Newton-Raphson Iteration Method Research Articles

Trajectory planning and automatic docking of LNG five-axis loading arm

PurposeIn response to the challenges posed by the conventional manual flange docking method in the LNG (Liquefied Natural Gas) loading process, such as low positioning accuracy, constraints on production efficiency and safety hazards, this study analyzed the LNG five-axis loading arm’s main functions and structural characteristics.Design/methodology/approachAn automated solution for the joints of the LNG loading arm was designed. The forward kinematic model of the LNG loading arm was established using the Denavit–Hartenberg (D-H) parameter method, and its workspace was analyzed. The Newton–Raphson iteration method was employed to solve the inverse kinematics of the LNG loading arm, facilitating trajectory planning. The relationship between the target position and the joint variables was established to verify the stability of the arm’s motion. Flange center identification was achieved using the Hough transform function. Based on the ROS platform, combined with Gazebo and Rviz, an experimental simulation of automatic docking of the LNG loading arm was conducted.FindingsThe docking errors in the XYZ directions were all less than 0.8 mm, meeting the required docking accuracy. Moreover, the motion performance of the loading arm during docking was smooth and free of abrupt changes, validating its capability to accomplish the automatic docking task.Originality/valueThe proposed trajectory planning and automatic docking scheme can be used for the rapid filling of LNG filling arms and LNG tankers to improve the efficiency of LNG transportation. In guiding the docking, the proposed automatic docking scheme is an accurate and efficient way to improve safety.

Static analysis using flexibility disassembly perturbation for material nonlinear problem with uncertainty

Nonlinear finite element analysis of large-scale structures usually requires a lot of calculation cost, because it is necessary to repeatedly inverse the modified stiffness matrix caused by nonlinearity in the calculation process. When considering the uncertainty in materials, the calculation of the nonlinear analysis will be more unbearable. To improve the computational efficiency, this work develops a new method for nonlinear analysis with material uncertainty based on flexibility disassembly perturbation (FDP) approach. The FDP is an algorithm that can quickly calculate the inverse of a stiffness matrix. The basic idea of the proposed method is to introduce the FDP formula into Newton-Raphson iteration method to accelerate the nonlinear iterative calculation. Three numerical examples, one statically determinate structure and two statically indeterminate structures, are used to verify the accuracy and efficiency of the proposed method. The results show that the calculation time of the proposed method is far less than that of the existing complete analysis and combined approximation algorithms. In terms of computational accuracy, for statically determinate structures, the proposed algorithm can obtain exact solutions that are identical to the complete analysis results, while for statically indeterminate structures, the proposed algorithm can obtain approximate solutions that are very close to the complete analysis results.

Prediction of Wind Turbine Gearbox Oil Temperature Based on Stochastic Differential Equation Modeling

Aiming at the problem of high failure rate and inconvenient maintenance of wind turbine gearboxes, this paper establishes a stochastic differential equation model that can be used to fit the change of gearbox oil temperature and adopts an iterative computational method and Markov-based modified optimization to fit the prediction sequence in order to realize the accurate prediction of gearbox oil temperature. The model divides the oil temperature change of the gearbox into two parts, internal aging and external random perturbation, adopts the approximation theorem to establish the internal aging model, and uses Brownian motion to simulate the external random perturbation. The model parameters were calculated by the Newton–Raphson iterative method based on the gearbox oil temperature monitoring data. Iterative calculations and Markov-based corrections were performed on the model prediction data. The gearbox oil temperature variations were simulated in MATLAB, and the fitting and testing errors were calculated before and after the iterations. By comparing the fitting and testing errors with the ordinary differential equations and the stochastic differential equations before iteration, the iterated model can better reflect the gear oil temperature trend and predict the oil temperature at a specific time. The accuracy of the iterated model in terms of fitting and prediction is important for the development of preventive maintenance.

Dynamic contact and stiffness characteristic analysis of angular contact ball bearings under combined external loads

A nonlinear dynamic model of angular contact ball bearing under combined external loads is established based on the nonlinear elastic Hertz contact theory and raceless control theory. The established dynamic model is solved by employing variable step size Newton Raphson iteration method and the validation of model is verified by comparing the proposed results with the corresponding results come from the existing literatures. The solution of the presented model has high accuracy compared with the existing experimental results. In addition, the computational efficiency of the proposed model is improved significantly by introducing iteration step size adjustment factor. According to the proposed model, the dynamic contact and stiffness characteristics of angular contact ball are studied systematically by investigating the effects of combined external load working conditions on the contact parameters including contact angle and contact force and the stiffness parameters including diagonal stiffness and off-diagonal stiffness. This research can provide the theoretical basis and technique guidance for the designation and manufacture of angular contact ball bearing under combined external loads.

Riding safety prediction of a high-speed train running on transition zone under foundation settlement

The settlement of piers and subgrade bending deformation are widely recognized as common issues in the transition zones of high-speed railway bridges. This study aims to investigate the settlement behavior within these transition zones and its impact on the dynamic interaction between trains and the track. To achieve this, a vehicle-track-transition zone mapping relationship model is developed to analyze both the settlement behavior and the resulting dynamic response characteristics. The study employs the finite element method and multi-body dynamics to construct the simulation model. Settlement effects are simulated using the Newton-Raphson iterative method, with the additional rail deformation caused by foundation settlement serving as the excitation for the vehicle-track-transition zone dynamic interaction system. In the numerical analysis, the dynamic effects of three key factors—train speed, transition zone length, and the amplitude of foundation settlement—are examined based on the performance of the vehicle-track-transition zone interaction. The time-frequency technique is utilized to comprehensively reveal and clarify the spatial-frequency characteristics of system responses influenced by settlement excitation. Moreover, the relationship between the safety-based settlement threshold and these three factors is calibrated.

A nonlinear interval finite element method for elastic–plastic problems with spatially uncertain parameters

This paper proposes a nonlinear interval finite element method for elastic–plastic analysis of structures with spatially uncertain parameters. The spatially uncertain parameters are described by the interval field, and the variation bounds of the elastic–plastic structural responses can be calculated effectively. Quantified by the interval field, the spatially uncertain parameters are represented by the interval Karhunen–Loève (K-L) expansion, based on which the nonlinear interval finite element equilibrium equation is formulated. An interval iterative method is then presented to solve the equilibrium equation and obtain an outer solution of the variation bounds of structural responses such as displacement. In this method, the Newton-Raphson iterative method is used to transform the nonlinear problem into a linear one, and then the interval iterative method is introduced to solve the interval linear equations. Three numerical examples are employed to illustrate the feasibility and accuracy of the proposed method.

Theoretical Evaluation of Lubrication Performance of Thrust-Type Foil Bearings in Liquid Nitrogen

The development of reusable liquid rocket turbopumps has gradually highlighted the disadvantages of rolling bearings, particularly the contradiction between long service life and high rotational speed. It is critical to explore a feasible bearing scheme offering a long wear life and high stability to replace the existing rolling bearings. In this study, liquid nitrogen is adopted to simulate the ultra-low temperature environment of liquid rocket turbopumps, and theoretical evaluations of the lubrication performance of thrust-type foil bearings in liquid nitrogen are conducted. A link-spring model for the bump foil structure and a thin-plate finite element model for the top foil structure are established. The static and dynamic characteristics of the bearings are analyzed using methods including the finite difference method, the Newton–Raphson iteration method, and the finite element method. Detailed analysis includes the effects of factors such as rotational speed, fluid film thickness, thrust disk tilt angle, and the friction coefficient of the bump foil interface on the static and dynamic characteristics of thrust-type foil bearings. The research results indicate that thrust-type foil bearings have a good load-carrying capacity and low frictional power consumption. The adaptive deformation of the foil structure increases the fluid film thickness, preventing dry friction due to direct contact between the rotor journal and the bearing surface. When faced with thrust disk tilt, the direct translational stiffness and damping coefficient of the bearing do not undergo significant changes, ensuring system stability. Based on the results of this study, the exceptional performance characteristics of thrust-type foil bearings make them a promising alternative to rolling bearings for the development of reusable liquid rocket turbopumps.

Size-dependent nonlinear bending of microbeams based on a third-order shear deformation theory

In this paper, the size-dependent nonlinear bending of microbeams subjected to mechanical loading is studied using a finite element formulation. Based on the von Kármán nonlinear relationship and the third-order shear deformation theory, a size-dependent nonlinear beam element is derived by using the modified couple stress theory (MCST) to capture the microstructural size effect. The element with explicit expressions for the element vector of internal forces and tangent stiffness matrix is derived by employing the transverse shear rotation as a variable. Nonlinear bending of microbeams under different mechanical loading is predicted with the aid of Newton–Raphson iterative method. Numerical investigation shows that the derived element is efficient, and it is capable of giving accurate results by several elements. The obtained results reveal the importance of the micro-size effect on the nonlinear behavior of the microbeams, and the deflections are overestimated when the microstructural effect is ignored. The effects of the material length scale parameter, boundary conditions and loading type on the bending response of the microbeams are studied and highlighted.

Pump System Model Parameter Identification Based on Experimental and Simulation Data

In this paper, the entire downhole fluid-sucker rod-pump system is replaced with a viscoelastic vibration model, namely a third-order differential equation with an inhomogeneous forcing term. Both Kelvin’s and Maxwell’s viscoelastic models can be implemented along with the dynamic behaviors of a mass point attached to the viscoelastic model. By employing the time-dependent polished rod force measured with a dynamometer as the input to the viscoelastic dynamic model, we have obtained the displacement responses, which match closely with the experimental measurements in actual operations, through an iterative process. The key discovery of this work is the feasibility of the so-called inverse optimization procedure, which can be utilized to identify the equivalent scaling factor and viscoelastic system parameters. The proposed Newton–Raphson iterative method, with some terms in the Jacobian matrix expressed with averaged rates of changes based on perturbations of up to two independent parameters, provides a feasible tool for optimization issues related to complex engineering problems with mere information of input and output data from either experiments or comprehensive simulations. The same inverse optimization procedure is also implemented to model the entire fluid delivery system of a very viscous non-Newtonian polymer modeled as a first-order ordinary differential equation (ODE) system similar to the transient entrance developing flow. The convergent parameter reproduces transient solutions that match very well with those from fully fledged computational fluid dynamics models with the required inlet volume flow rate and outlet pressure conditions.

Multiple nonlinearities in the process of embedding and pulling out of nails: A numerical approach

This paper presents a numerical approach to analyze the embedding and withdrawal process of nails. Multiple nonlinearities are considered: law of orthotropic large strain elasto-plastic materials and contact with friction. The Uzawa algorithm based on the bi-potential method is used to describe the nonlinearity of boundary conditions. A return mapping algorithm is applied to deal with the elasto-plastic constitutive laws. On the basis of the Updated Lagrangian formulation, we adopt a Rotationally Neutralized Objective hypothesis to describe the geometrically nonlinear behavior. The Newton–Raphson iterative method is employed to solve the nonlinear equation. The simulation results show the deformation and the stress distribution of wood in the process of the nail embedding and withdrawal. The effectiveness and accuracy of the numerical scheme are proved by comparing with the existing engineering experiments. The influence of friction coefficients on the nail embedding and withdrawal strength is also explored.

Novel enhanced thermal capabilities of Cu-Al2O3/water hybrid nanofluid in an oblique U-shape cavity: On the molecular behaviour through vorticity analysis

This paper presents the numerical investigation of natural convection heat transfer of copper-alumina/pure water hybrid nanofluid in an oblique U-shaped enclosure. The dimensionless governing equation is formed in the stream function-vorticity formulation using dimensionless variables. The Galerkin weighted residual finite element method with the damped Newton-Raphson iteration method is applied to the problem. The heat transfer performance for the system is investigated by varying the Rayleigh numbers, nanoparticle volume fractions and their ratios, and the oblique angles of the enclosure. The fluid flow, heat transfer, and vorticity analysis are conducted extensively for the Rayleigh number up to 106. It was found that the oblique enclosure dwindled the overall heat transfer performance. Correspondingly, the maximum vorticity is at the lowest with zero obliquenesses. The results are used to gain a deeper understanding of the fluid flow and thermal behaviour of the system to achieve more sustainable and greener energy management.

Nonlinear dynamic response of a temperature-dependent FGM spherical shell under various boundary conditions and thermal shocks: Examination of dynamic snap-through

In this study, a comprehensive exploration of the nonlinear dynamic snap-through phenomenon observed in shallow spherical shells composed of functionally graded materials (FGMs) is examined. The analysis encompasses the interplay of thermomechanical characteristics within metal and ceramic phases, taking into account their temperature-dependent behaviors. To address this problem, the transient heat conduction equation in a nonlinear form, accounting for the temperature dependence factor is derived. To solve this complexity, the Generalized Differential Quadrature (GDQ) method is employed, coupled with the Crank-Nicolson time integrating scheme, leveraging an iterative approach for precision. The formulation of nonlinear dynamic motion equations is based on Hamilton's principle and incorporates the utilization of nonlinear strain-displacement equations and uncoupled thermoelasticity. In the spatial domain, GDQ proves invaluable in solving these nonlinear, coupled equations. In the temporal domain, the Newmark procedure in conjunction with the Newton-Raphson iterative method are utilized to navigate through dynamic equations, yielding insights into shell's behavior over time. In the initial stages of the investigation, we validate our spherical shell formulation and methodologies by comparing shell's response with existing, simpler works. This step ensures the reliability and accuracy of our model. The primary objective is to assess the presence and characteristics of the thermal snap-through phenomenon within the shell under these diverse conditions.

Kinematic Analysis of the Draglink Mechanism Using the Newton Rhapson Iteration Method

Position, speed, and acceleration analysis are all included in kinematic analysis. Vectors of location, velocity, and acceleration can be expressed analytically in the form of complex numbers using the Newton Rhapson Iteration Method. The location vector of the point to be investigated must be found first, and then the acceleration and velocity vectors must be found by differentiating against time. This study analyzes the relationship between the θ1 value and the θ2, θ3, θ4, θ5, and x2 values in a drag-link mechanism. The Newton-Raphson iteration method is employed for kinematic analysis to solve nonlinear equations. In this research, the analysis results indicate a correlation between the θ1 value and the θ2, θ3, θ4, θ5, and x2 values. As θ1 increases, the θ2, θ3, θ4, and θ5 values also proportionally increase. The x2 value is also influenced by changes in θ1. This study combines the Newton-Raphson iteration method with graphical analysis using CAD software. The conclusion of this research highlights a significant relationship between the θ1 value and the θ2, θ3, θ4, θ5, and x2 values in the drag-link mechanism. The analysis provides valuable insights for modeling, designing, or controlling systems involving these variables.

Diagnosis of Analog Circuits: The Problem of Ambiguity of Test Equation Solutions

Diagnosis of analog electronic circuits is a crucial issue in computer-aided design. During the diagnosis, solving a test equation to identify the values of faulty parameters is usually necessary. The equation is nonlinear to the parameters, even for linear circuits. The nonlinearity of the equation implies the possibility of multiple solutions. No method exists that guarantees the determination of all the solutions of the test equation. However, even information about more than one existing solution is essential for the designer. It allows for the selection of another test at the design step and helps to obtain an unambiguous solution during the diagnosis. Information about the possibility of additional solutions is essential for simulation after test methods (e.g., identification and verification methods) and for simulation before test methods, so-called dictionary methods, especially those targeting multiple fault classification. The paper deals with the problem of multiple solutions of the test equation for nonlinear DC circuits and proposes a method for identifying the solutions using a deflation technique. The outcomes are compared with the results obtained using standard and adaptively damped Newton–Raphson iterative methods. The methods use randomly selected initial guesses to find multiple solutions. The effectiveness of all the methods for identifying multiple solutions was verified numerically and via laboratory tests.

The effects of nonlinear soil spatial variability on the nonlinear beam response


 
 
 
 The nonlinear analysis of a beam resting on nonlinear random tensionless soil was studied with the aim of quantifying the influence of the spatial variability of the tension soil characteristics on the behavior of the beam and illustrating the importance of the geometric nonlinear analysis of a beam. The soil–structure interaction mechanism is taken into account where the soil is modeled as nonlinear. Due to large deflections and moderate rotations of the beam, the Von-Kàrman type nonlinearity based on the finite element formulation of nonlinear beam response is adopted and the interfacial shearing resistance along the beam is taken into account. To assess the probabilistic nonlinear behavior of the beam resting on nonlinear random soil, a Monte Carlo approach was used and the response of the beam was statistically analyzed for different beam and soil parameters. The equation of motion is solved using the Newton-Raphson iterative method which is implemented by using a Matlab software. The results indicate that the probabilistic approach of the soil and the geometric nonlinearity of the beam serve a major role in the evaluations of the beam response (of the real response of the buried beam).
 
 
 

Analysis of Friction Characteristics of Valve Plate Pair in an Axial Piston Pump Considering Cylinder Block Dynamics

Abstract The lubrication properties and friction characteristics of the valve plate pair play a vital role in determining the overall lifespan of the axial piston pump, which makes the analysis of these parameters of significant importance. In this paper, the lubrication model of the cylinder block/valve plate sliding interface of the axial piston pump, considering elastic deformation and cylinder block dynamics, is established. The oil film carrying pressure and asperity microcontact pressure are calculated using the Reynolds equation, Greenwood–Williamson asperity microcontact model, and Hertz contact theory. The dynamic analysis is carried out, and the Newton–Raphson iterative method is introduced to solve the nonlinear equations. The influence of working pressure, cylinder speed, and sealing belt width on the friction characteristics of the valve plate pair is analyzed using the numerical calculation model. The simulation results demonstrate the dynamic changes of the cylinder block and the impact of them on lubrication properties and friction characteristics. The experimental results of the friction coefficient at different cylinder speeds are consistent with the simulation results in trend and accurately reflect the fluctuation of the friction coefficient.

Lesion detection and classification in dermoscopic images using optimal threshold based on Newton Raphson iterative method

Automatic image thresholding is commonly used in the area of computer vision and pattern recognition for object detection. This research work proposes a new method of lesion detection in dermoscopic images using an optimal threshold based on the Newton-Raphson iteration algorithm for diagnosing melanoma. The proposed method incorporates a new strategy of finding the optimal threshold using first-order and second-order edge derivatives. The first- and second-order derivatives values obtained from the images are applied in the Newton-Raphson method which, in turn, converges to a value after a number of iterations. The converged value is considered the optimal threshold and used as a parameter for the separation of lesion regions from healthy skin in dermoscopic images. To test the proposed system performance, the experiment is carried out on two standard data sets, the ISIC Archive and the PH2, of dermoscopic images using different classifiers such as the Naive Bayes (NB), AdaBoost and Bag of Visual words (BOVW). The proposed segmentation technique segments the lesion regions from skin images and Bag of visual words classifier classifies the dermoscopic images into different classes namely common nevi, atypical nevi and melanoma. The proposed thresholding-based segmentation performance is compared against the Otsu method and Otsu using genetic algorithm. The experimental findings reveal that the proposed Newton-Raphson iterative method surpasses various state-of-the-art and recent methods in relation to computational speed, error rate, sensitivity, and accuracy.

Combining closed-form and numerical solutions for the inverse kinematics of six-degrees-of-freedom collaborative handling robot

In the process of solving the inverse kinematics of six-degrees-of-freedom collaborative robots, the numerical solution has problems such as low accuracy and singular configurations. Moreover, due to the high coupling of its position and attitude, the direct closed-form solution fails. To address these problems, an inverse kinematics algorithm that combines closed-form and numerical solutions was proposed. The Jacobian matrix was established based on the forward kinematics equation of the six-degrees-of-freedom collaborative robot. Its inverse matrix was obtained by a singular value decomposition of the matrix using the Manocha elimination method to avoid the singularities of the Jacobian matrix. The optimal inverse kinematics solution was obtained using the Newton–Raphson iterative method. A computer simulation implemented in MATLAB and Visual C++ was used to evaluate the accuracy and speed of the proposed algorithm. The results of the trajectory planning experiments demonstrate that the algorithm satisfies the requirements for real-time smooth motion. This study of inverse kinematics lays the theoretical foundation for solutions to the inverse problem and real-time control of collaborative robots.

ZILLMER RESERVE ON ENDOWMENT LAST SURVIVOR LIFE INSURANCE USING LOMAX DISTRIBUTION

This article discusses Zillmer's reserves for endowment last survivor of life insurance. Zillmer reserves are a type of modification of premium reserves which are calculated using prospective reserves and the Zillmer rate. In Zillmer reserves, loading which is the difference between gross premium and net premium in the first policy year is greater than standard loading. In this article, the life insurance used is endowment last survivor of life insurance, where the reserve calculation for last survivor status is calculated for 3 cases, namely, both participants survive until the end of the policy, participant x survive but participant y died, and participant y survive but participant x died. So the purpose of this research is to find a way to make the loading value in 3 cases on the dwiguna last survivor of life insurance Zillmer reserves smaller. To achieve this goal, this article uses the Lomax distribution with the parameters estimated using maximum likelihood estimation and then determined by a Newton-Raphson iteration method. Based on the illustration, even though in the first policy year in cases where both participants survive until the end of the policy there was still a negative loading, overall Zillmer's reserves in each case continues to increase over time

Nonlinear dynamic analysis of a geometrically imperfect sandwich beam with functionally graded material facets and auxetic honeycomb core in thermal environment

In this study, a model for the nonlinear dynamic analysis of the geometrically imperfect sandwich beam with functionally graded material (FGM) facets and auxetic honeycomb core is proposed. The auxetic feature of the honeycomb material is realized by a homogenization method, which gives the expressions of the effective material coefficients in terms of material property and cellular geometric parameters. The nonlinear motion equation of the geometrically imperfect beam is derived based on the Reddy's higher shear deformation theory, von Kármán nonlinear theory, as well as general geometric imperfection function. The thermal effect on the material properties and structural rigidity is also taken into account in this model. The Newmark method and Newton–Raphson iterative method are employed to solve the nonlinear motion equation of the sandwich beam. In numerical examples, the dynamic response of the sandwich beam under two types of load, i.e. moving load and impulse load, are discussed in details. The influences of various factors (such as material parameter, geometric imperfection, and thermal condition) on the nonlinear dynamic behaviors of the sandwich beam are elaborately investigated. The numerical results show those factors can play significant roles in the bearing ability, structural stiffness, or nonlinear dynamic behaviors of the sandwich beam in certain conditions. Some key conclusions on the influences are drawn from the numerical results, which can be a useful reference for future investigations.