The Theory of Optimal Balancing of Mechanisms

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Abstract

This paper presents a general theory regarding the balancing of mechanisms. It starts with Stevenson’s theory [1], which proves that any mechanism can be dynamically perfectly balanced if there is a pair of counterweights that are eccentrically positioned in three reciprocating perpendicular axes, passing through the mass center of the body. The system of inertial forces are extended in Fourier series where only the first terms, the basic harmonics, are considered. The proposed goal is to stultify the effect of inertial forces and torques. This paper deals with a situation more appropriate to reality. In common cases there doesn’t exist the possibility of implementing counterweights in three perpendicular axes. In this situation only the minimization of inertial forces and torques remains as a possible solution. The method developed for this case is presented.

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  • [1] Stevensen E. N.: Balancing of Machines. In: ASME San Francisco California 72/52. 1972.

  • [2] Papp I. Máté M.: Transformarea generală a două sisteme ortogonale. In: Proceedings CDM 2005 ISBN-973-635-513-6. A IV-a conferinţă de dinamica maşinilor cu participare internaţională Braşov 28-30. mai 2005. Vol. II. 319–326.

  • [3] Papp I.: Optimization of Dynamical Balancing of Mechanisms According to Diminuation of Vibration Amplitude at a Given Point. In: International Conference in Mechanical Engineering Satu-Mare April 28-May 1 2005 285–287.

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