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Research Papers

Modeling the Inertial Torque Imbalance Within an Internal Combustion Engine: Quantifying the Equivalent Mass Approximation

[+] Author and Article Information
Noah D. Manring

Mechanical and Aerospace Engineering,
University of Missouri,
Columbia, MO 65211
e-mail: ManringN@missouri.edu

Muslim Ali

Mechanical and Aerospace Engineering,
University of Missouri,
Columbia, MO 65211
e-mail: mma26b@mail.missouri.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received January 10, 2017; final manuscript received October 31, 2017; published online March 28, 2018. Assoc. Editor: Douglas Bristow.

J. Dyn. Sys., Meas., Control 140(7), 071018 (Mar 28, 2018) (7 pages) Paper No: DS-17-1018; doi: 10.1115/1.4039282 History: Received January 10, 2017; Revised October 31, 2017

The objectives of this research are to explore the inertial-torque characteristics of an inline, internal combustion engine with connecting-rod joints that are evenly spaced about the centerline of the crankshaft, and to evaluate the goodness of a mass approximation that is customarily used in machine design textbooks. In this research, the number of pistons within the internal combustion engine is varied from 1 to 8. In order to generalize the results, the inertial-torque equations are nondimensionalized and shown to depend upon only four nondimensional groups, all related to the mass and geometry properties of the connecting rod. As shown in this research, the inertial-torque imbalance is greatest for an engine with two pistons, and that a dramatic reduction in the torque imbalance may be obtained for engine designs that use four or more pistons. It is also shown in this paper that the customary mass approximations for the connecting rod may be used to simplify the analysis for all engine designs without a significant loss of modeling accuracy.

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References

Norton, R. L. , 2012, Design of Machinery: An Introduction to the Synthesis and Analysis of Mechanisms and Machines, 5th ed., McGraw-Hill, New York.
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Arakelian, V. , and Briot, S. , 2010, “ Simultaneous Inertia Force/Moment Balancing and Torque Compensation of Slider-Crank Mechanisms,” Mech. Res. Commun., 37(2), pp. 265–269. [CrossRef]
Bagci, C. , 1995, “ A Simplified Approach for Balancing of Multi-Cylinder Engines,” 13th International Modal Analysis Conference, Nashville, TN, Feb. 13–16, pp. 879–884. http://semimac.org/wp-content/uploads/2015/12/sem.org-IMAC-XIII-13th-13-23-5-A-Simplified-Approach-Balancing-Multi-cylinder-Engines.pdf

Figures

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Fig. 1

A schematic of an inline, internal combustion engine using four pistons

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Fig. 2

A schematic of a single piston within the inline, internal combustion engine

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Fig. 3

Free-body diagrams for each linkage in the slider–crank mechanism

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Fig. 4

The traditional mass approximation that is made for the connecting rod

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Fig. 5

Nondimensional torque on the crank for one revolution of a single-piston engine (scales match Fig. 7)

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Fig. 6

Fast Fourier transform of the nondimensional torque on the crank of a single-piston engine (scales match Fig. 8)

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Fig. 7

Nondimensional torque on the crank for one revolution of a multiple-piston engine (scales match Fig. 5)

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Fig. 8

Fast Fourier transform of the nondimensional torque on the crank of a multiple-piston engine (scales match Fig. 6)

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Fig. 9

R2 values for the approximate calculation of the inertial torque imbalance, i.e., a statistical comparison for Eqs. (15) and (20)

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