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.     

Three dimensional cutting force analysis in end milling

The analysis of cutting forces plays an important part in the design of machine tool systems as well as in the planning, optimization, and control of machining processes. This paper presents a three-dimensional model of cutting forces in peripheral end milling in terms of material properties, cutting parameters, machining configuration, and tool/work geometry. Based on the relationship of the local cutting force and the chip load, the total cutting force model is established via the angle domain convolution integration of the local forces in the feed, cross feed, and axial directions. The integration is taken along the cutter axis and summarized across the cutting flutes. The convolution integral leads to a periodic function of cutting forces in the angle domain and an explicit expression of the dynamic cutting force components in the frequency domain. The closed-form nature of the expressions allows the prediction and optimization of cutting forces to be performed without the need of numerical iterations. To assess the fidelity of the analytical model, experimental data from end milling tests are presented in the context of three dimensional time waveforms, power spectra, and phase angles, in comparison to the values predicted by the model.     

Theoretical modelling of cutting forces in helical end milling with cutter runout

A theoretical cutting force model for helical end milling with cutter runout is developed using a predictive machining theory, which predicts cutting forces from the input data of workpiece material properties, tool geometry and cutting conditions. In the model, a helical end milling cutter is discretized into a number of slices along the cutter axis to account for the helix angle effect. The cutting action for a tooth segment in the first slice is modelled as oblique cutting with end cutting edge effect and tool nose radius effect, whereas the cutting actions of other slices are modelled as oblique cutting without end cutting edge effect and tool nose radius effect. The influence of cutter runout on chip load is considered based on the true tooth trajectories. The total cutting force is the sum of the forces at all the cutting slices of the cutter. The model is verified with experimental milling tests.     

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。     

New mathematical method for the determination of cutter runout parameters in flat-end milling

The cutting force prediction is essential to optimize the process parameters of machining such as feed rate optimization, etc. Due to the significant influences of the runout effect on cutting force variation in milling process, it is necessary to incorporate the cutter runout parameters into the prediction model of cutting forces. However, the determination of cutter runout parameters is still a challenge task until now. In this paper, cutting process geometry models, such as uncut chip thickness and pitch angle, are established based on the true trajectory of the cutting edge considering the cutter runout effect. A new algorithm is then presented to compute the cutter runout parameters for flat-end mill utilizing the sampled data of cutting forces and derived process geometry parameters. Further, three-axis and five-axis milling experiments were conducted on a machining centre, and resulting cutting forces were sampled by a three-component dynamometer. After computing the corresponding cutter runout parameters, cutter forces are simulated embracing the cutter runout parameters obtained from the proposed algorithm. The predicted cutting forces show good agreements with the sampled data both in magnitude and shape, which validates the feasibility and effectivity of the proposed new algorithm of determining cutter runout parameters and the new way to accurately predict cutting forces. The proposed method for computing the cutter runout parameters provides the significant references for the cutting force prediction in the cutting process.     

平头立铣刀铣削力模型中积分限的确定方法

在铣削力预报的研究中 ,通常采用的方法是将铣刀沿其轴线方向逐层划分为很薄的微单元 ,对每一个微单元可认为是一个单刃刀具的斜角切削过程 ,通过建立微单元上的切削力模型并沿轴线方向积分来求得总的切削力 ,轴向积分限通常是通过角度换算获取 ,比较繁琐。本文对刀具的几何特征进行了描述 ,建立了求取平头立铣刀铣削力模型角度积分限的通用方法 ,该方法通过分析刀具几何特征和加工类型 ,直接获取角度积分限 ,避免了繁琐的轴向积分限的计算 ,并通过算例验证了该方法的有效性。     

基于斜角切削的曲线端铣切削力建模

切削力预测是制定与优化加工工艺的重要环节。针对曲线端铣加工过程,提出一种基于斜角切削的切削力建模方法。将刀具沿轴向微分,以曲线微分几何计算微元刃上的工作基面。在微元刃的工作法平面参考系中,应用最小能量原理,构建微元刃中力矢量、速度矢量、流屑角、法向摩擦角、法向剪切角及剪应力等切削参数之间的约束。以单齿直线铣削试验对切削参数进行标定,其中法向摩擦角、法向剪切角及剪应力等可表示为瞬时未变形切屑厚度的函数。选取高强度钢PCrNi3MoVA试件,分别进行圆弧和Bézier曲线端铣加工试验。试验结果表明,曲线端铣时切削力的变化与瞬时进给方向和曲线曲率相关。切削力预测值的幅值大小和变化趋势与试验值一致,验证了该切削力建模方法的有效性。     

On modeling of cutting forces in micro-end milling operation

Micro-end milling is used for manufacturing of complex miniaturized components precisely in wide range of materials. It is important to predict cutting forces accurately as it plays vital role in controlling tool and workpiece deflections as well as tool wear and breakage. The present study attempts to incorporate process characteristics such as edge radius of cutting tool, effective rake and clearance angles, minimum chip thickness, and elastic recovery of work material collectively while predicting cutting forces using mechanistic model. To incorporate these process characteristics effectively, it is proposed to divide cutting zone into two regions: shearing- and ploughing-dominant regions. The methodology estimates cutting forces in each partitioned zone separately and then combines the same to obtain total cutting force at a given cutter rotation angle. The results of proposed model are validated by performing machining experiments over a wide range of cutting conditions. The paper also highlights the importance of incorporating elastic recovery of work material and effective rake and clearance angle while predicting cutting forces. It has been observed that the proposed methodology predicts the magnitude and profile of cutting forces accurately for micro-end milling operation.     

Cutting forces prediction in generalized pocket machining

Cutting force prediction is important for the planning and optimization of machining process. This paper presents an approach to predict the cutting forces for the whole finishing process of generalized pocket machining. The equivalent feedrate is introduced to quantify the actual speed of cutting cross-section in prediction of cutting force for curved surface milling. For convenience, to analyze the process with varying feed direction and cutter engagement, the milling process for generalized pocket is discretized into a series of small processes. Each of the small processes is transformed into a steady-state machining, using a new approximation method. The cutting geometries of each discrete process, i.e., feed direction, equivalent feedrate per tooth, entry angle, and exit angle are calculated based on the information refined from NC code. An improved cutting force model which involves the effect of feed direction on cutting forces prediction is also presented. A machining example of a freeform pocket is performed, and the measured cutting forces are compared with the predictions. The results show that the proposed approach can effectively predict the variation of cutting forces in generalized pocket machining.     

An Improved Method for the Determination of 3D Cutting Force Coefficients and Runout Parameters in End Milling

A simple improved method is suggested for determining constant cutting force coefficients, irrespective of the cutting condition and cutter rotation angle. This can be achieved through the combination of experimentally deternimed cutting forces with those from simulation, performed by a mechanistic cutting force model and a geometric uncut chip thickness model. Additionally, this study presents an approach that estimates runout-related parameters, and the runout offset and its location angle, using only one measurement of cutting force. This method of estimating 3D end milling force coefficients was experimentally verified for a wide range of cutting conditions, and gave significantly better predictions of cutting forces than any other methods. The estimated value of the runout offset also agreed well with the measured value.     

曲面铣削过程加工路径对切削力和磨损的影响研究

针对不同走刀路径下的复杂曲面加工过程进行球头铣刀铣削Cr12MoV加工复杂曲面研究,分析不同走刀路径下铣削力和刀具磨损的变化趋势。试验结果表明:通过对比分析直线铣削和曲面铣削过程中的最大未变形切屑厚度,可以得出单周期内曲面铣削的力大于直线铣削过程的力,铣削相同铣削层时环形走刀测得的切削力普遍大于往复走刀测得的切削力;以最小刀具磨损为优化目标,运用方差分析法分析得出不同走刀路径的影响刀具磨损的主次因素,同时利用残差分析方法建立球头铣刀加工复杂曲面刀具磨损预测模型,并通过试验进行验证。     

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.     

Calculations of chip thickness and cutting forces in flexible end milling

In the end milling process of a flexible workpiece, it is well recognized that the precise determination of the instantaneous uncut chip thickness (IUCT) is essential for the cutting force calculation. This paper will present a general method that incorporates simultaneously the cutter/workpiece deflections and the immersion angle variation into the calculation of the IUCT and cutting forces. Contributions are twofold. Firstly, considering the regeneration model, a new scheme for the IUCT calculation is determined based on the relative positions between two adjacent tooth path centers. Secondly, a general approach is established to perform numerical validations. On one hand, the engagement/separation of the cutter from the workpiece is instantaneously identified. On the other hand, the calculation of the IUCT is iteratively performed. To demonstrate the validity of the method, several examples are used to show the convergence history of the cutting force and the IUCT during the flexible end milling process. Both theoretical analyses and numerical results show that the regeneration mechanism is short lived and will disappear after several tooth periods in flexible static end milling process .     

Dynamic Force Modelling for a Ball-End Milling Cutter Based on the Merchant Oblique Cutting Theory

A new dynamic force model for a ball-end milling cutter is presented in this paper. Based on the principle of the power remaining constant in cuts, the Merchant oblique cutting theory has been successfully used for the differential cutting edge segment of a ball-end milling cutter. A concise method for characterising the relationship of the complex geometry of a ball-end milling cutter and the milling process variables is determined, so that the force coefficients can be decomposed. The geometric property of a ball-end milling cutter and the dynamics of the milling process are integrated into the general model to eliminate the need for the experimental calibration of each cutter geometry and milling process variable. The milling experiments prove that this model can predict accurately the cutting forces in three Cartesian directions.     

平前刀面球头铣刀的几何角度分析

分析了平前刀面球头铣刀的几何角度,给出了该铣刀的刀刃参数方程,推导了铣刀法向前角、刃倾角和主偏角计算公式。     

基于时域特性的铣刀磨损状态信息提取

在分析铣削加工过程特点的基础上，采用后刀面磨损带面积为铣刀磨损的评价指标，建立了基于切削力和主轴电机功率的铣刀磨损模型，探讨了基于时域特性的铣刀磨损状态信息提取的相关技术。理论分析和实验结果表明，切削力和主轴电机功率的量纲一系数Cv的变化与铣刀后刀面磨损带的磨损过程直接相关。采用切削力和主轴电机功率的量纲一系数Cv作为铣刀后刀面磨损带面积的监测信号能真实地反映其磨损过程。     

A solid modeler based ball-end milling process simulation

A system for geometric and physical simulation of the ball-end milling process using solid modeling is presented in this paper. A commercially available geometric engine is used to represent the cutting edge, cutter and updated part. The ball-end mill cutter modeled in this study is an insert type ball-end mill and the cutting edge is generated by intersecting an inclined plane with the cutter ball nose. The contact face between cutter and updated part is determined from the solid model of the updated part and cutter solid model. To determine cutting edge engagement for each tool rotational step, the intersections between the cutting edge with boundary of the contact face are determined. The engaged portion of the cutting edge for each tool rotational step is divided into small differential oblique cutting edge segments. Friction, shear angles and shear stresses are identified from orthogonal cutting data base available in the open literature. For each tool rotational position, the cutting force components are calculated by summing up the differential cutting forces. The instantaneous dynamic chip thickness is computed by summing up the rigid chip thickness, the tool deflection and the undulations left from the previous tooth, and then the dynamic cutting forces are obtained. For calculating the ploughing forces, Wu's model is extended to the ball-end milling process [21]. The total forces, including the cutting and ploughing forces, are applied to the structural vibratory model of the system and the dynamic deflections at the tool tip are predicted. The developed system is verified experimentally for various up-hill and down-hill angles.     

基于铣削力识别的铣削监测与铣刀故障诊断

为提高铣削过程监测与刀具故障诊断精度，通过测量铣床的频响函数和在铣削加工中的铣床振动加速度响应信号，用载荷识别的方法计算铣削力，分别得到了用4刀齿和2刀齿加工时横向铣削力的识别结果，所得到的铣削力曲线与加工工况吻合良好。以所识别铣削力为特征参量，用ART2神经网络进行了铣削过程监测与铣刀故障诊断，其结果比直接用振动响应信号进行监测与诊断更可靠，从而得到较好的监测诊断结论。     

航空钛合金铣削过程有限元数值模拟

基于材料损伤理论确定了切屑分离准则,建立了钛合金TC4构件铣削过程的有限元模型,利用商业有限元软件(ABAQUS),在给定切削参数条件下,采用不同几何参数(前角、后角、螺旋角)的刀具对钛合金TC4的铣削过程进行了有限元模拟,研究了切削力和切削温度随刀具角度变化的规律,结果表明:铣刀的前角在10°~20°,后角为12°~20°,螺旋角为30°~45°时比较适合钛合金TC4的铣削。     

Improved dynamic cutting force model in peripheral milling. Part II: experimental verification and prediction

Cutting trials reveal that a measure of cutter run-out is always unavoidable in peripheral milling. This paper improves and extends the dynamic cutting force model of peripheral milling based on the theoretical analytical model presented in Part I [1], by taking into account the influence of the cutter run-out on the undeformed chip thickness. A set of slot milling tests with a single-fluted helical end-mill was carried out at different feed rates, while the 3D cutting force coefficients were calibrated using the averaged cutting forces. The measured and predicted cutting forces were compared using the experimentally identified force coefficients. The results indicate that the model provides a good prediction when the feed rate is limited to a specified interval, and the recorded cutting force curves give a different trend compared to other published results [8]. Subsequently, a series of peripheral milling tests with different helical end-mill were performed at different cutting parameters to validate the proposed dynamic cutting force model, and the cutting conditions were simulated and compared with the experimental results. The result demonstrates that only when the vibration between the cutter and workpiece is faint, the predicted and measured cutting forces are in good agreement.