Leaf springs Design, calculation and testing requirements S. Karditsas, G. Savaidis, A. Mihailidis Aristotle University of Thessaloniki Thessaloniki, Greece A. Savaidis School of Pedagogical and Technological Education Athens, Greece R. Fragoudakis Tufts University Medford, MA, USA ABSTRACT For the design of serial leaf-springs, specific requirements regarding the dimensions of the vehicle configuration and the allowable developed stresses that occur under specific operating loading conditions are taken into account. The allowable stresses are obtained from Wöhler curves determined experimentally and providing the fatigue behaviour of the end product. In the present paper a parabolic 2-leaf-spring for front axles of heavy duty vehicles was used as an example for the design process using the Finite Element Methods simulating the on-vehicle operating conditions. A Wöhler curve was determined after the conduction of 6 cyclic 4-point bending tests and the developed strains were measured during the tests. Finally a Finite Element simulation of the experimental configuration was performed and the calculated stress distribution along the specimens was compared with the stresses developed during the tests. KEYWORDS Automotive, leaf springs, design, finite element method, fatigue INTRODUCTION For the suspension of carry-load vehicles many types of arrangements may be used depending on the type of the vehicle and the occurring operating loads. One advantageous type of suspension systems is the leaf-springs system, which needs less additional components than other suspension systems, thereby leading to lighter and lower-cost structures. Additionally, the leaf-spring s performance determines both the suspension and the guidance of the vehicle due to the fact that the leaf-spring is connected with both the axle and the steering system.
For the design of serial leaf-springs, specific requirements regarding the dimensions of the vehicle configuration and the allowable developed stresses that occur under specific operating loading conditions are taken into account. In particular, the vehicle manufacturer sets the requirement of the fatigue life of the leaf-springs under specific operating loading conditions referring to the corresponding vehicle. On the other hand, the leaf-spring manufacturer having experimentally assessed the fatigue behaviour of its end product under uniaxial or biaxial cyclic bending determines the S-N Wöhler curve that gives the maximum stresses the products can withstand. Thus, the engineer, having given the vehicle configuration s dimensions, aims to design a leaf-spring able to endure the maximum permissible stresses, which according to the vehicle manufacturer s S-N Wöhler curves correspond to the desired fatigue life. The present paper focuses on the design of serial parabolic 2-leaf-spring for front axles of heavy duty vehicles with nominal load of 9.2 tons on the axle using the Finite Element Methods as introduced and experimentally verified by Savaidis et al. [1] for the simulation of mono- and multi-leaf springs. For the FE analysis the necessary components of the onvehicle arrangement were modelled in order to take the real operating conditions into account. Additionally, a S a -N Wöhler curve has been experimentally determined. More specifically, 6 leaves were tested on a uniaxial 4-point bending test rig designed for that purpose. The stresses were measured during the tests and compared to the stresses calculated by the FE simulation of the experimental set-up. LOADING CONDITIONS The work of Grubisic and Fischer [2], Grubisic [3], Rupp and Grubisic [4] Savaidis et al. [5], Lange et al. [6] and Decker and Savaidis [7] regarding the driving of trucks on test tracks and public European roads proved that the loading conditions that have the most significant influence on the integrity of the front axles leaf-springs are the following: - pure vertical loading that occurs from straight ahead driving - vertical and longitudinal loading that occur simultaneously from braking. Fig. 1: Loads occurring from straight ahead driving and braking
The braking causes the so-called wind-up of the springs that tends to bend the springs in an S shape and thus may lead to extreme deformations and consequently to extreme stresses having values close to the yield strength of the material. Pure vertical loading leads to stresses lower than braking. The directions of the two loading conditions are shown in Fig. 1. The maximum values of the above two loading conditions are expressed in relation to the vehicle s half-payload (F n ), see equations (1), (2) and (3). Although they do not correspond to the most detrimental conditions, regarding the fatigue damage, they are taken into account for the accurate design and durability of the end product. Maximum vertical load (F v,max ) during straight-ahead driving: F = a F v,max n (1) Maximum vertical and longitudinal forces (F v,max and F br,max ) at full braking: F = b F (2) F v,max br,max n = c F (3) The factors a, b and c are different for each geographical region of operation. In the case of West Europe they have the following values: a = 2.5, b= 2, and c = 1.6. These maximum values are derived either from measurements conducted by the vehicle manufacturers or from standardized fatigue spectra like the ones addressed in the work of Grubisic and Fischer [2] and Grubisic [3]. n FINITE ELEMENT ANALYSIS The FE modeling of the 2-leaf-spring was performed according to the experimentally verified methodology introduced by Savaidis et al. [1] for leaf-springs and has the following main points: - Solid hexahedra elements of first order - Minimum of six elements over the thickness of each leaf - Average element length of approximately 5mm - Linear elastic material behavior accurately representing the behavior of the high strength spring steels For the simulation of the real operating conditions the accurate dimensions of the onvehicle configuration were taken into account. Additional components were modeled and used. Figure 2 gives a schematic overview of the on-vehicle configuration. Figure 3 shows the complete FE model of the 2-leaf model investigated.
Fig. 2: Parabolic mono-leaf spring for rear axles with on-vehicle configuration Fig. 3: Finite Element model of the parabolic 2-leaf-spring and the additional components The shackle at the rear eye and the bushings in the two eyes were modeled using rigid bars. All the components in the center clamped area were modeled. In contrast to Figure 2, in the case of the 2-leaf-spring in question only the elastomeric buffer, the so-called S-buffer, is used on the vehicle, positioned at distance 325mm measured from the center of the clamped area. Therefore only that one buffer was modeled using a non-linear spring element, whose force-deflection characteristic was provided by the vehicle manufacturer. The silencers prevent the friction contact between the two leaves. Their material behavior was simulated using the corresponding stress-strain curve provided by the vehicle manufacturer. The operating loads were applied on the middle node of leaf 1. The commercial software packages ANSA, ABAQUS and μeta were used for the pre-process, the solution and the post-process, respectively. RESULTS The aim of the FE analysis is the design of a leaf-spring, where the developed stresses under the two aforementioned loading conditions (a) are uniformly distributed along the
two leaves (stress plateau) and (b) they are lower than or equal to the maximum allowable stresses specified from the corresponding S max -N Wöhler curves of the leaf-spring manufacturer. For the achievement of these goals, various design parameters each of different influence on the behavior of the leaf-spring must be combined properly as presented by Karditsas et al. [8]. Both the stresses due to the maximum vertical load and due to braking are taken into account for the design. As mentioned above, the allowable stresses caused by maximum vertical loading are lower than the stresses that occur from braking because of the fact that during braking very extreme deformations may occur. In the present study the ratio of the maximum allowable stress of braking σ br to the maximum allowable stress of maximum vertical loading σ v,max is 1.214. Figures 4(a) and 4(b) show typical stress distributions along the tension surface of leaf 1 and leaf 2, respectively, for three loading conditions. The stress values are normalized by the maximum allowable stress that occurs at maximum vertical loading. (a) (b) Fig. 4: Stress distribution along (a) leaf 1 and (b) leaf 2 resulted for three loading conditions In case of maximum vertical load, the developed stresses are equal to the allowable stress for both leaves and appear on the front arms. In the case of braking, the maximum developed stresses are lower than the allowable ones on the rear arm of the second leaf and much lower on the rear arm of the first leaf. A uniform stress distribution has been achieved in the case of maximum vertical loading on the front arms of both leaves. In the case of braking, a quasi-uniform stress distribution appears on the rear arm of the second leaf whereas on the rear arm of the first leaf the distribution is slightly uniform presenting some irregularities due to the functioning of the S-buffer. However, this distribution can also be considered as uniform. The steep peak arises on the front arm of the first leaf at the area of 750 mm is due to the presence of the step shape of the leaf. Figure 5 shows the forms and positions of the leaf-spring that occur under vertical halfpayload, maximum vertical load and full braking in comparison to the unloaded condition. In case of full braking a slight wind-up phenomenon is obvious and the resulted S form of the leaf-spring which is represented from the black dashed line.
(a) (b) (c) Fig. 5: Forms and positions of the leaf-spring at (a) half-payload, (b) maximum vertical load and (c) full braking EXPERIMENTAL INVESTIGATION Specimens For the present study six cyclic 4-point bending tests were executed for the assessment of the fatigue behaviour of a specific end product of a leaf-spring manufacturer and the determination of the corresponding S a -N Wöhler curve. Six specimens of the end product were used, made of high-grade spring steel 56SiCr7. Their chemical composition is given in Table 1 according to EN 10089:2003-04. Table 1: Chemical composition of 56SiCr7 steel (weight %) acc. to EN 10089:2003-04 C Si Mn P S Cr 0.52-0.60 1.60-2.00 0.70-1.00 < 0.025 < 0.025 0.25-0.45 Fig. 6: Shape and dimensions of the specimens
Figure 6 shows the specimen geometry. The specimens have profile of type C according to the European Standard EN 10092-1:2003 that denotes a rectangular profile with semirounded edges. Their length is 1200 mm, their width 90 mm wide and their thickness is constant 12 mm. All samples were subjected to the same development process that includes heat and surface treatment. In order to achieve maximum hardness, the samples were first heated up to 850 o C and then immersed into an oil bath decreasing their temperature to approximately 50 o C. Then, the springs were tempered by heating to 500 o C for 30 minutes and then cooling slowly in air. After the heat treatment process, stress peening was applied on the springs, thereby improving their fatigue strength by inducing compression residual stresses onto a thin layer of material beneath the tension surface. The two described technologies improve effectively the fatigue life of the leaf-springs as presented by Fragoudakis et al. [9] and Savaidis [10]. Test rig For the execution of the 4-point cyclic bending tests, the test-rig shown in Figure 7 was designed. The load is introduced by a servohydraulic actuator and applied on the specimen at two points via two loading-cylinders positioned at distances ±250 mm from the center of the specimen. Each loading-cylinder is mounted on two metal plates welded on a hollow rectangular bar which is connected with the load cell in front of the actuator. The specimen is supported by two cylinders of 50 mm diameter positioned at distances ±500 mm from the longitudinal axis of the actuator. Fig. 7: 4-point bending test-rig Stress distribution In order to determine the stress distribution along the specimens, strain gages were used for the measurement of the occurring strains. The corresponding stresses were calculated taking into account the standardized Young s modulus for steel E=2.1 GPa. The strain gages were positioned on the side of the specimens subjected under tension at various positions along the area between the loading-cylinders (±250 mm from the center of the specimen), because under the 4-points bending conditions the maximum stresses are
developed on that region. The stresses developed during the tests were compared with the stresses obtained from the FE analysis performed, simulating the test-rig configuration for two levels of developed stresses. As shown in Figure 8 the agreement between calculated and measured stresses is satisfactory. The stress values are normalized by the maximum stress developed under the maximum applied force. Fig. 8: Stress distribution obtained from tests and FE analysis for two load levels Fatigue results All specimens were subjected to cyclic loading with an approximately constant force ratio R=0. The tests ran at two force/stress levels. Figure 9 shows the determined S a -N Wöhler curves. The solid line is the Wöhler curve for probability of survival 50% produced by regression. The dashed lines stand for the Wöhler curves with probability of survival of 10% and 90%. The slope of k=5.35 is typical for shot peened unnotched specimens. The stress values are normalized by the stress that corresponds to the upper level. Fig. 9: Determined S a -N Wöhler curve
SUMMARY AND CONCLUSIONS The present study dealt with the design process of leaf-springs taking into consideration specifications regarding the dimensions of the vehicle arrangement and the fatigue life requirement from the vehicle manufacturer for specific operating loads. A serial parabolic 2-leaf-spring for front axles of heavy duty vehicles was designed using the FE method. Vertical loads from straight ahead driving and biaxial loads from full braking of the vehicle are considered as design criteria. The stress limitations were exceeded and approximately uniform stress distribution was achieved along the length of the two leaves. Additionally, a S a -N Wöhler curve was experimentally created by means of six 4-points fatigue bending tests at two load levels. ACKNOWLEDGEMENT The General Secretariat for Research and Technology of Greece and the European Union are gratefully acknowledged for the financial support of the investigations within the framework of ESPA 2007-2013, Support of New, Small and Medium Enterprises. The company BETA CAE Systems S.A. is gratefully acknowledged for provision of the pre- and post-processing software suite ANSA/μETA. REFERENCES [ 1 ] Savaidis, G.; Malikoutsakis, M.; Savaidis, A.: FE simulation of vehicle leaf spring behavior under driving manoeuvres International Journal of Structural Integrity (2013), Vol. 4, pp.23-32 [ 2 ] Grubisic, V.; Fischer, G.: Automotive wheels, method and procedure for optimal design and testing SAE Technical Paper Series 830135 (1983), Michigan, USA [ 3 ] Grubisic, V.: Determination of load spectra for design and testing International Journal of Vehicle Design (1994), Vol. 15, pp. 8-26 [ 4 ] Rupp, A.; Grubisic, V.: Reliable determination of multiaxial road loads and tyre deformations on busses and heavy trucks for the design and proof out SAE Paper 973189 (1997) [ 5 ] Savaidis, G.; Riebeck, L.; Feitzelmayer, K.: Fatigue life improvement of parabolic leaf springs in the process of simultaneous engineering
Materials Testing (1999), Vol. 41, pp.234-40 [ 6 ] Lange, P.; Denzin, R.; Savaidis, G.: LKW-Parabelfedern Last-Beanspruchungsermittlung und Betriebsfestigkeitserprobung Materials Testing (2003), Vol. 45, pp. 70-7 [ 7 ] Decker, M.; Savaidis, G.: Measurements and analysis of wheel loads for design and fatigue evaluation of chassis components Fatigue and Fracture of Engineering Materials and Structures (2002), Vol. 25, pp. 1103-19 [ 8 ] Karditsas, S.; Savaidis, G.; Malikoutsakis, M.: Design of heavy duty parabolic front leaf-springs with respect to kinematics and stress behavior Proceedings 3 rd International Conference on Engineering Against Failure (2013), Kos, Greece [ 9 ] Fragoudakis, R.; Saigal, A.; Savaidis, G; Bazios, I; Malikoutsakis, M.; Pappas, G.; Karditsas, G.; Savaidis, A.: Fatigue assessment and failure analysis of shot-peened leaf springs Fatigue and Fracture of Engineering Materials and Structures (2013), Vol. 36, pp. 92-101 [ 10 ] Savaidis, A.: Surface properties and fatigue life of stress peened leaves Materials Testing (2013), Vol. 54, pp. 529-34 Corresponding author: s.karditsas@gmail.com