Formula For Force Research Articles

A non-destructive measurement method for axial force using torque in connecting bar with joint bearing ends

ABSTRACT The measurement of axial force in connecting bar is widely used in scenarios such as condition monitoring, motion controlling and fatigue analysing of mechanisms. By measuring the torque applied to the bar, this paper proposes an innovative method for non-destructive obtaining axial force in connecting bar with joint bearing ends. A mechanical analysis of joint bearing is conducted, and a theoretical model of axial force and torque is established. An experimental setup for measuring axial force and torque is constructed, and then the theoretical model is refined. The bar axial force and torque formula is calibrated at different torsional speeds, and the method correctness and reliability are verified experimentally. In summary, in a non-destructive way, this method is innovative and practical, addressing issues like inaccuracies in measuring bars with variable cross-section, even unknown material and inside structure, achieving relatively accurate measurement of axial force in connecting bar without damage.

Analysis of Frost Heaving Force in Seasonal Frost Region Tunnels: A Case Study of the Xiangyang Tunnel in China

Frost damage in seasonally frozen regions is a primary factor affecting tunnel safety, with frost heaving forces being the main external cause. Therefore, analyzing and calculating the distribution and magnitude of frost heaving forces on surrounding rock is essential for addressing frost damage in tunnels. When the frost heaving force exceeds the design strength, it can lead to the cracking of the lining concrete and a reduction in the tunnel's load-bearing capacity and support stability, posing serious safety risks during construction and operation. This paper is based on the Xiangyang Tunnel project and is grounded in elasticity theory for deriving the frost heaving force formula. Utilizing the von Mises criterion, it employs finite element software to perform thermal-structural coupling analysis, which provides insights into the temperature distribution within the tunnel and the stress distribution patterns of both the lining and the surrounding rock under the influence of frost heaving forces. In the shallow-buried section of the Xiangyang Tunnel, the maximum frost heaving force on the lining is concentrated at the junction of the arch and the base slab. In the deeply buried sections, the distribution of the frost heaving force in the lining is relatively uniform. In contrast, the surrounding rock's frost heaving force distribution follows a layered pattern from the inside out. Beyond a burial depth of 7 meters, the lining and surrounding rock frost heaving forces gradually decrease, approaching a constant value.

Post-Newtonian Effects in Compact Binaries with a Dark Matter Spike: A Lagrangian Approach

We apply the Lagrangian method to study the post-Newtonian evolution of a compact binary system with environmental effects, including a dark matter spike, and obtain the resulting gravitational wave emission. This formalism allows one to incorporate post-Newtonian effects up to any desired known order, as well as any other environmental effect around the binary, as long as their dissipation power or force formulae are known. In particular, in this work, we employ this method to study a black hole–black hole binary system of mass ratio 105 by including post-Newtonian effects of order 1PN and 2.5PN, as well as the effect of relativistic dynamical friction. We obtain the modified orbits and the corresponding modified gravitational waveform. Finally, we contrast these modifications against the LISA sensitivity curve in frequency space and show that this observatory can detect the associated signals.

Research on Radial Vibration Model and Low-Frequency Vibration Suppression Method in PMSM by Injecting Multiple Symmetric Harmonic Currents

Driven by frequency conversion, the windings of a three-phase permanent magnet synchronous motor (PMSM) contain both odd and even harmonic currents. Due to the motor’s pole–slot conductance modulation, the interaction between the magnetic fields generated by these harmonic currents and the permanent magnet field results in harmonic radial vibrations of the motor. This paper analyzes the three-phase currents of the prototype and derives the radial magnetomotive force (MMF) spatiotemporal models for symmetric harmonic currents. By integrating Maxwell’s magnetic force formula and vibration response formula, the radial vibration models for symmetric harmonic currents are developed. The characteristics of vibrations caused by odd and even harmonic currents, as well as positive sequence and negative sequence harmonic currents, are analyzed separately. A cyclic sequence, low-frequency vibration suppression control method incorporating multiple harmonic current injections was designed. Experimental results of this method are compared with those obtained using an ideal sinusoidal current. Except for the second harmonic vibration, all other vibrations are significantly suppressed, with a maximum suppression rate of 92.28%. The total vibration level is reduced by 12.7619 dB, and the average torque is reduced by 0.67% with the total harmonic distortion of the current at 2.89%. The experimental results show that the vibration method in this paper has little influence on the average torque of the motor, the current distortion rate is small, and the vibration suppression effect is good.

Analysis and Calculation of Cross-contact Force between Strands of Multi-layer Conductor

Abstract As a key component of the transmission line, the inter-layer cross-contact force of the internal strand is an important factor affecting the mechanical properties of the conductor. In this paper, the cross-contact characteristics between the strands of multi-layer conductors are analyzed. According to the relationship between the contact force and the contact distance between the strands, the finite element simulation of different material strands of different conductors at different cross angles is carried out. Through the analysis, it can be seen that the cross angle between the strands and the material of the strands have a significant impact on the contact force. Then, based on the existing Hertz contact theory model, the relationship between the contact force and the contact distance between the strands is modified, and the contact force and contact distance models suitable for different cross angles of the conductor strands are obtained, that is, the modified Hertz contact model. According to the simulation results, combined with the modified Hertz contact model, the contact force coefficient between the strands is fitted, and the calculation formula of contact force and contact displacement is proposed. The formula can be applied to the calculation of contact force at any intersection angle between strands. The calculation formula provides theoretical support for the accurate structural calculation of the conductor, which is helpful to the analysis and calculation of the contact friction between the strands.

An improved two phases-two points SPH model for submerged landslide

This research proposes an improved two phases-two points SPH model designed to simulate interactions between water and soil, particularly suitable for scenarios such as submerged landslides. This model treats water as a weakly compressible Newtonian fluid and soil as a cohesive-frictional material following an elastoplastic constitutive law, utilizing two layers of SPH particles to separately represent these two phases. An adaptive drag force formula is proposed that automatically switches between linear and nonlinear seepage modes based on the motion state of the porewater. Additionally, to improve the precision and stability of the model, a modified solid boundary condition and a method for calculating soil volume fraction are proposed, along with an SPH discretization formula that incorporates the effects of the volume fraction in a more effective way. The reliability of the improved two phases-two points SPH model is initially verified through two cases: a dry granular landslide and a submerged soil mass subjected to gravitational loading. Then, the effectiveness of the proposed improvement methods is further tested and validated through three submerged landslide cases with different grain diameters, demonstrating the applicability of the current model in simulating submerged landslides and its superiority in accuracy and stability compared to previous models.

Research and analysis of rock breaking mechanical model of single-roller PDC compound bit

In order to improve wear resistance and rock breaking efficiency of single-roller bit, a new type of bit, single-roller PDC compound bit is designed. The mechanical model of interaction between PDC teeth and rock of single-roller PDC compound bit is established, and the theoretical calculation formula of resultant force and torque generated by interaction between PDC teeth and rock on cone and bit is obtained. The rock-breaking experiment on the single-roller PDC compound bit are carried out. The results show that with the increase of front inclination angle, the axial force and radial force of PDC teeth decrease greatly at first and then tend to be stable, while the tangential force of PDC teeth decreases at first and then increases slightly; the axial force, radial force and tangential force all increase with the increase of the cutting depth; the maximum values of the three forces all appear at the position of the combined effect of the maximum cutting depth and the minimum front inclination angle. The maximum value of moment [Formula: see text] and [Formula: see text] both appear at the minimum value of h C and δ, while the maximum value of moment [Formula: see text] appears at the minimum value of δ. In order to reduce the acting moment generated by PDC cutter on the roller, the PDC cutter at different position heights can be designed with different front inclination angles. The rock breaking experiment results show that compared with the common single-roller bit, the single-roller PDC compound bit has higher rock breaking efficiency and better development prospect. When drilling in hard limestone, the single-roller PDC compound bit is more energy-efficient under higher WOB.

Experimental and numerical study on a multilayer magnetic field rotary eddy current inertial damper

To improve the output damping force of the eddy current damper, a multilayer magnetic field rotary eddy current inertial damper (MMF-RECID) is proposed. The MMF-RECID is an inerter-based eddy current damper. A prototype device of the MMF-RECID is manufactured and tested, and its mechanical properties are systematically investigated. Firstly, the configuration of the MMF-RECID is described, and the calculation formulas of the axial force are derived. Secondly, an MMF-RECID prototype is designed and fabricated, and the apparent mass and energy dissipation performance under recycled axial loading are investigated. Three-dimensional transient numerical simulations of eddy current damping are conducted using the ANSYS Electronics Desktop. The results show that the eddy current damping force exhibits velocity nonlinearity, and the test results are consistent with the simulation results. Next, the study focuses on parameters influencing the maximum eddy current damping torque generated by the copper plate and the corresponding critical rotating speed. These parameters encompass the number and size of the magnets, the thickness of the copper plate, and the air gap. Finally, the earthquake-reduction effect of a six-degree-of-freedom structure equipped with MMF-RECID is analyzed. This study demonstrates that the ball screw system of MMF-RECID achieves a multiplicative effect of apparent mass and eddy current damping force, the eddy current damping force of a multi-layer magnetic field versus a single-layer magnetic field conforms to the law of linear superposition, and the hysteresis curves are stable. The eddy current damping torque can be improved by increasing the number and size of the magnets, and decreasing the air gap. The thickness of the copper plate significantly affects both the maximum damping torque and the critical speed, and the optimal thickness range is between 2 mm and 4 mm.

Modelling aerodynamic forces and torques of spheroid particles in compressible flows

In the present study, we conduct numerical simulations of compressible flows around spheroid particles, for the purpose of refining empirical formulas for drag force, lift force, and pitching torque acting on them. Through an analysis of approximately a thousand numerical simulation cases spanning a wide range of Mach numbers, Reynolds numbers and particle aspect ratios, we first identify the crucial parameters that are strongly correlated with the forces and torques via Spearman correlation analysis, based on which the empirical formulas for the drag force, lift force and pitching torque coefficients are refined. The novel formulas developed for compressible flows exhibit consistency with their incompressible counterparts at low Mach number limits and, moreover, yield accurate predictions with average relative errors of less than 5%. This underscores their robustness and reliability in predicting aerodynamic loads on spheroidal particles under various flow conditions.

Improved artificial potential field method based on robot local path information

The artificial potential field (APF) is an important method for robot path planning. However, some information in APF is not fully utilized in practical applications. In this paper, an improved artificial potential field (IAPF) method is presented, in which the local path information is defined and used. And the calculation formulas for various forces in IAPF are given, which include repulsive force (R-force) of obstacle on the robot, the attractive force (A-force) of target on the robot, and the resultant force of R-force and A-force. Then, based on the local path information, a method for solving the robot falling into local optimality problem is proposed and used into IAPF. Finally, IAPF is respectively simulated and discussed in general scenario, complex scenario, and scenarios with the same and different size of circular obstacles. The results show that IAPF has higher efficiency than traditional artificial potential field (TAPF) method and can overcome the local optimality problem. At the same time, IAPF is compared with dynamic window method in the scenarios with the same and different size of circular obstacles. The results show that IAPF is more efficient than the dynamic window approach (DWA) for robot path planning.

Electromagnetic forces and their finite element computation

AbstractThis paper introduces the concepts of differential geometry that are necessary to establish a systematic definition for electromagnetic forces by means of a natural thermodynamic approach. It is shown that standard electromagnetic force formulae used in finite element computational electromagnetism are particular instances of that general approach. Finally, the paper offers a complete conceptual framework, as well as a mathematical toolbox, to derive electromagnetic force formulae for multi‐physics finite element models with complex materials.

Joint load-bearing behaviors and interface failure mechanism of encased coal samples under uniaxial compression

Concrete-encased coal pillars that serve as an effective support structure in coal mines have attracted increasing attention. This paper aims to explore the coupling bearing behaviors and the properties of interface force transfer between the interior coal and the encasing concrete. Laboratory uniaxial compression experiments were conducted on encased coal samples. Additionally, an interface force formula was derived based on deformation coordination and equilibrium conditions, and a mathematical formula was developed to estimate the load-bearing capacities of both the interior coal and the encased concrete. The research indicates that the stress–strain curve of the concrete-encased coal samples exhibits a distinct “double-peaked” phenomenon, and the load is transferred from the interior coal to the external concrete during the failure process. In the early stages of failure, the interface force enhances the strength of the coal pillar, while the lateral strain of the interior coal column exacerbates the damage to the encasing concrete. Moreover, the force at the concrete-coal interface is proportional to the axial loads and the mechanical properties of both materials. The strength of the coal pillar is significantly enhanced by lateral confinement. This study provides an experimental basis and theoretical analysis support for reducing the disaster of coal pillar instability.

Simplified Formula for Nominal Force at Critical Welds in the Lower Chord Node of a Novel Bracket-Crane Truss Structure

In the realm of practical engineering, engineers commonly employ rod system models for modeling and analysis, which consequently precludes them from calculating the nominal forces exerted on welds at intricate nodes. This paper addresses the design challenges of the innovative bracket-crane truss structure by proposing a simplified nominal force calculation formula for critical welds of the integrated node. This study commences with the establishment of the frame model and ABAQUS multiscale models, utilizing engineering project drawings and data, followed by a verification of the similarities between the two simulation methods. This similarity of outcomes provides a foundation for directly using the computational results from the frame model in future calculations of the forces at the weld locations. From a mechanical standpoint, this paper derives nominal force calculation formulas for horizontal and vertical welds at critical locations for three node types. Additionally, a formula for calculating nominal shear forces in vertical welds at the end plate of support nodes is introduced. The applicability of these derived formulas is subsequently validated, ensuring their efficacy in accurately capturing relevant forces at critical locations. The presented nominal force calculation formula serves as a valuable tool for optimizing the design and guaranteeing the structural integrity of the integrated node within this distinctive engineering context.

New Drag Force Formula of Bending Stems in Deriving Analytical Solutions of Velocity Profile for Flow Through Flexible Vegetation

AbstractInvestigations of water flow movements affected by vegetation is a research hotspot in vegetation ecological restoration. The theory and equations of the flow velocity distribution under the influence of rigid vegetation are relatively mature. This study proposes a new drag force equation that varies with the vegetation bending angle and a new analytical solution of the velocity profile. Comparisons between the model calculation and experimental data, results showed that this new proposed model produced accurate simulations for flow through flexible vegetation for various deflections. In addition, this analytical model was verified to be applicable to rigid vegetation without a bending angle. Moreover, the features of the parameters adopted in this analytical equation are discussed, and the empirical equation for these parameters are presented. This study further improves the research in the field of environmental fluid mechanics and can serve as a theoretical underpinning for the ecological restoration of river courses.

Label-Free Continuous Cell Sorting Using Optofluidic Chip.

In the field of biomedicine, efficiently and non-invasively isolating target cells has always been one of the core challenges. Optical fiber tweezers offer precise and non-invasive manipulation of cells within a medium and can be easily integrated with microfluidic systems. Therefore, this paper investigated the mechanism of cell manipulation using scattering force with optical fiber tweezers. We employed flat-ended single-mode fiber to drive and sort cells and derived the corresponding scattering force formula based on the T-matrix model. A single-mode optical tweezers system for cell sorting was developed, and an optofluidic experimental platform was constructed that effectively integrates the optical system with microfluidic chips. The chip, featuring an expanded cross-channel design, successfully achieved continuous separation of yeast cells (8~10 µm in diameter) and polystyrene microspheres (15~20 µm in diameter), with a sorting efficiency of up to 86% and maintaining viability in approximately 90% of the yeast cells. Compared to other sorting systems, this system does not require labeling and can achieve continuous sorting with cell viability at a lower cost of instrumentation.

Dynamic modeling of cable deployment/retrieval based on ALE-ANCF and adaptive step-size integrator

The towing vehicle must maintain a stable distance from the seafloor to ensure the accuracy and safety of deep-towed seismic systems. However, due to equipment limitations, controlling the towing depth is achievable solely by adjusting the length of the towing cable. In this study, an Absolute Nodal Coordinate Formulation (ANCF) with Arbitrary Lagrange-Euler (ALE)description is employed to model variable-length flexible towing cables. The inertial and elastic force formulas for ALE-ANCF, along with their corresponding Jacobian matrices, are derived in detail, and their coefficient matrices are precomputed to avoid Gaussian integration. The proposed adaptive step-size strategy enhances computational efficiency. Detailed investigation into the impact of cable deployment/retrieval on towing depth is conducted, revealing an almost linear relationship between length change and towing depth. In Addition, a proportional, integral, derivative (PID) controller with compensation is proposed for efficiently tracking the target depth and alleviating the perturbations from the mothership, illustrating the feasibility of PID control. These findings hold practical significance for enhancing the operational safety and efficiency of deep-towed seismic systems.

Analytical calculation method of circular-section rocking steel piers under horizontal cyclic load

The research object of this paper is to investigate the mechanical behavior and develop an analytical model of the prestressed circular-section rocking steel piers with external energy-dissipating devices under the horizontal cyclic load. Based on the method of monolithic beam analogy under monotonic loading, the concept of generalized rotation angle and intercept strain in the pre-decompression state was introduced. The geometrical equations for the pre- and post-decompression stages are deduced. The calculation formulas for internal forces of each component and the analytical calculation method for the entire process of the rocking steel pier under horizontal cyclic loading are established in detail. To reproduce the hysteresis curve of the test, some special test conditions, such as the retraction effect of prestressed tendons and increase of the compressed area due to the vertical plates, were considered in the analytical model. The results show that the analytical method based on generalized rotation angle and intercept strain can ensure an ideal transition of the hysteresis curve of the pier in pre- and post-decompression stages. Except for the pier with particularly severe local buckling and ovalization deformation, the calculated results obtained from the proposed analytical model agrees well with the test results for the rocking steel bridge piers. The effect of prestressed tendons and the P–Δ effect on the lateral load–displacement curve of rocking steel bridge biers was further analyzed through parametric study using the proposed model. The analytical calculation method presented in this paper provides a theoretical tool for seismic design of the rocking steel pier in engineering practice. This paper provides important guidance for the establishment of seismic design method of rocking steel piers.

A high-speed gear reshaping method for electric vehicles combining the effects of input torque and speed variation.

In this study, we introduce an optimization method for high-speed gear trimming in electric vehicles, focusing on variations in input torque and speed. This approach is designed to aid in vibration suppression in electric vehicle gears. We initially use Tooth Contact Analysis (TCA) and Loaded Tooth Contact Analysis (LTCA) to investigate meshing point localization, considering changes in gear tooth surface and deformations due to load. Based on impact mechanics theory, we then derive a formula for the maximum impact force. A 12-degree-of-freedom bending-torsion-axis coupled dynamic model for the helical gear drive in the gearbox's input stage is developed using the centralized mass method, allowing for an extensive examination of high-speed gear vibration characteristics. Through a genetic algorithm, we optimize the tooth profile and tooth flank parabolic modification coefficients, resulting in optimal vibration-suppressing tooth surfaces. Experimental results under various input torques and speeds demonstrate that the overall vibration amplitude is stable and lower than that of conventional gear shaping methods. Specifically, the root mean square of vibration acceleration along the meshing line under different conditions is 58.02 m/s2 and 20.33 m/s2, respectively. The vibration acceleration in the direction of the meshing line is 20.33 m/s2 and 20.02 m/s2 under varying torques and speeds, with 20.33 m/s2 being the lowest. Furthermore, the average magnitude of the meshing impact force is significantly reduced to 5015.2. This high-speed gear reshaping method not only enhances gear dynamics and reliability by considering changes in input torque and speed but also effectively reduces vibration in electric vehicle gear systems. The study provides valuable insights and methodologies for the design and optimization of electric vehicle gears, focusing on comprehensive improvement in dynamic performance.

Comprehensive Investigation of Winding Mechanical Properties in Generators under RISC: Impact of Position, Degree, and Eccentricity

This paper provides an in‐depth study of the winding mechanical properties in generators under rotor interturn short circuit (RISC) cases. Unlike previous studies, this research investigates not only the influence of RISC degrees, but also the RISC positions and the eccentricity on the winding mechanical properties. The electromagnetic force (EF) formulas as well as the electromagnetic‐structure coupling model are first proposed to derive the mechanical winding response characteristics, such as the vibration, deformation, the strain, and the stress. Subsequently, both finite element analysis (FEA) and experimental investigations are conducted to validate the theoretical findings. The results reveal that RISC introduces additional harmonics to the EF. Furthermore, as the eccentricity/RISC degree or the distance between the short circuit position and the N‐pole increases, the end winding vibrations become more pronounced. When comparing single eccentricity and RISC faults to cases where both faults occur simultaneously, it is observed that the combined faults have a more detrimental impact on the end winding mechanical properties. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

Research on a Calculation Method for the Horizontal Displacement of the Retaining Structure of Deep Foundation Pits

The precise calculation and effective control of the horizontal displacement of deep foundation pit retaining structures are critical for foundation pit support design and construction. Based on stress–strain linear elastomer theory and considering the deformation coordination between an enclosure wall and its internal support member, a formula for the redundant restraint force acting on the retaining wall was derived through the unit load method and the principle of elastic superposition. Moreover, a method for calculating the horizontal displacement of the retaining structure of a deep foundation pit was formulated, which is convenient for engineering applications. The method can also be used to calculate the horizontal displacement of cantilevered and anchored retaining structures when the loading conditions of the deep foundation pit and the relevant parameters of the enclosure structure are known. A case study was conducted on a standard section with an excavation width H of 19.3 m and an excavation depth h of 17.8 m. The structural parameters of the enclosure wall, along with the elastic support stiffness coefficient and soil layer parameters of the pit, were inputted into a MATLAB calculation code. Then, four internal support constraint forces Fi and the calculated values for the horizontal displacement of the enclosure wall were obtained after running the code. The calculated curve closely matched the curve of values measured in the field. The horizontal displacements of the top of the wall of several cement–soil gravity enclosure structures mentioned in the literature were also calculated. The results of these calculations were then compared with the measured data and corresponding data from the literature. The examples provided clear evidence demonstrating that the proposed method is highly reliable for calculating the horizontal displacement of deep foundation pit enclosure structures.