Design of Rail Vehicles with Passive and Active Suspensions Using Multidisciplinary Optimization, Multibody Dynamics and Genetic Algorithms


A methodology for the design optimization of rail vehicles with passive and active suspensions is presented. The methodology has the following features: (1) multibody dynamics is used for modelling and simulating complex realistic vehicle systems; (2) multidisciplinary optimization (MDO) methods are introduced to make coupled vehicle models and additional control systems a synergistic whole; (3) with genetic algorithms (GAs) and other effective search algorithms, the mechanical and control design variables can be optimized simultaneously; (4) with the scalarization technique, a vector optimization problem is converted into a scalar optimization problem. The proposed methodology is applied to several design optimization problems. First, a rail vehicle is optimized with respect to lateral stability. Second, the rail vehicle is designed so that ride quality is the sole design criterion. Third, the design variables are searched in the feasible design space so as to make the rail vehicle have optimal curving performance. Then, the rail vehicle is optimally designed for obtaining trade-off solutions among conflicting requirements from lateral stability, ride quality, and curving performance. Finally, the methodology is used to optimize the combined mechanical and control systems for vehicles with active suspensions. Of the results obtained, several of them contribute to the fields of rail vehicle dynamics and design, mechatronic systems, and numerical optimization. For automatically identifying the "critical speed" (above which a rail vehicle's response becomes unstable), a new approach combining sequential quadratic programming (SQP) with the Dynamic Mode Tracking (DMT) technique is proposed and developed. The new approach is compared with that using SQP alone. It is found that without DMT, several more SQP runs are often needed to find the critical speed because the relationship between mode damping and speed deviate from their actual shapes. In the process of optimizing the lateral stability of a rail vehicle model, the existence of sharply-discontinuous "cliffs" in the plots of critical speed versus suspension stiffness is identified and originally interpreted. In recognition of the cliff phenomenon, the definition of critical speed is generalized to make it a more practical measure of lateral stability. In the design optimization of a rail vehicle with respect to the lateral stability, vertical ride quality, and curving performance, the resulting Edgeworth-Pareto (EP) optimal sets clearly demonstrated the trade-off relation between lateral stability and curving performance. Moreover, the resulting EP-optimal sets visualize a well-known fact that a relatively weak coupling exists between the vertical and lateral motions of a rail vehicle. To identify effective algorithms for rail vehicle suspension design, the GA, SQP, and Simplex algorithms are compared in the processes of optimizing lateral stability and ride quality. Results show that the reliability of the SQP and Simplex for finding the global optimum decreases with an increase in number of design variables. However, despite non-smooth objective function surfaces with many local optimal points, the GA can reliably find global optima. By means of GAs, important design variables can be identified and the relative significance of design variable sets, e.g. inertial, geometric, and suspension (stiffness and damping) parameter sets, can be decided. When ride quality analysis is performed in the frequency domain based on a linear vehicle model, if SQP is used with a multibody dynamics program, e.g. a GEM, the numerical differntiation technique for computing gradients can be used efficiently as a link between the multibody program and SQP. As an application of the proposed methodology, an integrated design approach to mechatronic vehicle systems is used to resolve the conflicting requirements for ride comfort, suspension working spaces, and dynamic wheel loads in the optimization of quarter-vehicle models and half-vehicle models with active suspensions. Both deterministic and random track excitations and both rigid and flexible car body cases are considered. The approach is implemented in a GA-A'GEM-MATLAB simulation environment in such a way that the linear mechanical vehicle models are generated in the multibody program of A'GEM, the controllers and filters are modelled in MATLAB, and the coupled mechanical and control subsystems are optimized simultaneously using the GA. The numerical simulation results are reported and discussed.