Mathematical modeling of flux consumption during twin-wire welding

Mathematical models for flux consumption during twin-wire welding with direct current electrode positive and direct current electrode negative have been presented. The models illustrate the flux consumption in the form of a function relation between different process parameters. The present work is the result of a large number of experimental observations, modelling, and subsequent validation. The accuracy and predictability along with the use of shop-floor controllable parameters as model inputs make the proposed models useful for industrial application. The effects of process parameters have been further analyzed. The analysis revels that current, voltage, wire diameters and polarity are the major factors influencing the flux consumption during the twin wire welding, while welding speed and contact-tube-to-work-piece-distance are found to be significant with electrode negative. One of the important observations during the present investigation is regarding influence of dissimilar wire diameters at the lead and trail wires on the flux consumption. Mathematical analysis of magnetic field generated in the vicinity of the arc, particularly with dissimilar diameter, affects the arc deflection and affects the flux consumption.     

Mathematical modeling of sintering during powder forming processes

This paper describes a study of densification induced by local capillary forces during compaction of powder based materials. A coupled sinter-compaction model with an internal state parameter was proposed. An internal state parameter was assumed as the sintering stresses on contact areas between powder particles. The mechanical model describing the plastic deformation during the P/M forging of a preform is based on the plasticity theory of porous metals. The numerical investigation of P/M forming processes is based on the rigid-plastic finite element model. A finite element program taking into account the sintering effect during P/M forming is created. A numerical example is considered.     

精密电机有溶剂漆真空压力浸渍工艺研究及应用

针对军用精密电机槽满率高、工作环境恶劣等特性,要求其电枢浸漆处理后的绝缘稳定性好。从真空浸漆与真空压力浸漆效果比较、真空压力浸漆技术的工艺参数优化、不同保护非浸漆部位方式等方面进行了工艺研究。与传统方法相比,采用研究后的技术方法浸漆,挂漆量更大、湿热试验中电机的绝缘电阻稳定。解决了此前进行浸漆后电机在湿热状态下绝缘稳定性较差的难题,从而提高精密军用电机的绝缘一致性。     

一种以战备完好性为目标的备件数量数学模型

本文在给出一个新的战备完好性参数指标“功能保障水平”的基础上,提出以战备完好性为目标的备件数量数学模型,通过案例比较说明新的数学模型使用更为简便,模型精度更高．具有很好的使用价值。     

Mathematical modeling of fluxgate magnetic gradiometers

Issues of designing fluxgate magnetic gradiometers are considered. The areas of application of fluxgate magnetic gradiometers are determined. The structure and layout of a two-component fluxgate magnetic gradiometer are presented. It is assumed that the fluxgates are strictly coaxial in the gradiometer body. Elements of the classical approach to the mathematical modeling of the spatial arrangement of solids are considered. The bases of the gradiometer body and their transformations during spatial displacement of the gradiometer are given. The problems of mathematical modeling of gradiometers are formulated, basic mathematical models of a two-component fluxgate gradiometer are developed, and the mathematical models are analyzed. A computer experiment was performed. Difference signals from the gradiometer fluxgates for the vertical and horizontal position of the gradiometer body are shown graphically as functions of the magnitude and direction of the geomagnetic field strength vector.     

Mathematical modeling of human secondary osteons

This investigation explores the structural dimensions and patterns within single secondary osteons, with consideration of their biological variation. New data from images obtained previously of osteons observed through linearly polarized light, electron microscopy, and micro-x-ray, combined with recent findings on lamellae by circularly polarized light, confocal microscopy, synchrotron x-ray diffraction, and micro-x-ray, provide the basis for novel computerized models of single osteons and single lamellae. The novelty of such models is the concurrent representation of (1) collagen-hydroxyapatite orientation, (2) relative hydroxyapatite percentage, (3) distributions of osteocytes' lacunae and canaliculae, and (4) biological variations in dimensions of the relevant structures. The mathematical software Maple realizes the computerized models. While the parts of the models are constructed on a personal computer, the voluminous data associated with the representation of lacunar and canalicular distributions require a supercomputer for assembly of the models and final analysis. The programming used to define the models affords the option to randomize the dimensional specifications of osteons, lamellae, lacunae, and canaliculae within the experimentally observed numeric ranges and distributions. Through this option, the program can operate so that each run of the file produces a unique random model within the observed biological variations. The program can also be run to implement specific dimensional requirements. The modeling has applications in the microstructural study of fracture propagation and remodeling, as well as in the simulation of mechanical testing. The approach taken here is of wide application and could be of value in other areas of microscopy such as scanning electron microscopy, microcomputerized tomography scan, and magnetic resonance imaging on cancellous bone structures.     

Mathematical modeling for surface hardness in investment casting applications

Investment casting (IC) has many potential engineering applications. Not much work hitherto has been reported for modeling the surface hardness (SH) in IC of industrial components. In the present study, outcome of Taguchi based macro-model has been used for developing a mathematical model for SH; using Buckingham’s π-theorem. Three input parameters namely volume/surface-area (V/A) ratio of cast components, slurry layer’s combination (LC) and molten metal pouring temperature were selected to give output in form of SH. This study will provide main effects of these variables on SH and will shed light on the SH mechanism in IC. The comparison with experimental results will also serve as further validation of model.     

磁流变液减振器中磁场强度的数学建模及有限元分析

在论述磁流变液减振器工作机理的基础上,采用一种数学建模方法建立了磁流变液减振器中磁场强度的数学模型,然后运用ANSYS编写了相应程序对该磁场强度模型进行了有限元分析,将这两种方法得到的数据进行比较分析后,最终得到了磁场强度与磁流变液减振器主要设计参数和控制参数（激励电流和线圈匝数）之间的简化数学模型,为有效的在磁流变液减振器中控制阻尼孔处磁场强度等后续工作打下基础。     

Mathematical modeling of the cylindrical grinding process

This paper proposes a dynamic model of cylindrical grinding with a tool owning specified distribution of abrasive grains. Cutting forces have been calculated, the surface geometry formed after a grinding wheel pass has been determined, the influence of the process dynamics on cutting forces and machined surface geometry has been taken into account, and the effects of cutting condit on vibrations being generated in the process of grinding have been investigated.     

闭环伺服系统的数学建模和性能分析

在数控机床中,伺服系统是数控机床装置和机床的中间连接环节,是数控系统的重要组成部分。伺服系统接受来自伺服控制器的进给脉冲,经变换和放大转换为机床工作台的位移,使工作台跟随指令脉冲移动。讨论了闭环伺服数控系统的数学模型,对闭环伺服系统的动态、静态性能进行了详细的分析,该研究结果为提高数控加工的控制精度提供了理论基础。     

Mathematical modeling for the design of a generic custom-engineered form mill

This paper presents a mathematical model for the geometric design of a custom-engineered form milling (CEFM) cutter and develops an accurate 3D surface-based generic definition of the form mill. The proposed geometric definition of the CEFM cutter is developed in terms of biparametric surface patches using newly defined 3D rotational angles rather than the conventional 2D angles. The non-uniform rational B-spline curve fairing and sweep surface approaches are used to design the cutting edge and flank surface, respectively, of the cutter. To validate the methodology, an interface is developed that converts the proposed 3D parametric definition of the cutter into an intermediate neutral CAD format and then renders the cutter model in any CAD modeling environment. The accuracy of the mathematical model is verified by evaluating the deviation plot between the surfaces of the proposed cutter model and the surfaces developed using digitized data of an existing actual CEFM cutter. The satisfactory comparison verifies the shape design methodology for custom cutters presented in this paper. The method described here offers a simple and intuitive way of generating shape design of custom cutters for possible use in machining process simulations, finite element analysis, and other applications.     

Mathematical modeling of moving heat source shape for submerged arc welding process

An attempt is made in this paper to find out the analytical solution of the thermal field induced in a semi-infinite body by a moving heat source with Gaussian distribution by selecting appropriate inside volume for submerged arc welding process. Three different types of heat source shapes in the form of oval, double ellipsoidal, and conical forms were considered and compared with the experimental result. The study shows that for heat input of submerged arc welding process, the best suitable heat source shape is in the form of an oval. The study also shows two alternate ways of predicting the size of the heat-affected zone.     

Mathematical modeling based on contact mechanism due to elastic and plastic deformation of pad asperities during CMP

Technologies in semiconductor industry have been developed into a three-dimensional multilayer wiring for high integration of devices. Chemical mechanical planarization (CMP) process is one of the key technologies for achieving multilayer wiring, which enables global planarization. In addition, highly integrated devices can be realized by increasing the depth of focus in the photolithography process. However, in the inter-layer dielectric (ILD) CMP of the transistor, the uppermost oxide layer has the step due to the arrangement of the devices. The ideal material removal mechanism is to gradually remove materials from the top of the step height which allows for global planarization. However, in the CMP of the patterned wafers, simultaneous polishing of the upper and lower layers occurs when the step height reaches a certain height. This means that the polishing is strongly dependent on the structural characteristics of the pattern. Especially, the difference in the material removal rate depending on the pattern density acts as a constraint in terms of device layout. Therefore, it is essential to develop an accurate prediction model of material removal rate as a function of pattern density, size and arrangement. This study aims to define the mathematical planarization model according to contact mode between a polishing pad and patterned wafer. Considering that the real contact area between the actual polishing pad and the wafer is about 1 %, the mathematical model is derived based on the microscopic deformation of the pad asperities, not the macroscopic deformation of the bulk pad. Finally, we describe the verification between the theoretical material removal rate model and step height reduction and the actual CMP results. The root mean square error of the upper layer material rate, the lower material removal rate, and the step height reduction were 24.59 nm/min, 22.03 nm/min and 22.6 nm, respectively. Compared with the previous studies, the new model of this study improved the error by up to 50.9 %.

     

汽车摇臂机构的数学建模及最优化

运用空间坐标变换理论的有关知识,对双摇臂机构进行运动学分析,建立空间数学模型和基于转向误差最小的最优化模型.考虑车辆的真实行驰状况引入加权函数,从而实现真实工作条件的仿真.最后以一典型车辆为例,验证得出此方法可行且高效.     

Mathematical modeling of wear of journal bearings in outer space

The paper deals with a model of the wear process of journal bearings in outer space when they are exposed to significant temperature oscillations. Derived equations and experimental data are used to calculate the kinetics of wear of the bearings.     

Mathematical modeling and verification of pulse electrochemical micromachining of microtools

Pulse electrochemical micromachining (PECMM) is an unconventional manufacturing method suitable for the production of micro-sized components on a wide range of electrically conductive materials. PECMM in this study has been used to manufacture microtools. The non-contact nature of PECMM has necessitated the modeling of the process to estimate the anodic profile (microtool profile). This paper presents a mathematical model for predicting the diameter of the microtools fabricated by PECMM process. Tungsten microtools of diameters less than 100 μm were fabricated using an in-house built microelectrochemical machining system. Experimental results confirm the theoretical prediction of reduction in tool diameter with respect to increasing machining time. Further, from the experimental verification, it was found that the deviations in the tool diameters were within 9 % of the theoretical predictions.     

Mathematical modeling for finishing tooth surfaces of spiral bevel gears using pulse electrochemical dissolution

Gears with a complex curve tooth, such as spiral bevel and hypoid gears, lack an ideal technique for the final finishing process. Pulse electrochemical finishing (PECF) is considered a promising method for surface finishing due to its micro-removal characteristics. A PECF system for spiral bevel gear (SBG) is established according to the generation of SBG tooth surfaces. An SBG (module, 12?mm; number of teeth, 38) is selected as the processing test piece, and mathematical models are developed for analyzing the characteristics of PECF. The influence of the experimental variables, including applied voltage, interelectrode gap, and finishing time, on the total removal thickness and surface roughness is discussed. The calculated values are found to be approximately consistent with the experimental values. The other parameters, including the concentration of electrolyte, tool rotational speed, flow rate of electrolyte, and pulse period, are also studied. Results show that the roughness of the SBG tooth surface is reduced from Rz 7.13 to 4.32???m. The precision of the SBG is also improved.     

Mathematical modeling and machining parameter optimization for the surface roughness of face gear grinding

Face gear is an important part in the power transmission of helicopter, but its grinding is a difficult problem. In order to enhance the finishing machining surface quality of face gear, the mathematical formula of the residual height of motion trajectory of abrasive grains was obtained, and the model of grinding surface roughness of face gear was corrected. In addition, machining parameter optimization for grinding surface roughness on a five-axis blade grinding machine was investigated by orthogonal experiment method. The experiment results indicated that disk wheel spindle speed and feed velocity of the disk wheel are more significant effect factors among the three factors. The calculation results of model showed that the maximum error comparing with the experiment results is not more than 13.5 %, which suggests that the mathematical model is reasonable.