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.     

球头刀铣削过程动力学模型

建立了考虑刀杆柔性的球头铣刀铣削振动模型,探讨了交变轴向力对刀杆固有频率的影响。考虑刀具动态变形和工件表面波纹对切削厚度的再生反馈,建立了球头刀铣削动力学模型,对铣削中的动态铣削力和刀杆振动进行了仿真,证明了离线仿真可以对铣削过程动特性做出预测。     

五坐标端铣数控加工计算理论分析

本文介绍了五坐标端铣数控加工中的后跟角计算方法及刀位计算方法,分析了加工误差,包括直线逼近误差和刀轴摆动误差,提出了刀轴摆动误差补偿方法——刀具切触点偏置法,给出了走刀步长、走刀步距及刀具半径计算公式。     

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.     

螺旋棒铣刀铣削力建模与仿真

在对螺旋棒铣刀铣削力建模中考虑了切削厚度变化对铣削力影响的指数关系、铣刀偏心对实际切削厚度、切入与切出角、铣削力波动的影响,并提出采用实测各刀齿铣削最大值比求解铣刀偏心和识别铣削力系数的方法。在考虑铣刀偏心因素的情况下仿真与实测的铣削力达到非常好的一致性。提出的铣削力仿真方法充分反映了铣削力的实际状态,提高了铣削力仿真精度。     

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.     

带再生反馈的柔性立铣刀铣削过程模型

精确合理的铣削过程模型是研究铣削加工表面形貌的关键。首先根据线性弹性体基本假设,将铣削过程中刀杆所受的力和产生的变形均分解为动、静两部分;然后运用微分几何理论,考虑实际切削过程中的再生效应,导出动态铣削力集度表达式,进而建立刀杆的动态变形模型,并构造出一套与之相应的高效快速数值仿真算法,同时还给出刀杆静态变形量的计算方法;最后通过仿真实例说明该模型的合理性。     

METHODS FOR ON-LINE DIRECTIONALLY INDEPENDENT FAILURE PREDICTION OF END MILLING CUTTING TOOLS

Tracking the health of cutting tools under typical wear conditions is advantageous to the speed and efficiency of many manufacturing processes. Although techniques exist to monitor tool performance, most are dependent on cutting direction, sensor orientation, cutting procedure, or the use of computationally intensive mathematical models. In this work, several solutions are proposed such that real-time analysis of signal variance and frequency magnitudes is possible through the identification of trends in the transient behavior of tri-axial force dynamometer signals. Moreover, the nature of both the transient variance (the temporal change in signal variance) and the frequency magnitude trends are shown to be independent of direction through the observation of both linear and pocketing mill sequences. Ten autonomous methods for failure prediction are discussed, tested, and presented. Analysis methods are demonstrated through the implementation of procedures derived from autocorrelation, FFT type, and Autoregressive models. Methods demonstrating high levels of success are subsequently contrasted for forecast success and computational requirements. Forecast success is demonstrated by both FFT type and Autoregressive Models. Methods discussed have the potential for on-line implementation using current commercially available computational capacity.     

MAXIMIZATION OF CHATTER-FREE MATERIAL REMOVAL RATE IN END MILLING USING ANALYTICAL METHODS

ABSTRACT

Chatter vibrations in milling, which develop due to dynamic interactions between the cutting tool and the workpiece, result in reduced productivity and part quality. Various numerical and analytical stability models have been considered in the previous publications, where mostly the stability limit of axial depth of cut is emphasized for chatter-free cutting. In this paper an analytical stability model is used, and a simple algorithm to determine the stability limit of radial depth of cut is presented. It is shown that, for the maximization of chatter-free material removal rate, radial depth of cut is of equal importance with the former. A method is proposed to determine the optimal combination of depths of cut, so that chatter-free material removal rate is maximized. The application of the method is demonstrated on a pocketing example where significant reduction in the machining time is obtained using the optimal parameters. The procedure can easily be integrated to a CAD/CAM or virtual machining environment in order to identify the optimal milling conditions automatically.     

MAXIMIZATION OF CHATTER-FREE MATERIAL REMOVAL RATE IN END MILLING USING ANALYTICAL METHODS

Chatter vibrations in milling, which develop due to dynamic interactions between the cutting tool and the workpiece, result in reduced productivity and part quality. Various numerical and analytical stability models have been considered in the previous publications, where mostly the stability limit of axial depth of cut is emphasized for chatter-free cutting. In this paper an analytical stability model is used, and a simple algorithm to determine the stability limit of radial depth of cut is presented. It is shown that, for the maximization of chatter-free material removal rate, radial depth of cut is of equal importance with the former. A method is proposed to determine the optimal combination of depths of cut, so that chatter-free material removal rate is maximized. The application of the method is demonstrated on a pocketing example where significant reduction in the machining time is obtained using the optimal parameters. The procedure can easily be integrated to a CAD/CAM or virtual machining environment in order to identify the optimal milling conditions automatically.     

行星轮系传动效率与自锁分析的新方法

应用轮系的复铰图画表示法与基本回路方法,以2K-H轮系为例进行系统化的传动比、传动效率与自锁的分析,以作为2K-H轮系分析与设计的依据。首先,导入复铰运动链图画表示法,以有效地表示2K-H轮系;接着,以此图画表示法与基本回路方法推导在各种运动情况下2K-H轮系的传动比与传动效率方程式:最后,讨论了2K-H轮系传动效率与自锁的关系。     

球面铣刀制造中的数学模型研究

介绍了球面铣刀成形原理、刃口曲线求解模型、刃口曲线相关参数的优化模型、磨制后刀面的机构和相应数学模型，并用实例验证上述模型的可靠性，最后还讨论了砂轮磨损对刃口曲线的影响。为球面铣刀的国产化提供了参考。     

ENHANCING THE DEPTH OF CUT IN ABRASIVE WATERJET CUTTING OF ALUMINA CERAMICS BY USING MULTIPASS CUTTING WITH NOZZLE OSCILLATION

An experimental investigation is presented to increase the depth of cut in abrasive waterjet (AWJ) cutting of alumina ceramics by introducing a new cutting technique combining multipass operations with controlled nozzle oscillation. Plausible trends of the depth of cut per pass and total depth of cut with respect to the number of passes and the parameters in each pass are discussed. It shows that cutting with nozzle oscillation can significantly increase the depth of cut in the single-pass cutting mode, while further gains in the depth of cut can be made by using multipass cutting with nozzle oscillation. While multipass cutting can be used to increase the total depth of cut for machining thicker materials, it has been found that an average increase of 50.8% in the total depth of cut can be expected by using multipass cutting with nozzle oscillation as compared to single-pass cutting without nozzle oscillation within the same cutting time. Recommendations are finally made as a practical guide for the selection of process parameters in multipass AWJ cutting of alumina ceramics with controlled nozzle oscillation.     

超声波振动金刚石刀具对脆性材料临界切削深度的影响

通过脆性材料沟槽切削试验,研究了超声波直线振动金刚石刀具和超声波椭圆振动金刚石刀具对脆性材料临界切削深度的影响,与没加超声波振动的金刚石刀具相比,超声波振动金刚石刀具能增大对脆性材料塑性切削的临界切削深度。提出了超声波振动金刚石刀具切削脆性材料临界切削深度计算公式,分析了导致超声波振动金刚石刀具增大脆性材料塑性切削的临界切削深度的原因。     

SIMULATED ANNEALING TO ESTIMATE THE OPTIMAL CUTTING CONDITIONS FOR MINIMIZING SURFACE ROUGHNESS IN END MILLING Ti-6Al-4V

This study presents the estimation of the optimal effect of the radial rake angle of the tool, combined with cutting speed and feed in influencing the surface roughness result. Studies on optimization of cutting conditions for surface roughness in end milling involving radial rake angle are still lacking. Therefore, considering the radial rake angle, this study applied simulated annealing in determining the solution of the cutting conditions to obtain the minimum surface roughness when end milling Ti-6Al-4V. Considering a set of experimental machining data, the regression model is developed. The best regression model was considered to formulate the fitness function of the simulated annealing. It was recommended that the cutting conditions should be set at highest cutting speed, lowest feed and highest radial rake angle in order to achieve the minimum surface roughness of 0.1385 µm. Subsequently, it was found that by using simulated annealing, the minimum surface roughness was much lower than the experimental sample data, regression modelling and response surface methodology technique by about 27%, 26% and 50%, respectively.     

高相对密度钨球注射成形过程中的喷射现象

针对金属粉末注射成形过程中喷射所引起的气穴、不良流动等缺陷,对高相对密度钨球合金制品进行了注射成形试验,发现钨球注射成形初期存在喷射现象,喂料一进入型腔即发生剧烈扭曲变形。通过多种成形工艺参数的组合,并且根据非牛顿流体的剪切变稀特性,采用高速高压成形工艺使得注射过程在瞬间完成,从而消除喷射对金属粉末制品的影响。同时,采用Moldflow MPI软件对其成形过程进行仿真,结果表明基于欧拉法的传统模流仿真软件无法模拟喷射现象,从而提出采用拉格朗日法对喷射成形过程进行建模和仿真的构想。将上述喷射现象的研究结果与高相对密度钨球的实际生产现状相结合,提出在定模板的模具分形面一侧开排气道增强其排气能力,和采用高速高压注射成形工艺解决喷射所造成的质量问题。     

AN ANALYTICAL MODEL OF OBLIQUE CUTTING WITH APPLICATION TO END MILLING

A new analytical cutting force model is presented for oblique cutting. Orthogonal cutting theory based on unequal division shear zone is extended to oblique cutting using equivalent plane approach. The equivalent plane angle is defined to determine the orientation of the equivalent plane. The governing equations of chip flow through the primary shear zone are established by introducing a piecewise power law distribution assumption of shear strain rate. The flow stress is calculated from Johnson-cook material constitutive equation. The predictions were compared with test data from the available literature and showed good correlation. The proposed model of oblique cutting was applied to predict the cutting forces in end milling. The helical flutes are decomposed into a set of differential oblique cutting edges. To every engaged tooth element, the differential cutting forces are obtained from oblique cutting process. Experiments on machining AISI 1045 steel under different cutting conditions were conducted to validate the proposed model. It shows that the predicted cutting forces agree with the measurements both in trends and values.     

EFFECTS OF COOLANT SUPPLY METHODS AND CUTTING CONDITIONS ON TOOL LIFE IN END MILLING TITANIUM ALLOY

Titanium machining poses a great challenge to cutting tools due to its severe negative influence on tool life primarily due to high temperature generated and strong adhesion in the cutting area. Thus, various coolant supply methods are widely used to improve the machining process. On account of this, tool life and cutting force are investigated based on dry cutting, flood cooling, and minimum quantity lubrication (MQL) techniques. The experimental results show that MQL machining can remarkably and reliably improve tool life, and reduce cutting force due to the better lubrication and cooling effect.     

EFFECTS OF COOLANT SUPPLY METHODS AND CUTTING CONDITIONS ON TOOL LIFE IN END MILLING TITANIUM ALLOY

Titanium machining poses a great challenge to cutting tools due to its severe negative influence on tool life primarily due to high temperature generated and strong adhesion in the cutting area. Thus, various coolant supply methods are widely used to improve the machining process. On account of this, tool life and cutting force are investigated based on dry cutting, flood cooling, and minimum quantity lubrication (MQL) techniques. The experimental results show that MQL machining can remarkably and reliably improve tool life, and reduce cutting force due to the better lubrication and cooling effect.     

热弹性流体动力润滑椭圆接触问题的完全数值解

本文提出了一个热弹性流体动力润滑椭圆接触问题的完全数值解,并且描述了其相应的求解过程。通过联立求解允许润滑油粘度和密度沿油膜厚度方向变化的一般雷诺方程、弹性方程、润滑油膜的能量方程、固体的热传导方程以及润滑油的粘度方程和密度方程,求解出了不同滚动速度和滑滚比下的油膜压力分布、油膜厚度和形状、油膜内和固体内的三维的温度分布以及接触处的滑动摩擦系数和滚动摩擦系数。所得到的数值结果表明：在一般中、低速情况下,热效应对压力分布、油膜厚度以及滚动摩擦系数的影响较小,但对滑动摩擦系数的影响则相当显著;在接触区外,油膜温升相比之下是微小的,而接触区内的温升明显地随滚动速度和滑滚比的增加而增加;在油膜接触区内,存在着一个形状和位置都与压力峰基本一致的温度高峰区;在固体与油膜之间的两个分界面上,温升一般略低于油膜中层温升,而进入固体以后,温升沿垂直于油膜的方向迅速衰减。本文所研究的问题系稳态问题润滑剂仍被假定为牛顿流体。