# Modeling & analysis of connecting rod of four stroke single cylinder engine for optimization of cost & material.

Introduction

The main aim of the project is to determine the Von Misses stresses, Shear stresses, Maximum Principle stress, Equivalent Alternating stress, Total Deformation, Fatigue Analysis and Optimization in the existing Connecting rod. If the existing design shows the failure, then suggest the minimum design changes in the existing Connecting rod. A lot has been done and still a lot has to be done in this field. In this Project, only the static FEA of the connecting rod has been performed by the use of the software. This work can be extended to study the effect of loads on the connecting rod under dynamic conditions. Experimental stress analysis (ESA) can also be used to calculate the stresses which will provide more reasons to compare the different values obtained. Now a day a lot is being said about vibration study of mechanical component important role in its failure. So the study can be extended to the vibration analysis of the connecting rod. The study identified fatigue strength as the most significant design factor in the optimization process. Then the combination of finite element technique with the aspects of weight reduction is to be made to obtain the required design of connecting rod. [1]

Results & Discussion

Outputs include fatigue life, damage, factor of safety, stress biaxiality, fatigue sensitivity as shown in Figures.

(1) A contour plot of available life over the model. This result can be over the whole model or scoped to a given part or surface. This result contour plot shows the available life for the given fatigue analysis. If loading is of constant amplitude, this represents the number of cycles until the part will fail due to fatigue. If loading is non-constant, this represents the number of loading blocks until failure. Thus if the given load history represents one month of loading and the life was found to be 120, the expected model life would be 120 months.

(2) A contour plot of the fatigue damage at a given design life. Fatigue damage is defined as the design life divided by the available life. This result may be scoped. The default design life may be set through the Control Panel (Table 2.1)

(3) A contour plot of the factor of safety with respect to a fatigue failure at a given design life. The maximum FS reported is 15. Like damage and life, this result may be scoped. This calculation is iterative for nonconstant amplitude loading and may substantially increase solve time (Table 2.1).

(4) A stress biaxiality contour plot over the model. As mentioned previously, material properties are uniaxial but stress results are usually multiaxial. This result gives the user some idea of the stress state over the model and how to interpret the results. Biaxiality indication is defined as the principal stress smaller in magnitude divided by the larger principal stress with the principal stress nearest zero ignored. A biaxiality of zero corresponds to uniaxial stress, a value of -1 corresponds to pure shear, and a value of 0.97 corresponds to a pure biaxial state (Table 1). From the sample biaxiality plot shown below, most of the model is under a pure shear or uniaxial stress. This is expected since a simple torque has been applied at the top of the model. When using the biaxiality plot along with the safety factor plot above, it can be seen that the most damaged point occurs at a point of nearly pure shear. Thus it would be desirable to use S-N data collected through torsional loading if available. Of course collecting experimental data under different loading conditions is cost prohibitive and not often done.

(5) A fatigue sensitivity plot. This plot shows how the fatigue results change as a function of the loading at the critical location on the model. This result may be scoped to parts or surfaces. Sensitivity may be found for life, damage, or factory of safety. The user may set the number of fill points as well as the load variation limits.

[FIGURE 2.1 OMITTED]

[FIGURE 2.2 OMITTED]

[FIGURE 2.3 OMITTED]

[FIGURE 2.4 OMITTED]

[FIGURE 2.5 OMITTED]

[FIGURE 2.6 OMITTED]

[FIGURE 2.7 OMITTED]

[FIGURE 2.8 OMITTED]

Optimization Statement

Objective of the optimization task was to minimize the mass of the connecting rod under the effect of a load range comprising the two extreme loads, the peak compressive gas load, such that the maximum, minimum, and the equivalent stress amplitude are within the limits of the allowable stresses. The production cost of the connecting rod was also to be minimized. Furthermore, the buckling load factor under the peak gas load has to be permissible. [1]

Mathematically stated, the optimization statement would appear as follows:

Objective: Minimize Mass and Cost

Subject to:

* Compressive load = peak compressive gas load.

* Maximum stress < Allowable stress.

* Side constraints (Component dimensions).

* Manufacturing constraints.

* Buckling load > Factor of safety x the maximum gas load (Recommended FOS, 3 to 6).

Loads Applied

The load range under which the connecting rod was optimized is comprised of the compressive load of 4319 N. The compressive load of 4319 N is independent of the geometry of the connecting rod. The tensile load is, however, dependent upon the specific geometry, as it is a function of the mass, moment of inertia, and location of C.G.

[FIGURE 3.1 OMITTED]

Observations from the Optimization Exercise

(1) The literature survey suggests that connecting rods are typically designed under static loads. It appears that different regions are designed separately with different static loads (i.e. such as in Sonsino and Esper, 1994). Doing so increases the number of steps in the design process. In contrast, a connecting rod could very well be designed under dynamic loads. Doing so would reduce the number of steps in the design process.

(2) The applied load distribution at the crank end and at the piston pin end were based on experimental results (Webster et al., 1983). They were also used in other studies in the literature by Folgar et al. (1987) and Athavale and Sajanpawar (1991). Since the details were not discussed by Webster et al., the applicability of the loading to this connecting rod could not be evaluated.

(3) With manual optimization under static axial loading, at least 9.24% weight reduction could be achieved for the same fatigue performance as the existing connecting rod as shown in fig. 5.33. This is in spite of the fact that C-70 steel has 18% lower yield strength and 20% lower endurance limit. Clearly, higher weight reduction may be achieved by automating the optimization and more accurate knowledge of load distributions at the connecting rod ends. The axial stiffness is about the same as the existing connecting rod and the buckling load factor is higher than that for the existing connecting rod.

(4) C-40 has lower yield strength and endurance limit, As a result it was essential to increase weight in the pin end region. New fracture cracking materials are being developed (such as micro-alloyed steels) with better properties (Repgen, 1998). Using these materials can help significantly reduce the weight of the connecting rod in the pin end and crank end cap. However in the shank region, manufacturing constraints such as minimum web and rib dimensions for forgeability of the connecting rod present restrictions to the extent of weight reduction that can be achieved.

(5) Considering static strength, buckling load factor, and fatigue strength, it was found that the fatigue strength of the connecting rod is the most significant and the driving factor in the design and optimization of connecting rod.

Future Scope

A lot has been done and still a lot has to be done in this field. In this project, only the static FEA of the connecting rod has been performed by the use of the software Pro/E wildfire 3.0 for cad modeling and ANSYS WORKBENCH 9.0 for Finite Element Analysis. This work can be extended to study the effect of loads on the connecting rod under dynamic conditions. Experimental stress analysis (ESA) can also be used to calculate the stresses which will provide more reasons to compare the different values obtained.

Now days a lot is being said about vibrational study of mechanical component important role in its failure. So the study can be extended to the vibrational analysis of the connecting rod. We can change the material of the connecting rod for better result. Changing the geometry, but as it was the restriction from customer end, this is not covered in this project. We can notice from the design that the factor of safety considered for the design is too large which results in the wastage of the material and also increases its cost. So the need of the hour is the optimization of the connecting rod which will lead to a revolution in the manufacturing sectors of the automobile industry.

Conclusion

This research project investigated weight and cost reduction opportunities that steel forged connecting rods offer. This Project is concentrated on the calculation of the stresses developed in the connecting rod and to find region more susceptible to failure. The connecting rod chosen for the study is of 4 stroke single cylinder engine in which failure of the connecting rod results in the replacement of the whole connecting rod crankshaft assembly. FEA was performed using these results obtained from load analysis to gain an insight of the structural behavior of connecting rod and to determine design loads for further study. First the Cad Modeling of connecting rod with the help of Cad software Pro/E Wildfire 3.0 and then Load analysis was performed with different cases consideration. The analysis was carried out with computer aided simulation. The tool used for analysis is ANSYS WORKBENCH 9.0.The following conclusions can be drawn from this study:

(1) There is considerable difference in the structural behavior of the connecting rod between axial fatigue loading. The results obtained with the analysis tool are quite comfortable and can be used to optimize the model.

(2) The Optimization carried out in analysis gives deep insight by considering optimum parameter for suggestion of modification in the existing connecting rod.

(3) Optimization was performed to reduce weight. Weight can be reduced by changing the material of the current forged steel connecting rod to crackable forged steel (C-70).

(4) Fatigue strength was the most significant factor (design driving factor) in the optimization of this connecting rod.

(5) The parameter consideration for optimization are its 20% reduction in weight of connecting rod, while reducing the weight, the static strength, fatigue strength, and the buckling load factor were taken into account.

(6) The optimized geometry is 20% lighter than the current connecting rod. PM connecting rods can be replaced by fracture splitable steel forged connecting rods with an expected weight reduction of about higher than existing connecting rod, with similar or better fatigue behavior.

(7) By using other facture crackable materials such as micro-alloyed steels having higher yield strength and endurance limit, the weight at the piston pin end and the crank end can be further reduced. Weight reduction in the shank region is, however, limited by manufacturing constraints.

(8) The stresses developed in the four load cases of connecting rod are below the yield value.

(9) The stress multiaxiality is high, especially at the critical region of the crank end transition. Therefore, multiaxial fatigue analysis is needed to determine fatigue strength. Due to proportional loading, equivalent stress approach based on von Mises criterion can be used to compute the equivalent stress amplitude. Outputs include fatigue life, damage, factor of safety, stress biaxiality, fatigue sensitivity.

(10) The buckling occurs in the rod is basically maximum at the piston pin end.

(11) The software gives a view of stress distribution in the whole connecting rod which gives the information that which parts are to be hardened or given attention during manufacturing stage.

(12) The software also reveals the importance of the varying I-cross section which is provided for uniform stress distribution over the entire web of the connecting rod.

References

[1] Pravardhan S Shenoy, "Dynamic load analysis and optimization of connecting rod", 2004, Master's Thesis, University of Toledo

[2] James R Dale, "Connecting Rod Evaluation", January 2005

[3] R Vozenilek, C Scholz, P Brabec, "FEM Analysis of Connecting Rod:", 2004

[4] Adila Afzal, Ali Fatemi, "A Comparative study of Fatigue Behaviour and Life Prediction of Forged Steel and PM Connecting Rods", University of Toledo.

[5] Pro/E Wildfire 3.0 Reference Manual

[6] Hero Honda Splendor Company Manual

[7] ANSYS WORKBENCH 9.0 Reference Manual.

[8] Sonsino, C. M. and Esper, F. J., 1994, "Fatigue Design for PM Components," European Powder Metallurgy Association (EPMA).

[9] Hippoliti, R., 1993, "FEM method for design and optimization of connecting rods for small two-stroke engines

[10] J. Sugita, T. Itoh, T. Abe, Honda R. & D. "Engine Component Design System Using Boundary Element Method", 905206.

[11] Afzal, A., 2004, "Fatigue Behavior and Life prediction of Forged Steel and PM Connecting Rods," Master's Thesis, University of Toledo.

[12] R. C. Patel, "Elements of Heat engine", vol-I, II.

[13] Robert Cook, "Concepts and Application of FEA"

[14] Athavale, S. and Sajanpawar, P. R., 1991, "Studies on Some Modelling Aspects in the Finite Element Analysis of Small Gasoline Engine Components," Small Engine Technology Conference Proceedings, Society of Automotive Engineers of Japan, Tokyo, pp. 379-389.

[15] Rabb, R., 1996, "Fatigue failure of a connecting rod," Engineering Failure Analysis, Vol. 3, No. 1, pp. 13-28.

(1) S B Jaju and (2) P G Charkha

(1) Professor, (2) Student [M Tech (CAD-CAM)] (1,2) Department of Mechanical Engineering, G H Raisoni College of Engineering Nagpur, C R P F Gate No-3, Digdoh Hills, Hingna Road, Nagpur, Maharashtra, India-440016 Email: (1) sbjaju@gmail.com, (2) pgcharkha@gmail.com

The main aim of the project is to determine the Von Misses stresses, Shear stresses, Maximum Principle stress, Equivalent Alternating stress, Total Deformation, Fatigue Analysis and Optimization in the existing Connecting rod. If the existing design shows the failure, then suggest the minimum design changes in the existing Connecting rod. A lot has been done and still a lot has to be done in this field. In this Project, only the static FEA of the connecting rod has been performed by the use of the software. This work can be extended to study the effect of loads on the connecting rod under dynamic conditions. Experimental stress analysis (ESA) can also be used to calculate the stresses which will provide more reasons to compare the different values obtained. Now a day a lot is being said about vibration study of mechanical component important role in its failure. So the study can be extended to the vibration analysis of the connecting rod. The study identified fatigue strength as the most significant design factor in the optimization process. Then the combination of finite element technique with the aspects of weight reduction is to be made to obtain the required design of connecting rod. [1]

Results & Discussion

Outputs include fatigue life, damage, factor of safety, stress biaxiality, fatigue sensitivity as shown in Figures.

(1) A contour plot of available life over the model. This result can be over the whole model or scoped to a given part or surface. This result contour plot shows the available life for the given fatigue analysis. If loading is of constant amplitude, this represents the number of cycles until the part will fail due to fatigue. If loading is non-constant, this represents the number of loading blocks until failure. Thus if the given load history represents one month of loading and the life was found to be 120, the expected model life would be 120 months.

(2) A contour plot of the fatigue damage at a given design life. Fatigue damage is defined as the design life divided by the available life. This result may be scoped. The default design life may be set through the Control Panel (Table 2.1)

(3) A contour plot of the factor of safety with respect to a fatigue failure at a given design life. The maximum FS reported is 15. Like damage and life, this result may be scoped. This calculation is iterative for nonconstant amplitude loading and may substantially increase solve time (Table 2.1).

(4) A stress biaxiality contour plot over the model. As mentioned previously, material properties are uniaxial but stress results are usually multiaxial. This result gives the user some idea of the stress state over the model and how to interpret the results. Biaxiality indication is defined as the principal stress smaller in magnitude divided by the larger principal stress with the principal stress nearest zero ignored. A biaxiality of zero corresponds to uniaxial stress, a value of -1 corresponds to pure shear, and a value of 0.97 corresponds to a pure biaxial state (Table 1). From the sample biaxiality plot shown below, most of the model is under a pure shear or uniaxial stress. This is expected since a simple torque has been applied at the top of the model. When using the biaxiality plot along with the safety factor plot above, it can be seen that the most damaged point occurs at a point of nearly pure shear. Thus it would be desirable to use S-N data collected through torsional loading if available. Of course collecting experimental data under different loading conditions is cost prohibitive and not often done.

(5) A fatigue sensitivity plot. This plot shows how the fatigue results change as a function of the loading at the critical location on the model. This result may be scoped to parts or surfaces. Sensitivity may be found for life, damage, or factory of safety. The user may set the number of fill points as well as the load variation limits.

[FIGURE 2.1 OMITTED]

[FIGURE 2.2 OMITTED]

[FIGURE 2.3 OMITTED]

[FIGURE 2.4 OMITTED]

[FIGURE 2.5 OMITTED]

[FIGURE 2.6 OMITTED]

[FIGURE 2.7 OMITTED]

[FIGURE 2.8 OMITTED]

Optimization Statement

Objective of the optimization task was to minimize the mass of the connecting rod under the effect of a load range comprising the two extreme loads, the peak compressive gas load, such that the maximum, minimum, and the equivalent stress amplitude are within the limits of the allowable stresses. The production cost of the connecting rod was also to be minimized. Furthermore, the buckling load factor under the peak gas load has to be permissible. [1]

Mathematically stated, the optimization statement would appear as follows:

Objective: Minimize Mass and Cost

Subject to:

* Compressive load = peak compressive gas load.

* Maximum stress < Allowable stress.

* Side constraints (Component dimensions).

* Manufacturing constraints.

* Buckling load > Factor of safety x the maximum gas load (Recommended FOS, 3 to 6).

Loads Applied

The load range under which the connecting rod was optimized is comprised of the compressive load of 4319 N. The compressive load of 4319 N is independent of the geometry of the connecting rod. The tensile load is, however, dependent upon the specific geometry, as it is a function of the mass, moment of inertia, and location of C.G.

[FIGURE 3.1 OMITTED]

Observations from the Optimization Exercise

(1) The literature survey suggests that connecting rods are typically designed under static loads. It appears that different regions are designed separately with different static loads (i.e. such as in Sonsino and Esper, 1994). Doing so increases the number of steps in the design process. In contrast, a connecting rod could very well be designed under dynamic loads. Doing so would reduce the number of steps in the design process.

(2) The applied load distribution at the crank end and at the piston pin end were based on experimental results (Webster et al., 1983). They were also used in other studies in the literature by Folgar et al. (1987) and Athavale and Sajanpawar (1991). Since the details were not discussed by Webster et al., the applicability of the loading to this connecting rod could not be evaluated.

(3) With manual optimization under static axial loading, at least 9.24% weight reduction could be achieved for the same fatigue performance as the existing connecting rod as shown in fig. 5.33. This is in spite of the fact that C-70 steel has 18% lower yield strength and 20% lower endurance limit. Clearly, higher weight reduction may be achieved by automating the optimization and more accurate knowledge of load distributions at the connecting rod ends. The axial stiffness is about the same as the existing connecting rod and the buckling load factor is higher than that for the existing connecting rod.

(4) C-40 has lower yield strength and endurance limit, As a result it was essential to increase weight in the pin end region. New fracture cracking materials are being developed (such as micro-alloyed steels) with better properties (Repgen, 1998). Using these materials can help significantly reduce the weight of the connecting rod in the pin end and crank end cap. However in the shank region, manufacturing constraints such as minimum web and rib dimensions for forgeability of the connecting rod present restrictions to the extent of weight reduction that can be achieved.

(5) Considering static strength, buckling load factor, and fatigue strength, it was found that the fatigue strength of the connecting rod is the most significant and the driving factor in the design and optimization of connecting rod.

Future Scope

A lot has been done and still a lot has to be done in this field. In this project, only the static FEA of the connecting rod has been performed by the use of the software Pro/E wildfire 3.0 for cad modeling and ANSYS WORKBENCH 9.0 for Finite Element Analysis. This work can be extended to study the effect of loads on the connecting rod under dynamic conditions. Experimental stress analysis (ESA) can also be used to calculate the stresses which will provide more reasons to compare the different values obtained.

Now days a lot is being said about vibrational study of mechanical component important role in its failure. So the study can be extended to the vibrational analysis of the connecting rod. We can change the material of the connecting rod for better result. Changing the geometry, but as it was the restriction from customer end, this is not covered in this project. We can notice from the design that the factor of safety considered for the design is too large which results in the wastage of the material and also increases its cost. So the need of the hour is the optimization of the connecting rod which will lead to a revolution in the manufacturing sectors of the automobile industry.

Conclusion

This research project investigated weight and cost reduction opportunities that steel forged connecting rods offer. This Project is concentrated on the calculation of the stresses developed in the connecting rod and to find region more susceptible to failure. The connecting rod chosen for the study is of 4 stroke single cylinder engine in which failure of the connecting rod results in the replacement of the whole connecting rod crankshaft assembly. FEA was performed using these results obtained from load analysis to gain an insight of the structural behavior of connecting rod and to determine design loads for further study. First the Cad Modeling of connecting rod with the help of Cad software Pro/E Wildfire 3.0 and then Load analysis was performed with different cases consideration. The analysis was carried out with computer aided simulation. The tool used for analysis is ANSYS WORKBENCH 9.0.The following conclusions can be drawn from this study:

(1) There is considerable difference in the structural behavior of the connecting rod between axial fatigue loading. The results obtained with the analysis tool are quite comfortable and can be used to optimize the model.

(2) The Optimization carried out in analysis gives deep insight by considering optimum parameter for suggestion of modification in the existing connecting rod.

(3) Optimization was performed to reduce weight. Weight can be reduced by changing the material of the current forged steel connecting rod to crackable forged steel (C-70).

(4) Fatigue strength was the most significant factor (design driving factor) in the optimization of this connecting rod.

(5) The parameter consideration for optimization are its 20% reduction in weight of connecting rod, while reducing the weight, the static strength, fatigue strength, and the buckling load factor were taken into account.

(6) The optimized geometry is 20% lighter than the current connecting rod. PM connecting rods can be replaced by fracture splitable steel forged connecting rods with an expected weight reduction of about higher than existing connecting rod, with similar or better fatigue behavior.

(7) By using other facture crackable materials such as micro-alloyed steels having higher yield strength and endurance limit, the weight at the piston pin end and the crank end can be further reduced. Weight reduction in the shank region is, however, limited by manufacturing constraints.

(8) The stresses developed in the four load cases of connecting rod are below the yield value.

(9) The stress multiaxiality is high, especially at the critical region of the crank end transition. Therefore, multiaxial fatigue analysis is needed to determine fatigue strength. Due to proportional loading, equivalent stress approach based on von Mises criterion can be used to compute the equivalent stress amplitude. Outputs include fatigue life, damage, factor of safety, stress biaxiality, fatigue sensitivity.

(10) The buckling occurs in the rod is basically maximum at the piston pin end.

(11) The software gives a view of stress distribution in the whole connecting rod which gives the information that which parts are to be hardened or given attention during manufacturing stage.

(12) The software also reveals the importance of the varying I-cross section which is provided for uniform stress distribution over the entire web of the connecting rod.

References

[1] Pravardhan S Shenoy, "Dynamic load analysis and optimization of connecting rod", 2004, Master's Thesis, University of Toledo

[2] James R Dale, "Connecting Rod Evaluation", January 2005

[3] R Vozenilek, C Scholz, P Brabec, "FEM Analysis of Connecting Rod:", 2004

[4] Adila Afzal, Ali Fatemi, "A Comparative study of Fatigue Behaviour and Life Prediction of Forged Steel and PM Connecting Rods", University of Toledo.

[5] Pro/E Wildfire 3.0 Reference Manual

[6] Hero Honda Splendor Company Manual

[7] ANSYS WORKBENCH 9.0 Reference Manual.

[8] Sonsino, C. M. and Esper, F. J., 1994, "Fatigue Design for PM Components," European Powder Metallurgy Association (EPMA).

[9] Hippoliti, R., 1993, "FEM method for design and optimization of connecting rods for small two-stroke engines

[10] J. Sugita, T. Itoh, T. Abe, Honda R. & D. "Engine Component Design System Using Boundary Element Method", 905206.

[11] Afzal, A., 2004, "Fatigue Behavior and Life prediction of Forged Steel and PM Connecting Rods," Master's Thesis, University of Toledo.

[12] R. C. Patel, "Elements of Heat engine", vol-I, II.

[13] Robert Cook, "Concepts and Application of FEA"

[14] Athavale, S. and Sajanpawar, P. R., 1991, "Studies on Some Modelling Aspects in the Finite Element Analysis of Small Gasoline Engine Components," Small Engine Technology Conference Proceedings, Society of Automotive Engineers of Japan, Tokyo, pp. 379-389.

[15] Rabb, R., 1996, "Fatigue failure of a connecting rod," Engineering Failure Analysis, Vol. 3, No. 1, pp. 13-28.

(1) S B Jaju and (2) P G Charkha

(1) Professor, (2) Student [M Tech (CAD-CAM)] (1,2) Department of Mechanical Engineering, G H Raisoni College of Engineering Nagpur, C R P F Gate No-3, Digdoh Hills, Hingna Road, Nagpur, Maharashtra, India-440016 Email: (1) sbjaju@gmail.com, (2) pgcharkha@gmail.com

Table 2.1: Fatigue Results. Design Name Figure Scope Type Life Life None Model Life Damage None Model Damage 1.0x[10.sup.9] Safety Factor 1 Model Safety Factor 1.0x[10.sup.9] Biaxiality Biaxiality Indication 2 Model Indication Equivalent Equivalent Alternating Reversed Stress 3 Model Stress Alert Name Min Max Criteria Life 1,000,000.0 1,000,000.0 None Damage 1,000.0 1,000.0 None Safety Factor 1.13 15.0 None Biaxiality Indication -1.0 0.97 None Equivalent Alternating Stress 0.01 Mpa 76.22 Mpa None Table 2.2: Fatigue Results. Name Figure Scope Type Design Life Life None Model Life Damage None Model Damage 1.0x[10.sup.9] Safety Safety Factor 5 Model Factor 1.0x[10.sup.9] Biaxiality Biaxiality Indication 6 Model Indication Equivalent Equivalent Alternating 7 Model Reversed Stress Stress Name Min Max Alert Criteria Life 3,138.61 1,000,000.0 None Damage 1,000.0 318,612.73 None Safety Factor 0.23 15.0 None Biaxiality Indication -1.0 0.97 None Equivalent Alternating 5.67x[10.sup.-2 Stress MPa 381.17 MPa None Table 3.1.1: Values for Shape Results. Target Predicted Name Figure Scope Reduction Reduction "Shape Finder" 9 "Model" 20.0% 9.24% to 9.51% Table 3.1.2: Total Weights. Marginal Name Original Optimized (Discretionary) "Shape Finder" 0.13 kg 0.12 kg 3.46 x [10.sup.-4] kg

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Author: | Jaju, S.B.; Charkha, P.G. |
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Publication: | International Journal of Applied Engineering Research |

Article Type: | Report |

Date: | Jul 1, 2009 |

Words: | 2545 |

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