The modal twist axis: A method for describing the dynamical characteristics of single track vehicles

Static and dynamic properties of single-track vehicles components (such as frames, front forks and swing-arms) play a fundamental role from the point of view of vehicle stability, which is a key issue of single-track vehicles dynamics and safety. Nowadays, the stability of a vehicle is studied by means of multi-body codes, in which it is possible to implement models of the tires and of the components of the vehicle. Actually, the chassis and the forks of motorcycles are mechanical systems with distributed mass and stiffness properties, but in most simulation codes the elastic properties of the structural elements are modeled with lumped stiffness and damping elements. Very few research has been carried out on the identification of the lumped elements, of their natural frequencies and damping from laboratory tests. In the first section of the paper, the concept of modal twist axis is proposed to characterize the dynamic deformability of a structural element. The twist axis is defined as the intersection between the un-deformed plane of the structural element and the plane tangent to the free end of the structural element in deformed condition. If the identification of the twist axis is carried out in resonance condition, the modal twist axis is found. A method for measuring the modal twist axis position and orientation is described. It is based on impulse excitation by means of a modally tuned hammer and three accelerometers which are used for defining the deformed plane. In the second section of the paper, experimental results obtained on two motorcycle frames are shown. In order to know the modal shapes of the components at the measured natural frequencies, modal analysis is carried out. A correlation between the modal twist axis position and the mode of vibration is shown and discussed. In order to study the influence of the constraints on dynamic properties, the frames are tested in two different constraint conditions: rear constrained and front constrained. The last section of the paper shows the experimental results obtained by applying the proposed method to other motorcycle components, such as a front fork and a frame with the engine.