Towards the simulation of Internal Traverse Grinding – from mesoscale modelling to process simulations

The present work aims at the modelling and simulation of Internal Traverse Grinding of hardened 100Cr6/AISI 52100 using electro plated cBN grinding wheels. We focus on the thermomechanical behaviour resulting from the interaction of tool and workpiece in the process zone on a mesoscale. Based on topology analyses of the grinding wheel surface, two-dimensional single- and multigrain representative numerical experiments are performed to investigate the resulting load-displacement-behaviour as well as the specific heat generation due to friction and plastic dissipation. A thermoelastic-viscoplastic constitutive model is used to capture thermal softening of the material taken into account. Based on previous work, an adaptive remeshing scheme which uses a combination of error estimation and indicator methods, is applied to overcome mesh dependence. In consequence, the formulation allows to resolve the complex deformation patterns and to predict a realistic thermomechanical state of the resulting workpiece surface. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Towards the simulation of grinding processes – a thermoplastic single grain approach

The current work aims at the modelling and simulation of metal grinding processes with focus on the thermal behaviour resulting from the interaction of tool and workpiece. Starting from a two-dimensional model of a single grain, representative numerical experiments are carried out based on the variation of grain geometry and its spatial position relative to the workpiece to predict the resulting load-displacement-behaviour. Here, a thermoelastic viscoplastic constitutive model is used to capture thermal softening of the material taken into account. Referring to previous research, an adaptive remeshing scheme, based on a combination of error estimation and refinement indication is used to overcome mesh dependence, allowing to resolve the complex deformation patterns and to predict a realistic thermomechanical state of the resulting workpiece surface. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A two-scale simulation framework for Internal Traverse Grinding

We present a hybrid framework which aims at the modelling and simulation of Internal Traverse Grinding of hardened 100Cr6/AISI 52100 by using electro plated cBN grinding wheels. We focus on the thermo-mechanical loading conditions on the workpiece that results from the interaction of workpiece and tool. The modelling framework basically consists of three components, namely representative plane strain adaptive finite element simulations on a meso-scale, capturing the proximity of a single cBN grain when cutting through the workpiece bulk. Secondly, we incorporate a kinematic simulation on the process level to gain detailed simulation-based information on the transient grain-bulk-interaction. The third component of the framework consists of a macro-scale process model that uses the superposed results of the former two components as thermo-mechanical boundary conditions. Using this framework, we target the prediction of metallurgical effects, such as white layers, on the workpiece on the macro scale in the near future. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

特殊工件磨削加工问题研究

对特殊工件的磨削加工过程进行抽象、建模和求解.将砂轮和底座看成刚性坐标系,将工件所在的下台、中台、上台看成可平移旋转的变换坐标系,基于工件母线方程,以砂轮和工件母线相切为紧约束,运用平面坐标变换理论设计加工方案,并对方案进行了误差分析,最后考虑砂轮的实际磨损,分别提出圆柱形和轮式砂轮修整磨削策略.     

磨削加工具有复杂母线的旋转体的微分模型

综合运用微分几何、坐标变换、分段二次Hermite插值及微分方程等数学工具,将磨削加工具有复杂母线的旋转体的问题,通过建立微分模型,然后根据求出的解,设计出了具体的加工方案.对于具有抛物线母线的工件,给出了一个在上台电机进给速度恒定的条件下,加工时间尽可能短的加工方案.对于具有一般母线的工件,利用分段二次Hermite插值,转化为抛物线的情形,也得到了很好的解决.还编写了一系列Matlab程序,作为解决过程中的产品,它们的输出可以直接用于控制磨床,加工具有任意母线的工件.此外,在使得砂轮表面的磨损尽量均匀的问题上,做了富有创造性的探索,并且给出了一个使得圆柱形砂轮磨损比较均匀的加工方案.总体而言,模型具有适用范围广、加工精度高等优点.     

Parameter study of a multi-body friction oscillator

In many technical applications sliding contacts with multiple contact points or engagements exist, like between seals and rough surfaces, between grinding wheel and workpiece, or between granular material and storage box. In a simplified way these contacts can be represented by a friction oscillator with multiple bodies. The behavior of the friction oscillator with one body is already well known. However only few studies exist on the behavior of a friction oscillator with multiple bodies. In this study especially the dynamical behavior depending on the number of bodies, the friction characteristic and the velocity of the belt has been investigated. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Model based optimization of a statistical simulation model for single diamond grinding

We present a model for simulating normal forces arising during a grinding process in cement for single diamond grinding. Assuming the diamond to have the shape of a pyramid, a very fast calculation of force and removed volume can be achieved. The basic approach is the simulation of the scratch track. Its triangle profile is determined by the shape of the diamond. The approximation of the scratch track is realized by stringing together polyhedra. Their sizes depend on both the actual cutting depth and an error implicitly describing the material brittleness. Each scratch track part can be subdivided into three three-dimensional simplices for a straightforward calculation of the removed volume. Since the scratched mineral subsoil is generally inhomogeneous, the forces at different positions of the workpiece are expected to vary. This heterogeneous nature is considered by sampling from a Gaussian random field. To achieve a realistic outcome the model parameters are adjusted applying model based optimization methods. A noisy Kriging model is chosen as surrogate to approximate the deviation between modelled and observed forces. This deviation is minimized and the results of the modelled forces and the actual forces from conducted experiments are rather similar.     

Varying Workpiece Dynamics in Milling Stability Analysis

Dynamic stability of a milling process with varying workpiece dynamics is investigated. The milling tool moves along the workpiece with a prescribed feed rate, whereby the contact point shifts. Furthermore, the workpiece dynamics is affected by material removal. The resultant varying workpiece dynamics is taken into account by parametric model order reduction including modal truncation. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A two-scale simulation method accounting for thermal effects during turning

During chip formation in turning processes, mechanical work is dissipated into thermal energy by plastic deformations and frictional processes. In case of dry cutting, the generated heat is in part removed with the chips while the rest flows into the tool and the workpiece. Within the latter, the temperature increases due to this heat flow, which in turn causes thermal expansions that increase the cutting depth and thus induce deviations from the nominal workpiece geometry. These effects are treated separately by a local model for the chip formation and a global model for the whole workpiece in order to determine the temperature distribution inside the workpiece and the dependent thermal expansion. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

圆形工件正次品检验及再加工模型

针对圆形工件合格性检验问题建立了两个优化模型,运用Matlab软件进行编程求解,确定了圆心的位置,据此判断出工件一为正品,工件二为次品.接下来为判断能否将次品经过再加工使其成为正品,建立了模型三,并指出了对工件二的简单再加工方法.     

Simulation of electrochemical machining using the boundary element method with no saturation

The simulation of electrochemical machining (ECM) is based on determining the surface shape at each point in time. The change in the shape of the surface depends on the rate of the electrochemical dissolution of the metal (conducting material), which is assumed to be proportional to the electric field strength on the boundary of the workpiece. The potential of the electric field is a harmonic function outside the two domains—the tool electrode and the workpiece. Constant potentials are specified on the boundaries of the tool electrode and the workpiece. A scheme with no saturation in which the strength of the electric field created by the potential difference on the boundary of the workpiece is proposed. The scheme converges exponentially in the number of grid elements on the workpiece boundary. Given the rate of electrochemical dissolution, the workpiece boundary, which depends on time, is found. The numerical solutions are compared with exact solutions, examples of the ECM simulation are discussed, and the results are compared with those obtained by other numerical methods and the ones obtained using ECM machines.     

Simulation and analysis of rotary forging a ring workpiece using finite element method

The methods of dealing with some key problems in analyzing a rotary forging process with a finite element method are given. The presented mechanical model of the finite element analysis is in accordance with the actual conditions of the rotary forging process. A three-dimensional rigid–plastic finite element analysis code is developed in FORTRAN language and used to analyze the rotary forging process of a ring workpiece. Velocity fields and stress–strain fields of both contact and non-contact zones of the ring workpiece in the rotary forging are obtained. The deformation mechanism and metal flow laws of the contact zone surface of the ring workpiece in the rotary forging process are revealed. The pressure distributions of the contact surface along the radial and tangential directions and effects of rotary forging parameters on deformation characteristics are given.     

Model-based parameter optimization for arc welding process simulation

This paper presents a model-based parameter optimization for simulating a metal-inert gas welding process. The computational model used in this study is based on computational fluid dynamics methods and implemented using the finite volume approach on a 3D computational domain. The wire electrode, the arc plasma and the workpiece are treated as a self-consistent system. Important welding parameters, including arc current, wire feed rate, workpiece thickness, welding speed and geometry, as well as the metal alloy types used for the wire and workpiece, were implemented as adjustable parameters. By tuning these parameters, the performance of the arc welding can be predicted, and different settings can be compared to optimize welding performance.A benchmarking study of the arc model against experimental measurements is presented to demonstrate the model's capabilities in the prediction of the weld pool changes and thermal dynamics involved in the welding process. Two numerical case studies are presented to demonstrate the use of the model-based optimization to quantify welding pool variations with the change in welding parameters. The first case study is the determination of the optimal arc current and welding speed settings for different workpiece thicknesses. The optimization process shows that the predictions are not only in agreement with established experimental welding experience on the direct relationship between workpiece thickness and arc current, but more importantly quantify this relationship for a given workpiece thickness. The second case study focuses on the welding parameters optimization for different metal alloys. The comparison suggests that the welding parameters suitable for some aluminium alloys are less likely to be successful in welding magnesium alloys. A further model validation of Mg alloy AZ31 welding shows an agreement with experimental measurements. The work presented shows the potential of model-based parameter optimization to assist process engineers in the practical improvement of the welding process.     

A desktop computer model of the arc,weld pool and workpiece in metal inert gas welding

A sophisticated computational model of metal inert gas arc welding of aluminium alloys is presented. The arc plasma, the wire electrode and the workpiece are included in the computational domain self-consistently. The flow in the arc plasma and in the weld pool are calculated in three dimensions using equations of computational fluid dynamics, modified to take into account plasma effects and coupled to electromagnetic equations. The formation of metal vapour from the wire electrode and workpiece is considered, as is the mixing of the wire electrode alloy with the workpiece alloy in the weld pool. A graphical user interface (GUI) has been developed, and the model runs on standard desktop or laptop computers.The computational model is described, and results are presented for lap-fillet weld geometry. The importance of including the arc in the computational domain is shown. The predictions of the model show good agreement with measurements of weld geometry and weld composition. The GUI is introduced, and the application of the model to predicting the thermal history of the workpiece, which is the input information that is required for predicting important weld properties such as residual stress and distortion and weld microstructure, is discussed. Initial predictions of residual stress and distortion of the workpiece are presented.     

Analysis and numerical simulation of an induction–conduction model arising in steel heat treating

The goal of steel heat treating is to create a hard enough part over certain critical surfaces or volumes of the workpiece and at the same time keeping its ductility properties all over the rest of the workpiece.     

Transient Finite Element Simulation of the Temperature Field during Cryogenic Turning of Metastable Austenitic Steel AISI 347

The process chain in manufacturing often consists of many steps. As part of current researches the possibility of combining two process steps, turning and hardening, is investigated to optimize the manufacturing time and to decrease the energy consumption of the process. For metastable austenitic steels, deformation induced hardening during turning can be used to achieve surface hardening [1] and thus to increase the wear resistance [2] as well as the fatigue strength [3], by applying high passive forces onto the workpiece. This enables an austenite-martensite phase transformation, for which it is necessary to maintain low process temperatures, typically below room temperature. Thus, cryogenic coolants are applied [4]. For a better understanding of the influence of cutting parameters on the process temperatures and thus martensite formation, knowledge of the exact temperature distribution in the workpiece and in the contact zone between workpiece and tool is essential. Since the experimental determination of the temperature field is hardly possible, an inverse determination of the process temperatures via transient finite element simulation is performed. The present finite element approach only takes thermal loads into account. The simulations are performed in the finite element program FEAP (Finite Element Analysis Program) with an Eulerian mesh, which requires special consideration of the rigid body rotation of the workpiece. In order to prevent unphysical oscillations in the solution, introduced by the convective time derivative, a streamline upwind / Petrov–Galerkin stabilization scheme is utilized. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On nonlinear cutting response and tool chatter in turning operation

Tool chatter in turning process is addressed with a new perspective. Turning dynamics is investigated using a 3D model that allows for simultaneous workpiece-tool deflections in response to the exertion of nonlinear regenerative force. The workpiece is modeled as a system of three rotors, namely, unmachined, being machined and machined, connected by a flexible shaft. Such a configuration enables the workpiece motion relative to the tool and tool motion relative to the machining surface to be three-dimensionally established as functions of spindle speed, instantaneous depth-of-cut, material removal rate and whirling. The equations of motion for the model are coupled through the nonlinear cutting force. The model is explored along with its 1D counterpart, which considers only tool motions and disregards workpiece vibrations. Different stages of stability for the workpiece and the tool subject to the same cutting conditions are studied. Numerical simulations reveal diverse, oftentimes inconsistent, tool behaviors described by the two models. Most notably, observations made with regard to the inconsistency in describing machining stability limits raise the concern for using 1D models to obtain stability charts.     

Spindle Speed Variation for the Suppression of Regenerative Chatter

Summary. A phenomenon commonly encountered during machining operations is chatter. It manifests itself as a vibration between workpiece and cutting tool, leading to poor dimensional accuracy and surface finish of the workpiece and to premature failure of the cutting tool. A chatter suppression method that has received attention in recent years is the spindle speed variation method, whereby greater widths of cut are achieved by modulating the spindle speed continuously. By adapting existing mathematical techniques, a perturbative method is developed in this paper to obtain finite-dimensional equations in order to systematically study the mechanism of spindle speed variation for chatter suppression. The results indicate both modest increase of stability and complex nonlinear dynamics close to the new stability boundary. The method developed in this paper can readily be applied to any other system with time-delay characteristics.     

Dynamic response of a rotating ball screw subject to a moving regenerative force in grinding

This paper investigates the dynamic response of a rotating ball screw subjected to a moving regenerative force. The rotating ball screw is modeled as a rotating Timoshenko shaft with simply supports. The moving regenerative force describes the nonlinear interactions including the effects of wheel wear, time-delay, and the possibility of contact loss between the grinding wheel head and screw. The assumed mode method together with Runge–Kutta method is employed to analyze the system dynamic response. The total grinding depth is suggested to divide into several passes from rough grinding to fine grinding for obtaining fine surface. The effect of parameters such as the depth of cut and the rotational speeds of grinding wheel and screw are discussed for each pass. The numerical results show that the critical depth of cut depends on the rotational speeds of screw and grinding wheel. If the more the depth of cut is smaller than the critical depth of cut, the earlier the chatter occurs and the faster the vibration grows.     

On a thermomechanical milling model

This paper deals with a new mathematical model to characterize the interaction between machine and workpiece in a milling process. The model consists of a harmonic oscillator equation for the dynamics of the cutter and a linear thermoelastic workpiece model. The coupling through the cutting force adds delay terms and further nonlinear effects. After a short derivation of the governing equations it is shown that the complete system admits a unique weak solution. A numerical solution strategy is outlined and complemented by numerical simulations of stable and unstable cutting conditions.