Pieter Schalk Els

Efficient optimisation of a vehicle suspension system, using a gradient-based approximation method, Part 1: Mathematical modelling

A methodology is proposed for the efficient determination of gradient information, when performing gradient based optimisation of an off-road vehicles suspension system. The methodology is applied to a computationally expensive, non-linear vehicle model, that exhibits severe numerical noise. A recreational off-road vehicle is modelled in MSC.ADAMS, and coupled to MATLAB for the execution of the optimisation. The successive approximation method, Dynamic-Q, is used for the optimisation of the spring and damper characteristics. Optimisation is performed for both ride comfort and handling. The determination of the objective function value is performed using computationally expensive numerical simulations. This paper proposes a non-linear pitch-plane model, to be used for the gradient information, when optimising ride comfort. When optimising for handling, a non-linear four wheel model, that includes roll, is used. The gradients of the objective function and constraint functions are obtained through the use of central finite differences, within Dynamic-Q, via numerical simulation using the proposed simplified models. The importance of correctly scaling these simplified models is emphasised. The models are validated against experimental results. The simplified vehicle models exhibit significantly less numerical noise than the full vehicle simulation model, and solve in significantly less computational time.

Investigation of the applicability of the dynamic-Q optimisation algorithm to vehicle suspension design

To optimise the handling of a vehicle in conjunction with ride comfort is a challenge due to the fact that the suspension features determining these functions tend to oppose one another. The complexity and nonlinearity of the dynamics of suspension systems impose further difficulty. Furthermore, the suspension characteristics imply a large number of variables. The dynamic-Q optimisation method used here in conjunction with the dynamics simulation code DADS is a robust and reliable algorithm particularly suitable for solving engineering optimisation problems. It applies an existing dynamic trajectory optimisation algorithm to successive spherical quadratic approximate subproblems and can be used when analytical functions are not available and only discrete function values can be obtained via numerical simulation of engineering processes. The purpose of this investigation is to determine whether the dynamic-Q method is suitable for optimising the design of a vehicle suspension system modelled in DADS.

Investigation of hardware-in-the-loop for use in suspension development

Hardware-in-the-loop (HiL) is a testing method in which real-time measurements on physical hardware replace the mathematical model of the particular hardware during simulation. The development of a semi-active suspension prompted the need for such capability. HiL, implemented on a PC with a dSpaceTM board in conjunction with a hydrodynamic actuator, was compared to software simulations of single degree of freedom (DOF) and two DOF systems. HiL was also compared to a physical (ballast-based) two DOF system, comprising the rear suspension of a motorcycle. Comparisons between the HiL and software responses showed its suitability for testing suspension systems, thus providing a viable alternative to ballast-based suspension tests, using available hardware. The research also showed that actuator dynamics, filter types and amounts, and signal reference levels required special consideration.

Gradient-based approximation methods applied to the optimal design of vehicle suspension systems using computational models with severe inherent noise

The principal aim of this paper is to evaluate the feasibility of using gradient-based approximation methods for the optimisation of the spring and damper characteristics of an off-road vehicle, for both ride comfort and handling. The Sequential Quadratic Programming algorithm and the relatively new Dynamic-Q method are the two successive approximation methods used for the optimisation. The determination of the objective function value is performed using computationally expensive numerical simulations that exhibit severe inherent numerical noise. The use of forward finite differences and central finite differences for the determination of the gradients of the objective function within Dynamic-Q is also investigated. This is done in investigating methods for overcoming the difficulties associated with the optimisation of noisy objective functions. A recreational off-road vehicle is modelled in ADAMS, and coupled to MATLAB for the execution of the optimisation process. The full vehicle ADAMS model includes suspension kinematics, a load-dependent tyre model, as well as non-linear springs and dampers. Up to four design variables are considered in modelling the suspension characteristics. It is found that both algorithms perform well in optimising handling. However, difficulties are encountered in obtaining improvements in the design process when ride comfort is considered. Nevertheless, meaningful design configurations are still achievable through the proposed optimisation process, at a relatively low cost in terms of the number of simulations that have to be performed.

Semi-active rotary damper for a heavy off-road wheeled vehicle

Abstract The development, simulation and laboratory testing of two-state discrete adjustable semi-active rotary dampers for heavy off-road wheeled vehicles, which is a joint venture between the South African based company Reumech Ermetek and Horstman Defence Systems from the UK, is described. A brief history of semi-active damping and rotary dampers is given, after which the working principle and features of combining the two technologies is outlined. Three dimensional simulation is used to determine the ride comfort gains achievable with semi-active rotary dampers compared to the conventional translational dampers currently used on the vehicle under consideration. Simulations are performed over different terrains, including the APG track and discrete obstacles. Semi-active rotary dampers were integrated on the 6×6 GV6 Self-propelled Gun Howitzer in order to quantify the improvements in ride comfort, transient response and handling of the vehicle as indicated by the simulation results. The control system, control strategies and characterisation tests, which includes determination of on and off characteristics as well as valve response times, are discussed.

Profiling of rough terrain

This study concentrates on obtaining profiles of rough terrain suitable for vehicle dynamics simulations in a cost–effective manner. Commercially available inertial profilometers are unable to profile the terrains of interest due to their severe roughness. A mechanical profilometer is developed and evaluated by profiling obstacles with known profiles, as well as rough 3-D test track profiles. A good correlation between the profiled and actual terrains is achieved. Realistic three-dimensional (3-D) terrain models are generated from the terrain profiles. The Displacement Spectral Densities (DSDs) of the profiled terrains are found to contain discrete peaks; a straight line fit would not be an accurate estimation for the specific rough terrains. Comparisons between the terrains defined in the International Roughness Index (IRI) and the present study indicate that the roughness index of the terrains profiled with the mechanical profilometer is significantly higher than the terrains normally profiled by inertial profilometers.

Experimental Determination of Moments of Inertia for an Off-Road Vehicle in a Regular Engineering Laboratory:

Moments of inertia play a vital role in the motion of rigid bodies. Accurate information for moments of inertia is, however, not easily obtained for common bodies such as vehicles, aeroplanes, trains and humans. Presented in this text is a procedure, requiring minimal equipment expenditure, for the determination of the moments of inertia, for an off-road vehicle. The point of departure is rigid-body oscillation about a pivoting point, with a spring providing a restoring force. The moment of inertia about the pivoting point is then determined by both measuring the period of oscillation and calculating the gradient of the torque—angular acceleration curve. The results of the two methods for determining the pitch, roll and yaw moments of inertia of the body and chassis about the bodys centre of gravity are compared. It is found that calculation is very sensitive to distance measurements and accurate determination of the position of the centre of gravity. The procedure gives results of adequate accuracy considering the experimental effort and costs involved.

Efficient optimisation of a vehicle suspension system, using a gradient-based approximation method, Part 2: Optimisation results

Part 1 of this paper proposed a methodology for the efficient determination of gradient information, when optimising a vehicles suspension characteristics for ride comfort and handling. The non-linear full vehicle model, and simplified models for gradient information has been discussed, and validated. In this paper, the simplified models presented in Part 1 are used for gradient information simulations. The convergence histories of the optimisation are compared to those obtained when only the full, computationally expensive, vehicle model is used. For illustration of the proposed gradient-based optimisation methodology, up to four design variables are considered in modelling the suspension characteristics. The proposed methodology is found to be an efficient alternative for the optimisation of the vehicles suspension characteristics. The undesirable effects associated with noise in the gradient information is effectively reduced, using the simplified models. Substantial benefits are achieved in terms of computational time needed to reach a solution.

Heat transfer effects on hydropneumatic suspension systems

Abstract One of the problems experienced on hydropneumatic suspension systems, is the effect of temperature change on the spring characteristic, resulting in variations in spring rate and ride height. This problem can be analysed using an appropriate heat transfer model. Two major heat transfer modes are investigated, i.e. heat transfer between the gas and its surroundings and heat transfer between the damper oil and the gas. The analyses performed include the determination of the dynamic spring force characteristic, the effect of heat build-up on the spring force characteristic and the effect of heat build-up on the performance of the hydropneumatic spring and damper unit during vehicle tests. Mathematical modelling of the spring characteristic is performed by solving the energy equation for a gas in a closed container using the thermal time constant approach. The Benedict–Webb–Rubin equation of state is used for real gas behaviour. The mathematical model is verified against experimental data and good correlation is achieved. It is shown that hydropneumatic suspension systems have a significant amount of inherent damping due to heat transfer which produces no nett temperature change or heat build-up. The effect of heat build-up in the damper on the spring force characteristic is determined by laboratory tests. It is shown that heat generation in the damper, accompanied by a rise in gas temperature, has a detrimental effect on the spring force characteristic. Tests performed on experimental hydropneumatic spring and damper systems fitted to a test vehicle indicate that the effect is smaller in practice than anticipated. Heat build-up is strongly influenced by terrain roughness, vehicle speed, mission profile and damping levels.

Validation metric based on relative error

Engineers and scientists are often faced with the problem of objectively comparing time histories of measured and/or simulated data. This article presents a reliable and intuitive validation metric for use in the validation process. The proposed validation metric is able to quantify the agreement/disagreement between deterministic system response quantities of interest obtained from measurements on a physical system and predictions from a mathematical model. The validation metric is based on the relative error, and the challenges concerning the use of the relative error on periodic signals are addressed. The validation metric is compared to similar metrics and their advantages and limitations are discussed. The results show that the proposed validation metric gives a comprehensive error that is able to quantify the agreement between two periodic signals and is easily interpretable.