Grey relational analysis coupled with principal component analysis for optimization design of the cutting parameters in high-speed end milling

This paper investigates optimization design of the cutting parameters for rough cutting processes in high-speed end milling on SKD61 tool steel. The major characteristics indexes for performance selected to evaluate the processes are tool life and metal removal rate, and the corresponding cutting parameters are milling type, spindle speed, feed per tooth, radial depth of cut, and axial depth of cut. In this study, the process is intrinsically with multiple performance indexes so that grey relational analysis that uses grey relational grade as performance index is specially adopted to determine the optimal combination of cutting parameters. Moreover, the principal component analysis is applied to evaluate the weighting values corresponding to various performance characteristics so that their relative importance can be properly and objectively described. The results of confirmation experiments reveal that grey relational analysis coupled with principal component analysis can effectively acquire the optimal combination of cutting parameters. Hence, this confirms that the proposed approach in this study can be an useful tool to improve the cutting performance of rough cutting processes in high-speed end milling process.     

钛合金TC4高速铣削参数对铣削力的影响研究

钛合金高速铣削因其高效率、高质量、小变形等优点,广泛应用于航空、航天、船舶、军工制造等行业。针对难加工材料TC4(Ti-6Al-4V)的高速铣削加工技术,开展了铣削深度、铣削宽度、每齿进给量、主轴转速的四因素三水平正交试验,分析各铣削参数对铣削力的影响。实验过程中将铣削力分解为切向铣削力、径向铣削力和轴向铣削力,采用多元线性回归分析法,建立了各向铣削力模型,并进行了显著性检验。为验证模型的准确性,设计了新的加工实验进行验证。实验结果表明:该模型准确度高,能够预测铣削过程中的各向铣削力。     

The estimation of cutting forces and specific force coefficients during finishing ball end milling of inclined surfaces

The majority of cutting force models applied for the ball end milling process includes only the influence of cutting parameters (e.g. feedrate, depth of cut, cutting speed) and estimates forces on the basis of coefficients calibrated during slot milling. Furthermore, the radial run out phenomenon is predominantly not considered in these models. However this approach can induce excessive force estimation errors, especially during finishing ball end milling of sculptured surfaces. In addition, most of cutting force models is formulated for the ball end milling process with axial depths of cut exceeding 0.5 mm and thus, they are not oriented directly to the finishing processes. Therefore, this paper proposes an accurate cutting force model applied for the finishing ball end milling, which includes also the influence of surface inclination and cutter's run out. As part of this work the new method of specific force coefficients calibration has been also developed. This approach is based on the calibration during ball end milling with various surface inclinations and the application of instantaneous force signals as an input data. Furthermore, the analysis of specific force coefficients in function of feed per tooth, cutting speed and surface inclination angle was also presented. In order to determine geometrical elements of cut precisely, the radial run out was considered in equations applied for the calculation of sectional area of cut and active length of cutting edge. Research revealed that cutter's run out and surface inclination angle have significant influence on the cutting forces, both in the quantitative and qualitative aspect. The formulated model enables cutting force estimation in the wide range of cutting parameters, assuring relative error's values below 16%. Furthermore, the consideration of cutter's radial run out phenomenon in the developed model enables the reduction of model's relative error by the 7% in relation to the model excluding radial run out.     

Effects of cutting conditions on dynamic cutting factor and process damping in milling

This paper investigates how cutting conditions affect dynamic cutting factor and system process damping in a dynamic milling process. By considering variation of edge plowing force, a frequency domain method is presented to identify the dynamic cutting factor through measured vibration in a milling process, and cutting conditions most suitable for the identification experiments are also discussed. A series of experiments are carried out to investigate the effects of cutting conditions on the dynamic cutting factor. This factor is shown to be significantly affected by the cutting speed, but relatively independent of the feed per tooth and the radial depth of cut. An average process damping model is further constructed and shown to be effective in representing the time-varying damping function. The average process damping is shown to increase rapidly at lower cutting speed, but remain constant as the cutting speed beyond a critical value.     

端铣加工面尺寸误差预测

为了精确预测端铣加工面尺寸误差,利用铣削动态力卷积模型,引入表面生成窗概念,并考虑到工件与刀具的变形误差、机床空间误差与刀具偏摆的影响,建立了加工面尺寸误差预测模型。通过在铣床上进行实验,验证了该模型能够正确预测工件尺寸误差及其分布范围,且在铣刀轴向切深、主轴转速和进给速度一定的情况下,增加径向切深不会对工件尺寸误差产生显著影响。     

Surface topography in ball-end milling processes as a function of feed per tooth and radial depth of cut

A numerical model was developed that predicts topography and surface roughness in ball-end milling processes, based on geometric tool-workpiece intersection. It allows determining surface topography as a function of feed per tooth and revolution, radial depth of cut, axial depth of cut, number of teeth, tool teeth radii, helix angle, eccentricity and phase angle between teeth. It determines profile roughness parameters, as well as areal roughness parameters such as average roughness Sa, maximum peak-to-valley roughness St, volume of summit material V and a proposed new time coefficient Ct. It relates surface roughness to milling time. Moreover, feed per tooth and revolution f and radial depth of cut Rd were calculated that minimise parameters Sa·Ct, St·Ct and V·Ct. Minimum Sa·Ct and St·Ct provide minimum roughness with minimum milling time. Minimum V·Ct means minimum milling time with minimum material removal in manual polishing operation. At low radial depth of cut, roughness is low regardless of feed employed. On the contrary, at high radial depth of cut, roughness depends remarkably on feed: the higher the feed, the higher the roughness. In order to simultaneously minimise roughness and time, high f and low Rd should be used. In that case also volume of summit material is minimised.     

切削参数对子午线轮胎模具侧板切削比能及表面粗糙度的影响研究

以子午线轮胎模具侧板为研究对象进行铣削试验,着重研究主轴转速、每齿进给量、切削深度对轮胎模具侧板切削比能、材料去除率和表面粗糙度的影响规律。分析试验结果可知:切削比能随着切削参数的增大而减小,说明适当增大切削参数可以提高切削效率并节约能量;表面粗糙度随主轴转速增大呈先增大后减小的趋势,随切削深度和每齿进给量的增加而增大。结果表明:提高主轴转速既有利于降低切削比能(节能)也有利于改善表面粗糙度,增大每齿进给量和切削深度会降低切削比能但会恶化表面质量。因此,为同时达到高效节能和良好表面质量的要求,应尽量提高主轴转速。     

PAC5000模具钢的高速铣削加工试验研究

对PAC5000模具钢进行高速铣削单因素及正交试验研究,建立铣削力、表面粗糙度和表面残余应力的回归数学模型,分析各铣削参数对铣削力、表面粗糙度和表面残余应力的影响规律及影响程度。结果表明:铣削力、表面粗糙度随铣削速度的增加而减小,随背吃刀量、每齿进给量和侧吃刀量的增加而增大,各铣削参数对轴向铣削力的影响均很大,侧吃刀量是影响轴向铣削力的最主要因素;对平行和垂直于进给方向上的表面粗糙度最敏感的铣削参数分别是每齿进给量和背吃刀量,并且,对垂直于进给方向上的表面粗糙度影响最大;平行于铣削方向上的残余应力表现为压应力,垂直于铣削方向的残余应力表现为拉应力,提高铣削速度,可减小残余应力。     

Time domain model of plunge milling operation

Plunge milling operations are used to remove excess material rapidly in roughing operations. The cutter is fed in the direction of spindle axis which has the highest structural rigidity. This paper presents time domain modeling of mechanics and dynamics of plunge milling process. The cutter is assumed to be flexible in lateral, axial, and torsional directions. The rigid body feed motion of the cutter and structural vibrations of the tool are combined to evaluate time varying dynamic chip load distribution along the cutting edge. The cutting forces in lateral and axial directions and torque are predicted by considering the feed, radial engagement, tool geometry, spindle speed, and the regeneration of the chip load due to vibrations. The mathematical model is experimentally validated by comparing simulated forces and vibrations against measurements collected from plunge milling tests. The study shows that the lateral forces and vibrations exist only if the inserts are not symmetric, and the primary source of chatter is the torsional–axial vibrations of the plunge mill. The chatter vibrations can be reduced by increasing the torsional stiffness with strengthened flute cavities.     

TC4合金蜂窝冰固持低温铣削研究

广泛应用于航天领域的低刚度薄壁钛合金蜂窝材料,在铣削加工中面临卷曲、开焊、塌边等缺陷,需改进其固持和加工方法。材料通过冰固持方法处理,并进行高速深冷铣削加工;分析了蜂窝铣削性能和加工缺陷产生原因,提出了冰固持超低温铣削机理。结果表明,相比于传统固持加工方式,经冰固持低温铣削的钛合金蜂窝表面质量有很大提高,加工缺陷被有效抑制;切削深度对表面质量影响较大。切削参数对铣削力影响顺序:切深最大,可提高约3倍,其次是主轴转速,进给速度影响最小。冰固持低温方法提高了蜂窝强度,实现了超低温切削,改变了断屑方式。结论:冰固持低温切削为面内径向等效强度小、低刚度薄壁钛合金蜂窝材料高效加工提供了新方法。     

CuZn30微铣削表面完整性影响规律试验研究

采用直径φ1的硬质合金铣刀对CuZn30合金进行单因素槽铣试验,研究加工表面完整性、顶毛刺和切屑随铣削参数的变化规律。通过试验得到以下结论:切削参数对加工表面完整性影响比较显著,其中表面粗糙度随主轴转速的增大而减小,随每齿进给量增大而增大,切削深度对粗糙度影响不太显著。残余应力随着每齿进给量的增大有明显增大趋势,而主轴转速与切削深度对残余应力的影响不太显著。显微硬度随铣削参数变化没有显著的变化。顶毛刺主要受每齿进给量的影响,毛刺尺寸随着每齿进给量的增加先急速减小后趋于平稳,切屑形态主要受切削深度的影响,随着切削深度的增加,切屑由短小的碎屑逐渐变为平滑的连续卷曲切屑。     

高速铣削钛合金Ti6A4V铣削力试验研究

采用涂层硬质合金刀具对钛合金Ti6A14V进行了高速铣削试验.通过分析正交试验直观图,研究了铣削参数的变化对铣削力的影响,为合理选择铣削参数提供了可靠的依据.高速铣削试验表明:采用小的轴向切削深度和每齿进给量及较大的径向切削深度和切削速度有利于减小铣削力.基于概率统计和回归分析原理,建立了铣削力回归方程,并对回归方程进行了显著性检验,检验结果表明:所建立的回归方程呈高度显著检验状态,与实际情况拟合的较好.     

高速铣削模具钢3Cr2NiMo表面粗糙度试验研究

采用单因素试验法和正交试验法,在高速加工中心上对模具钢3Cr2NiMo进行切削试验,通过改变影响加工过程的切削参数:主轴转速、进给速度、轴向切削深度和径向切削深度,研究了影响工件加工表面粗糙度值程度的因素。结果表明:增大机床的主轴转速,粗糙度值显著降低,而增大进给速度、轴向铣削深度,粗糙度值增大,但增大的幅度不同,径向铣削深度的影响不明显。     

1Cr18Ni9Ti不锈钢斜面铣削力的实验研究

阐述了1Cr18Ni9Ti不锈钢的切削特性,应用正交试验法进行了球头刀铣削1Cr18Ni9Ti不锈钢斜面铣削力实验,以铣削速度、铣削深度、进给量、行间距和斜面与水平面的夹角为试验因素,以球头刀斜面铣削力为试验指标。根据实验结果,回归得出了预测1Cr18Ni9Ti不锈钢斜面铣削力的模型,并分析了各试验因素对铣削力的影响规律,最后给出了球头刀铣削1Cr18Ni9Ti不锈钢斜面时的推荐铣削参数值,并将其应用于不锈钢搅拌桨叶片加工。     

A pole/zero cancellation approach to reducing forced vibration in end milling

An analytical model for the forced vibration in an end milling process is derived and a criterion in selecting cutting parameters to reduce the forced vibration is presented in this paper. The analytic expression for the forced vibration due to the periodic milling force is obtained as the product of the Fourier transform of the milling force and the frequency response function of the structure dynamics. The pole/zero cancellation technique is then employed for reducing the forced vibration. Analysis shows that the suppression of forced vibration can be achieved by choosing cutting parameters so that one of the zeroes of the Fourier transform of the milling process function is near the pole of the structure dynamics. A design equation in terms of cutter geometry, axial depth of cut, spindle speed and structure resonant frequency is derived for the conditions when the forced vibration can be minimized. The presented analysis is illustrated through numerical simulation and verified by experimental results.     

模糊田口法在重切削制程中切削参数最佳化设计

为了快速有效获得重切削时良好的切削性能参数,以田口法与模糊逻辑相结合,对侧面铣削SUS304不锈钢重切削制程时的切削参数进行最佳化设计。由于评估重切削制程的刀具寿命与金属移除率两项主要切削性能,受到主轴转速、每刃进给、轴向切深与径向切深的影响,由此将4个切削参数设置为可控制因子。经过田口法将各品质特性转化为S/N比,通过模糊逻辑运算,采用多重品质特性指标(MPCI)求得切削参数最佳水准组合。试验结果表明:以模糊田口法获得的切削参数最佳水准组合,能够有效改善侧面重切削制程时的切削性能,为刀具制造厂或刀具使用者寻求最佳切削条件提供参考。     

PCBN刀具高速铣削TC4钛合金切削性能与工艺参数优化研究

针对钛合金TC4(Ti-6Al-4V)的加工特性,采用PCBN刀具,基于单因素试验,研究高速铣削条件下工艺参数对切削力、切削振动等的影响规律,提出综合考虑切削力、切削振动、表面粗糙度的工艺参数优选方法。研究表明:切削力和切削振动随切削速度v和每齿进给量f_z的增大呈现一定的波动,随径向切深a_e和轴向切深a_p的增大而增大,切削振动受切削力影响较为显著。考虑切削性能,以材料切除率为优化目标,以切削力、切削振动和表面粗糙度等为约束条件,建立工艺参数优选模型,可得到不同约束条件下工艺参数的优选组合。     

Heat partitioning in dry milling of steel

A predictive model for heat induced shape deviations would facilitate the optimization of dry milling strategies. Results from milling experiments aiming at a physically based regression model for the heat flux distribution along the contact arc are presented. The contact arc was discretised by varying the width of cut on four levels for each combination of cutting speed, feed speed, and depth of cut. Heat fluxes to the workpiece were iteratively determined in an inverse procedure. Heat partitioning not only depends on the thermal number as in orthogonal cutting but also on the feed speed and the depth of cut.     

On the dynamics of ball end milling: modeling of cutting forces and stability analysis

This paper presents a dynamic force model and a stability analysis for ball end milling. The concept of the equivalent orthogonal cutting conditions, applied to modeling of the mechanics of ball end milling, is extended to include the dynamics of cutting forces. The tool is divided into very thin slices and the cutting force applied to each slice is calculated and summed for all the teeth engaged. To calculate the instantaneous chip thickness of each tooth slice, the method of regenerative chip load calculation which accounts for the effects of both the surface undulations and the instantaneous deflection is used. To include the effect of the interference of the flank face of the tool with the finished surface of the work, the plowing force is also considered in the developed model. Experimental cutting forces are obtained using a five-axis milling machine with a rotary dynamometer. The developed dynamic model is capable of generating force and torque patterns with very good agreement with the experimental data. Stability of the ball end milling in the semi-finishing operation of die cavities is also studied in this paper. The tangential and radial forces predicted by the method of equivalent orthogonal condition are fitted by the equations F_t = K_t(Z)bh_av and F_r = K_r(Z)F_t, where b is the depth of cut and h_av is the average chip thickness along the cutting edge and Z is the tool axis coordinate. The polynomial functions K_t(Z) and K_r(Z) are the cutting force constants. The interdependency of the axial and radial depths of cut in ball end milling results in an iterative solution of the characteristic equation for the critical width of cut and spindle speed. In addition, due to different cutting characteristics of the cutting edge at different heights of the ball nose, stability lobes are represented by surfaces. Comparison of the time domain simulation for the shoulder removal process in die cavity machining with the analytical predictions shows that the proposed method is capable of accurate prediction of the stability lobes.     

Mechanics and dynamics of thread milling process

This paper presents the mechanics and dynamics of thread milling operations. The tool follows a helical path around the wall of the pre-machined hole in thread milling, which has varying tool-part engagement and cut area during one threading cycle. The variation of cut area that reflects the kinematics of threading as well as structural vibrations is modeled along the helical, threading path. The mechanics of the process are first experimentally proven, followed by the formulation of dynamic thread milling which is periodic in threading cycle, in a semi-discrete time domain. The stability of the operation is predicted as a function of spindle speed, axial depth of cut, cutter path and tool geometry. The mechanics and stability models are experimentally proven in opening M16×2 threads with a five-fluted helical tool on a Steel AISI1045 workpiece.