Forged steel (static & fatigue analysis) of single cylinder crankshaft of 2 stroke petrol engine using fracture strength approach by LEFM &

CDA

Dr. Pravin S. Nerkar, Mr. Pradeep J. GotheMechanical Engineering Department,

S.V.P.C.E.T. Nagpur, Maharashtra, India 441108psnerkar@yahoo.co.in, gothe.pradeep@gmail.com

_________________________________________________________________

ABSTRACT: Single cylinder petrol engine crankshaft is one of the crankshafts is an important part of an IC engine that converts the linear motion of the piston into rotary motion through the connecting rod. The crankshaft bending stiffness and axial stiffness should have ample strength to endure the bending and twisting moments to which it is subjected. This study describes the stress distribution of the forged steel crankshaft used in single cylinder 2-stroke vertical engines by using commercial Finite Elements Analysis software Hypermesh, Optistruct & Hyperview, FEMFAT. The failure analysis effects are substantial to improve the part design optimization at the early developing stage. Modal analysis was converting into static analysis means dynamic loading is converting into static analysis and Fatigue Analysis using Channel Max module in FEMFAT software and done resultant loading at the 720-degree rotation.

Keywords: Crankshaft, LEFM (Linear Elastic Fracture Mechanics), CDA, Fatigue, Finite Element Analysis.__________________________________________________________________

I. INTRODUCTION

The crankshaft is the main part with an intricate geometry in the single cylinder 2-Stroke I.C. engine, which convert the reciprocating displacement of the piston to a rotary motion with a four-bar link mechanism. The Crankshaft consisting of shaft part, two journal bearings, and one crankpin bearing. The Shaft parts which revolve in the main bearings, the crank pins to which the crank arms or webs end which is connected to the other end of the crank pins and the shaft parts. Al- Jazari was the first engineer to invent the Crankshaft which is considered the single most important invention after the wheel. A crankshaft is one of the most critically loaded components and it is subjected to cyclic loading due to the bending and twisting load for determines its fatigue life. The crankshaft is one of the most important moving parts in the internal combustion engine. It must be strong enough to take the downloaded force of the power stroked without excessive bending. In the Automotive industry, crankshaft analysis on the single cylinder is done irrespective of the size of the crankshaft. Hence this study can be used for any number of cylinder crankshafts. Different mesh quality models and its convergence are compared to finalize on the FE model to be used for the analysis. Identification of appropriate boundary conditions and loadings are also discussed and subsequent results of Finite Element Analysis (FEA) have been presented. The Prediction of crack growth, the time required for failure and other parameters essential in life assessment have been compared by both the methods. The stress values required for both the methods are estimated using FEA.

II. LITERATURE REVIEW

The crankshaft is an important engine component which is subjected to fluctuating or cyclic loads often resulting in fatigue failures [1]. There are several methods available to predict the life of the crankshaft and some of them are developed by researchers. The most commonly used methods to predict fatigue life includes stress-life (S-N), strain Life (E-N) and LEFM. S-N method is based on nominal stress life by using rain flow cycle counting. This method can be helpful to test fatigue life but the only disadvantage is that plasticity effect does not consider and provides poor accuracy for low cycle fatigue but, because of easy implementation and various data available, stress life method is most commonly used where S-N curve for that particular material is available. The strain-life approach

offers additional comprehensive analysis concerning plastic deformation at a localized region and is useful for low cycle fatigue. Nowadays LEFM is daily used by structural engineers engaged in performing the fatigue as well as a static assessment of real mechanical components [2].LEFM assume that crack is already present and detected onto which it predicts crack growth by considering stress intensity factor. LEFM theory is increasingly being applied to the practical engineering problems, including material selection, design, and analysis of engineering components [3]. A significant improvement in techniques for estimation of the remaining lifetime of pre-cracked components has also been made in the last decades; the Theory of critical Distance is one of such methods [4]. The material parameter with units of length, called critical distance, is taken to represent the fracture process under consideration. Taylor et. al. [5] has extensively used this method and applied to Ceramics, polymers, metals, and composites. The literature review explores the application of CDA on various engineering components, but a study on the crankshaft is still awaited. Some specific software pertaining to Fatigue crack propagation also has been developed such as FEMFAT. FEMFAT is one of the very good software available in the field of fatigue analysis and even very widely been used as well. Because of the complicated shape, size, topology, and topography of crankshafts with several fillets and radius the use of FEMFAT is showing the limitations on its application on crankshaft fatigue prediction. Hence, even not many references are also been cited on this subject. Another method known, as Power Engineering Tool (PET) is a Graphics User Interface (GUI) based computer model that calculates engine performance and the components fatigue performance at an early stage of design [6]. In this method, a crankshaft system model (CRANKSYM) is used to verify the high vibration level in bearing cap. CRANKSYM is also able to perform coupledAnalysis along with structural dynamics. It also calculates dynamic stresses on the crankshaft throughout the whole engine cycle for which a finite element model of complete assembly is required.

III. FINITE ELEMENT METHOD (FEM) IN FATIGUE

The FEM is a commonly used numerical method forStructural analysis, as this method is able to predict the behaviors, which are otherwise difficult to find out by theoretical calculation, a large number of degree of freedom involved in it. FEM can be used as an excellent tool to analyze and find out fatigue life estimation of the crankshaft by computer simulation and therefore it can help to reduce time and cost required for prototyping and to avoid numerous test series when laboratory tastings are not available. Since loading on the crankshaft is complex in nature, sophisticated analysis of crankshaft is required. Hence several commercial FEA tool is commonly used for the structural analysis, nowadays by automobile companies to check the durability of their products. Renault Company Henry et al. [7] developed a new crankshaft durability assessment tool based on the 3-D mesh, with an objective to improve fatigue analysis process. Nonlinear transient stress analysis for six-cylinder inline engine crankshaft was presented by Payer et al. [8] which shows that this method is highly sophisticated and efficient for determining the fatigue behaviors of the crankshaft. Prakash, et al. [9] used FEM and developed a program known as OPTISTRUCT which quickly gives natural frequency, displacement, and stresses. For finding out von misses and mean stress. Montazersadgh and Fatemi, [10] conducted dynamic simulation on a single cylinder four stroke engine and FEA was performed to get stress magnitude at a critical location. The pressure-volume diagram was used to calculate the load boundary conditions in a dynamic simulation model. The dynamic analysis was done analytically and verified in NASTRAN software. FEM model was created in HYPERMESH and boundary condition was applied according to engine mounting conditions. In fact, nowadays, finite element method is the most popular approach commonly used for tackling fracture mechanics problems and also acts as a tool for finding out the behavior of components, which made the task easy for design engineers, where the costly experimental setup was otherwise required. The method can be applied to linear as well as non-linear problems. Accordingly, many numerical simulation codes have emerged as commercial packages for use in durability applications. Some tools such as Ansys, Abaqus, Nastran and Marc have the facility to calculate the important term of fracture mechanics parameters such as the J-integral. Fatigue life estimation by using FEA yields very good results but none have an in-built crack generation and crack propagation capability. Moreover, the recently developed specific fatigue life estimation software such as FEMFAT, FESAFE, MSC Fatigue, Ansys-Fatigue, and nCODE are based on stress or strain life prediction methodology to predict the fatigue life of the engineering components only. However, there is a constraint in using this software that, it should be used along with other finite element software such as Optistruct, Ansys, Abaqus, Nastran, Marc, and Radioss for predicting the critical stress responsible for the failure. Fatigue life prediction achieved a high-level accuracy because FEA is involved and due to an increase in computational power and good mesh density. FEMFAT Software for fatigue analysis has yielded good results which are otherwise difficult to find out. One of such tools is FEMFAT in which stresses from the finite analysis are used to predict durability performance. It appears from the review of literature that, in spite of a great number of works in the field of crankshaft life estimation, studies on some specific aspects require further attention and LEFM and CDA methods have been selected for this study.

IV. COMPARATIVE EVALUATION OF ASSESSMENT TECHNIQUE

The objective of this work is to make a comparative evaluation of fatigue assessment techniques on forged steel crankshaft of a single cylinder diesel engine by using fracture mechanics approach viz. CDA and LEFM. The prediction of crack growth, the time required for failure and other parameters essential in life assessment have been compared by both the methods. The basics used in LEFM to predict the fatigue life of components is based on the fact that a crack already pre-exists in the component and that the life is directly dependent on the stress intensity factor, which in turn depends on initial crack length assumed or present. LEFM approach assumes initial crack and can determine crack propagation time, which further could be used to find a life of that component. The data required for this method such as the slope of the crack growth curve and material constant has been adopted from standard journals and handbooks. Maximum stress required for the study has been estimated from FEM analysis. Crack lengths of various sizes have been assumed right from 0.5mm to 8.0 mm with an interval of 0.5mm and the number of cycles of failure has been estimated. Graphs between several variables have been plotted to get the first hands-on results obtained in the analytical calculation. Similarly, the crankshaft has been evaluated using CDA method in which stress against distance plot from maximum stress area, characteristics length or critical length L has been found out for all the crack lengths from 0.5 mm to 8.0 mm with an interval of 0.5 mm, and failure is predicted. In this study, Optistruct has been used for stress analysis to evaluate the critical stresses in the crack zone and then LEFM and CDA method have been used to fatigue life prediction and comparison. Also to evident the comparison, an analytical approach has been developed to predict and compare the fatigue life.

4.1 THEORETICAL FORMULATION

A forged steel crankshaft of weight 4.9 kg, designed for 476 ccs, the single-cylinder diesel engine of power rating approximately 8.97 kW, has been used in the present fatiguelife estimation study. It is evident that the critical locations of the crankshaft failure are nothing but the critical fillet areas of joining pin with web and web with the main shaft, which is very much sensitive to the subjected repetitive fatigue loads. Fig. 1 shows the theoretical model of the crankshaft with the critical locations considered for the evaluation of fatigue life. Along with, Table 1 - 3 shows the crankshaft specification, material composition, and mechanical properties. The LEFM and CDA methods have been used to fatigue

Figure1: Crankshaft Model with Critical Locations.

Table 1. Specifications of the Engine and Crankpin

Table 2. Chemical Composition by Percent Weight.

Table 3. Summary of Material Properties of Forged Steel

Life prediction and comparison and the stresses are evaluated using FEM analysis. An analytical approach has also been developed to predict and compare the fatigue life.

4.2 Linear Elastic Fracture Mechanics

LEFM concept can be used for analyzing the behavior of cracked components under static or fatigue loadings conditions. This is an analytical method based on the stress intensity factor, which characterizes the stress distribution in the vicinity of the crack tip, and is used in design applications provided that gross yielding does not occur. Linear elastic fracture mechanics can be used to describeUltimate static failure of low toughness high strengthmaterials commonly used in aerospace, automobile, and other specialized applications. Under fatigue loading, for a wide range of materials, the crack growth rate can be correlated by the stress intensity factor. The basics used in LEFM is to predict the fatigue life of components based on the fact that a crack already pre-exists in the component and that the life is directly dependent on the stress intensity factor, which in turn depends on initial crack length assumed or present. Fracture mechanics on which LEFM is based requires that an initial crack size be known or assumed. For components with defects such as inclusions, casting defects and weldingporosities, etc. an initial crack size may be known or found out. In defect-free material, LEFM approach assumes initial crack and can determine crack propagation time, which further could be used to find a life of that component. With constant amplitude fatigue loading the crack propagation rate of a given crack depends primarily on the range of stresses in the fatigue cycle (σmax - σmin) and the crack length. In simple cases, the function of fatigue load and the crank length is defined as stress intensity factor and is expressed.

(1)

And, the stress intensity factor expressed by means of the stress intensity factor range, ΔK, defined by

(2)

The linear relation between crack growth and threshold stress intensity can be represented by Paris law.

(3)

The fatigue life of the component can be found out by integrating Eqn. 3, which in turn evaluates the number of cycles of failure that component withstands before failure. The number of cycles of failure (Nf) can be obtained as below.

(4)

After substituting the value of

(5)

(6)

Where, C and _ are material constant, _ varies from 1 to 2, m varies from 2 to 4, a0 is the initial crack size in mm, it is the critical crack length or final crack length in mm, Δσ is the maximum stress. The value of C (Intercepts) and m (Slope) is taken from [30].

(7)

4.3 Critical Distance Approach

The Theory of Critical Distances (TCD) is the name which describes a group of methods employed for the prediction of failure in cases where stress concentrations are present and where the failure mode involves cracking, such as fatigue and brittle fracture. The TCD is used for failure prediction of short cracks as well as for stress concentrations of arbitrary geometry, by using the results of FEA or any other computer-based methods. The theory of critical distances has two methods such as Point Method (PM) and Line Method (LM). This method uses parameter taken in front of the notch or stress concentration area. Accurate prediction of failure is possible when correct stress information is provided. In this paper, PM is used as this method is simple to use and can effectively predict failure in the component. The PM predicts that failure will occur if the stress at a distance L/2 from the notch root is equal to the plain strength of the material. The same principle will be applied for fatigue, replacing the stress with a stress range and the plain strength with the plain fatigue strength The critical distance represents the length ahead of notch and stress along this distance reduces as it moves away from the notch. The stress distance plot is plotted in which stress along with focus path defined by the user is plotted against the distance of that path. This curve life prediction and comparison and the stresses are evaluated using FEM analysis. An analytical approach has also been developed to predict and compare the fatigue life.

Figure 2. Illustration of TCD (Point Method) using Elastic Stress as Function of Distance, the Fatigue Strength of Specimen Δσ0 Occurs at Critical Distance L/2.

Symposium on International Automotive Technology 2013 is used to predict the failure of engineering components. From the stress distance plot, the important material parameter σo can be found out at L/2 distance from the notch, known as critical stress.In PM stress at a single point is considered and criticalstress value is found out at a distance L/2 from the notch or stress concentration region by using stress distance plot. If the critical distance and accurate estimation of stresses are known, PM is best to determine the failure. Following relations are used to determine critical distance.

(8)

The above equation (8) allows the critical distance to be expressed as a function of the fracture toughness Kth and also linked with critical distances (L/2). The PM calculates a stress value and equates it to a characteristic strength for the material to consider the propagation of a crack of finite size, and thus uses the material parameters K th. PM will be most convenient if the results of the FEA are available for the component. In particular, failure can be predicted by modifying the critical stress so that the stress to be used is not the maximum stress (at the notch root) but the stress at a point located at a certain distance from the notch.

4.4 Finite Element Analysis4.4.1 Boundary and Loading Condition

The crankshaft is a constraint with a ball bearing side (pump side) from one end and with a journal bearing (flywheel side) on the other end. The ball bearing is press fit to the crankshaft and does not allow the crankshaft to have any motion other than rotation about its main central axis. Since only 180° of the bearing surfaces facing the load direction constraint the motion of the crankshaft, this constraint was defined as a fixed semi-circular surface as wide as the ball bearing width on the crankshaft. The other side of the crankshaft is on a journal bearing. Therefore, this side was modeled as a semi-circular edge facing the load at the bottom of the fillet radius fixed in a plane perpendicular to the central axis and free to move along the central axis direction. Fig. 3 show these defined boundary conditions in the FE model of the crankshaft. Definition of a fixed edge is based on the degrees of freedom in a journal bearing, which allows the crankshaft to have displacement along its central axis. The distribution of load over the connecting rod bearing is uniform pressure on 120° of the contact area. The dynamic load is predicted from the engines pressure and crank-angle diagram as shown in Fig. 3. The dynamic load from the pressure and crank-angle diagram has been estimated to be around 24.57 KN has been used to evaluate the pressure boundary for the stress analysis on the forged steel crankshaft.

Figure 3. A Problem definition and Boundary conditions of Crankshaft

Figure 3. B Problem definition and Boundary conditions of Crankshaft

Figure 4. Pressure Crank-Angle Diagram.

4.4.2 FEM Analysis

A grid independence test was performed on the FEM model with the global size of 4 mm and 5 mm and the three-layer mesh to capture the critical fillet regions of interest. It has been found that there were variations in the stress calculations of around 2%, which is very much under acceptable limits of numerical calculations. Hence a decision was taken to use the global size of 5 mm mesh in the present study.

V. RESULTS AND DISCUSSION

The dynamically loaded stress analysis result from FEM predicts the maximum stress appears at location 4b at all loading situations, which can be seen through Fig. 6. Hence, for further study on the crack stress analysis, it has been deciding to create the crack at the 4b location, ranging from 0.5 mm crack to 8 mm crack for LEFM and CDA method calculations. The crack models of various crack length and depth at location 4b are shown in Fig. 5. It also shows the mesh generation in and around of the crack to capture the true stress values for LEFM and CDA analysis for life prediction.

Figure 5. Mesh Design of Crankshaft Model with 8.0 mm Crack Length.

Figure 6. Von-misses Stress at Bottom Crankpin Fillet Area.

Figure. 7 show the stress concentration plots for various crack length from 0.5 mm to 8 mm.

Figure 7. Stresses around the Cracks for 0.5 mm to 8 mm.

5.1 Life Prediction of Crankshaft Using

5.1.1 Linear Elastic Fracture Mechanics

In the present study to evaluate the linear elastic fracture mechanics theory for an automotive crankshaft specimen, the stress intensity factors have been calculated for every crack length in the specimen using principal stress range as shown in Eqn 2. The results obtained through the LEFM method are presented in Table 4. The fatigue life of crank shaft specimen using LEFM and a graph plotted between stress intensity factor KI and crack length has been shown in Fig. 8.

Table 4. Fatigue Life of Crankshaft Specimen Using LEFM.

It is observed from the FEA analysis of the automotive crankshaft specimen that, with an increase in crack length there is an increase in critical stress concentration in and around the crack. The increase in stress concentration contributes to increasing the stress intensity factor KI, which in turn depicts the reduction in life cycles of the crankshaft specimen. The comparison of calculated stress intensity factor KI with the experimental critical stress intensity factor KC value at every crank length shows that the crankshaft fails at the transition a crack growth from

1.0 mm to 1.5 mm. The increase in stress intensity factor with respect to increasing crack length is also been depicted through Fig. 8.

Figure 8. Stress Intensity Factor for Various Cracks Length for the Crankshaft.

The estimated number of reversal to the failure of the automotive crankshaft specimen with respect to crack lengths is presented in Fig. 9. It can be observed that the life of the specimen without crack is found out to be around in the range of 7x104 number of reversal to failure, but with just initiation of crack in the specimen the life is reduced to the range of 6x104 number of reversal to failure, and further increase in the crack length in the specimen it further decreases to around 1000 number of reversal to failure. Similarly, the stress curve derived for the same specimen using finite element based stress values and the number of reversal to failure is shown in Fig. 10, which also shows a similar trend as shown in Fig. 9. Concentration feature is estimated by examining the stresses along the path drawn normal to the underlying surface at the point of maximum stress concentration. The relevant stress parameter used is the maximum principal stress. If the stress at a distance L/2 along this path is greater than the critical stress i.e. plain strength (yield stress) of the material, the CDA predicts that a crack will propagate from that defect and the body will fail.In the present study of life prediction of automotive Crankshaft specimen, the applied stresses, and yield stresses are presented in Table 5 and the result shows that the plate fails at the transition crack growth from 5.0 mm to 6.0 mm.

Figure 9. Number of Reversal to Failure with CrackLength

Figure 10. Stress Amplitude with Number of Reversal to failure.

5.1.2 Critical Distance Approach (CDA)

In critical distance PM the material is assumed to possess a characteristic material length parameter, L. The value of L can be found out by using Eqn. 5, utilizing two material properties such as, applied stress Amplitude and the crack propagation threshold ΔKth, whereas, the applied stress amplitude is defined as the range of stress (i.e. the difference between the maximum and minimum stress in the cycle) at which failure occurs in a specified number of cycles. Once the critical parameters (L/2 and applied stress amplitude) are known, fatigue failure of the specimen containing stress

Table 5. Fatigue Life of Crankshaft Specimen using CDA.

Fig. 11 shows a graph obtained by plotting the stress as a function of distance from the notch root, taken along a line drawn normal to maximum stress point. The plot is known as stress–distance curve. The line is called a focused path; to consider the effect of the stress field in the vicinity of the crack. The value of principal stress is taken from the crack tip

Figure 11. Stress - Normal Distance Plot for Various Crack Length.

running across the specimen, normal to the loading axis. It can be observed from the figure that with an increase in distance from the crack there is a decrease in stress value and achieves asymptotic lower equilibrium value.

6. CONCLUSIONS

The dynamic loaded stress analysis of the crankshaft has been performed to predict and compare the fatigue life of the crankshaft by LEFM and CDA method and evidenced by the analytical method. The analysis depicts the following pertinent features.

1. Critical locations on the crankshaft geometry areall located on the fillet areas because of high-stressgradients in these locations which result in high-stress concentration factors.2. Analytical and FEA results do not show closethe agreement, because FEA results indicate non-symmetric bending stresses on the crankpin bearing, whereas using an analytical method predicts bending stresses to be symmetric at this location. Also, there is no provision of incorporating explicitly the crack effects into the analytical calculations. The lack of symmetry is a geometry deformation effect, indicating the need for FEA modeling due to the relatively complex geometry of the crankshaft. Also the lack of crack modelling for the purpose of capturing the crack and its growth, indicating the need for FEA modelling.3. It has been observed that the predictions from LEFM and CDA represent the similar nature of fatigue prediction and are comparable in predicting the life of the crankshaft at the transition from one crack length to another. Also, the present study provides an insight of LEFM and CDA methods along with its benefits to the design engineers to correctly assess the life of crankshaft at an early stage of design. This study also gives a detailed overview of the failure analysis process including analytical methods and result integration for predicting the life of components as compared to life estimation by means of analysis tools.

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