Fatigue Design of Automotive Suspension Coil Springs

SAE TECHNICAL PAPER SERIES 2002-01-0656 Fatigue Design of Automotive Suspension Coil Springs Abderrahman OUAKKA, Michel LANGA ALLEVARD REJNA AUTOSUSPENSIONS Centre de Recherche et Développement de Technologies 201, Rue de Sin-le-Noble, BP. 629 59506 Douai Cedex, France abderrahman.ouakka@allevard-rejna.com michel.langa@allevard-rejna.com Copyright 2002 Society of Automotive Engineers, Inc. ABSTRACT Due to environmental factors and fuel economy, most cars are now required to undergo weight reduction. For this purpose, Allevard Rejna Autosuspensions has undertaken a broad research program based upon numerical and experimental approaches in order to increase the fatigue life of their automotive suspension coil springs. The aim is to predict the performance of the coil spring and the damage introduced, either in the spring manufacturing processes or during service, by other factors than fatigue tests. For the present, our attention will be restricted to illustrating an application using a finite element simulation and a multiaxial fatigue analysis, correlating fatigue life, surface defects and residual stresses. INTRODUCTION The fatigue life of a suspension spring depends mainly on the following factors : Load cycles Design: spring and cups Process: materials & residual stresses The first item is evidently set by the car maker and is beyond the control of the spring manufacturer. Three alternatives thus remain open to us : Optimize the shape of the spring/cup pair Increase the hardness of the material Increase the residual compression stresses. As the courses of action regarding materials and processes are nearing the technological limits specific to large series manufacture, it was important to find new ways to optimize the spring design in its environment in order to meet increasing demands in terms of weight, packaging and strength. In order to meet this need, design tools using virtual prototyping remains the only solution that can take in account the complexity of the phenomena and allows multi-criteria optimization within shorter lead time. After having presented the approaches on which these tools are based, we give some practical examples to highlight their pertinence. MULTIAXIAL FATIGUE APPROACH Any manufacturing process will introduce residual stresses in mechanical parts and structures that can considerably alter their in-service performance, especially their high-cycle fatigue strength. These initial stresses are worthless unless they remain stable in service. In fact, by superimposing themselves on the load applied, they change the stress distribution in accordance with the appropriate relaxation kinetics. In the case of suspension springs, a loss of around 30% in relation to the initial profile in those areas most subjected to stress has been demonstrated. Figure 1 shows that an asymptotic state is reached after 100 cycles. Under this stabilized state, fatigue cracks most often appear in the surface layers. Session : Fatigue Research and Application : Fatigue Design in European Automotive Industry 1/6

APPLICATION TO THE CASE OF SPRINGS Presented below is an application of the fatigue criterion described above to a lightweight version of a coil spring. These characteristics and its operating environment are illustrated in figure 2. Figures 3 and 4 represent the distribution of the Von Mises stress field at the extreme positions of the constant fatigue cycle (Rebound and Bump positions). These results have been drawn from a conventional analysis using finite element methods [5]. Fig-1. Relaxation phenomena under fatigue loading The integration of these phenomena in a predictive fatigue strength calculation was the real problem of designing parts subjected to multiaxial stresses. The designer must therefore have at its disposal a highcycle multiaxial fatigue criterion. Our approach is based on Dang Van s criterion [1]. DANG VAN S CRITERION The model proposed by Dang Van is based on dislocation theory and has been drawn from the work of Orowan [2] and Yolobori [3]. Fig-2. Spring Specification : Total Number of Coils: 4.5 Mean Diameter: 152 mm Spring Height: 352 mm Wire Diameter: 13.60 mm Spring Rate: 28.82 N/mm Fig-3. Rebound Position This criterion concerns crack initiation at a microscopic level owing to the fact that the damage starts at the level of off-axis grains that, under the effect of the loading, suffer localized plastic slip. This phenomenon established on a microscopic scale requires the use of multi-scale methods (micro-macro). We may thus write: σ( t) = Σ () t + ρ (1) Fig-4. Bump Position When these results are subjected to special posttreatment using Dang Van's criterion (2), by analyzing the instantaneous stress field, we obtain the distribution of the break risk factor along the length of the spring. This analysis reveals the most critical spots as shown in figure-5. ρ : stabilized local residual stresses. Σ () t : macroscopic stresses at moment t. σ (t) : local stresses at moment t. Dang Van postulates that crack initiation occurs at grain level if at each moment of the cycle we have: f ( (t)) = τ + α.p β 0 σ (2) τ : instantaneous shear stress relative to a critical plane. p : instantaneous hydrostatic pressure. α, β : two material constants which can be identified from two different fatigue limit strength measurements. For example in alternate bending and alternate twisting. Fig-5. Damage fatigue and potentially critical spots Session : Fatigue Research and Application : Fatigue Design in European Automotive Industry 2/6

A series of tests were conducted to determine: the break zones the fatigue life Figure 6 illustrates the test-calculation comparison and shows that the break points observed experimentally do correspond to the peak probability of a break risk along the length of the spring, as predicted by Dang Van s analysis. This criterion enables us to predict the effect of surface defects on fatigue life. Figure 8 shows the reduction in fatigue strength of the above-mentioned type of spring containing defects of varying depths in the most critical zone. Fig-8: Impact of surface defects on fatigue strength. Fig-6. Comparison between real break and Dang Van s prediction Taking into account the residual stresses and surface condition obtained by the manufacturing process, it is possible to estimate fatigue life by comparing on Dang Van s diagram, the loading path of the critical spot and the design line taken from Wöhler s curves (figure 7). This figure also illustrates the performance of two processes in terms of residual stresses. We can see that process 1 does not enable the target fatigue life to be attained whatever the depth of the defect. Process 2 is clearly adequate with regard to project feasibility for roughness type defects ( 30 µm). For both processes, the fatigue life falls by 50% when comparing the fatigue life for a smooth surface of 10 µm with that of a surface containing a defect 60 µm deep. To conclude, this study shows that the Dang Van's fatigue approach allows a fine analysis of suspension spring behaviour to be made. OPTIMIZATION INTRODUCTION A design study for such mechanical part must meet from three different requirements : 1. Functionality (stiffness, compactness, side load, etc.) 2. Service strength (fatigue life) 3. Technological feasibility (metallurgy, process, etc.) Fig-7. Dang Van's diagram The relative error between the fatigue life calculated and that measured does not exceed 5%. If all of the above criteria are to be taken into account, a compromise approach is necessary, enabling not just one solution to be proposed, but a whole spectrum of solutions, of which the most technically feasible and less costly will be chosen. Session : Fatigue Research and Application : Fatigue Design in European Automotive Industry 3/6

This means taking into account the techniques of both the design and methods departments in order to reconcile the shape proposals of one with the technological constraints of the other. above. We can see that there is a one-to-one relationship between this profile and the one in figure 6. Fatigue optimization can be considered from two aspects : the first relating to the process and the second to the product. PROCESS OPTIMIZATION The thermomechanical background to spring manufacture rests upon a number of parameters which affect the fatigue strength of the finished product. One of the most significant stages in the process is shot peening. The performance of this operation is demonstrated by : the mechanical and geometrical characteristics of the shot: E : Young s modulus, D : Diameter, the elastic-plastic characteristics of the spring: E : Young s modulus, S : yield strength, H : hardening coefficient and impact speed V. In the case of a simple isothermal shot peening operation, figure 8 shows us how these parameters are classified in terms of roughness and residual surface stresses obtained from numerical modelling. Fig-10. Optimum profile of residual stresses to ensure target lifetime throughout the spring. In conjunction with figure 9, we can choose the best compromise between the process parameters that provide the desired level of residual stresses with a given degree of roughness. It is of course impossible to apply this curve on an industrial basis, but we can adjust our shot peening parameters in order to inject the maximum value of the peaks all over the spring. In other words, treat the whole spring in the same way as the most stressed zone. PRODUCT OPTIMIZATION % Our aim is to obtain the criteria regarding the geometrical corrections to be made to the reference design, while maintaining its functional properties, in order to : shift the break zones to particular locations. increase the lifetime by improving the distribution of service stress fields. One of the most common methods used for this is the automatic learning expert system [6]. Automatic Learning Fig-9: Classification of influential parameters After a Dang Van type calculation, it is possible to evaluate the profile and optimal levels of the residual compression stresses necessary and sufficient to achieve a specified fatigue life in the entire spring. In figure 10, this profile is showed in terms of hydrostatic pressure P in surface in the case of the spring presented This approach is based on a database of examples defined by experts in the field. Its pertinence depends greatly on the quantitative wealth of the learning base. The main steps are : First, generate rules from the learning base. Second, apply the rules in the test base in order to verify their validity. Session : Fatigue Research and Application : Fatigue Design in European Automotive Industry 4/6

Third, use these rules to solve the problem. Automatic learning methods allow expert knowledge to feedback from real experiences. The problem description is critical as it conditions the learning rules and thus the system s efficiency in regard to optimization. Optimizing the spring on its own. Figure 12 demonstrates the optimal spatial positions of the C-Shape coiling axis represented by field D where the multi-criteria optimization indicator I < 1. I <1 4mm x j In order to optimize a spring type shape, it is essential to define an initial geometry. This must be as simple as possible, represented by a minimum of parameters [X 1,, X n ]. 0 4mm x i In the given example, these parameters are closely linked to the spatial coiling axis of the spring, which in this study is cylindrical. Figure 11 shows the impact of a C or S-shaped spring on the local variations in geometry of the spring. D: Allowable space Fig-12. Multi-criteria optimization indicator : C-Shape We may therefore allow some geometrical variations during spring manufacturing without any critical effect, in that this field is not restricted to a single solution. Figure 13 illustrates just one of these solutions. X 3 X 3 X 1 X 2 X 1 X 2 Final Shape C-Shape S-Shape Fig-11. Geometrical parameters of the spring to be changed according to its coiling axis Initial Shape The spring can be optimized by changing these parameters according to laws we need to establish. These changes are applied to groups of parameters or to single parameters according to their linear interdependence. These laws, which we later refer to as multi-criteria optimization lindicator I, are established according to the following items : 1. maximum gap between the coils, 2. side load close to a target value, 3. better distribution of the stress fields, 4. break zone located at mid-height, 5. lowest possible break risk, entailing in maximal fatigue life with a fixed level of residual stresses. Fig-13. An optimal solution that meets the functional and endurance criteria applied to the Spring on its own in the case of the C-Shape. In the case of the S-Shape, it is impossible to obtain a compromise which combines all the functional and endurance requirements: I > 1, figure 14. Session : Fatigue Research and Application : Fatigue Design in European Automotive Industry 5/6

I >1 4mm xj CONCLUSION The present optimization design program results from our research that has shown that certain problems relating to durability and the process may be dealt with in terms of shape. 0 4mm x i The efficiency of this optimization depends on the ability : to evaluate the requirements, to modify the shape. The reliability of the optimizer could not be reached without using such new approaches as : Fig-14. Multi-criteria optimization indicator: S-Shape Optimizing the Spring/Cup system In addition to the above five criteria defining the multicriteria optimization indicator I, we now need to add a sixth item which is : weight reduction of the cups. The spring shape chosen is illustrated in figure 15. The reduction in weight of the cups is found in the reduced diameters of the end coils. It is important to note that the spring axis is neither C-Shaped nor S-Shaped, the main changes lying in the elevations of the coils. Initial Shape Final Shape 1. a relevant multiaxial fatigue criterion, 2. an adequate automatic learning approach. ACKNOWLEDGMENTS The authors would like to thank Ky Dang Van, Director of Research at the CNRS, for all his advice and comments enabling us to correctly integrate his criterion into our Research Center. REFERENCES 1. K. Dang Van, 1973, Sur la résistance à la fatigue des métaux. Sciences et Techniques de l'armement, Mémorial de l'artillerie Française, 47, 3 ème Fascicule, pp 647-722. 2. E. Orowan, 1939, Theory of the fatigue metals. Proceeding of the Royal Academy, A171, London. 3. T.Yokobori and T.Yoshmura, 1966, A criterion for fatigue fracture under multiaxial alternating stress state. Report of the Research Institute for Strength and Fracture of Materials, Tohoku University, Sendai, Japan. 4. K. Dang Van, 1999, Introduction to fatigue fatigue analysis in mechanical design by the multiscale approach. In K. Dang Van, I.V. Papadoupoulos (Eds), High-Cycle Metal Fatigue in the Context of Mechanical Design, CISM Courses and Lectures, n 392 Springers Verlag, pp 57-88. 5. M.Langa and A.Ouâkka, 2001, Optimisation du ressort de suspension dans l'environnement véhicule : apports de l'outil de simulation numérique. J. Mécanique & Industrie, Editions Scientifiques et Médicales Elsevier SAS, pp 181-188. 6. P. Navidi and J. Zarka, 1993, Clever Optimal Design of Materials and Structures. In Proceedings of Second French-Korean Conference on Numerical Analysis of Structures, Seoul. Fig-15. Optimal solution that meets the functional and endurance criteria applied to the Spring/Cup pair. Session : Fatigue Research and Application : Fatigue Design in European Automotive Industry 6/6