Sensitivity analysis methods are investigated for the optimal design of multibody systems. In order to overcome the shortcomings inherent in existing methods, a "mixed" method is developed. The beneficial features of the finite difference and the direct differentiation methods, and equations of motion in the joint coordinates are employed in this method. As a realistic application of the sensitivity analysis, a Four-Wheel-Steering vehicle with complete suspension systems and comprehensive analytical tire model is implemented. This model keeps full nonlinearity in the governing equations of motion for accuracy, and it is simulated using an existing general-purpose multibody dynamics simulation package. However, by using the transient dynamic analysis of the nonlinear model, optimal design parameters are dependent on driving scenarios. Therefore, the transient behavior of the system is represented by a series of steady state configurations. Hence, a steady state analysis procedure which finds a steady state configuration from an arbitrary initial condition is developed. By using the steady state analysis and the sensitivity analysis, the optimal steering ratios between the angles of the front and the rear wheels are obtained over various driving conditions. A steering control strategy is developed for the vehicle simulation to follow a prescribed path. Finally, the simulation results using the optimal steering ratio are compared against the results of the conventional two-wheel steering and the steering ratio based on the linear bicycle model.

The main aim of this research project is to extend theories of four-wheel-steering as developed by J. Ackermann to include an individually steered four-wheel steering system for passenger vehicles. Ackermann’s theories, including theories available in this subject area, dwell much on vehicle system dynamics developed from what is called single track model and some call it a bicycle model. In the bicycle model, the front two wheels are bundled together. Similarly, the rear wheels are bundled together. The problem with this is that it assumes two front wheels or two rear wheels to be under the same road, vehicle and operating conditions. The reality on the ground and experiments that are conducted are to the contrary. Therefore this study discusses vehicle disturbance rejection through robust decoupling of yaw and lateral motions of the passenger vehicle. A mathematical model was developed and simulated using Matlab R2008b. The model was developed in such a way that conditions can be easily changed and simulated. The model responded well to variations in road and vehicle conditions. Focus was in the ability of the vehicle to reject external disturbances. To generate yaw moment during braking, the brake on the left front wheel was disconnected. This was done because lateral wind generators, as used by Ackermann, were not available. The results from both simulations and experiments show disturbance rejection in the steady state. Copyright / Dissertation (MSc)--University of Pretoria, 2010. / Mechanical and Aeronautical Engineering / unrestricted

O comportamento da dinâmica lateral de veículos automotivos com esterçamento nas quatro rodas é estudado com o auxílio de uma ferramenta computacional de modelagem e simulação de sistemas multicorpos. São utilizadas duas estratégias de controle do esterçamento das rodas traseiras para a avaliação de suas principais características. Uma das estratégias esterça as rodas traseiras em função do ângulo de esterçamento do volante, e a outra esterça as rodas traseiras em função do ângulo de esterçamento do volante e da velocidade longitudinal do veículo. O teste utilizado para as análises é a entrada degrau de esterçamento, onde é avaliada a resposta transitória e de regime da aceleração lateral, da velocidade de guinada e do ângulo de rolagem dos veículos. Os resultados das simulações mostram que os veículos com esterçamento nas quatro rodas têm o tempo de resposta da velocidade de guinada maior, e da aceleração lateral e do ângulo de rolagem menores que o veículo convencional. Também apresentam uma diminuição no ganho da aceleração lateral, da velocidade de guinada e do ângulo de rolagem. Além disso apresentam uma característica subesterçante mais acentuada. Essas características são mais evidentes no veículo com estratégia de controle função do esterçamento do volante. Os resultados obtidos correspondem ao comportamento dos veículos com esterçamento nas quatro rodas apresentado na literatura. / The lateral dynamic behavior of the automotive vehicles is studied with the aid of a computational tool for multibody systems modeling and simulation. Two rear wheel steering control strategies are used for evaluation of the main four wheel steering characteristics. One strategy steer the rear wheels as a function of the steering wheel angle, and the other one, steer the rear wheels as a function of the steering wheel angle and the speed. The steer step input is the test used, where the lateral acceleration, the yaw rate and the roll angle transient and stead state response are evaluated. The simulation results show that the four wheel steering vehicles have a slower yaw rate time response, and a fast lateral acceleration and roll angle time response than the conventional vehicle. Also four wheel vehicles show a reduction in lateral acceleration, yaw rate a.nd roll angle gain. Moreover they are more understeer than the conventional vehicle. These characteristics are particularly more evident on the vehicle with steer dependent system. The obtained results correspond with four wheel steering vehicles behavior founded in literature.

O comportamento da dinâmica lateral de veículos automotivos com esterçamento nas quatro rodas é estudado com o auxílio de uma ferramenta computacional de modelagem e simulação de sistemas multicorpos. São utilizadas duas estratégias de controle do esterçamento das rodas traseiras para a avaliação de suas principais características. Uma das estratégias esterça as rodas traseiras em função do ângulo de esterçamento do volante, e a outra esterça as rodas traseiras em função do ângulo de esterçamento do volante e da velocidade longitudinal do veículo. O teste utilizado para as análises é a entrada degrau de esterçamento, onde é avaliada a resposta transitória e de regime da aceleração lateral, da velocidade de guinada e do ângulo de rolagem dos veículos. Os resultados das simulações mostram que os veículos com esterçamento nas quatro rodas têm o tempo de resposta da velocidade de guinada maior, e da aceleração lateral e do ângulo de rolagem menores que o veículo convencional. Também apresentam uma diminuição no ganho da aceleração lateral, da velocidade de guinada e do ângulo de rolagem. Além disso apresentam uma característica subesterçante mais acentuada. Essas características são mais evidentes no veículo com estratégia de controle função do esterçamento do volante. Os resultados obtidos correspondem ao comportamento dos veículos com esterçamento nas quatro rodas apresentado na literatura. / The lateral dynamic behavior of the automotive vehicles is studied with the aid of a computational tool for multibody systems modeling and simulation. Two rear wheel steering control strategies are used for evaluation of the main four wheel steering characteristics. One strategy steer the rear wheels as a function of the steering wheel angle, and the other one, steer the rear wheels as a function of the steering wheel angle and the speed. The steer step input is the test used, where the lateral acceleration, the yaw rate and the roll angle transient and stead state response are evaluated. The simulation results show that the four wheel steering vehicles have a slower yaw rate time response, and a fast lateral acceleration and roll angle time response than the conventional vehicle. Also four wheel vehicles show a reduction in lateral acceleration, yaw rate a.nd roll angle gain. Moreover they are more understeer than the conventional vehicle. These characteristics are particularly more evident on the vehicle with steer dependent system. The obtained results correspond with four wheel steering vehicles behavior founded in literature.

In this thesis the requirements for a rear wheel steering mechanism aimed to be implementedon KTH:s Formula Student car were evaluated. The requirements were obtainedby using already known loads, an analysis of how the quickly the driver turns the steeringwheel during track driving from video material and the Formula Student rulebook whichthe car is designed after. After the requirements were produced a number of concepts wereproduced and evaluated against each other. The concept that was given the highest scorewas a rack and pinion concept with a rotary actuator which was developed further.The design was made by first selecting an actuator with a planetary gearbox that couldfulfill the speed and load requirements and afterwards with CAD a design that could beintegrated on the car was made. The concept weighed around 1,7 kg and was compatiblewith the requirements. / I detta arbete undersöktes kraven som ställs på ett bakhjulsstyrningssystem för implementering på KTH:s Formula Student bil. Kraven togs fram genom att använda redan kända laster, en analys av hur snabbt föraren svänger utifrån videomaterial samt regelboken som alla formulastudentbilar är konstruerade efter. Efter att kraven tagits fram utvärderades ett antal koncept där det bästa konceptet, kuggstångsmekanism med ett roterande ställdon utvecklades vidare. Prototypdesignen gjordes genom att först välja ett ställdon med planetväxellåda som skulle klara av kraven och därefter med hjälp av CAD skapa en integrerbar design. Det färdiga konceptet väger ca 1,7 kg och klarar alla ställda krav.