Master's Thesis in Mechanical Engineering Improved lifetime of a rubber spring in an articulated hauler through product development Authors: Pontus Nilsson, Jan Tordsson Surpervisor LNU: Klas Qvarnström Examinar, LNU: Andreas Linderholt Course Code: 4MT31E Semester: Spring 2017, 15 credits Linnaeus University, Faculty of Technology Department of Mechanical Engineering Abstract Dampening systems are important in heavy vehicles utilized in rough terrains, with purpose to reduce shocks and vibrations with negative influences on the vehicle and, more importantly, on the operator of the vehicle. During the years the heavy vehicles require sturdier construction parts, due to demands on higher load capacity, where the easy solution to scale up the construction parts is not always applicable for dampening systems with nonlinear behavior. Hence, the sturdiness in the design of these dampening systems requires improvement. In this thesis the design of the rubber spring used as rubber spring in Volvo’s articulated hauler A40G is treated. The aim of this thesis is to find alternative design solutions on the rubber spring, improving its lifetime. The usual failure of these rubber springs is crack propagation in the rubber body. In the method of this thesis, alternative design solution are generated in concepts though brain storming, which are adjusted to achieve the desired behavior of the rubber spring through calculations and tested in performance through simulations in Abaqus. From analyzing the generated data, it is concluded that among the tested design solutions, a combination of fewer plates and shaping the plates as thin bowls, results in highest potential increase in lifetime. Key words: Rubber spring, elastomer, principal stretch, nominal stress, maximum surface stress, lifetime 2 Pontus Nilsson Jan Tordsson Acknowledgement First, we would share our gratitude to our supervisor Klas Qvarnström; Senior Engineer in Mechanical Design lecturing in Product Development at Linnaeus University in Växjö, our teacher in Scientific Methodology and Planning Thomas K Bader; Associated Professor in the Department of Building Technology at Linnaeus University, and our examiner Andreas Linderholt, Head of Mechanical Engineering Department at Linnaeus university. With their support we were able to carry out this thesis project. Furthermore, we would also like to thank Volvo Constriction Equipment in Braås for welcoming us to work with the improvement of Volvo’s A40G rubber spring design. We are thankful to our supervisor Dennis Andersson; Design Engineer at Volvo Construction Equipment AB, for arranging meetings on Volvo, providing clear data requested about the rubber spring and clearly emphasizing occurring lack of content in our work and Marcus Andersson; Manager of Structure Engineering at Volvo Construction Equipment in Braås, for introducing us to Volvo and this project. We would also like to thank Magnus Andersson; Specialist on Structural Dynamics & Vibration Induced Fatigue, for aiding us to understand the behavior of rubber while developing our calculation model and Martin Kroon, Professor in Fracture Mechanics, Material Mechanics and Constructive Modelling at Linnaeus University in Växjö, for helping us adjusting our simulation models in Abaqus. Pontus Nilsson & Jan Tordsson Växjö June 2016 3 Pontus Nilsson Jan Tordsson Table of contents ABSTRACT ........................................................................................................................ 2 ACKNOWLEDGEMENT ................................................................................................. 3 TABLE OF CONTENTS .................................................................................................. 4 1 INTRODUCTION ...................................................................................................... 6 1.1 BACKGROUND AND PROBLEM DESCRIPTION ................................................................... 6 1.2 AIM AND PURPOSE ......................................................................................................... 8 1.3 HYPOTHESIS AND LIMITATIONS...................................................................................... 8 1.4 RELIABILITY, VALIDITY AND OBJECTIVITY .................................................................... 9 2 LITERATURE REVIEW ....................................................................................... 10 2.1 CRACK INITIATION AND PROPAGATION IN CIRCULAR RUBBER BEARINGS SUBJECTED TO CYCLIC COMPRESSION ............................................................................................................. 10 2.2 MODELLING OF ELASTOMERIC BEARINGS WITH APPLICATION OF YEOH’S HYPERELASTIC MATERIAL MODEL ..................................................................................................................... 13 3 THEORY .................................................................................................................. 17 3.1 MECHANICAL PROPERTIES OF RUBBER ......................................................................... 17 3.1.1 Crack development ............................................................................................. 17 3.1.2 Strain energy density .......................................................................................... 18 3.2 ABAQUS ....................................................................................................................... 19 3.3 BRAINSTORMING ......................................................................................................... 20 3.4 PUGH MATRIX .............................................................................................................. 20 4 METHOD AND IMPLEMENTATION ................................................................ 21 4.1 GENERATE ALTERNATIVE DESIGN SOLUTIONS ............................................................. 21 4.1.1 Description of the current rubber spring ........................................................... 21 4.1.2 Compile alternative design solutions ................................................................. 23 4.2 DERIVE THE CALCULATION MODEL CALCULATION ...................................................... 25 4.2.1 Define leading equation ..................................................................................... 25 4.2.2 Relate concept-solutions to leading equation ..................................................... 27 4.2.3 Adjust critical dimensions to desired behaviors ................................................. 52 4.3 GENERATE DATA DESCRIBING LIFETIME OF EACH CONCEPT ......................................... 66 4.3.1 Test models in Abaqus ........................................................................................ 66 5 RESULT AND ANALYSIS ..................................................................................... 70 5.1 RESULTS ...................................................................................................................... 70 5.1.1 Concepts with compensated critical dimensions ................................................ 70 5.1.2 Simulations in Abaqus ........................................................................................ 71 5.2 ANALYZE RESULTS ...................................................................................................... 74 5.2.1 Evaluate validation of data received from axial/vertical compression simulation 74 5.2.2 Evaluate data received from radial/horizontal displacement simulation ........... 76 5.2.3 Evaluate concept performance in Pugh matrix .................................................. 79 6 DISCUSSION ........................................................................................................... 82 4 Pontus Nilsson Jan Tordsson 7 CONCLUSION ........................................................................................................ 85 8 REFERENCES ......................................................................................................... 87 APPENDIX A ................................................................................................................... 89 APPENDIX B ................................................................................................................... 91 APPENDIX C ................................................................................................................... 96 APPENDIX D ................................................................................................................... 97 APPENDIX E ................................................................................................................... 99 5 Pontus Nilsson Jan Tordsson 1 Introduction 1.1 Background and problem description Today there is a big need in several industries for transportation of heavy loads over rough terrain. Due to the rough terrain the freighter is subjected to vibrations and repeated shocks, which shortens the lifespan of the carrier. These vibrations and shocks can cause considerable discomfort and have a negative influence on the health of the operator. In the carrier, the frame is affected by extreme loads, since it is carrying the freighter´s weight and the weight of the transported load. Since the frame is affected by these extreme static and dynamic loads, it is easily worn out. Usually, a damping system is attached to the frame, to dampen these dynamic loads and prolong its lifetime [1]. There are several damping systems in use, for example Schacman F2000 heavy truck use multi leaf springs [2]. Scania use air suspension containing air springs on their heavy trucks [3]. Dump trucks are often used in rough terrains, for example in mining and building sites, for transportation of loose materials. One example of dump trucks are Volvo CE’s articulated haulers. Volvo started to develop the articulated hauler in Braås, Sweden in the 1960s. Since then it has been a reliable carrier due to its ability to transport heavy loads in difficult terrain. Today Volvo is one of the largest manufacturers in the world of articulated haulers. Since the first articulated hauler where constructed it has been under constant development, to meet customer demands. The demand for transporting heavier loads has pushed Volvo to develop larger articulated haulers. Volvo´s first articulated hauler. DR 631 (Gravel Charlie), had a load capacity of 10 ton (t) [4]. Today Volvo´s smallest articulated hauler, A25G, has a load capacity of 24 t and their largest articulated hauler, A60H, has a load capacity of 55 t [5]. The increased load capacity requires a sturdier construction, which Volvo CE sometimes solves by scaling up different parts of the construction. One part adjusted with this method is the damping system of the dump body, which is a spring element called “elephant foot”, see Figure 1 and Figure 2. This is a rubber spring made from steel plates and rubber. Today Volvo´s largest articulated haulers are close to the required lifespan of the rubber spring, just by scaling it up. 6 Pontus Nilsson Jan Tordsson Figure 1 Rubber spring inside Volvo’s A40G Figure 2 Rubber spring 7 Pontus Nilsson Jan Tordsson 1.2 Aim and purpose The aim of this thesis project is to find alternative design solutions on a rubber spring to improve its lifetime, with a case study on Volvo’s spring system. To achieve the main aim all of the following sub aims has to be fulfilled: • Determine critical dimensions that relates to the desired behaviors. • Adjust these critical dimensions for each design solution to achieve the desired behaviors. The purpose of this thesis is to improve the lifetime of an existing rubber spring, through product development. 1.3 Hypothesis and limitations The load capacity and fatigue life of a rubber spring does not increase linearly with its size. It is supposed that a small modification in construction design can increase strength more than increased size. This study will focus on the development to improve Volvo´s rubber spring. Due to limited time, the data used to evaluate the lifetimes of the alternative designs will only be generated from ABAQUS simulations and hand calculations. The materials in the current design are used with the design solutions, so fatigue due to the environmental factors is not taken into consideration in this thesis. 8 Pontus Nilsson Jan Tordsson 1.4 Reliability, validity and objectivity Simulations in Abaqus, generates reliable data, since it is based on computational calculations. If the input is defined correctly in the software, the resulting data from the simulations are valid. Mathematical hand calculations are reliable, since it will give the same results with the same input. Since some approximation is necessary when deriving the calculation method, the calculation output is less valid. Literature studies are reliable but may lack validity if the information is not evaluated correctly. On the one hand, data collected for testing and calculating purpose should be more valid, since it is objective data. On the other hand, subjective data collected for inspirational purpose may lack validity, since the authors of this thesis may not be able to apply the subjective data to the particular situation. This may be a problem later in the thesis, where the validity of the collected subjective data only can be evaluated when the data is applied to the final result of this thesis. The product development tools aid the participants of this thesis to be efficient during the development process. If the participants lack experience of the product, treated in the development process, the data generated from the development tools may lack validity. Since the design changes are small, the comparison between lifetimes of the new designs and the existing design should increase in validity. With guidelines, received from interviews with experienced product developers, the reliability of this method should increase. From studying the behavior of the existing design of the rubber spring through simulations and interviews with engineers at Volvo CE, the validity of the generated data from this method should increase. 9 Pontus Nilsson Jan Tordsson 2 Literature Review 2.1 Crack Initiation and Propagation in Circular Rubber Bearings Subjected to Cyclic Compression In article [6], the fatigue crack initiation and propagation in circular rubber bearings, affected by dynamic compression, is analyzed through hand calculations and finite element analysis. The analysis in this article is based on cyclic compression experiments on neoprene rubber bearings, see Figure 3, earlier executed by authors of this article. From these experiments, the authors conclude that crack initiates at the interface between the rubber and the plates, see Figure 4. Figure 4 Observations on specimen Figure 3 Example of the hockey puck like tested with different cyclic loads [6] circular neoprene rubber bearing http://en.chenggongyi.com/ueditor/php/upload/ image/20170405/1491401939341903.jpg (2017-05-20) 10 Pontus Nilsson Jan Tordsson