Fatigue design and test on Chevron rubber springs ...

Fatigue design and test on Chevron rubber springs used in rail vehicles R. K. Luo, W. J. Mortel & A. D. Spinks Department of Engineering and Technology, Trelleborg Industrial AVS, 1 Hoods Close, Leicester LE4 2BN, UK.

X. P. Wu School of Civil Engineering and Architecture, Central South University, Changsha, Hunan, 410075 China

ABSTRACT: This paper is about the fatigue design issues on rubber-to-metal bonded springs used in railway industry. The investigation, based on the actual fatigue loads, is carried out on these failed and modified products using a method of continuum mechanics. To simplify the simulation, a non-linear quasi-static analysis is carried out and then the residual stresses are superimposed to obtain the effective stress range to predict the metal crack initiation. For the rubber parts of the spring a three-dimensional effective stress criterion is employed to predict the fatigue crack initiation. The fatigue crack initiation for the metal parts of the failed component is predicted at 225 K cycles under specified fatigue load against total metal broken at 700 K cycles from the test. For the rubber spring, subsequently modified and optimised, the total fatigue life for the metal parts of the component, is 8.0 million cycles against 1.75 million cycles from the test without any crack observed. The rubber fatigue crack initiation is predicted at 90 K cycles against crack onset around 79 K cycles and crack length 40 mm at 145 K cycles from the test. From the design point of view it is important to optimize the rubber profile under this very tight allowable space to provide the maximum support of the metal interleaves and at the same time to meet the minimum requirements of the manufacture process. 1 INTRODUCTION The Chevron Springs are operating worldwide in a diversity of service applications including LRV, Metro, Freight wagons, High Speed Passenger Coaches and Locomotives. This paper is about the fatigue design issues on rubber-to-metal bonded springs used in railway industry. The spring, as shown in Figure 1 during a fatigue test, consist of metal plates (cold-bent to a V shape) and bonded with four rubber layers through a moulding process. There are residual stresses left in the metal plate during the manufacture process. Recently a need to improve time and cost efficiencies to meet customer’s requirement(1.25 million cycles) has caused an unexpected early fatigue failure(0.7 million cycles) of the component with no immediate explanation(see figure 2), which leads to an integrated fatigue evaluation project involving a number of departments. Previous dynamic analyses has produced excellent fatigue predictions for a railway vehicle bogie frame under actual operating environment without residual stresses, see Luo etc. But in this situation there are very high residual stresses involved. It is well know that residual stresses can play a key role on the fatigue lives of engineering components.

Figure 1. The Chevron rubber springs on the test rig

Figure 2. A metal failure of the Chevron rubber spring (after 0.7 million cycles)

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1.1 Metal fatigue with residual stress There are several experimental methods available to determine residual stresses. They include magnetic field, boring, slicing, surface and deep hole drilling, X-ray diffraction and neutron diffraction method etc. Webster etc.used the neutron strain scanning technique to measure the internal residual stress distributions of rails and compared with conventional destructive strain gauge results and theoretical predictions. Theoretical work has also done by many researchers. Chien etc. employed both linear elastic mechanics and linear fracture mechanics approaches to investigate the fatigue influence of residual stresses induced by the fillet rolling process on a ductile cast iron crankshaft section under bending loads. Their results have shown that it can only determine the crack initiation life for small cracks initiated on the surface, but cannot indicate whether cracks can propagate through or arrest in the compressive residual stress zone. Larue and Daniewicz used the crack closure-based methodology to simulate fatigue crack growth from a hole with a preexisting compressive residual stress via twodimensional elastic–plastic finite element analyses. They pointed out that predictions from the closurebased method are highly dependent on the constitutive relationship between the crack growth rate and the effective stress intensify factor range used, highlighting the need for experimental methods to reliably measure this correlation. The influence on residual stresses by heat treatment is also conducted. Williams etc. investigated the fatigue behavior of a low-alloy powder metallurgy (P/M) sintered steel. Significant compressive surface stresses were generated during the machining of the fatigue specimens. A heat-treatment at 175 °C after machining had no effect on these residual stresses, but polishing the surface resulted in a 20% reduction in compressive stresses. Webster and Ezeilo have concluded that reliable predictions of fatigue performance is possible as long as the accurate profile of the stresses is available. For the accurate assessment of fatigue lifetimes a detailed knowledge of the residual stress profile is required. 1.2 Rubber fatigue In parallel with the metal fatigue it is also necessary to evaluate the rubber performance. Similar to the metal fatigue analysis there are two methods to deal with the rubber fatigue caused by mechanical failure: continuum mechanics (total life) and fracture mechanics (defect-tolerant). Roughly speaking the total

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fatigue life in continuum mechanics is defined as the sum of the number of cycles to initiate a fatigue crack to some predefined size. The defect-tolerant in fracture mechanics is based on that there are inherent flaws in all engineering products. The useful fatigue life is defined as the number of cycles to propagate the dominate crack from this initial size to some critical dimension. The principal differences may be dependent on how the crack initiation and the crack propagation stages of fatigue are quantitatively defined. For the fracture mechanics approach it has been found that the most appropriate formulation is in terms of the strain energy release rate and there is a limiting tearing energy below which no crack propagation occurs, see Lake and Thomas. Gent etc. analysed bonded rubber cylinders, linking the crack propagation to the tearing energy. They obtained a life prediction equation in the form of power law. Busfield etc. used energy release rate to predict fatigue crack growth in three modes of deformation and validated with the experiment results. It is shown that the maximum strain energy release rate can be used to predict the direction of crack growth. The fatigue crack growth for one of the applications (a gearbox mount) under investigation was predicted within a factor of 2 at different displacements for all three modes of deformation. Timbrell and Muhr etc. used the strain energy release rate to investigate the failure of the “O” ring and provided some guidance to use this approach. Mars and Fatemi have reviewed the development of analysis approaches for predicting fatigue life in rubber. They concluded that the crack initiation has received less attention and an adequate multiaxial nucleation life approach is needed to accurately predict fatigue life in rubber component. Luo and Wu etc. used a threedimensional effective stress criterion, taking all principal stress tensors into consideration, to predict fatigue crack initiation and validated against several engineering applications of anti-vibration rubber components. Charrier and Verron etc. suggested that the crack initiation method should be preferred at the early design stage for anti-vibration components. In a summary instead of conducting detailed fatigue crack growth analysis the best approach here is to target the fatigue crack initiation on both metal and rubber parts of the component. The investigation, based on the actual fatigue loads, was carried out on these failed and modified products using a method of continuum mechanics. It was assumed that the residual stresses were well kept in the metal part. To simplify the simulation, a non-linear quasistatic analysis was carried out and then the residual

stresses were superimposed to obtain the effective stress range to predict the metal crack initiation. For the rubber parts a three-dimensional effective stress criterion was employed to predict the fatigue crack initiation. The fatigue failure was taken as visual crack observation (normally 1-2 mm). 2 MATERIAL FATIGUE PROPERTIES 2.1

Metal fatigue resistance

The metal part is made from steel with yielding stress 355 MPa. The fatigue life of the metal part of the Chevron rubber spring can be estimated from the principal stress histories in the critical area in the structure using a duration curve from a design code. The current British Standard design code of practice for fatigue design and assessment of steel structures is BS7608. In BS7608, the material properties, the SN relationships, have been established from statistical analysis of available experimental data (using linear regression analysis of log S and log N) with minor empirical adjustments to ensure compatibility of results between the various classes. The equations for the S-N curve relationship may be written in a basic form as Nσ rm = k0 H d

(1)

Where N is the number of cycles to failure, σ r is the stress range, m, k 0 and H are constants, and d is the number of the standard deviations below the mean. The standard basic design S-N curves (mean minus two standard deviations) are shown in Figure 3.

Fatigue resistance can be represented by a curve which indicates a component failure at constant dynamic amplitude under a certain number of cycles. Normally a stress range against a cycle number forms a curve (S-N) to characterise the resistance of the material. Here the fatigue life estimation method was based on previously-obtained data for the rubber material used and on an effective stress (σf). σf was a function of the principal Cauchy stress ranges ( σ 1 , σ 2 and σ3 are the maximum, middle and minimum principal stresses respectively) taking multiaxial loading effect.

σ f = σ 12 + Aσ 22 + Bσ 32

σ 1 > 0, σ 1 ≥ σ 2 ≥ σ 3 , − 1 < A (or B ) ≤ 1 (2) Here A and B are weightings and the following assumptions are made. a. There is no fatigue damage when a point is under compression in all directions. b. A (or B) is taken as positive when σ2 (or σ3) is positive (ie tensile). c. The fatigue damage caused by any one of the other two principal directions will not exceed that caused by σ1. General speaking Equation (2) describes an ellipsoidal failure envelope, as shown in Figure 4. Under this definition any point on the ellipsoidal surface gives the same fatigue damage caused by a repeated cyclic loading. σ3

σf

σ2 σ1

Figure 4. Illustration of the effective stress criterion Figure 3. The S-N curve of the metal

2.2 Rubber fatigue resistance The material properties used are associated with a moderately filled (nominal 59IRHD) synthetic polyisoprene with good low creep performance.

There are now some procedures under consideration to give A and B. In one of the procedures, A (or B) is given the maximum value (1) for safety, provided that σ2 (or σ3)> 0 and the value 0 if σ2 (or σ3 )≤0. That is

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A (or B ) = 1, when σ 2 (or σ 3 ) > 0

(3)

A (or B ) = 0, when σ 2 (or σ 3 ) ≤ 0 The worst case is

(4)

σ f = σ 12 + σ 22 + σ 32

σ1 ≥ σ 2 ≥ σ 3 > 0

(5) This criterion has all characteristics of a stress tensor and can be easily integrated with finite element codes (for example, Abaqus) and used in engineering applications. Under uniaxial loading condition ( σ 2 = σ 3 = 0 ), the criterion is degenerated as σ f = σ 1 , which is the maximum tensile stress criterion. More details and definitions can be seen in Luo etc. The rubber crack initiation is a result of the cumulative damage when visual cracks appeared(normally 1-2 mm). The fatigue resistance curve of the rubber material is shown in Figure 5.

failed component. A typical fatigue load was applied to both models. The results are shown in Figure 6 and Figure 7 respectively. It is clear that the stress value was dropped by 5.5% (from 600 MPa to 576 MPa) when adding extra rubber. It is possible that the excessive bending moment caused the earlier fatigue failure. The principle for the service life extension lies on the reduction of the stress range. Therefore having more rubber support on the metal interleaf can reduce the dynamic bending stresses. Further two three- dimensional-model (half of the part) have been used to evaluate the failed part and modified part respectively. The two models have used similar finite element mesh to form a comparable base and have approximately 160,000 degrees of freedom each. The modified component has more rubbers between each layer than does the failed component. At the same time it is also necessary to meet the minimum clearance requirement for the manufacture process to improve time and cost efficiencies.

Figure 5. S-N curve of the rubber material

3 FINITE ELEMENT MODELS AND FATIGUE LOAD Finite element analysis has been used to predict the stress distributions and evaluate the fatigue behaviour. During fatigue tests a pair of the components has been arranged as a whole unit. The two parts have been fixed on a frame with 22 degrees apart, formed as a Vee shape. The nominal loading range is 60 kN. 3.1

Two-dimensional finite element models

In order to quickly evaluate the effects on stress values due to bending moment. A pair of two-finite element models of a cross section of the rubber springs, one was for failed component and the other was for a modified component, were generated. The difference between the two models is that the lengths of the rubber layers of the modified component are several millimetres longer than those of the

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Figure 6 Stress profile of the failed component

Figure 7 Stress profile of the modified component

4 METAL FATIGUE VERIFICATION The simulation of fatigue loading was carried out on both failed and modified Chevron rubber springs. The stress profiles of the failed part is shown in Figure 8. The stress ranges are valued at 613 MPa at first interleaf of the failed component and 460Mpa, also at the first interleaf, for the modified component respectively. The critical areas are at the apex of the first interleaf from the back plate. The interleaf broken from the fatigue test for the failed part has validated the location predicted, see Figure 2. There is also a second highest stress area at the middle interleaf of the failed component but there is no failure observed.

metal interleaf fracture, see Figure 2). This is a reasonable estimation. It indicates a good agreement between the simulation and the test from the failed part. From the design point of view it is clearly explained that the unexpected early failure was due to the less rubber support for the metal interleaves. For the modified component, when the same principle was applied, a fatigue crack initiation of 8 million cycles was obtained. The prediction would meet the 1.25 million cycle requirement. Based on the above prediction, it was decided to start the prototype manufacture and test procedure. Finally the modified component successfully completed 1.25 million cycles without metal broken, more requirement kept this test moving towards 1.75 million cycles. After the test finished all the metal parts have been carefully examined and no fatigue cracks found. 5 RUBBER FATIGUE VERIFICATION

Figure 8 Stress profile of the failed part ( the maximum value is 612.5 MPa)

The location of the early failure has been identified and validated. The next one is to validate the duration of the fatigue life based on the following approach. As said before, the fatigue duration curves from BS7608 were used for the fatigue evaluation. The curves can be applied to both weld and non-welded structures. When it is used to estimate a service life, the result is the cumulative damage and hence the time taken for crack initiation to occur. The life derived from this standard is dependent not only upon stress ranges and the number of cycles encountered, but also upon the acceptable probability of failure. Here the class B with a 2.3 per cent probability of failure is used to validate the fatigue analysis. The steel has minimum yield stress 355 MPa. After the metal was bent to the required shape, a 355 MPa compression residual stress was generated on the inner surface. Therefore the stress range can be reduced to 258 MPa (from 613 MPa) for the failed part and 105 MPa (from 460 MPa) and the modified part respectively. Based on the duration curve (Figure 3) the fatigue life for the failed part is about 225 K cycles against test result about 700 K cycles (total

In parallel with the metal fatigue prediction the rubber fatigue evaluation for the modified component was also carried out based on the threedimensional effective stress method. Figure 9 shows the effective stress profile of the modified component. The critical area is at the second layer of the rubber from the back and located about 10 mm below the rubber top free surface. The value of the effective stress σf is 3.55 MPa. From the rubber design curve in Figure 5 the corresponded cycle number for 3.55 MPa is about 90K.

Figure 9 Effective stress profile (the red colour showing the critical area)

Figure 10 shows the top part of the rubber spring after 79K fatigue loading cycles. The blisters at the apex of the second layer of the rubber part can be clearly seen on the enlarged photo. There are no other sites showing the blisters. The fatigue crack appeared on the same area after the fatigue test passed 145 K cycles. The length of the crack is about 40 mm long.

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Figure 10 Rubber blisters in the Chvron rubber spring after 79K cycles, the position of the blister is the same location as FEA indicated

6 DISCUSSIONS For the fatigue design of the anti-vibration component it is important to optimize the rubber profile under this very tight allowable space to provide the maximum support of the metal interleaves and at the same time to meet the need for time and cost saving requirements of the manufacture process. It is indicated that when a component is subjected to a bending dominated fatigue loading it may have significant influence on the service life even by a small change of the supporting areas. The modified component has now manufactured and successfully entered the service. It is demonstrated that this approach can be employed at a suitable design stage for both metal and rubber fatigue evaluation on anti-vibration springs.

7 ACKNOWLEDGEMENTS The authors thank Trelleborg IAVS allowing to publish this paper. Also the authors are very grateful to Mr. Foster and Mr. Crewe in Product Test Laboratory, Mr. Livingston in Engineering Support Department, Mr. Booth from Tooling Department, Mr. Edgar from Material Test Laboratory and Mr. Kenney from Quality Department for their support. X.P. Wu, one of the authors, would like to thank the support from National Natural Science Foundation of China(50578160/50878214);the Key Grant Science and Technology Research Planning Projects of The Ministry of Railway of Peoples Republic of China (2008G032-12;2008G017-C). REFERENCES Luo, R.K. , Gabbitas B. L. & Brickle B. V. , 1994, Fatigue life evaluation of a railway vehicle bogie using an integrated dy

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