基于铣削力/力矩模型的铣削表面几何误差模型

在端铣加工过程中 ,影响铣削表面的因素包括铣削力 /铣削扭矩、机床和工件的性质等等。通过研究这些因素 ,基于铣削力 /铣削扭矩和瞬时未变形切屑厚度的关系 ,建立了一个考虑了铣削力 /铣削扭矩的解析模型 ,用来预报在端铣情况下工件的表面几何误差。与数值模型相比 ,解析模型能够更好地来研究工艺参数和工件质量、产品设计、工艺规划和控制之间的关系。并且可以对铣削工艺的设计和优化提供帮助。一系列的试验验证了模型的有效性 ,并且通过仿真结果得到一些有用的结论     

A SIMPLIFIED CUTTING FORCE MODEL FOR LIGHT-CUT BALL-END MILLING APPLICATIONS

In light-cut milling operations, specific correlations have been identified empirically between the maximum cutting force on a cutter and its associated cutting parameters, and a series of ball-end milling tests for P20 tool steel has been conducted to establish the nature of these correlations. The experimental results indicate that the maximum cutting force on a cutter can be expressed as a logarithmic function of the associated cutting parameters. This paper describes the structure and testing of a simplified cutting force model for planar milling based on these results.     

CORRELATION-BASED ESTIMATION OF CUTTING FORCE COEFFICIENTS FOR BALL-END MILLING

This article presents a methodology to estimate cutting force coefficients based on the least squares approximation using correlation factor between the estimated and measured cutting forces in order to determine the corresponding tool angular position. This method can be applied on measured cutting force data over any small interval of time that need not contain information of the time instant when the cutting tool enters the workpiece, which has been the main requirement in the conventional method. This allows a quick estimation of the cutting force coefficients regardless of the chosen cutting conditions and tool-workpiece material, which is often the case in industrial machining processes. This proposed method has been validated by comparison of cutting force coefficients obtained using conventional estimation technique for a slot ball-end milling test. Besides being useful for predictive evaluation of forces, such estimation of cutting force coefficients of the cutting force model can be useful for understanding variations in cutting process over the tool life and can assist in online monitoring and process optimization.     

难加工材料型腔圆角数控铣削的切削力预测

在难加工材料型腔的数控铣削过程中,圆角区域的加工阶段,径向切削深度和真实进给量的变化很大程度上影响切削力,造成扎刀、撞刀、振动等很多的问题, 影响工件的加工准确度和刀具的寿命,甚至使得加工无法顺利进行.文中建立端铣刀和圆角轮廓几何关系的数学模型,提出普遍适用于矩形与梯形型腔圆角的切削力预测方法.最后,对型腔圆角切削力的变化规律预测方法进行验证.     

基于斜角切削理论的立铣切削力预测研究

为了预测立铣加工的切削力,把立铣刀的切削刃离散为一系列无限小的斜角切削单元。对于每个微元斜角切削单元,应用斜角切削理论来建立切屑通过时剪切区的应力、应变、应变率和温度的控制方程。采用数值方法根据控制方程计算出流动应力,并根据斜角切削和铣削之间的力变换关系,把流动应力转化为铣削力。最后,对45钢进行了多组不同切削参数的立铣实验,仿真和实验的对比结果验证了所提出模型的有效性。该方法同样可以用于其他加工方式（如车削和钻削）的建模。     

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。     

STABILITY LOBES PREDICTION FOR CORNER RADIUS END MILL USING NONLINEAR CUTTING FORCE COEFFICIENTS

There are a vast number of different types of end mill tools used in the manufacturing industry, each type with a unique shape. These tool shapes have a direct influence on the cutting force it generates during machining. This article presents a more accurate approach to predicting the stability margin in machining by considering the cutting force coefficients and axial immersion angle as variables along the axial depth of cut. A numerical approach to obtaining a converged solution to the stability model is presented. The results obtained are validated using experimental results and a very good agreement is seen.     

整体式立铣刀三维建模及切削力预测研究

针对立铣刀三维建模困难及铣削时切削力难以预测等问题,根据微分几何原理建立立铣刀数学模型。基于数学模型将铣刀切削刃离散成斜角切削单元,根据剪切区应力、应变和温度控制方程,由材料本构方程计算流动应力,通过坐标变换关系建立铣削力预测模型。得到的铣削力与已有铣削试验数据一致,验证了铣削力模型的有效性。     

PRECISION CUTTING OF MOLDING DIE USING SQUARE END MILL

The precision cutting of a molding die is realized using a square end mill on a 5-axis control machine. In this study, first the tool setting errors are analyzed and the compensation method of the errors is proposed. The effectiveness of compensation in precision cutting is confirmed. Next, the form accuracy of the spiral tool pass is compared with contour one in precision cutting of a spherical surface. Finally, the molding die with spherical surface is manufactured using a square end mill made out of single-crystal diamond based on the results of the compensation of the errors and the comparison of the two tool passes, and the form accuracy and surface roughness of the molding die are measured.     

HIGH FREQUENCY MEASUREMENTS OF CUTTING FORCES IN MILLING BY INVERSE FILTERING

Accurate estimates of cutting forces are important in the evaluation of different cutting tool geometries and concepts. However, dynamic influences from the measurement system affect the result, which can make the obtained cutting force data erroneous and misleading. This article presents a method to obtain an inverse filter which compensates for the dynamic influences of the measurement system. Using this approach, unwanted dynamic effects of the measurement system can be counteracted, making it possible to retain information related to the cutting forces contained in the high frequency region. The advantage of the proposed method is illustrated by comparing simulated, inverse- and low-pass filtered forces to unfiltered forces under different cutting conditions. The results show that inverse filtering increases the usable frequency range of the force dynamometer and thereby provide more reliable results compared to both low-pass and unfiltered forces.     

基于斜角切削的曲线端铣切削力建模

切削力预测是制定与优化加工工艺的重要环节。针对曲线端铣加工过程,提出一种基于斜角切削的切削力建模方法。将刀具沿轴向微分,以曲线微分几何计算微元刃上的工作基面。在微元刃的工作法平面参考系中,应用最小能量原理,构建微元刃中力矢量、速度矢量、流屑角、法向摩擦角、法向剪切角及剪应力等切削参数之间的约束。以单齿直线铣削试验对切削参数进行标定,其中法向摩擦角、法向剪切角及剪应力等可表示为瞬时未变形切屑厚度的函数。选取高强度钢PCrNi3MoVA试件,分别进行圆弧和Bézier曲线端铣加工试验。试验结果表明,曲线端铣时切削力的变化与瞬时进给方向和曲线曲率相关。切削力预测值的幅值大小和变化趋势与试验值一致,验证了该切削力建模方法的有效性。     

EQUIVALENT NORMAL CURVATURE APPROACH MILLING MODEL OF MACHINING FREEFORM SURFACES

A new milling methodology with the equivalent normal curvature milling model machining freeform surfaces is proposed based on the normal curvature theorems on differential geometry. Moreover, a specialized whirlwind milling tool and a 5-axis CNC horizontal milling machine are introduced. This new milling model can efficiently enlarge the material removal volume at the tip of the whirlwind milling tool and improve the producing capacity. The machining strategy of this model is to regulate the orientation of the whirlwind milling tool relatively to the principal directions of the workpiece surface at the point of contact, so as to create a full match with collision avoidance between the workpiece surface and the symmetric rotational surface of the milling tool. The practical results show that this new milling model is an effective method in machining complex three- dimensional surfaces. This model has a good improvement on finishing machining time and scallop height in machining the freeform surfaces over other milling processes. Some actual examples for manufacturing the freeform surfaces with this new model are given.     

AN 'EFFECTIVE CUTTING TOOL THERMAL CONDUCTIVITY' BASED MODEL FOR TOOL-CHIP CONTACT IN MACHINING WITH MULTI-LAYER COATED CUTTING TOOLS

This paper presents a new modeling approach, based on Oxley's predictive model, for predicting the tool-chip contact in 2-D machining of plain carbon steels with advanced, multi-layer coated cutting tools. Oxley's original predictive model is capable of predicting machining parameters for a wide variety of plain carbon steels, however, the tool material properties and their effects are neglected in the analysis. In the present work, the effect of the tool material, more particularly, the effect of multiple coating layers and the individual coating thicknesses on the tool-chip contact length in orthogonal machining is incorporated. The results from the model predict the tool-chip contact length with respect to major cutting parameters such as feed and rake angle, work material parameters such as the carbon content in the steel, and varying thicknesses and combinations of coating layers. This model enables more precise cutting tool selection by predicting the relative tribological impact (in terms of tool-chip contact length) for a variety of multi-layer coated tools.     

MATHEMATICAL MODEL OF MILLING TEMPERATURE AND TEMPERATURE FIELD ANALYSIS FOR THREE-DIMEN-SIONAL COMPLEX GROOVE MILLING INSERT

The mathematical mode1 on the temperature of the waved-edge is constructed accordingto Jaeger's theory of moving solid and based on the used temperature model of the fiat insert. It ispossible to forecast the milling temperature through programming. The comParable experimentshave been done between the two new three-dimension groove inserts (waved-edge insert, great edgeinsert) and flat fake insert. The theoretic forecast is in good agreement with the experimental result.     

奇点分析单元法在断裂问题中的应用

将裂纹应力计算问题导向哈密顿体系，利用分离变量法及本征函数向量展开等方法，推导出裂纹尖端的尖力奇性解的计算公式。结合变分原理，提出一种解决应力奇性计算的奇点分析单元。将此分析单元与有限元法相结合，可以进行某些断裂力学或复合材料等应力奇性问题的计算及分析。数值计算结果表明，该方法具有精度同，使用十分方便、灵活等优点，是哈密顿体系优越性的一次具体体现。     

不等距立铣刀切削力模型的建立及试验分析

在特定铣削条件下,建立了多齿不等距铣刀的切削力模型,并通过正交试验验证所建的切削力模型;通过分析不同的切削参数对切削力系数的影响,综合确定了在小切削宽度铣削过程中合理选用切削参数的基本原则。     

Application of a variable flow stress machining theory to helical end milling

A methodology of modeling chip geometry of flat helical end milling based on a variable flow stress machining theory is presented in this article. The proposed model is concerned with the variation of the width of cut thickness. The nonuniform chip thickness geometry is discretized into several segments based on the radial depth of cut. The chip geometry for each segment is considered to be constant by taking the average value of the maximum and minimum chip thickness. The maximum chip thickness for each chip segment is computed based on the current width of cut, feed per tooth and the cutter diameter. The subsequent radial depth of cut is subtracted from the discretized size of the width of cut to obtain the minimum chip thicknesses. The forces for each segment are summed to obtain the total forces acting on the system of the workpiece and the tool. The cutting forces can be predicted from input data of work material properties, cutter configuration and the cutting conditions used. The validation of the proposed model is achieved by correlating experimental results with the predicted results obtained.     

Analysis of cutting force coefficients in high-speed ball end milling at varying rotational speeds

In high-speed ball end milling, cutting forces influence machinability, dimensional accuracy, tool failure, tool deflection, machine tool chatter, vibration, etc. Thus, an accurate prediction of cutting forces before actual machining is essential for a good insight into the process to produce good quality machined parts. In this article, an attempt has been made to determine specific cutting force coefficients in ball end milling based on a linear mechanistic model at a higher range of rotational speeds. The force coefficients have been determined based on average cutting force. Cutting force in one revolution of the cutter was recorded to avoid the cutter run-out condition (radial). Milling experiments have been conducted on aluminum alloy of grade Al2014-T6 at different spindle speeds and feeds. Thus, the dependence of specific cutting force coefficients on cutting speeds has been studied and analyzed. It is found that specific cutting force coefficients change with change in rotational speed while keeping other cutting parameters unchanged. Hence, simulated cutting forces at higher range of rotational speed might have considerable errors if specific cutting force coefficients evaluated at lower rotational speed are used. The specific cutting force coefficients obtained analytically have been validated through experiments.     

INVESTIGATION OF SIZE-EFFECTS IN MACHINING WITH GEOMETRICALLY DEFINED CUTTING EDGES

The miniaturization of cutting processes shows process specific size-effects like the exponential increase of the specific cutting force k _c with decreasing depth of cut h. Experiments were carried out in an orthogonal turning process. The influence of different process parameters on the results was investigated separately to identify process specific size-effects. Two materials were studied: a normalized steel AISI 1045 and an annealed AISI O2. To complement the experiments, parameter variations were performed in two-dimensional, thermo-mechanically coupled finite element simulations using a rate-dependent material model and analyzed by similarity mechanics. The influence of rounded cutting-edges on the chip formation process and the plastic deformation of the generated surface were determined numerically. The complex physical effects in micro-cutting were analyzed successfully by finite element simulations and compared to experiments.     

INVESTIGATION OF SIZE-EFFECTS IN MACHINING WITH GEOMETRICALLY DEFINED CUTTING EDGES

The miniaturization of cutting processes shows process specific size-effects like the exponential increase of the specific cutting force k_c with decreasing depth of cut h. Experiments were carried out in an orthogonal turning process. The influence of different process parameters on the results was investigated separately to identify process specific size-effects. Two materials were studied: a normalized steel AISI 1045 and an annealed AISI O2. To complement the experiments, parameter variations were performed in two-dimensional, thermo-mechanically coupled finite element simulations using a rate-dependent material model and analyzed by similarity mechanics. The influence of rounded cutting-edges on the chip formation process and the plastic deformation of the generated surface were determined numerically. The complex physical effects in micro-cutting were analyzed successfully by finite element simulations and compared to experiments.