This study aims to evaluate the use of mathematical optimisation algorithms for the optimisation of a vehicle’s spring and damper characteristics, with respect to ride comfort and handling. Traditionally the design of a vehicle’s suspension spring and damper characteristics are determined by a few simple planar model calculations, followed by extensive trial-and-error simulation or track testing. With the current advanced multi-body dynamics computer software packages available to the design engineer, the integration of traditional mathematical optimisation techniques with these packages, can lead to much faster product development. This, in turn results in a reduction of development costs. A sports utility vehicle is modelled by means of a general-purpose computer programme for the dynamic analysis of a multi-body mechanical system. This model is validated against measurements from road tests. The mathematical model is coupled to two gradient-based mathematical optimisation algorithms. The performance of the recently proposed Dynamic-Q optimisation algorithm, is compared with that of the industry-standard gradient based Sequential Quadratic Programming method. The use of different finite difference approximations for the gradient vector evaluation is also investigated. The results of this study indicate that gradient-based mathematical optimisation methods may indeed be successfully integrated with a multi-body dynamics analysis computer program for the optimisation of a vehicle’s suspension system. The results in a significant improvement in the ride comfort as well as handling of the vehicle. / Dissertation (MEng (Mechanical Engineering))--University of Pretoria, 2006. / Mechanical and Aeronautical Engineering / unrestricted

The efficient optimisation of vehicle suspension systems is of increasing interest for vehicle manufacturers. The main aim of this thesis is to develop a methodology for efficiently optimising an off-road vehicle’s suspension for both ride comfort and handling, using gradient based optimisation. Good ride comfort of a vehicle traditionally requires a soft suspension setup, while good handling requires a hard suspension setup. The suspension system being optimised is a semi-active suspension system that has the ability to switch between a ride comfort and a handling setting. This optimisation is performed using the gradient-based optimisation algorithm Dynamic-Q. In order to perform the optimisation, the vehicle had to be accurately modelled in a multi-body dynamics package. This model, although very accurate, exhibited a high degree of non-linearity, resulting in a computationally expensive model that exhibited severe numerical noise. In order to perform handling optimisation, a novel closed loop driver model was developed that made use of the Magic Formula to describe the gain parameter for the single point driver model’s steering gain. This non-linear gain allowed the successful implementation of a single point preview driver model for the closed loop double lane change manoeuvre, close to the vehicle’s handling limit. Due to the high levels of numerical noise present in the simulation model’s objective and constraint functions, the use of central finite differencing for the determination of gradient information was investigated, and found to improve the optimisation convergence history. The full simulation model, however, had to be used for the determination of this gradient information, making the optimisation process prohibitively expensive, when many design variables are considered. The use of carefully chosen simplified two-dimensional non-linear models were investigated for the determination of this gradient information. It was found that this substantially reduced the total number of expensive full simulation evaluations required, thereby speeding up the optimisation time. It was, however, found that as more design variables were considered, some variables exhibited a lower level of sensitivity than the other design variables resulting in the optimisation algorithm terminating at sub-optimal points in the design space. A novel automatic scaling procedure is proposed for scaling the design variables when Dynamic-Q is used. This scaling methodology attempts to make the n-dimensional design space more spherical in nature, ensuring the better performance of Dynamic-Q, which makes spherical approximations of the optimisation problem at each iteration step. The results of this study indicate that gradient-based mathematical optimisation methods may indeed be successfully integrated with a multibody dynamics analysis computer program for the optimisation of a vehicle’s suspension system. Methods for avoiding the negative effects of numerical noise in the optimisation process have been proposed and successfully implemented, resulting in an improved methodology for gradient-based optimisation of vehicle suspension systems. / Thesis (PhD)--University of Pretoria, 2008. / Mechanical and Aeronautical Engineering / unrestricted

In modern heat transfer, shape and geometric optimisation are new considerations in the evaluation of thermal performance. In this research, we employed constructal theory and design to present three-dimensional theoretical and numerical solutions of conjugate forced convection heat transfer in heat generating devices with cooling channels of different cross-sectional shapes. In recent times, geometric configurations of cooling channel have been found to play an important role in thermal performance. Therefore, an efficient ways of optimally designing these cooling channels shapes is required. Experimentation has been extensively used in the past to understand the behaviour of heat removals from devices. In this research, the shapes of the cooling channels and the configurations of heat-generating devices were analytically and numerically studied to minimise thermal resistance and thus illustrate cooling performance under various design conditions. The cooling channels of five different cross-sectional shapes were studied: Circular, square, rectangular, isosceles right triangular and equilateral triangular. They were uniformly packed and arranged to form larger constructs. The theoretical analysis is presented and developed using the intersection of asymptotes method. This proves the existence of an optimal geometry of parallel channels of different cross-sectional shapes that penetrate and cool a volume with uniformly distributed internal heat generation and heat flux, thus minimising the global thermal resistance. A three-dimensional finite volume-based numerical model was used to analyse the heat transfer characteristics of the cross-sectional shapes of various cooling channels. The numerical computational fluid dynamics (CFD) package recently provided a more cost-effective and less time-consuming means of achieving the same objective. However, in order to achieve optimal design solutions using CFD, the thermal designers have to be well experienced and carry out a number of trial-and-error simulations. Unfortunately, this can not always guarantee an accurate optimal design solution. In this thesis a mathematical optimisation algorithm (a leapfrog optimisation program and DYNAMIC-Q algorithm) coupled with numerical CFD was employed and incorporated into the finite volume solver, –FLUENT, and grid (geometry and mesh) generation package, – GAMBIT to search and identify the optimal design variables at which the system would perform optimally for greater efficiency and better accuracy. The algorithm was also specifically designed to handle constraint problems where the objective and constraint functions were expensive to evaluate. The automated process was applied to different design cases of cooling channels shapes. These cooling channels were embedded in a highly conductive solid and the peak temperature was minimised. The trend and performance of all the cooling channel shapes cases studied were compared analytically and numerically. It was concluded that an optimal design can be achieved with a combination of CFD and mathematical optimisation. Furthermore, a geometric optimisation of cooling channels in the forced convection of a vascularised material (with a localised self-cooling property subjected to a heat flux) was also considered. A square configuration was studied with different porosities. Analytical and numerical solutions were provided. This gradient-based optimisation algorithm coupled with CFD was used to determine numerically the optimal geometry that gave the lowest thermal resistance. This optimiser adequately handled the numerical objective function obtained from numerical simulations of the fluid flow and heat transfer. The numerical results obtained were in good agreement with results obtained in the approximate solutions based on scale analyses at optimal geometry dimensions. The approximate dimensionless global thermal resistance predicted the trend obtained in the numerical results. This shows that there were unique optimal design variables (geometries) for a given applied dimensionless pressure number for fixed porosity. The results also showed that the material property had a significant influence on the performance of the cooling channel. Therefore, when designing the cooling structure of vascularised material, the internal and external geometries of the structure, material properties and pump power requirements would be very important parameters to be considered in achieving efficient and optimal designs for the best performance. Finally, this research investigated a three-dimensional geometric optimisation of conjugate cooling channels in forced convection with an internal heat generation within the solid for an array of cooling channels. Three different flow orientations based on constructal theory were studied numerically- firstly, an array of channels with parallel flow; secondly, an array of channels in which flow of every second row was in a counter direction and finally, an array of channels in which the flow direction in every channel was opposite to that of previous channel. The geometric configurations and flow orientations were optimised in such a way that the peak temperature was minimised subject to the constraint of fixed global volume of solid material. The optimisation algorithm coupled with CFD was also used to determine numerically the optimal geometry that gave the lowest thermal resistance. The use of the optimisation algorithm coupled with the computational fluid dynamics package; render the numerical results more robust with respect to the selection of optimal structure geometries, internal configurations of the flow channels and dimensionless pressure difference. / Thesis (PhD(Eng))--University of Pretoria, 2012. / Mechanical and Aeronautical Engineering / unrestricted