Dynamic Force Model Research Articles

DEM–CFD analysis of fluidization behavior of Geldart Group A particles using a dynamic adhesion force model

A discrete particle model for flows of Group A particles in Geldart's classification is studied. In general, Group A particles are fine and light, so that the adhesion force has a strong effect on their fluidization behavior. Inter-particle adhesion force of Group A particle was measured first. Secondly, the DEM–CFD coupling simulation with the measured adhesion force was performed, and the simulated results were compared with the experimental data about a small-scale fluidized bed for verification of the simulation. It was found from the results that there were considerable differences between their flow patterns. In order to reveal the cause of the differences, the effect of the adhesion force in the contact force model was studied on the motion of a single particle colliding with a wall.From the analysis on the particle–wall collision process, it is found that the spring constant used in the DEM model has a large effect on the particle's sticking behavior on the wall. The dynamic adhesion force model is proposed based on the present analytical investigation, and it is found that the present model well expresses the effects of the adhesion force on the flow structure for the case of a small adhesion effect.

Analogue Simulation of Dynamic Interaction of Sea Ice and a Pier Column Structure

The process of interaction of sea ice and a pier column structure was studied by using analogue simulation method in the paper, and the dynamic ice force acting on the pier column structure was achieved. Combining with theory analysis, it modified the dynamic ice force model suggested by Croteau. The results showed that the loading stiffness suggested by Croteau is too big to use in the dynamic ice force model and the Withalm formula and simulated results are more suitable. It suggested the calculation formulas of relative displacement in ice force unloading stage and the continuous ice force in ice force continuous stage.

Multi-Toothed Milling Force Model and Simulation for Form Milling the Gear of the Hypoid Gears

Prediction of the forces in milling hypoid gear was often needed in order to establish automation and optimization of the tooth-milling processes. Based on the geometrical theory of the format face-milling, the multi-toothed milling forces theoretical model for form milling the gear of the hypoid gears is presented, the milling force factors were calibrated via single factor experiments and the simulation programs were prepared. Experiments were carried out to verify the availability of the multi-toothed dynamic milling force model, the experimental results is consistent with the simulation results.

Use of multiscale particle simulations in the design of nuclear plant decommissioning

The application of a digital modelling method that can faithfully take account of three-dimensional shape and inherent physical and chemical properties of each particulate component provides an essential tool in decommissioning design. This is useful in handling of high, medium and low level radioactive waste. The processes involve making decisions on where to cut existing plant components and then how to pack these components into boxes, which are then cemented and kept for long term storage as the level of radioactive declines with time. We illustrate the utility of the method and its ability to take data at plant scale (m-scale) and then deduce behaviours at sub millimetre scale in the packed containers. A variety of modelling approaches are used as a part of this approach including cutting algorithms, geometric and dynamic (distinct element) force models, and lattice Boltzmann methods. These methods are applicable to other complex particulate systems including simulation of waste, building recycling, heap leaching and related minerals processes. The paper introduces the basic concepts of this multi-scale and multi-model approach.

Orbital effects of Sun’s mass loss and the Earth’s fate

I calculate the classical effects induced by an isotropic mass loss of a body on the orbital motion of a test particle around it; the present analysis is also valid for a variation of the Newtonian constant of gravitation. I perturbatively obtain negative secular rates for the osculating semimajor axis a, the eccentricity e and the mean anomaly , while the argument of pericenter ω does not undergo secular precession, like the longitude of the ascending node Ω and the inclination I. The anomalistic period is different from the Keplerian one, being larger than it. The true orbit, instead, expands, as shown by a numerical integration of the equations of motion in Cartesian coordinates; in fact, this is in agreement with the seemingly counter-intuitive decreasing of a and e because they only refer to the osculating Keplerian ellipses which approximate the trajectory at each instant. By assuming for the Sun it turns out that the Earth's perihelion position is displaced outward by 1.3 cm along the fixed line of apsides after each revolution. By applying our results to the phase in which the radius of the Sun, already moved to the Red Giant Branch of the Hertzsprung-Russell Diagram, will become as large as 1.20 AU in about 1 Myr, I find that the Earth's perihelion position on the fixed line of the apsides will increase by AU (for ); other researchers point towards an increase of AU. Mercury will be destroyed already at the end of the Main Sequence, while Venus should be engulfed in the initial phase of the Red Giant Branch phase; the orbits of the outer planets will increase by AU. Simultaneous long-term numerical integrations of the equations of motion of all the major bodies of the solar system, with the inclusion of a mass-loss term in the dynamical force models as well, are required to check if the mutual N-body interactions may substantially change the picture analytically outlined here, especially in the Red Giant Branch phase in which Mercury and Venus may be removed from the integration.

Solar System planetary tests of $${\dot c/c}$$

Analytical and numerical calculations show that a putative temporal variation of the speed of light c, with the meaning of space-time structure constant c ST, assumed to be linear over timescales of about one century, would induce a secular precession of the longitude of the pericenter $${\varpi}$$ of a test particle orbiting a spherically symmetric body. By comparing such a predicted effect to the corrections $${\Delta\dot\varpi}$$ to the usual Newtonian/Einsteinian perihelion precessions of the inner planets of the Solar System, recently estimated by E.V. Pitjeva by fitting about one century of modern astronomical observations with the standard classical/relativistic dynamical force models of the EPM epehemerides, we obtained $${\dot c/c =(0.5\pm 2)\times 10^{-7} {\rm yr}^{-1}}$$ . Moreover, the possibility that $${\dot c/c\neq 0}$$ over the last century is ruled out at 3−12σ level by taking the ratios of the perihelia for different pairs of planets. Our results are independent of any measurement of the variations of other fundamental constants which may be explained by a variation of c itself (with the meaning of electromagnetic constant c EM). It will be important to repeat such tests if and when other teams of astronomers will estimate their own corrections to the standard Newtonian/Einsteinian planetary perihelion precessions with different ephemerides.

Intelligent design of cutting tools using smart material

Shaving metal from a workpiece to produce desired geometric shape is carried out in turning machine tool. Attenuating a micro level vibration of a cutting tool using smart materials can save old machines and enhance flexibility in designing new generations of machine tools. The finite element method is employed to investigate structural stiffness, damping, and switching methodology using smart material in tool error attenuation. In this work, a dynamic force model is deployed to investigate the effectiveness of using such technique in toolpost dynamic control. Effects of short and open circuit conditions on tool critical frequencies for different structural stiffness ratios are assessed. In the transient solution for tool tip displacement, the pulse width modulation (PWM) technique is implemented for smart material activation to compensate for the radial disturbing cutting forces. A Fuzzy Algorithm is developed to control actuator voltage level enhancing improved dynamic performance. The influence of minimum number of PWM cycles in each disturbing force cycle is investigated in controlling the tool error growth. A methodology is developed to utilize toolpost static force–displacement diagram to obtain required activation voltage to shrink error under different dynamic operating conditions. Time delay of applied voltage during error attenuation is evaluated at different frequencies.

Nonlinear seismic response analysis of arch dam-foundation systems- part II opening and closing contact joints

A time-domain method for the analysis of arch dam-foundation rock dynamic interaction during earthquake was proposed, and the dynamic relaxation technique was adopted to obtain the initial static response for dynamic analysis by [Du et al. (2005). The paper has been contributed to Bulletin of earthquake engineering]. In this paper, a nonlinear explicit method in time domain considering the opening and closing effect of contact joints on arch dam during earthquake is further proposed by introducing the dynamic contact force model into the method. The simulation accuracy of dynamic contact force model is verified by comparing its calculation result and test result of scale model on shaking table. Finally, the influence of joints on the seismic response of Xiaowan arch dam is studied by the proposed method and some conclusions are given.

A Spectral Model for Forces Due to Ice Crushing

This paper presents a model of dynamic ice forces on vertical offshore structures. The model concerns a loading scenario where a competent ice sheet is drifting and crushing against the structure. Full scale data obtained on two offshore structures were used in the derivation of a method that applies both to narrow and wide structures. A large amount of events with directly measured local forces was used to derive formulas for spectral density functions of the local ice forces. A nondimensional formula that was derived for the autospectral density is independent of ice thickness. Coherence functions were used to define cross-spectral density functions of the local ice forces. The two kind of spectral density functions were used to obtain the spectral density of the total ice force. The method takes into account both the spatial and time correlation between the local forces. Accordingly, the model provides a tool to consider the nonsimultaneous characteristics of the local ice pressures while assessing the total ice force.

A note on the evidence of the gravitomagnetic field of Mars

According to general relativity, the gravitomagnetic Lense–Thirring force of Mars would secularly shift the orbital plane of the Mars Global Surveyor (MGS) spacecraft by an amount of 1.5 m, on average, in the cross-track direction over 5 years. The determined cross-track post-fit residuals of MGS, built up by neglecting just the gravitomagnetic force in the dynamical force models and without fitting any empirical cross-track acceleration which could remove the relativistic signal, amount to 1.6 m, on average, over a 5 year time interval spanning from 10 February 2000 to 14 January 2005. The discrepancy with the predictions of general relativity is, thus, about 6%.

Segregation of cohesive powders in a vibrated granular bed

The effects of small amounts of added liquid on the segregation behavior of a granular system under vertical vibration by DEM simulation are investigated in this study. The cohesive forces of grains are incorporated into DEM simulations via a simplified dynamic liquid bridge force model. The simulation results show that capillary forces in addition to viscous forces have an important effect on the segregation phenomenon. The segregation rate of larger intruder rises to the top of the bed is found to depend on the liquid content. The segregation rate is sharply increased when a small amount of liquid is added to granular system. A transition to the reduction of segregation rate occurs at a critical liquid content. It has shown that this transition can be interpreted as the increase of attractive force between grains due to viscous force. The viscous forces make the particles stick more tightly to each other and retard the movement of particles, thus reducing the segregation rate. The segregation rate is also related to the convection motion of the granular system. The presence of convection enhances the segregation rate of wet granular materials.

Non-Linear Dynamics of a Rotor-Bearing-Seal System

The non-linear dynamic behaviors of a rotor-bearing-seal coupled system are investigated by using Muszynska’s non-linear seal fluid dynamic force model and non-linear oil film force, and the result from the numerical analysis is in agreement with the one from the experiment. The bifurcation of the coupled system is analyzed under different operating conditions. It is indicated that the dynamic behavior of the rotor-bearing-seal system depends on the rotation speed, seal clearance and seal pressure of the rotor-bearing-seal system. The system state trajectory, Poincare maps, frequency spectra and bifurcation diagrams are constructed to analyze the dynamic behavior of the rotor center. Various non-linear phenomena in the coupled system, such as periodic motion and quasi-periodic motion are investigated. The results show that the system has the potential for chaotic motion. The study may contribute to a further understanding of the non-linear dynamics of such a rotor-bearing-seal coupled system.

Dynamics of Initial Penetration in Drilling: Part 1—Mechanistic Model for Dynamic Forces

This two-part paper is aimed at developing a theoretical and numerical simulation basis for initial penetration phenomena that profoundly influence hole tolerances and shape. In Part 1, dynamic force models are developed followed by models of the drill’s dynamic behavior in Part 2. Next, these models are combined and used to predict initial penetration behavior and hole shape. A comparison of simulated and experimental results concludes Part 2. In this part, by considering the effects of drill grinding errors and drill deflections, dynamic cutting chip thickness models are developed which, in combination with workpiece surface inclination effects, allow the formulation of expressions for the dynamic chip thickness and cutting chip cross-sectional area. By using these quantities to replace their static counterparts, static drilling force models are extended to facilitate the prediction of dynamic cutting forces. Separate thrust, torque, and radial force models for the major cutting edges, secondary cutting edge, and for the indentation zone are formulated. The effects of drill installation errors on the radial cutting forces acting on the chisel edge and the major cutting edges are also included.

An Experimental Study of Cutting Forces in High-Speed End Milling and Implications for Dynamic Force Modeling

The characteristics of high-speed machining (HSM) dynamic milling forces was investigated. Recent studies in chip segmentation are discussed. A Mikron 700 High-Speed Machining Center was used in the end-milling of AISI H13 tool steel using PVD TiN coated two flute micrograin carbide tools. Dynamic force signals were studied using a real-time data acquisition system for spindle speeds from 3,750 to 31,500 rpm for a 6 mm dia tool. Frequency domain studies were also carried out for a larger tool of 12 mm dia for spindle speeds between 10,000 and 40,000 rpm. The trend and frequency domain aspects of the dynamic forces were evaluated and discussed. The fundamental concept of modeling cutting forces based on chip morphology is revisited. A new basis for modeling dynamic forces from the static component and harmonic contributions is presented. This approach for modeling the dynamic HSM force signal accounts for secondary harmonics.

Dynamics of Initial Penetration in Drilling: Part 2—Motion Models for Drill Skidding and Wandering With Experimental Verification

This part of the paper is aimed at the development of models for the drill tip’s transverse and angular motions, the definition of models for establishing the drilled hole’s profile and, by combining these results with the dynamic force models of Part 1, the formulation of the complete model for drill skidding and wandering. An experimental verification of the models concludes the paper. For the development of the drill motion models the drill is simplified as a pretwisted beam subjected to a compressive axial load and radial forces acting on its tip. The governing equations are developed using Hamilton’s principle. Subsequently, the weak form of the governing equation is formulated to facilitate their solution by the finite element method. The corresponding boundary conditions for the motion model are also defined for three drilling phase, i.e., drill skidding, drill wandering and stabilized drilling. Based on the drill tip’s wandering locus and drill rotation, a mathematical model for describing the drilled hole’s profile is developed.

2522 カンティレバーの過渡振動を用いた分子液架橋のダイナミクス : 動的凝着力の導入(S79-1 情報機器コンピュータメカニクス(1),S79 情報機器コンピュータメカニクス)

The lubricant thickness and retractive velocity dependency of the adhesion force between the diamond tip and the disk surface were measured while the tip was withdrawn from the disk surface with PFPE lubricant film. The dynamic adhesion force model was also adopted to analyze the transient vibration of the cantilever after the tip was separated from the disk surface. This method clearly visualized the non-linear phenomena occurred at the initial separation, the rupture of the liquid bridge, and also the minute fluctuation in the inclination of the adhesion decreasing profile. The PFPE lubricant having functional end groups (Zdol2000) with the thicknesses of 29nm and 63nm and the retractive velocities of 29, 57, 111, 219μm/s were employed to measure the lubricant thickness and velocity dependencies. The contact force which occurred at the separation between the diamond tip and the disk surface was maximum value in the adhesion profile and largely attributable to the lubricant thickness and slightly to the retractive velocity.

Cutting dynamic force modelling of endmilling operation

In the paper, a mechanistic cutting force model was suggested and the result was predicted in cutting process. The experimental coefficient modelling method was developed for the formulation of theoretical cutting force by considering the specific cutting force coefficient. Also, the specific cutting force that is the multiplication of specific cutting force coefficient and uncut chip thickness was used for the calculation of estimated force in endmilling in each direction. In this study, the cutting force mechanics of endmilling process are presented for theoretical force model in simple endmilling operations by considering the geometric shape of the workpiece part and it was compared with the measured force. As a result, the model presented shows a good consistency with the real measured force and the suggested model can be used for the prediction of force history in endmilling operation which has a different and complex conditions of start and exit immersion angle.

Dynamic Friction Models for Road/Tire Longitudinal Interaction

Summary In this paper we derive a new dynamic friction force model for the longitudinal road/tire interaction for wheeled ground vehicles. The model is based on a dynamic friction model developed previously for contact-point friction problems, called the LuGre model. By assuming a contact patch between the tire and the ground we develop a partial differential equation for the distribution of the friction force along the patch. An ordinary differential equation (the lumped model) for the friction force is developed, based on the patch boundary conditions and the normal force distribution along the contact patch. This lumped model is derived to approximate closely the distributed friction model. Contrary to common static friction/slip maps, it is shown that this new dynamic friction model is able to capture accurately the transient behaviour of the friction force observed during transitions between braking and acceleration. A velocity-dependent, steady-state expression of the friction force versus the slip coefficient is also developed that allows easy tuning of the model parameters by comparison with steady-state experimental data. Experimental results validate the accuracy of the new tire friction model in predicting the friction force during transient vehicle motion. It is expected that this new model will be very helpful for tire friction modeling as well as for anti-lock braking (ABS) and traction control design.

HOPF BIFURCATION ANALYSIS OF A ROTOR/SEAL SYSTEM

The Hopf bifurcation behaviour of a symmetric rotor/seal system was investigated using Muszynska's non-linear seal fluid dynamic force model. For a perfectly balanced system, the instability from certain critical equilibrium positions is proved to be the result of Hopf bifurcation and only the supercritical type is found for a specific rotor system using Poore's algebraic criteria. Hence, a stable periodic orbit bifurcates from the critical equilibrium position after the threshold speed is exceeded. Due to the dimensionless whirl frequency being found to be close to 12 over quite a large range of system parameters, the periodically perturbed Hopf bifurcation in 12 subharmonic resonance is dealt with for an imbalanced rotor system. The bifurcation of the averaged system, obtained using the centre manifold procedure and averaging method, is analyzed. The results show that non-synchronized whirl of the imbalanced rotor can either be a quasi-periodic motion resulting from a Hopf bifurcation, or a half-frequency whirl from period doubling bifurcation, determined by the structure parameters of the system and operation conditions. Numerical simulation verifies the analytical results.

A comprehensive chatter prediction model for face turning operation including tool wear effect

This paper presents a three-dimensional mechanistic frequency domain chatter model for face turning processes, that can account for the effects of tool wear including process damping. New formulations are presented to model the variation in process damping forces along nonlinear tool geometries such as the nose radius. The underlying dynamic force model simulates the variation in the chip cross-sectional area by accounting for the displacements in the axial and radial directions. The model can be used to determine stability boundaries under various cutting conditions and different states of flank wear. Experimental results for different amounts of wear are provided as a validation for the model.