scholarly journals The Mathematical Model for the Tippe Top Inversion

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
R. Usubamatov ◽  
M. Bergander ◽  
S. Kapayeva
Keyword(s):  
Classical Mechanics ◽  
Support Surface ◽  
Gyroscopic Effect ◽  
Complex Design ◽  
Tippe Top ◽  
Angular Velocities ◽  
Gyroscopic Effects ◽  
The Mathematical Model ◽  
Spinning Disc ◽  
Rotating Objects

The dynamics of rotating objects is an area of classical mechanics that has many unsolved problems. Among these problems are the gyroscopic effects manifested by the spinning objects of different forms. One of them is the Tippe top designed as the truncated sphere which is fitted with a short, cylindrical rod for rotation. The unexplainable gyroscopic effect of the Tippe top is manifested by its inversion towards the support surface. Researchers tried to describe this gyroscopic effect for two centuries, but all modelings were on the level of assumptions. It is natural because the Tippe top has a more complex design than the simple spinning disc, which gyroscopic effects did not have an analytical solution until recent time. The latest research, in the area of gyroscopic effects, reveals the action of the system of several interrelated inertial torques on any spinning object. The gyroscopic inertial torques are generated by their rotating mass. These inertial torques and the variable ratio of the angular velocities of the spinning object around axes of rotations constitute the fundamental principles of gyroscope theory. These physical principles of dynamics of rotating objects enable to description and compute of any gyroscopic effects and also the Tippe top inversion.

Study on Ultra-Precision Ball Surface Floating Polishing Kinematics Mechanism

2006 ◽  
Vol 532-533 ◽  
pp. 109-112
Author(s):  
Xun Lv ◽  
Ju Long Yuan ◽  
Dong Hui Wen ◽  
Qian Fa Deng ◽  
Fei Yan Lou
Keyword(s):  
Chemical Conversion ◽  
Processing Parameters ◽  
Precision Machining ◽  
High Tech ◽  
National Defense ◽  
Ball Surface ◽  
Angular Velocities ◽  
Ultra Precision ◽  
Relationship Of ◽  
The Mathematical Model

The high precision balls are requested in national defense, astronautics and high-tech commercial domain urgently. Conventional precision machining methods are sensitive to uniformity of abrasives and machining environment. After precision machining, there are easily to produce thick damaged layer on the ball surface because of machining stress and chemical conversion. On the basis of the floating polishing mechanism, a new scatheless ultra-precision polishing method of ball surface can solve the problems of abrasives uniformity effectively and damaged layer. In order to ensure that the new polishing method polishes ball surface equally, the appropriate angular velocities of the ball should be selected. This paper sets up the mathematical model about the motion of ball. By analyzing and simulating the relationship of the angular velocities, the best processing parameters are acquired.

scholarly journals Motion Simulation for Triangular-Shaped Autonomous Underwater Vehicle (TAUV) with Controllable Rudder

2021 ◽  
Vol 2107 (1) ◽  
pp. 012046
Author(s):  
I Y Amran ◽  
K Isa
Keyword(s):  
Mathematical Model ◽  
Autonomous Underwater Vehicle ◽  
Research Work ◽  
Underwater Vehicle ◽  
Open Loop ◽  
Vehicle Speed ◽  
Motion Simulation ◽  
Loop Control ◽  
Angular Velocities ◽  
The Mathematical Model

Abstract The dynamic model and motion simulation for a Triangular-Shaped Autonomous Underwater Vehicle (TAUV) with independently controlled rudders are described in this paper. The TAUV is designed for biofouling cleaning in aquaculture cage fishnet. It is buoyant underwater and moves by controlling two thrusters. Hence, in this research work, the authors designed a TAUV that is propelled by two thrusters and maneuvered by using an independently controllable rudder. This paper discussed the development of a mathematical model for the TAUV and its dynamic characteristics. The mathematical model was simulated by using Matlab and Simulink to analyze the TAUV’s motion based on open-loop control of different rudder angles. The position, linear and angular velocities, angle of attack, and underwater vehicle speed are all demonstrated in the findings.

Study on Gyroscopic Effect of Magnetic Flywheel Rotor

2011 ◽  
Vol 130-134 ◽  
pp. 970-975
Author(s):  
Xiang Long Wen ◽  
Cao Cao
Keyword(s):  
Feedback Control ◽  
High Speed ◽  
System Stability ◽  
Rotor Speed ◽  
Gyroscopic Effect ◽  
Pd Control ◽  
The Stability ◽  
Gyroscopic Effects ◽  
Zero Points ◽  
Flywheel Rotor

In the high-speed, gyroscopic effects of the flywheel rotor greatly influence the rotor stability. The pole-zero points move to right of s-plane and the damping terms of the pole points become smaller. The stability of the system will get worse with the increasing of rotor speed when the traditional decentralized PD controller is used only. In the paper, a cross-feedback control with decentralized PD control is used for compensating gyroscopic effect. The simulation results show that the system stability is better using the cross-feedback control with decentralized PD control than using the traditional decentralized PD control.

Friction-Induced Vibration in Lead Screw Systems: Mathematical Modeling and Experimental Studies

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
O. Vahid ◽  
N. Eslaminasab ◽  
M. F. Golnaraghi
Keyword(s):  
Experimental Studies ◽  
Lead Screw ◽  
Axial Forces ◽  
Angular Velocities ◽  
Regions Of Stability ◽  
Identification Approach ◽  
Simulation Results ◽  
The Mathematical Model ◽  
Steady State Amplitude ◽  
Friction Induced Vibration

Lead screw mechanisms are used to convert rotary to linear motion. The velocity-dependent coefficient of friction at the contact between lead screw and nut threads can lead to self-excited vibrations, which may result in excessive noise generated by the system. In this paper, based on a practical example of a powered automotive seat adjuster, the nonlinear dynamics of lead screw systems is studied. A test setup is developed to perform experiments on the horizontal motion drive. The experimental results are used in a novel two-step identification approach to estimate friction, damping, and stiffness parameters of the system. The identified parameters together with other known system parameters are used in the numerical simulations. The accuracy of the mathematical model is validated by comparing numerical simulation results with actual measurements in cases where limit cycles are developed. Using simulation results for a range of lead screw angular velocities and axial forces, regions of stability were found. Also, the effects of damping and stiffness parameters on the steady-state amplitude of vibration were investigated.

The Second Order Optimum Synthesis of a Compound Mechanism With Flexible Member

1992 ◽  
Author(s):  
Caifang Meng ◽  
Zuo Dai ◽  
Jianzhong Cha
Keyword(s):  
Mathematical Model ◽  
Second Order ◽  
Software Environment ◽  
Intelligent Optimization ◽  
Optimization Software ◽  
First Order ◽  
Optimum Synthesis ◽  
Angular Velocities ◽  
The Mathematical Model ◽  
Flexible Member

Abstract An optimum synthesis of a compound mechanism with flexible member (CMFM) is reported in this paper. First, the concepts of the first order optimum synthesis (FOOS) and the second order optimum synthesis (SOOS) are given. Then, the SOOS for the CMFM in a complete period and a half of period are carried out based on the mathematical model established for the SOOS of the CMFM. The results of the SOOS are obtained through the IIO software, an integrated intelligent optimization software environment, and the differences between specified and generated angular velocities are analyzed.

Herbie: Demonstration of Gyroscopic Effects by Means of a RC Vehicle

2011 ◽  
Author(s):  
Robert Huber ◽  
Jan Clauberg ◽  
Heinz Ulbrich
Keyword(s):  
Angular Momentum ◽  
High Speed ◽  
Time Derivative ◽  
Classical Mechanics ◽  
Mechanical Systems ◽  
The Body ◽  
Basic Principles ◽  
Isaac Newton ◽  
Leonhard Euler ◽  
Gyroscopic Effects

Classical mechanics is mainly based on two mechanical principles, the principle of linear momentum (Isaac Newton) and the principle of angular momentum (Leonhard Euler). The principle of angular momentum implies that the time derivative of the angular momentum equals the sum of all torques, acting on the body. Concerning all types of education it is particularly important that theoretical basic principles are profoundly understood. This often enables to understand difficult mechanical systems by drawing parallels between complex mechanical systems and simple basic principles. One way to generate profound understanding of theoretical correlations is to use interesting experimental examples. In this paper, a teaching model is presented, which has the ability both to demonstrate the effects of the principle of angular momentum and to catch the attention of students. For this purpose, a remote-controlled model car was built carrying a high-speed gyroscope on its top. The gyroscope can cause that the car turns over to the inside of a turn against the centrifugal force. Even more, it is possible to drive in a circle on the inner tires of the RC vehicle.

scholarly journals Study on Design of Non-Circular Gears for Speed Control of the Squid Belly Opening and Gutting Machine (SBOGM)

2021 ◽  
Vol 11 (7) ◽  
pp. 3268
Author(s):  
Hyo-Seong Jang ◽  
Chang-Hyun Lee ◽  
Gun-Young Park ◽  
Chul Kim
Keyword(s):  
Angular Velocity ◽  
Velocity Ratio ◽  
Operating Conditions ◽  
Structural Safety ◽  
Spur Gears ◽  
Operating Environments ◽  
Complex Design ◽  
Angular Velocities ◽  
Rotational Motions ◽  
Precise Expression

Non-circular gears can maintain rotational motions of general gears and implement all varying rotational motions of the cam. They adjust the angular velocity of driven gear according to operating conditions and make precise changes in angular motion. The design of non-circular gears has not been sufficiently studied because of their particularity and complex design methods unlike spur gears. In the gutting section of the Squid Belly Opening and Gutting Machine (SBOGM), spur gears generate rotational impact due to constant angular velocities, causing noise and equipment damage; so, efficiency should be improved by varying sectional angular velocity. Therefore, we derived pitch curves by selecting angular velocity ratio considering operating environments, and the tooth profile was designed by calculating module for each section according to radius through theorical analysis for precise expression of angular velocity ratio. To confirm reliability of design, angular velocity ratio and structural safety of designed non-circular gears were verified using, commercial software, ‘DAFUL 2020 R1′.

scholarly journals MATHEMATICAL MODEL FOR SOLVING THE NAVIGATION PROBLEM AND ANGULAR ORIENTATION SPACECRAFT

2019 ◽  
Vol 27 (4) ◽  
pp. 101-108
Author(s):  
Ilya Andreevich Sidorov ◽  
Alexander Alekseevich Manoilenko
Keyword(s):  
Mathematical Model ◽  
Moving Average ◽  
Center Of Mass ◽  
Exponential Smoothing ◽  
Infinite Impulse Response ◽  
Navigation Systems ◽  
Angular Orientation ◽  
Magnetometer Data ◽  
Angular Velocities ◽  
The Mathematical Model

Currently, there is an increased interest in the creation of strapdown inertial navigation systems (SINS), which make up the information core of modern airborne systems for the orientation and navigation of spacecraft (SC). An urgent problem arises, which is associated with the development of high-precision algorithms for estimating and filtering data from the sensors of the SC  motion parameters, the mathematical model of the SINS, calculating its errors and analyzing the effect of errors on the characteristics of the navigation system and orientation of the SC. A mathematical model is proposed for solving the problem of navigation and angular orientation of a small SC equipped with electromagnetic control elements, taking into account the filtering of “noisy” magnetometer data. The requirements are set for the accuracy of the angular orientation and stabilization of the SC in the mode of maintaining the triaxial orientation of the SC in the orbital coordinate system (OCS) and for the duration of the damping mode of the angular velocities obtained by the SC during separation from the launch vehicle (LV), and the mode of the initial construction of the triaxial orientation of the SC in OCS. The mathematical model includes: a model of the motion of the center of mass of the SC in the osculating elements of the orbit with specified parameters, a model of the angular motion of the SC around the center of mass, a model of the Earth’s magnetic field (EMF) and a model of filtering magnetometer data. As an arithm for filtering data from a magnetometer on the components of the magnetic induction vector of the EMF, a one-parameter algorithm of exponential smoothing (exponential moving average) is used, which belongs to the class of first-order filters with an infinite impulse response. The results of numerical simulation of  the dynamic processes of navigation and the angular orientation of the SC after separation from the LV taking into account the filtering of magnetometer data by the method of exponential smoothing using mathematical models are presented, and the accuracy of the angular orientation and stabilization of the SC is estimated.

scholarly journals Optimalization of Design Parameters of Experimental Installation Concerning Preparation of Liquid Feed Mixtures

Processes ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 2104
Author(s):  
Pavel Solonscikov ◽  
Jan Barwicki ◽  
Peter Savinyh ◽  
Marek Gaworski
Keyword(s):  
Initial Conditions ◽  
Experimental Studies ◽  
Classical Mechanics ◽  
Electrical Energy ◽  
Design Parameters ◽  
Regression Equations ◽  
Liquid Feed ◽  
Main Factors ◽  
The Mathematical Model ◽  
Theoretical Mechanics

The article describes the initial conditions for the development of universal mechanization means for the process of mixing dry and liquid components. The essence of the method is to study the motion of a particle with different constructive and physical properties of the medium. The mathematical model of particle motion is based on theoretical mechanics and hydraulics. In this case, the main purpose of the study is to find the optimal design parameters for the installation. At the beginning, a theoretical analysis of the installation was carried out using the methods of classical mechanics and hydraulics. Experimental studies were carried out in several stages. At the beginning, one-factor experiments were conducted, followed by allocating the main factors and determining their interaction. Then, using the methods of planning the experiment, we obtained the regression equations and further optimized the parameters to summarize the main findings of the article. Modern installations should have versatility in any technological line; for example, an installation is presented that can not only mix, but further transport the mixture like a conventional pump, while providing a dosing device that is necessary for the feeding of dry components. Theoretical studies have been carried out in which the design of the impeller is substantiated at various speeds. Experimental studies to determine the design parameters of the installation are in continuous operation. The degree of homogeneity was Θ = 74%, with β2 = 80 … 100° and βst = 65 … 102°, while the value of the consumption of electrical energy is equal to Eel = 0.265 … 0.28 kWh/t.

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