In uniform circular motions, the blade’s mass moves with acceleration that generates the centrifugal forces (Fig. The equations of the inertial torques generated by the blades are defined by the following approach. Usubamatov, "Mathematical model for motions of gyroscope suspended from a flexible cord", Cogent Engineering, vol. The mathematical models for inertial torques generated by the mass of the propeller’s hub are the same as for the spinning disc [ 24 R. ![]() The mass moments of inertia for propellers with several blades are defined by the expression J p = nJ + J h, where J is the mass moments of inertia of the blade, n is the number of the blades, and J h is the mass moments of inertia of the hub. Schematic of the propeller design with two ( a), three ( b), four ( c) and six ( d) blades. The blades numbered as I, II, III, IV, V, and VI. The propeller blade’s centre mass m is located on the circle whose radius is r and the mass centre of the hub is m h. The action of inertial forces is considered on a propeller running with a constant angular velocity of ω in a counterclockwise direction when viewed from the tip of axis oz (Fig. The inertial forces acting on the propeller are generated by its centre mass of the hub and centre mass of the blades, whose locations and actions are different. The typical design of an aircraft propeller is represented by the several blades mounted on the cylindrical hub that can be considered as the spinning rotor. This work considers the action of the inertial torques on the aircraft’s propeller with the different number of blades.Ģ. New mathematical models for inertial torques give significant impact to the gyroscope theory and enable for describing all gyroscope properties. Sah, "Analysis of a Coriolis Acceleration", Journal of Advanced Science and Engineering Research, vol. Recent investigations of the physical principles of gyroscope motions demonstrating that the centrifugal, common inertial, Coriolis forces, and the change in the angular momentum manifest the action of gyroscope’s resistance and precession torques [ 22 R. However, the origin of gyroscope effects is more complex than those represented in the known theories. Ferrari, "Gyroscope’s Precession and the Principle of Equivalence", Ann. Kurosu, "Gyroscopic Force Measuring System", Transactions of SICE, pp. This is the reason that gyroscope theory still attracts researchers seeking to find answers on gyroscope challenges [ 20 K. Wum, "Error analysis and test study of fibre optic gyroscope north-finder", Proceedings of SPIE, vol. Physical Review Letters 64, APS Journal, Vol. McHugh, Gyroscope-weighing experiment with a null result. From this, researchers have spawned artificial terms, such as gyroscope effects and others that contradict the physics laws [ 18 J. ![]() Mathematical models for gyroscope properties in known publications do not match practical applications for gyroscopic devices. Nevertheless, the action of these inertial forces on gyroscopes is not presented by mathematical models. Yavrucuk, "Gimbal angle restricted control moment gyroscope clusters", Proceedings of 4th International Conference on Recent Advances in Space Technologies (RAST), pp. Butikov, "Inertial rotation of a rigid body", Eur. Some researchers intuitively pointed to the action on the spinning rotor of other inertial forces [ 14 E. Lee, "Vorticity, gyroscopic precession, and spin-curvature force", Phys. Jonsson, "Gyroscope precession in special and general relativity from basic principles", Am. However, all known manuscripts contain numerous assumptions, simplifications, as well as explaining the gyroscope effects in terms of the change in the angular momentum only [ 12 R.M. , 3rd edMcGraw-Hill Book Company: New York. Uicker, Theory of Machines and Mechanisms. There are many publications regarding gyroscope theory as well as many approaches and mathematical solutions that describe gyroscopic properties [ 10 J. , 12th edPrentice Hall, Pearson: Singapore. ![]() Hibbeler, Engineering Mechanics - Statics and Dynamics. All fundamental textbooks of classical mechanics have chapters that represent gyroscope theory [ 8 R.C. ![]() Numerous publications have been dedicated to computing of gyroscopic effects in engineering. The applied theory of gyroscope emerged mainly in the twentieth century due to increasing the angular velocities of the spinning components of the movable machines. Since those time brilliant, famous, outstanding, and ordinary scientists studied gyroscopic effects and published fundamental manuscripts that describe interesting gyroscope properties. Industrial Revolution involved scientists to pay the attention to the remarkable gyroscope property expressesed in permanent maintaining the axis of a spinning rotor in a space.
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