Inertial forces acting on a gyroscope

Usubamatov, Ryspek

doi:10.1007/s12206-017-1211-0

Cited by 36 publications

(54 citation statements)

References 9 publications

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“…Substituting defined parameters (Eqs. (4) - (6)) and equations of the torques (Table 1) into Eqs. (1) and (2) and transformation yields the following system of differential equations:…”

Section: Methodsmentioning

confidence: 99%

“…Equations of inertial torques are represented in Table 1. 6 Table 1 contains the following symbols and components of the equations that marked by subscript signs indicating the axis of action: 2 2 J m R = is the rotor's mass moment of inertia around the spinning axle; m is the mass of the rotor; R is the external radius of the rotor; i ω is the angular velocity of a rotor around axis i and ω is the angular velocity of a spinning rotor; T r.x is the resistance torque acting around axis ox, T py is the precession torque acting around axis oy;T ct.i , T in.i, T cr.i and T am.i is the torque acting around axis i that generated by the centrifugal, common inertial forces, Coriolisforces and the angular momentum respectively. This work presents the mathematical model for the free motion of the tilted rolling disc on the flat surface under the action of the eight inertial torques around two axes.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of motion for a rolling disc on the flat surface

subamatov¹

2018

IRATJ

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Nomenclature m -Mass of a disc g -Gravity acceleration i -Index for axis ox or oy J -Mass moment of inertia of a disc J i -Mass moment of inertia of a disc around axis i l -Radius of the disc rolling along the curvilinear path R -Radius of a disc T -Load torque T am.i, T cti, T cr.i, T in.i -Torque generated by the change in the angular momentum, centrifugal, Coriolis and common inertial forces respectively, and acting around axis i T r.i, T pi -Resistance and precession torque respectively acting around axis i t -Time γ -Angle of inclination of a disc η -Coefficient of correction ω -Angular velocity of a disc ω i -Angular velocity of precession around axis iAbstract Background: Recent investigations in gyroscopic effects have demonstrated that their origin has more complex nature that represented in known publications. Actually, on a gyroscope are acting simultaneously and interdependently eight inertial torques around two axes. This torques is generated by the centrifugal, common inertial and Coriolis forces as well as the change in the angular momentum of the masses of the spinning rotor. The action of these forces manifests in the form of the inertial resistance and precession torques of gyroscopic devices. New mathematical models for the inertial torques acting on the spinning rotor demonstrate fundamentally different approaches and results of solving the problems of gyroscopic devices.The tendency in contemporary engineering is expressed by the increasing of a velocity of rotating objectslike turbines, rotors, discs and othersthat lead to the proportional increase of the magnitudes of inertial forces forming their motions. This work considers a typical example for computing of the inertial torques acting on the free rolling disc, which can be a bicycle wheel, rims, hoops, discs, and similar designs that express the gyroscopiceffects.

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“…Substituting defined parameters (Eqs. (4) - (6)) and equations of the torques (Table 1) into Eqs. (1) and (2) and transformation yields the following system of differential equations:…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of motion for a rolling disc on the flat surface

subamatov¹

2018

IRATJ

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“…The precession torque is generated by the action of the common inertial forces (for simplicity inertial forces) of the gyroscope's mass elements and by the well-known torque that is generated by the change in the angular momentum of the spinning rotor. These resistance and precession torques act simultaneously and interdependently, and are strictly perpendicular to each other around their axes [23]. 1 contains the following symbols: J is the rotor's massmoment of inertia around the spinning axle; i ω is the angular velocity of precession of a spinning rotor around axis i and ω is the angular velocity of a spinning rotor.…”

Section: Methodsmentioning

confidence: 99%

“…All inertial forces generate the gyroscope's resistance and precession torques that are interrelated and occur at one time. The physics and mathematical models of these inertial torques are well described [21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Properties of Inertial Torques Acting on Gyroscopes

Usubamatov

2017

RAEJ

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The gyroscopic devices are primary arrangements for navigation and control systems that the contemporary aerospace, ships and other industries have been widely adopted. The main remarkable property of the gyroscope is represented in permanent maintaining the axis of a spinning rotor in a space. This gyroscope property is the result of action of the several internal inertial torques produced by the external load torque. Internal inertial torques of the gyroscope are generated by action of the components of centrifugal, common inertial and Coriolis forces as well as the change in the angular momentum. These inertial forces are produced by rotating mass elements and the center mass of the spinning rotor. The action of all gyroscope's internal torques are interrelated simultaneously around gyroscope axes, and are manifested the resistance and precession torques. The designers of gyroscopic devices can compute their acting forces and motions based on equations of the internal torques. However, gyroscope's inertial torques possess several properties, which correct usage enables getting correct results in computing of gyroscope parameters. This manuscript describes the properties of the inertial torques acting on a gyroscope that should be used for mathematical models of the gyroscope motions.

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“…Therefore, researchers continue to find true mathematical models of gyroscopic effects [10][11][12][13][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.…”

Section: Introductionmentioning

confidence: 99%

Gyroscopic Torques Acting on Crushing Mill

Usubamatov¹

2019

ARME

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Numerous mechanisms with rotating objects in engineering manifest gyroscopic effects, which mathematical models formulated on the law of kinetic energy conservation and the action of inertial torques. Known theories of gyroscopic effects are far from the practical result of the action inertial torques on the rotating objects. The new study demonstrates that the gyroscopic effects are the result of the simultaneous and interdependent action of the resistance and precession torques of rotating objects around different axes. The centrifugal and Coriolis forces are generated the first torques and the second one by the common inertial forces and the change in the angular momentum of the rotating mass of a spinning object. The principle of gyroscope effects has been applied in the crushing pendulum mills used for ore, seeds, etc., where the intense pressure is desired. The new principles of the action of internal and external torques on the crushing mill enable for the computing the actual forces that produce the work. This manuscript represents the mathematical model for the actual torques and power that manifest the crushing mill.

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Inertial forces acting on a gyroscope

Cited by 36 publications

References 9 publications

Analysis of motion for a rolling disc on the flat surface

Analysis of motion for a rolling disc on the flat surface

Properties of Inertial Torques Acting on Gyroscopes

Gyroscopic Torques Acting on Crushing Mill

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