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.     

Cutting force model considering tool edge geometry for micro end milling process

The analysis of the cutting force in micro end milling plays an important role in characterizing the cutting process, as the tool wear and surface texture depend on the cutting forces. Because the depth of cut is larger than the tool edge radius in conventional cutting, the effect of the tool edge radius can be ignored. However, in micro cutting, this radius has an influence on the cutting mechanism. In this study, an analytical cutting force model for micro end milling is proposed for predicting the cutting forces. The cutting force model, which considers the edge radius of the micro end mill, is simulated. The validity is investigated through the newly developed tool dynamometer for the micro end milling process. The predicted cutting forces were consistent with the experimental results.     

An enhanced method for cutting force estimation in peripheral milling

A new model for cutting force estimation is presented in this paper. It is based on the specific cutting force coefficient, which is defined as a function of chip thickness. The distinguishing feature of the proposed cutting force model is the use of average chip thickness for cutting force calculation on each position of the cutting tool, in such a way that only one iteration is needed on every angular position of the tool. This model is based on the actual workpiece–tool interaction which provides information about the real position of the cutting edge. It provides an alternative to other studies in scientific literature commonly based on numerical integrations. With this model, it is possible to estimate the cutting forces not only under steady-state conditions but also under variable machining conditions of axial and radial depth of cut.     

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.     

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.     

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.     

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.     

薄壁零件高速铣削振动试验与分析

切削速会加强振动随针对薄壁零件在高速铣削加工过程中存在的振动问题,为有效抑制加工振动,采用单因素试验,对每齿进给量、度、工彳车径向轴向切深、径向切深等加工参数进行了研究。试验结果显示：每齿进给量并不是越小越好;转速过高过低都振动：切深增随轴向切深增大振动增强;随径向切深增大振动逐渐减弱,较大轴向切深下,径向切深小于1mm时,大而增强。综合数据优选：薄壁零件高速铣削时,每齿进给量在0．1～0．15mm之间;转速在11000—14000r／min之间;较小的轴向切深和较大径向切深会有效抑制加工振动。     

基于切削层形状的动态铣削力试验研究及建模

选取轴向切深、每齿进给量、径向切深和主轴转速为试验因素,采用YDX-Ⅲ9702型压电式铣削测力仪,进行了动态铣削力正交实验。针对立铣刀侧铣加工,研究了单刃铣削的临界条件,为设计试验方案提供了理论依据。结合铣削过程,采用角度积分方法求解铣削力模型,避免了轴向积分的繁琐计算。精确地建立了简捷且适应性强的基于切削层形状的动态铣削力预测模型,模型的仿真结果和试验数据相吻合。     

HSM-ADAPTED TOOL PATH CALCULATION FOR POCKETING

High-speed milling imposes a precise choice of cutting conditions, because the feed rate and the radial depth of cut influence the maximum forces on cutting edges. But the control of these cutting conditions for pocket machining is very difficult due to the complex tool path shape. Our work is focused on the improvement of the geometrical definition of the tool path, in order to ensure a better respect of the cutting conditions required for HSM. Initially, we study variations in the radial depth of cut and the real feed rate, when the tool follows usual tool paths for pocketing. Numerical simulations and experimental measurements are used. Next, a new tool path computation method that increases the real feed rate and respects radial depth of cut requirements is proposed. The computation takes into account both the geometrical requirements and the HSM dynamic requirements. Such tool paths reduce machining time and respect initial cutting parameters which are favorable for process reliability and tool life.     

HSM-ADAPTED TOOL PATH CALCULATION FOR POCKETING

High-speed milling imposes a precise choice of cutting conditions, because the feed rate and the radial depth of cut influence the maximum forces on cutting edges. But the control of these cutting conditions for pocket machining is very difficult due to the complex tool path shape. Our work is focused on the improvement of the geometrical definition of the tool path, in order to ensure a better respect of the cutting conditions required for HSM. Initially, we study variations in the radial depth of cut and the real feed rate, when the tool follows usual tool paths for pocketing. Numerical simulations and experimental measurements are used. Next, a new tool path computation method that increases the real feed rate and respects radial depth of cut requirements is proposed. The computation takes into account both the geometrical requirements and the HSM dynamic requirements. Such tool paths reduce machining time and respect initial cutting parameters which are favorable for process reliability and tool life.     

Research of production times and cutting of the spur gears by end mill in CNC milling machine

In the current study, differently from the conventional manufacturing methods, cutting of spur gear by the end mill in the computer numerically controlled (CNC) vertical milling machine was purposed. For this aim, two different approaches, radial and axial cutting methods, were introduced. However, the cutting process is performed by use of only the radial cutting method. Parametric equations of tool paths for cutting the spur gear were derived. Regarding those equations, by using the macro-program of the Dyna 2009 Myte type CNC milling machine, a CAM program is developed. By varying the parameters in the tool paths such as module, number of teeth, face width of the spur gear, cutting depth, and cutting angle, spur gear was cut and the production time was obtained. Furthermore, the dimensions of new manufactured spur gear were measured by gear tooth vernies. The dimensions were also calculated by using mathematical expressions and it was concluded that the measured values are well agreeable with the calculated values. It was observed that the production time increases with increasing the module value or number of teeth and decreasing the cutting angle or the cutting depth.     

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.     

Optimization of end mill tool geometry parameters for Al7075-T6 machining operations based on vibration amplitude by response surface methodology

This paper aims at developing a statistical model to envisage vibration amplitude in terms of geometrical parameters such as radial rake angle, nose radius of cutting tool and machining parameters such as cutting speed, cutting feed and axial depth of cut. Experiments were conducted through response surface methodology experimental design. The material chosen is Aluminum (Al 7075-T6) and the tool used was high speed steel end mill cutter with different tool geometry. Two channels piezoelectric accelerometers were used to measure the vibration amplitude. The second order mathematical model in terms of machining parameters was built up to predict the vibration amplitude and ANOVA was used to verify the competency of the model. Further investigation on the direct and interactive effect of the process parameter with vibration amplitude was carried out for the selection of process parameter so that the vibration amplitude was maintained at the minimum which ensures the stability of end milling process. The optimum values obtained from end milling process are Radial rake angle-12°, Nose radius-0.8 mm, Cutting speed-115 m/min, Cutting feed rate-0.04 mm/tooth, axial depth of cut-2.5 mm. The vibration amplitude exhibited negative relationship with radial rake angle and nose radius. The dominant factors on the vibration amplitude are feed rate and depth of cut. Thus it is envisaged that the predictive models in this study could produce values of the vibration amplitude close to the experimental readings with a 95% confidence interval.     

Extracting cutting constants via harmonic force components for a general helical end mill

Mechanistic cutting constants serve well in predicting milling forces, monitoring the milling process as well as in helping to understand the mechanistic phenomena of a machining process for a unique pair of workpiece and cutter materials under various types of cutting edge geometry. This paper presents a unified approach in identifying the six shearing and ploughing cutting constants for a general helical end mill from the dynamic components of the measured milling forces in a single cutting test. The identification model is first presented assuming the milling force is measured with a known phase angle of the cutter spindle. When the phase angle of the cutter rotation is not available, as is the case for most milling machines, it is shown that the true phase angle can be identified through the theoretical phase relationship between the different harmonic components of the milling forces measured with an arbitrary phase angle. The numerical simulation and the experimental results for ball and cylindrical end mills are presented to demonstrate and validate the identification methods.     

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.     

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.     

型腔边界拐角精加工刀轨生成算法的研究

在识别粗加工余料区域的基础上,从均匀径向切削深度、平滑刀轨路径等方面考虑,研究并实现了型腔边界拐角处的精加工刀轨生成算法。采用将拐角区域加工分为多个循环进行渐进切削的策略,可减小径向切深。同时,每一切削循环内切削段和空程刀轨段、各循环之间均采用圆弧过渡,刀轨路径满足一阶连续,从而可减小切削力的变化幅度和方向突变,提高加工精度。     

Prediction of vibration amplitude from machining parameters by response surface methodology in end milling

Decreasing vibration amplitude during end milling process reduces tool wear and improves surface finish. Mathematical model has been developed to predict the acceleration amplitude of vibration in terms of machining parameters such as helix angle of cutting tool, spindle speed, feed rate, and axial and radial depth of cut. Central composite rotatable second-order response surface methodology was employed to create a mathematical model, and the adequacy of the model was verified using analysis of variance. The experiments were conducted on aluminum Al 6063 by high-speed steel end mill cutter, and acceleration amplitude was measured using FFT analyzer. The direct and interaction effect of the machining parameter with vibration amplitude were analyzed, which helped to select process parameter in order to reduce vibration, which ensures quality of milling.     

HIGH SPEED MILLING OF GRAPHITE ELECTRODE WITH ENDMILL OF SMALL DIAMETER

Graphite becomes the prevailing electrode material in electrical discharging machining (EDM)currently.Orthogonal cutting experiments are carried out to study the characteristics of graph- ite chip formation process.High speed milling experiments are conducted to study tool wear and cutting forces.The results show that depth of cut has great influence on graphite chip formation.The removal process of graphite in high speed milling is the mutual result of cutting and grinding process. Graphite is prone to cause severe abrasion wear to coated carbide endmills due to its high abrasive- ness nature.The major patterns of tool wear are flank wear,rake wear,micro-chipping and breakage. Cutting forces can be reduced by adoption of higher cutting speed,moderate feed per tooth,smaller radial and axial depths of cut,and up cutting.