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TECHNICAL PAPERS: Internal Combustion Engines

Fully Coupled Rigid Internal Combustion Engine Dynamics and Vibration—Part I: Model Development

[+] Author and Article Information
D. M. W. Hoffman, D. R. Dowling

Department of Mechanical Engineering, The University of Michigan, Ann Arbor, MI 48109-2121

J. Eng. Gas Turbines Power 123(3), 677-684 (Jan 01, 2001) (8 pages) doi:10.1115/1.1370399 History: Received July 01, 2000; Revised January 01, 2001
Copyright © 2001 by ASME
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Figures

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Schematic diagram of the engine dynamics and vibration modeling. Models are commonly divided into two pieces: one for moving internal components and one for engine block deflections. The fully coupled model (FCM) captures complete coupling between these two model pieces; the one-way coupled model (OWCM) only includes coupling from the piston-rod-crankshaft model to the engine block deflection model.
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Engine mount forces versus frequency for the fully coupled model (FCM) six-cylinder fired-engine running at an average crankshaft rotational speed of 1200 rpm and using measured cylinder-to-cylinder variations without (○) and with (×) a two percent increase in the mass of piston No. 1. Piston mismatch has a dominant effect on the vertical response (z-direction) on the front mount at first order (20 Hz) with a smaller effect at second order (40 Hz). Force magnitudes are only shown at half and whole-order frequencies.
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Schematic showing the seven-degree-of-freedom fully coupled rigid-engine dynamics and vibration model and its coordinates. A single-cylinder (cylinder number n) is shown. Engine block deflections are described using three translations and three rotations. The rotational angle of the crankshaft is the final degree-of-freedom. The dark blocks denote engine mounts (resilient supports). Each resilient support is represented by three orthogonally placed linear springs and viscous dampers.
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One-way coupled model (OWCM) and fully coupled model (FCM) results for a freely spinning (Tload=0 and Fcn=0) single-cylinder engine showing the instantaneous engine crankshaft rotational speed versus time. The FCM exhibits parasitic energy losses to engine mount dissipation and slows down when compared to the OWCM.
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One-way coupled model (OWCM) and fully coupled model (FCM) freely spinning engine energy balance for a single-cylinder engine with and without engine mount damping. The top line shows the damped OWCM summed energy increasing with time. The dotted line shows the undamped FCM mechanical energy constant with time. The thinnest line overlying the dotted line shows the damped FCM summed energy constant with time. The next line down shows the damped FCM mechanical energy decreasing with time, and the thickest solid line shows the damped FCM dissipated energy increasing with time. The damped FCM summed energy is simply the sum of the mechanical energy and the dissipated energy.
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Freely spinning single-cylinder engine mount forces versus crankshaft rotation at an average crankshaft rotational speed of 1200 rpm. The thin solid line is the fully coupled model (FCM) prediction, and the darker solid line is the one-way coupled model (OWCM) prediction. The differences between the model predictions are not only in first and second-order magnitudes but also in phasing.
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Running six-cylinder engine mount force magnitudes versus frequency from the fully coupled model (FCM). The engine is running at an average crankshaft rotational speed of 2100 rpm. The circles (○) represent results with measured cylinder-to-cylinder variations and the crosses (×) are without such variations. Here, half-order frequencies starting at 17.5 Hz are excited by cylinder-to-cylinder variations along with the third-order pulses of the combustion pressure. Force magnitudes are only shown at half and whole-order frequencies.

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