Modeling and Analytical Solution of Chatter Stability for T-slot Milling

T-slot milling is one of the most common milling processes in industry. Despite recent advances in machining technology, productivity of T-slot milling is usually limited due to the process limitations such as high cutting forces and stability. If cutting conditions are not selected properly the process may result in the poor surface finish of the workpiece and the potential damage to the machine tool. Currently, the predication of chatter stability and determination of optimal cutting conditions based on the modeling of T-slot milling process is an effective way to improve the material removal rate(MRR) of a T-slot milling operation. Based on the geometrical model of the T-slot cutter, the dynamic cutting force model was presented in which the average directional cutting force coefficients were obtained by means of numerical approach, and leads 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 was also created to satisfy the special requirement of T-slot milling. Thereafter, a dynamic simulation model of T-slot milling was implemented using Matlab software. In order to verify the effectiveness of the approach, the transfer functions of a typical cutting system in a vertical CNC machining center were measured in both feed and normal directions by an instrumented hammer and accelerators. Dynamic simulations were conducted to obtain the predicated SLD under specified cutting conditions with both the proposed model and CutPro?. Meanwhile, a set of cutting trials were conducted to reveal whether the cutting process under specified cutting conditions is stable or not. Both the simulation comparison and experimental verification demonstrated that the satisfactory coincidence between the simulated, the predicted and the experimental results. The chatter-free T-slot milling with higher MRR can be achieved under the cutting conditions determined according to the SLD simulation.     

Effects of Cutting Parameters on Tool Insert Wear in End Milling of Titanium Alloy Ti6A14V

Titanium alloy is a kind of typical hard-to-cut material due to its low thermal conductivity and high strength at elevated temperatures, this contributes to the fast tool wear in the milling of titanium alloys. The influence of cutting conditions on tool wear has been focused on the turning process, and their influence on tool wear in milling process as well as the influence of tool wear on cutting force coefficients has not been investigated comprehensively. To fully understand the tool wear behavior in milling process with inserts, the influence of cutting parameters on tool wear in the milling of titanium alloys Ti6Al4 V by using indexable cutters is investigated. The tool wear rate and trends under different feed per tooth, cutting speed, axial depth of cut and radial depth of cut are analyzed. The results show that the feed rate per tooth and the radial depth of cut have a large influence on tool wear in milling Ti6Al4 V with coated insert. To reduce tool wear, cutting parameters for coated inserts under experimental cutting conditions are set as: feed rate per tooth less than 0.07 mm, radial depth of cut less than 1.0 mm, and cutting speed sets between 60 and 150 m/min. Investigation on the relationship between tool wear and cutting force coefficients shows that tangential edge constant increases with tool wear and cutter edge chipping can lead to a great variety of tangential cutting force coefficient. The proposed research provides the basic data for evaluating the machinability of milling Ti6Al4 V alloy with coated inserts, and the recommend cutting parameters can be immediately applied in practical production.     

Effects of cutting parameters on tool insert wear in end milling of titanium alloy Ti6Al4V

Titanium alloy is a kind of typical hard-to-cut material due to its low thermal conductivity and high strength at elevated temperatures, this contributes to the fast tool wear in the milling of titanium alloys. The influence of cutting conditions on tool wear has been focused on the turning process, and their influence on tool wear in milling process as well as the influence of tool wear on cutting force coefficients has not been investigated comprehensively. To fully understand the tool wear behavior in milling process with inserts, the influence of cutting parameters on tool wear in the milling of titanium alloys Ti6Al4V by using indexable cutters is investigated. The tool wear rate and trends under different feed per tooth, cutting speed, axial depth of cut and radial depth of cut are analyzed. The results show that the feed rate per tooth and the radial depth of cut have a large influence on tool wear in milling Ti6Al4V with coated insert. To reduce tool wear, cutting parameters for coated inserts under experimental cutting conditions are set as: feed rate per tooth less than 0.07 mm, radial depth of cut less than 1.0 mm, and cutting speed sets between 60 and 150 m/min. Investigation on the relationship between tool wear and cutting force coefficients shows that tangential edge constant increases with tool wear and cutter edge chipping can lead to a great variety of tangential cutting force coefficient. The proposed research provides the basic data for evaluating the machinability of milling Ti6Al4V alloy with coated inserts, and the recommend cutting parameters can be immediately applied in practical production.     

A Cutting Force Model for a Waved-Edge End Milling Cutter

This paper presents a model for predicting the cutting forces for waved-edge milling cutters that are widely used in rough machining. The development of the model is based on the analysis of the complicated cutting edge of waved-edge cutter. According to the existing local cutting force model and from the relationship of local cutting force and chip load, local cutting force can be derived. Then the model is obtained by dividing the cutter into a number of differential elements in the axial direction and summarising the resultant cutting force produced by each differential cutter disc engaged in the cut. A numerical algorithm is introduced for the calculation of total force and the calibration of the relevant parameters in the model. A series of experiments under different cutting conditions are conducted to confirm the validity of the developed model. The agreement between the experimental and simulative results is satisfactory, which shows that the model is effective for cutting force prediction in end milling with waved-edge cutters. ID="A1"Correspondance and offprint requests to: Prof. L. Zheng, Institute of Manufacturing Engineering, Department of Precision Instruments and Mechanology, Tsinghua University, Beijing, 100084, P. R. China. E-mail: lzheng@tsinghua.edu.cn     

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%).     

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     

铣刀磨损对铣削稳定性及表面位置误差的影响

为了分析刀具正常磨损后铣削颤振稳定域和表面位置误差,对刀具不同磨损状态下的切削力系数进行辨识,基于全离散法研究刀具正常磨损后铣削颤振稳定域和表面位置误差特性。发现当刀具正常磨损后,铣削系统的稳态临界切深呈现上升的趋势;随着工件表面洛氏硬度的提高,铣削系统稳态临界切深逐步下降,刀具正常磨损后临界切深与后刀面无磨损临界切深的差别逐步变小;在稳定域的局部会出现表面位置误差增加的情况。试验表明,该理论模型可以有效优化刀具正常磨损后的加工参数。     

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.     

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.     

A SIMPLIFIED SOLUTION FOR THE DEPTH OF CUT IN MULTI-PATH BALL END MILLING

Abstract

The axial depth of cut is an important factor in the dynamic cutting force analysis of milling. In multi-path ball end milling, it varies with the cutting edge position angle. General equations are derived from which the instant depth of cut in ball end milling can be calculated. Examples are given for four path increment modes. The cutting condition in each mode is discussed with respect to the depth of cut. The conditions needed to disengage the tip of the ball end mill from the cut are determined. The "step-up" increment mode has the most favorable cutting condition for cutter tip relief and high cutting velocity. In order to obtain an instant evaluation of the cutting stability, the equations of maximum depth of cut in ball end milling are derived. The exact solutions are obtained from the general equations for the instant depth of cut. More conservative estimates are obtained from the simplified solutions. The results in this paper can be used as a guide in NC part programming to select an optimal cutting strategy and to ensure a stable cutting process in ball end milling.     

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.     

A SIMPLIFIED SOLUTION FOR THE DEPTH OF CUT IN MULTI-PATH BALL END MILLING

The axial depth of cut is an important factor in the dynamic cutting force analysis of milling. In multi-path ball end milling, it varies with the cutting edge position angle. General equations are derived from which the instant depth of cut in ball end milling can be calculated. Examples are given for four path increment modes. The cutting condition in each mode is discussed with respect to the depth of cut. The conditions needed to disengage the tip of the ball end mill from the cut are determined. The "step-up" increment mode has the most favorable cutting condition for cutter tip relief and high cutting velocity. In order to obtain an instant evaluation of the cutting stability, the equations of maximum depth of cut in ball end milling are derived. The exact solutions are obtained from the general equations for the instant depth of cut. More conservative estimates are obtained from the simplified solutions. The results in this paper can be used as a guide in NC part programming to select an optimal cutting strategy and to ensure a stable cutting process in ball end milling.     

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.     

基于动力学不确定性的重型切削工艺参数优化

针对数控重型切削加工过程的切削稳定性具有不确定性的特点,提出了在切削稳定性和机床工作能力的约束下,获得最大材料去除率的工艺参数优化方法。根据重型切削加工的工艺特点建立三维动力学模型,以机床的固有频率、阻尼比、刚度和切削力系数作为不确定因素,结合排零定理和边理论对其进行不确定性分析,获得稳健的切削稳定性叶瓣图,结合切削深度、刀具直径和刀具齿数的关系,为加工过程选择能获得最大切削深度的刀具。在此基础上,建立工艺参数优化模型,选择最佳的轴向切削深度、径向切削深度和主轴转速的组合,最后以一台加工中心上某型号发动机缸体表面的粗加工过程为例进行了验证。     

铣削TC4钛合金的刀具磨损对比试验

TC4钛合金是典型难加工材料之一,极易造成工具磨损。本文通过铣削TC4钛合金试验,跟踪铣削过程中铣刀每个齿的磨损量及磨损形态,比较了不同细晶粒硬质合金铣刀的磨损过程。结果表明,铣刀切削刃发生崩刃会直接缩短铣刀的使用寿命。     

基于UG的小直径立铣刀应力场有限元分析

为了提高加工精度,对小直径立铣刀的应力场进行了有限元分析。通过铣削力试验,对不同切削参数下立铣刀的铣削力进行动态采集,利用UG建模模块进行立铣刀实体建模,根据铣削力试验结果给出边界条件,在立铣刀有限元模型上加载载荷,利用UG有限元分析模块获得了立铣刀切削过程中切入、切出的瞬时应力场云图,显示了切削中立铣刀应力场的变化规律。     

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     

Counterbalance of cutting force for advanced milling operations

The goal of this work is to concurrently counterbalance the dynamic cutting force and regulate the spindle position deviation under various milling conditions by integrating active magnetic bearing (AMB) technique, fuzzy logic algorithm and an adaptive self-tuning feedback loop. Since the dynamics of milling system is highly determined by a few operation conditions, such as speed of spindle, cut depth and feedrate, therefore the dynamic model for cutting process is more appropriate to be constructed by experiments, instead of using theoretical approach. The experimental data, either for idle or cutting, are utilized to establish the database of milling dynamics so that the system parameters can be on-line estimated by employing the proposed fuzzy logic algorithm as the cutting mission is engaged. Based on the estimated milling system model and preset operation conditions, i.e., spindle speed, cut depth and feedrate, the current cutting force can be numerically estimated. Once the current cutting force can be real-time estimated, the corresponding compensation force can be exerted by the equipped AMB to counterbalance the cutting force, in addition to the spindle position regulation by feedback of spindle position. On the other hand, for the magnetic force is nonlinear with respect to the applied electric current and air gap, the characteristics of the employed AMB is investigated also by experiments and a nonlinear mathematic model, in terms of air gap between spindle and electromagnetic pole and coil current, is developed. At the end, the experimental simulations on realistic milling are presented to verify the efficacy of the fuzzy controller for spindle position regulation and the capability of the dynamic cutting force counterbalance.     

THE SURFACE INTEGRITY IN MACHINING HARDENED STEEL SKD11 FOR DIE AND MOLD

Milling cutters were evaluated by tool wear, cutting force and vibration. Surface integrity of grinding and milling were investigated by comparing residual stress distributions, metallurgical structure, hardened layer depth and surface roughness. And influence of cutting tool wear on surface integrity was investigated. Experimentations revealed that the preferable surface integrity would be obtained if the proper milling cutter as well as a small wear criterion were adopted to avoid the advent of tempered martensite. The research results pointed out the feasibility of taking milling as the finish machining process instead of grinding in machining hardened steel with high efficiency.