Prediction of dynamic cutting force and regenerative chatter stability in inserted cutters milling

Currently, the modeling of cutting process mainly focuses on two aspects: one is the setup of the universal cutting force model that can be adapted to a broader cutting condition; the other is the setup of the exact cutting force model that can accurately reflect a true cutting process. However, there is little research on the prediction of chatter stablity in milling. Based on the generalized mathematical model of inserted cutters introduced by ENGIN, an improved geometrical, mechanical and dynamic model for the vast variety of inserted cutters widely used in engineering applications is presented, in which the average directional cutting force coefficients are obtained by means of a numerical approach, thus leading to an analytical determination of stability lobes diagram (SLD) on the axial depth of cut. A new kind of SLD on the radial depth of cut is also created to satisfy the special requirement of inserted cutter milling. The corresponding algorithms used for predicting cutting forces, vibrations, dimensional surface finish and stability lobes in inserted cutter milling under different cutting conditions are put forward. Thereafter, a dynamic simulation module of inserted cutter milling is implemented by using hybrid program of Matlab with Visual Basic. Verification tests are conducted on a vertical machine center for Aluminum alloy LC4 by using two different types of inserted cutters, and the effectiveness of the model and the algorithm is verified by the good agreement of simulation result with that of cutting tests under different cutting conditions. The proposed model can predict the cutting process accurately under a variety of cutting conditions, and a high efficient and chatter-free milling operation can be achieved by a cutting condition optimization in industry applications.     

球头铣刀切削力计算机预报模型的数值仿真

借助建立的铣刀切削力、扭矩和切削功率的计算机预报模型 ,对平前刀面球头铣刀的切削性能进行了数值仿真研究 ;通过分析各种切削参数对切削性能的影响规律 ,获得了不同切削条件下球头铣刀切削力和扭矩的特征和变化趋势     

一种机夹刀片式型线铲刀的设计与研究

为降低加工玉米铣刀波刃形型线铲刀工具费用,研制了机夹刀片式型线铲刀,采用机夹刀片结构型式,刀体采用弯头型式,不仅节约了该刀具费用,而且还大大减小了切削中的振动,改善了加工效果.     

Dynamic Force Modelling for a Ball-End Milling Cutter Based on the Merchant Oblique Cutting Theory

A new dynamic force model for a ball-end milling cutter is presented in this paper. Based on the principle of the power remaining constant in cuts, the Merchant oblique cutting theory has been successfully used for the differential cutting edge segment of a ball-end milling cutter. A concise method for characterising the relationship of the complex geometry of a ball-end milling cutter and the milling process variables is determined, so that the force coefficients can be decomposed. The geometric property of a ball-end milling cutter and the dynamics of the milling process are integrated into the general model to eliminate the need for the experimental calibration of each cutter geometry and milling process variable. The milling experiments prove that this model can predict accurately the cutting forces in three Cartesian directions.     

异形PDC齿切削破岩提速机理研究

在室内切削实验基础上基于有限元二次开发建立了异形齿切削及全钻头破碎非均质花岗岩的三维数值仿真模型,研究了12种形状聚晶金刚石复合片(PDC)齿切削非均质岩石过程中的切向力、法向力、岩屑、破岩比功,并研究了齿形对全尺寸钻头破岩效率的影响。研究结果表明：锥形齿的切向力最小,破岩比功最高,对应的锥形齿钻头的进尺也最小;三平面齿的法向力和切向力均为最大;破岩比功最低的齿为双曲面齿;进尺最大的全钻头齿形为更易吃入岩石的鞍形齿、双曲面齿以及斧形齿。     

硬质合金倒角铣刀的设计与优化

针对大型电站设备制造中难加工材料及复杂零件加工过程中刀具破损严重的问题，设计了双层齿铣刀、直齿铣刀和斜齿铣刀三种刃形的倒角铣刀，并利用l-deas软件进行了三维实体造型，采用三种齿形铣刀进行了铣削试验研究。在大量实验数据的基础上，对三种齿形铣刀在铣削力上进行了对比评判，优化出使用效果最佳的铣刀为双层齿倒     

确定铣削力模型中刀具偏心参数的一种算法

对数控加工中球头铣刀铣削力建模时刀具偏心参数的确定进行了研究。在铣削力模型的建立中考虑了刀具偏心的影响,推导出刀具偏心参数的表达式,考虑到刀具单刃切削条件,提出了刀具偏心参数的确定算法。在通过铣削力试验数据计算铣削力系数的过程中,采用上述算法确定了刀具的偏心参数,用于铣削力的仿真预测中,仿真结果和铣削力试验的结果表明,算法效果良好。     

THE GEOMETRY, SPECIFICATION AND PREDICTIVE FORCE MODELS FOR PLANE FACED BALL-END MILLING CUTTERS AND OPERATIONS

In this paper the geometry and specification of ball-end milling cutters are studied and discussed followed by an outline of the development of computer-aided predictive models for the three force components, torque and power in plane faced ball-end milling operations, based on the 'Unified-Generalised Mechanics of Cutting Approach'. The models allow for six milling modes, namely; slotting, 'on-centre' end-milling and 'off-centre' end-milling, each machining at the cutter ball-end cutting edge only or at the cutter ball-end and cylindrical periphery cutting edges for two or more flute cutters. The models include all the tool and cut geometrical variables and the cutting speed as well as the tool-workpiece material combination (via the database of basic cutting quantities). The models are verified through extensive numerical simulation studies and a comprehensive experimental testing programme. Good qualitative and quantitative correlation has been found between predicted and measured fluctuating and average force components and torque.     

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.     

Mechanistic modelling of the milling process using complex tool geometry

Mechanistic models of the milling process must calculate the chip geometry and the cutter edge contact length in order to predict milling forces accurately. This task becomes increasingly difficult for the machining of three dimensional parts using complex tool geometry, such as bull nose cutters. In this paper, a mechanistic model of the milling process based on an adaptive and local depth buffer of the computer graphics card is compared to a traditional simulation method. Results are compared using a 3-axis wedge shaped cut – a tool path with a known chip geometry – in order to accommodate the traditional method. Effects of cutter nose radius on the cutting and edge forces are considered. It is verified that there is little difference (1.4% at most) in the predicted force values of the two methods, thereby validating the adaptive depth buffer approach. The numerical simulations are also verified using experimental cutting tests of aluminium, and found to agree closely (within 12%).     

Milling of MAR-M247 nickel-based superalloy with high temperature and ultrasonic aiding

This study investigates the properties of machining MAR-M247 nickel-based superalloy combined ultrasonic vibration with high-temperature aided cutting. Taguchi experimental design was adopted to identify the influence of machining parameters on the machining characteristics. The six machining parameters, namely cutting tools for different materials; depth of cut; cutting speed; feed rate; working temperature; and, ultrasonic power. The machining characteristics analyzed include surface roughness, flank wear, cutting force, and milling temperature. According to the experimental results, when the cutting speed is greater than 90 m/min, P-type tungsten-carbide cutters with or without a Ti-alloy coating were unable to endure the very high temperatures generated in milling MAR-M247 nickel-based superalloy. The tungsten-carbide cutters melted and fractured. Due to the insufficient toughness of cermet cutters, the periodic high-impact stress causes severe cutter fractures when the cutting speed is greater than 60 m/min. When the cutting speed was less than 40 m/min, the cutter temperature was not significantly increased. Thus no melting or fracture of the cutters was found. Furthermore, when the cutting speed was less than 40 m/min, and fluid containing nano-particles of 5–23 nm in size was used, the cutter-workpiece friction force was reduced and the cutter life was extended.     

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。     

一种新型的广义铣削力模型

基于微分几何理论建立了任意形状铣刀的数学模型,给出适用于任意形状铣刀的三维单元铣削力模型。该铣削力模型考虑了铣刀的法向前角,认为作用单元体上的铣削力由作用于前后刀面上的正压力和摩擦力组成,并表示为与瞬时切厚有关的非线性函数。     

Method for recognizing wave dynamics damage in high-speed milling cutter

Under the influence of a high-speed, interrupted-cutting impact load, a great difference is existed among the internal load propagation of a milling cutter. Furthermore, the cutter damage caused by partial particle severe vibration has restricted the improvement of a high-speed milling energy efficiency; thus, the essence of wave dynamics damage in milling cutter remains has yet to be revealed. In this paper, through the relation between the systematic whole vibration and the particle motion, the dynamic response of milling cutter’s particle to cutting force load can be solved by the particle motion differential equation which is constructed with a one-dimensional string dynamic system. A combination of Newton’s second law and the constitutive equation of milling cutter material establishes the wave dynamics equation of milling cutter components. An approach for solving the wave front position and wave velocity of milling cutter’s stress wave is proposed, and the propagation path of transient cutting force to the milling cutter is communicated. The attenuation model of stress wave reflection is established to provide a method for revealing the stress wave transmission and distribution in milling cutter. The constitutive relation of milling cutter components under the impact load is obtained by split Hopkinson pressure bar experiment. A force connection method is adopted to make the trans-scale correlation analysis between continuum medium mechanics and molecular dynamics, thereby revealing the wave dynamics damage characteristics of a high-speed milling cutter. The results show that the potential damage position and types of milling cutter can be distinguished by the above method.     

Cutting Force Model for a Small-diameter Helical Milling Cutter

In the milling process, the major flank wear land area (two-dimensional measurement for the wear) of a small-diameter milling cutter, as wear standard, can reflect actual changes of the wear land of the cutter. By analyzing the wearing characteristics of the cutter, a cutting force model based on the major flank wear land area is established. Characteristic parameters such as pressure parameter and friction parameter are calculated by substituting tested data into their corresponding equations. The cutting force model for the helical milling cutter is validated by experiments. The computational and experimental results show that the cutting force model is almost consistent with the actual cutting conditions. Thus, the cutting force model established in the research can provide a theoretical foundation for monitoring the condition of a milling process that uses a small-diameter helical milling cutter.     

平头立铣刀铣削力模型中积分限的确定方法

在铣削力预报的研究中 ,通常采用的方法是将铣刀沿其轴线方向逐层划分为很薄的微单元 ,对每一个微单元可认为是一个单刃刀具的斜角切削过程 ,通过建立微单元上的切削力模型并沿轴线方向积分来求得总的切削力 ,轴向积分限通常是通过角度换算获取 ,比较繁琐。本文对刀具的几何特征进行了描述 ,建立了求取平头立铣刀铣削力模型角度积分限的通用方法 ,该方法通过分析刀具几何特征和加工类型 ,直接获取角度积分限 ,避免了繁琐的轴向积分限的计算 ,并通过算例验证了该方法的有效性。     

基于三角级数展开的铣削合力频谱推导及刀具偏心估算

基于一元切削力机理模型将立铣刀的切削合力分解为公称力和偏心力,采用周期信号的三角级数展开公称力和偏心力,得到其谐波幅值和相位的表达式。基于以上表达式,推导出偶数齿刀具偏心力的偶数次谐波幅值为0,三齿刀具偏心力的刀齿频率谐波幅值也为0。提出了一种用切削合力的主轴和刀齿频率谐波估算刀具偏心距和偏心角的方法,实验结果表明,采用该方法计算出的偏心值接近实测值。从理论上证明了偶数齿刀具的偏心力不存在偶数次谐波成分,所提出的估算方法只需一套估算式和一次切削实验,且数值计算比较容易。研究结果可用于偶数齿刀具的加工过程偏心和磨损辨识及其偏心量估算。     

铣削过程刀具破损原因的探讨

探讨了切出过程中的负剪切现象及其对刀具破损的影响。采用高速摄影及测量切出时铣削力的变化,并通过弹性力学分析证明：切出时的负剪切现象使卷曲的切屑以刀刃为轴线转动,导致刀楔的应力严重恶化是刀具破损的主要原因。最后提出了一些防止刀具破损的措施。     

Machining strategy in five-axis milling using balance of the transversal cutting force

Several solutions can be considered to resolve the problem of positioning a cutting tool on a free-form surface when five-axis milling. To choose a unique solution, in addition to the cutter–workpiece contact, an additional criterion can be taken into account. This may concern the local geometry of the surface or yet again the width milled to maximise the metal removal rate, but technological criteria relating to the cutting phenomenon and the quality of the surface produced are not considered. The present article introduces a strategy applying positioning combined with balancing of the transversal cutting force. This method involves using the ploughing effect of the milling cutters by simultaneously engaging the teeth located to the front of the cutter in relation to the feed movement and also those to the rear. The positioning obtained stabilises the cutter and contributes to making a net improvement in its dynamic behaviour. This leads in turn to significantly higher quality of the milled surface. The article presents a method to apply balancing of the transversal cutting force to two types of machining passes and elaborates an associated strategy to plan cutter paths enabling an improvement in surface quality to be achieved.     

A High-Precision Surface Grinding Model for General Ball-End Milling Cutters

The paper presents a high-precision manufacturing model for grinding the surface profiles of general ball-end milling (GBEM) cutters. The geometric shape of the grinding wheel is derived with a positive cone angle specifically for grinding the GBEM cutters. The concepts of radial equidistant lines and oblique equidistant surfaces are employed to model the front ball-end profile, the front cutting surface, the rear cutting surface, and the cutting-edge curve of the GBEM cutter. The front cutting surface model is obtained by computing the intersection of the rotating tool surface and the motion enve-ope of the grinder. The cutting-edge curve model is estimated by computing the intersection curve of the front cutting surface and the ball head of the GBEM cutter. A special model of the grinding mechanism is also derived and used to produce the rear surface of the cutter. Both the cutting-edge curve and the surface model are solved simultaneously in order to ensure that the cutting-edge curve leans physically against the rear-cutting surface. The geometry of the full front-end cutter shape and the parameters of the associated manufacturing processes are numerically optimised to ensure best grinding quality is achieved on the surfaces of the GBEM cutter. The concept of oblique equidistant surfaces is applied to produce a family of cutters of similar shapes with an accuracy corresponding to a user-specified allowable tolerance. One numerical example is presented to illustrate the usefulness and effectiveness of the proposed modelling methodology. Numerical results indicate that the proposed manufacturing model and grinding procedure are capable of producing a family of GBEM cutters accurate to a specified tolerance.