Force Decomposition Method Research Articles

A method for quantitatively depicting the influence of vortices on the pressure forces acting on a hydrofoil in cavitating flow with tip clearance

In this paper, the force decomposition method (FDM) is proposed for decomposing the pressure forces acting on the immersed body. The major improvement in FDM is the applicability in RANS and LES simulations with non-constant density flows, e.g. cavitating flow. In the single-phase flow over a circular cylinder (Re = 3900), the FDM results show excellent agreement with the pressure force given by conventional method. In the cavitating flow over a hydrofoil with tip clearance, FDM can also reproduce the same tendency of the pressure force with an average deviation below 17%. In this case, the vorticity and kinematic effect induced force dominates the pressure force. In order to isolate the effect of attached cavitation near the suction side and tip clearance cavitation, a method combing domain cutting (manually) and cell extracting (by a threshold of vorticity magnitude) is proposed. The lift caused by vorticity force is mainly affected by the vortices shedding from the suction side of the hydrofoil. Also, the tip clearance region should not be ignored, where the lift generation by TLV is the interaction of strong shear and rotating flows.

Enhanced performance of a self-propelled flexible plate by a uniform shear flow and mechanism insight

The hydrodynamics of a two-dimensional self-propelled flexible plate in a uniform shear flow is explored using a penalty-immersed boundary method. The leading edge of the plate is enforced into a prescribed harmonic oscillation in the vertical direction but free to move in the horizontal direction. It is found that as the shear rate increases, the input power, the propulsive velocity, and the efficiency increase. This finding means that the plate enables to get substantial hydrodynamic benefits from the shear flow. Using the force decomposition method based on the weighted integral of the second invariant of the velocity gradient tensor, the hydrodynamic force exerted on the plate is decomposed into a body-acceleration force, a vortex-induced force, and forces due to viscous effects. The results show that the body-acceleration force is the main driving force of the self-propelled motion, and that it is almost invariant with the shear rate. The vortex-induced force offers a significant contribution to the drag, and it decreases with the shear rate. The viscous friction force provides a pure drag, and it increases with the propulsion velocity. Further investigation on the vortex evolution and the vortex-induced force shows that the incoming shear flow destroys the trailing-edge vortex that sheds during the downward half period and, therefore, reduces the vortex-induced drag, which is the reason for the enhanced propulsive performance in the shear flow. The result obtained in this study provides new insight into the self-propulsion mechanism in complex incoming flows.

Vortex force map for incompressible multi-body flows with application to wing–flap configurations

The vortex force map method for incompressible viscous flows with multiple bodies is derived in this work. The method breaks the fluid force into inertial, vortex-pressure, viscous-pressure and skin-friction components, and it could be used to analyse the fluid dynamic forces on individual bodies in a multi-body assembly. For the first time, we provide a graphical representation of the vortex-pressure force – the vortex force map – for individual bodies in a multi-body assembly. We have shown that the vortex force map in a multi-body set-up differs from single-bodied counterparts from modifications to their hypothetical potential through a nonlinear cross-coupling, and that the inertial and viscous-pressure contributions contain influences from other bodies explicitly. We then demonstrate the multi-body vortex force decomposition method with a wing–flap starting flow problem using computational fluid dynamics data, identifying the positive and negative force-generating critical regions or directions. It is found that the dominant force is the vortex-pressure force, and the force variation against time is closely related to the evolution of the vortex structures. Furthermore, we showed that the existence of another body significantly alters the force contribution roles of vortices in the flow.

Stiffness modeling of some 4-DOF over-constrained parallel manipulators with various constrained wrench forms

This study aims to build a unified stiffness model of three 4-degree of freedom (DOF) over-constrained parallel manipulators (PMs), which comprise a novel PM with four constrained forces, a PM with four constrained torques, as well as a PM with two constrained forces and two constrained torques. First, with the geometrical conditions as a starting point, a research is discussed on the constrained wrenches and kinematics analysis of the three PMs. Second, oriented to different constrained wrench forms in the three over-constrained PMs, the wrenches directly causing deformations are determined based on the deformation and force decomposition method, and the correlations between the wrenches and their corresponding deformations are explored according to the material mechanics. Third, all of the above analysis, combined with the virtual work principle of deformed body and the static balance principle, a unified stiffness model which is suitable for the three 4-DOF over-constrained PM with various constrained wrench forms is established. Lastly, an integrated finite element (FE) simulation model of the three PMs is built to verify the correctness of the analytic stiffness model. This study proposes a general and straightforward approach to solve the stiffness problem of 4-DOF over-constrained PMs with various constrained wrench forms.

Full-Aircraft Energy-Based Force Decomposition Applied to Boundary-Layer Ingestion

This Paper introduces a generic force decomposition method derived from mechanical energy conservation. A transformation from relative to absolute reference frame captures the power transfer from pressure and skin-friction forces on aircraft surfaces to mechanisms in the flowfield. A unique flow-feature extraction procedure isolates these mechanisms into different regions including the jet-plume substructures as well as shocks and shear layers located externally to the jet. Featured is a novel shear-layer identification metric that captures both laminar and turbulent regions. The resulting energy balance is rearranged into a force decomposition formulation with contributions attributed to shocks, jets, lift-induced vortices, and the remaining wake. Boundary-layer ingestion is used to demonstrate the method where a potential for energy recovery factor is introduced and defines the amount of energy available at the trailing edge of an unpowered body. Computational fluid dynamics results of a fuselage suggest 10% of its drag power is available for reuse. Computational fluid dynamics studies of a boundary-layer ingesting propulsor show local minima in power consumption at a given thrust split for particular combinations of fan pressure ratio and amount of boundary layer ingested. A noteworthy finding reveals significant contributions of volumetric pressure work, a term often neglected in previous work.

Gait compensatory mechanisms in unilateral transfemoral amputees

Individuals with unilateral transfemoral amputation depend on compensatory muscle and joint function to generate motion of the lower limbs, which can produce gait asymmetry; however, the functional role of the intact and residual limb muscles of transfemoral amputees in generating progression, support, and mediolateral balance of the body during walking is not well understood. The aim of this study was to quantify the contributions of the intact and the residual limb's contralateral muscles to body center of mass (COM) acceleration during walking in transfemoral amputees. Three-dimensional subject-specific musculoskeletal models of 6 transfemoral amputees fitted with a socket-type prosthesis were developed and used to quantify muscle forces and muscle contributions to the fore-aft, vertical, and mediolateral body COM acceleration using a pseudo-inverse ground reaction force decomposition method during over-ground walking. Anterior pelvic tilt and hip range of motion in the sagittal and frontal planes of the intact limb was significantly larger than those in the residual limb (p<0.05). The mean contributions of the intact limb hip muscles to body COM support, forward propulsion and mediolateral balance were significantly greater than those in the residual limb (p<0.05). Gluteus maximus contributed more to propulsion and support, while gluteus medius contributed more to balance than other muscles in the intact limb than the residual limb. The findings demonstrate the role of the intact limb hip musculature in compensating for reduced or absent muscles and joint function in the residual limb of transfemoral amputees during walking. The results may be useful in developing rehabilitation programs and design of prostheses to improve gait symmetry and mitigate post-operative musculoskeletal pathology.

Practical Residual Force Decomposition Method for Damage Identification of Existing Reticulated Shells

The non-destructive damage identification approaches for existing structures become more of a concern due to safety requirements. However, the application of damage identification method is still limited for complex spatial structures. In this paper, a practical residual force decomposition (RFD) method is proposed to identify damaged members in existing reticulated shell structures. A parameterized model is built by taking the stiffness reduction into consideration. In the proposed RFD method, the significant damage can be recognized corresponding to the changes of the observed eigenvector of the reticulated shells, and the eigenvector changes can be easily transferred to a set of multivariate linear equations to locate the members with significant stiffness reduction. The inputs of the equations are discussed including the additional constraints and the selection of effective modes. According to the different proportion of the numbers of members and joints, three situations of the solution are discussed. Especially when the solution is not unique, the importance coefficients of structural members are introduced as additional constraints through Ritz vector sensitivity analysis and application of the Modal Assurance Criterion. Two illustrative examples including a single-layer Kiewitt-6 reticulated shell and a structural model of international convention center are adopted to demonstrate the effectiveness of the approach. The results show that the proposed method can yield a suitable damage identification.

Microcontact mechanism in silicon wafer self-rotating grinding based on force decomposition

Carrying out silicon wafer self-rotating grinding using a cup-type diamond grinding wheel is a typical ultra-precision machining technique of silicon wafers. Studying the mechanism of the self-rotating grinding is the basis of the processing. The research takes the microcontact between the micro-element in the grinding wheel and the silicon wafer extracted during the steady ductile-regime grinding as the object and builds a mechanical model. On this basis, the research investigates the microscopic mechanism of the self-rotating grinding using the force decomposition method. The force decomposition in the normal direction using the Hertz theory in contact mechanics and the cavity model obtained the distributions of the load and stress on the silicon wafer in the elastic and plastic contact, as well as the corresponding stress distribution on the micro-element in the grinding wheel. The force decomposition in the tangential direction based on the microscopic friction theory yields the sliding friction. The superposition of normal and tangential forces reveals the overall distribution of microcontact stress. The analysis results are validated by comparing with corresponding experimental and simulation results.

Contact Force Decomposition Using Contact Pressure Distribution

Many robotics applications involving contact with objects require the decomposition of an external force measured by a force sensor into its normal and shear components. In this paper, we present a general and effective contact force decomposition method based on the contact pressure distribution. The contact pressure distribution can be measured easily using recently developed flexible pressure sensor arrays. Our method requires no preprocessing and provides accurate force decomposition, even for concave external objects. These advantages are demonstrated by simulations and experiments.

On the steady-state probability distribution of nonequilibrium stochastic systems

A driven stochastic system in a constant temperature heat bath relaxes into a steady state which is characterized by the steady state probability distribution. We investigate the relationship between the driving force and the steady state probability distribution. We adopt the force decomposition method in which the force is decomposed as the sum of a gradient of a steady state potential and the remaining part. The decomposition method allows one to find a set of force fields each of which is compatible to a given steady state. Such a knowledge provides a useful insight on stochastic systems especially in the nonequilibrium situation. We demonstrate the decomposition method in stochastic systems under overdamped and underdamped dynamics and discuss the connection between them.

The distributed diagonal force decomposition method for parallelizing molecular dynamics simulations

Parallelization is an effective way to reduce the computational time needed for molecular dynamics simulations. We describe a new parallelization method, the distributed-diagonal force decomposition method, with which we extend and improve the existing force decomposition methods. Our new method requires less data communication during molecular dynamics simulations than replicated data and current force decomposition methods, increasing the parallel efficiency. It also dynamically load-balances the processors' computational load throughout the simulation. The method is readily implemented in existing molecular dynamics codes and it has been incorporated into the CHARMM program, allowing its immediate use in conjunction with the many molecular dynamics simulation techniques that are already present in the program. We also present the design of the Force Decomposition Machine, a cluster of personal computers and networks that is tailored to running molecular dynamics simulations using the distributed diagonal force decomposition method. The design is expandable and provides various degrees of fault resilience. This approach is easily adaptable to computers with Graphics Processing Units because it is independent of the processor type being used.

Simulation of Two-Component Development Process for Frontloading Design

This report describes simulation technologies for digital frontloading of two-component development process in electrophotography. Electrophotography entails using multiphysics involving phenomena with yet unclear mechanisms such as air breakdown, tribocharging and powder dynamics. Thus, it requires much effort and many resources to develop electrophotography products. Numerical simulation is widely recognized as one of valid approaches to overcome these difficulties in product design. A tool for simulating the two-component development process has been developed including particle motion calculation using the Distinct Element Method and electric filed calculation using the Finite Element Method. The tool working on PC clusters is equipped with force decomposition method as a high-efficiency parallel computation algorithm to reduce calculation time. In addition, GUIs, and an online portal for PC clusters has been developed to support product designers utilizing the simulation tool. Validity of the tool was confirmed by comparison of developed toner mass and developer mass on development roller with the experimental results.

An independent distortional analysis method of thin-walled multicell box girders

When a thin-walled multicell box girder is subjected to an eccentric load, the distortion becomes an important global response in addition to flexure and torsion. The three global responses appear in a combined form when a conventional shell element is used thus it is not an easy task to examine the three global responses separately. This study is to propose an analysis method using conventional shell element in which the three global responses can be separately decomposed. The force decomposition method which was designed for a single-cell box girder by Nakai and Yoo is expanded herein to multicell box girders. The eccentric load is decomposed in the expanded method into flexural, torsional, and multimode distortional forces by using the force equilibrium. From the force decomposition, the combined global responses of multicell box girders can be resolved into separate responses and the distortional response which is of primary concern herein can be obtained separately. It is shown from a series of extensive comparative studies using three box girder bridge models that the expanded method produces accurate decomposed results. Noting that the separate consideration of individual global response is of paramount importance for optimized multicell box girder design, it can be said that the proposed expanded method is extremely useful for practicing engineers.

Force decomposition model for tool-wear in turning with grooved cutting tools

The lack of a satisfactory methodology to predict the tool-wear progression/tool-life in a machining operation with a grooved tool necessitates development of quantitative predictive models for tool-wear. This paper presents a new methodology for decomposing and distributing the resultant force generated in machining with a grooved tool within the three major tool-wear regions: edge region, secondary-face region, and groove backwall region. By measuring the edge force from the experiments, the forces acting on the other two major wear regions can be found from the kinematics of the 3-D chip-flow and the geometry of the tool insert. The Coulomb coefficient of friction is assumed only at the groove backwall region. The effect of chip side-flow is considered by measuring the chip side-flow angle from experiments using high speed filming techniques. With the new methodology, the decomposed forces acting on the wear regions can be related to the dominant wear modes of a grooved tool. The new methodology implicitly includes the influencing parameters on tool-wear, including cutting conditions, tool geometry and chip-groove geometry, since changes in these parameters are reflected in the cutting forces. This force decomposition method offers a new approach for predicting the cutting tool-wear analytically using the measured cutting forces.