piston assembly mass as the other extreme. A finite element routine was first used to calculate the displace- ments and stresses in the rod, which were then used ...
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Design Optimization of the Connecting Rod For Maximize Reliability: A 3-D Finite Element Analysis Aldousar, S.M. (1) A connecting rod should be designed with high reliability. It should be strong enough to remain rigid under the loading, while light enough to reduce the inertia forces which are produced when the rod and piston stop, change directions, and start again at the end of each stroke. In this study an optimization was performed on a steel forged connecting rod for an engine car. In this study a numerical shape optimization procedure in combination with a 3-D finite element model was used in order to optimize the shape and the volume of a stainless steel connecting rod. The design was to minimize the maximum von Mises stresses occurred at the connecting rod in case of the tensile and compressive loading conditions, at the same time decreasing the volume of the connecting rod. The results of this study indicate that the shape of the connecting rod can be improved by increasing the outer radii of the crank-pin end and piston-pin end, and using a hollow tapered slot at the shank section between the crank and the piston ends. This optimal shape reduces the maximum von Mises stress by about 6% for tensile load and by about 45% for compressive load. The new design reduces the volume of the connecting rod by 10.5%.
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onnecting rods are widely used in variety of engines. The function of connecting rod is to transmit the thrust of the piston to the crankshaft, by translating the transverse motion to rotational motion. It consists of a pin-end, a shank section, and a crank-end. Pin-end and crank-end pinholes are machined to permit accurate fitting of bearings. One end of the connecting rod is connected to the piston by the piston pin. The other end revolves with the crankshaft and is split to permit it to be clamped around the crankshaft. The two parts are then attached by two bolts. The connecting rod is subjected to a complex state of loading. It undergoes high cyclic
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loads of the order of 108 to 109 cycles, which range from high compressive loads due to combustion, to high tensile loads due to inertia. Therefore, durability of this component is of critical importance. Due to these factors, the connecting rod has been the topic of research for different aspects. The following is brief literature survey reviews for some of these aspects. Webster et. al. [1] explained the loading of connecting rod in a diesel engine. Tension and compression loadings are used based on experimental results. For tension loading the crank and piston ends were found to have a sinusoidal pressure distribution on the contact surface with pins and connecting rod. It was concluded that the highest stress levels occurred in four locations: the upper area of the cap end on the axis of the symmetry, the transition region of the bolt section and the lower rib, the transition region of the lower rib and the shaft, and the connecting rod’s bolt head. Yoo et. al. [2] performed shape optimization of an engine connecting rod using variable equations of elasticity, material derivative idea of continuum mechanics, and an adjoint variable technique to calculate shape design sensitivities of stress. The results were then used in an iterative optimization algorithm to numerically solve for an
optimal design solution. The stress constrains were imposed on principal stresses of inertia and firing loads, fatigue strength was not addressed. Serag et. al. [3] developed approximate mathematical formulae to define connecting rod weight and cost as objective functions and also the constraints. The optimization was achieved using a geometric programming technique. Constraints were imposed on the compression stress, the bearing pressure at the crank and the piston pin ends. Fatigue was not addressed. The cost function was expressed in some exponential form with the geometric parameters. Sarihan and Song [4] optimized the wrist pin end of an engine connecting rod with an interface fit. They generated an approximate design surface and performed optimization of this design surface. The objective and constraint functions were updated in an iterative process until convergence was achieved. The load cycle that was used consisted of compressive gas load corresponding to a maximum torque and a tensile load corresponding to inertia load. The modified Goodman equation with alternating and mean octahedral shear stress was used for fatigue analysis. Research on development of lightweight connecting rods based on fatigue resistance analysis of microalloyed steel was conducted by
Fig. 1: The initial shape of the connecting rod
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Fig. 2: The 3-D finite element mesh of the initial shape Kuratomi et. al. [5]. The study found that the microalloyed steel exhibits lower fatigue strength than the quenched and tempered steel for smooth specimens, but equivalent or higher fatigue strength for notched specimens. The study concluded that microalloyed steel connecting rods exhibit higher fatigue strength than quenched and tempered steel and are 10% lighter in weight. Pai [6] presented an approach to optimize the shape of a connecting rod subjected to a load cycle which consisted of the inertia load deducted from gas load as one extreme and peak inertia load exerted by the piston assembly mass as the other extreme. A finite element routine was first used to calculate the displacements and stresses in the rod, which were then used in another routine to calculate the total life. Fatigue life was defined as the sum of crack initiation and crack growth lives, with crack growth life obtained using fracture mechanics. Afzal [7] investigates and compares fatigue behavior of forged steel and powder metal connecting rods. The experiments included strain-controlled specimen testing, with specimens obtained from the connecting rods, as well as load-controlled connecting rod bench testing. Fatigue properties obtained from specimen testing are then used in life predictions of the connecting rods. The stress concentration factors were obtained from finite element analysis. Specimen testing shows long-life fatigue strength of the forged steel to be 27% higher than that for powder metal. Folgar et al. [8] developed a fiber FP/ Metal matrix composite connecting rod with the aid of FEA, and loads
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obtained from kinematic analysis. Fatigue was not addressed at the design stage. However, prototypes were fatigue tested. The investigators identified design loads in terms of maximum engine speed, and loads at the crank and piston pin ends. They performed static tests in which the crank end and the piston pin end failed at different loads. Clearly, the two ends were designed to withstand different loads. Balasubramaniam et al. [9] reported computational strategy used in Mercedes-Benz using examples of engine components. In their opinion, 2D FE models can be used to obtain rapid trend statements, and 3D FE models for more accurate investigation. The various individual loads acting on the connecting rod were used for performing simulation and actual stress distribution was obtained by superposition. The loads included inertia load, firing load, the press fit of the bearing shell, and the bolt forces. No discussions on the optimization or fatigue, in particular, were presented. Ishida et al. [10] measured the stress variation at the column center and column bottom of the connecting rod, as well as the bending stress at the column center. They found that at the higher engine speeds, the peak tensile stress does not occur at 360° crank angle or top dead center. It was also observed that the R ratio varies with location, and at a given location it also varies with the engine speed. The maximum bending stress magnitude over the entire cycle (0° to 720° crank angle) at 12,000 rev/min, at the column center was found to be about 25% of the peaktensile stress over the same cycle. El-Sayed and Lund [11] presented a method to consider fatigue life as a constraint in optimal design of structures. They also demonstrated the concept on a SAE key hole specimen. In this approach a routine calculates the life and in addition to the stress limit, limits are imposed on the life of the component as calculated using FEA results. An optimisation method by Hedia [12] was presented which calculates and predicts optimal shape of the lon-
Fig. 3: The connecting rod with tensile load at crank end with cosine distribution over 180° and piston end restrained over 180°
Fig. 4: The connecting rod with tensile load at piston end with cosine distribution over 180° and crank end restrained over 180°
Fig. 5: The connecting rod with compressive load at crank end uniformly distribution over 120° and piston end restrained over 120°
Fig. 6: The connecting rod with compressive load at piston end uniformly distribution over 120° and crank end restrained over 120° gitudinal profile for transition length of a tension bar, which connects two different diameters. This method was applied to maximise the crack initiation time by minimising the fatigue notch factor Kf . It was observed that the maximization of crack initiation time with higher value of the statisti-
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Werkstoffe cal parameter, k, is also a minimisation of stress concentration factor, kt, at the same time. A tension bar with four different transition length, t (t/d = 0.333, 0.4167, 0.5 and 0.583) were considered. The crack initiation time of the optimal shape for all cases was increased by 17%, 12%, 9% and 7%, respectively. The stress concentration factor was reduced by 20%, 17%, 15% and 12.5%, respectively. The present analysis is a numerical shape optimization of a connecting rod. The aim of this work is to maximize the reliability, which is represented by reducing the maximum von Mises stresses obtained with the initial shape and in the same time reduce the weight of the connecting rod in order to reduce the cost and the inertia force.
Finite Element Modeling of the Connecting Rod A real connecting rod of an engine car was selected for modeling. The initial shape of the connecting rod with its real dimensions is shown in Fig. 1. A 3-D finite element mesh was generated using SOLID95 element type. For generating the 3-D mesh the ANSYS commercial package was used. The elastic modulus of the connecting rod is 206.7 GPa and the Poisson’s ratio is 0.3. The 3-D finite element mesh for the initial model is shown in Fig. 2.
tal results by Webster et. al. [1]. The normal pressure on the contact surface is given by: P = Po cos θ (1) The load is distributed over an angle of 180°. The total resultant load is given by: Pt = ∫ Po (cos2 θ) r t d θ = Po r t π/2 (2) The normal pressure constant Po is, therefore, given by: Po = Pt / ( r t p / 2)
where r is the radius of the crank or piston-pin and t is the thickness of the contact surface in the crank or in the piston-pin ends. For compressive loading of the connecting rod, the crank and the piston pin ends are assumed to have a uniformly distributed loading through 120° contact surface. The normal pressure is given by: P = Po (4)
Loading and Restraints Usually the worse case load is considered in the design process. Literature review suggests that investigators use maximum inertia load, inertia load, or inertia load of the piston assembly mass as one extreme load corresponding to the tensile load, and firing load or compressive gas load corresponding to maximum torque as the other extreme design load corresponding to the compressive load. Therefore, in this study, the crank and piston pin ends are assumed to have a sinusoidal distributed loading over the contact surface area, under tensile loading. This is based on experimen-
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In order to validate the FEA model, the stresses in the shank region half way along the length of the connecting rod (i.e mid-span) were compared under two conditions of compressive load application. First, a uniformly distributed load was applied at the piston pin end, while the crank end was restrained. Second, a uniformly distributed load was applied at the crank end, while the piston pin end was restrained. Since the magnitude of the loads is identical under the two conditions, we can expect the stresses to be same at a location away from the loading and restraints (i.e mid-span) under the two conditions. A similar comparison was also made for tensile load application. There is very good agreement under the two conditions for both compressive and tensile loads.
The total resultant load is given by: Pc = ∫ Po (cos θ) r t d θ = Po r t √3 (5) The normal pressure constant is given by: Po = Pc / ( r t √3)
Boundary Conditions
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Validation of Finite Element Models
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In this study four finite element models were analyzed. Finite element analysis for both tensile and compressive loads was conducted. Two cases were analyzed for each case, one with load applied at the crank end and restrained at the piston pin end, and the other with load applied at the piston pin end and restrained at the crank end. These four cases are shown in Figs. 3 through 6. When the tensile load is applied at the crank end, the piston pin inner surface is completely restrained along 180° (i.e. X, Y, Z, translations of all nodes on this surface are set to zero. Similarly, when the connecting rod is under axial compressive load, 120° of contact surface area is totally restrained.
Fig. 7: The optimal shape of the connecting rod.
Method of Analysis and Optimization Technique The above 3-D finite element model was used in combination with a numerical shape optimization procedure in order to optimize the shape of the connecting rod. The finite element method and optimization procedure was carried out using the ANSYS commercial package. For the
Fig. 8: The 3-D finite element mesh of the optimal shape
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a)
b)
Fig. 9: von Mises stress distribution with elastic tensile load at crank end. The piston end was restrained (a) initial design, (b) optimal design. optimization procedure to be carried out a specific program was written using the ANSYS Parametric Design Language (APDL). The objective function for this problem is to minimize the volume of the connecting rod, reducing the weight of the connecting rod will in turn
reduce the inertia loads and improve the performance of the engine. Reducing the volume of the connecting rod will be under a constraint of remaining the maximum von Mises stress obtained using the initial shape of the connecting rod to be at or below its initial value. The connecting rod has to be interchangeable with the existing one in the current engine. This requires some of the dimensions in the existing connecting rod to be maintained. These unchangeable dimensions are: the diameters of the crank pin hole, the piston pin hole, the overall thickness of the connecting rod, and the central distance between the crank and the piston-pin ends. Taking this fact into consideration, the design variables for this shape optimization are represented in Fig. 1. These design variables are illustrated below: a) t is the thickness of the slot in the shank section between the crank and the piston-pin ends. This design variable is started from the initial thickness (10mm) to zero, which means that the shank section is hollowed. b) R1 and R2 which are the outer radii in the crank end of the connecting rod. c) R3 and R4 which are the outer radii in the piston-pin end of the connecting rod. d) Y1 and Y2 which are the two radii of the slot in the shank section. e) Y which is the central distance between the two arcs Y1 and Y2 (i.e. the length of the slot). The upper and lower values of the design variables from (b) to (e) is choosed such that to maintain the connecting rod in its reasonable shape.
a)
b)
Fig. 11: von Mises stress distribution with elastic tensile load at piston end. The crank end was restrained (a) initial design, (b) optimal design. than the initial shape. In the shank section the slot for the optimal shape is longer and the thickness for the slot equals zero, which means that the optimal shape of the connecting rod has a hollow slot in the shank section. The volume of the optimal connecting rod is 10.5% less than the volume of the initial connecting rod.
Results
Fig. 10: comparison between the maximum von Mises stress for the initial and optimal designs with elastic tensile load at crank end, and the piston end was restrained
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Numerical shape optimization procedure is carried out using the ANSYS program, the optimal shape of the connecting rod is shown in Fig. 7. The 3-D finite element mesh for the optimal shape is shown in Fig. 8. For the optimal shape, it’s found that the outer radii in the crank end as well as in the piston-pin end are greater
Fig. 12: comparison between the maximum von Mises stress for the initial and optimal designs with elastic tensile load at piston end, and the crank end was restrained
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a)
b)
Fig. 13: von Mises stress distribution with elastic compressive load at crank end. The piston end was restrained (a) initial design, (b) optimal design. A comparison between the results for both the initial design and the optimal design can be explained below: 1. von Mises stress distribution with tensile load at crank end, and the piston-pin end was restrained for the initial and optimal designs is shown in Fig. 9 a, b, respectively. It is found that the maximum von
Mises stress for this loading condition is reduced for the optimal shape by about 5% compared with the initial shape. The maximum von Mises stress for the initial design and for the optimal design is shown in Fig. 10 2. von Mises stress distribution with tensile load at piston-pin end, and the crank end was restrained for the initial and optimal designs is shown in Fig. 11 a, b, respectively. It is found that the maximum von Mises stress for this loading condition is reduced for the optimal shape by about 6% compared with the initial shape. The maximum von Mises stress for the initial design and for the optimal design is shown in Fig. 12 3. von Mises stress distribution with compressive load at crank end, and the piston pin end was restrained for the initial and optimal designs is shown in Fig. 13 a, b, respectively. It is found that the maximum von Mises stress for this loading condition is reduced for the optimal shape by about 50% compared with the initial shape. The maximum von Mises stress for the initial design and for the optimal design is shown in Fig. 14 4. von Mises stress distribution with compressive load at pistonpin end, and the crank end was restrained for the initial and optimal designs is shown in Fig. 15 a, b, respectively. It is found that the maximum von Mises stress for this loading condition is reduced for the optimal shape by about 41% compared with the initial shape. The maximum von Mises stress for the initial design and for the optimal design is shown in Fig. 16.
Fig. 15: von Mises stress distribution with elastic compressive load at piston end. The crank end was restrained (a) initial design, (b) optimal design. as well as in the piston side are grater than the initial design. The optimal shape is 10.5% less in volume than the initial design. This reduction will reduce the weight of the engine component, thus reducing inertia loads, reducing engine
Conclusions Fig. 14: comparison between the maximum von Mises stress for the initial and optimal designs with elastic compressive load at crank end, and the piston end was restrained
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The shape of the connecting rod is optimized. The optimal shape is found to be a connecting rod with a hollow tapered slot at the shank section between the crank and the piston-pin ends. The outer radii in the crank side
Fig. 16: comparison between the maximum von Mises stress for the initial and optimal designs with elastic compressive load at piston end, and the crank end was restrained
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Metall-Forschung weight and improving engine performance and fuel economy. The optimal shape reduces the maximum von Mises stress in case of tensile loading by about 6%. However, the optimal shape reduces the maximum von Mises stress in case of compressive loading by about 45%.
References [1] Webster, W. D., Coffel, R., Alfaro, D., “A three dimensional finite element analysis of a high speed diesel engine connecting rod”, SAE Technical Paper 831322, (1983), pp. 83-96. [2] Yoo, Y. M., Haug, E. J., Choi, K. K., “Shape optimal design of an engine connecting rod”, Journal of Mechanisms, Transmissions and Automation in Design, Transactions of ASME, Vol. 106, (1984), pp. 415-419. [3] Serag, S., Sevien, L., Sheha, G., ElBeshtawi, I., “Optimal design of the
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connecting-rod”, Modelling, Simulation and Control, B, AMSE Press, Vol. 24, No. 3, (1989), pp. 49-63. [4] Sarihan, V. and Song, J., “Optimization of the wrist pin end of an automobile engine connecting rod with an interface fit”, Journal of Mechanical Design, Transactions of the ASME, Vol. 112, (1990), pp. 406-412. [5] Kuratomi, H., Uchino, M., Kurebayashi, Y., Namiki, K., Sugiura, S., “Development of lightweight connecting rod based on fatigue resistance analysis of microalloyed steel”, SAE Technical Paper 900454, (1990), pp. 57-61. [6] Pai, C. L., “The shape optimization of a connecting rod with fatigue life constraint”, Int. J. of Materials and Production Technology, Vol. 11, No. 5-6, (1996), pp. 357-370. [7] Afzal, A., “Fatigue behavior and life prediction of forged steel and PM connecting rods”, Master’s Thesis, University of Toledo, (2004). [8] Folgar, F., Wldrig, J. E., and Hunt, J. W., “Design, Fabrication and Performance of Fiber FP/Metal Matrix Composite Connecting Rods,” SAE Technical Paper Series 1987, Paper No. 870406, (1987)
[9] Balasubramaniam, B., Svoboda, M., and Bauer, W., “Structural optimization of I.C. engines subjected to mechanical and thermal loads,” Computer Methods in Applied Mechanics and Engineering, Vol. 89, pp. 337-360. (1991) [10] Ishida, S., Hori, Y., Kinoshita, T., and Iwamoto, T., “Development of technique to measure stress on connecting rod during firing operation,” SAE 951797, pp. 1851-1856, (1995) [11] El-Sayed, M. E. M., and Lund, E. H., “Structural optimization with fatigue life constraints,” Engineering Fracture Mechanics, Vol. 37, No. 6, pp. 11491156, (1990) [12] Hedia H.S. „Shape Optimization of fillet to minimize the fatigue notch factor“ METALL- Intl. Journal for Metallurgie, 58. Jahrgang · 7-8, (2004)
(1) S.M. Aldousari, Prod. Eng. &Mechanical systems Design Dept. Faculty of Engineering King Abdel Aziz University. Box P.O. 80204, Jadh 21589, Saudia Arabia
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