Torque Balance Research Articles

Analysis of Dynamic Engaged Characteristics of Wet Clutch in Variable Speed Transmission of a Helicopter

The working principle and motion process of an aviation wet clutch are analyzed. The initial velocity before the friction pair engaged is solved. The transient Reynolds equation is modified, and an oil film bearing capacity model and a micro-convex bearing capacity model are derived. The film thickness equation between N friction pairs and a pressure-plate is derived. A dynamic engaged model of springs, pistons, friction pairs, and pressure plates are established. The torque balance equation is established of two pairs of friction pairs. The friction torque, rate of change in the oil film, and law of relative change in speed are obtained. The results demonstrate that the spring preload and the viscosity of the lubricating oil have a significant influence on the engagement characteristics. Increasing the quality of the friction plate will reduce the time of engagement, whereas the quality of the friction plate has slight effect on the friction torque characteristics and oil film thickness. The initial speed generated by the collision process will reduce the output speed, sharply increase the torque peak at the lock, and increase the shift shock.

Design and Analysis of a Flexible, Elastic, and Rope-Driven Parallel Mechanism for Wrist Rehabilitation.

This paper proposes a bionic flexible wrist parallel mechanism to simulate human wrist joints, which is characterized by a rope-driven, compression spring-supported hybrid mechanism. Specifically, to realize the movement of the wrist mechanism, a parallel structure is adopted to support the mobile platform and is controlled by a cable, which plays the role of wrist muscles. Because the compression spring is elastic, it is difficult to directly solve inverse kinematics. To address this problem, the external force acting on the moving platform is firstly equivalent to the vector force and torque at the center of the moving platform. Then, based on inverse kinematic and static analyses, the inverse motion of the robot model can be solved according to the force and torque balance conditions and the lateral spring bending equation of the compression spring. In order to verify the proposed method, kinematics, statics, and parallel mechanism workspace are further analyzed by the software MATLAB. The obtained results demonstrate the effectiveness and feasibility of the designed parallel mechanism. This work offers new insights into the parallel mechanism with flexible joints in replicating the movements of the human wrist, thus promoting the development of rehabilitation robots and rope-driven technology to some extent.

Identities for droplets with circular footprint on tilted surfaces

Exact mathematical identities are presented between the relevant parameters of droplets displaying circular contact boundary based on flat tilted surfaces. Two of the identities are derived from the force balance, and one from the torque balance. The tilt surfaces cover the full range of inclinations for sessile or pendant drops, including the intermediate case of droplets on a wall (vertical surface). The identities are put under test both by the available solutions of a linear response approximation at small Bond numbers as well as the ones obtained from numerical solutions, making use of the Surface Evolver software. The subtleties to obtain certain angle-averages appearing in identities by the numerical solutions are discussed in detail. It is argued how the identities are useful in two respects. First is to replace some unknown values in the Young–Laplace equation by their expressions obtained from the identities. Second is to use the identities to estimate the error for approximate analytical or numerical solutions without any reference to an exact solution.

Research on viscoelastic fluid unsteady flow model based on torque loss correction

To address the complexity of unsteady shear flow in the initial start-up stage of rheometers, a model considering torque losses in motors and fixtures was developed based on the true torque balance relationship at the rotor boundary of the rheometer and the constitutive equation of the viscoelastic rheological model. The viscoelastic fluid transient flow model was established, and the real wall stress expression of unsteady shear flow of the viscoelastic fluid in the initial stage was obtained. The reliability of the model was verified by comparing the result from the analytical model with numerical calculation. The impact of the geometric dimensions of the test system and the material viscoelastic characteristics on the transient test was analyzed. The results show that the non-uniform velocity distribution has little effect on the initial strain response in the gap of the actual test system of the rheometer. The oscillation curves of strain and stress obtained by numerical and analytical methods coincide completely, proving the reliability of the model in characterizing the transient flow. For a Jeffery fluid, the elastic modulus G mainly affects the oscillation period and amplitude, the parallel viscosity pots η1 mainly impact the amplitude and oscillation attenuation speed, and the series clay pots η2 mainly influence the slope of the strain curve. The greater the system inertia, the more significant the creep oscillation in the unsteady flow process. The coupling between the test system inertia and the viscoelasticity fluid is the essential cause of the creep oscillation. Combined with the mechanical response characteristics of rheometer, a Jeffery model based on short term correction and torque loss was established. The model can accurately describe the strain time curve of gelled crude oil in the initial unsteady flow stage. The results of this study can help understand the rheological properties of materials in the transient start-up process.

On the well posedness of static boundary value problem within the linear dilatational strain gradient elasticity

In this paper, it is proven an existence and uniqueness theorem for weak solutions of the equilibrium problem for linear isotropic dilatational strain gradient elasticity. Considered elastic bodies have as deformation energy the classical one due to Lamé but augmented with an additive term that depends on the norm of the gradient of dilatation: only one extra second gradient elastic coefficient is introduced. The studied class of solids is therefore related to Korteweg or Cahn–Hilliard fluids. The postulated energy naturally induces the space in which the aforementioned well-posedness result can be formulated. In this energy space, the introduced norm does involve the linear combination of some specific higher-order derivatives only: it is, in fact, a particular example of anisotropic Sobolev space. It is also proven that aforementioned weak solutions belongs to the space H^1(div,V), i.e. the space of H^1 functions whose divergence belongs to H^1. The proposed mathematical frame is essential to conceptually base, on solid grounds, the numerical integration schemes required to investigate the properties of dilatational strain gradient elastic bodies. Their energy, as studied in the present paper, has manifold interests. Mathematically speaking, its singularity causes interesting mathematical difficulties whose overcoming leads to an increased understanding of the theory of second gradient continua. On the other hand, from the mechanical point of view, it gives an example of energy for a second gradient continuum which can sustain externally applied surface forces and double forces but cannot sustain externally applied surface couples. In this way, it is proven that couple stress continua, introduced by Toupin, represent only a particular case of the more general class of second gradient continua. Moreover, it is easily checked that for dilatational strain gradient continua, balance of force and balance of torques (or couples) are not enough to characterise equilibrium: to this aim, externally applied surface double forces must also be specified. As a consequence, the postulation scheme based on variational principles seems more suitable to study second gradient continua. It has to be remarked finally that dilatational strain gradient seems suitable to model the experimentally observed behaviour of some material used in 3D printing process.

Analytical model for quasi-linear flow response to resonant magnetic perturbation in resistive-inertial and viscous-resistive regimes

In this work, a quasi-linear model for the plasma flow response to the resonant magnetic perturbation (RMP) in a tokamak has been self-consistently developed in the resistive-inertial and viscous-resistive regimes purely from the two-field reduced MHD model. Models for the plasma response to RMP are commonly composed of equations for the resonant magnetic field response (i.e., the magnetic island) and the torque balance of plasma flow. However, in previous plasma response models, the magnetic island and the torque balance equations are often derived separately from reduced MHD and full MHD equations, respectively. By contrast, in this work, we derive both the magnetic island response and the torque balance equations in a quasi-linear model for the plasma flow response entirely from a set of two-field reduced MHD equations. Such a quasi-linear model can recover previous plasma flow response models within certain limits and approximations. Furthermore, the theoretical origins and physical meanings of quasi-linear forces and moments in the flow response equation are also clarified.

Emergent Elasticity in Amorphous Solids.

The mechanical response of naturally abundant amorphous solids such as gels, jammed grains, and biological tissues are not described by the conventional paradigm of broken symmetry that defines crystalline elasticity. In contrast, the response of such athermal solids are governed by local conditions of mechanical equilibrium, i.e., force and torque balance of its constituents. Here we show that these constraints have the mathematical structure of a generalized electromagnetism, where the electrostatic limit successfully captures the anisotropic elasticity of amorphous solids. The emergence of elasticity from local mechanical constraints offers a new paradigm for systems with no broken symmetry, analogous to emergent gauge theories of quantum spin liquids. Specifically, our U(1) rank-2 symmetric tensor gauge theory of elasticity translates to the electromagnetism of fractonic phases of matter with the stress mapped to electric displacement and forces to vector charges. We corroborate our theoretical results with numerical simulations of soft frictionless disks in both two and three dimensions, and experiments on frictional disks in two dimensions. We also present experimental evidence indicating that force chains in granular media are subdimensional excitations of amorphous elasticity similar to fractons.

Balanced carving turns in alpine skiing

ABSTRACT In this paper, we analyse the model of pure carving turns in alpine skiing and snowboarding based on the usual assumption of approximate balance between forces and torques acting on the skier during the turn. The approximation of torque balance yields both lower and upper limits on the skier speed, which depend only on the sidecut radius of skis and the slope gradient. We use the model to simulate carving runs on slopes of constant gradient and find that pure carving is possible only on slopes of relatively small gradient, with the critical slope angle in the range of . The exact value depends mostly on the coefficient of snow friction and to a lesser degree on the sidecut radius of skis. Comparison with the practice of ski racing shows that the upper speed limit and the related upper limit on the slope gradient set by the model are too restrictive and so must be the assumption of torque balance used in the model. A more advanced theory is needed.

Indo-Atlantic plate accelerations around the Cretaceous-Paleogene boundary: A time-scale error, not a plume-push signal

AbstractIt has been suggested that plume arrival at the base of the lithosphere introduces a push force that overwhelms the balance of torques driving plate circuits, leading to plate-tectonic reorganizations. Among the most compelling evidence in support of a “plume-push” mechanism is the apparent coincidence between eruption of the Deccan flood basalts around 67–64 Ma and a short-lived increase in Indian (and decrease in African) plate speed. Using existing and newly calculated high-resolution plate-motion models, we show that plate divergence rates briefly increased throughout the Indo-Atlantic circuit, contrary to the expected effects of plume-push. We propose that this circuit-wide spike in divergence rates is best explained as the artifact of a magnetic reversal time-scale error around the much studied Cretaceous-Tertiary boundary, and that the period spanning chrons C29–C28 lasted 70% longer than currently assumed. Corrected for this error, the residual long-term patterns of Indo-Atlantic plate motions and accompanying plate-tectonic reorganization are explicable in terms of maturation of the circuit’s spreading ridges, without invoking a significant plume-push force.

Correlation between bone mineral density, isokinetic peak torque and postural balance in postmenopausal women

Background: Postmenopausal women typically present loss of bone mineral density (BMD), muscular strength, and postural balance. However, there is no consensus in the literature on the correlation between these variables. Objectives: Our objective was to verify the correlation between BMD, isokinetic peak torque of knee extensors and flexors, and static postural balance in postmenopausal women. Methods: Fifty-one postmenopausal women underwent BMD evaluation through dual-energy X-ray absorptiometry (DXA) for four bone regions (lumbar spine, femoral neck, total hip, and trochanter). Muscular strength of knee extensors and flexors was evaluated in an isokinetic dynamometer at 60 and 180 degrees per second in the dominant lower limb. Static postural balance was evaluated on a force platform during five different tasks (bipodal eyes open, bipodal eyes closed, semi-tandem eyes open, semi-tandem eyes closed, and unipodal). Statistical analysis involved Spearman’s correlation coefficient (rho). Results: There was no significant correlation between BMD and isokinetic peak torque of knee extensors and flexors. Approximately half (27 of 60) of the postural balance variables presented significant inverse correlations (p < 0.05) with BMD and of these, the majority (22 of 27) presented moderate correlation (rho between -0.49 and -0.30). Most correlations were for bipodal support tasks with eyes open and eyes closed. Conclusion: Greater postural oscillation in different balance tasks was correlated with lower BMD in postmenopausal women. Therefore, it is suggested that intervention protocols for women with impaired BMD, especially osteoporotic, consider balance training as part of rehabilitation.

Numerical simulation of hydrodynamic and cavitation performance of pumpjet propulsor with different tip clearances in oblique flow

This work mainly analyzes the variation laws of exciting force, pulsating pressure, velocity distribution and hydrodynamic parameters of PJP at different tip clearances (δ=0.5 mm, δ = 1 mm, δ = 2 mm) and different oblique flow angle (0°, 10°, 20°). In this study, the turbulence model SSTk-ω and Reynolds-Stokes equations (RANSE) method have been adopted. The fully structured grid and full channel model have been adopted. And the grid independence of three different tip clearances was verified. In this study, the variation laws of exciting force, pressure coefficient and the hydrodynamic coefficients differences have been studied at the different tip clearances and different oblique flow angle. And the time-domain data of the pulsating pressure of PJP with cavitation conditions or without cavitation conditions was presented, and then which was converted to frequency domain data by fast Fourier transform (FFT). The results show that the torque balance performance of the PJP is broken in oblique flow. The tip clearances have a little effect than the oblique flow angle. The maximum efficiency loss is 19.17% at high oblique angle. The bearing force had a certain phase difference in different tip clearance, the phase shift to the right as the tip clearances increases. At the small advance J = 1.18, the efficiency with cavitation is greater than non-cavitation condition in oblique flow. In addition, the velocity distribution and the water vapor phase volume fraction of rotor outlet in different oblique flow angles and different tip clearances have been investigated.

Theoretical model for the motion of a ring spinning traveler

The motion of the traveler has an important influence on the spinning quality of a ring spinning frame, the yarn breakage rate, and the design and use of the traveler. Current theoretical models assuming a flat balloon are not applicable to high spinning speeds, and so a mathematical model of the time variations of the yarn winding radius and traveler turning radius is established by considering the effects of air resistance and the Coriolis force. A relationship among the rotation speed of the traveler, the winding speed of the spun yarn, and the rotation speed of the spindle is obtained by considering the twisting and winding process and the winding behavior of the tube yarn. Then, from moment balance, a formula is obtained for the traveler torque balance, and the variations in the three spatial inclinations of the traveler are obtained. Finally, using image processing techniques, image feature points are extracted for analysis, and the theoretical model is optimized based on the results. Experimental results show that the mathematical model can accurately predict the time variations of the camber and rake angles of the traveler. This work can provide a theoretical foundation for the development of high-speed ring spinning machines.

Force networks, torque balance and Airy stress in the planar vertex model of a confluent epithelium.

The vertex model is a popular framework for modelling tightly packed biological cells, such as confluent epithelia. Cells are described by convex polygons tiling the plane and their equilibrium is found by minimizing a global mechanical energy, with vertex locations treated as degrees of freedom. Drawing on analogies with granular materials, we describe the force network for a localized monolayer and derive the corresponding discrete Airy stress function, expressed for each N-sided cell as N scalars defined over kites covering the cell. We show how a torque balance (commonly overlooked in implementations of the vertex model) requires each internal vertex to lie at the orthocentre of the triangle formed by neighbouring edge centroids. Torque balance also places a geometric constraint on the stress in the neighbourhood of cellular trijunctions, and requires cell edges to be orthogonal to the links of a dual network that connect neighbouring cell centres and thereby triangulate the monolayer. We show how the Airy stress function depends on cell shape when a standard energy functional is adopted, and discuss implications for computational implementations of the model.

A Novel Comprehensive Model of Wet Clutch During the Engagement Process

With the development of vehicles towards higher power density and reliability, the wet clutch, which is the critical component in transmission system, always encounters the problems of ablation, wear, and breakage. To solve this problem, a novel comprehensive model is developed for the wet clutch to reveal its intrinsic working mechanism. Firstly, a dynamic clearance varying model and a torque balance model are developed for the wet clutch to explain the bearing mechanism along the axial and circumferential directions. After that, the friction coefficient, which varies depending on the interface pressure, slipping speed and temperature, is obtained. By developing the temperature prediction model, a theoretical coupling model is finally established for the engagement process of wet clutch. From the simulation results, the coupling model is sufficient to describe the changing trend of several critical parameters, including the viscous torque, the asperity torque, the contact status on the friction interface, the temperature rise and the friction coefficient, etc.

Investigation of the onset of the breakup of a permeating oil droplet at a membrane surface in crossflow filtration: A new model and CFD verification

In this work, a new model is introduced to determine the crossflow velocity required to dislodge permeating oil droplets at the surface of a membrane. Oil droplets at the surface of a membrane face either of four fates; namely, pinning, permeation, rejection, or breakup. The conditions at which the first three fates are realized have been, to a large extent, satisfactorily explored. The conditions for the breakup, however, do not seem to be very well defined. Although there exist few attempts to define conditions for breakup by crossflow field, they seem insufficient and lack consistency with the physics. It is, therefore, the aim of this work to provide elaborate analysis based on a clear understanding of the physics involved and the forces contributing to the breakup. A mathematical formula is developed to estimate that critical crossflow velocity at which break up occurs. This formula is derived based on the balance of torques that are generated by the interplaying forces. These forces are essentially surface tension forces and drag force. When the droplet encounters a pore opening it forms an interface and if the pressure across the opening is larger than the entry pressure, the interface advances inside the pore. When the receding interface of the droplet reaches the pore opening, the droplet pauses and anchors itself by that portion of the droplet in the pore. The droplet then continues to deform in accordance with the interplay of the imposed drag force and the generated surface force. The droplet wraps around the pore opening and the central angle of encounter increases per the imposed drag force. When the central angle of encounter reaches π radians, this represents the critical configuration beyond which the droplet breaks down to two parts. As the droplet deforms while anchored in its place, the contact line around the pore opening uncover the surface and starts to contribute towards the torque about the pivoting point. The balance of torques generated by the drag force and the interfacial force at that portion of the contact line, which makes a central angle of π radians, is used to determine that critical velocity beyond which the droplet breaks up. Several verification exercises are conducted using computational fluid dynamics (CFD) analysis to build confidence in the derived formula of the critical crossflow velocity. Based on the comparisons, the newly derived formula compares very well with the data obtained using CFD analysis.

The liquid regime of waxy oils suspensions: A magnetic resonance velocimetry analysis

In view of better understanding the properties of waxy crude oils of great practical importance, we study the rheological behavior evolution of model waxy suspensions during transient shear tests, and its variation with concentration in a wide range. Macroscopic tests show a strong destructuring process with the increasing imposed shear rate (starting from rest), while negligible restructuring is observed during shear rate decrease. MRI (Magnetic Resonance Imaging) velocimetry of the suspension during the same tests allow to observe that, in most of the concentration range tested, the material flows only in a limited thickness close to the inner cylinder, and the thickness of this shear-band decreases for increasing concentration but marginally evolves as the apparent shear rate is widely increased then decreased. This means that the extent of the liquid region is governed by the initial start-up flow conditions, and the apparent viscosity variations during the next steps (at other shear rate values) are not associated with an increase of the flowing region but with the evolution of the structure in the liquid region. For the specific case of the lowest wax content analyzed, the thickness of the unsheared region decreases considerably after shearing at a high shear rate. In this case the torque balance in the sample is capable of overcoming the yield stress of the unsheared region. We also show that despite very different (initial) elastic moduli and yield stresses in the solid regime (a factor of several orders of magnitude over the whole range of concentration), we essentially have the same power-law behavior of the fluid in the shear-band, even when the shear-band thickness is close to the particle size.

Investigating the frictional force distributions and inter-stage imbalance of a two-stage brush seal

Although a two-stage brush seal (TSBS) plays an important role in gas turbine machinery, few studies have investigated the complex flow and tip frictional force distributions of the TSBS. This article contributes to the ongoing investigation of the TSBS by proposing a 3D slice model employing computational fluid dynamics to analyze the flow and tip frictional force characteristics of a contacting TSBS using the torque balance principle and linear superposition methods. Our calculations reveal that as the inter-stage imbalance of the pressure decreases, so do the aerodynamic and tip frictional forces between the upstream and downstream bristle packs. In addition, the effects of the number of bristle axial rows and protection clearance height on the inter-stage imbalance are analyzed. The results indicate that the TSBS exhibited significantly less leakage and lower aerodynamic and tip frictional forces than a single-stage brush seal. However, the inter-stage pressure differential results in an inter-stage imbalance in the aerodynamic and tip frictional forces that can be aggravated under high pressure conditions. This study determined that reasonable adjustments can be made to the number of bristle axial rows and protection clearance heights of the upstream and downstream stages to alleviate this inter-stage imbalance. The findings of this study contribute to the design and implementation of more efficient TSBSs.Although a two-stage brush seal (TSBS) plays an important role in gas turbine machinery, few studies have investigated the complex flow and tip frictional force distributions of the TSBS. This article contributes to the ongoing investigation of the TSBS by proposing a 3D slice model employing computational fluid dynamics to analyze the flow and tip frictional force characteristics of a contacting TSBS using the torque balance principle and linear superposition methods. Our calculations reveal that as the inter-stage imbalance of the pressure decreases, so do the aerodynamic and tip frictional forces between the upstream and downstream bristle packs. In addition, the effects of the number of bristle axial rows and protection clearance height on the inter-stage imbalance are analyzed. The results indicate that the TSBS exhibited significantly less leakage and lower aerodynamic and tip frictional forces than a single-stage brush seal. However, the inter-stage pressure differential results in an inter-stage i...

Forces and variational compatibility for equilibrium liquid crystal director models with coupled electric fields

Expressions are obtained for force and couple densities and stress tensors in macroscopic models for nematic liquid crystals subjected to electric fields. The coupling between the liquid crystal orientational properties and the electric field is taken into account via a free energy of Oseen-Frank type expressed as an integral functional of the director field and the electric potential field. The variational model here also allows for a gravitational field and a magnetic field, and the differences among these three common types of force fields (gravitational, magnetic, and electric) are discussed. Also included in the free energy is a surface anchoring potential, and its effect on boundary traction and couple stress is explored. The electric field is assumed to arise from electrodes held at constant potential. Flexoelectric effects are included, and as a consequence, the material is no longer a linear dielectric medium. It is shown that the equilibrium solutions of the Euler-Lagrange equations satisfy appropriate expressions of force balance and torque balance, obtained from a virtual-work principle, and a connection is made between this and ideas related to Noether's Theorem. The development here builds from theories of Ericksen related to the notion of "variational compatibility," and this connection is made. Comparisons are also made to the extensive literature in physics and continuum mechanics on electromagnetic field/matter interaction.

Steady flow in a rapidly rotating spheroid with weak precession: I

The celebrated Poincaré (1910) steady solution, the uniform vorticity flow in a precessing spheroid, which is realized in the inviscid interior region outside the boundary layer in the strong spin and weak precession limit, is derived, as a unique solution analytically without any prior assumption on the spatial structure, and its singular behavior for a sphere is resolved. Assuming that the spin and precession axes are respectively parallel and perpendicular to the symmetry axis of the spheroid, we denote the spin and precession angular velocities by and respectively, and define the Reynolds number Re = and the Poincaré number , where a is the equatorial radius and ν is the kinematic viscosity of fluid. An ellipsoidal coordinate system is introduced, which makes it possible to express the solution explicitly in a separable form. It is shown that only the uniform vorticity flow can develop as a steady flow in the inviscid limit. The vorticity, relative to the spinning spheroid, is in magnitude and points to or against the z-axis for an oblate (c < 1) or a prolate (c > 1) spheroid. This expression of vorticity magnitude diverges to infinity for a sphere (c = 1), where the inviscid solution is degenerate. This apparent singular behavior of the vorticity is resolved by introducing viscosity and analyzing the flow by invoking the torque balance equation for a spheroid close to a sphere in the limit , where . It is found that the vorticity vector changes the orientation smoothly by 180° over and that the parallel and the perpendicular (to the spin axis) components of vorticity is expressed, up to the nontrivial leading order, as the twice of −0.7876Po2/[(2.620δ)2 + (0.2585δ + 1 − c)2] and , respectively. The latter is included in Busse ()'s formula, whereas the former is new. An analysis of the same flow as the present paper from a different approach was performed recently by Zhang et al (). Unfortunately, however, an inconsistency is found in their results.

Dynamics of the pedestal transport during edge localized mode cycles at ASDEX Upgrade

The dynamic behaviour of the ion and electron energy, particle and momentum transport measured during type-I edge localized mode (ELM) cycles at ASDEX Upgrade is presented. Fast measurements of the ion and electron temperature profiles revelead that the ion and electron energy transport recover on different timescales, with the electrons recovering on a slower timescale (Cavedon et al 2017 Plasma Phys. Control. Fusion 59 105007). The dominant mechanism for the additional energy transport in the electron channel that could cause the delay in the electron temperature gradient () recovery is attributed to the depletion of energy caused by the ELM. The local sources and sinks for the electron channel in the steep gradient region are much smaller compared to the energy flux arriving from the pedestal top, indicating that the core plasma may dictate the local dynamics of the recovery during the ELM cycle. A model for the edge momentum transport based on toroidal torque balance that takes into account the existence of poloidal impurity asymmetries has been developed. The analysis of the profile evolution during the ELM cycle shows that the model captures the dynamics of the rotation both before the ELM crash and during the recovery phase.