Flow field simulation and establishment for mathematical models of flow area of spool valve with sloping U-shape notch machined by different methods

Precise function expression of the flow area for the sloping U-shape notch orifice versus the spool stroke was derived. The computational fluid dynamics was used to analyze the flow features of the sloping U-shape notch on the spool, such as mass flow rates, flow coefficients, effiux angles and steady state flow forces under different operating conditions. At last, the reliability of the mathematical model of the flow area for the sloping U-shape notch orifice on the spool was demonstrated by the comparison between the orifice area curve derived and the corresponding experimental data provided by the test. It is presented that the bottom arc of sloping U-shape notch （ABU） should not be omitted when it is required to accurately calculate the orifice area of ABU. Although the theoretical flow area of plain bottom sloping U-shape notch （PBU） is larger than that of ABU at the same opening, the simulated mass flow and experimental flow area of ABU are both larger than these of PBU at the same opening, while the simulated flow force of PBU is larger than that of ABU at the same opening. Therefore, it should be prior to adapt the ABU when designing the spool with proportional character.

Development of Mathematical Model of Slag Flow Field and Temperature Field in ESR System

The heat transfer phenomena and driving forces of slag bath flow in ESR process were analyzed, and the mathematical models in ESR system were reviewed and evaluated. The electromagnetic force is the main driving force for the flow formation in the ESR slag pool, and the temperature difference in the pool creates a convective flow in the system. The shape of the electrode tip has an effect on electromagnetic field distribution in slag pool, thus affects the flow pattern. Finally an improved mathematical model of slag pool flow was proposed.

STUDY ON THE MATHEMATICAL MODEL FOR DRILL WANDERING MOTION

Based on the kinematic relationship of the drill, drill point and workpiece and the coordinate systems founded,the mathematical models of the drill point wandering motion for the drill initial penetration, i. e. the formulae for the drill point center locus, hole shape and cutting edge locus, are established. According to these formulae the hole shape to be made is simulated and analyzed. It is verified that the bending chatter of the drill during the drill penetrating is the main cause to form a polygon like hole.

Predictive Modeling and Parameter Optimization of Cutting Forces During Orbital Drilling

To optimize cutting control parameters and provide scientific evidence for controlling cutting forces,cutting force modeling and cutting control parameter optimization are researched with one tool adopted to orbital drill holes in aluminum alloy 6061.Firstly,four cutting control parameters(tool rotation speed,tool revolution speed,axial feeding pitch and tool revolution radius)and affecting cutting forces are identified after orbital drilling kinematics analysis.Secondly,hybrid level orthogonal experiment method is utilized in modeling experiment.By nonlinear regression analysis,two quadratic prediction models for axial and radial forces are established,where the above four control parameters are used as input variables.Then,model accuracy and cutting control parameters are analyzed.Upon axial and radial forces models,two optimal combinations of cutting control parameters are obtained for processing a13mm hole,corresponding to the minimum axial force and the radial force respectively.Finally,each optimal combination is applied in verification experiment.The verification experiment results of cutting force are in good agreement with prediction model,which confirms accracy of the research method in practical production.

Study on mathematical model of cutting force in micromachining

With the development of micromachining technology,it is very important to study the mechanism of micromachining,determine the micromachining parameters and ensure the products’quality during the micromachining process.Combined with the micromechanism between tool and workpiece during micromachining process,the sources of the micro-cutting force were analyzed,the micro-cutting physical model was constructed,and the microstress model interacted between the cutting arc edge of the tool and the material of the workpiece was analyzed.Combined with the surface friction and elastic extrusion mechanism between the cutting tool and workpiece,the micro-cutting force model was constructed from two aspects.The micro-cutting depth is deeper than the minimum cutting depth and the micro-cutting depth is shallower than the minimum cutting depth,then the minimum cutting depth value was calculated.Combined with the dislocation properties and microcrystal structure of workpiece’s material,the internal stress of the micromachining force model based on the gradient plasticity theory was calculated,and the force model of the micro-cutting process was studied too.It is significant to control the precision of micromachining process during the micromachining process by constructing the micromachining process force model through studying the small deformation of the material and the mechanism of micromachining.

Mathematical Modelling of Work of Modern Friction-Polymer Shock Absorbers and Determining the Dynamical Force during the Impact

Shock absorbers are main elements into construction of train wagons that secure protection from longitudinal forces which appear during transitional regimes of movement. Besides, development of new constructive solutions for shock absorbers is quite popular development of their working mathematical models. This paper presents modem shock absorber with elastic block made from polymer elements that increase quantity of absorbed energy. This is achieved by increasing the stiffness characteristic of polymer elastic block. The construction is relatively simple and technology used to create the construction is with more or less low price. If there is not enough elastic stiffness of the polymer block, there is a possibility for not meeting the UIC （International Union of Railways） norms for absorbed energy. Therefore, according to the mentioned characteristic, shock absorbers are divided into three groups. The mathematical model presented in this paper allows calculating the necessary elastic characteristic of the polymer block for a short time. Differential equation of movement of the shock absorber elements is presented in this paper. Force change of polymer block for various impact velocities participates in the differential equation of movement where initial velocity V0 and the current meaning of the velocity x are taken into consideration. The presented equation is solved by using program language MATLAB/Simulink by developing a simulation model.

Mathematical Modelling of Cutting Force as the Most Reliable Information Bearer on Cutting Tools Wearing Phenomenon

Being one of their prominent exploitative characteristics, cutting tools durability depends on the character, intensity and the speed of wearing. Identification of tool wearing is of great significance for the purpose of avoiding sooner or later replacement of tools. The parameters of tool wearing can be measured by out-process and in-process-measuring systems. Given the extremely limiting role of the former in modern production lines, development of the latter （the indirect measuring systems） has gained prominence, The basis of indirect measuring systems comprises a set of various signals originating from the units of the system under treatment which stand in certain correlations with the wearing parameters. The paper presents mathematical models of axial force designed on the basis of experimental research in drilling tempered steel by twist drills made of high-speed steel manufactured by powder metallurgy.

Mathematical model of burden distribution for the bell-less top of a blast furnace

Due to the difficulty in measuring the burden trajectory directly in an actual blast furnace （BF）, a mathematical model with Coriolis force and gas drag force considered was developed to predict it. The falling point and width of the burden flow were obtained and analyzed by the model, the velocities of particles at the chute end were compared with and without the existence of Coriolis force, and the effects of chute length and chute torque on the falling point were also discussed. The simulation results are in good agreement with practical measurements with laser beams in a 2500 m3 BF.

Preset model of bending force for 6-high reversing cold rolling mill based on genetic algorithm

The hydraulic roll-bending device was studied, which was widely used in modem cold rolling mills to regulate the strip flatness. The loaded roll gap crown mathematic model and the strip crown mathematic model of the reversing cold rolling process were established, and the deformation model of roll stack system of the 6-high 1 250 mm high crown （HC） reversing cold rolling mill was built by slit beam method. The simulation results show that, the quadratic component of strip crown decreases nearly linearly with the increase of the work roll bending force, when the shifting value of intermediate roll is determined by the rolling process. From the first pass to the fifth pass of reversing rolling process, the crown controllability of bending force is gradually weakened. Base on analyzing the relationship among the main factors associated with roll-bending force in reversing multi-pass rolling, such as strip width and rolling force, a preset mathematic model of bending force is developed by genetic algorithm. The simulation data demonstrate that the relative deviation of flatness criterions in each rolling pass is improved significantly and the mean relative deviation of all five passes is decreased from 25.1% to 1.7%. The model can keep good shape in multi-pass reversing cold rolling process with the high prediction accuracy and can be used to guide the production process.

Force Parameter Model of 3-Roll Mills for Continuous Cold Rolling Wires

Based on experimental data, the mathematical model of rolling force parameters of 3-roll mills was studied. The structure ofthe model was theoretically set up and the coefficients were determined by static analysis of the data. The torque in continuous rollingwas measured, and the characteristics and efficiency of 3-roll mills are investigated.

Mathematical Model of Dynamics of Micropolar Orthotropic Elastic Thin Bars with Free Fields of Displacements and Rotations

In the present paper, initial-boundary value problem of plane stress state of micropolar theory of elasticity is considered for orthotropic material in the domain of thin rectangle. General hypotheses are formulated, which are the qualitative results of the asymptotic method of integration of the stated initial-boundary value problem. On the basis of the accepted hypotheses general applied one-dimensional models of dynamics of bending deformation of micropolar orthotropic elastic thin bars with free fields of displacements and rotations are constructed with and without consideration of shear deformations. With the help of the constructed models different dynamic problems of micropolar bars can be studied. Here concrete problems of free and forced vibrations of hinged supported micropolar orthotropic elastic thin bar are studied. Numerical analysis is done and specific features of dynamic characteristics of micropolar material are revealed. Particularly, it is shown that there is a frequency of vibrations of the micropolar bar that does not depend on bar sizes.

Optimal Design and Force Control of a Nine-Cable-Driven Parallel Mechanism for Lunar Takeoff Simulation

Traditional simulation methods are unable to meet the requirements of lunar takeo simulations, such as high force output precision, low cost, and repeated use. Considering that cable-driven parallel mechanisms have the advantages of high payload to weight ratio, potentially large workspace, and high-speed motion, these mechanisms have the potential to be used for lunar takeo simulations. Thus, this paper presents a parallel mechanism driven by nine cables. The purpose of this study is to optimize the dimensions of the cable-driven parallel mechanism to meet dynamic workspace requirements under cable tension constraints. The dynamic workspace requirements are derived from the kinematical function requests of the lunar takeo simulation equipment. Experimental design and response surface methods are adopted for building the surrogate mathematical model linking the optimal variables and the optimization indices. A set of dimensional parameters are determined by analyzing the surrogate mathematical model. The volume of the dynamic workspace increased by 46% after optimization. Besides, a force control method is proposed for calculating output vector and sinusoidal forces. A force control loop is introduced into the traditional position control loop to adjust the cable force precisely, while controlling the cable length. The e ectiveness of the proposed control method is verified through experiments. A 5% vector output accuracy and 12 Hz undulation force output can be realized. This paper proposes a cable-driven parallel mechanism which can be used for lunar takeo simulation.

High temperature and high pressure rheological properties of high-density water-based drilling fluids for deep wells

To maintain tight control over rheological properties of high-density water-based drilling fluids, it is essential to understand the factors influencing the theology of water-based drilling fluids. This paper examines temperature effects on the rheological properties of two types of high-density water-based drilling fluids （fresh water-based and brine-based） under high temperature and high pressure （HTHP） with a Fann 50SL rheometer. On the basis of the water-based drilling fluid systems formulated in laboratory, this paper mainly describes the influences of different types and concentration of clay, the content of a colloid stabilizer named GHJ-1 and fluid density on the rheological parameters such as viscosity and shear stress. In addition, the effects of aging temperature and aging time of the drilling fluid on these parameters were also examined. Clay content and proportions for different densities of brine-based fluids were recommended to effectively regulate the rheological properties. Four theological models, the Bingham, power law, Casson and H-B models, were employed to fit the rheological parameters. It turns out that the H-B model was the best one to describe the rheological properties of the high-density drilling fluid under HTHP conditions and power law model produced the worst fit. In addition, a new mathematical model that describes the apparent viscosity as a function of temperature and pressure was established and has been applied on site.

Numerical modeling of DPSK pressure signals and their transmission characteristics in mud channels

A numerical model and transmission characteristic analysis of DPSK （differential phase shift keying） pressure signals in mud channels is introduced. With the control logic analysis of the rotary valve mud telemetry, a logical control signal is built from a Gate function sequence according to the binary symbols of transmitted data and a phase-shift function is obtained by integrating the logical control signal. A mathematical model of the DPSK pressure signal is built based on principles of communications by modulating carrier phase with the phase-shift function and a numerical simulation of the pressure wave is implemented with the mathematical model by MATLAB programming. Considering drillpipe pressure and drilling fluid temperature profile along drillpipes, the drillpipe of a vertical well is divided into a number of sections. With water-based drilling fluids, the impacts of travel distance, carrier frequency, drillpipe size, and drilling fluids on the signal transmission were studied by signal transmission characteristic analysis for all the sections. Numerical calculation results indicate that the influences of the viscosity of drilling fluids and volume fraction of gas in drilling fluids on the DPSK signal transmission are more notable than the others and the signal will distort in waveform with differential attenuations of the signal frequent component.

EFFECT OF INTERPHASE LIFT FORCE ON THE FLUID FLOW IN AN AIR-STIRRED CYLINDRICAL VESSEL

In the present paper, based on the two-phase model (Eulerian model), the two dimensional fluid flow liz air-stirred water systems is simulated, and the effect of interphase lift force on the fluid flow is specially discussed. In the Eulerian two-phase model, gas and liquid phase are considered to be two different continuous fluids interacting with each other through the finite inter-phase areas. The exchange between the phases is represented by source terms in conversation equations. Turbulence is assumed to be a property of the liquid phase, k - ε model is used to describe the behavior of the liquid phase. The dispersion of phases due to turbulence is represented by introducing a diffusion term in mass consecrvation equation. The contribution of bubble movement to the turbulent energy and its dissipation rate is taken into accounted by adding extra volumetric source terms to the equations of turbulent enemy and its dissipation rate. The comparison between the mathematical simulation and experiment data indicates that the interphase lift force has a big effect on the flow behavior, and considering both drug force and lift force as interphase forces is important to accurately simulate the gas-water two-phase fluid flow in air-stirred systems. The interphase lift force makes bubbles move away from the centerline, the gas concentration is decreased near the centerline, and increased near the wall. The lift force is smaller than drug force at the same place, especially far away from the centerline.

Rheological properties of oil-based drilling fluids at high temperature and high pressure

The rheological properties of two kinds of oil-based drilling fluids with typically composition were studied at pressures up to 138 MPa and temperatures up to 204 ℃ using the RheoChan 7400 Rheometer.The experimental results show that the apparent viscosity,plastic viscosity and yield point decrease with the increase of temperature,and increase with the increase of pressure.The effect of pressure on the apparent viscosity,plastic viscosity and yield point is considerable at ambient temperature.However,this effect gradually reduces with the increase of temperature.The major factor influencing the rheological properties of oil-based drilling fluids is temperature instead of pressure in the deep sections of oil wells.On the basis of numerous experiments,the model for predict the apparent viscosity,plastic viscosity and yield point of oil-based drilling fluids at high temperature and pressure was established using the method of regressive analysis.It is confirmed that the calculated data are in good agreement with the measured data,and the correlation coefficients are more than 0.98.The model is convenient for use and suitable for the application in drilling operations.

Test Study on Current Force on Mooring Ships

In respect of an offshore berthing pillar, the test study result of current force acting on mooring ships is described in this paper. Empirical and semi-empirical relationships of current force coefficient are given according to the angle between the flow direction and the ship's longitudinal axis, which are coincident with the result of theoretical analysis.

Impulse force reductions and their effects on WBV exposures in high impact shovel loading operations

When shovels load the dump trucks with over 100-ton passes under gravity dumping conditions, they will create a large impact force on the dump truck body which generates high frequency shock waves which expose the operators to whole body vibrations （WBV）. The main cause of such truck vibrations is the large impact force due to the gravity dumping of large tonnage passes. Therefore a rigorous mathematical model has been developed for the impact force containing all the necessary factors upon which it depends. Latter, a thorough analysis shows that percentage reduction of 7.19%, 9.40%, 13.27%, 14.8%, 17.30% and 18.13% can he achieved by reducing the dumping distance to 6.33 m, 6.0 m, 5.5 m, 5.33 m, 5.0 m and 4.9 m, respectively, as compared to when the dumping distance was 7.33 m. Even more reduction in the magnitude of impact force can he observed if the shovel pass gets divided into more than two sub-passes. Therefore, these models can he used to figure out the number of sub-passes into which a single ore pass can he divided and/or the extent to which the dumping distance can he reduced which would reduce the impact force significantly enough to obtain safer yet economic operations.

Comparison of rheological analytic model with numerical simulation in powder injection molding filling process

Mathematical model of filling disk-shaped mold cavity in steady state was studied.And the mathematical model under vibration field was developed from the model in steady state.According to the model of filling disk-shaped mold cavity in steady state,the filling time,the distribution of velocity field and the pressure field were obtained.The analysis results from rheological analytic model were compared with the numerical simulation results using Moldflow software in the powder injection molding filling process.Through the comparison,it is found that it is unreasonable to neglect the influence of temperature when calculated the pressure changing with the time at the cavity gate,while it can be neglected in other situations such as calculating the distribution of the velocity fields.This provides a theoretical reference for the establishment of correct model both in steady state and under vibration force field in the future.

Research on a Diamond Tip Wear Mechanism in Atomic Force Microscope-based Micro/nano-machining

The object is to investigate the wear of an atomic force microscope (AFM) diamond tip when conducting micro/nano machining on single crystal silicon surface. The experimental research and theoretical analysis were carried out on the worn tip in terms of wear rate, wear mechanism and the effect of the tip wear on micro machining process. The wear rate was calculated as 1.7(10～10mm 3/(N·m) by using a theoretical model combined with the experimental results. Through an integration of an AFM observation on the worn tip features with the FEM simulation of the stress distribution, in addition to the unit cutting force calculation on the AFM diamond tip, the wear mechanism of the AFM diamond tip was concluded as mainly chemical wear, and the wear process was also elaborated as well.