Elasto-plastic leaf spring model applied to the parabolic leaf spring

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Introduction

Mathematical and computer modelling have been playing an increasingly important role in the Computer Aided Engineering (CAE) process of many products in the last 60 years. 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, by both the client and the manufacturer, are becoming ever more stringent. These requirements have lead to the investigation of procedures and methodologies that will reduce the development time of new vehicles without inhibiting the quality of the vehicle.

Problem statement

The development life cycle presented in Figure 1.3 requires a CAE process with validated simulation models of components, subsystems and systems. In the context of this study, components are elements such as the leaf springs, with the subsystems being the suspension system, and the system the full vehicle. This study forms part of a larger project that is concerned with obtaining a library that contains simulation models of components and subsystems that can be used to create full vehicle simulation models that can be used in the CAE process.

Introduction to suspension system of interest

Figure 1.4 shows the suspension system that will be considered in this study. The figure shows the suspension system with a multi-leaf spring consisting of 8 blades (or leaves) having a uniform cross-section through the length of the blade. The leaf spring and radius rod constrains the axle in the vertical, longitudinal and lateral directions. The suspension system is attached to the chassis via the hangers. In this configuration the leaf spring is supported by the front and rear hangers instead of a fixed-shackled end configuration (see Figure 1.5 for an example of a fixed-shackled end configuration).

Literature study

A literature study was conducted to obtain an idea of the leaf spring models that have been developed and whether they are able to give accurate predictions of the force-displacement behaviour of the leaf spring as well as reaction forces on the vehicle attachment points. The application of the different leaf spring modelling methods in vehicle simulations is noted along with whether they were validated and for which parameters.

CHAPTER 1
1. Problem statement
2. Introduction to suspension system of interest
3. Literature study
3.1. Leaf spring models in previous studies
3.1.1.Analytical/Empirical models
3.1.2.Equivalent models
3.1.3.Discrete methods (or finite segment methods)
3.1.4.Finite element methods
3.1.5.Neural network models
3.2. Summary of leaf spring modelling techniques
3.3. Conclusion
4. Overview of study
CHAPTER 2
1. Six component load cell (6clc)
2. Characterisation of the suspension system using the multi-leaf spring
2.1. Force-displacement characteristic
2.1.1.In-service setup
2.1.1.1.Effect of U-bolt preload on the force-displacement characteristic 3
2.1.2.Spring only setup
2.1.2.1.Effect of longitudinal spacing of hangers
2.1.2.2.Deflection shape of the multi-leaf spring
3. Characterisation of the suspension system using the parabolic leaf spring
3.1. Force-displacement characteristic
3.1.1.In-service setup
3.1.1.1.Effect of U-bolt preload on force-displacement characteristics 3
3.1.2.Spring only setup
3.1.2.1.Effect of longitudinal spacing of hangers
3.1.2.2.Deflection shape of the parabolic leaf spring
4. Conclusion
CHAPTER 3
1. Introduction
2. Elasto-plastic leaf spring model
2.1. The behaviour of materials and leaf springs
2.1.1.Deformation behaviour and models of materials
2.1.2.Mechanisms in crystalline materials vs. mechanisms in multi-leaf springs 4
2.1.2.1.Mechanisms in crystalline materials
2.1.2.2.Mechanisms in multi-leaf springs
2.1.2.3.Solid-solid contact (Tribological process)
2.1.2.4.Conclusion
2.2. Mechanical properties of a multi-leaf spring
2.3. Elasto-plastic leaf spring models
2.3.1.Elastic-linear model
2.3.2.Elastic-nonlinear model
2.4. Validation of the elasto-plastic leaf spring model
2.4.1.Elastic-linear model
2.4.2.Elastic-nonlinear model
2.5. Conclusion
3. Elasto-plastic leaf spring model applied to the parabolic leaf spring
3.1. Extracting mechanical properties for the elastic-linear parabolic leaf spring model
3.2. Validation of elastic-linear leaf spring model emulating the parabolic leaf spring
3.3. Conclusion
4. Loaded length changes of a simply supported leaf spring
4.1. Method to account for loaded length changes
4.2. Validation of loaded length calculation combined with EPLS model
4.2.1.Multi-leaf spring
4.2.2.Parabolic leaf spring
4.3. Conclusion
5. Artificial neural networks
5.1. Neural network model
5.1.1.Reducing noise on neural network predictions
5.1.2.Generalization
6. Conclusion
CHAPTER 4
1. Introduction
2. Modelling of the spring only setup
2.1. ADAMS/Car leaf spring model
2.1.1.ADAMS/Car leaf spring Model 1
2.1.2.ADAMS/Car leaf spring Model 2
3. Validation of the spring only model
3.1. Validation of the spring only model using Model 1
3.2. Validation of the spring only model using Model 2
4. Conclusion
CHAPTER 5
1. Introduction
2. Qualitative validation metrics
2.1. Literature survey
2.1.1.Russell’s error measure
2.1.2.Sprague & Geers’ metric
2.2. Validation metric based on relative error
2.2.1.Relative error (RE)
2.2.2.Challenges in using the %RE as validation metric
2.2.3.Summary of the modified %RE validation metric
3. Comparison of validation metrics
3.1. Analytical functions
3.1.1.Ability to rank models and identify the best model
3.1.2.Reliability and usefulness of validation metrics
3.1.3.Combination of S&G and the modified %RE
3.2. Case studies
3.2.1.Case study 1: Known error between signals
3.2.2.Case study 2: Elasto-plastic leaf spring model
3.2.3.Case study 3: Comparison of accuracy and efficiency of leaf spring
modelling methods
4. Conclusion
CHAPTER 6
1. Conclusions
2. Recommendations
2.1. Chapter 2
2.2. Chapter 3
2.2.1.Elasto-plastic leaf spring model
2.2.2.Neural network model
2.3. Chapter 4
2.4. Chapter 5
Bibliography