated using modal expansion of a free-free beam. The model allows for a complete pitch-plane representation in which motive forces can propel the truck forward over varying terrain, including hills. The effect of frame flexibility on vehicle dynamics can then be studied. This is an extension of the typical half-car model in which suspension motion is assumed vertical, pitch angles are small, and longitudinal dynamics are completely decoupled or omitted. Model output shows the effect of frame flexibility on vehicle responses such as forward velocity, pitch angle, and payload acceleration. Participation of individual modes can be seen to increase as road input approaches their natural frequency. The bond graph formalism allows for any or all flexible frame modes to be easily removed from the model if their effects are negligible, and for inclusion of more complex submodels for components such as suspension and engine if desired.