Unbalanced Force Research Articles

Vibration Response Analysis of a Time-varying Stiffness Wheel with Contrate Gear under Unbalanced Excitation

The vibration and response of multi-contact interface micro-motion time-varying stiffness wheel are analyzed, and the nonlinear vibration response characteristics caused by the unbalance force of multi-contact interface contrate gear face of a gas turbine rotor are studied. Firstly, the local sliding model of dry friction-damped contact is extended to establish a holistic and local unified sliding model. The equivalent stiffness and damping of the damping device are calculated by means of the equivalent linearization method and the first harmonic balance method. Finally, the finite element model of multi-contact contrate gear rotor wheel is established to analyze the influence of different unbalanced masses on vibration response under nonlinear frictional contact. The results show that the response caused by the unbalance mass of multi-contact interface wheel with contrate gear is mainly radial response, and the peak value of resonance response increases with the increase of unbalance force.

Analytical Cogging Torque and Unbalanced Magnetic Force Calculations in Slotted Surface-PM Machines Assuming Finite Iron Permeability

Analytical Cogging Torque and Unbalanced Magnetic Force Calculations in Slotted Surface-PM Machines Assuming Finite Iron Permeability

Investigation of Five-Phase Flux-Switching Permanent Magnet Machines for EV and HEV Applications

As a member of stator permanent magnet (PM) brushless machines, flux-switching (FS) PM machine features outstanding advantages, e.g., robust rotor structure, easy temperature management, high torque density, etc. In this paper, the five-phase FSPM machines for electric vehicle (EV) and hybrid electric vehicle (HEV) applications are investigated. Firstly, the working principle of such machine is analyzed by air-gap field modulation theory. Then, the feasible slot/pole combination is discussed, considering flux leakage, back electro-magnetic force (EMF) quality and unbalanced magnetic force (UMF). Besides, in order to further choose the recommendable slot/pole combination, the torque performances are studied and compared by taking the 20-stators-slot FSPM machines as examples, such as rated torque, overload capability, flux weakening capability and fault tolerance capability. Further, in order to optimize the slot/pole combination which suffers from severe UMF, two different techniques for UMF reduction are proposed, including chamfering both in stator and rotor side. Finally, finite element analysis is employed to verify the analytical analyses. Meanwhile, a 20/18 prototyped machine is manufactured and tested. It is found that the experimental results verify the effectiveness of the analytical analyses.

Induction Motor Vibrations Caused by Mechanical and Magnetic Rotor Eccentricity

Vibration reduction of induction motors is a significant problem that requires effective models for the effects of mechanical and electromagnetic unbalanced forces. This article presents a mathematical model of dynamics for induction motors with rotor mass eccentricity and static and dynamic magnetic eccentricity. The model allows for the influence of the gyroscopic torque of the rotor and considers the elastic-damping characteristics of each of the stator supports and their location. The model has eight degrees of freedom, which makes it possible to simulate transverse and axial vibrations of various designs’ rotors and housings of induction motors. The results of modeling the dynamics for a three-phase squirrel cage induction motor with 11 kW capacity agreed with those obtained by other authors. Simultaneously, new results were also obtained within the research. The simulation results showed that the static magnetic eccentricity causes the appearance of additional critical speed of the motor, and its value decreases in proportion to the growth of the number of pole pairs. The change of the moment of inertia of the motor at a mismatch of the main axis of symmetry of the stator and the rotor axis of rotation allowed for obtaining an actual frequency spectrum of free oscillations, including the rotational motion of the stator. Since the actual static magnetic eccentricity can additionally increase at operating frequencies due to the increase of bearing clearance caused by dynamic unbalanced load, it should be considered in the analysis of unbalanced magnetic pull. The angle of static magnetic eccentricity significantly affects the magnitude of radial vibrations. This feature should also be considered when selecting the locations of balancing weights during the rotor balancing procedure.

Bionic magnetic superhydrophobic and patterned surfaces for droplet programmable manipulation

Droplet manipulation holds importance across various domains, including microfluidics, bioassays, water harvesting, and transportation. Drawing inspiration from nature, specifically the superhydrophobic surface of lotus leaves and the patterned surface of desert beetles, this research explores the creation of bionic magnetic superhydrophobic and patterned surfaces with programmable manipulation of droplets, including transport, mixing, and single-droplet multiplex dispersion. The surfaces are prepared using a straightforward laser selective etching technique, during which droplets easily bounce off the laser-etched surface, exhibiting low adhesion, whereas they adhere firmly to non-etched areas. The introduction of a magnetic field induces surface deformation, facilitating droplet transport under unbalanced forces on the bionic surface. Further, the feasibility of using patterned surfaces as platforms for chemical microreactions is confirmed through chemical reactions. This study offers insights into the development of functional surfaces and highlights their potential applications in rapid, high-throughput detection.

Theoretical and experimental applications of a rotor balancing technique without using trial weights based on augmented Kalman filter

Unbalance is the most common fault of rotating machines and efforts devoted to developing balancing techniques are the goal of several researchers around the world. The most common balancing approach is the well-known influence coefficient method, which requires the use of trial weights to determine the relationship between unbalance forces and vibration responses of the rotor; consequently, it is time-consuming regarding industrial applications. The present contribution investigates the augmented Kalman filter (AKF) technique to balance a flexible rotor without using trial weights. There are few studies in this area and the majority of the previous research works are dedicated to theoretical studies using simple or reduced rotor models. This paper considers a finite element (FE) model of a realistic rotor system and investigates the effectiveness of the AKF as a balancing technique by considering several unbalance conditions. Therefore, the novelty of the present contribution is characterized by a complete numerical and experimental AKF based balancing procedure that is performed by using a realistic rotor system. As mentioned above, limited experimental contributions are found in the literature involving real-world applications. Additionally, a sensitivity analysis on the force covariance matrix is proposed to investigate the most favorable conditions to apply the AKF technique in the context of rotor balancing. The methodology proved to be effective to deal with a variety of rotor balancing applications.

Quench analysis of a no-insulation REBCO magnet based on the ADI method considering the coupling effect of the cryostat

A no-insulation (NI) REBCO superconducting magnet is under development at Wuhan National High Magnetic Field Center, China. The magnet with the liquid helium cryostat system has a compact structure to reduce the space required for operation. During a quench, the fast-changing spatial magnetic field around the NI magnet may induce a strong eddy current in the conductive parts of the cryostat. The eddy current and its associated Lorentz force will generate mechanical stress on the cryostat, especially on the thermal shield (TS). The mechanical strength of the cryostat needs verification in the preliminary design. Furthermore, the degree to which the electromagnetic coupling between the cryostat and NI magnet might impact the quench behaviors of the NI magnet remains uncertain. In this paper, a multi-physics quench model is newly developed for the NI REBCO magnet, and the alternating direction implicit method is employed for the solver of the thermal model to improve computational efficiency. This simulation model can consider the electromagnetic coupling effect between the NI magnet and cryostat by constructing a partial element equivalent circuit. A quench analysis has been performed and we found that: (1) The cryostat can function as a secondary shorted circuit to the NI magnet and slow down the quench speed to a certain extent. (2) During the rather fast inductive quench phase, the cryostat will experience an attraction force towards the quench propagation frontier. (3) A quench propagation from one end of the magnet can cause a significant z-axis unbalanced force on the TS. (4) Cryostat materials with drastically changed electrical conductivity can significantly affect their mechanical responses during a quench. However, the eddy current density and maximum Von Mises stress on the TS are barely affected by the thickness of the TS and the contact resistance of the NI REBCO magnet.

Coordination control between vibration suppression and energy regeneration for vehicles driven by in-wheel motors under regenerative braking condition

In this paper, focusing on regenerative braking condition, a coordination control method is proposed to achieve the vibration suppression and braking energy recovery of vehicles driven by In-Wheel Switch Reluctance Motor (IWSRM). Firstly, a vehicle vertical dynamic model, including SRM drive system, vehicle braking system, and quarter SRM-suspension system, is established based on the analysis of the generating and vibration characteristics of IWSRM. Then, after analyzing the effects of eccentricity and electromagnetic excitation, the vertical unbalanced radial force is used as control signal in design of the control method. Moreover, for ensuring the recovered energy and reduce vertical vibration, the optimal key control parameters varying with the vehicle speed and braking strength are obtained by genetic algorithm. To achieve verification of the control method, the several vehicle performance indexes are selected as observation objects, which are analyzed and compared to other control methods, and the results indicate the control method can effectively weaken the vertical acceleration and improve the vehicle ride comfort without significantly decreasing regenerative braking energy. Finally, a hardware in the loop experiment is conducted, and the effectiveness and real-time ability of the proposed method can be verified.

Coalescence-Induced Droplet Jumping on Superhydrophobic Surfaces with Annular Wedge-Shaped Micropillar Arrays.

The coalescence-induced droplet jumping on superhydrophobic surfaces has extensive application potential in water harvesting, thermal management of electronic devices, and microfluidics. The rational design of the surface structure can influence the interaction between the droplet and the surface, thereby controlling the velocity and direction of the droplet's jumping. In this study, we fabricate the superhydrophobic surface with annular wedge-shaped micropillar arrays, examine the dynamic behavior of condensate droplets on the surface, and measure the temporal and spatial variations of droplet density, average radius, and surface coverage with wedge-shaped micropillars of varying sizes. In addition, the energy analysis of the coalescence-induced droplet jumping reveals that the two primary factors influencing the jumping are the relative size and position of the droplets and micropillars. Further numerical simulations find that the wedge-shaped micropillars cause an asymmetric distribution of pressure within the droplet and at the solid-liquid contact surface, which generates an unbalanced force driving the droplet in the gradient direction of the wedge-shaped micropillar, causing the droplet to jump off the surface with both vertical and gradient-direction velocities. The capacity of the wedge-shaped micropillar surface to transport droplets in the gradient direction increases and then decreases as the relative size of the droplets and micropillars increases. The relative position of the droplet center-of-mass line perpendicular to the bottom edge of the wedge micropillars' trapezoidal shape is more favorable for droplet transport. This work reveals the influence mechanism of surface structure on the velocity and direction of droplet jumping, and the results can guide the microstructure design of superhydrophobic surfaces, which has significant implications for the application of droplet jumping.

Droplet splitting on chemically heterogeneous surface: A 3D lattice Boltzmann study

The uniform splitting of droplets on heterogeneous surfaces without external stimuli has gained increasing attention due to its wide and flexible applications. To precisely control and predict the droplet splitting, the 3D multiphase lattice Boltzmann model (LBM) is used to study the mechanism of the impact splitting on a hydrophilic surface with a superhydrophobic strip. A parallel implementation of the 3D multiphase LBM is presented to improve the performance by using an effective kernel fusion to reduce the off-chip memory data traffic. Two splitting modes with single or double liquid bridge are contrasted and analyzed. The results show that the size of the air bubble trapped during the impacting process leads to various splitting modes. By calculating the unbalanced Young's force in the three-phase contact lines, unbalanced surface tension at the superhydrophobic/hydrophilic surface is observed. In addition, we find that the increase in the initial velocity of the drop can not only shorten the splitting time but also lead to a change in splitting mode. The increase in the wettability contrast of the surface can stably shorten the splitting time. However the splitting time did not linearly shorten with the increase in strip width. Our findings would advance the understanding of drop impact splitting and possibly inspire new guidance for the design of functional interfaces. The present study also provides an efficient parallel implementation to simulate the 3D droplet motion on heterogeneous surfaces.

Control of vibrations in rotating mechanical elements

We observe commonly disturbances in rotating machinery elements when driven to rotate. These disturbances present themselves as a displacement or trepidation caused by unbalanced masses. The occurrence of balancing depends on eccentricity present, which means that the center of mass and rotating element center are not coincident. The presence of these unbalanced forces - whose magnitude is proportional to the eccentricity, unbalanced mass, and the angular velocity squared - results in severe vibrations and can overload bearings with catastrophic consequences. The main origin of these unbalances is the heterogeneous distribution of the masses around the rotation axis. So, to avoid the overload on bearings and warp the shaft, some control methods such as balancing should be done. In the present work, a dynamic balancing was carried out with a specimen employing a balancer rig. In this experiment, different auxiliary equipment, computer systems, and proprietary software were used. It was possible with this software to automate the measurements, analyze, and obtain a report about balancing results as well. The specimen was made of steel and possessed two mounted nylon disks with oblong holes on them. These oblong holes permitted the fixation of trial masses and correction masses. The degree of balancing quality was determined according to the ISO standard G 6.3; these degrees of balancing guarantee an accuracy level of quality according to the specific application in rotating machines. The balancing on the specimen was correctly applied, and the results have demonstrated that this procedure, balancing, is essential to mitigating excessive vibration and preventing overload in bearings caused by unbalancing in rotating mechanical elements.

Study on the design of single-seat control valve with stable flow regulation and its fluid flow characteristics and thermal stress

Aiming at technical problems such as unstable flow at small openings and uneven force on the valve core, the single-seat control valve with stable flow regulation is researched and designed. The tapered surface of the outer edge of the valve core can cooperate with the valve seat when the valve core is running stably, resulting in higher flow regulation accuracy and more stable regulation. The mechanical characteristics and flow characteristics are analyzed. The fluid flow simulation analyzes the pressure, velocity, density, mass flow rate and volume flow rate of the fluid under small and large openings of the single-seat control valve. The relationship between the maximum pressure, maximum velocity, maximum density, mass flow rate and volume flow rate of the inlet and outlet with the opening are analyzed from small opening to large opening and smaller opening. The spool motion simulation analyzes the relationship between actuator driving force, unbalanced force, linear displacement, velocity and acceleration with time. The thermal stress simulation analyzes the thermal temperature, resultant heat flow, thermal stress, thermal strain and safety factor, and the material strength meets the requirements. The valve body pressure test, valve seat sealing test, full stroke and switching time test, drift and jitter test, starting deviation test, basic error and return difference test and dead zone test are carried out on the single-seat control valve. The test results all meet the requirements. The simulation results are compared and analyzed with the test results, and the simulation results are consistent with the test result.

Dynamic modeling and nonlinear analysis for lateral–torsional coupling vibration in an unbalanced rotor system

Imbalance is a common problem in rotating machinery. In addition to the unbalanced force, lateral–torsional coupling vibration can also be induced by the mass imbalance. However, the related nonlinear behaviors and coupling mechanism are still not well understood, especially when lateral-angular motion is incorporated in a model. In this paper, a model for coupling lateral and torsional vibrations of an unbalanced rotor is developed by Lagrangian dynamics, in which the coupling of lateral-angular and torsional motions is first considered. Based on the model, the lateral responses, torsional responses, coupling excitation characteristics and coupling mechanisms are investigated in detail. The results show that mass imbalance can lead to nonlinear time-varying characteristics in the dynamic equations. When the imbalance is small, the lateral vibration can be degraded to a traditional imbalance problem. Meantime, very small transient torsional vibration with torsional natural frequency ft in frequency domain can be observed at the beginning. The coupling excitation applying on the torsional DOF caused by the lateral synchronous whirling is demonstrated to behave the feature of static torque, consequently, there actually exists no steady-state torsional vibration in small unbalanced rotor. Under largely unbalanced conditions, both resonant and unstable behavior can be observed in the lateral and torsional responses. The combined resonance is induced by the lateral translational–torsional coupling, while the instability is caused by lateral angular–torsional coupling. By increasing the lateral damping, the instability phenomenon can be suppressed, and the lateral amplitude in the resonance region can be effectively reduced.

A new analytical method for stability analysis of rock blocks with basal erosion in sub-horizontal strata by considering the eccentricity effect

Abstract. The basal cavity of a rock block formed due to differential weathering is an important predisposing factor for rockfall in hard–soft interbedded rocks, which induces an eccentricity situation at the base of the rock block. Rock block falling due to the non-uniform distribution with the failure modes of toppling or sliding is defined as biased rockfall in this study. Taking into account the non-uniform stress distribution due to the eccentricity effect, a new analytical method is proposed for three-dimensional stability analysis of biased rockfall. The development of non-uniform stress distribution stress calculated by this analytical method was verified by numerical simulation. The biased rockfall progresses from partial damage of the soft underlying layer, caused by non-uniform distributed stress, to toppling and sliding of overhanging hard rock block due to overall unbalanced force. Therefore, a set of factors of safety (Fos's) against partial damage (compressive and tensile damage of the soft underlying layer) and overall failure (toppling and sliding of the hard rock block) are used to determine the rockfall susceptibility level. The analytical method is applied and validated using biased rockfalls on the northeastern edge of the Sichuan Basin in southwest China, where a significant number of rockfalls consisting of overhanging thick sandstone and underlying mudstone occur. The evolution process of biased rockfalls is divided into four stages, initial state, basal cavity formation, partially unstable and failure. The proposed method is validated by calculating Fos's of the typical unstable rock blocks in the study area. As the cavity continues to grow, the continuous retreat of mudstone causes stress redistribution between the hard and soft rock layers. This results in damage to the underlying soft rock layer due to the development of the non-uniform distribution, ultimately leading to the failure of the hard rock block. The critical retreat ratio is determined to be 0.33, which is used to classify the low and moderate rockfall susceptibility in the eastern Sichuan Basin. The proposed analytical method provides insights into the evolution of biased rockfall and a means for early identification and susceptibility assessment of rockfall.

Novel nodal relaxation algorithm with its application on nonlinear analysis of tensegrity-based structures

This study proposes a robust technique for static and dynamic nonlinear analysis of tensegrity-based structures using a novel method, entitled the Node Relaxation algorithm (NR). Regular numerical algorithms are usually invalid in dealing with flexible tensegrities due to singularities arising from large displacements and/or rotations following any alteration of the internal actuated components or externally applied loads. Especially in tackling dynamic problems, it becomes even more challenging to predict structural deformation when its member forces are varied constantly. In this paper, a novel iterative algorithm, consisting of consecutive releasing and restraining of each node, is raised to oblige the structural form to gradually evolve to its final equilibrium configuration. The tangential unbalance force on each node, selected as the sensitivity index, is employed to accelerate the structure searching for its stable state. The Newmark-β method is also adopted to update the position of free nodes in each iterative step, which assists the NR algorithm in finding updated equilibrium structural configuration during the nonlinear dynamic analysis. Two kinds of tensegrity-based structures, namely the spring-rod tensegrity and the cable-rod tensegrity, are given as the illustrative examples to confirm the effectiveness and robustness of the presented method.

Unbalanced magnetic pull in angular eccentricity magnetic screw

AbstractThis paper investigates the unbalanced magnetic force (UMF) produced by angular eccentricity in a magnetic screw. The principle of eccentricity is briefly outlined and an analytical expression that can be used to predict UMF of a magnetic screw is established. A 3D magnetic screw model with helically magnetized permanent magnets (PM) has been built and simulated in ANSYS Maxwell with different angular eccentricities. Comparing the finite elements (FE) simulation and analytical calculation results, there is a certain difference in the UMF of the magnetic screw, which is also caused by the asymmetry of the magnetic screw structure. It has been shown that compared to the linear tubular PM motor with the same thrust force capability, the magnetic screw has a much small UMF, which greatly simplifies the mechanical design of the magnetic screw.

Study on the asynchronous effect of projectile starting and blocking sheet opening in recoilless gun

As the switch for the start-up of the nozzle at the rear of the recoilless gun, the opening pressure of the blocking sheet directly affects the balance of the recoilless gun during the shooting process. The opening time of the blocking sheet is obtained through high-speed camera by capturing the tail flame. Using piezoelectric pressure sensors, the pressure at different positions along the barrel were measured. Furthermore, the pressure at the moment of opening the blocking sheet was determined based on its opening time. A significant force jump (Δf = 146.9 kN) in the unbalanced recoil experienced by the recoilless gun during the initial firing stage was identified based on the theory of one-dimensional recoilless gun balanced interior ballistics. This jump arises from the opening pressure of the blocking sheet surpassing the projectile's starting pressure (P0). This research can provide a reference for the design of recoilless weapons related to unbalanced force.

An efficient monolithic multiscale numerical manifold model for fully coupled nonlinear saturated porous media

This paper presents an efficient monolithic computational homogenization model for transient nonlinear hydro-mechanical analysis within the framework of Numerical Manifold Method (NMM). The proposed model is on the same theoretical basis as the FE2 method. The scale transitions are achieved through the extended Hill-Mandel theorem so that the microscopic fluid and solid dynamic effects are fully incorporated. The two-scale simulations are solved in a monolithic manner and the microscopic problems of all macroscopic integration points are decoupled from each other to prevent size of the system of equations from soaring to exceedingly large. By conveying microscale unbalanced forces and tangent operators to the macroscale level, the micro- and macroscale problems are solved in the same Newton loop such that unnecessary microscopic iterations based on estimated macroscopic variables in the conventional nested homogenization m are avoided. By solving benchmark numerical examples, the proposed model proves to be capable of capturing transient hydro-mechanical responses accurately. Moreover, in contrast to the conventional nested homogenization model, the proposed model saves around 40% of computational costs for nonlinear hydro-mechanical analysis. Using the framework of numerical manifold, the presented model can be easily extended to multiscale analyses involving complex boundaries, interfaces and fractures.

Sliding Behavior of Droplets on a Tilted Substrate with a Chemical Step.

Controlling and predicting the motion of droplets on a heterogeneous substrate have received widespread attention. In this paper, we numerically simulate the droplet sliding through a "chemical step", that is, different wetting properties at two sides of the step, on a tilted substrate by the multiphase lattice Boltzmann method (LBM). Three kinds of equilibrium statuses are reproduced by observing the deformation of the droplet and the velocities of the front contact line. This study shows the droplet obtains a driving force to break through the step by deformation in the initial stage that the droplet is blocked. The droplet spreads to two sides along the step when the front end is blocked and is stretched after the front end is passed over the step. The lengths of the lateral spreading and the longitudinal stretching and the time required to pass over the step depend on the strength of the step. In the sliding process, the kinetic energy is converted into surface energy as the droplet is blocked, and the gravitational potential energy is converted into surface and kinetic energy following the droplet passes over the step. If the droplet can slide through the step, the more strength in the step, the more the gravitational potential energy is converted, and the more the surface energy increases. When the strength of the step is small, unbalanced Young's force hinders the contact line moving forward after the central part of the front end of the droplet breaks through the step. While the velocity of droplet sliding slows down with the increasing strength of the step, the unbalanced Young's force pushes the contact line forward against the resistance. These observations throw insight into the dynamics of the droplets sliding on a heterogeneous surface, which may facilitate potential applications like microfluidics and liquid transportation.

A Simple Eddy Potential Vorticity Flux Closure

AbstractIt is shown that within the limits of quasi‐geostrophic scaling, biharmonic mixing of potential vorticity is equivalent to biharmonic lateral friction together with biharmonic isopycnal thickness mixing in primitive equations, all with the same viscosity. The problem of unbalanced zonal forces related to the planetary vorticity gradient disappears using a biharmonic instead of a harmonic closure. The former is appropriate for eddy‐permitting ocean models which are replacing now more and more the non‐eddy‐resolving model versions in coupled state‐of‐the‐art climate models. Numerical experiments demonstrate that including biharmonic thickness mixing has some benefits regarding stronger eddy production in marginally eddying ocean models, in particular when the grid size is larger than the baroclinic Rossby radius. Going to finer grids where relative vorticity dominates, however, using only biharmonic friction becomes similar to biharmonic mixing of potential vorticity, justifying the long‐standing use of biharmonic friction in reasonably well resolved eddy‐permitting ocean models.