Int. J. Mech. Eng. & Rob. Res. 2014 Rohit Tamrakar et al., 2014 Research Paper ISSN 2278 0149 www.ijmerr.com Vol. 3, No. 2, April 2014 2014 IJMERR. All Rights Reserved DESIGN OPTIMIZATION AND FINITE ELEMENT ANALYSIS OF PISTON USING PRO-e Rohit Tamrakar 1 *, Rohit Sharma 1, Gajendra Singh 1 and Nitul Sharma 1 *Corresponding Author: Rohit Tamrakar, rohit.tamrakar@gmail.com In this paper we have performed design optimization of piston by using global sensitivity study along with finite element analysis through PRO-E. First a piston has been modeled and then finite element analysis has been performed to know about the structural and thermal loading effects. Then design optimization is performed to get the optimum mass by determining the optimum value of crown thickness and skirt length of the piston by limiting various conditions like maximum temperature, maximum principle stress, von misses stress and maximum strain energy. Keywords: Piston, Global sensitivity analysis INTRODUCTION Piston is one of the most vital component of I.C engine. Piston is contained by the engine cylinder. Its function is to transfer the force from the expanding gases is the cylinder to the crankshaft through connecting rod. Its service requires great attention. The material of the piston is chosen according to its strength, wear properties, density and thermal expansion properties. Hotter engines require more stable alloys to maintain close tolerances without scuffing. Many pistons used to be made from hypoeutectic aluminum alloys. Now days we see hypereutectic alloys (Carley et al., 2004). Global sensitivity analysis provides information about the respective significance/ contribution of structural input random parameters (or combinations thereof) onto considered responses. The identification of non relevant and relevant structural parameters for model reduction purposes is one of the major tasks. Global sensitivity analysis may also improve the understanding of the model behavior and may clarify interactions among input parameters (Uwe Reuter et al., 2008). The modeling of piston is done using Pro- E software according to the environmental and structural conditions. Then the modeled was 1 Department of Mechanical Engineering, MANIT, Bhopal 462051, India. 93
imported to Pro-Mechanica module of Pro-E software to perform Finite Element Analysis (FEA) to know about the structural and thermal loading effects. Then the design optimization is carried out to have optimum mass of the piston by limiting various conditions like maximum temperature, maximum principle stress, von misses stress and maximum strain energy. Graphs have been obtained for each parameter after global sensitivity study and equations are developed for each of the graph. Using these equations the optimum value of crown thickness and skirt length of the piston has been obtained. MATERIAL CHARACTERISTIC The materials chosen for this analysis is alloy of Aluminum-AL-4032 (Dmitri Kopeliovich, Table 1: Composition of Al 4 O 3 2 Element Weight % Al 85.0 Si 12.2 Cu 0.90 Mg 1.0 Ni 0.90 Table 2: Structural Properties (at Room Temperature) Property Value Density (x1000 kg/m³) 2.69 Poisson s Ratio 0.33 Elastic Modulus (GPa) 70-80 Tensile Strength (MPa) 380 Hardness (HB500) 120 Shear Strength (Mpa) 260 Fatigue Strength (MPa) 110 2012; and Understanding Cold Finished Aluminum Alloys). Al 4 O 3 2 is a medium highstrength heat treatable alloy. Good flow characteristics provided by high silicon content leads to both structural and automotive applications (Gilbert Kaufman, 1999). Table 3: Thermal Properties Property Value Temperature ( C) Thermal Expansion (10-6 / C) 19.4 20-100 Thermal Conductivity (W/m-K) 155 25 Table 4. Elastic Properties (At Room Temperature) Property Value Elastic Resistivity (10-9 -m) 43 Engine Specific Data The engine specific data are as follows: (Carvalheira and Gonçalves, 2006). The Specification Value Bore/mm 33.0 Stroke/mm 37.0 Con Rod Length/mm 69.0 Displacement/cm³ 31.65 Compression Ration 15 Combustion Chamber Hemispheric No. of Inlet Valve 1 No. of Exhaust Valve 1 Inlet Valve Open Timing/( BTDC) 10 Inlet Valve Open Timing/( ABDC) 75 Exhaust Valve Open Timing/( BBDC) 44 Exhaust Valve Open Timing/( ATDC) 0 Fueling System Table 5: Engine Specific Data Indirect Injection Coolant Temperature 90 C Oil Temperature 100 C 94
boundary conditions required for thermal and mechanical FEA are: Figure 2: Piston with Thermal Loading Maximum Cylinder Pressure 9.0 MPa Cycle Average Heat Flux 405 000 W/m 2 These results were obtained for a spark ignition timing of 10 deg BTDC and an equivalence ratio of 0.74 at 5000 rpm: Structural Load Application A gas load of 7700 N is applied on the top surface of the Piston. Side is taken as 1/10 th of gas load and applied on the sides. Gas load is equally distributed on the Boss, i.e., P/2 on each Boss surface. Piston is not allowed to rotate in any direction, it is only allowed to move along y-axis. Figure 3: Piston Model Figure 1: Structural Load on Piston Model Figure 4: Piston (Mesh Model) Thermal Load Application Heat Load of 447.968 W is applied on crown of piston. Convection coefficient is taken as 2233 W/m 2 K. Model The model was created using PRO/ ENGINEER software. Then the model was imported to the Mechanica module of PRO/ ENGINEER, where after defining the 95
boundary conditions and loads, analysis was performed. RESULTS AND DISCUSSION Design Optimization for Thermal Load Design optimization in thermal loading is done by taking two parameters which are Crown thickness and Skirt Length. The optimum value of these two parameters has been calculated for minimum mass condition and for minimum temperature condition. The graph obtained is as follows: Figure 7: Variation of Mass w.r.t Skirt Length Figure 5: Variation of Mass w.r.t Crown Thickness Note: Skirt length = 100 mm Mass = 16.5 gm Skirt length = 300 mm Mass = 24.5 gm Note: Crown thickness = 4 mm Mass = 18 gm Crown thickness = 7 mm Mass = 25 gm Figure 6: Variation of Temp. w.r.t Crown Thickness Figure 8: Variation of Max Temp. w.r.t Skirt Length Note: Crown thickness = 4 mm Temp. =187.5 C Crown thickness = 7 mm Temp. = 178 C Note: Skirt length = 100 mm Temp. = 88 C Skirt length = 300 mm Temp. = 83 C 96
The above graph shows that there is not much variation in Temp. w.r.t Skirt length mass of piston is directly proportional to the Crown Thickness and Skirt Length. Design Optimization for Structural Load Design optimization in Structural loading is done by taking two parameters which are Figure 9: Variation of Max. Principle Stress w.r.t Crown Thickness crown thickness and skirt length. The optimum value of these two parameters has been calculated for minimum Stress (Principle Stress, Von Mises Stress). The graph obtained is as follows: Above two graphs shows that there is not much variation in the Stress w.r.t to Crown Figure 11: Variation in Max. Principle Stress wrt Skirt Length Note: Crown thickness = 4 mm Max Principle Stress = 9.144595 x 10 8 N/mm 2 Crown thickness = 7 mm Max Principle Stress = 9.144630 x 10 8 N/mm 2 Note: Crown thickness = 100 mm Max Principle Stress = 1.5 x 10 10 N/mm 2 Crown thickness = 300 mm Max Principle Stress = Negligible Figure 10: Variation of Von Mises Stress w.r.t Crown Thickness Figure 12: Variation of Von Mises Stress w.r.t Skirt Length Note: Crown thickness = 4 mm Von Stress = 8.488 x 10 8 N/mm 2 Crown thickness = 7 mm Von Stress = 8.488 x 10 8 N/mm 2 Note: Crown thickness = 4 mm Von Stress = 1.2 x 10 10 N/mm 2 Crown thickness = 7 mm Von Stress = Negligible 97
Thickness, so they can be neglected while optimizing the design parameter. Above two graphs shows that as the Skirt length increase the Stress on the Piston decreases and after certain length become negligible as compared to initial stress. From the graph obtained between piston variables and various properties a mathematical equation is generated for each graph which by the help of curve fitting software, with the help of these equation a mathematical model can be created for piston variables which will further help in designing of piston. Equations for Crown Thickness and Mass For the data obtained from the graph b/w mass and crown thickness the best fitted equation is a linear equation which is: y = ax + b From the data value of a and b is calculated which are: a = 2.4 b = 0.00823 The equation is y = 2.4x + 0.00823 Equations for Crown Thickness and Temperature For the data obtained from the graph b/w temperature and crown thickness the best fitted equation is a first order hyperbolic equation which is: a y b x From the data value of a and b is calculated which are: a = 0.08625 b = 166.2 The equation is: 0.08625 y 166.2 x Equation for Skirt Length and Mass For the data obtained from the graph b/w mass and skirt length the best fitted equation is a linear equation which is: y = ax + b From the data value of a and b is calculated which are: a = 0.388 b = 0.01254 The equation is: y 0.388x 0.01254 Equation for Skirt Length and Temperature For the data obtained from the graph b/w skirt length and temperature the best fitted equation is a second order hyperbolic equation which is: y a b x 2 From the data value of a and b is calculated which are: a = 5.63E-07 b = 0.06135 The equation is: 5.66 10 y 2 x 4 182.8 98
CONCLUSION From the above results following has been concluded: Mass varies linearly wrt crown thickness in the given range. Temperature varies according to first order hyperbolic equation w.r.t Crown Thickness in the given range. Strain energy varies according to second order hyperbolic equation w.r.t Crown Thickness in the given range. There is not much variation in the Stress wrt Crown Thickness. Mass varies linearly w.r.t Skirt Length in the given range. Temperature varies according to second order hyperbolic equation w.r.t Skirt Length in the given range. Strain Energy drops suddenly with a small increase in skirt length and after certain length it become constant. There is not much variation in the Stress w.r.t Skirt Length. REFERENCES 1. Alcoa Global Cold Finished Products Understanding Cold Finished Aluminum Alloys. 2. Carley, Larry and Piston Design (2004), An Evolution Tale, Babcox. 3. Carvalheira P and Gonçalves P (2006), Report on Fea of Two Engine Pistons Made of Aluminum Cast Alloy A390 and Ductile Iron 65-45-12 Under Service Conditions, Presented at 5 th International Conference on Mechanics and Materials in Design, July 24-26, Held at the Faculty of Engineering, University of Porto, Portugal. 4. Dmitri Kopeliovich (2012), Wrought Aluminum Silicon-Alloys (4xxx), in http:// www.efunda.com 5. Gilbert Kaufman J (1999), Properties of Aluminum Alloys, The Aluminum Association, ASM International. 6. Uwe Reuter et al. (2008), Global Sensitivity Analysis in View of Non Linear Structural Behaviour. 99
APPENDIX Figure 1: Temperature Distribution on Piston Figure 2: Temperature Distribution on Piston Figure 3: Distribution of Max, Principle Stress Figure 4: Distribution of Shear Stress Figure 5: Distribution of Von Mises Stress 100