Experimental and Modeling Study of the Regular Polygon Angle-spiral Liner in Ball Mills

Load behavior is one of the most critical factors affecting mills' energy consumption and grinding efficiency,and is greatly affected by the liner profiles. Generally, as liner profiles vary, the ball mill performances are extremely different. In order to study the performance of the ball mill with regular polygon angle-spiral liners(RPASLs), experimental and numerical studies on three types of RPASLs, including regular quadrilateral, pentagonal and hexagonal, are carried out. For the fine product of desired size, two critical parameters are analyzed: the energy input to the mill per unit mass of the fine product, E*, and the rate of production of the fine product, F*. Results show that the optimal structure of RPASLs is Quadrilateral ASL with an assembled angle of 50°. Under this condition, the specific energy consumption E* has the minimum value of 303 J per fine product and the production rate F* has the maximum value of 0.323. The production rate F* in the experimental result is consistent with the specific collision energy intensity to total collision energy intensity ratio E_s/E_t in the simulation. The relations between the production rate F* and the specific energy consumption E* with collision energy intensity E_s and E_t are obtained. The simulation result reveals the essential reason for the experimental phenomenon and correlates the mill performance parameter to the collision energy between balls,which could guide the practical application for Quadrilateral ASL.     

The use of generalized magnetic parameters for magnetic structural analysis and nondestructive testing

The results of studies regarding the dependence of the product of the coercive force and the initial magnetic susceptibility of a nickel single crystal with an intermediate orientation on the shear stress are analyzed. It is concluded that an increase in the aforementioned product for a nickel single crystal upon cold plastic deformation is due to refining of magnetic domains that is caused by formation of cells and subgrains within the single crystal. The tentative size of magnetic domains was determined based on the value of generalized magnetic parameter . The variations in the product and in the calculated dimensions of magnetic domains in polycrystalline nickel are analyzed using data reported by Kersten-Gottschalt. It was also shown that, the density of dislocations being constant, the generalized magnetic parameter is sensitive to changes in the sizes of nonferromagnetic inclusions, whereas in the case of small nonferromagnetic inclusions, an increase in the generalized parameter is due to an increase in the density of dislocations.Translated from Defektoskopiya, Vol. 40, No. 7, 2004, pp. 62–76.Original Russian Text Copyright © 2004 by Bida.     

Effects of Anisotropy and Substrate Shape on Atomic Friction Force in Two-Dimensional Model

Understanding the effects of anisotropy and substrate shape on atomic friction force is critically needed for the designed development of nanoscale friction devices. The simulation of atomic force microscope on various substrate shapes using the 2D Prandtl–Tomlinson model is investigated in the framework of three representative surface lattices: \({\hbox {MoS}}_2\), NaCl and highly oriented pyrolytic graphite surfaces. The results show that the lateral force map reveals a significant contrast between different surface lattice shapes yielding lattice rows which differ from their neighboring ones. Careful analysis of the friction force during the individual friction scanning revealed that the friction forces over the narrow maxima domains were lower than those over the narrow wells domains. Depending on crystal orientation and the potential shape, variations in the frictional force can also be seen in the simulations. It has been numerically observed that frictional force depends on the crystal orientation as well as on the shape of the substrate potential. Velocity dependence of the kinetic friction force has the form of a power law \(F_{k}-F_{k0}={\hbox {cst}} \, v_{\mathrm{s}}^{2/3}\), for small scanning velocities. The effects of the shape parameter r on this law have been shown.     

Tire–Road Contact Stiffness

When a rubber block is squeezed against a nominal flat but rough surface, the rubber bottom surface will penetrate into the substrate roughness profile. The relation between penetration depth \(w\) (or the average interfacial separation \(\bar{u}\) ) and the applied squeezing pressure \(p\) determines the (perpendicular) contact stiffness \(K=\hbox {d}p/\hbox {d}w=-\hbox {d}p/\hbox {d}\bar{u}\) , which is important for many applications. We have measured the relation between \(p\) and \(\bar{u}\) for a rubber block squeezed against 28 different concrete and asphalt road surfaces. We find a linear relation between \({\mathrm{log}}p\) and \(\bar{u}\) , in agreement with theory predictions. The measured stiffness values correlate rather well with the theory prediction.     

Wear and Lubrication Behaviors of Cu-Based Friction Pairs with Asperity Contacts: Numerical and Experimental Studies

This paper aims to investigate the wear and lubrication behaviors of wet Cu-based friction pairs. A mixed lubrication model in plane contacts is developed, and the tests of pin-on-disk are carried out. Wear losses are measured by the oil spectrum analysis method. The wear loss, the real contact area ratio, and the load sharing ratio are analyzed. Effects of sliding velocity, temperature, and pressure are considered. The results show that the temperature is the most significant influence on the wear loss of lubricated Cu-based friction pairs. As the temperature rises from 30 to 150 °C, wear loss increases from less than 0.4 mg to about 2.3 mg. The wear factor of the lubricated Cu-based friction pair in asperity contact areas is \(K_{c} = 9.4 \times 10^{ - 9}\) (g/Nm). When the lubricated wear is slight, the oil spectrum analysis method is an effective approach to accurately determine the wear loss.     

Studies of chipping mechanisms for dicing silicon wafers

The purpose of this study was to investigate the chipping modes produced in the die edges of dicing silicon wafer using the thin diamond blades. The effects of dicing directions and different wafer types on the chipping size were studied. Furthermore, scratching tests were also used to assist the analysis of studying chipping conditions of the silicon wafer. The experimental results showed that the trace behaviors produced by the diamond indenter in the scratching test of silicon wafer can be divided into the three stages: rubbing, plastic deformation, cracking. The plastic pile up and crack of the scratching traces on the wafer mainly propagate along the development of the easiest slip direction family <110>. The chipping modes produced in dicing silicon wafer can be broadly classified as four types: (1) 30° chipping; (2) 60° chipping; (3) 90° chipping; (4) irregular chipping, which causes these mechanisms of chipping modes due to the meeting between the radial cracks of 30°, 60°, and 90° along the easiest slip direction family <110> and the lateral cracks along the easiest cleavage plane family {111}. When using the thin diamond blade diced on the (111) silicon wafer along the $ {\left[ {\overline{1} 10} \right]} $ direction, the size of top chipping produced was smaller than that of along the $ {\left[ {11\overline{2} } \right]} $ direction. Besides, for the (100) plane of silicon wafer, the size and the distribution of the chipping modes produced along the $ {\left[ {\overline{1} 10} \right]} $ and $ {\left[ {\overline{1} \overline{1} 0} \right]} $ directions were similar.     

The curved wall jet over a circular cylinder before the interaction of two opposing curved wall jets

A curved wall jet before the interaction of two identical curved wall jets over a circular cylinder was investigated experimentally. Using hot-wire anemometry, the mean velocity, Reynolds stresses, and high order moments of the fluctuating velocity were measured. The turbulent kinetic energy and shear stress budgets were evaluated using the measured data. The correlation coefficient, ${{\overline {uv} } \mathord{\left/ {\vphantom {{\overline {uv} } {u'v'}}} \right. \kern-0em} {u'v'}}$ , the normal stress ratio, ${{\overline {v^2 } } \mathord{\left/ {\vphantom {{\overline {v^2 } } {\overline {u^2 } }}} \right. \kern-0em} {\overline {u^2 } }}$ , and the principal direction of the Reynolds stress are presented. The effects of curvature and adverse pressure gradient on these diistributions are also discurssed. The turbulent kinetic energy and shear stress budgets in two regions before the interaction are analyzed in detail to illuminate the effect of the adverse pressure gradient on the turbulent transport.     

Stochastic flow-shop scheduling with minimizing the expected number of tardy jobs

In this research, minimizing the expected number of tardy jobs in a dynamic m machine flow-shop scheduling problem, i.e., $ {F_m}\left| {{r_j}\left| {{\text{E}}\left[ {\sum {{U_j}} } \right]} \right.} \right. $ is investigated. It is assumed that the jobs with deterministic processing times and stochastic due dates arrive randomly to the flow-shop cell. The due date of each job is assumed to be normally distributed with known mean and variance. A dynamic method is proposed for this problem by which the m machine stochastic flow-shop problem is decomposed into m stochastic single-machine sub-problems. Then, each sub-problem is solved as an independent stochastic single-machine scheduling problem by a mathematical programming model. Comparison of the proposed method with the most effective rule of thumb for the proposed problem, i.e., shortest processing time first rule shows that the proposed method performs 23.9 % better than the SPT rule on average for industry-size scheduling problems.     

Application of symbolic manipulation to inverse dynamics and kinematics of elastic robots

An inverse dynamics and kinematics of a flexible manipulator is derived in symbolic form based on the recursive Lagrangian assumed mode method. A PC-based program has implemented the algorithm to automatically generate the inverse dynamics and kinematics for an elastic robot in a symbolic form. A case study is given to illustrate how to use this program for inverse dynamic and kinematic generation. Simulation results for a case study by considering different mode shape are compared with the rigid case.Nomenclature A _i joint transformation relates systemi to systemi-1 - E _i link transformation relates the deflection of systemi to systemi - F _i joint torque acting on jointi - g gravity vector expressed at the base coordinates - J inertia = - K kinetic energy of the system - l _i length of linki - M _i a mass concentrated at the joint i - m _i number of modes used to describe the deflection of link i - n number of links - q _h joint variable of thehth joint - q _hk time-varying amplitude of mode k of link h - R vector of remaining dynamics and external forcing terms = - r _i vector locating the centre of mass of linki - R _j dynamics from the joint equation j, excluding second derivatives of the generalized coordinates - R _if dynamics from the deflection equation jf, excluding second derivatives of the generalized coordinates - V potential energy - W _i transformation from the base to theith link - transformation from the base to the systemî - z the vector of generalised coordinates = - link density     

Wear, Plasticity, and Rehybridization in Tetrahedral Amorphous Carbon

Wear in self-mated tetrahedral amorphous carbon (ta-C) films is studied by molecular dynamics and near-edge X-ray absorption fine structure spectroscopy. Both theory and experiment demonstrate the formation of a soft amorphous carbon (a-C) layer with increased sp² content, which grows faster than an a-C tribolayer found on self-mated diamond sliding under similar conditions. The faster $\hbox{sp}^{3} \rightarrow\,\hbox{ sp}^{2}$ transition in ta-C is explained by easy breaking of prestressed bonds in a finite, nanoscale ta-C region, whereas diamond amorphization occurs at an atomically sharp interface. A detailed analysis of the underlying rehybridization mechanism reveals that the $\hbox{sp}^{3}\, \rightarrow\hbox{ sp}^{2}$ transition is triggered by plasticity in the adjacent a-C. Rehybridization therefore occurs in a region that has not yet experienced plastic yield. The resulting soft a-C tribolayer is interpreted as a precursor to the experimentally observed wear.     

The magnetic field of an arbitrary shaped defect in a plane-parallel plate

The problem of an arbitrarily shaped defect in a ferromagnetic half-space and a plane-parallel plate plate is solved. The solution is expressed as an integral equation in which the integration was performed only over the defect surface. This integral equation is solved by the iteration method, which allows one to represent the solution as a series in powers of the small parameter \(\lambda /2\pi \left( {\lambda = \frac{{\mu - 1}}{{\mu + 1}}} \right)\). The numerical results are obtained for a defect in the form of an ellipsoid.     

Atomic structure of extended defects in boron-implanted silicon layers

The structure of extended defects introduced into Si by means of boron implantation followed by thermal annealing at T = 900 °C is studied by the method of high-resolution transmission electron microscopy and computer modeling for different values of the implantation dosage (D) and concentration of boron atoms in substitutional positions B₀ \((C_{B_0 } )\) injected into the Si lattice before implantation. It is shown that the Frank dislocation loops of both interstitial (I) and vacancy (V) type at a ratio of 4: 1 are observed in Si samples with D = 10¹⁶ cm^?2 up to \(C_{B_0 } \) = 0.8·10²⁰ cm^?3. The atomic structure of the I-type Frank dislocation loops is heavily deformed, which suggests segregation of finely dispersed boron in the defect plane. At the same time, the structure of the V-type Frank dislocation loops tends to be reconstructed due to interaction with self-interstitials. At \(C_{B_0 } \) = 2.5·10²⁰ cm^?3, the I-type Frank dislocation loops are found to transform to perfect dislocation loops, and boron precipitates with a high density appear in Si. Based on the results obtained, probable reasons for vacancy deficit formation in boron-implanted Si are discussed.     

Internal energy minimization in biarc interpolation

The problem of scheduling n multioperation jobs on a single machine such as the flexible manufacturing system is considered. Each job comprises up to F operations, which belong to several distinct families, and a sequence-independent setup time is incurred whenever an operation is to be processed following an operation of a different family. A job completes when all of its operations have been processed. Two variants with maximum lateness and total completion time as optimality criterion are considered. The problems are denoted as $1\left| {s_f ,{\text{assembly}},GT} \right|L_{\max } $ and $1\left| {s_f = 1,{\text{assembly}},GT,p_{ij} = 0\,{\text{or}}\,1} \right|\sum {C_j } $ . The decision is to sequence all the families in order to minimize the predefined criterion. This environment has a variety of real world applications such as flexible manufacturing systems scheduling and food industry scheduling. A heuristic is presented and a branch and bound is developed for benchmarking. Experimental results show that the heuristic provides good results and the branch and bound procedure is efficient. These results may narrow down the gap between easy and hard cases of the general problem.     

Boundary Layer Behaviour in Circular EHL Contacts in the Elastic-Piezoviscous Regime

The solution of elastohydrodynamically lubricated contacts at high loads and/or low speeds can be described as a Hertzian pressure with inlet and outlet boundary layers: zones where significant pressure flow occurs. For the soft lubrication regime (elastic-isoviscous), a self-similar solution exists in the boundary layers satisfying localized equations. In this paper, the boundary layer behaviour in the elastic-piezoviscous regime is investigated. The lengthscale of the boundary layers and the scaling of pressure and film thickness are expressed in non-dimensional parameters. The boundary layer width scales as \(1/\sqrt{M}\) (equivalent to \({\bar{\lambda }}^{3/8}\) ), the maximum pressure difference relative to the Hertzian solution as \(1 / \root 3 \of {M}\) (equivalent to \({\bar{\lambda }}^{1/4}\) ) and the film thickness as \(1/\root 16 \of {M}\) (equivalent to \({\bar{\lambda }}^{3/64}\) ) with \(M\) the Moes non-dimensional load and \({\bar{\lambda }}\) a dimensionless speed parameter. The Moes dimensionless lubricant parameter \(L\) was fixed. These scalings differ from the isoviscous-elastic (soft lubrication) regime. With increasing load (decreasing speed), the solution exhibits an increasing degree of rotational symmetry. The pressure varies less than 10 % over an angle less than 45 degrees from the lubricant entrainment direction. The results provide additional fundamental understanding of the nature of elastohydrodynamic lubrication and give physical rationale to the finding of roughness deformation depending on the “inlet length”. The findings may contribute to more efficient numerical solutions and to improved semi-analytical prediction methods for engineering based on physically correct asymptotic behaviour.     

Improved feature-based test statistic for assessing suitability of the preliminary samples for constructing control limits of \bar{X} chart

In spite of using a large number of subgroups (m) of small samples (n), the estimated control limits of $ \bar{X} $ chart in phase I can be erroneous unless the preliminary samples are drawn from a stable process. As a result, the performance of the chart in phase II can be significantly affected. The pattern in the $ \bar{X} $ chart, exhibited by the plots of the subgroup averages of the preliminary samples, will be different depending on stability and instability of the process while the preliminary samples were collected. Based on this concept, a new feature-based test statistic (FTS) is proposed for evaluating suitability of the preliminary samples for the designing of the $ \bar{X} $ chart. The FTS, for given m, approximately follows $ N[1,{\text{ SD(}}m{)]} $ , where SD(m) is a function of m. The goodness of the approximation and effectiveness of the test are evaluated using simulated data. The results show that both are satisfactory for m?>?=48. The proposed statistic is also quite effective in detecting unstable process condition resulting in a cyclic pattern. The computation of FTS involves some complexities. However, now-a-days computers are widely available and so computation difficulty may not be a problem.     

Plastic deformation depth modeling on grinding of gamma Titanium Aluminides

This work reports on the subsurface plastic deformation depth (PDD) as a result of grinding of γ-TiAl, where the effects of grit size and shape, workpiece speed, and wheel depth of cut were studied. A grinding model based on a stochastic distribution of the chip thickness was used to estimate the expected maximum normal force per grit ( ${F''_{n\:{\rm max}}}$ ), which was correlated to the PDD. It was found that the PDD shows a linear correlation with ${F''_{n\:{\rm max}}}^{0.5}$ . The results suggest that the indentation model is still valid for grinding if ${F''_{n\:{\rm max}}}^{0.5}$ is used as a PDD predictor variable instead of the total grinding force.     

Three half-axis tool orientation optimization for spiral machining of blades

A regular three-axis computer numerical control (CNC) machine combined with an automatic indexing rotary table (AIRT) is always used to produce four-axis machining for blades in many medium-sized and small industries. Generally, AIRT has the characteristic of low precision, which often leads to obvious tool marks like overcut on the machined blade surface. To overcome this problem, a machining technique, named as $ 3\frac{1}{2} $ -axis spiral machining method that uses the simplicity of three-axis tool positioning and the flexibility of four-axis tool orientation, is developed and implemented. Key issues are focused on transformations of tool orientations from four-axis to $ 3\frac{1}{2} $ -axis and concrete contributions are twofold. First, universal principles are proposed to transfer tool orientations for general convex and concave surfaces. Second, with respect to the pressure and suction surfaces of blades in $ 3\frac{1}{2} $ -axis spiral machining, a unified transformation method is also addressed in detail. A cutting test shows that overcut marks that easily occur in four-axis spiral machining can be effectively controlled by using the proposed $ 3\frac{1}{2} $ -axis machining technique.