Shimmy of Aircraft Main Landing Gears

The landing gear is an important aircraft system, which has to meet many different design requirements. It is a highly loaded structure, which is designed for minimum weight. Shimmy is a dynamic instability of the landing gear, which is caused by the interaction of the dynamic behaviour of the landing gear structure and tyres. The unstable lateral and yaw vibration of the landing gear can reach considerable amplitudes and may even result in severe damage to the aircraft. Shimmy is easily ignored in the design process, which may be caused by a of lack of knowledge on the shimmy phenomenon, absence of suitable analysis tools or the non-availability of e.g. tyre characteristics. Computer simulations are very important to evaluate the shimmy stability of a landing gear. Experience has shown that it will be very difficult to rigorously prove shimmy stability from experiments, e.g. full-scale flight tests or laboratory tests using a drum. Three fields of research are covered in this thesis: • shimmy fundamentals • modelling of the tyre dynamic behaviour • the development and validation of a detailed landing gear model Analytical expressions for the shimmy stability have been derived for a number of relatively simple systems using the Hurwitz criterion. In particular, an analytical solution has been found for a system where the wheel has a mechanical trail and both the yaw and lateral stiffness of the hinge point are taken into account. The stability boundaries can be represented by two shifted parabolas in the mechanical trail versus yaw stiffness plane; this analytical result is very important to understand the interaction between the different variables. The model may be enhanced by including the gyroscopic behaviour of the rotating wheel and structural damping. The shimmy stability can also be analysed in the frequency domain by considering the landing gear structure and tyre as a feedback system and applying the Nyquist criterion. A design study is performed using a twin wheeled landing gear, having three mechanical degrees of freedom (lateral, roll and yaw). The stability of the baseline configuration can be improved considerably by modifying the length of the mechanical trail, lateral stiffness, yaw stiffness and wheel track. It appears that a small positive mechanical trail is better avoided; this is substantiated by the analytical results. Other methods to improve the stability have been investigated: modification of the cant angle, the introduction of a bob mass, tuned mass, shimmy damper or co-rotating wheels. Furthermore the stability of a bogie landing gear has been evaluated both analytically and using a more complex model; the results indicate that this configuration is far less susceptible to shimmy. Different linear tyre models have been developed for application in a shimmy analysis; in particular the models of Von Schlippe, Smiley, Pacejka (straight tangent and parabolic approximation), Kluiters, Rogers, Keldysh and Moreland are discussed. Expressions for the transfer functions with respect to side and turn slip are derived and equivalence conditions can be established between some of the tyre models. A comparison is made using transfer functions, step response and energy considerations. In addition, the impact of the tyre model on system stability is studied for a number of simple mechanical systems. Some guidelines regarding the values of different tyre parameters are given using measurement data and literature. A detailed model will be required to assess shimmy stability in the design stage or when solving actual shimmy problems. The stiffness of a landing gear is dependent on the shock absorber deflection due to changes in torque link geometry and distance between upper and lower bearing. The flexibility of the back-up structure and wing results in a significant reduction of the lateral stiffness of the landing gear at wheel axle level. Modal testing can be performed to assess eigenfrequencies and mode shapes of the landing gear, but measurements show that the results may be highly amplitude dependent due to free-play and friction. Free-play and friction are also important for the shimmy stability and will have to be included in a detailed model. The shimmy damper may have a non-linear characteristic consisting of a preloaded spring and velocity squared damping force. Various component tests will be required to determine parameters or to validate the characteristics of the model. A detailed simulation model was developed using the MECANO multi-body software package. The flexible slider element proved to be very convenient for modelling the landing gear structure. Full-scale tests on the aircraft may be used to perform a limited validation of the simulation model. During taxi runs an external disturbance is required to provoke a dynamic response of the landing gear. This may be achieved by running over a diagonally positioned plank, introducing an unbalance mass or asymmetrical braking. In a landing event the asymmetrical spin-up of the wheels is the main excitation source. Generally, only limited data will be available when a shimmy event occurs, which makes it difficult to perform a detailed assessment. An interesting exception is a shimmy vibration which occurred on a test aircraft, equipped with an instrumented landing gear. The unstable motion is analysed in detail. This event has also been simulated using the MECANO model, aiming to match the landing conditions as closely as possible. A reasonable agreement can be obtained between simulation model and measurement. Future research may aim at an accurate determination of tyre characteristics and correlation between different tyres. The dynamic tyre model can be extended to describe the non-linear tyre behaviour at large side slip angles more accurately. Also some enhancements of the landing gear and airframe model are possible, in particular the dynamic behaviour of the wing and brakes may be included. Friction may be rather important for an accurate simulation of the landing gear behaviour; in this field both additional experimental data and improved modelling techniques may be required.