Formula For Force Research Articles

Numerical Calculation and Experimental Study of the Axial Force of Aero Fuel Centrifugal Pumps

Axial force is one of the important factors affecting the life and reliability of centrifugal pumps. Based on the SST turbulence model, the unsteady internal flow field of an aero fuel centrifugal pump under various working conditions was analyzed by using the finite volume method and the axial force of the impeller component was predicted. The position servo force measuring system was used to measure the axial force of the fuel centrifugal pump and the theoretical formula of axial force was modified according to the numerical results and experimental values. The study shows that the pressure distribution of the front and rear pump chambers presented uneven circumferential distribution under the influence of dynamic and static interference through numerical simulation. The simulated head number is basically consistent with the test result and the maximum error of the axial force value obtained by the numerical calculation and the experimental value was 9.7% under different speeds, which verified the accuracy of the numerical simulation. Furthermore, the modified formula can accurately calculate the axial force of the fuel centrifugal pump with an error of less than 9.88%. The results of the study provide a theoretical basis for the calculation and balance of axial force in an aero aero fuel centrifugal pump.

Experimental and Finite Element Analyses of Adjustable Foundation Bolts in Transmission Towers

Uneven settlement of transmission tower foundations can result in catastrophic events, such as tower collapse and line failures, disrupting power transmission operations. To address the challenging repairs caused by uneven foundation settlement of transmission towers, we propose an adjustable foundation bolt (AFB). This paper provides a detailed theoretical analysis of the AFB’s stability and load-bearing capacity, including critical buckling force formulas and maximum normal stress expressions. Finite element simulations confirm the precision of our theoretical formulations. Additionally, we introduce a method using baffles to enhance its load-bearing capacity, analyzing the impact of different numbers of baffles through numerical simulations. The experimental results validate the effectiveness of baffles in enhancing structural load-bearing capacity. The device brings convenience and efficiency to the maintenance of transmission towers.

Study of the dynamic interactions between helix-stiffened cement mixing piles and soft soil under oblique incidence of SV waves in arbitrary space

Helix stiffened cement mixing (HSCM) piles are extensively utilized in soft soil sites due to their excellent seismic and pullout resistance. Initially, the equivalent nodal force formulas for each face under the oblique incidence of SV waves in any spatial direction are derived based on the viscous-spring artificial boundary. The method's applicability in studying pile–soil interactions is verified based on existing pile–soil tests. Subsequently, the HSCM pile–soil model is constructed using finite element software through a Python program. Various analyses of accelerations, relative displacements, soil reactions, and pile–soil dynamic p-y curves are conducted using two different directions of incidence angles (horizontal and vertical) and various types of seismic waves. Subsequently, the backbone line of the dynamic p-y curve is plotted, revealing the pile–soil interaction mechanism under spatial oblique incidence. Finally, Matlock's formula is modified to ensure its applicability to pile–soil interactions under spatially oblique incidence. The results demonstrate that loading the Kobe wave causes the peak acceleration in the x direction, the peak pile–soil relative displacement, and the peak pile-side soil reaction force to increase by 22.64 %, −18.90 % and 18.42 %, respectively, compared to those of the El Centro wave.

Generalized Linear Driving Force Formulas for Diffusion and Reaction in Porous Catalysts

Approximate models are a fast and most often precise tool for determining the effectiveness factor for heterogeneous catalysis processes that are realized in the real world. They are also frequently applied as robust transient models describing the work of a single catalyst pellet or as a part of a more complex model, for example, a reactor model, where mass balances for the gas phase and solid phase are necessary. So far, approximate models for diffusion and reaction processes have been presented for processes described by a single balance equation. In the present work, approximate models without the mentioned limitation are presented and discussed. In addition, simple rules are shown for the development of other complex approximate models without tedious derivation in the complex domain. The formulas considered in this work are typical long-time approximations of the transient process. The accuracy is good, especially in the range of small and intermediate Thiele modulus values.

Numerical simulation of the electromagnetic field in the secondary cooling zone of arc-shaped slabs

The magnetic field characteristics due to electromagnetic stirring in the secondary cooling zone of an extra-thick slab during continuous casting are numerically determined using Maxwell's equations, with particular emphasis on the distribution of magnetic induction intensity and electromagnetic force, as well as the influence of process parameters on the magnetic field. The orientation of the electromagnetic force is the same when the electromagnetic stirrers at the 30° and 60° posistions of the arc-shaped slab are powered in the same direction; otherwise, the orientation is opposite. The magnetic induction at the centre of the section of the stirrer's central axis at the 30° positio, as well as the current, frequency, and fitting formulae, are as follows: B = {0.075I(1/A)-0.3} mT and B = {-1.75f(1/Hz)+22} mT. The electromagnetic force and current fitting formula at the central point of the B-B section is F = {0.03168I2(1/A2)-03.762I(1/A)+326.7} N/m3, and the fitting formula of electromagnetic force and frequency at the centre point is divided into two segments. The first takes the form of a parabola: = {-21((f-4.3)-(1/Hz)2)+970} N/m3, and the second segment is negative linear: F = {-1.65f(1/Hz)+51.5} N/m3.

Sayed`s Theory of Dark Energy and Dark Matter Forces Nature

Allah (God) is the Creator of the wonderful accelerated expansion of universe. The nature of Dark energy (DE) and matter (DM) is enigmatic mystery of the modern astrophysics. This article is a theory establishes the nature and laws of DE and DM forces. They are among the forces controlling the universe harmony and homogeneity. The derived equations were based on the published Sayed quantum gravity force formula. The Sayed`s Dark energy force (SDEF) formulas indicate that they are function in quantum gravity force (FQG), energy density(ρ), cosmological (Ʌ), Hubble (H), and Planck (h) constants. The formulas were verified and validated. For Planck and cosmos scales, the Dark energy force, energy density, and Ʌ were calculated and found to be 2.538x1084 N, 10-26 Kg/m3, and 10-52 m-2 respectively. These values are in high concordance with the declared values. The results obtained show that the DE force represents more than ¾ of the universe forces as the observations. The disputed Hubble constant was also calculated and found to be in the range; ~2.2 x10-18 s-1. It can also be stated and emphasized that the light speed violation (E≠mc2) is a must to solve the DE nature and many other universe mysteries.

Co‐excitation control of a four‐degree‐of‐freedom magnetic bearing switched reluctance motor based on mathematical models

AbstractIn traditional magnetic bearing motors, the magnetic bearing and the motor are usually driven and controlled separately, resulting in higher controller costs and limiting further expansion of their applications. The author presents a four‐degree‐of‐freedom (4DOF) magnetic bearing switched reluctance motor (MBSRM), consisting of two 8‐pole active radial magnetic bearings (RMBs) and two two‐phase 4/2‐pole switched reluctance motors (SRMs), driven simultaneously by a set of asymmetrical power converters together. Firstly, the structure, winding configuration and co‐excitation working principles of the 4DOF‐MBSRM system are described in detail. Then the radial force formula for an 8‐pole RMB and the torque mathematical model for a 4/2‐pole SRM are briefly derived based on equivalent magnetic circuits, respectively. Furthermore, a co‐excitation control strategy for the 4DOF MBSRM is developed wherein an instantaneous radial force is used to control its rotor shaft levitation, an instantaneous torque is employed for rotational control at low and medium speeds, and an average torque is used for high speed operation. Finally, the good performance of the co‐excitation control for the proposed 4DOF‐MBSRM is proved by simulation analysis.

Simplified Nonlinear Damping Force Formula for Rotary Eddy Current Dampers and Comparative Hazard Analysis under Seismic Excitation with Fluid Viscous Dampers

Simplified Nonlinear Damping Force Formula for Rotary Eddy Current Dampers and Comparative Hazard Analysis under Seismic Excitation with Fluid Viscous Dampers

Pull-off of viscoelastic spherical contact

This paper studied the adhesive contact between a viscoelastic sphere and a rigid plane, and presented a dimensionless first-order differential equation to directly describe the relationship between the applied load and the contact radius. By adopting a combination strategy, the singularity of Muller’s dimensionless first-order differential equation was avoided well. To study the dependence of the pull-off force on the initial applied load, a table-based linear and logarithmic interpolation method was presented to determine the contact radius at the pull-off. The dependence of the square root (ζmax) of the ratio of the effective adhesion work at the upper bound to the equilibrium adhesion work on Muller’s parameter β and material constant n was deduced theoretically. And the relationship between the contact radius at the upper bound and ζmax was also deduced theoretically. In addition, the ratio of the pull-off force to the maximum pull-off force was determined to be cubic function of the ratio of the contact radius at the pull-off to that at the upper bound numerically. If β, n and the initial applied load were given, utilizing these relationships, the pull-off force and the maximum pull-off force could be predicted well. Lastly, Violano-Chateauminois-Afferrante JKR-like formula for the pull-off force and the upper bound was verified.

Axial Crushing Theory and Optimization of Lattice-Filled Multicellular Square Tubes.

A lattice-filled multicellular square tube features a regular cross-sectional shape, good energy consumption, and good crashworthiness, which is suitable for the design of energy absorbers in various protection fields such as automobiles, aerospace, bridges, etc. Based on the super folding theory, two reference planes are set to refine the energy consumption zone of the super folding element in this study. The energy consumption calculation of convex panel stretching is involved, and the critical crushing force formula is introduced in this study. Meanwhile, the calculation method from a single-cell square tube to a multicellular thin-walled square tube is extended and the structural optimization is investigated, in which the NSGAII algorithm is used to obtain the Pareto front (PF) of the crashworthiness performance index of the square multicellular tubes, the Normal Boundary Intersection (NBI) method is adopted to select knee points, and the influence of different cross-sectional widths on the number, as well as the thickness, of cells are discussed. This study's results indicate that the theoretical value is consistent with that obtained from the numerical simulation, meaning that the improved theoretical model can be applied to predict the crashworthiness of multicellular square cross-sectional tubes. Also, the optimization method and study results proposed in this study can provide a reference for the design of square lattice multicellular tubes.

Design and mechanical properties analysis of a cellular Waterbomb origami structure

Cellular structures are commonly used to design energy-absorbing structures, and origami structures are becoming a prevalent method of cellular structure design. This paper proposes a foldable cellular structure based on the Waterbomb origami pattern. The geometrical configuration of this structure is described. Quasi-static compression tests of the origami tube cell of this cellular structure are conducted, and load-displacement relationship curves are obtained. Numerical simulations are carried out to analyze the effects of aspect ratio, folding angle, thickness and number of layers of origami tubes on initial peak force and specific energy absorption (SEA). Calculation formulas for initial peak force and SEA are obtained by the multiple linear regression method. The degree of influence of each parameter on the mechanical properties of the single-layer tube cell is compared. The results show that the cellular structure exhibits negative stiffness and periodic load-bearing capacity, as well as folding angle has the most significant effect on the load-bearing and energy-absorbing capacity. By adjusting the design parameters, the stiffness, load-bearing capacity and energy absorption capacity of this cellular structure can be adjusted, which shows the programmable mechanical properties of this cellular structure. The foldability and the smooth periodic load-bearing capacity give the structure potential for application as an energy-absorbing structure.

Energy transfer efficiency and rock damage characteristics of a hydraulic impact hammer with different tool shapes

The energy transfer efficiency and damage characteristics are the theoretical basis for the selection and optimization of hydraulic impact hammer tools. In this paper, quarter three-dimensional models of the piston-tool-rock system are established based on the continuum and discontinuum element method. The incident and reflected stress waves and rock damage characteristics obtained from the simulation model are in good agreement with experimental and theoretical results. The effects of piston impact velocity, tool shape, rock strength, confining pressure and repeated impacts on rock damage zone and energy transfer efficiency between tool and rock are analyzed. The force-penetration curves and penetration coefficients under different impact velocities, rock strength, and confining pressure conditions are obtained. The results illustrate that the energy transfer efficiency and penetration coefficient increase with the increase of rock strength, confining pressure and tip area of tool, but decrease with the increase of impact velocity. Based on the simulation results, a prediction formula for penetration force with consideration of the shape of the tool tip is proposed and the calculation accuracy is verified. Finally, the proportion of energy actually used for rock fracturing is analyzed.

Numerical Study on Wave Dissipation and Mooring Force of a Horizontal Multi-Cylinder Floating Breakwater

A three-dimensional numerical model was established based on ANSYS-AQWA (R19.0) software for the purpose of analyzing the hydrodynamic characteristics of a floating breakwater. This study examines three distinct floating breakwaters with different cross-sectional designs in order to evaluate their respective wave dissipation capabilities. It is suggested that the horizontal multi-cylinder floating breakwater exhibits a superior ability to dissipate waves when compared to both the single-cylinder and square pontoon configurations and can be deemed the most advantageous shielding strategy for potential engineering applications. Subsequently, this study examines the effects of influential parameters, including a large cylinder diameter, a small cylinder diameter, the angular position of the small cylinder, and the height and period of the incident wave, on the wave transmission coefficient. An empirical formula for the wave transmission coefficient was derived based on the numerical results. Additionally, the effects of influential parameters, including wind speed, current velocity, incident wave height and period, and water depth, on the maximum total mooring force were investigated. Furthermore, an empirical formula for the maximum total mooring force is proposed for practical implementation in engineering.

Rolling force model of V-shaped variable thickness rolling based on energy approach

V-shaped Variable Thickness Rolling (V-VTR) serves as a specialized cold rolling method for manufacturing rolled profiled strips, particularly useful for quickly preparing rolled profiled strips with large thickness ratios. In the process of variable thickness rolling, metal predominantly flows in the lateral direction. However, there is a scarcity of theoretical models for calculating the rolling force of variable thickness rolling, leading to a void in theoretical guidance for both device design and product thickness control. To fill this gap, we introduce a novel mathematical model specifically designed to calculate the rolling force, considering the lateral flow of the metal. Initially, the deformation pattern is investigated and subsequently modeled. Then, the models for kinematically permissible velocity and strain fields are developed, and their validity is confirmed through both experimental data and simulation analysis. Incorporating factors like strain energy and frictional work, a formula for rolling force of variable thickness rolling is derived based on the upper bound theory. The efficacy of this newly proposed rolling force model is confirmed through experimental testing, which indicates that the formula offers a high degree of accuracy.

A method for rapid demolition of a crossline arch bridge: a case study

To reduce the adverse impact of demolition of the symmetrical rigid frame arch bridge overcrossing the highway with over-saturated traffic flow, a rapid demolition method based on the Self-Propelled Modular Transporter (SPMT) technique was developed in this study. The calculation formulae for reaction forces of the supporting brackets, as well as driving force and stability of SPMTs, were derived by analyzing the stability, synchronization, and influencing parameters of the cut bridge body—transport system. In addition, a monitoring system during the whole process was developed to ensure the demolition safety. An application of demolishing a crossline symmetrical rigid frame arch bridge in China within 5 h has been presented. The results showed that the proposed method can be successfully applied in real projects, leading to significant reduction in traffic impact, energy consumption, and environmental pollution.

Aerodynamic force by Lamb vector integrals in unsteady compressible flows

PurposeThis study aims to propose an aerodynamic force decomposition which, for the first time, allows for thrust/drag bookkeeping in two-dimensional viscous and unsteady flows. Lamb vector-based far-field methods are used at the scope, and the paper starts with extending recent steady compressible formulas to the unsteady regime.Design/methodology/approachExact vortical force formulas are derived considering inertial or non-inertial frames, viscous or inviscid flows, fixed or moving bodies. Numerical applications to a NACA0012 airfoil oscillating in pure plunging motion are illustrated, considering subsonic and transonic flow regimes. The total force accuracy and sensitivity to the control volume size is first analysed, then the axial force is decomposed and results are compared to the inviscid force (thrust) and to the steady force (drag).FindingsTwo total axial force decompositions in thrust and drag contributions are proposed, providing satisfactory results. An additional force decomposition is also formulated, which is independent of the arbitrary pole appearing in vortical formulas. Numerical inaccuracies encountered in inertial reference frames are eliminated, and the extended formulation also allows obtaining an accurate force prediction in presence of shock waves.Originality/valueNo thrust/drag bookkeeping methodology was actually available for oscillating airfoils in viscous and compressible flows.

Analytical approach to the design of a high-force density double-sided linear switched reluctance motor

This paper presents an analytical approach to the design of a high–force density double-sided linear switched reluctance motor (LSRM). The design is based on an analytical formulation of the average propulsion force determined using the non-linear energy conversion loop, in which the unaligned magnetization curve is assumed to be a straight line and the aligned magnetization curve is represented by two straight lines. The main dimensions of the LSRM are determined in accordance with the machine requirements, the proposed average propulsion force formula and the geometrical relationships that were presented in a previous paper. The present paper uses two dimensional finite element analysis that has been corrected to take into account the end effects in order to refine and/or to validate the proposed design. Finally an LSRM prototype was built following the proposed design and was verified by experimental measurements.

Magneto-thermoelastic coupled resonance characteristics of a rotating functionally graded ferromagnetic cylindrical shell under double harmonic line loads

The magneto-thermoelastic coupled resonance of a rotating functionally graded (FG) ferromagnetic cylindrical shell subjected to double harmonic line loads in magnetic and temperature fields is investigated. In accordance with Donnell's thin shell theory on the physical neutral surface, the nonlinear geometric equations are determined. Utilizing the thermoelastic constitutive relationships, combining with the gradient characteristics and temperature dependence of physical parameters, the governing equations of kinetic energy and strain energy are given. Based on the magnetoelasticity theory, and considering the nonlinear magnetization of ferromagnetic metal, the calculation formulas of Lorentz force and magnetizing force acting on the shell are deduced. The magneto-thermoelastic coupled dynamic equations are derived by applying Hamilton principle and discretized by Galerkin method. Subsequently, considering the different resonance forms, the multiple scales method and Lyapunov stability theory are employed to obtain the theoretical solutions and stability discriminants. Numerical examples are carried out to plot the characteristic diagrams with different parameters, which are used to analyze the characteristics of nonlinear coupled resonance. Furthermore, the primary resonance and combination resonance are selected to analyze the bifurcation and chaotic behavior. Results show that the variation of different parameters affects obviously the resonance amplitude and stability. The changes of amplitude and position of hard excitation can lead to resonance region drift. Amplitude, frequency, and position of excitation have significant effects on bifurcation and chaos. The motion state of cylindrical shell is transmitted from periodic response to chaotic response through the accumulation of period-doubling bifurcation.

Refined secondary Bjerknes force equation for double bubbles with pulsation, translation, and deformation

The secondary Bjerknes force (SBF) is the time-averaged interaction between two bubbles driven in a sound field. We derived a refined formula for the interaction force, incorporating the radial vibration and translational and deformational motions of the bubble. The coupling of pulsation, translation, and deformation enhances the interaction between bubbles but also weakens their stability, making it easier for bubbles to merge or break during motion. The effects of the coupling mode on the magnitude and direction of SBFs coupled with pulsation, translation, and deformation were numerically analyzed and studied. Under certain sound-field conditions, the SBF increased with increasing pressure amplitude, initial radius, and initial velocity, while decreased as the distance increased. In addition, the SBF irregularly increased with increasing frequency.

Prospects for mathematical modeling in mining system development: accounting for global oscillations and seismic waves

The article discusses the potential of mathematical modeling in understanding the impact of vibrations and seismic waves, aiming at enhancing the sustainability of systems within the mining industry. It explores the dynamic response of a tall, elastic structure with a uniform cross-section and a fixed cylindrical fluid reservoir, subject to various complex boundary conditions. The study delves into the vibrational behavior of the structure when exposed to seismic and harmonic forces, calculating frequency, vibration periods, and deriving formulas for stress, tension, deformation, bending moments, and shear forces in different parts of the structure through both theoretical and experimental approaches. Additionally, the article derives the differential equation for the free oscillation of a tall hydraulic structure in pure bending with an incorporated mass load under appropriate boundary conditions, identifying specific vibration frequencies and periods. The forced vibration scenario is also examined, focusing on the structure's foundation movement due to external harmonic forces. Numerical computation technology is utilized to analyze the change laws of principal quantities that describe both free and forced vibrational movements of the hydraulic structure, showcasing the applicability of these models in predicting and mitigating the effects of seismic activities on mining infrastructure.