Gyroscopic Torques Acting on Crushing Mill

Abstract

Gyroscopic effects manifest at numerous rotating objects in engineering. Correct computing of and gyroscopic properties enables for the functioning of the gyroscopic devices in engineering. Since the Industrial Revolution published many gyroscope theories as well as many approaches and mathematical solutions that describe the gyroscope properties [1-4]. Numerous publications described the gyroscope effects and applications in engineering [5,6]. All of them describe gyroscope properties only in terms of the law of conservation of energy and the angular momentum. Nevertheless, the nature of gyroscope effects is more complex and known theories do not match the practice of gyroscopic devices [7-9]. Therefore, researchers continue to find true mathematical models of gyroscopic effects [10-14]. New research in the area of the gyroscope theory gives the new mathematical models for inertial forces acting on a gyroscope [15,16]. These publications demonstrate that on rotating objects act the several inertial forces of their mass-elements that express the resistance and precession torques. The centrifugal and Coriolis forces of the rotating masselements result in the resistance torques. The common inertial forces and the change in the angular momentum result in the precession torques. Table 1 represents the equations of the inertial torques acting on rotating objects. The action of the new inertial and external torques of the rotating objects should be considered for the mathematical modeling of the work of mechanism in engineering (Table 1).