球头铣刀动力学模型及其铣削加工稳定性的研究

根据螺旋刃球头铣刀的几何模型,考虑切削加工时刀齿的有交切削区及再生效应,建立球头铣刀的单刃切削力模型;进行模态实验和参数识别,建立螺旋刃球头铣刀的动力学模型;在Matlab环境下,基于龙格-库塔法对球头铣刀铣削加工过程稳定性进行仿真,结果表明:该模型能很好地描述切削过程中的稳定性及振动等动学特性,对于实际铣削加工过程及实验机的优化设计具有指导意义。     

螺旋玉米铣刀铣削TC4材料的切削参数优化研究

针对螺旋玉米铣刀铣削TC4材料受力不均匀,加工效率低的问题,对螺旋玉米铣刀单刀片模型及切削力模型进行分析,通过AdvantEdge FEM软件进行相关的螺旋玉米立铣刀刀片结构参数,刀体参数设置,网络划分等得到螺旋玉米铣刀加工过程中的切削力及切削过程中的温度仿真图形,并以此仿真参数基础,进行验证加工。研究结果表明:对螺旋玉米铣刀铣削力分析后,能为加工TC4材料时更合理的选择切削用量,提高难加工材料的加工效率,减少刀具的磨损。     

新型双刃可转位球头立铣刀设计及其加工仿真研究

球头立铣刀是数控机床上加工复杂曲面的高性能结构化刀具,为了提高球头立铣刀的性能,设计了一款新型双刃可转位球头立铣刀,并在CAD/CAM软件Pro/E中建立其三维实体模型;导入金属切削工艺有限元软件AdvantEdge中进行铣削加工模拟仿真,得到加工过程中切削性能参数随时间的变化关系,并与某标准整体式球头立铣刀的铣削加工进行对比分析。结果表明:该铣刀的性能均较优,验证了文中设计的可行性,分析结果为球头立铣刀的设计优化与加工应用提供了参考。     

铣刀的力学和动力学广义建模

本文介绍工业上使用最多的立铣和镶齿铣刀的广义数学模型.立铣刀的几何形状用环绕刀体参量外形的螺旋槽建模.镶齿铣刀的刀刃几何,用每一刀片的局部坐标系定义,并用刀具总坐标系在刀体上对其定位和定向.对两种情况用数学表达了刀刃的坐标.使用铣削时的纯运动学,包括刀具和工件两者的结构振动,估计每一切削点处的切屑厚度.用沿与工件接触的每一切削刃或刀齿积分处理,可预断出任意立铣刀和镶齿铣刀的切削力、振动、表面粗糙度及颤振稳定性图.对螺旋锥球头、大圆孤立铣刀和镶片铣刀,预断和测量出的切削力、表面粗糙度和稳定性图,为提出的广义立铣分析的有效性作了说明.集成到先进切削加工模拟程序中的算法,可用于铣削加工中的工艺计划,以避免颤振、扭矩和功率极限约束及尺寸形成误差.     

不同螺旋角度立铣刀切削性能研究

主要介绍在特定的铣削条件下,不同螺旋角度铣刀如何影响其切削性能。先利用DEFORM软件仿真不同螺旋角度立铣刀的铣削过程,得到了切削力变化曲线,从切削力大小变化来分析铣刀的切削性能。接着进行实体铣削实验,用不同螺旋角度铣刀铣削不同材质的工件,除了螺旋角度外,其他的参数如前后角等规定统一,铣削完后观察不同螺旋角度的铣刀对已铣削工件表面粗糙度的影响,并记录数据。最后对比两者数据,分析得出螺旋角度越大切削力越小、工件表面越光滑的结论。     

球头铣刀铣削斜面的三维有限元仿真研究

在能源动力、汽车、航空航天、模具制造等关键零部件的加工过程中,球头铣刀因其特有的刀具几何结构,常作为零件加工的最终成型刀具。考虑到在球头铣刀立铣加工中不同的刀具与工件相对姿态会对切削过程产生不同的影响,本文研究切屑形成和不同走刀方式下切削过程中各物理量(切削力、切削温度等)的变化情况,结合有限元仿真技术在切削加工中的应用,建立硬质合金球头铣刀铣削斜面的有限元模型,模拟相同切削参数下,八种不同走刀方式的球头铣削过程,分析刀具切入切出工件时切屑的形成过程,探究切削力和切削温度的变化规律。仿真结果表明:不同的走刀方式,平均切削合力各不相同,同时切屑和工件的最大切削温度也出现较大差异,而斜坡上坡逆铣的走刀方式所对应的平均切削合力和最大切削温度均最优。     

通用螺旋立铣刀的力学和动力学模型(一)

在工业上使用各种形状的螺旋立铣刀.在航空和宇航、汽车和模具工业上,广泛使用螺旋圆柱、螺旋球头、圆锥螺旋球头、大圆角和专用立铣刀.每种铣刀的形状可能不同,但在每个刀刃切削点切削过程的力学和动力学是共同的.本文介绍工业上使用的大多数螺旋立铣刀的广义数学模型.立铣刀形状用绕参数包络包缠的螺旋槽建模.沿参数螺旋槽的刀刃点的坐标用数学表出.应用包含刀具和工件两者振动结构的纯铣削运动学,估计出每一切削点处的切屑厚度.沿和工件接触的每一切削刃进行积分,对任意立铣可预测出切削力、振动、尺寸表面粗糙度和颤振稳定性图.预测出的切削力、表面粗糙度和稳定性图,对于球头、螺旋锥球头和大圆角立铣,可证实本文提出的广义立铣分析方法的可行性.     

面齿轮高速铣削表面粗糙度建模与实验分析

根据对面齿轮高速铣削齿面表面粗糙度的形成机理,分析了面齿轮高速铣削加工中的面齿轮齿面方程,建立了面齿轮高速铣削加工中的铣刀运动轨迹方程。根据高速铣削加工过程中球头铣刀刀刃实际扫成面的交点方程的坐标系,求出高速铣削残留高度。根据球头铣刀受力偏心和弯曲变形,求出面齿轮高速铣削瞬态铣削高度,进而编写M文件计算不同参数变化时对表面粗糙度的影响,通过计算值与实测值的对比,其最大误差在12.8%,结果表明,粗糙度数学模型计算值和实测值基本一致。     

铣削过程中不同铣刀螺旋角对切削力系数影响研究

铣削加工中,铣刀螺旋角的大小对切削力系数具有决定性影响,进而影响整个铣削过程中的稳定性。为了实现正确计算不同螺旋角铣刀铣削过程中对切削力大小的影响,文章提出两种切削力系数计算方法,分别是基于传统实验测量和正交斜变换的混合计算方法以及泰勒级数法。首先根据现有知识和相关理论建立了混合计算方法和泰勒级数法的数学模型;然后利用abaqus软件对五种不同螺旋角铣刀进行铣削仿真实验得到混合计算方法所需要的切削角和剪切力,用提出的两种方法分别计算铣削过程中的三向切削力;最后通过仿真实验获得的三向切削力值对比证明了混合计算方法和泰勒级数法计算螺旋角对切削力系数影响的准确性。     

变齿距铣刀高速微铣削的动态特性及稳定性研究

在高速微铣削加工过程中,提高生产效率和零件质量的需求日益强烈,这使得机床一直在系统的动态稳定性极限附近工作,而机床颤振的存在是限制微铣削加工生产率的主要障碍.基于颤振稳定性的准确预测,能采取一些措施来提高动态稳定性极限,例如通过改变铣刀结构.提出了数值分析与铣削实验相结合的方法,采用变齿距微铣刀来研究铣削加工的动态特性和稳定性.另外提出了采用时域仿真的输出力来表征加工稳定性的新方法,采用变齿距铣刀可以非常有效地提高某些速度范围的颤振稳定性.对于选定刀具的加工,这种方法可以用于加工优化,或在设计阶段预测刀具新型结构的性能.     

Mechanistic identification of specific force coefficients for a general end mill

The paper presents expressions for semi-empirical mechanistic identification of specific cutting and edge force coefficients for a general helical end mill from milling tests at an arbitrary radial immersion. The expressions are derived for a mechanistic force model in which the total cutting force is described as a sum of the cutting and edge forces. Outer geometry of the end mill is described by a generalized mathematical model valid for a variety of end mill shapes, such as cylindrical, taper, ball, bull nose, etc. The derivations follow a procedure originally proposed for a cylindrical end mill. The procedure itself is improved by including the helix angle in evaluation of the average edge forces. The resulting expressions for the specific force coefficients are verified by simulations and experiments.     

Mechanics and dynamics of general milling cutters.: Part I: helical end mills

A variety of helical end mill geometry is used in the industry. Helical cylindrical, helical ball, taper helical ball, bull nosed and special purpose end mills are widely used in aerospace, automotive and die machining industry. While the geometry of each cutter may be different, the mechanics and dynamics of the milling process at each cutting edge point are common. This paper presents a generalized mathematical model of most helical end mills used in the industry. The end mill geometry is modeled by helical flutes wrapped around a parametric envelope. The coordinates of a cutting edge point along the parametric helical flute are mathematically expressed. The chip thickness at each cutting point is evaluated by using the true kinematics of milling including the structural vibrations of both cutter and workpiece. By integrating the process along each cutting edge, which is in contact with the workpiece, the cutting forces, vibrations, dimensional surface finish and chatter stability lobes for an arbitrary end mill can be predicted. The predicted and measured cutting forces, surface roughness and stability lobes for ball, helical tapered ball, and bull nosed end mills are provided to illustrate the viability of the proposed generalized end mill analysis.     

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.     

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.     

Prediction of cutting forces in milling of circular corner profiles

This paper proposes an approach to predict the cutting forces in peripheral milling of circular corner profiles in which varying radial depth of cut is encountered. The geometric relationship between an end mill and the corner profile is investigated and a mathematical model is presented to describe the different phases of the cutter/workpiece contact. The milling process for circular corner is discretized into a series of steady-state cutting processes, each with different radial depth of cut determined by the instantaneous position of the end mill relative to the workpiece. A time domain analytical model of cutting forces for the steady-state machining conditions is introduced to each segmented process for the cutting force prediction. The predicted cutting forces can be calculated in terms of tool/workpiece geometry, cutting parameters and workpirece material property, as well as the relative position of the tool to workpiece. Experiments are conducted and the measured forces are compared to the predictions for the verification of the proposed method.     

Runout effects in milling: Surface finish, surface location error, and stability

This paper investigates the effect of milling cutter teeth runout on surface topography, surface location error, and stability in end milling. Runout remains an important issue in machining because commercially-available cutter bodies often exhibit significant variation in the teeth/insert radial locations; therefore, the chip load on the individual cutting teeth varies periodically. This varying chip load influences the machining process and can lead to premature failure of the cutting edges. The effect of runout on cutting force and surface finish for proportional and non-proportional tooth spacing is isolated here by completing experiments on a precision milling machine with 0.1 μm positioning repeatability and 0.02 μm spindle error motion. Experimental tests are completed with different amounts of radial runout and the results are compared with a comprehensive time-domain simulation. After verification, the simulation is used to explore the relationships between runout, surface finish, stability, and surface location error. A new instability that occurs when harmonics of the runout frequency coincide with the dominant system natural frequency is identified.     

A three-dimensional analytical cutting force model for micro end milling operation

In the present day manufacturing arena one of the most important fields of interest lies in the manufacturing of miniaturized components. End milling with fine-grained carbide micro end mills could be an efficient and economical means for medium and small lot production of micro components. Analysis of the cutting force in micro end milling plays a vital role in characterizing the cutting process, in estimating the tool life and in optimizing the process. A new approach to analytical three-dimensional cutting force modeling has been introduced in this paper. The model determines the theoretical chip area at any specific angular position of the tool cutting edge by considering the geometry of the path of the cutting edge and relates this with tangential cutting force. A greater proportion of the helix face of the cutter participating in the cutting process differs the cutting force profile in micro end milling operations a bit from that in conventional end milling operations. This is because of the reason that the depth-of-cut to tool diameter ratio is much higher in micro end milling than the conventional one. The analytical cutting force expressions developed in this model have been simulated for a set of cutting conditions and are found to be well in harmony with experimental results.     

On cutting parameters selection for plunge milling of heat-resistant-super-alloys based on precise cutting geometry

In plunge milling operation the tool is fed in the direction of the spindle axis which has the highest structural rigidity, leading to the excess high cutting efficiency. Plunge milling operation is one of the most effective methods and widely used for mass material removal in rough/semi-rough process while machining high strength steel and heat-resistant-super-alloys. Cutting parameters selection plays great role in plunge milling process since the cutting force as well as the milling stability lobe is sensitive to the machining parameters. However, the intensive studies of this issue are insufficient by researchers and engineers. In this paper a new cutting model is developed to predict the plunge milling force based on the more precise plunge milling geometry. In this model, the step of cut as well as radial cutting width is taken into account for chip thickness calculation. Frequency domain method is employed to estimate the stability of the machining process. Based on the prediction of the cutting force and milling stability, we present a strategy to optimize the cutting parameters of plunge milling process. Cutting tests of heat-resistant-super-alloys with double inserts are conducted to validate the developed cutting force and cutting parameters optimization models.     

Simulation of flank milling processes

The paper presents prediction of cutting forces when flank milling ruled surfaces with tapered, helical, ball end mills. The geometric model of the workpiece is imported from standard CAD systems, and the tapered helical ball end mill is modeled as the combination of sphere and cone primitives in ACIS^© solid modeling environment. The intersection of cutter and part with a ruled surface is evaluated, and the cutter entry into and exit angles from the work material are modeled, and stored as a function of tool center coordinates along the path. The cutter entry and exit angles, the immersion angles, are used as boundary conditions in predicting the cutting forces along the path. The methodology allows prediction of cutting load distribution on the tool and part, as well optimization of machining cycle times by scheduling the feedrate in such a way that torque, power and static deflections can be maintained at safe levels.