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- 1. Finite Element Analysis on Piston Skirt Deformation - Sudharsan Srinivasan
- 2. 1. ABSTRACT For a vehicle engine, the piston is the essential part that bears heavy mechanical and thermal loads; therefore it has very many influences on the reliability and durability of an engine. So the piston greatly hinders the increase of power of an engine. Piston dynamics and friction are two important characteristics determining the performance and the efficiency of an internal combustion engine. In this project an approach to the behavioral analysis of the piston skirt is presented that is based mainly on the Finite Element Method representation. The Finite Element Method was used to predict the deformation of the piston skirt and also the stress distribution across the piston. 2
- 3. 2. INTRODUCTION A piston is a cylindrical engine component that slides back and forth in the cylinder bore by forces produced during the combustion process. The piston acts as a movable end of the combustion chamber. The stationary end of the combustion chamber is the cylinder head. Pistons are commonly made of a cast aluminum alloy for excellent and lightweight thermal conductivity. Thermal conductivity is the ability of a material to conduct and transfer heat. Aluminum expands when heated and proper clearance must be provided to maintain free piston movement in the cylinder bore. Insufficient clearance can cause the piston to seize in the cylinder. Excessive clearance can cause a loss of compression and an increase in piston noise. A complete illustration of the piston and its parts are shown below. Figure 1 – Piston Features. Piston features include the piston head, piston pin bore, piston pin, skirt, ring grooves, ring lands, and piston rings. The piston head is the top surface (closest to the cylinder 3
- 4. head) of the piston which is subjected to tremendous forces and heat during normal engine operation. A piston pin bore is a through hole in the side of the piston perpendicular to piston travel that receives the piston pin. A piston pin is a hollow shaft that connects the small end of the connecting rod to the piston. The skirt of a piston is the portion of the piston closest to the crankshaft that helps align the piston as it moves in the cylinder bore. Some skirts have profiles cut into them to reduce piston mass and to provide clearance for the rotating crankshaft counterweights. A ring groove is a recessed area located around the perimeter of the piston that is used to retain a piston ring. Ring lands are the two parallel surfaces of the ring groove which function as the sealing surface for the piston ring. A piston ring is an expandable split ring used to provide a seal between the piston and the cylinder wall. Piston rings are commonly made from cast iron. Cast iron retains the integrity of its original shape under heat, load, and other dynamic forces. Piston rings seal the combustion chamber, conduct heat from the piston to the cylinder wall, and return oil to the crankcase. Piston ring size and configuration vary depending on engine design and cylinder material. Piston rings commonly used on small engines include the compression ring, wiper ring, and oil ring. A compression ring is the piston ring located in the ring groove closest to the piston head. The compression ring seals the combustion chamber from any leakage during the combustion process. When the air-fuel mixture is ignited, pressure from combustion gases is applied to the piston head, forcing the piston toward the crankshaft. The pressurized gases travel through the gap between the cylinder wall and the piston and into the piston ring groove. Combustion gas pressure forces the piston ring against the cylinder wall to form a seal. Pressure applied to the piston ring is approximately proportional to the combustion gas pressure. A wiper ring is the piston ring with a tapered face located in the ring groove between the compression ring and the oil ring. The wiper ring is used to further seal the combustion 4
- 5. chamber and to wipe the cylinder wall clean of excess oil. Combustion gases that pass by the compression ring are stopped by the wiper ring. An oil ring is the piston ring located in the ring groove closest to the crankcase. The oil ring is used to wipe excess oil from the cylinder wall during piston movement. Excess oil is returned through ring openings to the oil reservoir in the engine block. Two-stroke cycle engines do not require oil rings because lubrication is supplied by mixing oil in the gasoline, and an oil reservoir is not required. Pistons are usually made of an aluminum alloy. They are a sliding fit in the cylinders. This serves several purposes as follows: Transmits the force of combustion to the crankshaft through the connecting rod. Acts as a guide for the upper end of the connecting rod. Serves as a carrier for the piston rings that are used to seal the compression in the cylinder. The piston must withstand incredible punishment under temperature extremes. The following are examples of conditions that a piston must withstand at normal highway speed: As the piston moves from the top of the cylinder to the bottom (or vice versa), it accelerates from a stop to a speed approximately 50 mph at midpoint, and then decelerates to a stop again. It does this approximately 80 times per second. The piston is subjected to pressures on its head in excess of 1,000 psi. The piston head is subjected to temperatures well above 600°F. Piston is one of the main components composing an engine and a lot of empirical knowledge and advanced technologies are fully used for the piston design. It has to be able to handle the abrupt changes in temperature and pressure just above its crown due to combustion, hence during a cycle it has to handle efficiently the thermal and pressure loads as well as maintaining the geometry with minimum deformation. The design of a piston is crucial in determining the efficiency of an engine. Piston quality depends on optimal geometrical design, body mass and material selection that ensures minimal 5
- 6. energy loss due to inertia, heat transfer and bore interaction. Structure strength must be retained against mechanical failure. However, finding the optimal set of the design parameters is a very challenging job as at every crank angle the piston experiences different loading. Consequently, the computational tools become very important in piston design. Over the years several piston models have been developed. Early piston models were primarily developed to investigate the piston dynamics and its impact on the cylinder bore that result in engine vibration and noise, in particular the piston slap phenomenon. The effects from the lubrication and the piston skirt elasticity in the piston dynamics were either not considered or assumed insignificant. Nevertheless, valuable information insights and principles obtained from these studies regarding the piston dynamics have contributed to the later efforts that attempt to couple lubrication and piston dynamics. There are essentially two types of piston used in today’s automotive engine and we will be analyzing about the Mono piston type. 2.1 Mono Piston By far the most common, and the one used in all passenger car engines, is the mono piston. As the name suggests, the piston comprises of a single component, which is usually made from aluminum. The upper part of the piston that supports the combustion force and holds the piston rings is called the crown. The lower part of the piston that supports the lateral forces against the inner walls is called the skirt. The piston is linked to the connecting rod via the wrist pin on which both components are hinged. An example of a mono piston assembly can be seen in Figure 2 below. Figure 2 - Schematic drawing of a mono piston assembly. 6
- 7. 2.2 Articulated Piston In some heavy duty diesel engines, due to extremely high combustion temperatures and pressures, it is desirable to have a stainless steel crown section. However, an aluminum skirt is still preferable due to its low weight and elasticity. Two components of different materials cannot be rigid joined together in the piston, as their differing coefficients of expansion would lead to failure. Instead, articulated pistons comprise a stainless steel crown and an aluminum skirt which are separate components and are hinged separately on the wrist pin. An example of an articulated piston assembly can be seen in Figure 3 below. Figure 3 - Schematic drawing of an articulated piston assembly. The piston motion equations are traditional Newton’s law of vertical and lateral motion and rotation applied to the piston in standard manner. The forces and moments acting on a piston are exemplified in Figure 4. These forces and moments come from interactions of the piston with the liner, rings, wrist pin, connecting rod, cylinder pressure and inertia. Figure 4 – Forces & Moments acting on the piston. 7
- 8. 3. Finite Element Analysis Finite Element Analysis (FEA) is a computer-based numerical technique for calculating the strength and behavior of engineering structures. It can be used to calculate deflection, stress, vibration, buckling behavior and many other phenomena. It can be used to analyze either small or large-scale deflection under loading or applied displacement. It can analyze elastic deformation, or “permanently bent out of shape” plastic deformation. The computer is required because of the astronomical number of calculations needed to analyze a large structure. The power and low cost of modern computers has made Finite Element Analysis available to many disciplines and companies. In the Finite Element Method, a structure is broken down into many small simple blocks or elements. The behavior of an individual element can be described with a relatively simple set of equations. Just as the set of elements would be joined together to build the whole structure, the equations describing the behaviors of the individual elements are joined into an extremely large set of equations that has the behavior of the whole structure. The computer solves these large sets of simultaneous equations. From the solution, the computer extracts the behavior of the individual elements. Fro this, it can get the stress and deflection of all the parts of the structure. The term “Finite Element” distinguishes the technique from the use of infinitesimal “differential elements” used in calculus, differential equations and partial differential equations. The method is also distinguished from finite difference equations, for which although the steps into which space is divided are finite in size, there is little freedom in shapes that the discreet steps can be taken. Finite element analysis is a way to deal with structures that are complex than can be dealt with analytically using partial differential equations. FEA deals with complex boundaries better than finite differential equations will, and gives answers to “real world” structural problems. 3.1 How is Finite Element Analysis Useful Finite Element Analysis makes it possible to evaluate a detailed and complex structure, in a computer, during the planning of the structure. The demonstration in the computer of 8
- 9. the adequate strength of the structure and the possibility of improving the design during planning can justify the cost of this analysis work. In the absence of Finite Element Analysis, development of structures must be based on hand calculations only. For complex structures like an automobile, the simplifying assumptions required to make any calculations possible can lead to a conservative and heavy design. A considerable factor of ignorance can remain as to whether the structure will be adequate for all design loads. Significant changes in designs involve risk. With FEA, the weight of a design can be minimized, and there can be a reduction in the number of prototypes built. 3.2 Types of Analysis on Structures Structures can be analyzed for small deflection and elastic material properties (linear analysis), small deflection and plastic material properties (material non-linearity), large deflections and elastic material properties (geometric non-linearity) and for simultaneous large deflection and plastic material properties. Loads on structures can be represented by using the force of gravity on the mass of the structure, by applying distributed pressure over surfaces of the structure, or by applying forces directly to positions in the structure. Displacements of the structure can be specified at positions in the structure. This can include boundary conditions that imply symmetric structures where only one portion of the structure is modeled. 3.3 FEA Applications In theory there is no limit to the number of applications that FEA can be used for. FEA was born and nurtured in the automotive and aerospace industries but has since spread to encompass all other sectors of industry, from medical instruments and F1 car design to plastic molding and watch springs. If it can be designed, then it can be modeled using FEA. 3.4 Finite Element Analysis Modeling Issues FEA is approximate: The first issue to understand in finite element analysis is that it is fundamentally an approximation. The underlying mathematical model may be an 9
- 10. approximation of the real physical system (for example, the Bernoulli beam ignoring shear deformation). The finite element itself approximates what happens in its interior with interpolation formulas. The interior of a 2-D or 3-D finite element has been mapped to the interior of an element with a perfect shape, so a severely distorted element cannot deform in a manner that has an accurate match to the real physical response. Integration over the body of the element is often approximated by Gaussian Quadrature. The continuity of deformation between connected elements is interrupted at some level. Badly shaped elements can give less accurate results. A linear analysis is an approximation of the real behavior. The boundary conditions approximate how the structure is supported by the outside world. The material properties assumed are approximate. Stress and strain results are based on the derivatives of the displacement solution, amplifying the errors. Meshing: Production of good quality mesh is a major issue. The mesh should be fine enough for good detail where information is needed, but not too fine, or the analysis will require considerable time and space in the computer. A mesh should have well-shaped elements – only mild distortion and moderate aspect ratios. This can require considerable user intervention, despite FEA software promotional claims of automatic good meshing. Warning about Nodal Coupling: Nodal coupling has its uses: one is a quick and dirty representation of a bolted or riveted connection with shell elements. More exotic applications can be invented. When nodal coupling is used to represent a bolted connection of 3D shells, the nodes that are coupled must occupy the same position in space. Otherwise, body rotation at that part of the structure will result in artificial mechanism acting on the structure. High local stresses, and an external couple would result if the coupled nodes were not located at the same position. Application of boundary conditions: Structural FEA displacement boundary conditions are the limitations on movement of the structure at places such as anchor locations. The boundary conditions in a finite element model must limit translation or rotation in a manner appropriate to the case at hand. Boundary conditions can be used to imply symmetric behavior in a structure that has symmetry, so that the model size can be halved, quartered or similarly reduced, if the loading of the structure is also symmetrical. Boundary conditions can also be used to imply anti-symmetry, for example, where a warping displacement is applied to a symmetric structure. 10
- 11. There are occasions when a displacement boundary condition needs to be applied to a single node so that the structure can rotate around the support point. This single node support, however, can result in a serious local stress spike. Application of loading in a manner that’s of satisfactory accuracy, without becoming overly complex: It is often sufficient to apply forces directly to a small set of nodes. However, better representation of loading can be needed to avoid local stress spikes in some analyses. Application of pressure over a region of elements, producing the desired force, can help avoid a local stress spike. Bucking analysis & failure: It can be pursued in two ways: Linear Eigen-value buckling and geometrically non-linear (large displacement) buckling analysis. Eigen-value buckling (also known as Euler buckling or classical buckling) will be sufficient for some structures, but much greater details about stress amplification and margin of safety can be found with geometrically non-linear analysis. Note that margin of safety is not a simple concept in a non-linear analysis. The margin of safety will be based on the difference between the intended design load and either the load that reaches failure conditions or the load that exceeds allowable set by design codes. 3.5 Failure Modes 1. Static loads lead to stresses exceeding yield over a significant region. 2. Loads on bolts, rivets, spot-welds, plug-welds, stitch-welds, fillet-welds, bevel-welds, full penetration-welds, adhesives, nails, tie-rods, links or other connection devices are too high. 3. Strains reach fracture levels in brittle materials. 4. Surface strains cause damage to protective coatings. 5. Buckling of components leads to local damage or progressive collapse. 6. Combined bending and compression leads to excessive stress and failure. 7. Fatigue or sudden fracture is reached. 8. Vibration frequencies are located where applied loading causes damage through large amplitude response. 11
- 12. 3.6 Steps in Finite Element Analysis There are a number of steps in the solution procedure using finite element methods. 1. Specifying Geometry: First the geometry of the structure to be analysed is defined. This can be done either by entering the geometric information in the finite element package through the keyboard or mouse, or by importing the model from a solid modeller like Pro/ENGINEER. 2. Specify Element Type & Material Properties: Next, the material properties are defined. In an elastic analysis of an isotropic solid these consist of the Young's modulus and the Poisson's ratio of the material. 3. Mesh the Object: Then, the structure is broken (or meshed) into small elements. This involves defining the types of elements into which the structure will be broken, as well as specifying how the structure will be subdivided into elements (how it will be meshed). This subdivision into elements can either be input by the user or, with some finite element programs (or add-ons) can be chosen automatically by the computer based on the geometry of the structure (this is called auto meshing). 4. Apply Boundary Conditions & External Loads: Next, the boundary conditions (e.g. location of supports) and the external loads are specified. 5. Generate Solution: Then the solution is generated based on the previously input parameters. 6. Post – Processing: Based on the initial conditions and applied loads, data is returned after a solution is processed. This data can be viewed in a variety of graphs and displays. 7. Refine the Mesh: Finite element methods are approximate methods and, in general, the accuracy of the approximation increases with the number of elements used. The number of elements needed for an accurate model depends on the problem and the specific results to be extracted from it. Thus, in order to judge the accuracy of results from a single finite element run, you need to increase the number of elements in the object and see if or how the results change. 8. Interpreting Result: This step is perhaps the most critical step in the entire analysis because it requires that the modeller use his or her fundamental 12
- 13. knowledge of mechanics to interpret and understand the output of the model. This is critical for applying correct results to solve real engineering problems and in identifying when modelling mistakes have been made (which can easily occur). The eight steps mentioned above have to be carried out before any meaningful information can be obtained regardless of the size and complexity of the problem to be solved. 3.7 FEM Convergence Testing The convergence testing is started with mesh - discretization, observe and record the solution. The problem is repeated with a finer mesh (i.e. more elements) and then the results are compared with the previous test. If the results are nearly similar, then the first mesh is probably good enough for the particular geometry, loading and constraints. If the results differ by a large amount however, it will be necessary to try a finer mesh yet. Finer meshes come with a cost however: more calculation time and large memory requirements (both disk and RAM)! It is desired to find the minimum number of elements that gives a converged solution. 13
- 14. 4. Modeling & Analysis 4.1 Modeling of Piston Assembly Computer Aided Three Dimensional Application Software (CATIA) was found by Dassault Systems of France. It was first used by BOEING Engineers and now it is used widely in aerospace & automobile applications. It has become the global language for all automobile manufacturers. It is widely used in surface modelling of automobile body. It is highly user friendly. Its latest version is V5 and the release is R14 and the capabilities of CATIA are immense. Modeling in CATIA is comparatively easier than in any other modeling software. CATIA has various supportive features such as easy profile drawing, extrude, shell, pocket, revolve, rib. The modeling of the piston assembly is subdivided into following parts: a) Sketching the profile of the piston and body. b) Performing operation on the sketch to generate 3-D feature. c) Additional features. The piston modeled in Catia is sown below. Figure 5 – Piston Model. 14
- 15. 4.2 Steps Involved in FEA of the Piston Assembly The analysis is done as per standard procedure as follows: a) Modeling. b) Material application (Aluminum) as per the specifications. c) Boundary conditions and loads are loaded as per the real time working environment. d) Meshing is done using 10 noded tetrahedron element. e) Solution phase. 4.3 Material property The material properties for the piston and piston – pin are as mentioned below: S. No Property Piston 1. Young’s modulus 68 x 109 Nmm-2 2. Poison ratio 0.35 3. Yield strength 400 x 106 Nmm-2 4. Density 2.7 g/cm3 5. Thermal expansion 24 X 10-6/°C Table 1 – Material Property. 4.4 Boundary condition In a numerical simulation, it is impossible and unnecessary to simulate the whole universe. Generally we choose a region of interest in which we conduct a simulation. The interesting region has a certain boundary with the surrounding environment. Numerical simulations also have to consider the physical processes in the boundary region. Different boundary conditions may cause quiet different simulation results. Improper sets of boundary conditions may introduce non-physical influences on the simulation system, while a proper set of boundary conditions can avoid that. The boundary conditions applied here in the simulation are: a) Fixed restraints. b) Pressure force applied on the piston crown. c) Connecting rod force applied on the piston-boss. 15
- 16. The pressure force is applied on the top face of the piston crown due to gas force acting during the combustion. The connecting rod force is calculated as follows: Piston acceleration, a p = rω 2 (cos θ + λ cos 2θ ) 2πn 2 × π × 410 Here θ = 360°, r = 0.05 m, ω = = = 42.94 rad 60 60 s r 0.05 λ= = = 0.307 l 0.163 a p = 0.05 × (42.94) 2 × (cos 360 + (0.307) cos 720 ) = 120.5 m s2 Connecting rod force, Fitr = −(m pa + mc −tr )a p Here mpa = 2.043 kg, mc-tr = 0.735 kg Fitr = −(2.043 + 0.735) × 120.5 = −335 N where, ap = Piston acceleration in m . s2 θ = Crank angle in Degree. r = Crank radius in m. ω = Angular velocity in rad . s n = Engine speed in rpm. l = Length of the connecting rod in m. λ = Utilization factor, r . l Fitr = Connecting rod force in N. mpa = Mass of piston assembly in kg. mc-tr = Mass of connecting rod in translational side in kg. In fixed restraints condition the piston boss outer face and the piston boss inner area are constrained in 3 translational and 3 rotational directions (ux, uy, uz =0, θx, θy, θz = 0). And the connecting rod force is applied on the piston boss area. The described boundary condition is exemplified in the following figures. 16
- 17. Figure 6 – Boundary Condition. Figure 7 –Boundary Condition. 17
- 18. 4.5 Element selection Once the component is modeled and boundary conditions are applied, the next in analysis is to discretize the component by using pre-defined elements in the analysis package. The piston assembly analysis is a three dimensional analysis. Hence a 3D element is used. Various 3D elements could be used for discretization. The best element should be chosen to get accurate results and convergence. Solid 95 element type is preferred over the Solid 45 element. Because solid 95 is a higher order version of Solid 45(8 noded element), it can tolerate irregular shapes without as much loss of accuracy. Solid 95 have compatible displacement shapes and are well suited to model curved boundaries. 4.6 Comparison of Solid 95 Elements Criteria Tetrahedral Option Pyramid Option Prism Option Diagram No of Nodes 10 13 15 Solving Time Comparatively Less Large Large Matrix Size RAM Comparatively Less Large Large required/ Table 2 –Comparison of Solid 95 Elements. Based on the comparison details, the best element to achieve accurate meshing, solution with least solving time and least memory required would be the 10 Noded Tetrahedron. Also Solid 95 elements have special features to support Plasticity, Creep, Stress stiffening, Swelling, Deflection, Large Strain, Birth and Death, Adaptive Descent. 18
- 19. 5. Results & Discussion I. FE Analysis on piston deformation at pressure = 3.8 Mpa & speed = 410 rpm. Figure 8 –Displacement Contour. Figure 9 – Displacement Contour. 19
- 20. Figure 10 – Von Mises Stress Contour. Figure 11 – Von Mises Stress Contour. 20
- 21. II. FE Analysis on piston deformation at pressure = 5.5 Mpa & speed = 1060 rpm. Figure 12 - Displacement Contour. Figure 13 - Displacement Contour. 21
- 22. Figure 14 – Von Mises Stress Contour. Figure 15 - Von Mises Stress Contour. 22
- 23. III. FE Analysis on piston deformation at pressure = 6 Mpa & speed = 1580 rpm. Figure 16 - Displacement Contour. Figure 17 - Displacement Contour. 23
- 24. Figure 18 – Von Mises Stress Contour. Figure 19 – Von Mises Stress Contour. 24
- 25. Maximum Pressure Speed, Reaction Force, Maximum Von S. No Displacement, Mpa RPM N Mises Stress, Nm-2 mm 1 3.8 410 -335 0.0857 4.93 x 107 2 5.5 1060 -2227 0.124 7.13 x 107 3 6 1580 -4943 0.135 7.8 x 107 Table 3 –Displacement & Von Mises Stress at different cases. 25
- 26. 6. Conclusion The piston has been designed to study the skirt deformation under several operating conditions using finite element method. Empirical equations are used to calculate the connecting rod forces and the boundary conditions are developed to simulate the exact constraints with some simplifications. In the final observation the skirt deformation was maximum on the thrust side of the piston and the reasons for this are the eccentricity in the piston pin and the firing chamber. The piston skirt profile relates to the piston slap phenomena that affect the skirt liner impact forces, skirt lubrication, friction and liner cavitations. By predicting the secondary motion of the piston, the power cylinder system can be modified in early design phase. However, the piston design changes made to improve piston guidance in cylinder and thereby reduce piston slap noise often have a negative impact on piston friction. 26
- 27. 7. References Andreas Panayi, Harold Schock, Boon-Keat Chui & Mikhail Ejakov, “Parameterization and FEA Approach for the Assessment of Piston Characterstics”, SAE Paper No. 2006-01-0429. S.H.Mansouri & V.W.Wong, “Effects of Piston Design Parameters on Piston Secondary Motion and Skirt-Liner Friction”, SAE Paper No. 2004-01-2911. You Zhang, Yong Zhang, Bin Gao & Baozhong Zhang, “Structure Design & FEA of LHR Piston for Vehicle Engines”, SAE Paper No. 981488. Shivakanth N.Kurbet & R. Krishna Kumar, “Mechanics and Stress Analysis of Piston Ring in Multibody Single Cylinder Internal Combustion Engine – FE Analysis”, SAE Paper No. 2001-01-3371. Tetsuya Kimura, Kazuki Takahashi & Shigeru Sugiyama, “Development of a Piston Secondary Motion Analysis Program with Elastically Deformable Piston Skirt”, SAE Paper No. 1999-01-3303. Mikhail A. Ejakov, Analytical Powertrain Department, Ford Motor Company – Piston/Piston Ring Dynamics CAE. B.Lawton & D.E.G.Crutcher, “Mechanical Stresses in Pistons, Gudgeon Pins & Connecting rods”, IMechE 2002. B.L.Ruddy & F.H.Kinsella, “Computer Aided Engineering for Pistons, Rings & Pins”, IMech 1990. Conor P.McNally, “Development of a Numerical Model of Piston Secondary Motion for Internal Combustion Engines”. 27

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