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New Method to Measure the Fill Level of the Ball Mill I——Theoretical Analysis and DEM Simulation 被引量:4
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作者 HUANG Peng JIA Minping ZHONG Binglin 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2010年第4期460-467,共8页
The accurate measurement of the fill level in the ball mill has not been resolved because of the interplay of many variable factors, which led the mill to be operated under the uneconomical condition and lost a lot of... The accurate measurement of the fill level in the ball mill has not been resolved because of the interplay of many variable factors, which led the mill to be operated under the uneconomical condition and lost a lot of energy. At present, some methods, such as vibration method and acoustic method, have been applied for measuring the fill level by the researchers. Aiming at the problem of the traditional methods for measuring the fill level, that is, the feature variables of the fill level suffer the influences of the ball load and the water content of the coal, a novel method to measure the fill level is proposed and a possible relation between the fill level and the angular position of the maximum vibration point on the mill shell is investigated. The angular positions of the maximum vibration point on the mill shell for different fill level cases are calculated theoretically under two assumptions, respectively. Meanwhile the charge motions of the mill for different fill level cases are simulated with the discrete element method (DEM). And the simulation results are verified by comparing the motion trajectories of steel balls and power draft of the mill. The simulated movement trajectories of the outmost layer steel balls in the mill are monitored and analyzed to obtain the angular positions of the maximum vibration point on the mill shell. Both the results of the theoretical calculation and the 3D DEM simulation show that the position of the maximum vibration point on the mill shell moves to a lower angular positions as the fill level decreasing, which provides a new idea for measuring the filllevel accurately. 展开更多
关键词 ball mill fill level discrete element method (DEM) SIMULATION
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Convergence ball and error analysis of Ostrowski-Traub’s method 被引量:1
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作者 BI Wei-hong WU Qing-biao REN Hong-min 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2010年第3期374-378,共5页
Under the hypotheses that the second-order and third-order derivatives of a function are bounded, an estimate of the radius of the convergence ball of Ostrowski-Traub's method is obtained. An error analysis is given ... Under the hypotheses that the second-order and third-order derivatives of a function are bounded, an estimate of the radius of the convergence ball of Ostrowski-Traub's method is obtained. An error analysis is given which matches the convergence order of the method. Finally, two examples are provided to show applications of our theorem. 展开更多
关键词 Ostrowski-Traub's method nonlinear equation convergence ball estimate of radius error analysis
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Simulation of a Laboratory Scale Ball Mill via Discrete Element Method Modelling 被引量:1
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作者 Mohsen Mhadhbi 《Advances in Materials Physics and Chemistry》 2021年第10期167-175,共9页
Discrete Element Method (DEM) is a powerful tool for simulating different types of mills. It also used for computing different types of particles such as rocks, grains, and molecules.</span></span><span... Discrete Element Method (DEM) is a powerful tool for simulating different types of mills. It also used for computing different types of particles such as rocks, grains, and molecules.</span></span><span style="white-space:normal;"><span style="font-family:""> </span></span><span style="white-space:normal;"><span style="font-family:"">DEM has been widely used in the field of rock mechanics. In the present work,</span></span><span style="white-space:normal;"><span style="font-family:""> </span></span><span style="white-space:normal;"><span style="font-family:"">DEM approach is applied to model the milling media (powder particles and balls) inside a planetary ball mill and to estimate the distribution of particles of a dry powder during milling. In fact, the efficiency of the DEM strongly depends on the input parameters. The DEM simulation results indicated that</span></span><span style="white-space:normal;"><span style="font-family:""> </span></span><span style="white-space:normal;"><span style="font-family:"">DEM is a promising tool for the simulation of the dynamic particles motion and interactions within planetary ball mill. These results could be utilized to further develop the synthesis performance, anticipate the reaction, and reduce the wear in the dry milling reactions. 展开更多
关键词 MODELLING Discrete Element method Milling Media Planetary ball Mill SIMULATION
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HOMOCENTRIC CONVERGENCE BALL OF THE SECANT METHOD
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作者 Liang Kewei 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2007年第3期353-365,共13页
A local convergence theorem and five semi-local convergence theorems of the secant method are listed in this paper. For every convergence theorem, a convergence ball is respectively introduced, where the hypothesis co... A local convergence theorem and five semi-local convergence theorems of the secant method are listed in this paper. For every convergence theorem, a convergence ball is respectively introduced, where the hypothesis conditions of the corresponding theorem can be satisfied. Since all of these convergence balls have the same center x^*, they can be viewed as a homocentric ball. Convergence theorems are sorted by the different sizes of various radii of this homocentric ball, and the sorted sequence represents the degree of weakness on the conditions of convergence theorems. 展开更多
关键词 secant method semi-local convergence theorem local convergence theorem convergence ball homocentric ball.
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The convergence ball and error analysis of the two-step Secant method
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作者 LIN Rong-fei WU Qing-biao +2 位作者 CHEN Min-hong KHAN Yasir LIU Lu 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2017年第4期397-406,共10页
Under the assumption that the nonlinear operator has Lipschitz continuous divided differences for the first order,we obtain an estimate of the radius of the convergence ball for the two-step secant method.Moreover,we ... Under the assumption that the nonlinear operator has Lipschitz continuous divided differences for the first order,we obtain an estimate of the radius of the convergence ball for the two-step secant method.Moreover,we also provide an error estimate that matches the convergence order of the two-step secant method.At last,we give an application of the proposed theorem. 展开更多
关键词 two-step secant method estimate of radius convergence ball Lipschitz continuous
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Research and experimental analysis of precision degradation method based on the ball screw mechanism
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作者 孔德顺 GAO Xiangsheng JIANG Huizeng 《High Technology Letters》 EI CAS 2023年第3期247-256,共10页
As a key transmission component in computer numerical control(CNC) machine tools,the ball screw mechanism(BSM) is usually investigated under working load conditions. Its accuracy degradation process is relatively long... As a key transmission component in computer numerical control(CNC) machine tools,the ball screw mechanism(BSM) is usually investigated under working load conditions. Its accuracy degradation process is relatively long,which is not conducive to the design and development of new products. In this paper,the normal wear depth of the BSM nut raceway is calculated under the variable speed operation condition using the fractal wear analysis method and the BSM’s accelerated degradation proportional wear model. Parameters of the acceleration degradation model of the double-nut preloaded ball screw pair are calculated based on the physical simulation results. The accelerated degradation test platform of the BSM is designed and manufactured to calculate the raceway wear model when the lubrication condition is broken under the variable-speed inertial load and the boundary lubrication condition under the uniform speed state. Three load forces and two samples are selected for the accelerated degradation test of the BSM. The measured friction torque of the BSM is employed as the evaluation index of the accuracy degradation test. In addition,the life cycle of the accuracy retention is accurately calculated by employing the parameters of the physical simulation model of the BSM. The calculations mentioned above can be used to estimate BSM’s accuracy performance degradation law under normal operating conditions. The application of the proposed model provides a new research method for researching the precision retention of the BSM. 展开更多
关键词 ball screw mechanism(BSM) fractal theory wear model accelerated degradation method friction torque precision retention
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Finite element simulation of ball spinning of NiTi shape memory alloy tube based on variable temperature field 被引量:2
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作者 江树勇 张艳秋 +2 位作者 赵亚楠 唐明 李春峰 《Transactions of Nonferrous Metals Society of China》 SCIE EI CAS CSCD 2013年第3期781-787,共7页
As a new attempt,ball spinning was used to manufacture the nickel-titanium shape memory alloy(NiTi SMA) tube at elevated temperature.The NiTi bar with a nominal composition of Ni50.9Ti49.1(mole fraction,%) was sol... As a new attempt,ball spinning was used to manufacture the nickel-titanium shape memory alloy(NiTi SMA) tube at elevated temperature.The NiTi bar with a nominal composition of Ni50.9Ti49.1(mole fraction,%) was solution treated and was used as the original tube blank for ball spinning.Based on the variable temperature field and the constitutive equation,rigid-viscoplastic finite element method(FEM) was applied in order to simulate the ball spinning of NiTi SMA tube.The temperature field,the stress field,the strain field and the load prediction were obtained by means of FEM.FEM results reveal that there is a temperature increase of about 160 ℃ in the principal deformation zone of the spun part.It can be found from the stress fields and the strain fields that the outer wall of NiTi SMA tube is easier to meet the plastic yield criterion than the inner wall,and the plastic deformation zone is caused to be in a three-dimensional compressive stress state.The radial strain and the tangential strain are characterized by the compressive strain,while the axial strain belongs to the tensile strain.The variation of spinning loads with the progression of the ball is of great importance in predicting the stable flow of the spun part. 展开更多
关键词 NiTi alloy NiTi tube shape memory alloy finite element method ball spinning
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基于Crystal Ball的泥沙来源指纹判别及不确定性评价 被引量:2
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作者 史忠林 陈佳村 +3 位作者 严冬春 文安邦 龙翼 吴毅 《中国水土保持》 2019年第7期55-57,I0001,共4页
土壤固有的空间变异性及对侵蚀强度响应程度的不同,造成利用采集的少量样品中指纹因子的平均值或中位数来表征物源或泥沙时存在较大的不确定性,进而影响物源贡献判别结果的可靠性。已有的蒙特卡洛模拟算法通常基于较为复杂的计算机语言... 土壤固有的空间变异性及对侵蚀强度响应程度的不同,造成利用采集的少量样品中指纹因子的平均值或中位数来表征物源或泥沙时存在较大的不确定性,进而影响物源贡献判别结果的可靠性。已有的蒙特卡洛模拟算法通常基于较为复杂的计算机语言,对一般研究者来说具有一定的挑战性。介绍一种简便快捷的分析软件Crystal Ball,并结合实例分析了其在流域泥沙来源判别中的应用。 展开更多
关键词 泥沙来源 指纹技术 CRYSTAL ball 蒙特卡洛方法
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Analysis of dynamic characteristics of self-aligning ball bearing 被引量:1
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作者 袁丁 蒋书运 《Journal of Southeast University(English Edition)》 EI CAS 2010年第3期410-414,共5页
A dynamics model of the self-aligning ball bearing is proposed based on the Jones-Harris method (JHM), and a computer program is developed to solve the equations by using the Newton-Raphson method. A parametric anal... A dynamics model of the self-aligning ball bearing is proposed based on the Jones-Harris method (JHM), and a computer program is developed to solve the equations by using the Newton-Raphson method. A parametric analysis of the centrifugal force and the gyroscopic moment, the contact loads, the contact angles, the radial deformation and the radial stiffness is carried out. The analytical results show that the applied loads and the rotational speed are two main factors that can influence the distributions of the contact loads and values of the contact angles. The centrifugal force and the gyroscopic moment increase with the increase in the rotational speed, resulting in the decrease of the inner raceway contact load and the increase of the outer raceway contact load. The outer raceway contact angle increases under the centrifugal force; on the contrary, the inner raceway contact angle decreases. Furthermore, the differences between the inner and the outer contact angles increase with the increase in the rotational speed. The higher rotational speed results in the decrease in radial stiffness for the self-aligning ball bearing, and the raceway curvature coefficient, to some extent, also influences the radial stiffness. 展开更多
关键词 self-aligning ball bearing dynamic characteristics Jones-Harris method (JHM) Newton-Raphson method bearing stiffness
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ANALYSIS OF MECHANICS IN BALL SPINNING OF THIN-WALLED TUBE 被引量:18
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作者 JIANG Shuyong REN Zhengyi 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2008年第1期25-30,共6页
Ball spinning is applied to manufacturing thin-walled tube with high precision and high mechanical properties. On the basis of plastic mechanics, by simplifying ball spinning of thin-walled tube as plane strain proble... Ball spinning is applied to manufacturing thin-walled tube with high precision and high mechanical properties. On the basis of plastic mechanics, by simplifying ball spinning of thin-walled tube as plane strain problem, slab method is used for the purpose of calculating the contact deformation pressure. The spinning force components, the torsional moment, the deformation power and the deformation work are calculated further as well. The influence of the two important process parameters such as the feed ratio and the ball diameter on the spinning force components is analyzed in order to further control the spinning force components by regulating the two process variables during the ball spinning process. The stress and strain state in deformable zone as well as mechanics boundary conditions in ball spinning are obtained. The effect of the three spinning force components on the formability of the spun part is analyzed and validated through the ball spinning experiments. The theoretical and experimental results show that the radial spinning component plays a significant role in ball spinning of thin-walled tube, and the mechanics situation in backward ball spinning contributes to enhancing the plasticity of the metal material, but that in forward ball spinning contributes to advancing the axial flow of the metal material. 展开更多
关键词 Power spinning Tube spinning ball spinning Spinning force Slab method
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Quasi Dynamic Calculation of Local Stiffness of Angular Contact Ball Bearings 被引量:2
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作者 Zhen-Huan Ye Chuan-Wei Zhang +2 位作者 Le Gu Li-Qin Wang De-Zhi Zheng 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2013年第3期22-26,共5页
In order to describe the performance of thin wall bearing on rotor system more accurate,the simplified model of bearing local stiffness was proposed. The load distribution and local contact deformation in angular cont... In order to describe the performance of thin wall bearing on rotor system more accurate,the simplified model of bearing local stiffness was proposed. The load distribution and local contact deformation in angular contact ball bearings were calculated using quasi dynamic calculation method. Based on the relationship of local load to contact deformation,the calculation model of local bearing stiffness was subsequently built to get radial and axial components of local stiffness. Effects of external loads on the local bearing stiffness were analyzed. The results showed that local stiffness in bearings is symmetric to the axis of radial load,and its value has a maximum on the symmetry axis along the radial load direction. External radial and axial load have different effects on local bearing stiffness. 展开更多
关键词 local stiffness angular contact ball bearings quasi dynamic method
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Dynamic Analysis of Flexible Cage of High-speed Angular Contact Ball Bearing 被引量:1
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作者 邓四二 谢鹏飞 +1 位作者 杨海生 高银涛 《Defence Technology(防务技术)》 CAS 2012年第2期98-103,共6页
A dynamics formula was established for the flexible cage of high-speed angular contact ball bearing. A modified Craig-Bampton component mode synthetic method was used to establish the formula with regard to the flexib... A dynamics formula was established for the flexible cage of high-speed angular contact ball bearing. A modified Craig-Bampton component mode synthetic method was used to establish the formula with regard to the flexibility of cage and based on a dynamic analysis of angular contact ball bearing,and a rigid-flexible multi-body dynamic analysis program was developed using ADAMS,which is verified by a computation example of Gupta. The results show that it's not likely to keep the rotation smoothness of cage when the ratio of pocket clearance to guiding clearance and the ratio of radial load to axial load become too large or too small. By comparison,the flexible cage runs more smoothly than the rigid cage. 展开更多
关键词 MECHANICS angular contact ball bearing CAGE Craig-Bampton method flexible body dynamics ADAMS
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An investigation into ball burnishing process of magnesium alloy on CNC lathe using different environments 被引量:1
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作者 Suleyman Cinar Cagan Catalin Iulian Pruncu Berat Baris Buldum 《Journal of Magnesium and Alloys》 SCIE EI CAS 2020年第4期1061-1070,共10页
Ball burnishing routine permits through a simple,fast and economical manner to obtain free chip on the manufactured parts.It generates a superior surface finish by rotating a ball tool against a workpiece.The burnishi... Ball burnishing routine permits through a simple,fast and economical manner to obtain free chip on the manufactured parts.It generates a superior surface finish by rotating a ball tool against a workpiece.The burnishing process is commonly developed in industry in order to improve the surface quality,which is a critical issue in the manufacturing sector.An experimental study were carried out to determine the best surface quality for magnesium alloy subjected to d iff ere ni medium.Burnishing of magnesium alloy was performed varying four different mediums and combining different burnishing parameters.To design the experiment were used the classical Taguchi method through which were developed the L16 orthogonal array.This strategy allowed to detect the driving parameters that generate the best surface roughness value by computing the signal-to-noise ratio.The driving parameters values for this study are 400 N(force),0.05 mm/min(feed rate),three number of passes and boron oil as medium.The results are paramount important for designing heavy parts used in transportation vehicles such as automobiles,airplanes,high-speed trains etc. 展开更多
关键词 Magnesium alloy Surface roughness MEDIUM Taguchi method ball burnishing
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AN ESTIMATION OF FUZZY RELIABILITY OF DISTINCT ELEMENT METHOD IN PREDICTION OF SURFACE SUBSIDENCE DUE TO COAL MINING 被引量:1
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作者 张玉卓 《Journal of Coal Science & Engineering(China)》 1998年第2期7-12,共6页
The quantitative evaluation of errors involved in a particular numerical modelling is of prime importance for the effectiveness and reliability of the method. Errors in Distinct Element Modelling are generated mainly ... The quantitative evaluation of errors involved in a particular numerical modelling is of prime importance for the effectiveness and reliability of the method. Errors in Distinct Element Modelling are generated mainly through three resources as simplification of physical model, determination of parameters and boundary conditions. A measure of errors which represent the degree of numerical solution 'close to true value' is proposed through fuzzy probability in this paper. The main objective of this paper is to estimate the reliability of Distinct Element Method in rock engineering practice by varying the parameters and boundary conditions. The accumulation laws of standard errors induced by improper determination of parameters and boundary conditions are discussed in delails. Furthermore, numerical experiments are given to illustrate the estimation of fuzzy reliability. Example shows that fuzzy reliability falls between 75%-98% when the relative standard errors of input data is under 10 %. 展开更多
关键词 RELIABILITY fuzzy sets ERRORS Distinct Element method ball
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Heavy-Ball型动量方法的最优个体收敛速率 被引量:10
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作者 程禹嘉 陶蔚 +1 位作者 刘宇翔 陶卿 《计算机研究与发展》 EI CSCD 北大核心 2019年第8期1686-1694,共9页
动量方法作为一种加速技巧被广泛用于提高一阶梯度优化算法的收敛速率.目前,大多数文献所讨论的动量方法仅限于Nesterov提出的加速方法,而对Polyak提出的Heavy-ball型动量方法的研究却较少.特别,在目标函数非光滑的情形下,Nesterov加速... 动量方法作为一种加速技巧被广泛用于提高一阶梯度优化算法的收敛速率.目前,大多数文献所讨论的动量方法仅限于Nesterov提出的加速方法,而对Polyak提出的Heavy-ball型动量方法的研究却较少.特别,在目标函数非光滑的情形下,Nesterov加速方法具有最优的个体收敛性,并在稀疏优化问题的求解中具有很好的效果.但对于Heavy-ball型动量方法,目前仅仅获得了平均输出形式的最优收敛速率,个体收敛是否具有最优性仍然未知.对于非光滑优化问题,通过巧妙地设置步长,证明了Heavy-ball型动量方法具有最优的个体收敛速率,从而说明了Heavy-ball型动量方法可以将投影次梯度方法的个体收敛速率加速至最优.作为应用,考虑了l1范数约束的hinge损失函数优化问题.通过与同类的优化算法相比,实验验证了该理论分析的正确性以及所提算法在保持稀疏性方面的良好性能. 展开更多
关键词 一阶梯度方法 动量方法 个体收敛速率 Heavy-ball方法 稀疏性
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Modelling of the High-Energy Ball Milling Process 被引量:1
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作者 Mohsen Mhadhbi 《Advances in Materials Physics and Chemistry》 2021年第1期31-44,共14页
In this paper, the milling parameters of high energy ball mill (Fritsch Pulverisette 7) like vial geometry, number and size of balls and speed of the mill were modelled and discussed. Simulations through discrete elem... In this paper, the milling parameters of high energy ball mill (Fritsch Pulverisette 7) like vial geometry, number and size of balls and speed of the mill were modelled and discussed. Simulations through discrete element method (DEM) provide correlation between the milling parameters. A mathematical model is used to improve and develop this process. The results show that the loss of powder mass can remarkably improve the performance of milling. The balls made of stainless-steel have a positive effect on the milling efficiency. The simulation shows that the high ball milling velocities can contribute to faster particle size reduction. 展开更多
关键词 ball Mill Modelling Discrete Element method Planetary ball Mill High-Energy ball Milling
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Structural optimization for ball valve made of CF8M stainless steel 被引量:5
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作者 Seung-Gyu KIM Seok-Heum BAEK Young-Chul PARK 《中国有色金属学会会刊:英文版》 CSCD 2009年第B09期258-261,共4页
The mechanical and chemical properties of CF8M were studied through experiments. An application of CF8M in valve body was analyzed by using finite element method(FEM) to evaluate the structural safety. An optimization... The mechanical and chemical properties of CF8M were studied through experiments. An application of CF8M in valve body was analyzed by using finite element method(FEM) to evaluate the structural safety. An optimization containing several variables based on the response surface method(RSM) was conducted to find the optimum dimension of the valve. The results show that using this process can save valve mass as well as the computational expense effectively. 展开更多
关键词 结构优化 球阀 不锈钢 化学性能 有限元法 结构安全 最佳尺寸 FEM
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General issues of FEM in backward ball spinning of thin-walled tubular part with longitudinal inner ribs 被引量:5
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作者 江树勇 任正义 +1 位作者 吴滨 武桂香 《中国有色金属学会会刊:英文版》 EI CSCD 2007年第4期793-798,共6页
Backward ball spinning was applied for manufacturing thin-walled tubular parts with longitudinal inner ribs. Rigid-plastic finite element method(FEM) was used for simulating the backward ball spinning process in order... Backward ball spinning was applied for manufacturing thin-walled tubular parts with longitudinal inner ribs. Rigid-plastic finite element method(FEM) was used for simulating the backward ball spinning process in order to calculate the height of the inner ribs. With a view to guarantee a better simulation accuracy, it is essential to enhance and improve some general problems of FEM, such as generation of initial velocity field, choice of penalty factor, determination of boundary conditions, treatment of rigid region and description of convergence criteria. It is evident that whether the problems with respect to FEM are dealt with appropriately or not, they have a significant influence on the modeling accuracy and efficiency. By reasonable solving the general problems, rigid-plastic FEM can successfully simulate the height of the inner ribs and the calculated values are in good agreement with the measured values. 展开更多
关键词 反相球状旋压 强力旋压 有限元法 纵向内肋
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Fully discrete Jacobi-spherical harmonic spectral method for Navier-Stokes equations
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作者 黄伟 郭本瑜 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2008年第4期453-476,共24页
A fully discrete Jacobi-spherical harmonic spectral method is provided for the Navier-Stokes equations in a ball. Its stability and convergence are proved. Numerical results show efficiency of this approach. The propo... A fully discrete Jacobi-spherical harmonic spectral method is provided for the Navier-Stokes equations in a ball. Its stability and convergence are proved. Numerical results show efficiency of this approach. The proposed method is also applicable to other problems in spherical geometry. 展开更多
关键词 fully discrete Jacobi-spherical harmonic spectral method Navier-Stokes equations in a ball mixed coordinates
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基于AdaBelief的Heavy-Ball动量方法 被引量:1
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作者 张泽东 陇盛 +1 位作者 鲍蕾 陶卿 《模式识别与人工智能》 EI CSCD 北大核心 2022年第2期106-115,共10页
同时使用动量和自适应步长技巧的自适应矩估计(Adaptive Moment Estimation,Adam)型算法广泛应用于深度学习中.针对此方法不能同时在理论和实验上达到最优这一问题,文中结合AdaBelief灵活调整步长提高实验性能的技巧,以及仅采用指数移... 同时使用动量和自适应步长技巧的自适应矩估计(Adaptive Moment Estimation,Adam)型算法广泛应用于深度学习中.针对此方法不能同时在理论和实验上达到最优这一问题,文中结合AdaBelief灵活调整步长提高实验性能的技巧,以及仅采用指数移动平均(Exponential Moving Average,EMA)策略调整步长的Heavy-Ball动量方法加速收敛的优点,提出基于AdaBelief的Heavy-Ball动量方法.借鉴AdaBelief和Heavy-Ball动量方法收敛性分析的技巧,巧妙选取时变步长、动量系数,并利用添加动量项和自适应矩阵的方法,证明文中方法对于非光滑一般凸优化问题具有最优的个体收敛速率.最后,在凸优化问题和深度神经网络上的实验验证理论分析的正确性,并且证实文中方法可在理论上达到最优收敛性的同时提高性能. 展开更多
关键词 AdaBelief Heavy-ball动量方法 个体收敛速率 深度神经网络
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