Three-Dimensional Implicit Curve Interpolation

An approach to 3D implicit curve interpolation in computer numerical systems (CNC) is presented. A 3D implicit curve is the intersection of two implicit surfaces. Geometric entities of 3D implicit curves are related to motion entities along the curve. The results are then used to develop real-time 3D implicit curve interpolation. An improved interpolation scheme has been proposed to augment the initial interpolation scheme to eliminate the cumulative point deviations. Simulations of implicit curve interpolation have been carried out to verify the effectiveness of the proposed algorithm. They also demonstrate that under typical machining conditions, the interpolation error for the improved scheme is well within the accuracy requirements of typical machines. The example has an application potential for tool-path interpolation when tool paths are obtained by intersecting an implicit design surface by drive cylinders. These show that the proposed algorithm is potentially useful for the machining of implicit surfaces.     

用于五轴联动数控机床的曲线插补控制策略

为实现复杂曲面零部件的高速高精数控加工,提出了一种用于五轴联动数控机床的曲线插补控制策略.实现该控制策略的数控机床控制器将控制任务分为非实时任务和实时任务两部分.非实时任务包括刀具路径信息中位置矢量的曲线插值计算和刀位矢量的曲线插值计算;实时任务包括位置矢量插值曲线和刀位矢量插值曲线的实时插补计算,以及插补点坐标的逆机床运动变换.加工实验表明,该插补加工方法町以用于五坐标数控机床的运动控制,具有良好的应用前景.     

Effect of electropulsing on springback during V-bending of Ti-6Al-4V titanium alloy sheet

Because the intermediate-stage forming surface and the intermediate-stage forming tool path of the complex shape model are difficult to generate, the existing multi-stage CNC incremental forming takes the regular rotary body model or the square model as the research objects, and all adopt the three-axis CNC incremental forming mode. In this paper, a method for generating the intermediate-stage surface by using a longitude line that can reflect the personality of the surface and the five-axis CNC multi-stage incremental forming tool path was proposed. Firstly, the vertexes of the triangular facets of the STL model are used to generate the longitude lines which can reflect the characteristic of the surface, then the longitude lines are offset according to the multi-stage forming strategy and the characteristics of each surface associated with the longitude lines so that the intermediate-stage longitude lines could be generated, and then the intermediate-stage surfaces are built using the intermediate-stage longitude lines. Finally, the cutter location points of each intermediate stage are obtained by cutting the intermediate-stage surfaces, and the postures of the five-axis CNC pressing tool are determined according to the normal vector of the cutter location points. The case studies show that the proposed method can well generate the five-axis CNC multi-stage incremental forming path for the complex shape sheet metal part. The results of the numerical simulation analysis and forming experiments show that the proposed method is applicable.     

Galling initiation due to frictional heating

The lifetime of sheet metal forming (SMF) tools is often limited by galling, a wear type that affects the surface quality of the products and the lifetime of SMF tools. Since SMF tools represent high economical value, it is clear that improvement and prediction of tool life is of high industrial importance. Therefore, models are required that can predict friction and wear related phenomena in SMF-processes, in particular galling. This paper demonstrates the application of a wear model, which is able to predict the initiation of galling in lubricated sheet metal forming processes, to laboratory results gained with the TNO slider-on-sheet tribometer. Experiments are conducted with different (coated) tool surfaces, in sliding contact with stainless steel sheet, using two lubricants. By comparing the critical temperature of the generated boundary layer with the flash temperature at the interface of the sheet and individual tool summits, it is possible to predict whether or not galling initiation will occur. It is shown that the laboratory results are in good agreement with the predicted results of the presented wear model. Galling initiation in lubricated sheet metal forming processes, can be avoided by the application of smooth tool surfaces with enhanced thermal conductivity and lubricants which form boundary layers with a high critical temperature.     

一种改进的自动翻法线算法

针对有限元单元中包含曲面信息的特点,提出了一种改进的自动翻法线算法——片内种子单元法。该算法能够利用生成的有限元单元中包含曲面片信息的特点,分别对各曲面片独立地进行翻法线操作,对曲面片之间存在裂缝、重叠等缺陷有较强的适应性。该算法能快速准确地使工具有限元单元的法线保持一致,为后续板料成形数值模拟中的接触算法提供必要的前提条件。     

Incremental forming path-generated method based on the intermediate models of bulging simulation

This paper discusses the strategy of incremental forming and presents a novel forming strategy for tool path generation. To equalize the strain distribution of sheet metal and improve the forming limit, multistage forming is made to reference a hydraulic bulging forming. Under the liquid pressure, a plate sheet gradually approaches the final shape. A hydraulic bulging numerical simulation is used to obtain a series of intermediate surfaces. Then, CNC codes can be generated in CAM software based on the surfaces. The codes are the tool spatial feed paths for single-point incremental sheet metal forming. The paper focuses on the feasibility investigation, and the experiment proved it. The behaviors of forming and the distribution of thickness are also discussed and concluded that the forming limit of the sheet can be improved by imitating the approach between intermediate surfaces.     

A method for visualization of surface texture anisotropy in different scales of observation

Anisotropy of functional surfaces can in many practical cases significantly influence the surface function. Tribological contacts in sheet forming and engine applications are good examples. This article introduces and exemplifies a method for visualization of anisotropy. In a single graph, surface texture properties related to the anisotropy as a function of scale are plotted. The anisotropy graph can be used to explain anisotropy properties of a studied surface such as texture direction and texture strength at different scales of observation. Examples of milled steel surfaces and a textured steel sheet surface are presented to support the proposed methodology. Different aspects of the studied surfaces could clearly be seen at different scales. Future steps to improve filtering techniques and an introduction of length-scale analysis are discussed.     

Stress recovery techniques for natural element method in 2-D solid mechanics

This paper is concerned with the stress recovery for the natural element method in which the problem domain is discretized with Delaunay triangles and the structural behavior is approximated with Laplace interpolation functions. Basically, the global and local patch recovery techniques based on the L ₂-projection method are adopted. For the local patch recovery, the local element patches are defined by the supports of each Laplace interpolation function. For the comparison purpose, the local stress recovery is also performed using Lagrange-type basis functions that are used for 3- and 6-node triangular elements. The stresses that are recovered by the present global and local recovery techniques are compared each other and compared with the available analytic solution, in terms of their spatial distributions and the convergence rates. As well, the dependence of the recovered stress field on the type of test basis functions that are used forbnov-Galerkin (BG) and Petrov-Galerkin (PG) natural element methods is also investigated.

     

An accurate interpolator for FTS diamond turning of optical free-form surface

The ultra-precision components with freeform surfaces are used in a wide range of areas such as automotive, aerospace, optical, metrology artifacts, and data storage. Fast tool servo (FTS) diamond turning has been considered as one of the leading techniques to produce such components. We present four points mean value interpolator for FTS diamond turning. Performance is compared between the NURBS interpolations with the proposed interpolation using Matlab, which shows that the proposed interpolation not only improves the surface accuracy of the freeform surface, but also meets the real-time requirement.     

Springback prediction of the vee bending process for high-strength steel sheets

The precise prediction of springback is a key to assessing the accuracy of part geometry in sheet bending. A simplified approach is developed by considering the thickness ratio, normal anisotropy, and the strain-hardening exponent to estimate the springback of vee bending based on elementary bending theory. Accordingly, a series of experiments is performed to verify the numerical simulation. The calculation of the springback angle agrees well with the experiment, which reflects the reliability of the proposed model. The effects of process parameters such as punch radius, material strength, and sheet thickness on the springback angle are experimentally tested to determine the dominant parameters for reducing the springback angle in the sheet bending process for high-strength steel sheets. Moreover, the effects of the thickness ratio, normal anisotropy, and the strain-hardening exponent on the springback angle in the vee bending process for high-strength steel sheets are theoretically studied. Therefore, improving understanding on and control of the springback reduction of the vee bending process in practical applications is possible.     

A study of techniques in the evaluation of springback and residual stress in hydroforming

The increasing need for high strength complex hollow bodies for automotive application is pushing towards the use of sheet hydroforming techniques in conjunction with high strength steels. Unfortunately high strength steels are characterised by high springback levels. In this paper the springback and residual stresses have been analysed by means of laboratory trials carried out using the double sheet hydroforming technique. The attention has been focused on the upper blank of TRIP800 steel. The analysis has been performed using different approaches: i) characterisation of sample accuracy by means of a 3D coordinate measuring machine using a new proposed method based on the standard deviation calculation; ii) FE-analysis of both hydroforming and springback stages using an implicit FEM code; iii) residual stress evaluation by means of X-ray diffraction and laser cutting techniques. The effect of pressure, die insert geometry and friction at the blank holder on springback and residual stresses have been analysed and discussed in detail.     

Galling resistance and wear mechanisms – cold work tool materials sliding against carbon steel sheets

One of the major causes for tool failure in sheet metal forming is transfer and accumulation of adhered sheet material to the tool surfaces, generally referred to as galling. In the present work, the galling resistance of several tool materials was investigated against two-phase ferritic-martensitic carbon steel under dry sliding test conditions. Tribological evaluation was carried out at different contact pressures by using a slider-on-flat-surface (SOFS) tribometer. For all selected test conditions, a consistent ranking of the materials was obtained with best performance observed for nitrogen alloyed powder metallurgy tool steel. Worst galling resistance was observed by nodular cast iron.     

Realistic simulation of surface defects in five-axis milling using the measured geometry of the tool

Managing macro- and micro-geometry of surfaces during manufacturing processes is a key factor for their following uses. Indeed, micro-geometry and surface topography are directly linked to the performances of functions (contact, friction, lubrication, etc.) by texture parameters to ensure the desired local geometry. Common models for simulation of surface topography are based on ideal geometry of the machining tool and cannot represent surface defects. The actual prediction and simulation of defects are one step forward in a competitive context. In this paper, the realistic model proposed aims to simulate and predict as finely as possible local defects of machined surfaces taking into account the actual edge geometry of the cutting tool. The combined use of the machining kinematics and of the measured geometry of the cutting edges leads to the representation of the geometrical envelope of the surface using a Zbuffer technique. Simulation assessment is carried out by the analysis of 3D surface topography parameters such as surface complexity and relative area and by a comparison of simulation results to an experimental case of study.     

Tool path generation by offsetting curves on polyhedral surfaces based on mesh flattening

Polyhedral surfaces are used as representation model for CAM and process planning purposes because of its simplicity for data exchange and geometric computation. However, there are few tool path planning strategies for such surfaces but isoplanar method. This paper presents a contour offset approach to tool path generation for three-axis ball-end milling of polyhedral surfaces, based on a novel method for offsetting curves on polyhedral surfaces. One of its salient features is to reduce the task of removing complex interfering of offsets from 3D physical surfaces to 2D plane by flattening mesh surfaces and avoid costly 3D Boolean set operations and relatively expensive distance calculation. Moreover, in practical implement, the procedures of calculating offset points and removing interfering loops are merged and carried out simultaneously results in an efficient tool path generation method. Empirical examples illustrate the feasibility of the proposed method.     

汽车零部件热成形极限裕度云图的构建与应用

在热冲压工艺中,热冲压钢板处于高温状态,不同位置温度分布有明显差异,传统方法难以评价冲压件的成形性,考虑温度的三维成形极限图能有效评价热冲压件的成形性能,但无法判断热冲压件的安全裕度。针对上述问题,在考虑温度的三维成形极限图的基础上,首先提出了成形裕度的计算方法;然后结合数值模拟和理论分析手段,构建了适用于评价高强钢板热冲压的安全裕度云图;最后对某汽车B柱热冲压不同工艺过程进行了仿真分析,并与试验进行了对比。结果表明,在不同工艺参数和板料尺寸下,构建的裕度云图均能有效预测高强钢板热冲压件的开裂部位和程度。     

NUMERICAL APPROACH TO DETERMINING INSTANTANEOUS CONTACT REGION FOR CONJUGATE SURFACES

According to the defect of traditional method of determining instantaneous contact regions for conjugate surfaces, a numerical approach to the determination is proposed. A local coordinate system is built by using the surface unit tangent and unit normal at the contact point. Considering that the gap forming the boundary of instantaneous contact region in the direction of the common normal vectors is given, a system of nonlinear equations is built to find the instantaneous contact boundary in local coordinate system, a modified Powell＇s hybrid algorithm of finite-difference approximation to the Jacobian used to solve the system. The new method simplifies the task of determining instantaneous contact regions without calculating curvatm＇e and relative curvature. The validity of the proposed approach is verified by an example of hypoid gears.     

覆盖件冲压仿真参数化建模方法

针对在覆盖件冲压成形领域对快速、自动化的有限元网格建模方法的迫切需求,提出一种快速的汽车覆盖件冲压仿真建模的思路与方法.将覆盖件冲压工艺设计与冲压成形仿真前处理集成,使用散乱三角面片模型,在自主开发的CAE前处理软件中,进行参数化的工艺补充面和压料面设计.模型的网格剖分与冲压工艺设计同时进行,自动生成整套模具的网格模型供冲压仿真计算.为了真实地模拟板料网格的流动,提出了参数化的真实拉深筋的模型建模方法和板料网格的预细分方法.完成了相关软件的开发.多个汽车覆盖件冲压工艺设计和冲压仿真计算实例说明了该方法的有效性.     

Usage of 3D roughness parameters adapted to the experimental simulation of sheet-tool contact during a drawing operation

The multipass strip drawing tests of sheet metal car body parts in cylinder/sheet/cylinder contact geometry is particularly well adapted to the simulation of sheet/tool contact conditions during a stamping operation. Within this framework, a rough sheet rubs against a smooth tool. During the sliding contact, a modification in the average size of plateaus appears, the locations where the shear stress and normal pressures are transmitted. Owing to a profilometrical relocation technique between each tool passage, we use statistical parameters corresponding to the average width and length of the plateaus. The observed flattening of the plateaus and the quantity of free wear particles modifying the third body in the contact are particularly more important in the case of aluminum sheets than in those of mild steel sheets.     

Iso-parametric tool path generation from triangular meshes for free-form surface machining

The polyhedral model is widely used in the manufacturing industry. However, apart from the iso-planar method, the tool path generation methods for polyhedral machining are very limited. In such a case, the given tool paths are no longer boundary-conformed or efficient. This paper presents a new approach to iso-parametric tool path generation for triangular meshes. The strategy proposed herein first parameterizes the triangular faces via a harmonic map. The cutter-contact (CC) points and the path interval are then calculated based on the machining tolerance requirements and the iso-parametric tool paths are finally generated. The method is implemented on a computer and some illustrative examples are provided to show the effectiveness of the developed algorithm. The main advantage of the proposed method is that the tool paths can be generated naturally along the boundary of a polyhedral model, thus eliminating internal tight-radius corners in conventional paths. This leads to substantial reductions of tool wear and machining time. In addition, the proposed method can also be used in other non-iso-parametric tool path planning methods for triangular meshes and compound surfaces machining.     

Influence of Tool Material and Surface Roughness on Galling Resistance in Sliding Against Austenitic Stainless Steel

Transfer and accumulation of adhered sheet material, generally referred to as galling, is a major cause for tool failure in sheet metal forming. In the present work, the galling resistance of three different tool materials was evaluated in lubricated sliding against austenitic stainless steel using a SOFS tribometer. All tool materials were prepared to four different surface roughnesses, ranging from a polished surface with R _a = 0.05 μm to a ground surface with R _a = 0.3 μm. The overall best performance was obtained for polished nitrogen alloyed powder metallurgy (PM) tool steel, where galling was detected only at the highest load evaluated, 700 N. However, for both the D2 type tool steel and nodular iron, best performance was observed for the surface possessing a surface roughness of 0.1 μm. The improved galling resistance for the rougher surfaces was related to filling of grinding scratches with sheet material during the initial stage of sliding, prolonging the development of protruding sheet material on the tools surface. Similar trend was not observed for the PM steel, which was related to width of the scratches originating from the surface preparation, in relation to tool microstructure.