Accurate estimation of engine vibrations is essential in the design of new engines, engine mounts, and the vehicle frames to which they are attached. Mount force prediction has traditionally been simplified by assuming that the reciprocating dynamics of the engine can be decoupled from the three-dimensional motion of the block. The accuracy of the resulting one-way coupled models decreases as engine imbalance and cylinder-to-cylinder variations increase. Further, the form of the one-way coupled model must be assumed a priori, and there is no mechanism for generating an intermediate-complexity model if the one-way coupled model has insufficient fidelity. In this paper, a new dynamic system model decoupling algorithm is applied to a Detroit Diesel Series 60 in-line six-cylinder engine model to test one-way coupling assumptions and to automate generation of a proper model for mount force prediction. The algorithm, which identifies and removes unnecessary constraint equation terms, is reviewed with the aid of an illustrative example. A fully coupled, balanced rigid body model with no cylinder-to-cylinder variations is then constructed, from which $x$, $y$, and $z$ force components at the left-rear, right-rear, and front engine mounts are predicted. The decoupling algorithm is then applied to automatically generate a reduced model in which reciprocating dynamics and gross block motion are decoupled. The amplitudes of the varying components of the force time series are predicted to within 8%, with computation time reduced by 55%. The combustion pressure profile in one cylinder is then changed to represent a misfire that creates imbalance. The decoupled model generated by the algorithm is significantly more robust to imbalance than the traditional one-way coupled models in the literature; however, the vertical component of the front mount force is poorly predicted. Reapplication of the algorithm identifies constraint equation terms that must be reinstated. A new, nondecoupled model is generated that accurately predicts all mount components in the presence of the misfire, with computation time reduced by 39%. The algorithm can be easily reapplied, and a new model generated, whenever engine speed or individual cylinder parameters are changed.

1.
Norling
,
R. L.
, 1978, “
Continuous Time Simulation of Forces and Motion Within an Automotive Engine
,” Society of Automotive Engineers SAE Paper No. 780665, Warrendale, PA.
2.
Suh
,
C.-H.
, and
Smith
,
C. G.
, 1997, “
Dynamic Simulation of Engine-Mount Systems
,” Society of Automotive Engineers SAE Paper No. 971940, Warrendale, PA.
3.
Shaio
,
Y.-J.
,
Pan
,
C.-H.
, and
Moskwa
,
J. J.
, 1994, “
Advanced Dynamic Spark Ignition Engine Modeling for Diagnostics and Control
,”
Int. J. Veh. Des.
0143-3369,
15
, pp.
578
596
.
4.
Hoffman
,
D. M. W.
, and
Dowling
,
D. R.
, 2001, “
Fully Coupled Rigid Internal Combustion Engine Dynamics and Vibration—Part I: Model Development
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
123
, pp.
677
684
.
5.
Stein
,
J. L.
, and
Wilson
,
B. H.
, 1995, “
An Algorithm for Obtaining Proper Models of Distributed and Discrete Systems
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
117
(
4
), pp.
534
540
.
6.
Rideout
,
D. G.
,
Stein
,
J. L.
, and
Louca
,
L. S.
, 2004, “
System Partitioning and Physical-Domain Model Reduction Through Assessment of Bond Graph Junction Structure
,”
Proceedings of the IMAACA’04
, International Mediterranean Modeling Multiconference, Genoa, Italy.
7.
Rideout
,
D. G.
,
Stein
,
J. L.
, and
Louca
,
L. S.
, 2005, “
System Partitioning and Improved Bond Graph Model Reduction Using Junction Structure Power Flow
,”
Proceedings of the International Conference on Bond Graph Modeling ICBGM’05
, New Orleans, LA, Society for Computer Simulation, San Diego, CA, pp.
43
50
.
8.
Louca
,
L. S.
,
Stein
,
J. L.
,
Hulbert
,
G. M.
, and
Sprague
,
J.
, 1997, “
Proper Model Generation: An Energy-Based Methodology
,”
Proceedings of the International Conference on Bond Graph Modeling ICGBM’97
, Phoenix, AZ, Society for Computer Simulation, San Diego, CA.
9.
Karnopp
,
D. C.
,
Margolis
,
D. L.
, and
Rosenberg
,
R. C.
, 1990,
System Dynamics: A Unified Approach
,
Wiley
,
New York
.
10.
Tiernego
,
M. J.
, and
Bos
,
A. M.
, 1985, “
Modelling the Dynamics and Kinematics of Mechanical Systems With Multibond Graphs
,”
J. Franklin Inst.
0016-0032,
319
, pp.
37
50
.
11.
Rideout
,
D. G.
, 2004, “
System Partitioning and Physical-Domain Proper Modeling Through Assessment of Power-Conserving Model Structure
,” Ph.D. thesis, University of Michigan, Ann Arbor, MI.
12.
Hoffman
,
D. M. W.
, 1999, “
In-Line Internal Combustion Engine Dynamics and Vibration
,” Ph.D. thesis, University of Michigan, Ann Arbor, MI.
13.
Karnopp
,
D. C.
, and
Margolis
,
D. L.
, 1979, “
Analysis and Simulation of Planar Mechanism Systems Using Bond Graphs
,”
ASME J. Mech. Des.
0161-8458,
101
, pp.
187
191
.
14.
20SIM, Version 3.5, 2005, Controllab Products b. v., Enschede, Netherlands.
15.
Sendur
,
P.
,
Stein
,
J. L.
,
Peng
,
H.
, and
Louca
,
L. S.
, 2002, “
A Model Accuracy and Validation Algorithm
,”
Proceedings of the 2002 ASME International Mechanical Engineering Conference and Exhibition
, New Orleans, LA, American Society of Mechanical Engineers, New York, NY.
16.
Rideout
,
D. G.
, and
Stein
,
J. L.
, 2003, “
An Energy-Based Approach to Parameterizing Parasitic Elements for Eliminating Derivative Causality
,”
Proceedings of the International Conference on Bond Graph Modeling ICBGM’03
, Orlando, FL, Society for Computer Simulation, San Diego, CA, pp.
121
127
.