Optimization of Flywheel Design for Internal Combustion Engines

Scholars' Mine Masters Theses Student Theses and Dissertations 1965 Optimization of flywheel design for internal combustion engines Dady Jal Patel Follow this and additional works at: https://scholarsmine.mst.edu/masters_theses Part of the Mechanical Engineering Commons Department: Recommended Citation Patel, Dady Jal, "Optimization of flywheel design for internal combustion engines" (1965). Masters Theses. 5715. https://scholarsmine.mst.edu/masters_theses/5715 This thesis is brought to you by Scholars' Mine, a service of the Missouri S&T Library and Learning Resources. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact [email protected]. OPTIMIZATION OF FLYWHEEL DESIGN FOR INTERNAL COMBUSTION ENGINES BY DADiY JAL PATEL A THESIS submitted to the faculty of the UNIVERSITY OF MISSOURI AT ROLLA in partial fulfillment of the requirements for the Degree of MASTER OF SCIENCE IN MECHANICAL ENGINEERING Rolla, Missouri Approved by ~ f.~ (Advisor) ~ ii ABSTRACT A new approach to the problem of flywheel design has been developed, thus eliminating some of the problems of conventional design. The term flywheel design, in this thesis, refers to the the determination of the flywheel iner tia (mass moment of inertia) only. Two versatile computer programs were set up to obtain the flywheel inertia and the turning moment diagram for a large variety of internal combustion engines, and use was made of these programs to optimize the inertia of the flywheel with respect to speed. As an illustration the data of a 1960 Co~vair engine were selected, and the results obtained from the computer pro grams agreed well with the ones used in practice. iii ACKNOWLEDGMENTS The author wishes to thank Professor Charles L. Ed wards for the idea that led to this work. He desires to express his ·gratitude to Professor Kenneth E. Spencer. Dr. Harry J. Sauer . and Professor Lyman L. Francis for their guidance and criticism during the conduction of this research. A vote of thanks goes to Professor Herbert R. Alcorn for his assistance in programming. iv TABLE OF CONTENTS TITLE PAGE • • • • • • • • • • • • • • • • • • • i ABSTRACT • • • • • • • • • • • • • • • • • • • • 11 ACKNOWLEDGEMENTS • • • • • • • • • • • • • • • • iii TABLE OF CONTENTS • • • • • • • • • • • • • • • iv LIST OF FIGURES • • • • • • • • • • • • • • • • vi LIST OF TABLES • • • • • • • • • • • • • • • • • vii I. INTRODUCTION • • • • • • • • • • • • • • • 1 II. REVIEW OF LITERATURE • • • • • • • • • • • 3 III. DISCUSSION • • • • • • • • • • • • • • • 9 A. Determination of the Torque Crank Angle Dia gram of the Engine and the Evaluation of the Flywheel Inertia •••••••••••••• 9 l. Logic Used in Developing the Computer Pro- gram for Inertia Evaluation · • • • • • • 9 a. Evaluation of the gas pressure torque • • • • • • • • • • • • lO b. Evaluation of the torque due to the inertia forces and the resulting torque due to gas pressure and inertia forces combined • • • • • • • 16 c. Determination ot the combined torque diagrams for the various cylinder combinations • • • • • • • • 18 d. Determination of the area under the torque crank angle diagram • • • • • 20 e. Determination of the mean torque line • • • • • • • • • • • • • • • • 22 f. Evaluation of the roots, that is, the intersection ot the torque curve with the mean torque line • • 22 v g. Determination of the maximum and minimum speed points on the torque crank angle diagram • • ••• • 23 h. Evaluation of the largest positive net area above and below the mean torque line • • • • • • 25 i. Calculation of the rotating inertia 25 2. Programs and Their Handling • • • • 25 a.. Computer program for the evaluation of the flywheel inertia • • • • 25 (l} Notations for the Read State- ment of Program No. l • • 37 ( 2} The sequence in which the an- swers will be obtained • • • 38 (3} Column headings for the Punched Cards obtained in the output • • • • • • • • • 38 ·b. Calcomp Plotter Program for obtaining the torque crank angle diagram of the engine • • • • • • 39 Notations used in the Program No. 2 • • • • • • • • • • 42 B. Optimization of Flywheel Inertia with Res- pect to Speed • • • • • • • • • • • • 42 c. Illustrative Problem • • • • • • • • • • 44 IV. CONCLUSIONS AND RECOMMENDATIONS • • • • • • 48 v. BIBLIOGRAPHY • • • • • • • • • • • • • • 49 VI. APPENDIX • • • • • • ... • • • • • • • • • • 50 56 VII. VITA • • • • • • • • • • • • • • • vi LIST OF FIGURES Figure Page 1 Arbitrary torque crank angle diagram of an internal combustion engine • • ••••• • • • 4 2 Torque crank angle diagram of a six cylinder engine • • • • • • • • • • • • • • • • • 6 3 Pressure volume diagram for Otto cycle • • • • 10 4 Pressure volume diagram for Diesel engine • • 13 5 Resolution of the net force in the engine mechanism • • • • • • • • 15 6 Torque crank angle diagram as a result of gas pressure alone in a four stroke engine • • • • • 16 7 Torque crank angle diagram as a result of pressure alone in a two stroke engine 16 8 Torque crank angle diagram showing the combina tion of the gas pressure torque with the inertia torque • • • • • • • • • • • • • 18 9 Combined torque crank angle diagram for a four cylinder, in line engine • •. • • • • ••• 19 10 Combined torque crank angle diagram for a Vee engine with two banks of one cylinder each • 20 11 Area bounded by a function: : y = f(x) • • 21 12 Magnified view of a curve between a and b, showing the presence of a root • • • • • 22 13 Arbitrary torque crank angle diagram showing the positive and negative areas, above and below the mean torque line • • • • • • • • • • • • • 23 14 Torque at various intervals of the crank • • • • 26 15 Horsepower versus speed relation for a six cylinder, opposed piston engine • • • • • • • • 43 16 Turning moment diagram of a 1960 Corvair engine. 55 vii LIST OF TABLES Table Page 1 Coefficient of speed fluctuation • • • • • • • • 8 2 Inertia variation with speed • • • • • • • • • • 47 l I. INTRODUCTION Flywheels have been known to man for ages, and have symbolized progress. One of their most outstanding appli cations has been in the field of internal combustion engines. Flywheels, although very simple by nature, have a very complicated design analysis. Each engine ~ requires an individual flywheel design and industries affiliated with the manufacture of internal combustion engines, find it a problem to make new designs for all their engines. The reason being the analysis is long, tedious, inaccurate and time consuming. Accuracy drops off, due to the choosing of large intervals in the torque crank angle analysis to ease repetitive calculation, slide rule application, and use of a planimeter or of graphical integration for area calculation. Besides "to err is human" and the designer is liable to commit mistakes at any stage in his calcula tions. Hence the usual procedure followed, is to take standard flywheels (specified by manufacturers) within the range of the approximate calculations of the designer, try them on the engine, and by trial and error come up with one which gives the smoothest performance of the engine. It is evident, from above, that most engines are fitted with flywheels not having the best design. As nearly all the parts of a present day internal combustion engine have been optimized, the author feels it necessary to maintain this high degree of perfection in the flywheel, Thus, a 2 theoretical investigation was conducted and a method de veloped, which enables industries to have flywheels opti mized for their engines without appreciable la~or . or cost. This investigation has been split into two parts, namely the determination of the inertia of the flywheel and the optimization of this inertia with respect to speed. Importance has been laid on the evaluation of the flywh el inertia, as it constitutes a major factor in fly wheel design nd it is this part of the analysis that of fers a blockade to moat designers. The author has made use of an IBM 1620 computer which offers a quick and reli able solution and has programming error detection facili ti s. Th program yields results tor either a two stroke or four stroke, diesel or gas, single cylinder or multi cylinder, radial or vee engine. Designers interested in obtaining the torque crank angle diagram for further appli cation can make uae of the Calcomp plotter program. Th 1 cond part, which deals with the optimization of flyvh el inertia, invokes the knowledge that the horsepow er of an engin varies with speed and thus the inertia varie with speed. An inveatigation was made on an Cor vair engine vhoae apeed ranged from 1200 rpm to 3800 rpm, and the result eatabliahed that the optimum inertia oocura at idlins speed. 3 II. REVIEW OF LITERATURE A flywheel as defined by Professor Joseph Shigley, is a mechanical filtering element in a circuit through which power is flowing. Energy is supplied by the engine at a variable rate and taken from the engine at a constant rate. This causes the shaft to vary in speed during one cycle. The flywheel helps to reduce this speed fluctuation and even out the ripples of the torque crank angle diagram by absorbing energy when it is delivered (by the engine) at a rate in excess of the load requirements and by releasing it when delivered by the engine at a rate less than load requirements. Thus, it acts as a smoothing or equalizing element in any mechanical power-transmission circuit which has a back and forth flow of energy. Most books on theory of machines and dynamics of ma- chinery have dealt with the topic of flywheel inertia evaluation but very few have shown the mathematical approach to this problem. Lord Kelvin has stated: "I often say that when you can measure what you are speaking about and express it in num bers you know something about it; but when you cannot express it in numbers, your know ledge is of a meager and unsatisfactory kind: it may be the beginning or knowledge, but you have scar o~lx in your thoughts advanced to the stage of science, whatever the matter be." The literature reviewed here has been of the kind Lord Kelvin would greatly approve or, namely, evaluation 4 from first principles.

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