Dynamic Load and Stress Analysis of a Crankshaft

Transcription

1 Dynamic Load and Stress Analysis of a Crankshaft Farzin H. Montazersadgh and Ali Fatemi The University of Toledo Copyright 27 SAE International ABSTRACT In this study a dynamic simulation was conducted on a crankshaft from a single cylinder four stroke engine. Finite element analysis was performed to obtain the variation of stress magnitude at critical locations. The pressure-volume diagram was used to calculate the load boundary condition in dynamic simulation model, and other simulation inputs were taken from the engine specification chart. The dynamic analysis was done analytically and was verified by simulation in ADAMS which resulted in the load spectrum applied to crank pin bearing. This load was applied to the FE model in ABAQUS, and boundary conditions were applied according to the engine mounting conditions. The analysis was done for different engine speeds and as a result critical engine speed and critical region on the crankshaft were obtained. Stress variation over the engine cycle and the effect of torsional load in the analysis were investigated. Results from FE analysis were verified by strain gages attached to several locations on the crankshaft. Results achieved from aforementioned analysis can be used in fatigue life calculation and optimization of this component. INTRODUCTION Crankshaft is a large component with a complex geometry in the engine, which converts the reciprocating displacement of the piston to a rotary motion with a four link mechanism. This study was conducted on a single cylinder four stroke cycle engine. Rotation output of an engine is a practical and applicable input to other devices since the linear displacement of an engine is not a smooth output as the displacement is caused by the combustion of gas in the combustion chamber. A crankshaft changes these sudden displacements to a smooth rotary output which is the input to many devices such as generators, pumps, compressors. A detailed procedure of obtaining stresses in the fillet area of a crankshaft was introduced by Henry et al. [1], in which FEM and BEM (Boundary Element Method) were used. Obtained stresses were verified by experimental results on a 1.9 liter turbocharged diesel engine with Ricardo type combustion chamber configuration. The crankshaft durability assessment tool used in this study was developed by RENAULT. The software used took into account torsional vibrations and internal centrifugal loads. Fatigue life predictions were made using the multiaxial Dang Van criterion. The procedure developed is such it that could be used for conceptual design and geometry optimization of crankshaft. Guagliano et al. [2] conducted a study on a marine diesel engine crankshaft, in which two different FE models were investigated. Due to memory limitations in meshing a three dimensional model was difficult and costly. Therefore, they used a bi-dimensional model to obtain the stress concentration factor which resulted in an accuracy of less than 6.9 percent error for a centered load and 8.6 percent error for an eccentric load. This numerical model was satisfactory since it was very fast and had good agreement with experimental results. Payer et al. [3] developed a two-step technique to perform nonlinear transient analysis of crankshafts combining a beam-mass model and a solid element model. Using FEA, two major steps were used to calculate the transient stress behavior of the crankshaft; the first step calculated time dependent deformations by a step-by-step integration using the newmark-betamethod. Using a rotating beam-mass-model of the crankshaft, a time dependent nonlinear oil film model and a model of the main bearing wall structure, the mass, damping and stiffness matrices were built at each time step and the equation system was solved by an iterative method. In the second step those transient deformations were enforced to a solid-element-model of the crankshaft to determine its time dependent stress behavior. The major advantage of using the two steps was reduction of CPU time for calculations. This is because the number of degrees of freedom for performing step one was low and therefore enabled an efficient solution. Furthermore, the stiffness matrix of the 1

2 solid element model for step two needed only to be built up once. In order to estimate fatigue life of crankshafts, Prakash et al. [4] performed stress and fatigue analysis on three example parts belonging to three different classes of engines. The classical method of crankshaft stress analysis (by representing crankshaft as a series of rigid disks separated by stiff weightless shafts) and an FEMbased approach using ANSYS code were employed to obtain natural frequencies, critical modes and speeds, and stress amplitudes in the critical modes. A fatigue analysis was also performed and the effect of variation of fatigue properties of the material on failure of the parts was investigated. This was achieved by increasing each strain-life parameter (σ f, ε f, b and c) by 1% and estimating life. It was shown that strength and ductility exponents have a large impact on life, e.g. a 1% increase of b leads to 93% decrease in estimated life. A geometrically restricted model of a light automotive crankshaft was studied by Borges et al. []. The geometry of the crankshaft was geometrically restricted due to limitations in the computer resources available to the authors. The FEM analysis was performed in ANSYS software and a three dimensional model made of Photoelastic material with the same boundary conditions was used to verify the results. This study was based on static load analysis and investigated loading at a specific crank angle. The FE model results showed uniform stress distribution over the crank, and the only region with high stress concentration was the fillet between the crank-pin bearing and the crank web. Shenoy and Fatemi [6] conducted dynamic analysis of loads and stresses in the connecting rod component, which is in contact with the crankshaft. Dynamic analysis of the connecting rod is similar to dynamics of the crankshaft, since these components form a slide-crank mechanism and the connecting rod motion applies dynamic load on the crank-pin bearing. Their analysis was compared with commonly used static FEA and considerable differences were obtained between the two sets of analysis. Shenoy and Fatemi [7] optimized the connecting rod considering dynamic service load on the component. It was shown that dynamic analysis is the proper basis for fatigue performance calculation and optimization of dynamically loaded components. Since a crankshaft experiences similar loading conditions as a connecting rod, optimization potentials of a crankshaft could also be obtained by performing an analytical dynamic analysis of the component. A literature survey by Zoroufi and Fatemi [8] focused on durability performance evaluation and comparisons of forged steel and cast iron crankshafts. In this study operating conditions of crankshaft and various failure sources were reviewed, and effect of parameters such as residual stress and manufacturing procedure on the fatigue performance of crankshaft were discussed. In addition, durability performance of common crankshaft materials and manufacturing process technologies were compared and durability assessment procedure, bench testing, and experimental techniques used for crankshafts were discussed. Their review also included cost analysis and potential geometry optimizations of crankshaft. In this paper, first dynamic load analysis of the crankshaft investigated in this study is presented. This includes a discussion of the loading sources, as well as importance of torsion load produced relative to bending load. FE modeling of the crankshaft is presented next, including a discussion of static versus dynamic load analysis, as well as the boundary conditions used. Results from the FE model are then presented which includes identification of the critically stressed location, variation of stresses over an entire cycle, and a discussion of the effects of engine speed as well as torsional load on stresses. A comparison of FEA stresses with those obtained from strain gages of a crankshaft in a bench test is also presented. Finally, conclusions are drawn based on the analysis preformed and results presented. LOAD ANALYSIS The crankshaft investigated in this study is shown in Figure 1 and belongs to an engine with the configuration shown in Table 1 and piston pressure versus crankshaft angle shown in Figure 2. Although the pressure plot changes for different engine speeds, the maximum pressure which is much of our concern does not change and the same graph could be used for different speeds [9]. The geometries of the crankshaft and connecting rod from the same engine were measured with the accuracy of.2 mm (.1 in) and were drawn in the I-DEAS software, which provided the solid properties of the connecting rod such as moment of inertia and center of gravity (CG). These data were used in ADAMS software to simulate the slider-crank mechanism. The dynamic analysis resulted in angular velocity and angular acceleration of the connecting rod and forces between the crankshaft and the connecting rod. Fz Figure 1: Crankshaft geometry and bending (F x ), torsional (F y ), and longitudinal (F z ) force directions Fx Fy 2

3 Table 1: Configuration of the engine to which the crankshaft belongs Crankshaft radius Piston Diameter Mass of the connecting rod Mass of the piston assembly Connecting rod length I zz of connecting rod about the center of gravity Distance of C.G. of connecting rod from crank end center Maximum gas pressure 37 mm 89 mm.283 kg.417 kg mm kg-m mm 3 Bar Angular Velocity (rad/s) 1 8 Velocity Acceleration Crankshaft Angle (Deg) Figure 3: Variation of angular velocity and angular acceleration of the connecting rod over one complete engine cycle at a crankshaft speed of 28 rpm Angular Acceleration (rad/s^2) Cylinder Pressure (bar) Crankshaft Angle (Deg) Figure 2: Piston pressure versus crankshaft angle diagram used to calculate forces at the connecting rod ends There are two different load sources acting on the crankshaft. Inertia of rotating components (e.g. connecting rod) applies forces to the crankshaft and this force increases with the increase of engine speed. This force is directly related to the rotating speed and acceleration of rotating components. Variation of angular acceleration and angular velocity of the connecting rod for the engine speed of 36 rpm is shown in Figure 3. The second load source is the force applied to the crankshaft due to gas combustion in the cylinder. The slider-crank mechanism transports the pressure applied to the upper part of the slider to the joint between crankshaft and connecting rod. This transmitted load depends on the dimensions of the mechanism. Forces applied to the crankshaft cause bending and torsion. Figure 1 demonstrates the positive directions and local axis on the contact surface with the connecting rod. Figure 4 shows the variations of bending and torsion loads and the magnitude of the total force applied to the crankshaft as a function of crankshaft angle for the engine speed of 36 rpm. The maximum load which happens at 3 degrees is where combustion takes place, at this moment the acting force on the crankshaft is just bending load since the direction of the force is exactly toward the center of the crank radius (i.e. F y = in Figure 1). This maximum load situation happens in all types of engines with a slight difference in the crank angle. In addition, most analysis done on engines with more cylinders (e.g. 4, 6, and 8) is on a portion of the crankshaft that consists of two main journal bearings, two crank webs, and a connecting rod pin journal. Therefore, analysis done for this single cylinder engine can be extended to larger engines. Force (kn) Bending Total Crankshaft Angle (Deg) Torsional Figure 4: Bending, torsional, and the resultant force at the connecting rod bearing at the engine speed of 36 rpm 3

4 In many studies the torsional load is neglected for the load analysis of the crankshaft, and this is because torsional load is less than 1 percent of the bending load [1]. In this specific engine with its dynamic loading, it is shown in the next sections that torsional load has no effect on the range of von Mises stress at the critical location. The main reason of torsional load not having much effect on the stress range is that the maxima of bending and torsional loading happen at different times (see Figure 4). In addition, when the peak of the bending load takes place the magnitude of torsional load is zero. Figure compares the magnitude of maximum torsional and bending loads at different engine speeds. As can be seen in this figure, the maximum of total load magnitude, which is equal to the maximum of bending load decreases as the engine speed increases. The reason for this situation refers to the load sources that exist in the engine at 3 degree crank angle. At this crank angle these two forces act in opposite directions. The force caused by combustion which is greater than the inertia load does not change at different engine speeds since the same pressure versus crankshaft angle is used for all engine speeds. The load caused by inertia increases in magnitude as the engine speed increases. Therefore, as the engine speed increases, a larger magnitude of inertia force is deducted from the combustion load, resulting in a decrease of the total load magnitude. at the fillets where the stresses are higher due to stress concentrations. As a crankshaft is designed for very long life, stresses must be in the linear elastic range of the material. Therefore, all carried analysis are based on the linear properties of the crankshaft material. The meshed crankshaft with 122,441 elements is shown in Figure 6. The dynamic loading of the crankshaft is complicated because the magnitude and direction of the load changes during a cycle. There are two ways to find the stresses in dynamic loading. One method is running the FE model as many times as possible with the direction and magnitude of the dynamic force. An alternative and simpler way of obtaining stress components is superposition of static loading. The main idea of superposition is finding the basic loading positions, then applying unit load on each position according to dynamic loading of the crankshaft, and scaling and combining the stresses from each unit load. In this study both methods were used with 13 points over 72 degrees of crankshaft angle. The results from 6 different locations on the crankshaft showed identical stress components from the two methods. Max Bending Max Torsion Range of Bending Range of Torsion 2 2 Force Magnitude (kn) Engine Speed (RPM) Figure : Comparison of maximum and range of bending and torsional loads at different engine speeds FE MODELING OF THE CRANKSHAFT The FE model of the crankshaft geometry has about 1 quadratic tetrahedral elements, with the global element length of.8 mm and local element length of.762 mm Figure 6: FEA model of the crankshaft with fine mesh in fillet areas It should be noted that the analysis is based on dynamic loading, though each finite element analysis step is done in static equilibrium. The main advantage of this kind of analysis is more accurate estimation of the maximum and minimum loads. Design and analyzes of the crankshaft based on static loading can lead to very conservative results. In addition, as was shown in this section, the minimum load could be achieved only if the analysis of loading is carried out during the entire cycle. The minimum value of von Mises stress which is obtained at the minimum load is needed for the stress range calculation and considering it zero will lead to smaller values for the stress range. As the dynamic loading condition is analyzed, only two main loading conditions are applied to the surface of the crankpin bearing. These two loads are perpendicular to each other and their directions are shown in Figure 1 as 4

5 F x and F y. Since the contact surface between connecting rod and crankpin bearing does not carry tension, F x and F y can also act in the opposite direction to those shown in Figure 1. Any loading condition during the service life of the crankshaft can be obtained by scaling and combining the magnitude and direction of these two loads. Boundary conditions in the FE model were based on the engine configuration. The mounting of this specific crankshaft is on two different bearings which results in different constraints in the boundary conditions. One side of the crankshaft is fixed to the engine block by a ball bearing and the other side is rolling over a journal bearing. When under load, only 18 degrees of the bearing surfaces facing the load direction constraint the motion of the crankshaft. Therefore, a fixed semicircular surface as wide as the ball bearing width was used to model that section. This indicates that the surface can not move in either direction and can not rotate. The other side was modeled as a fixed thin semicircular ring which only holds the crankshaft centerline in its original position and acts as a pivot joint. In other words, the journal bearing is modeled in a way that allows the crankshaft to rotate about axis 1 as well as slide in direction 3 as occurs in a journal bearing. These defined boundary conditions are shown in Figure 7. Boundary conditions rotate with the direction of the load applied. element. Figure 1 shows the maximum stress, mean stress, and stress range at the engine speed of 2 rpm at different locations. It can be seen that element number 2 not only has the maximum von Mises stress, but it also carries the largest stress range and mean stress among other locations. This is important in fatigue analysis since the range and mean stress have more influence than the maximum stress. This is another reason for why having the stress history of critical elements are more useful than static analysis of the crankshaft. 6 A A 3 2 Figure 8: Locations on the crankshaft where the stress variation was traced over one complete cycle of the engine, and locations where strain gages were mounted 7 1 c A-A a b d Applied load; constant pressure over Fixed ring in directions 1 & 2 over 18 o Fixed surface in all degrees of freedom over 18 o Stress Magnitude 1 Figure 7: Boundary conditions used in the FEA model RESULTS AND DISCUSSION OF STRESS ANALYSIS - Crankshaft Angle (Deg) Some locations on the geometry were considered for depicting the stress history. These locations were selected according to the results of FE analysis, and as expected, all the selected elements are located on different parts of the fillet areas due to the high stress concentrations at these locations. Selected locations are labeled in Figure 8 and the von Mises stresses with sign for these elements are plotted in Figure 9. The critical loading situation is at the crank angle of 3 where the combustion exerts a large impact on the piston. At this time all stresses are at their highest level during stress time history in a cycle. As can be seen, location number 2 experiences the highest stress at this moment. Therefore, element number 2 was selected as the critical Figure 9: von Mises stress history (considering sign of principal stress) at different locations at the engine speed of 2 rpm

6 Stress Magnitude Maximum Minimum Range Mean remains the same with and without considering torsional load. This is due to the location of the critical point which is not influenced by torsion since it is located on the crankpin bearing. Other locations such as 1, 6, and 7 in Figure 8 experience the torsional load. Figure 12 shows changes in minimum, maximum, mean, and range of von Mises stress at location 7 with considering torsion and without considering it during service life at two different engine speeds. It can be seen that the minimum von Mises stress does not change since the minimum happens at a time when the torsional load is zero. The effect of torsion is about 16 percent increase in the stress range at this location Total min stress Total max stress Total stress range Total mean stress Min stress without Torsion Max stress without Torsion Stress range without Torsion Mean stress without torsion - Location Number 1 8 Figure 1: Comparison of maximum, minimum, mean, and range of stress at the engine speed of 2 rpm at different locations on the crankshaft Figure 11 shows the effect of engine speed on minimum, maximum, mean and range of stress. This figure indicates the higher the engine speed, the lower the von Mises stress. It should, however, be noted that there are many other factors regarding service life of an engine. Other important factors when the engine speed increases are wear and lubrication. As these issues were not of concern in this study, further discussion is avoided. Stress Magnitude Engine Speed (RPM) Figure 12: Effect of considering torsion in stresses at location 7 at different engine speeds von Mises Stress Magnitude Min Max Mean Range Engine Speed (RPM) Figure 11: Variation of minimum stress, maximum stress, mean stress, and stress range at location 2 on the crankshaft as a function of engine speed The effect of torsional load was discussed in the load analysis section, and was pointed out that it has no effect on the stress range of the critical location. The von Mises stress at location number 2 shown in Figure 9 Stress results obtained from the FE model were verified by experimental component test. Strain gages were mounted at four locations on the crankpin bearing. These locations are labeled as a, b, c, and d in Figure 8. The FE model boundary conditions were changed according to the fixture of the test assembly. The fixture constraints the motion of the shaft on the left side of the crankshaft in Figure 8 and a load is applied on the right side of the crankshaft with a moment arm of 44 cm. Therefore, the crankshaft is experiencing bending as a cantilever beam. Applying load in the direction of axis 2 in Figure 7 will result in stresses at locations a and b, and applying load in the direction of axis 1 in the same figure will result in stresses at locations c and d. Analytical calculations based on pure bending equation, Mc/I, show the magnitude of stresses to be the same and equal to 72 MPa at these locations, for a 89 N load. The values obtained from experiments are tabulated in Table 2. FEA results are also shown and compared with experimental results in this table. As can be seen, differences between FEA and strain gage results are less than 7 percent for different loading 6

7 conditions. This is an indication of the accuracy of the FE model used in this study. Table 2: Comparison of stress results from FEA and strain gages located at positions shown in Figure 8 Load (N) FEA Location a EXP % Difference FEA Location b EXP % Difference % % % % Load Location c Location d (N) FEA EXP % Difference FEA EXP % Difference % % % % Comparison of stresses at locations c and d resulting from loading in direction 1 in Figure 7 show symmetric stress values from FEA, experiment, and analytical method. The results from these three methods are close to each other. However, stresses obtained form FEA results and experiment show different stresses (i.e. nonsymmetric) at locations a and b, resulting from loading in direction 2 in Figure 7. On the other hand, stresses calculated from the analytical method are symmetric at these two locations (+/-72 MPa) and different from the obtained values from FEA and experiment. Therefore, the use of FE model in the analysis is necessary due to geometry complexity. Stress results from FE and analytical results have similar symmetric values for stresses on the main bearing away from fillet areas. FE results show different stress values on the fillet area of main bearing. The reason is the eccentric cylinders geometry which will result in changes in K t value around the fillet area. Load variation over a cycle results in variation of stress. For proper calculations of fatigue damage in the component there is a need for a cycle counting method over the stress history. Using the rainflow counting method [11] on the critical stress history plot (i.e. location 2 in Figure 9) shows that in an entire cycle only one peak is important and can cause fatigue damage in the component. The result of the rain count flow over the stress-time history of location 2 at the engine speed of 2 rpm is shown in Figure 13. It is shown in this figure that in the stress history of the critical location only one cycle of loading is important and the other minor cycles have low stress amplitudes. von Mises Stress Magnitude Time Figure 13: Rain flow count of the von Mises stress with consideration of sign at location 2 at engine speed of 2 rpm CONCLUSIONS The following conclusions could be drawn from this study: 1. Dynamic loading analysis of the crankshaft results in more realistic stresses whereas static analysis provides an overestimate results. Accurate stresses are critical input to fatigue analysis and optimization of the crankshaft. 2. There are two different load sources in an engine; inertia and combustion. These two load source cause both bending and torsional load on the crankshaft. 3. The maximum load occurs at the crank angle of 3 degrees for this specific engine. At this angle only bending load is applied to the crankshaft. 4. Considering torsional load in the overall dynamic loading conditions has no effect on von Mises stress at the critically stressed location. The effect of torsion on the stress range is also relatively small at other locations undergoing torsional load. Therefore, the crankshaft analysis could be simplified to applying only bending load.. Critical locations on the crankshaft geometry are all located on the fillet areas because of high stress gradients in these locations which result in high stress concentration factors. 6. Superposition of FEM analysis results from two perpendicular loads is an efficient and simple method of achieving stresses at different loading conditions according to forces applied to the crankshaft in dynamic analysis. 7. Experimental and FEA results showed close agreement, within 7% difference. These results indicate non-symmetric bending stresses on the crankpin bearing, whereas using analytical method predicts bending stresses to be symmetric at this location. The lack of symmetry is a geometry deformation effect, indicating the need for FEA 7

8 modeling due to the relatively complex geometry of the crankshaft. 8. Using the rainflow cycle counting method on the critical stress history plot shows that in an entire cycle only one peak is important and can cause fatigue damage in the component. REFERENCES 1. Henry, J., Topolsky, J., and Abramczuk, M., 1992, Crankshaft Durability Prediction A New 3-D Approach, SAE Technical Paper No. 9287, Society of Automotive Engineers 2. Guagliano, M., Terranova, A., and Vergani, L., 1993, Theoretical and Experimental Study of the Stress Concentration Factor in Diesel Engine Crankshafts, Journal of Mechanical Design, Vol. 11, pp Payar, E., Kainz, A., and Fiedler, G. A., 199, Fatigue Analysis of Crankshafts Using Nonlinear Transient Simulation Techniques, SAE Technical Paper No. 979, Society of Automotive Engineers 4. Prakash, V., Aprameyan, K., and Shrinivasa, U., 1998, An FEM Based Approach to Crankshaft Dynamics and Life Estimation, SAE Technical Paper No. 986, Society of Automotive Engineers. Borges, A. C. C., Oliveira, L. C., and Neto, P. S., 22, Stress Distribution in a Crankshaft Crank Using a Geometrucally Restricted Finite Element Model, SAE Technical Paper No , Society of Automotive Engineers 6. Shenoy, P. S. and Fatemi, A., 26, Dynamic analysis of loads and stresses in connecting rods, IMechE, Journal of Mechanical Engineering Science, Vol. 22, No., pp Shenoy, P. S. and Fatemi, A., "Connecting Rod Optimization for Weight and Cost Reduction", SAE Paper No , SAE 2 Transactions: Journal of Materials and Manufacturing 8. Zoroufi, M. and Fatemi, A., "A Literature Review on Durability Evaluation of Crankshafts Including Comparisons of Competing Manufacturing Processes and Cost Analysis", 26th Forging Industry Technical Conference, Chicago, IL, November 2 9. Fergusen, C. R., 1986, Internal Combustion Engines, Applied Thermo Science, John Wiley and Sons, New York, NY, USA 1. Jensen, E. J., 197, Crankshaft strength through laboratory testing, SAE Technical Paper No. 726, Society of Automotive Engineers 11. Stephens, R. I., Fatemi, A., Stephens, R. R., and Fuchs, H. O., 21, Metal Fatigue in Engineering, 2nd edition, John Wiley and Sons, New York, NY, USA 8