Analysis of the balance of the crank-slider drive mechanism of the cutting apparatus by the method of principal point vectors

Abstract

BACKGROUND: During the motion of the crank-slider drive mechanism of the cutting apparatus of a mounted mower, various points of its links move with acceleration, leading to arise of inertial forces, which cause additional loads in kinematic pairs, significantly affecting the strength of all structural elements. The effective dynamic load can be reduced by balancing inertial forces and moments, which is achieved through optimal placement and selection of the masses of the corresponding counterweights.

AIM: In the special technical literature, balancing of mechanisms using the method of principal point vectors is not widely used due to demand of appropriate mathematical models of lever mechanisms based on vector analysis for the effective application of this method. The combined use of this method with the mathematical model of the crank-slider mechanism presented in the work, based on the use of vector analysis, opens up new research opportunities in this direction.

METHODS: A mathematical model of the crank-slider drive mechanism of the cutting apparatus, based on the use of vector analysis, which has been successfully used by the author for a long time in the design of various lever mechanisms, is presented. The proposed vector analysis method is based on the coordinate transformation method.

RESULTS: The presented mathematical model of the crank-slider drive mechanism of the cutting apparatus made it possible to describe the kinematics of all its hardpoints, to determine the motion path of the vector of the general center of mass and its acceleration. Using the principal point vector method, an analysis of the balance of the studied mechanism was carried out, and the parameters of the counterweights (mass and mount arms) on the extension of the links were selected, helping to ensure complete static balancing and three cases of partial balancing of the mechanism. In addition, various graphical dependencies were obtained.

CONCLUSION: The use of the method of principal point vectors together with the developed mathematical model of the crank-slider drive mechanism of the cutting apparatus, based on the use of vector analysis, made it possible to analyze the balance of the studied mechanism, as well as to carry out a complete static balancing and three cases of its partial static balancing.

Keywords

crank-slider mechanism / cutting apparatus / vector analysis / balancing / counterweight / center of mass / principal point vector method

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