An Enhanced Force Model for Sculptured Surface Machining

The ball-end milling process is used extensively in machining of sculpture surfaces in automotive, die/mold, and aerospace industries. In planning machining operations, the process planner has to be conservative when selecting machining conditions with respect to metal removal rate in order to avoid cutter chipping and breakage, or over-cut due to excessive cutter deflection. These problems are particularly important for machining of sculptured surfaces where axial and radial depths of cut are abruptly changing. This article presents a mathematical model that is developed to predict the cutting forces during ball-end milling of sculpture surfaces. The model has the ability to calculate the workpiece/cutter intersection domain automatically for a given cutter path, cutter, and workpiece geometries. In addition to predicting the cutting forces, the model determines the surface topography that can be visualized in solid form. Extensive experiments are performed to validate the theoretical model with measured forces. For complex part geometries, the mathematical model predictions were compared with experimental measurements.     

凸曲面拼接模具球头铣刀的瞬时铣削力预测

在曲面模具拼接区域球头铣刀铣削过程中,刀具载荷变化大,瞬态铣削力有突变现象,影响模具拼接区域的加工精度和表面质量。为了预测拼接区域球头铣刀的瞬态铣削力,首先,建立考虑冲击振动的球头铣刀三维次摆线轨迹方程,得到瞬时未变形切屑厚度模型;然后,基于铣削微元的思想,建立凸曲面双硬度拼接模具球头铣刀的瞬态铣削力模型,该模型能够综合考虑拼接区冲击振动、硬度变化、刀具工件切触角度变化对瞬态铣削力的影响;最后,进行凸曲面拼接区域球头铣刀铣削加工实验。实验结果表明,预报的瞬态铣削力和实验测量结果在幅值上和变化趋势上具有一致性,在平稳切削时最大铣削力预测误差值基本在15%以内,验证了该模型能有效地预报凸曲面模具拼接区域球头铣刀的瞬态铣削力。     

An Enhanced Force Model for Sculptured Surface Machining

Abstract

The ball-end milling process is used extensively in machining of sculpture surfaces in automotive, die/mold, and aerospace industries. In planning machining operations, the process planner has to be conservative when selecting machining conditions with respect to metal removal rate in order to avoid cutter chipping and breakage, or over-cut due to excessive cutter deflection. These problems are particularly important for machining of sculptured surfaces where axial and radial depths of cut are abruptly changing. This article presents a mathematical model that is developed to predict the cutting forces during ball-end milling of sculpture surfaces. The model has the ability to calculate the workpiece/cutter intersection domain automatically for a given cutter path, cutter, and workpiece geometries. In addition to predicting the cutting forces, the model determines the surface topography that can be visualized in solid form. Extensive experiments are performed to validate the theoretical model with measured forces. For complex part geometries, the mathematical model predictions were compared with experimental measurements.     

基于Z-MAP方法的球头铣刀铣削力的建模

瞬时刚性切削力的建模是铣削加工物理仿真的基础,然而,球头铣刀的刀齿形状复杂,加工过程中姿态多变,瞬时刚性铣削力的建模难度较大。在考虑刀具姿态调整的情况下,通过齐次坐标变换建立了刀齿的运动轨迹,提出了一种识别刀具和工件瞬时接触区的改进Z-MAP算法,通过计算当前刀齿的参考线与工件的边界面或刀齿扫掠面的交点求出瞬时未变形切屑厚度,并采用非线性回归的方法辨识了切削力系数,在此基础上使用微元积分法建立了瞬时切削力的计算模型。为了验证仿真模型的可靠性,分别进行了垂直加工和倾斜加工试验,试验和仿真结果具有较高的一致性,表明该建模仿真方法是有效的,可以为实际加工中参数的选择和优化提供理论依据。     

Extraction of 5-axis milling conditions from CAM data for process simulation

5-axis milling is widely used in machining of parts with free-form surfaces and complex geometries. Although in general 5-axis milling increases the process capability, it also brings additional challenges due to complex process geometry and mechanics. In milling, cutting forces, tool deflections, and chatter vibrations may reduce part quality and productivity. By use of process simulations, the undesired results can be identified and overcome, and part quality and productivity can be increased. However, machining conditions and geometry, especially the tool–work engagement limits, are needed in process models which are used in these simulations. Due to the complexity of the process geometry and continuous variation of tool–work engagement, this information is not readily available for a complete 5-axis milling cycle. In this study, an analytical method is presented for the identification of these parameters from computer-aided manufacturing data. In this procedure, depths of cut, lead, and tilt angles, which determine the tool–workpiece engagement boundaries, are directly obtained the cutter location file analytically in a very fast manner. The proposed simulation approach is demonstrated on machining of parts with relatively complex geometries.     

法向圆弧锥齿轮数控加工研究

研究了法向圆弧锥齿轮的数控加工原理与技术,设计了成形铣刀,给出了刀具与工件的接触条件以及刀具与工件之间的相对运动。斜航式法向圆弧锥齿轮数控加工实验表明,该锥齿轮数控加工原理正确,工艺简单,且加工精度较高。     

Error Compensation of Thin Plate-shape Part with Prebending Method in Face Milling

Low weight and good toughness thin plate parts are widely used in modern industry, but its flexibility seriously impacts the machinability. Plenty of studies focus on the influence of machine tool and cutting tool on the machining errors. However, few researches focus on compensating machining errors through the fixture. In order to improve the machining accuracy of thin plate-shape part in face milling, this paper presents a novel method for compensating the surface errors by prebending the workpiece during the milling process. First, a machining error prediction model using finite element method is formulated, which simplifies the contacts between the workpiece and fixture with spring constraints. Milling forces calculated by the micro-unit cutting force model are loaded on the error prediction model to predict the machining error. The error prediction results are substituted into the given formulas to obtain the prebending clamping forces and clamping positions. Consequently, the workpiece is prebent in terms of the calculated clamping forces and positions during the face milling operation to reduce the machining error. Finally, simulation and experimental tests are carried out to validate the correctness and efficiency of the proposed error compensation method. The experimental measured flatness results show that the flatness improves by approximately 30 percent through this error compensation method. The proposed method not only predicts the machining errors in face milling thin plate-shape parts but also reduces the machining errors by taking full advantage of the workpiece prebending caused by fixture, meanwhile, it provides a novel idea and theoretical basis for reducing milling errors and improving the milling accuracy.     

薄壁工件铣削加工变形的预测

以铣削力模型和ABAQUS有限元分析软件为基础,采用考虑了刀具/工件变形耦合效应、材料去除效应以及工件变形引起铣削力加载点变化等因素的仿真预测方法,建立了薄壁工件加工变形预测的有限元分析模型,并对航空钛合金框体工件进行了铣削加工变形预测及试验验证,仿真结果与试验数据吻合较好。     

铣刀盘激光熔覆修复过程的温度场与应力场有限元仿真

为了判定铣刀盘激光熔覆修复过程是否会发生热致应力开裂的问题,对铣刀盘激光熔覆修复过程的三维温度场和应力场进行模拟。根据铣刀盘损伤特征建立铣刀盘的三维修复模型,利用结构化网格划分方法构建修复后的铣刀盘分析模型及边界,将单元生死技术和ANSYS APDL自编程序相结合,重现铣刀盘激光熔覆修复成形过程。研究表明,大温度梯度和几何约束限制使刀盘修复部位产生高的残余应力,最大值为384 MPa。实际应用表明,铣刀盘修复后未产生开裂缺陷,修复效果良好,验证了仿真的正确性。     

Cutter workpiece engagement region and surface topography prediction in five-axis ball-end milling

Based on the machining tool path and the true trajectory equation of the cutting edge relative to the workpiece, the engagement region between the cutter and workpiece is analyzed and a new model is developed for the numerical simulation of the machined surface topography in a multiaxis ball-end milling process. The influence of machining parameters such as the feed per tooth, the radial depth of cut, the angle orientation tool, the cutter runout, and the tool deflection upon the topography are taken into account in the model. Based on the cutter workpiece engagement, the cutting force model is established. The tool deflections are extracted and used in the surface topography model for simulation. The predicted force profiles were compared to the measured ones. A reasonable agreement between the experimental and the predicted results was found.     

An Integrated Model of a Fixture-Workpiece System for Surface Quality Prediction

Surface quality is a major factor affecting the performance of a component. The machined surface quality is strongly influenced by the external loads during the fixturing and machining processes. In machining process development, it is highly desirable to predict the quality of a machined surface. For this purpose, an integrated finite element analysis (FEA) model of the entire fixture–workpiece system is developed to investigate the influence of clamping preload and machining force on the surface quality of the machined workpiece. The effects of fixture and machine table compliance (from experimental data), and the workpiece and its locators/clamps contact interaction, and forced vibration, on the machined surface quality are taken into account. This simulation model provides a better understanding of the causes of surface error and a more realistic prediction of the machined surface quality. The deck face of a V-type engine block subjected to fixture clamping and a face milling operation is given as an example. A comparison between the simulation result and experimental data shows a reasonable agreement.     

基于有限元仿真的拼接模具铣削用刀具优化

对ABAQUS软件进行了二次开发,以实现拼接模具铣削过程仿真前处理的快速建模。对铣削力、应力和刀具温度进行仿真,并与铣削实验结果对比,验证了仿真模型的准确性。对不同前角、后角、螺旋角及刃口半径的球头铣刀铣削拼接模具的过程进行模拟仿真,采用遗传算法优化铣刀结构,将优化后的结构参数与传统结构参数代入刀具磨损、工件表面质量的对比实验,从而验证了优化的有效性。研究表明,对仿真前处理进行快速建模的二次开发运行成功,模拟结果准确。研究结果为降低制造成本、提高铣刀寿命和工件表面质量提供了理论参考。     

Redesigned Surface Based Machining Strategy and Method in Peripheral Milling of Thin-walled Parts

Currently, simultaneously ensuring the machining accuracy and efficiency of thin-walled structures especially high performance parts still remains a challenge. Existing compensating methods are mainly focusing on 3-aixs machining, which sometimes only take one given point as the compensative point at each given cutter location. This paper presents a redesigned surface based machining strategy for peripheral milling of thin-walled parts. Based on an improved cutting force/heat model and finite element method(FEM) simulation environment, a deflection error prediction model, which takes sequence of cutter contact lines as compensation targets, is established. And an iterative algorithm is presented to determine feasible cutter axis positions. The final redesigned surface is subsequently generated by skinning all discrete cutter axis vectors after compensating by using the proposed algorithm. The proposed machining strategy incorporates the thermo-mechanical coupled effect in deflection prediction, and is also validated with flank milling experiment by using five-axis machine tool. At the same time, the deformation error is detected by using three-coordinate measuring machine. Error prediction values and experimental results indicate that they have a good consistency and the proposed approach is able to significantly reduce the dimension error under the same machining conditions compared with conventional methods. The proposed machining strategy has potential in high-efficiency precision machining of thin-walled parts.     

球头铣刀骨铣削力有限元建模与试验验证

在骨科手术中,铣削力对骨裂纹和加工表面质量影响较大。由于临床球形骨铣刀结构复杂,目前尚无有效的理论模型预测切削力。通过引入三维有限元模型模拟球形铣刀加工骨材料过程,评估不同加工参数下的铣削力值。搭建骨铣削试验平台模拟临床操作中的铣削过程,并利用采集到的加工信号分析铣削力。通过试验结果与仿真结果的对比,验证了有限元仿真模型的合理性。该骨铣削有限元模型能够满足不同加工参数下铣削力预测精度的要求,方便指导医生根据不同要求选择合适的加工参数。     

Surface topography analysis in high speed finish milling inclined hardened steel

The surface texture of a milled surface is an inherently important process response in finish milling. It is one of the most commonly used criteria to determine the machinability of a particular workpiece material. However, literature survey on the study of the surface topography analysis relating to the cutter path orientations when high speed finish inclined milling is scant. Previous works were either involved in conventional milling of easy-to-cut workpiece materials or machining at different workpiece inclination angles. Furthermore, none of the previous work has detailed the true surface topography of the machined surface with regards to the cutter condition. Instead, the works provided quantitative values in terms of the Ra value. This article is concerned with evaluating cutter path orientations on an inclined workpiece angle of 75° to simulate finish milling of free form moulds and dies. Surface topography effects are assessed with regards to different cutter path orientations on its surface. The aims of this study are to provide an in-depth understanding on the surface texture produced by various cutter path orientations when high speed finish inclined milling hardened steel at a workpiece inclination angle of 75° using surface topography analysis and determine the best cutter path orientation with respect to the best surface texture achieved. 3D topography maps together with 2D surface profiles are used to assess the experimental results. The conclusion is that milling in a single direction vertical upward orientation gave the best workpiece surface texture.     

基于正交切削模拟的零件铣削加工变形预测研究

提出了基于正交切削模拟的零件铣削加工变形的预测方法,建立了三维铣削加工的有限元模型。基于正交切削加工模拟结果,利用铣削温度、铣削力的分析模型求解了三维铣削加工的瞬态温度和瞬态切削力,并将其作为动态载荷应用于三维切削加工的有限元模型,模拟了零件的三维铣削加工过程,预测了零件的变形。通过模拟结果与现场加工情况对比,证明该预测方法是行之有效的。     

Theoretical modelling of cutting forces in helical end milling with cutter runout

A theoretical cutting force model for helical end milling with cutter runout is developed using a predictive machining theory, which predicts cutting forces from the input data of workpiece material properties, tool geometry and cutting conditions. In the model, a helical end milling cutter is discretized into a number of slices along the cutter axis to account for the helix angle effect. The cutting action for a tooth segment in the first slice is modelled as oblique cutting with end cutting edge effect and tool nose radius effect, whereas the cutting actions of other slices are modelled as oblique cutting without end cutting edge effect and tool nose radius effect. The influence of cutter runout on chip load is considered based on the true tooth trajectories. The total cutting force is the sum of the forces at all the cutting slices of the cutter. The model is verified with experimental milling tests.     

Multidisciplinary design optimization of a milling cutter for high-speed milling of stainless steel

The milling cutter’s fracture strength is more important than its chemical stability and thermal conductivity in high-speed milling. The multidisciplinary design optimization (MDO) method is employed to optimize the fracture-resistant performance of a milling cutter in this work. An experimental study on high-speed milling of the martensitic stainless steel 0Cr13Ni4Mo is conducted. The cutting forces and cutting temperature in the milling process are measured to provide initial data for the structural optimization of the milling cutter. The mathematical models of cutting force and cutting temperature are studied. Considering that the induced stress in the milling cutter is generated by thermomechanical coupling, the thermoelastic–plastic governing equation in the milling process is introduced in this work. The sensitivity of the structural parameters to the maximum equivalent stress of the milling cutter is calculated, and the structural parameters that have the greatest effects on the maximum equivalent stress are determined as design variables for the cutters’ optimization. The MDO procedure for the cutter’s optimization consists of updating of solid model, finite element analysis of thermomechanical coupling, postprocessing, and optimization algorithm. The MDO results show that the optimized milling cutter has a better fracture-resistant performance than the initial one. The maximum deformation, overall equivalent stress, and deformation are decreased.     

Swept surface-based approach to simulating surface topography in ball-end CNC milling

The parts, in automotive, aerospace, die/mold industry, which have extremely high demands on the quality and integrity of the surface, are usually milled by CNC machine tools. In order to obtain the desirable surface quality, it is an effective way to choose the appropriate cutting parameters before machining by simulating the surface topography formed in the milling process. To do so, this paper develops a model based on the swept surface of the cutting edge and N-buffer model for predicting the surface topography and studies the effect of various cutting parameters. In this developed model, the mathematical equation of the cutting edge is first given, and then based on the relative motion between the cutter and the workpiece, the swept surface of the cutting edge along the tool path is accurately analyzed and modeled from the perspective of kinematics, which is used to describe realistically the cutting interaction between the cutter and the workpiece. Subsequently, the milling process is simulated by an improved N-buffer model by means of the proposed accurate interpolation method for calculating the cusp height. This procedure presents the advantage of not requiring any numerical iteration or approximation to gain the cusp height of any point on workpiece. On basis of the model, the effect of the cutting parameters such as spindle speed, feedrate, inclination angle, path interval, and cutter runout is investigated. Finally, the real machining experiments are performed and compared with the predicted results. The simulated surface topography shows a good agreement with the experimental one. This demonstrates that the developed model can predict accurately the surface topography and also provide the great potential for the surface quality control and the cutting parameter selection in actual production.     

浅谈数控铣削中刀具半径补偿的功能及应用

通过分析数控铣削加工中合理建立和灵活运用刀具半径补偿对零件进行编程与加工的过程,说明可以根据工件轮廓尺寸编制加工程序,以及预先存放在内存中的刀具中心偏移量,系统能自动计算刀具中心轨迹,并控制刀具进行加工;在加工过程中,只需根据工件坐标系的位置进行对刀,便可使用同一程序而对零件实现粗、精加工,以简化编程,并提高加工品质。