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A Study of the Displacement of a Wankel Rotary Engine
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English
Abstract
The volumetric displacement of a Wankel rotary engine is a function of the trochoid ratio and the pin size ratio, assuming the engine has a unit depth and the number of lobes is specified. The mathematical expression which defines the displacement contains a function which can be evaluated directly and a normal elliptic integral of the second type which does not have an explicit solution. This paper focuses on the contribution of the elliptic integral to the total displacement of the engine. The influence of the elliptic integral is shown to account for as much as 20% of the total displacement, depending on the trochoid ratio and the pin size ratio. Two numerical integration techniques are compared in the paper, namely, the trapezoidal rule and Simpson's 1/3 rule. The bounds on the error, associated with each numerical method, are analyzed. The results indicate that the numerical method has a minimal effect on the accuracy of the calculated displacement, for a practical number of integration steps. The paper also evaluates the influence of manufacturing tolerances on the calculated displacement and the actual displacement. Finally, a numerical example of the common three-lobed Wankel rotary engine is included for illustrative purposes.
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Citation
Beard, J. and Pennock, G., "A Study of the Displacement of a Wankel Rotary Engine," SAE Technical Paper 930684, 1993, https://doi.org/10.4271/930684.Also In
References
- Ansdale R. F. with a special contribution by Lockley D.J. 1969 The Wankel RC Engine: Design and Performance A.S. Barnes and Company, Inc. Cranbury, New Jersey
- Beard J.E. Pennock G.R. Stanisic M.M. 1989 “The Effects of the Design Parameters on the Generated Curvature and Displacement of Epitrochoidal Gerotor Pumps” Trans. SAE, Journal of Commercial Vehicles, Section 2 98 217 228 SAE Technical Paper No. 891831
- Beard J.E. Pennock G.R. 1990 “The Effects of the Design Parameters on the Displacement and Compression Ratio of the Wankel Rotary Compressor” Proc. of the 10th International Compressor Engineering Conference Purdue University West Lafayette, Indiana July 17 20 1 24 33
- Beard J.E. Hall A.S. Jr. Soedel W. 1991 “Comparison of Hypotrochoidal and Epitrochoidal Gerotors” Trans. ASME, Journal of Mechanical Design June 113 2 133 141
- Beard J.E. Yannitell D.W. Pennock G.R. 1992a “The Effects of the Generating Pin Size and Placement on the Curvature and Displacement of Epitrochoidal Gerotors” Mechanism and Machine Theory Pergamon Press 27 4 373 389
- Beard J.E. Pennock G.R. 1992b “Calculation of the Displacement of a Wankel Rotary Compressor” Proc. of the 11th International Compressor Engineering Conference Purdue University West Lafayette, Indiana July 14 17 1 11 19
- Byrd P.F. Friedman M.D. 1954 Handbook of Elliptic Integrals for Engineers and Physicists Springer-Verlag, Berlin 8
- Chapra S.C. Canale R.P. 1988 Numerical Methods for Engineers Second Chapter 15, Sections 15.1 and 15.2 478 498 McGraw-Hill Book Company, Inc. New York
- Colbourne J.R. 1974 “The Geometry of Trochoidal Envelopes and Their Application in Rotary Pumps” Mechanism and Machine Theory Pergamon Press 9 3/4 421 435
- Colbourne J.R. 1975 “Gear Shape and Theoretical Flow Rate in Internal Gear Pumps” Trans, of Canadian Society of Mechanical Engineering 3 4 215 223
- Hall A.S. Jr. 1968 “Pin Gearing” ASME Paper 68-MECH-58, Proc. of ASME Mechanisms Conference Atlanta, Georgia October 5 9
- Leemhius R.S. Soedel W. 1978 “Vector Loop Analysis of Wankel Compressors and Engines” ASME Paper 78-DET-78
- Sadler JP. Nelle D.E. 1979 “Design Analysis of an Epicyclic Rotary Pump Mechanism” Trans, of ASME, Journal of Mechanical Design January 101 1 99 107
- Schell C.P. 1969 “Define the Geometry of the Inner and Outer Tooth Contours of a Gear Type Oil Pump” General Motors Engineering Journal July August September 1969 53 54
- Wankel F. 1965 Rotary Piston Engines , translated by Ansdale R.F. Iliffe Books, Ltd. London
- Wydra L. 1986 “Development of Outer-Envelope Trochoidal Compressors” Proc. of the 8th International Compressor Engineering Conference Purdue University West Lafayette, Indiana July 16 19 1 282 291
- Yamamoto K. 1981 Rotary Engine Toyo Kogyo Co., Ltd. Japan