Inertia Torque Research Articles

Variable Mass Control and Parameter Identification of Spacecraft Orbit Refueling Process

A maintainable refueling vehicle is the future development direction of the space system. In the process of fuel filling, capture docking, and configuration transformation, the most significant factor that affects the attitude control of the system is the continuous or sudden change of the angular torque of the system. In this paper, we study the control system of the variable mass body in an on-orbit service in the process of configuration transformation. The large errors of torque of inertia may make the narrow sense TEA (torque equilibrium attitude) of the system deviate greatly from the earth-oriented attitude. In order to avoid the error caused by the partial linearization of the system model, the feedback linearization method of the nonlinear system is used to design the controller to realize the tracking of the narrow sense TEA in the process of configuration transformation. Different from the traditional attitude control method, in order to avoid the high cost of the control system caused by the change of system mass characteristics and the change of system angular torque, CMG (control moment gyroscope) angular torque is introduced into the controller. We design a joint controller of attitude control and angular torque management, which can effectively stabilize the system and reduce the angular torque saturation of the attitude control system during the on-orbit service.

Corrected Inertial Torques of Gyroscopic Effects

The published manuscripts in the area of gyroscope theory were presented mainly by the simplified approaches in which mathematical models contain many uncertainties. New research in machine dynamics opened breakthrough directions in gyroscopic effects of rotating objects that give the correct solutions. The pioneering work meets many problems when solving the scientific innovations that are accompanied by successes and omissions. New mathematical models for the gyroscopic inertial torques were derived with incorrect processing of the integral equations that give distorted results. The gyroscopic devices in engineering manifest gyroscopic effects as the action of the inertial torques which computing is crucial for mathematical describing of their motions. The corrected mathematical processing of the equations for the inertial torques acting in a gyroscope is presented in this manuscript.

Gyrotactic mechanism induced by fluid inertial torque for settling elongated microswimmers

Marine plankton are usually modeled as settling elongated micro-swimmers. For the first time, we consider the torque induced by fluid inertia on such swimmers, and we discover that they spontaneously swim in the direction opposite to gravity. We analyze the equilibrium orientation of swimmers in quiescent fluid and the mean orientation in turbulent flows using direct numerical simulations. Similar to well-known gyrotaxis mechanisms, the effect of fluid inertial torque can be quantified by an effective reorientation time scale. We show that the orientation of swimmers strongly depends on the reorientation time scale, and swimmers exhibit strong preferential alignment in upward direction when the time scale is of the same order of Kolmogorov time scale. Our findings suggest that the fluid inertial torque is a new mechanism of gyrotaxis that stabilizes the upward orientation of micro-swimmers such as plankton.

Identification of a Step-And-Brake Controller of a Human Based on Prediction of Capturability.

An explicit mathematical form of a human’s step-and-brake controller is identified through motion measurement of the human subject. The controller was originally designed for biped robots based on the reduced-order dynamics and the model predictive control scheme with the terminal capturability condition, and is compatible with both stand-still and stepping motions. The minimal number of parameters facilitates the identification from measured trajectories of the center of mass and the zero-moment point of the human subject. In spite of the minimality, the result only suited the human’s behaviors well with slight modifications of the model by taking direction-dependency of the natural falling speed and the inertial torque about the center of mass into account. Furthermore, the parameters are successfully identified even from the first half of motion sequence, which means that the proposed method is available in designing on-the-fly systems to evaluate balancing abilities of humans and to assist balances of humans in walking.

Stable Simultaneous Inertia and Disturbance Torque Identification for SPMSM Drive Systems Subject to Mismatched Rotor Flux Linkage

In surface-mounted permanent magnet synchronous motor (SPMSM) drives, the distinguished orthogonal-principle-based method is presently popular for handling simultaneous inertia and disturbance torque estimation due to its simplicity and ease of implementation. Nevertheless, it is facing challenges posed by the rotor flux-linkage mismatch, zero-derivative constraint, and operating-condition limitation. To cope with these issues, this article presents an alternative scheme, which explores a stable simultaneous inertia and disturbance torque estimation with the real-time flux-linkage correction. First, an Adaline-based estimator is developed to acquire the disturbance torque. With an input-adaptive learning rate designed by the Lyapunov theory, this estimator can prevent potential convergence failure. Then, an extended sliding-mode observer for inertia estimation is proposed regarding the inertia as a new system state. By using the identified disturbance torque to devise an adaptive feedback gain, this observer guarantees the asymptotic error convergence. Finally, to counteract the flux-linkage mismatch, a flux-linkage observer with a time-varying learning rate is constructed utilizing the Adaline technique. Moreover, it attains robust convergence and only has one to-be-adjusted parameter. The effectiveness of our scheme is validated by abundant simulations and real-time experiments.

Fixed-time neuroadaptive practical tracking control based on extended state/disturbance observer for a QUAV with external disturbances and time-varying parameters

This paper investigates the fixed-time neural network adaptive (FNNA) tracking control of a quadrotor unmanned aerial vehicle (QUAV) to achieve flight safety and high efficiency. By combining radial basis function neural network (RBFNN) with fixed time adaptive sliding mode algorithm, a novel radial basis function neural network adaptive law is proposed. In addition, an extended state/disturbance observer (ESDO) is proposed to solve the problem of unmeasurable state and external interference, which can obtain reliable state feedback and interference input. Unlike most other ESO applications, this paper does not set the uncertainty model and external disturbances as total disturbances. Instead, the external disturbances are observed by extending the states and the observed states are fed back to the controller to cancel the disturbances. In view of the time-varying resistance coefficient and inertia torque in the QUAV model, the neural network is introduced so that the controller does not need to consider these nonlinear uncertainties. Finally, a numerical example is given to verify the effectiveness of the coupled non-simplified QUAV model.

Corrected Internal Torques of Gyroscopic Effects

The dynamics of the rotating objects is the complex piece of the classical mechanics which example presented by gyroscopic effects. Researchers study gyroscope problems during the centuries and obtained not comforting analytical results. The physics of gyroscopic effects does not have an adequate description. The recent investigation finally solved the gyroscope problems in principle but some mathematical models for gyroscopic inertial torques contained mechanical errors. The corrected gyroscope theory opened breakthrough directions in the solutions to dynamics of rotating objects. This publication presents a summation of the gyroscope theory that gives a general presentation of its principal parts.

Physics and mathematical model for boomerang flight

The boomerang flight is presented in the known publications by the action of aerodynamic forces and gyroscopic precession torque. This solution does not give a true answer because gyroscopic effects are expressed by the action of the eight interrelated inertial torques generated by the rotating objects. The publications with numerical modeling do not describe the physics of the boomerang flight. Today, the solution of this problem is presented by the mathematical model with the action of the lift forces and inertial torques generated by the rotating boomerang. The boomerang flight is described by the methods of theories of aerodynamics and gyroscopic effects that express the kinetic energy of the boomerang motion and rotation. The mathematical model for the boomerang flight contains multifunctional and interrelated expressions of two theories, which manual solution is sophisticated, but solved by computer software without numerical modeling. The analytical solution for the boomerang flight describes its physics and presents a good example for the educational process of engineering mechanics and aerodynamics.

О моделировании нагрузки гребных электродвигателей ледоколов при проведении стендовых и виртуальных испытаний систем электродвижения

Object and purpose of research. This paper discusses ice loads on shaft-lines of icebreakers and ice-going ships as their propellers interact with ice. These loads are needed as inputs for development and fine-tuning of electric propulsion control systems, including those involving load test rigs, with the final purpose of ensuring reliable and safe operation of electric propulsion plants in ice navigation conditions. Materials and methods. This study is based on the publications about ice loads on shafting of electric propulsion plants. It analyses the terminology used in the papers on this subject. It also analyses the data on ice-induced shafting torques, as obtained from full-scale trials of Akademik Tryoshnikov ice-class research vessel. Main results. The paper describes typical cases of extreme ice loads on the propulsion system, with the input data characterizing these loads and needed, in particular, for numerical simulation of ice loads on shafting in order to fine-tune electric propulsion control system by means of computer-based simulations or laboratory tests. The paper shows the importance of considering the inertial elements of the shaft line for correct determination of limit loads. It also formulates the challenges that have to be solved in order to obtain efficient control systems for electric propulsion plants of icebreakers and ice-going ships. It determines the requirements to special full-scale trials needed to validate calculation methods for shafting loads. Conclusion. Electric propulsion systems of ice-going ships must have highly efficient control tools for the propulsion motor that would ensure its reliable and safe operation as propeller interacts with ice. Such a tool is quite hard to obtain because shafting loads are quite various and difficult to predict. One of the ways to improve an electric propulsion system is to build up a test rig with the load part simulating various scenarios of shafting loads as per the mathematical model specially developed for this purpose and validated by the accumulated database of full-scale ice loads on shaft lines. The paper also demonstrates that propulsion motor control system must properly take into account not only external loads but also inertial torques of shaft line, motor rotor and propeller with added water mass.

Revisiting the flight dynamics of take-off of a butterfly: experiments and CFD simulations for a cabbage white butterfly.

ABSTRACTWe conducted measurements of the taking-off motion of a butterfly (Pieris rapae) and numerical simulations using a computational model reflecting its motion. The computational butterfly model is composed of a thorax, an abdomen, and four wings (left and right wings with fore and hind parts), i.e. a six-link, rigid-body system. The present model is more sophisticated than any models that have ever been constructed in existing studies. In the butterfly model, the body trajectory and thoracic pitching angle can be calculated from the equations of motion, whereas the abdominal angle and wings’ joint angles are prescribed by the measured data. We calculated the flow field, aerodynamic force and torque generated by the butterfly model using the immersed boundary–lattice Boltzmann method. As a result, the butterfly generates the horizontal vortex ring and aerodynamic lift force during the downstroke, while it generates the vertical vortex ring and aerodynamic thrust force during the upstroke. The leg impulsion is essential in the upward motion of the taking-off butterfly rather than the aerodynamic lift force by the flapping wings. The inertial forces of the abdomen and wings are comparable in magnitude with the aerodynamic forces, but the net influence of the inertial forces on the position of the butterfly is not significant due to the offsetting of the body and wing inertia. The net aerodynamic and gravitational torques raise the thorax of the butterfly, and the net inertial torques suppress the rise of the thorax.

Corrected Mathematical Models for Motions of the Gyroscope with one Side Free Support

Abstract: The recent publications about gyroscope effects explained their physics and described them by mathematical models based on the action of forces and inertial torques of classical mechanics. This new analytical approach finally solved the old problem of the dynamic of rotating objects and showed their kinetic energy is the base of gyroscopic effects. Gyroscopic effects result from the action of the two sets of interrelated inertial torques acting about two axes. Each set contains torques generated by the centrifugal, Coriolis forces, and the change in the angular momentum. Detailed study of the inertial torque of the centrifugal force showed its expression derived with an error of mathematical processing. This error gives a less value for the angular velocity of the slow rotation of the gyroscope about one axis that cannot be measured. The angular velocity of the fast rotation of the gyroscope about the other axis is measured but remains of the same value that gives the expression of the torque with error. This manuscript presents the corrected mathematical model for the motion of the gyroscope suspended from the flexible cord.

Comment on 'Angles in the SI: a detailed proposal for solving the problem'

Abstract Paul Quincey makes a compelling argument for recognizing angle as a base quantity with the radian as the base unit. Solid angle is then a derived quantity with the steradian a coherent derived unit equal to one square radian. The author demonstrates how familiar equations of rotational motion appear to result from dimensionally consistent explicit-radian equations by 'setting the radian equal to one'—which he calls the radian convention. Quincey also claims, based (solely) on assumed analogies with translational motion, that for rotation, the so-called 'improved' units for torque, angular momentum and moment of inertia must be J/rad, J/(rad/s) and J/(rad/s)2, respectively, and that the conventional units (N m, kg m2 s-1 and kg m2) result from application of the radian convention to these quantities. However, based on fundamental physical principles, I show here that, although the radian convention may help in understanding a confusing notational change applied to angular displacement and its time derivatives when comparing explicit-radian equations to their equivalent familiar forms, it cannot be applied to torque, angular momentum or moment of inertia. The dimensionally correct SI units for these quantities are, respectively, the well-established angle-independent units: newton metre, kilogram metre-squared per second and kilogram metre-squared.

Reply to Comment on ‘Angles in the SI: a detailed proposal for solving the problem’

Abstract The Comment by B P Leonard [Metrologia, in press (2022)] primarily proposes that if angle is treated as a base quantity, with the radian as its base unit, it would be wrong to change the units for torque (from N m to J rad-1), angular momentum (from J s to J s rad-1) and moment of inertia (from kg m2 to kg m2 rad-2), as was proposed in the Letter being commented on [Quincey, Metrologia 58 053002 (2021)]. This Reply clarifies the situation by looking directly at the consequences of the two proposals. Apart from the comfort of retaining the familiar units for these quantities, the benefit of Leonard's proposal would be the preservation of a few favoured equations used in specific situations, while the general relationships between many physical quantities would need to change. The revised units proposed in the Letter would leave all the established general relationships unchanged, and are the best option for allowing the longstanding problem of angles being wrongly treated as numbers within the SI to be resolved. This Reply includes some historical context, which describes how Euler implicitly introduced the idea that “the radian is another name for the number one” into the mathematics used for rotating objects, at a time long before anyone had thought about unit systems.

Simulation of induction motor behavior under voltage sags using alternative transient program

The primary source of voltage sags is a short circuit fault in the power system. Three-phase fault can result in a more severe effect on the equipment. The voltage sags have affected significantly on performance degradation of the induction motor. The motor behaviors can be investigated in terms of rotation speed, torque, peak current, and recovery time during and after voltage sags. This study is to investigate induction motor behavior under voltage sags using the alternative transient program (ATP) draw software in simulation models. Distinct rated capacity, mechanical inertia, and loads torque (constant, linear, and variable) of the motor were used to investigate the motor’s behavior during and after sag end. Voltage sags resulted from three-phase fault at the certain locations in industrial power systems. The motor rotation speed decreases in slightly distinct during voltage sag but recovery times required to motors are longer for the large capacity motors. The large motors create the larger inrush current can reach more than five times its nominal. The motors with constant load toque subjected to voltage sag lead loss control in speed.

AN EFFICIENT NUMERICAL SCHEME FOR STATIC TORQUE PROFILING OF SWITCHED RELUCTANCE MACHINE WITH EXPERIMENTAL VALIDATIO

In AC and DC drives, the use of switched reluctance machine (SRM) is becoming popular as it has a few preferences over AC and DC drives in a simple and robust construction without brushes, low inertia, and high torque to weight ratio, without rotor windings, simple circuit power converter, etc. SRM is widely used in variable speed and servo drives. Because of the double saliency structure and the high nonlinearity of magnetic material, it is difficult to represent the flux-linkage and static torque characteristic of the SRM. This work promotes the use of an improved numerical integration scheme for the static characteristics of SRM. The static torque function that depends on the rotor position and the phase current of the flux linkage features family (for different rotor positions) is improved in the proposed work. Firstly, we use an experimental setup for the electromagnetic characteristic of SRM. Then, we use the improved scheme to develop an efficient mathematical model for static characteristics and finally simulate the static characteristic of SRM through MATLAB code. In the last step, we compare the performance of the proposed integrator model with an existing approach for better efficiency of the static characteristic of SRM with experimental validation.

Modal Analysis of Passive Engine Mount Assembly using Finite Element Analysis

Engine mounts play a vital role in reduction of noise and vibration. For an internal combustion engine, there exist two basic dynamic disturbances: a) the firing pulse due to the combustion of fuel in the cylinder and b) the inertia force and torque caused by the rotating and reciprocating parts. The firing pulses will cause a torque to act on the engine block about an axis parallel to the crank. The inertial forces are both parallel to the piston axis and perpendicular to the crank and piston axes. This dissertation describes the finite element approach for modal and static structural analysis of the engine mount used on an inline four-cylinder petrol engine. A 3D model of the mount was created with the help of Solid-Edge V19 software and the same was analysed for natural frequencies and total deformation using Ansys Workbench software. Further, torsional stiffness of the mount was obtained using finite element analysis and validated using experimental testing. Viscoelastic behaviour of rubber has also been discussed with the help of a Generalized Maxwell model (GMM). GMM was chosen after reviewing all the commonly used models. Later, an in-depth analysis of transmissibility was carried out using finite element analysis approach and a 6-DOF Mathematical model approach. Random vibration analysis was carried out and the resulting RMS accelerations were compared with the ISO-2631 standard.

Cross-channel distribution and streamwise dispersion of micro-swimmers in a vertical channel flow: A study on the effects of shear, particle shape, and convective inertial torque

In quiescent water, gyrotactic micro-swimmers swim upward on average. This anti-gravity swimming behavior is usually thought to be caused by micro-swimmers' bottom-heaviness. However, recent research has shown the importance of convective inertial torque in the orientational dynamics of settling elongated particles, and the torque can cooperate with self-propulsion to result in an effective gyrotactic mechanism. In this paper, we compare the cross-channel distribution and streamwise dispersion of micro-swimmers with and without convective inertial torque in a two-dimensional vertical channel flow, using a recently proposed generalized Taylor dispersion method. Meanwhile, we incorporate other effects such as shear-shape interaction and wall accumulation. Reflective boundary condition and Robin boundary condition are imposed to represent periodic boundaries and mimic motility-induced wall accumulation effect, respectively. For non-gyrotactic inertialess elongated micro-swimmers, a transition from high-shear trapping regime to low-shear trapping regime appears, consistent with results in previous studies. For micro-swimmers with an effective gyrotaxis intensity resulting from the convective inertial torque, their macroscopic transport properties are essentially the same as those of inertialess micro-swimmers with the same aspect ratio and an equal physical gyrotaxis intensity. The non-monotonic variations of effective drift velocity and dispersivity as functions of the flow rate are also characterized. Additionally, upstream swimming behavior, which is reflected by negative drift velocity, is found in weak flows for both gyrotactic micro-swimmers and non-gyrotactic micro-swimmers with motility-induced wall accumulation.

About the dynamic error of strain gauge torque measuring devices

The dynamic error of devices belongs to the number of errors that are difficult to estimate. The mechanism for forming this error on the example of torsional torque dynamometersis briefly considered as the most common in the practice of research on the energy of agricultural machines. The limiting ratios of frequencies of external influences and natural vibrations of strain-measuring devices are given. Recommendations are made to reduce dynamic error in torque strain analysis. The present review and the accumulated experience of strain gauge research allows us to recommend some directions for reducing dynamic errors in torque measurements. In order for a strain gauge to keep up with changes in torque in its inertial characteristics, it must have the smallest torque inertia. In order to reduce the probability of high-frequency harmonics from the elastic vibrations of the strain gauge, it must be sufficiently rigid. From this point of view, strain rods, strain sprockets, etc., having a moment of inertia greater than that of the same gear parts, are irrational. Based on modern micromodules and power supplies, the system can have a small mass and have no significant effect on the inertial characteristic of the strain gauge.

Physics of a Spinning Object Cyclic Inversion at an Orbital Flight

The opening up of space flights is going on with physical discoveries. One of them was a spinning object cyclic inversion revealed on the MIR space station classified in 1985. Later, the NASA International Space Station openly showed the same effect. This physical effect was an object of stare studying by physicists and mathematicians. They developed only approximated and numerical models on the level of assumptions. The inversion of the spinning objects in the condition of free flight is the subject of gyroscope theory. The mass of the spinning object at the orbital flight generates the system of the interrelated inertial torques that results from the action of the inertial torques produced by the curvilinear motion of the object around the earth. This system of the torques acting on the spinning object at an orbital flight manifests its cyclic inversions, which is the gyroscopic effects. The theory of the gyroscopic effects describes the method of application of the system of the inertial torques, the physics of all gyroscopic effects that manifested by any rotating objects under any condition of their motions.

Inertial torques acting on a spinning sphere

New studies of the dynamics of rotating objects have shown the origin of their gyroscopic effects is more sophisticated than presented in publications. Their rotating mass acting on bodies generates the system of the kinetically interrelated inertial torques. The method for developing mathematical models for inertial torques of the spinning objects shows their dependencies on geometries. The inertial torques generated by the disc, ring, paraboloid, and others have confirmed this statement. The derived analytical method presents a new direction for the dynamics of classical mechanics. The several inertial torqueses acting on any movable spinning objects in space were unknown until recent times. The gyroscopic effects of rotating objects in engineering and a new method for computing their inertial torques are the challenges for researchers. The novelty of this manuscript is the mathematical models for the inertial torques generated by the rotating mass acting on the spinning solid and hollow sphere.