Validated leaf spring suspension models

Abstract

Mathematical and computer modelling have been playing an increasingly important role in the Computer Aided Engineering (CAE) process. Simulation offers great advantages in the development and analysis phase of products and offers a faster, better and more cost effective way than using physical prototypes alone. The ever increasing demand for new and improved products in the vehicle industry has decreased the time available for the development of new vehicles, but at the same time the demands on quality, reliability and mass that are set for the vehicle are becoming ever more stringent. These requirements have lead to the investigation of procedures and methodologies such as virtual prototyping that will reduce the development time of new vehicles without inhibiting the quality of the vehicle. In order to perform effective and reliable simulations in the CAE process, accurate simulation models of the vehicle and its associated systems, subsystems and components are required. In the vehicle dynamics context simulation models of the tyres, suspension, springs, damper, etc, are needed. This study will look at creating a validated model of a leaf spring suspension system used on commercial vehicles. The primary goal set for the model is to be able to predict the forces at the points where the suspension system is attached to the vehicle chassis as the model is to be used in full vehicle durability simulations. The component which will receive a considerable amount of attention in this study is the leaf spring. Leaf springs have been used in vehicle suspensions for many years. Even though leaf springs are frequently used in practice they still hold great challenges in creating accurate mathematical models. It is needless to say that an accurate model of a leaf spring is required if accurate full vehicle models are to be created. As all simulation models in this study are required to be validated against experimental measurements a thorough experimental characterisation of the suspension system of interest, as well as two different leaf springs, are performed. In order to measure the forces between the suspension attachment points and the chassis, two six component load cells were developed, calibrated, verified and validated. This study will primarily focus on the modelling of a multi-leaf spring as well as a parabolic leaf spring. The study starts with a literature study into the various existing modelling techniques for leaf springs. A novel leaf spring model, which is based on a macro modelling view point similar to that used for modelling material behaviour, is developed. One of the modelling techniques found in the literature, i.e. neural networks, is also used to model the leaf spring. The use of neural networks is applied and some of the challenges associated with the method are indicated. The accuracy and efficiency of the physics-based elasto-plastic leaf spring model and the non physics-based neural network model are compared. The modified percentage relative error metric is compared to two other quantitative validation metrics that were identified from the literature study. It is concluded that the modified percentage relative error has certain limitations but that it is able to give an accurate and representative account of the agreement/disagreement between two periodic signals around zero. The modified percentage relative error is used to obtain the accuracies of the elasto-plastic leaf spring models and the neural network model. Both models give good results with the neural network being almost 3 times more computationally efficient. The elasto-plastic leaf spring model, for the multi-leaf spring, is further extended to model the behaviour of a parabolic leaf spring. Qualitative validation using experimental data shows that the elasto-plastic leaf spring model is able to accurately predict the vertical behaviour of both the multi-leaf spring as well as the parabolic leaf spring. The elasto-plastic leaf spring model was also combined with a method that is able to capture the effect of changes in the spring stiffness due to changes in the loaded length. Quantitative validation shows that the method proposed for accounting for the change in stiffness due to changes in the loaded length is able to capture this characteristic of the physical leaf spring. Following a systematic modelling approach the elasto-plastic multi-leaf spring model is incorporated into a model of a simplified version of the physical suspension system. The qualitative validation results from this model show that the model is able to accurately predict the forces that are transmitted from the suspension system to the chassis. The models created in this study can be used in future work and, with the addition of more detail the models, can be extended to create a model of the complete suspension system.