IC engines dynamic problems

The aims of the course are to provide theoretical and practical study about dynamic behavior of the engine mechanism. The analysis of engine dynamics problems such as: balancing of inertia forces and their moments, crankshaft angular speed variations and crankshaft torsion vibrations require analytical approach, mathematical modelling of the phenomena and experimental testing in order to identify unknown parameters and verify analytical results.

The merger of theoretical knowledge of mechanics, basics of strength of constructions and machine elements and its applications on specific problems of engine dynamics. Training students for mathematical modeling of engine mechanisms dynamic as well as for experimental testing of phenomena originating from engine dynamics: crankshaft angular speed variations and crankshaft torsion vibrations.

1. Dynamic equations of engine crankshaft motion. Mass moment of inertia of crank mechanism; variability of mass moment of inertia and its influence on crankshaft motion. Torques influencing crankshaft motion: gas force torques; inertia forces torques; friction torques; external load torques. Methods of crankshaft rotational speed variability reduction. Possibilities of engine working process diagnostics based on the measurement of crankshaft rotational speed variability. 2. Engine crank mechanism as torsional vibrations system. Equivalent torsional system; reduction of system elements masses and lengths; degrees of freedom; modes and frequencies of free torsional vibrations. Determination of the free vibrations frequencies based on Holzer method. Forced torsional vibrations; harmonic analysis of forcing torques; system resistances and damping; main harmonics of forcing torque, resonance and critical engines rotational speeds. Technical possibilities of torsional vibration damping; torsional vibration dampers. Evaluation of amplitudes and stresses of resonant torsional vibrations.

1.Evaluation of variable mass moment of inertia of engine crank mechanism; practical examples. 2.Gas, inertia and friction forces torques evaluation. Crankshaft rotational speed evaluation. 3. Experimental measurements of engine angular speed. Possibilities of experimental errors evaluation and their elimination. 4. Connections between angular speed variations and engine working process and the possibilities of diagnostics based on angular speed measurements. 5. Practical examples of engine crank mechanism equivalent torsional system evaluation (reduction of system masses and lengths). Evaluating of free torsional vibrations frequencies. 6. Forcing torques and their main harmonics evaluation. Engine critical rpm evaluation. 7. Experimental measurements of engine crankshaft torsional vibrations.

No prerequisites required.

1. M.C. Živković: Internal combustion engines, part 2. Engine design 1, Kinematics and dynamics of piston mechanism. Faculty of Mech. Eng., Belgrade, 1983. (in Serbian) 2. J.P Den Hartog: Mechanical Vibrations, New York Toronto London McGROW-HILL Book Company, 1956. 3. M.Tomić: Engine design 1-Handouts, available in PDF format in IC engines department. (in Serbian) 4.Test bench for engine testing; angular encoders for front and rear crankshaft end. Computer acquisition system for high speed measurements; system of pressure traducers and amplifiers for in-cylinder pressure recordings.

Total assigned hours: 65

New material: 30
Elaboration and examples (recapitulation): 20

Auditory exercises: 0
Laboratory exercises: 0
Calculation tasks: 0
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Review and grading of calculation tasks: 10
Review and grading of lab reports: 0
Review and grading of seminar papers: 5
Review and grading of the project: 0
Test: 0
Test: 0
Final exam: 0

Activity during lectures: 0
Test/test: 0
Laboratory practice: 50
Calculation tasks: 0
Seminar paper: 20
Project: 0
Final exam: 30
Requirement for taking the exam (required number of points): 60

M.C. Živković: Internal combustion engines, part 2. Engine design 1, Kinematics and dynamics of piston mechanism. Faculty of Mech. Eng., Belgrade, 1983. (in Serbian); H. Maaß and H. Klier,Kräfte, Momente und deren Ausgleich in der Verbrennungskraftmaschine. Wien: Springer, 1981.; H. Maaß and H. Klier:Theorie der Triebwerksschwingungen der Verbrennungskraftmaschine, Springer, 1985.; H. Maaß and H. Klier:Torsionsschwingungen in der Verbrennungskraftmaschine, Springer, 1985.; A. S. Rangwala, Reciprocating Machinery Dynamics. New Age International, Jan. 2006.