Moment Of Inertia Research Articles

Engineering method for determining the axial moment of inertia of a circular segment

Engineering method for determining the axial moment of inertia of a circular segment

On some methods of determining proper frequencies torsional oscillations in metal-working machines

Forced torsional vibrations that occur in machine tool drives are one of the pressing problems of modern machine tool industry. The reasons for these fluctuations may be imbalances of rotating masses, structural imperfections of bearing units, operating or technological process features (for metal-cutting machines – eccentric clamping of the workpiece, processing of non-round workpieces, etc.). In this work, using the example of a real metal-cutting machine, the task of dynamic analysis of the drive of the main movement of the machine with determination of the natural frequencies of torsional vibrations is realized. The real object is replaced by a dynamic model (DM). When constructing the DM, the inertial and rigidity characteristics are determined from the conditions: – the kinetic energy of the object is equivalent to the kinetic energy of the DM (from this condition the axial moments of inertia of the concentrated masses of the row model are obtained); – the potential energy of elastic deformations of the object is equivalent to the potential energy of deformation of the DM (from this condition the rigidity coefficients of the DM are obtained). The natural frequencies of the row DM were determined in three ways: 1) by solving the frequency equation (exact method) in combination with the method of reducing the number of masses of A.P. Cherevkov; 2) partial systems method (fundamental frequency only); 3) method of residuals (Tolle). The following conclusions were made: 1) the main (smaller) frequency can be found by any of the methods considered (since the results of the three methods coincided); 2) when simplifying the DM using the method of partial systems, the criterion for the possibility of further simplifications over the specified frequency range should be taken into account; the transition from a three-mass DM to a two-mass one if the criterion in this calculation was not met led to an error in determining the value of the fundamental frequency of about 10%; 3) dynamic calculations of machines using DM and methods for determining natural frequencies make it possible, based on known frequencies of disturbing forces, to identify possible near-resonant operating modes and avoid them in advance by making changes to the design of the machine at the design stage

Performance potential of fully-passive airborne wind energy system based on flapping airfoil

In the field of renewable energy, high-altitude wind energy emerges as a promising source, particularly at altitudes (>300 m) where conventional wind turbines cannot reach. Currently, the Airborne Wind Energy System (AWES) stands as the major technology for high-altitude wind energy harvesting, but confronts challenges including increasing performance enhancement, system robustness, and cost reduction. In response to these challenges, we developed a fully-passive AWES that employs a self-excited flapping airfoil to efficiently transfer wind energy to the ground. We study and optimize this fully-passive AWES with fluid-structure interaction method in a numerical wind tunnel, achieving a notable power coefficient of 1.17 and efficiency of 20 % with an average tether angle near 30°. We find that a thin airfoil with a slight camber near the leading edge outperforms other profiles. Increasing the pitching axis distance, the imbalance distance, the spring stiffness, and the pitching moment of inertia can improve the energy harvesting performance, but decreased the system robustness. We offer essential guidelines for setting initial parameters of the AWES, facilitating the design and deployment of this innovative technology. This work underscore that the fully-passive AWES is capable of realizing high-altitude wind energy harvesting with simplified structure and outstanding energy-harvesting performance.

The Design and the Control Principle of a Direct Low-Speed PMSM Servo-Drive Operating under a Sign-Changing Load on the Shaft

The paper relates to the development of an algorithm applicable for maintaining the rotational speed of low-speed drives using PMSM motors and operating under a sign-changing load. The moment of inertia of rotating parts does not play the role of a mechanical stabilizer for the speeds discussed in the article. Simulation studies are presented with the aim of developing a rotational speed control algorithm that utilizes only positional feedback and the previously assumed sign-changing load on the shaft. For the purposes of this research, a mathematical model was developed to calculate transient processes in a PMSM machine operating in the conditions of a sign-changing load on the shaft. This model assumes a deterministic control principle adapted to the known nature of the load change. In this model, the mutual influence occurring between the phase fluxes, the electromagnetic torque, the electric currents and the rotor position angle are established on the basis of FEM analysis of a two-dimensional magnetic field using a quasi-stationary approximation. Principles applicable for controlling a direct low-speed servo drive based on a PMSM machine operating with a known variable shaft load using only positional feedback and a predetermined shaft load change law are defined. The proposed regulation method is verified in an experimental manner. For this purpose, an experimental setup was built, which includes a PMSM with a load imitator on a variable sign shaft, an inverter providing sine-shaped power supply to the machine and a digital dual-processor control system. The discussed rotational speed stabilization algorithm was implemented in the form of a program for a microcontroller, which forms a part of the control system. The results of experimental tests confirm the adequacy of mathematical modeling and the effectiveness of the proposed rotational speed stabilization algorithm.

The rotational inertia of a rigid body

The role of moment for inertia in rotational dynamics is equivalent to mass in linear dynamics and can be understood as an object's resistance to rotational motion. It establishes the relationship between several quantities such as angular momentum, angular velocity, torque, and angular acceleration. Accurately calculating the moment of inertia is crucial for designing various rotating systems and mechanical devices in engineering. For example, when dealing with rotating mechanical parts or machines, their moment of inertia ensures stability and performance in design needs to be considered. In physics and engineering, the analysis of rotational motion for rigid bodies relies on the concept of moment of inertia. It allows us to understand the dynamic behavior of a rigid body around an axis, including applications such as rotational stability, gyroscopic motion, and conservation of angular momentum. In this paper, the rotational inertia of a rigid body is studied by different method. Calculating the moment of inertia helps us gain a deeper understanding of an object's inertial properties during rotational motion while providing an important foundation for engineering design, scientific research, and material analysis.

Promoting abstract thinking and scientific argumentation in the teaching of physics

thinking and scientific argumentation are two of the more important high-order cognitive skills that students at secondary level need to develop in the learning of physics. In this paper a new methodology based on constructivism’s view of education is presented by using counterintuitive experiments under a POE strategy (Predict, Explain, Observe). The experiments consist in a race of two soda can, one of them previously shaken, over an inclined plane; and the movement of a double cone object, built by two joined funnels, over two convergent inclined rails. The unexpected outcome of both experiments challenges the prior ideas of the students and provokes a higher engagement in their learning process. The results of a pilot experience applying this methodology suggest that using counterintuitive experiments under PEO strategy is an effective methodology to introduce the teaching of abstract concepts as moment of inertia and centre of mass. It also helps identifying students’ prior knowledge, promoting the use of scientific reasoning, and training students in the activation of their abstraction skills.

Nonlinear Trajectory Tracking Controller for Underwater Vehicles with Shifted Center of Mass Model

This paper addresses the issue of trajectory tracking control for an autonomous underwater vehicle in the presence of parameter perturbations and disturbances in three-dimensional space. The control scheme is based on a combination of the backstepping method, the adaptive integral sliding mode control scheme, and velocity transformation resulting from the decomposition of the inertia matrix, which is symmetric. In addition, adaptive laws were applied to eliminate the effects of parameter perturbations and external disturbances. The main feature of the proposed approach is that the vehicle model is not fully symmetric but contains quantities due to the shift of the center of mass. Another important feature of the control scheme is the ability to detect some of the consequences caused by reducing the vehicle model by neglecting dynamic couplings. Numerical results on the five degrees of freedom (DOF) vehicle model show the efficiency, effectiveness, and robustness of the developed controller.

Improving Rotational Stability and Enhancing Efficiency with Variable Inertial Flywheels and Magneto-rheological Fluids

Variations in the rotational speed of a flywheel are naturally resisted by the moment of inertia. A high moment of inertia must be maintained to minimize angular velocity variations. Conversely, a significant moment of inertia makes it difficult to start spinning machines. A flywheel with a variable moment of inertia has been suggested to solve this issue. Although fluctuations between the masses' radii across the flywheel's axis may be used to approximate true inertia, the variable inertial flywheel's (VIF) control mechanisms are somewhat complex. Magneto-rheological (MR) Fluids can be utilized to avoid the complexity of the VIF. The applied device parameters determine the design and construction of the VIF system using a relatively simple control technique. To determine the relation between the semi-active VIF control system and the input parameters of a rotating electrical machine to decrease energy losses, adequate data from a VIF coupled with an induction motor (IM) system is gathered in this study. An analysis was done on the system, and the outcome showed a possible improvement in the performance of IM. This study significantly reduces power consumption and smooth speed build-up possibility for the proposed system.

Controlling the Variable Inertia of Flywheel: A Scientific Review

Due to the variation of the moment of inertia, flywheels, a well-known mechanical system, can balance the energy output by preventing fluctuations in rotational speed. Examples of prevalent applications are the engine with internal combustion and industrial apparatus. A flywheel with a considerable moment of inertia is mandatory to accomplish reduced angular velocity variations. A flywheel with a variable moment of inertia can be recommended for specific applications to obtain sustainable energy savings. Variations in the masses' radii from the flywheel axis can yield the concept of true inertia. Still, the control techniques for the variable inertial flywheel (VIF) are relatively complex. This paper critically analyses the available literature on VIF control methods and focuses on their application.

Optimization of cold-formed steel beam cross-sections for pallet rack storage systems

This paper aims to obtain optimized cold-formed beam cross-sections for industrial pallet rack storage systems. The optimal sections were obtained by applying fitness functions aimed at reducing cross-sectional area and/or displacement and solving them using the Genetic Algorithm. These functions imposed a behavioral constraint so that all optimized solutions had the same resistant bending moment. The calculation of the characteristic resistant bending moment was carried out according to the direct strength method, with load factors defined by the elastic stability analysis with CUFSM, in an analysis routine implemented on the MATLAB platform. Four parameterized sections were studied, verifying the optimum set of height, width and stiffening elements that met the objectives defined by functions, assuming reference values of a rectangular hollow section. Manufacturing constraints were also taken into account. The results show that it is possible to manufacture cold-formed beams that consume less material and/or have a better moment of inertia in relation to the reference section, without compromising the strength of the structural element.

Blind parameter identification of implicit differential equations using the collocation discretization and homotopy optimization methods

In this paper, our objectives are to estimate the moments of inertia and reconstruct the inputs of a two-link pendulum that models a human arm. A blind parameter identification routine to determine the inertia properties of human limbs without input data based on a combination of collocation discretization and homotopy optimization is suggested. Without the input data, inertia parameters are structurally unidentifiable. Complementary equations in terms of the ratio of inertia parameters in the cost function and the rate of change of the inputs in the constraints are introduced to make the problem structurally identifiable. Numerous simulations are performed to validate our approach. Experiments to record human upper arm and forearm oscillatory movements were also performed, and moment of inertia terms were evaluated. The significance of the proposed method is that the method can be used to evaluate the moments of inertia of human body segments only from the experimental kinematic data. The advantages of the method are: numerical integration of dynamic and sensitivity equations is avoided and the record of the inputs to the system is not needed.

Collision Study on New Aluminum Alloy W-Beam Guardrail

Highway guardrails are safety installations set along the sides or center of roads to prevent vehicles from veering off the roadway, thereby protecting pedestrians and vehicles. However, traditional W-beam guardrails have issues such as poor energy absorption, susceptibility to rust, short lifespan, and a high risk of vehicles running off the road during severe collisions. Therefore, this study employs the partial differential equations of the vertical motion of beams to investigate the relationship between the deformation of wave beams and their moment of inertia. The cross-sectional shape of traditional W-beam guardrails was optimized accordingly. Combining this with the high ductility of aluminum alloy Al 6061-T6, a new aluminum alloy W-beam guardrail was proposed. Finite element simulation models of traditional steel guardrails, new steel guardrails, and the new aluminum alloy guardrail were established to evaluate the performance of the three types of guardrails. The results show that the deformation of the wave beam is inversely proportional to the square root of its moment of inertia. Compared to traditional W-beam guardrails, the moment of inertia of the new guardrail’s cross-section increased by 28.6%. In finite element collision simulations, the new guardrail reduced deformation by 12.8%, lowered the risk of vehicles running off the road, and improved safety performance.

Proposition for the effective moment of inertia to determine the deflection in a composite slab

The objective of this work is to propose a mathematical expression for calculating the effective moment of inertia of a composite slab that utilizes steel formwork incorporated into the concrete, and consequently, to verify the deflection. The analysis of the behavior and strength of composite steel and concrete slabs covers several parameters, such as load-deflection curves, load-end slip curves, and load-steel strain curves. Among these parameters, the load versus deflection curve at the mid-span perform a crucial role in the evaluation and verification of deflection. Regarding the calculation of deflection, generally, the technical standards recommend that the moment of inertia of the composite section be given by the simple average of the moments of inertia of the uncracked and cracked sections. However, experimental investigations have shown that this procedure inadequately characterizes composite slab behavior, resulting in underestimated effective moment of inertia and reduced deflection, especially when subjected to higher loads. Using the results of experimental tests on a composite slab built with a specific steel sheeting carried out at the Structures Laboratory of the Federal University of Minas Gerais, this work evaluated several expressions suggested by technical standards and authors of scientific articles aiming to validate a proposal for determining the moment of effective inertia in composite slabs that adequately represents the behavior load versus deflection during the entire loading phase until collapse. From this evaluation it is possible to recommend the proposed equation for design verification in the case of the service limit state for excessive deformations.

Dynamics of some compact structures and moment of inertia in f(ℛ,𝒯 ) gravity

The primary objective of this study is to conduct a thorough examination of relativistic structures within the framework of [Formula: see text] gravity, where [Formula: see text] is the Ricci scalar and [Formula: see text] is the trace of the energy–momentum tensor. We investigate the emerging characteristics of compact stars, focusing on the [Formula: see text] model, where [Formula: see text] is the coupling constant. In the initial sections of the paper, we concentrate on the examination of exact interior solutions involving perfect fluid. With this aim, we introduce the metric coefficient [Formula: see text], where [Formula: see text] and [Formula: see text] are arbitrary constants to be computed from the matching conditions and [Formula: see text] is a positive odd integer. It is worth noticing that we select a group of 10 significant compact stars from recent studies, namely, Vela [Formula: see text], EXO [Formula: see text], [Formula: see text], SMC[Formula: see text], Her[Formula: see text], PSR [Formula: see text], PSR[Formula: see text], Cen[Formula: see text], [Formula: see text] and LMC[Formula: see text]. To investigate the viability of our model, we conduct various checks, including the analysis of energy density and pressure components, equilibrium, and energy conditions, stability analysis and the adiabatic index. An important part of this work provides the slowly rotating property of stars, accompanied by the derivation of the moment of inertia. The relationship of mass, energy density, radius and moment of inertia for stellar objects are observed. Our findings demonstrate that obtained results are physically acceptable and consistent with our considered model.

Mass, Centre of Gravity Location and Inertia Tensor of Electric Vehicles: Measured Data for Accurate Accident Reconstruction

Accurate accident reconstruction requires the knowledge of the mass properties of vehicles, namely the centre of gravity location, the mass and the inertia tensor. Such data are seldom available, especially in case of newly produced electric vehicles. In this paper, vehicle inertia measurements, performed at Politecnico di Milano, refer to a number of electric vehicles. In addition to the “simple” measurement of vehicle inertia, measured mass properties are analysed to derive the proper empirical formulae for the estimation of the centre of gravity height and the moments of inertia. Both internal combustion and electric vehicles are considered. Data show a significant difference in the mass properties of the two types of vehicles. The proposed formulae can be effectively employed to quickly obtain a reasonable estimation of the mass properties of any vehicle. The results show that electric vehicles are characterised by higher values of mass with respect to internal combustion vehicles, but they present a lower centre of gravity location and proportionally lower values of the moments of inertia.

Evolution of Stellar Rotation in Open Clusters

Understanding stellar rotation and the role of magnetic braking remains a major outstanding problem in astrophysics. In this paper, stellar rotation of the young open cluster Blanco 1 is investigated and compared with other clusters with ages ranging from ∼35 Myr to ∼950 Myr and star masses in the range 0.2 < M⊙ < 1.4. It is proposed that rotation rates of stars in young open clusters are determined by the early angular momentum acquired during formation and not by magnetic braking effects, which operate on longer time scales. On the convective C Sequence, for lighter stars, the early angular velocity is related directly to the moment of inertia. However, for the interface or I Sequence, differential rotation exists and observed rotation rates are essentially the rotation rates of the outer convection zone. It is estimated that the convection zone can rotate at over 10× the rate of the inner radiative zone for heavier stars. This differential rotation process can drive saturated interface dynamos that lead to large rotational mass dependences which can be described by a simple energy transfer model. Comparing with clusters of different ages magnetic braking outlines the evolution of older clusters from young clusters. For old clusters such as Praesepe the majority of stars have experienced spin down, that can be described by a simple model based on an additional momentum loss proportional to the angular momentum of the early cluster, which for the I Sequence is consistent with the well known Skumanich relation.

Theoretical and experimental study of unsteady behavior of marine diesel engine under fluctuating back pressure condition

In order to meet the increasingly urgent emission reduction requirements, underwater exhaust has emerged as a promising technology for marine diesel engines and has received widespread attention in recent years. However, under fluctuating high back pressure conditions, the diesel engine as a whole operates in an unsteady state, with significant fluctuations in output power and exhaust temperature, posing a serious threat to their stability and safety. This paper focuses on the unsteady operating characteristics of diesel engines and its impact on the engine output power, efficiency and safety under fluctuating high back pressure conditions. Firstly, based on model order reduction and the first Lyapunov approximation theorem, the theoretical derivation reveals that the filling and emptying effects in the intake and exhaust pipes and the shaft moment of inertia of the turbocharger are the main causes of the unsteady of the engine under fluctuating high back pressure conditions. The factors influencing the strength of engine unsteadiness, including wave period, wave amplitude, mean back pressure and engine properties, are identified. Then, diesel engine experiments under different fluctuating high back pressure conditions are performed and the conclusions derived from the theoretical analysis are validated through experiments. Based on the research results mentioned above, this paper proposes a criterion to determine the unsteadiness of diesel engines. Through comparison with experimental data, it is found that this criterion effectively reflects the strength of engine unsteadiness, with a correlation coefficient of 0.9169 with the unsteady parameter.

Description of moment of inertia and the interplay between anti-pairing and pairing correlations in 244Pu and 248Cm* *Xiao-Tao He Supported by the the National Key R and D Program of China (2023YFA1606503)

A variable moment of inertia (VMI) inspired interacting boson model (IBM), which includes many-body interactions and a perturbation possessing (5) (or (5)) symmetry, is used to investigate the rotational bands of the mass region. A novel modification is introduced, extending the Arima coefficient to the third order. This study is dedicated to the quantitative analysis of evolving trends in intraband γ-transition energy as well as the kinematic and dynamic moments of inertia (MoIs) within the rotational bands of Pu and Cm. The computed outcomes exhibit an exceptional degree of agreement with experimental observations across various conditions. The significance of including a higher-order Arima coefficient is further examined by contrasting it with the previously proposed model. The calculated results demonstrate the significance of both the anti-pairing and pairing effects in the evolution of the dynamic MoI. Additionally, these insights reveal the importance of a newly introduced parameter in accurately depicting complex nuclear behaviors, such as back-bending, up-bending, and downturn in the MoI.

Studying the rotational dynamics of a meter stick using the Arduino board and 3D printed parts

We present a low-cost experimental apparatus designed for studying the rotational dynamics of a meter stick. This apparatus uses everyday laboratory supplies, 3D printed parts, and an Arduino board for data acquisition. It consists of a common bearing fixed to a vertical axle, connected to the meter stick through a 3D printed spindle adapter. A thread attached to a hanging weight and winded around the spindle applies a constant external torque to the stick. The moment of inertia of the apparatus may be changed by incorporating weights into the apparatus through 3D printed adapters. An Arduino board records the time interval between consecutive half turns of the stick, allowing the calculation of the angular displacement over time. The data collected from experiments is compared with theoretical models. Among others, the effect of the applied torque, air resistance and moment of inertia of the stick is studied. This experimental apparatus is particularly suitable for undergraduate students enrolled in a classical mechanics course, offering them a practical, hand-on experience while remaining cost-effective.

Stochastic optimal tuning for flight control system of morphing arm octorotor

PurposeThis study aims to discuss the simultaneous longitudinal and lateral flight control of the octorotor, a rotary wing unmanned aerial vehicle (UAV), for the first time under the effect of morphing and to improve autonomous flight performance.Design/methodology/approachThis study aims to design and control the octorotor flight control system with stochastic optimal tuning under morphnig effect. For this purpose, models of different arm lengths of the octorotor were drawn in the Solidworks program. The morphing was carried out by simultaneously lengthening or shortening the arm lengths of the octorotor. The morphing rate was estimated by using simultaneous perturbation stochastic approximation (SPSA). The stochastic gradient descent algorithm, which is frequently used in machine learning, was used to estimate the changing moments of inertia with the change of arm lengths. The proportional integral derivative (PID) controller has been preferred as an octorotor control algorithm because of its simplicity of structure. The PID gains required to control both longitudinal and lateral flight were also estimated with SPSA.FindingsWith SPSA, three longitudinal flight PID gains, three lateral flight PID gains and one morphing ratio were estimated. PID gains remained within the limits set for SPSA, giving satisfactory results. In addition, the cost index created was 93% successful. The gradient descent algorithm used for the moment of inertia estimation achieved the optimum result in 1,570 iterations. However, in the simulations made with the obtained data, longitudinal and lateral flight was successfully carried out.Originality/valueOctorotor longitudinal and lateral flight control was performed quickly and effectively with the proposed method. In addition, the desired parameters were obtained with the optimization methods used, and the longitudinal and lateral flight of the octorotor was successfully carried out in the desired trajectory.