Abstract
Kinematics of a rotating object about a fixed axis is well described in science of classical mechanics. All fundamental publications and textbooks contain a mathematical model for an acceleration of a rotating object about a fixed axis that is used for computing of forces acting on an object. Practice of usage for computing an acceleration a rotating object did not show some claims to the known equation. Nevertheless, the detailed analysis of the mathematical model for kinematics of a rotation of an object with acceleration demonstrates its incorrectness. The value of the actual acceleration of the rotating object is less than computed by the known equation. This is reason that running mechanisms are operating without fails because the value of acting forces is bigger than actual one. It means, the component of mechanisms is stronger and heavier than necessary. This paper addresses an acceleration analysis of a rotating object about a fixed axis and presents the mathematical model for computing an acceleration that can be used in engineering.
Highlights
Machines and mechanisms running at a high-speed are considered by a kinematic analysis of their velocities and accelerations, and subsequently analyzed as a dynamic system in which forces due to accelerations are analyzed using the principles of kinetics [1-3]
Computing of the dynamic force that is a product of an acceleration and mass is important for the reliable work of a machine
Fundamental solution of acceleration analysis of a rotation object about an axis that represented in textbooks is not perfect and cannot give correct equations for computing radial and absolute accelerations
Summary
Machines and mechanisms running at a high-speed are considered by a kinematic analysis of their velocities and accelerations, and subsequently analyzed as a dynamic system in which forces due to accelerations are analyzed using the principles of kinetics [1-3]. Many fundamental methods and approaches exist to find accelerations in classical mechanisms that represented in the textbooks [4-6]. There are numerous publications that consider special cases of kinematics and dynamics of machinery [7-9]. The complex motions of the objects are considered by numerical methods if known analytic approaches cannot give correct solutions [10,11]. Science of classical mechanics enables solving all problems of kinematics and dynamics of machinery. Practice of machines and mechanisms demonstrate numerous conditions with increasing the regimes of their work. High velocities and forces acting on machines request high responsibility in computing of their parameters
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