The Design, Qualification and Maintenance of Vibration-Free Landing Gear

Dynamic behaviour of motorcycles front wheel are not different to similar wheel suspensionmotion of airplanes and road vehicles. In every case self excited oscillations caused bythe tire occur. Only the different design of wheel suspension produces some differentcoupling. The deviation of a moving wheel on a horizontal plane from straight rolling iscaused by unstable lateral contact forces. The kinematical generation of such forces canbe imaginated looking on the elastic tire. A first order time-depending behaviour togetherwith inertia mass and damping of the wheel using the HURWITZstability criterion givesimportant insight into the main parameters of the problem.Nevertheless the nonlinearities of the system overshadow this clear insight. Cornering forceand cornering moment are nonlinear functions of cornering angle, so the use of the wellknown “Magic Formula’’ together with the black box method of control theory is a logicalextension. The problem of instability arises again when the wheel is excited from wavysurface or similar from mass unbalances of the tire. A direct time depending of the lateraltire forces can be used to show parametric instability of the system (MATHIEUequation).The rolling of the wheel on a non-smooth surface needs then to introduce methods ofdiscrete system approach. The paper presents an overview of the problem of shimmy.