Robust design of a vehicle suspension fatigue life using multibody simulation N. El Masri1, R. d’Ippolito2, M. Hack3, N. Tzannetakis1 1: NOESIS Solutions, Interleuvenlaan 68, B-3001 Leuven, Belgium 2: LMS Italiana, Via Locchi 6, I-28100 Novara, Italy 3: LMS Deutschland GmbH, Kaiserslautern, Germany Abstract: Product designers worldwide are confronted with highly competitive though conflicting demands to deliver more complex products with increased quality in ever shorter development cycles. Optimising design performance with purely test-based approaches is no longer an option and numerical simulation methods are widely used to model, assess and improve the product design based on virtual prototypes. However, variability in design parameters and in operating conditions leads to scatter in actual performances and must be incorporated in the simulation process to guarantee the robustness of the design. This paper presents the application of state-of-the-art robust design techniques to a vehicle suspension system. A multibody model of a vehicle with a virtual test ground has been created to predict the durability response of three main components of the suspension system. These components have been made flexible to assess the effect of variability in geometrical and material characteristics on the robustness of the durability performance. The results of the robustness assessment have been used to improve the durability performance of the suspension and reduce the scattering in the output quantities of interest. With the robust design methodology, engineers can obtain a better understanding of the effect of variability sources by including noise, signal and control factors directly into the design loop. Based on the analysis results, the robustness of the design can be assessed and improved if needed. Keywords: robust design, multibody simulation, durability, optimisation 1. Introduction The use of virtual prototyping accelerates Time-To-Market by speeding up the design process and by requiring less physical testing and prototypes. It reduces manufacturing costs by optimising the design at early stage and, by this, allows also achieving lower warranty costs. It drives innovation, allowing several different designs to be explored in short time and at low cost. Robustness and reliability are issues that can be addressed at the design stage and improve the understanding of the design. Multibody simulations are an important part of virtual prototyping especially in case of vehicle design. The study of multibody dynamics is the analysis of the dynamic behaviour of interconnected rigid or flexible bodies and of their movement under the influence of forces, generally involving linear and non-linear equations of motion. Application and research areas for multibody systems are: vehicles (road and rail), space structures, astronomy, robotics, mechanisms, aircrafts and biomechanics. Thus vehicle dynamics can be considered as an own field of research, due to the many specific subcomponents related to multibody simulations like suspension, steering assembly, gear unit, combustion engine, etc. Methods used in various applications are however the same, therefore all considerations about the multibody simulations of vehicles are valid for other application fields [1][2]. However, simulation is typically run in a deterministic way, that is, for a given set of input variables, the corresponding output will always be the same. Thus, in all phases of engineering analysis of a technical component over its products lifetime, all decisions are “crisp”. They are either ‘yes/no’ decisions or they involve the specification of precise values or of a range of values. But in the real world, due to the variability of the input variables, the performance of the component or system being designed is usually not a “precise” value but exhibits a scatter around a mean value. Robustness analysis aims to estimate the sensitivity of outputs to the inputs variability, described in terms of random variables characterized with probabilistic distributions. The standard deviation is generally used as a measurement of the robustness of the outputs: the smaller the output standard deviation, the more robust the output. In this paper, a robustness study has been carried out to improve the reliability of the fatigue performance of a vehicle suspension. Thus, the probability that the accumulated fatigue exceeds a selected threshold is assessed and optimised to meet design requirements. Page 1/7 2. Test case: vehicle suspension To explain the methodology used to assess the design robustness and reliability, a typical vehicle dynamics application case has been considered in this paper. In the present paper, a model of a suspension system has been considered (see Figure 1). Figure 1: Multi-body model of the suspension system with tire. The model considered for the analysis includes three components: a knuckle, a tie rod and a lower arm. The suspension subsystem is part of a complete vehicle that has been analysed with a multi-body simulation. This simulation computes the loads and the reaction forces generated by simulating the full vehicle run along a virtual track, representative of the real terrain profile and typical of the operational condition of the vehicle. The loads and the reaction forces computed in this way have been then used as input load histories for the assessment of the accumulated fatigue damage in the three subcomponents. 2.1 Durability analysis The computation of the fatigue damage accumulated has been carried out by using a Finite Element approach. It is well known that fatigue is the degradation of a material due to repeated cyclic loading. For metals, this typically means that there is an initiation of small cracks from active slip bands in grains on the free surface of a specimen, component or structure. These small cracks eventually link to form large cracks that either break or severely degrade the performance of a component. Two basic approaches have been developed to estimate the crack initiation life of components and to address fatigue analysis and design for durability: the stress-life approach and the strain-life approach. The goal of both approaches is to estimate the crack initiation life of structures by combining a mechanics-based analysis of stresses or strains with the results of basic material property tests. The type of fatigue analysis approach to use depends on the type of failure mode that is expected for the structure. Figure 2: Flexible model of the considered elements of the suspension For the present case, flexible models of the three suspension subcomponents have been created. These FE models are characterized by a mesh associated to the geometry of the component. In this way, when the geometry is changed due to some modifications of the thickness, fillet radius or other design dimension, the mesh is automatically recomputed. This allows the automation of the analysis process, starting from the modification of the geometry till the computation of the durability results. However, this process is fully deterministic and perfectly repeatable. In reality, when repeated fatigue life tests are performed, one does not find exactly repeated results, but rather a scattered set of results. There are natural variations in material properties, component dimensions, customer service loads and manufacturing tolerances. Probabilistic distributions can be used to characterize the variation of these variables and include this variability in the design process. This better explains and predicts the scatter obtained in fatigue test results. 2.2 Design variables In order to characterize the variability of the durability performance, 6 design parameters have been identified and characterized with a probabilistic Page 2/7 approach. This statistical characterization is representative of the real variability due to geometrical tolerances, material properties and vehicle configurations. In particular, 3 geometrical, 2 material properties and 1 vehicle mass configuration parameters have been considered. The characterized parameters are listed in Table 1. Name Distribution Mean Standard Deviation Knuckle Fillet Normal Undisclosed 0.4mm Radius Lower Arm Normal Undisclosed 0.4mm Thickness Tie Rod Radius Normal Undisclosed 0.4mm Tie Rod Tensile Normal Undisclosed 2·107 Pa Strength Knuckle Tensile Normal Undisclosed 2·107 Pa Strength Vehicle Mass Normal Undisclosed 0.0025 Scale Table 1: Input design parameters The definition of the input variables adopts a probabilistic approach, using random variables. The selection of the proper probability density models has been made based on data available from the different production processes and vehicle configurations, but due to confidentiality of this data, the full statistical basis for the random variable characterization cannot be disclosed. These design parameters have been used to perform design changes, based on their statistical characterization. The methodologies used for the robustness assessment based on the probabilistic characterization are here briefly outlined. 3. The reliability problem statement To better explain the procedure used to apply the probabilistic methodologies, a short overview of the theory behind them is here reported. When sufficient data is available to allow a probabilistic formulation, the variabilities of an engineering design can be characterized by the variations of a set of random variables x=[xTi] with i=1..n [1] The probability distribution of each random variable xi is described either by its cumulative distribution function (CDF, Fxi(xi) ) or by its probability density function (PDF, fxi(xi) ) and is often bounded by tolerance limits on the system parameter values. The system performance is ()described by Performance Functions (PF, Gjx with j=1...m) that, for a structural design, are usually the selected failure criteria. Thus, given Gj(x), one of the m system PFs, and gj, a fixed performance index (or performance measure) of the structure, the system is considered to fail if Gj(x)
