Analysis of cutting force coefficients in high-speed ball end milling at varying rotational speeds

In high-speed ball end milling, cutting forces influence machinability, dimensional accuracy, tool failure, tool deflection, machine tool chatter, vibration, etc. Thus, an accurate prediction of cutting forces before actual machining is essential for a good insight into the process to produce good quality machined parts. In this article, an attempt has been made to determine specific cutting force coefficients in ball end milling based on a linear mechanistic model at a higher range of rotational speeds. The force coefficients have been determined based on average cutting force. Cutting force in one revolution of the cutter was recorded to avoid the cutter run-out condition (radial). Milling experiments have been conducted on aluminum alloy of grade Al2014-T6 at different spindle speeds and feeds. Thus, the dependence of specific cutting force coefficients on cutting speeds has been studied and analyzed. It is found that specific cutting force coefficients change with change in rotational speed while keeping other cutting parameters unchanged. Hence, simulated cutting forces at higher range of rotational speed might have considerable errors if specific cutting force coefficients evaluated at lower rotational speed are used. The specific cutting force coefficients obtained analytically have been validated through experiments.     

Improved dynamic cutting force model in ball-end milling. Part I: theoretical modelling and experimental calibration

An accurate cutting force model of ball-end milling is essential for precision prediction and compensation of tool deflection that dominantly determines the dimensional accuracy of the machined surface. This paper presents an improved theoretical dynamic cutting force model for ball-end milling. The three-dimensional instantaneous cutting forces acting on a single flute of a helical ball-end mill are integrated from the differential cutting force components on sliced elements of the flute along the cutter-axis direction. The size effect of undeformed chip thickness and the influence of the effective rake angle are considered in the formulation of the differential cutting forces based on the theory of oblique cutting. A set of half immersion slot milling tests is performed with a one-tooth solid carbide helical ball-end mill for the calibration of the cutting force coefficients. The recorded dynamic cutting forces are averaged to fit the theoretical model and yield the cutting force coefficients. The measured and simulated dynamic cutting forces are compared using the experimental calibrated cutting force coefficients, and there is a reasonable agreement. A further experimental verification of the dynamic cutting force model will be presented in a follow-up paper.     

高速铣削过程铣削力建模及析因试验分析

根据铣削过程和铣刀的几何模型,建立铣削力的瞬时表达式和平均切削力公式,给出基于响应曲面法的切削力系数的二次多项式。综合应用析因试验设计和统计分析理论,计算切削力系数的回归系数模型并分析了切削参数对切削力系数的影响规律。     

基于主轴电流的铣削力间接监测方法

实时准确地监测铣削状态对于提高加工质量与加工效率具有重要意义,切削力作为重要的加工状态监测对象,因其监测设备昂贵且安装不便而受到限制,为此提出一种考虑刀具磨损的基于主轴电流的铣削力监测方法.首先基于切削微元理论建立了考虑后刀面磨损的铣削力模型,并通过铣削实验进行铣削力模型系数标定;然后对主轴电流与铣削力的关系进行理论建...     

高速铣削超高强度钢的切削力及表面粗糙度研究

选用涂层硬质合金刀具对300M超高强度钢进行高速铣削试验,通过单因素试验和多因素正交试验法,得出铣削参数(主轴转速、每齿进给量、铣削深度)对切削力及表面粗糙度的影响规律及主次关系。对正交试验结果做最小二乘法分析,建立切削力及表面粗糙度与铣削参数之间的经验模型;对经验模型的回归方程及系数做显著性检验,并对其进行参数优化,得出铣削参数的最优组合。结果表明:主轴转速和铣削深度对切削力的作用较大,而每齿进给量对其影响相对较弱;每齿进给量对表面粗糙度作用最强,铣削深度次之,主轴转速对其作用最弱。     

Cutting force prediction for ball nose milling of inclined surface

Ball nose milling of complex surfaces is common in the die/mould and aerospace industries. A significant influential factor in complex surface machining by ball nose milling for part accuracy and tool life is the cutting force. There has been little research on cutting force model for ball nose milling on inclined planes. Using such a model ,and by considering the inclination of the tangential plane at the point of contact of the ball nose model, it is possible to predict the cutting force at the particular cutting contact point of the ball nose cutter on a sculptured surface. Hence, this paper presents a cutting force model for ball nose milling on inclined planes for given cutting conditions assuming a fresh or sharp cutter. The development of the cutting force model involves the determination of two associated coefficients: cutting and edge coefficients for a given tool and workpiece combination. A method is proposed for the determination of the coefficients using the inclined plane milling data. The geometry for chip thickness is considered based on inclined surface machining with overlapping of previous pass. The average and maximum cutting forces are considered. These two forces have been observed to be more dominating force-based parameters or features with high correlation with tool wear. The developed cutting force model is verified for various cutting conditions.     

基于斜角切削理论的钛合金螺旋铣孔切削力建模

通过分析螺旋铣孔的加工原理和计算加工过程中的运动向量,结合侧刃和底刃对切削力的影响,建立了螺旋铣孔过程的切削力解析模型。提出了基于斜角切削的切削力系数辨识方法,并根据斜角切削过程几何关系推导出摩擦角、剪切角、剪切应力的约束方程。开展切削力系数辨识试验和钛合金螺旋铣孔试验对仿真值进行验证,结果表明,切削力的仿真值与试验值误差较小,平均误差为9.55%,从而验证了斜角切削系数辨识方法的有效性和切削力模型的正确性。     

Identification of instantaneous cutting force coefficients using surface error

Cutting force coefficients are the key factors for efficient and accurate prediction of instantaneous milling force. To calibrate the coefficients, this paper presents an instantaneous milling force model including runout and cutter deformation. Also, forming of surface error is analyzed, and a surface error model considering runout is proposed. Using surface errors of two experiments completed with the same cutting conditions but different axial depth only, cutter deformation is obtained. Then, a new approach for the determination of instantaneous cutting force coefficients is provided. The method can eliminate influences of the other factors except cutter deformation and runout. A series of experiments are designed, and the results are used to identify the parameters. With the evaluated coefficients and runout parameters, the instantaneous milling force and surface error are predicted. A good agreement between predicted results and experimental results is achieved, which shows that the method is efficient, and effect of runout on surface error is not negligible.     

用广义傅里叶级数法分析棒铣刀颤振问题

采用广义傅里叶级数法分析棒铣刀的颤振问题。在考虑了主轴陀螺效应的基础上，着重分析了切向铣削力参数和径向铣削力参数对铣削系统稳定性的影响，比较了广义傅里叶级数法与基于奈奎斯特稳定性判据的非线性优化法的结果。为了验证广义傅里叶级数法的有效性和准确性，对模型进行了时域仿真。分析结果表明，在考虑了铣刀刀轴陀螺效应之后，影响颤振的因素虽然很多，但铣削力参数（包括切向参数和径向参数）是主要的，铣削力参数对不稳定区的大小和位置都有明显的影响。     

Cutting torque and tangential cutting force coefficient identification from spindle motor current

This article presents an enhanced methodology for cutting torque prediction from the spindle motor current, readily available in modern machine tool controllers. This methodology includes the development of the spindle power model which takes into account all mechanical and electrical power losses in a spindle motor for high-speed milling. The predicted cutting torque is further used to identify tangential cutting force coefficients in order to predict accurately the cutting forces and chatter-free regions for milling process planning purposes. The developed model is compared with other studies available in the literature, and it demonstrates significant improvements in terms of the completeness and accuracy achieved. The developed model is also validated experimentally, and the obtained results show good compliance between the predicted and the measured cutting torque. The developed enhanced procedure is very appealing for industrial implementation for cutting torque/force monitoring and tangential cutting force coefficient identification.     

A study on the cutting force and chip shrinkage coefficient in high-speed milling of A6061 aluminum alloy

In this paper, finite element (FE) simulation for high-speed milling of aluminum alloy was performed using a ductile fracture model with Mohr–Coulomb criterion proposed by Bai and Wierzbicki (BW). To verify the model, predicted cutting forces were compared to experimental results in the same cutting conditions. Then, further simulations were performed to estimate the cutting forces and chip shrinkage coefficients subjected to different cutting parameters such as cutting speeds, cutting depths, and clearance angles of a cutting tool. The obtained results were also used to determine optimal cutting parameters using the Taguchi method. The analysis of variance (ANOVA) was employed to investigate the influence percentage of each cutting parameter on cutting force and chip shrinkage coefficient. The simulation results showed that inclusion of strain rate in numerical model significantly improved the accuracy of estimated cutting force in comparison to experiment. The optimum values obtained for high-milling process were cutting speed 1000 m/min, cutting depth 1 mm, clearance angle 15°, and rake angle 4°.     

基于动力学约束的端面铣削工艺参数优化

工艺参数优化对提高切削过程的加工效率和加工成本具有重要意义。将铣削系统动力学作为主要约束条件,提出端面铣削工艺参数的多目标优化模型。基于铣削系统动力学分析,得到了综合切削稳定性、工件表面粗糙度、主轴转速、切削力、切削功率等约束的工艺参数多目标优化模型。通过调节权重系数实现优化方向的控制,并采用快速粒子群算法对工艺参数进行优化计算。工艺优化实例及试验表明,采用基于动力学约束的工艺参数优化方法可以获得较好的工艺参数优化结果。     

超声振动铣削加工参数对切削力的影响

为了改善传统铣削钛合金的加工条件,研究了进给方向超声振动辅助铣削对切削力的影响。定值计算了不同振动频率、振幅、铣削速度时的净切削时间比,建立了对工件施加超声振动的铣削加工三维有限元模型,根据仿真结果讨论了加工参数对进给方向切削力瞬时值的影响,并结合净切削时间比分析了加工参数对三个方向切削力平均值的影响。研究表明:施加超声振动后切削力明显减小;振动频率小于40kHz和振幅小于30μm时切削力平均值同净切削时间比变化趋势一致,当频率或振幅超过上述值时,刀具、工件间的摩擦力对切削力平均值的影响显著。     

A new method for cutting force prediction in peripheral milling of complex curved surface

The instantaneous uncut chip thickness and entry/exit angle of tool/workpiece engagement vary with tool path, workpiece geometry and cutting parameters in peripheral milling of complex curved surface, leading to the strong time-varying characteristic for instantaneous cutting forces. A new method for cutting force prediction in peripheral milling of complex curved surface is proposed in this paper. Considering the tool path, cutter runout, tool type(constant/nonconstant pitch cutter) and tool actual motion, a representation model of instantaneous uncut chip thickness and entry/exit angle of tool/ workpiece engagement is established firstly, which can reach better accuracy than the traditional models. Then, an approach for identifying of cutter runout parameters and calibrating of specific cutting force coefficients is presented. Finally, peripheral milling experiments are carried out with two types of tool, and the results indicate that the predicted cutting forces are highly consistent with the experimental values in the aspect of variation tendency and amplitude.     

A force-model-based approach to estimating cutter axis offset in ball end milling

Cutter runout due to cutter axis offset is quite common in a milling process, yet it is difficult to directly measure the runout geometry of a ball end cutter during the cutting process. This paper presents an analytical method for the estimation of cutter radial offset via forces in ball end milling. Closed form expression for the total milling force in the presence of cutter offset is first obtained. Fourier series coefficients for the offset related force component are shown to be expressed explicitly in terms of the offset geometry and serve as the basis for the identification of the offset geometry from the measured cutting forces. The offset geometry including its magnitude and the phase angle are directly calculated from the measured force component at the spindle frequency through two algebraic expressions. The identification method is finally validated by milling experiments.     

一种新的螺旋刃球头铣刀铣削力模型

为提高铣削加工的安全性和生产效率，有必要在加工实际进行之前准确地预测切削过程的物理信息，如铣削力、刀具振动等。给出了球头铣刀丸线几何模型，采用理论削力分析与实验--系数识别相结合的方法建立了新的螺旋刃球头铣刀的铣削力模型。对不同切削条件下的铣削力进行了仿真，与实验测量数据吻合良好，证明离线仿真可以对铣削力做出较准确的预测。     

石英玻璃微铣削加工的离散元模拟与试验分析

针对石英玻璃的微铣削过程,采用离散元模拟软件PFC3D建立真实的离散元模型,模拟裂纹的生成与扩展情况,得到铣削力曲线图以及铣削过程的较优加工工艺参数,并通过铣削力试验验证了石英玻璃三维离散元模型有效性及离散元法模拟石英玻璃切削过程的合理性。基于模型和试验一致,得出不同铣削参数下铣削力的变化规律。结果表明:铣削力随主轴转速的增加则先减小后增加再减小,随切削深度和进给速度的增加而增加,随刀具倾角的增加则先增加后减小。     

Chatter stability prediction in milling using time-varying uncertainties

The chatter stability in milling severely affects productivity and quality of machining. Tool wear causes both the cutting coefficient and the process damping coefficient, but also other parameters to change with cutting time. This variation greatly reduces the accuracy of chatter prediction using conventional methods. To solve this problem, we consider the cutting coefficients of the milling system to be both random and time-varying variables and we use the gamma process to predict cutting coefficients for different cutting times. In this paper, a time-varying reliability analysis is introduced to predict chatter stability and chatter reliability in milling. The relationship between stability and reliability is investigated for given depths and spindle speeds in the milling process. We also study the time-varying chatter stability and time-varying chatter reliability methods theoretically and with experiments. The results of this study show that the proposed method can be used to predict chatter with high accuracy for different cutting times.     

Investigation of the milling stability based on modified variable cutting force coefficients

The cutting force signal distortion is caused by the dynamic characteristics of cutting force testing system. In order to handle this issue, we propose two improvements in the traditional inverse filtering technology. Firstly, we use three-spline interpolation method instead of the curve fitting method to fit the frequency response function of the test system which basically improves the accuracy of fitting. Secondly, the low-pass filter is added before the inverse filter to eliminate the influence of the high-frequency noise signal on the cutting force signal. We choose the cavity-free surface of outer covering parts of mold of automobile as research objects. The inverse filter dynamic compensation technology has been used to remove the influence of the dynamic characteristics of the test system and the high-frequency noise on the cutting force signal. The effectiveness of the proposed method is verified by relative milling experiments. Based on the experimentally measured forces after dynamic compensation, the modified cutting force coefficients are obtained using the average milling force method. The variation law of the cutting force coefficients with the axial depth, the radial width, and the feed rate is examined. Based on the modified variable cutting force coefficients, the 3D stability of the ball end milling cutter surface has been obtained using full-discretization approach. Combining the results from the cutting experiment and the nonlinear method, the stability prediction based on the modified variable cutting force coefficient can improve the prediction accuracy. The results provide theoretical support for the optimization of the machining process of the cavity-free surface of outer covering parts of mold of automobile.