Process modeling and toolpath optimization for five-axis ball-end milling based on tool motion analysis

In free-form surface machining, the prediction of five-axis ball-end milling forces is quite a challenge due to difficulties of determining the underformed chip thickness and engaged cutting edge. Part and tool deflections under high cutting forces may result in poor part quality. To solve these concerns, this paper presents process modeling and optimization method for five-axis milling based on tool motion analysis. The method selected for geometric stock modeling is the dexel approach, and the extracted cutter workpiece engagements are used as input to a force prediction. The cutter entry?Cexit angles and depth of cuts are found and used to calculate the instantaneous cutting forces. The process is optimized by varying the feed as the tool?Cworkpiece engagements vary along the toolpath, and the unified model provides a powerful tool for analyzing five-axis milling. The new feedrate profiles are shown to considerably reduce the machining time while avoiding process faults.     

An intelligent feedrate scheduling based on virtual machining

Off-line feedrate scheduling is an advanced methodology to automatically determine optimum feedrates for NC code modification. However, most existing feedrate scheduling systems have limitations in generating the optimised feedrates because they use the material removal rate or the cutting force model which is dependent on cutting conditions. This paper proposes a feedrate scheduling system based on an improved cutting force model that can predict cutting forces accurately in general end milling situations. Original blocks of NC code were divided into smaller ones with the optimised feedrates to adjust the peak value of cutting forces to a constant value. The acceleration and deceleration characteristics for a given machine tool were considered for realistic feedrate scheduling. Moreover, a modified type of Z-map model was developed to reduce the entry/exit angle calculation error in the cutting force prediction and named the moving edge node Z-map (ME Z-map). Pocket machining experiments show that the proposed method is accurate and efficient in maintaining the cutting force at a desired level.     

Prediction of cutting forces in helical milling process

The prediction of cutting forces is important for the planning and optimization of machining process in order to reduce machining damage. Helical milling is a kind of hole-machining technique with a milling tool feeding on a helical path into the workpiece, and thus, both the periphery cutting edges and the bottom cutting edges all participated in the machining process. In order to investigate the characteristics of discontinuous milling resulting in the time varying undeformed chip thickness and cutting forces direction, this paper establishes a novel analytic cutting force model of the helical milling based on the helical milling principle. Dynamic cutting forces are measured and analyzed under different cutting parameters for the titanium alloy (Ti–6Al–4V). Cutting force coefficients are identified and discussed based on the experimental test. Analytical model prediction is compared with experiment testing. It is noted that the analytical results are in good agreement with the experimental data; thus, the established cutting force model can be utilized as an effective tool to predict the change of cutting forces in helical milling process under different cutting conditions.     

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.     

Feedrate optimisation/scheduling on sculptured surface machining: a comprehensive review, applications and future directions

Free-form or sculptured surface milling is one of the continually used manufacturing processes for die/mould, aerospace (especially turbine blades), precision machine design, bio-medical devices and automotive industries. Developments of machining technologies for quality enhancement of machining results have become a very important fact in current real industry. Therefore, reducing milling time, tool wear, cutter deflection and improving surface texture quality and machining operations through adaptation and optimisation of tool feedrates based on changing surface geometry in sculptured surface machining is a great step in this direction. Various feedrate optimisation strategies have different feedrate rescheduling control parameters such as chip thickness, material removal rate (MRR), min(mrr,chip,force), max(expo.Acc/dec) and resultant forces. Some commercial CAM softwares come with MRR-based feedrate optimisation algorithms which have a very short calculation time. However, commercial feedrate scheduling systems have some limitations in generating the scheduled feedrates because they use the MRR or the cutting force model which is dependent on milling conditions. However, for the processes in which machining precision/accuracy is very important, it is inevitable that mechanistic force-based feedrate optimisation approaches, for which the calculation time is improved, will be integrated into commercial CAM software packages. Here, developing only the mechanistic cutting force-based algorithm is not enough. In this paper, improvement and optimisation of machining feedrate value, which is one of the cutting parameters which has a tremendous effect on the precise machining of free-form surfaces, was discussed by using the virtual machining framework. For this purpose, the boundary representation solid modelling technique-based free-form milling simulation and feedrate optimisation system integrated with commercial CAD/CAM software is developed for three-axis ball-end milling. This review study includes the information regarding the following topics: The algorithms developed for the feedrate value optimisation, MRR calculation approaches, cutting force computation methods, details of algorithms, the effects on the surface accuracy, the effects on the machining time, the capabilities of the present commercial CAM software packages, the encountered difficulties and overcoming those difficulties, recent developments and future research directions.     

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。     

螺旋铣孔工艺的切削稳定性及工艺参数规划

以螺旋铣孔工艺时域解析切削力建模、时域与频域切削过程动力学建模、切削颤振及切削稳定性建模为基础,研究了螺旋铣孔的切削参数工艺规划模型和方法。切削力模型同时考虑了刀具周向进给和轴向进给,沿刀具螺旋进给方向综合了侧刃和底刃的瞬时受力特性;动力学模型中同时包含了主轴自转和螺旋进给两种周期对系统动力学特性的影响,并分别建立了轴向切削稳定域和径向切削稳定域的预测模型,求解了相关工艺条件下的切削稳定域叶瓣图。在切削力和动力学模型基础之上,研究了包括轴向切削深度、径向切削深度、主轴转速、周向进给率、轴向进给率等切削工艺参数的多目标工艺参数规划方法。最后通过试验对所规划的工艺参数进行了验证,试验过程中未出现颤振现象,表面粗糙度、圆度、圆柱度可以达到镗孔工艺的加工精度。     

Feedrate scheduling strategy for free-form surface machining through an integrated geometric and mechanistic model

In free-form surface machining, it is essential to optimize the feedrate in order to improve the machining efficiency. Conservative constant feedrate values have been mostly used up to now since there was a lack of physical models and optimization tools for the machining processes. The overall goal of this research is the integration of geometric and mechanistic milling models for force prediction and feedrate scheduling in five-axis CNC free-form surface machining. For each tool move, the geometric model calculates the cut geometry, and a mechanistic model is used along with a maximum allowable cutting force to determine a desired feedrate. The results are written into the part NC program with optimized feedrates. When the integrated modeling approach based feedrate scheduling strategy introduced in this paper was used, it was shown that the machining time can be decreased significantly along the tool path.     

Development of an automatic arc welding system using SMAW process

In end milling of pockets, variable radial depth of cut is generally encountered as the end mill enters and exits the corner, which has a significant influence on the cutting forces and further affects the contour accuracy of the milled pockets. This paper proposes an approach for predicting the cutting forces in end milling of pockets. A mathematical model is presented to describe the geometric relationship between an end mill and the corner profile. The milling process of corners 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. For the cutting force prediction, an analytical model of cutting forces for the steady-state machining conditions is introduced for each segmented process with given radial depth of cut. The predicted cutting forces can be calculated in terms of tool/workpiece geometry, cutting parameters and workpiece material properties, as well as the relative position of the tool to workpiece. Experiments of pocket milling are conducted for the verification of the proposed method.     

基于载荷控制的拐角铣削进给优化*

针对模具型腔拐角铣削过程,提出一种考虑刀具变形及铣削力变化的基于载荷控制的进给量优化方法。根据拐角的铣削中刀具与工件接触情况的不同,将铣削过程分为五个阶段,分别分析拐角铣削时刀具切削刃真实运动轨迹,建立拐角圆弧运动轨迹下瞬时切屑厚度模型,提高切屑厚度模型在拐角加工中的预测精度。修正铣削力预测模型,使其满足拐角加工过程不同阶段的要求。选取刀具变形量为约束条件,计算不同阶段的允许最大载荷,利用二分迭代法得到该载荷下对应的进给量值。考虑到数控机床的运动加速度限制,对得到的优化进给量值进行二次优化,以满足实际加工的要求。仿真结果表明,在进给优化后的拐角铣削过程中,载荷变化趋于平稳,加工时间缩短。进行拐角加工验证试验,数值仿真计算和试验测量结果表明,建立的铣削力模型能够很好地预测拐角铣削过程。所建立的优化模型为模具型腔的高精、高效加工提供理论支持。     

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.     

3D FEM Simulation of Milling Force in Corner Machining Process

To optimize milling force and machining accuracy quality in corner milling process, the changing law of milling force is revealed by Finite Element Method(FEM). Based on DEFORM software a serial of 3D FEM models for corner milling process are devloped. Tool curved trajectory is achieved by establishing accurate relationship of tool location with milling time. Adaptive remeshing technique and iterative algorithm are adopted to ensure convergence of FEM model. Component force characteristics are revealed by analyzing FEM simulation results. It indicates that the milling force in Y direction becomes negative comparing with forces in X and Z direction. Magnitude of forces in three directions decreases with increase of spindle speed, while it increases with increase of milling feedrate. The simulation results for cutting force are in good agreement with those obtained from experiment. The FEM simulation model is first successfully established for corner milling process in this study, and the results provide a guide for optimizing cutting parameters in cutting process.     

基于数字化加工的铣削力预测系统的开发

切削用量的实时获取是切削力预测的关键技术之一。基于数字化加工技术,通过在加工仿真过程中对三维实体图形进行分析,获得实时的切削参数,实现了切削力的实时预测;开发了一个针对铣削加工的切削力预测软件系统,通过铣削试验验证了该系统的正确性。     

Feedrate optimization for variant milling process based on cutting force prediction

Machining process modeling, simulation and optimization is one of the kernel technologies for virtual manufacturing (VM). Optimization based on physical simulation (in contrast to geometrical simulation) will bring better control of a machining process, especially to a variant cutting process – a cutting process so complex that cutting parameters, such as cutting depth and width, change with cutter positions. In this paper, feedrate optimization based on cutting force prediction for milling process is studied. It is assumed that cutting path segments are divided into micro-segments according to a given computing step. Heuristic methods are developed for feedrate optimization. Various practical constraints of a milling system are considered. Feedrates at several segments or micro-segments are determined together but not individually to make milling force satisfy constraints and approach an optimization objective. After optimization, an optimized cutting location data file is outputted. Some computation examples are given to show the optimization effectiveness. This revised version was published online in October 2004 with a correction to the issue number.     

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。     

Investigation on ball end milling of P20 die steel with cutter orientation

The generation mechanism of machining-induced residual stresses is a complex nonlinear and thermal–mechanical coupling problem. The cutting forces and cutting temperature produced in machining process must be considered simultaneously. The influence of cutter orientation and feed per tooth on the cutting speed, cutting forces, cutting temperature, and residual stresses is discussed in the present study. Effective cutting speed in accordance with the inclination angle in feed direction is analyzed. The cutting forces are gained by milling experiment, and the cutting temperature is obtained by finite element method. Moreover, the influence of the effective cutting speed on the cutting forces and cutting temperature is stated, and the relationship among the cutting forces, cutting temperature, and residual stresses is discussed. The experimental and numerical methods are both adopted in this study to give a better understanding of the milling process. After analysis of the phenomenon, several conclusions are made. The inclination angle in feed direction affects the effective cutting speed, and then the cutting forces, cutting temperature, and residual stresses are affected. Priority selection of inclination angle in feed direction is suggested from 5° to 30° in order to reduce the cutting forces. The overall trend of the workpiece temperature presents the parabolic shape, while the chip temperature increases with the increasing inclination angle in feed direction. Residual stress in feed direction almost increases with the increasing feed per tooth, which is not obvious in the general scope of the feed rate. The inclination angle of 5° and 15° is the priority in order to produce residual compressive stresses in cross feed direction.     

Analytical modelling of slot milling exit burr size

A computational model was recently proposed by authors to approximate the tangential cutting force and consequently predict the thickness of the exit up milling side burr. To calculate the cutting force, the specific cutting force coefficient with respect to material properties was used. The model was sensitive to material yield strength and few cutting and tool geometrical parameters. However, the effects of cutting speed, tool coating, and tool rake angle on burr size were neglected. Other phenomena that could affect the burr size such as friction and abrasion were not taken into account either. Therefore, in the current work, a mechanistic force model is incorporated to propose a burr size prediction algorithm. The tangential and radial forces are calculated based on using specific cutting force coefficients in each direction. Furthermore, using the new approach, the burr size is predicated and the effects of a broad range of cutting parameters on burr size and friction angle are evaluated. Experimental values of burr size correlated well with prediction. It was found that the cutting speed has negligible effects on force and burr size. Lower friction angle was recorded when using larger feed per tooth. Consequently, thinner exit up milling side burr was obtained under high friction angle.     

基于有限元数值模型和进给速度优化的薄壁件侧铣变形在线控制

为实现在加工过程中对薄壁件侧铣产生的较大切削变形进行在线控制,提出基于有限元数值模型和进给速度优化的在线控制策略。根据薄壁件切削过程的有限元仿真结果,建立数控机床进给速度、切削力、工件切削变形间的数值模型,进而确定用于控制变形的最优目标切削力。在具有开放式模块化的数控系统平台上开发了切削力信号实时采集、滤波功能和基于Brent-Dekker算法的进给速度在线优化策略,并根据滤波后的切削力及相应算法在加工过程中实时调整机床进给速度,保证切削力逐渐接近最优控制目标而实现切削变形的在线控制。试验结果表明,经过进给速度在线优化后的切削过程可将薄壁件侧铣变形控制在规定范围内,同时提高了切削效率。     

基于铣削力精确建模的工件表面让刀误差预测分析

航空航天制造业结构件的高速铣削加工中,在切削力作用下由整体铣削刀具挠度变形所引起的工件表面让刀误差,严重制约零件的加工精度和效率。针对这一问题,通过建立铣削力精确预测模型,结合刀具刚度特点,对工件让刀误差进行预测分析。将切削速度和刀具前角对切削力的影响规律引入二维直角单位切削力预测模型,并通过试验进行相关系数标定。借助等效前角将直角切削力预测系数应用到斜角切削力的预测,通过矢量叠加构建整体刀具三维切削力模型。分析刀具挠度变形对铣削层厚度及铣削接触中心角范围影响规律。基于离散化的刀具模型和切削力模型,建立铣削载荷条件下刀具等效直径悬臂梁模型弯曲变形计算方法。构建以刀具变形对铣削过程影响作用规律为反馈的刚性工件表面让刀误差及切削力柔性预测模型,通过整体铣刀铣削试验验证所建立理论模型的预测精度。     

Prediction of cutting forces along Pythagorean-hodograph curves

This paper proposes a new approach to predicting cutting forces in milling operations. The approach attempts to find the analytic relationship between cutting forces and the tangential direction of the tool path when a tool moves along an analytical curve, i.e., a Pythagorean-hodograph curve that describes a group of analytic curves with special properties, in a milling operation. In conventional methods for the prediction of cutting forces in milling operations, cutting forces are estimated by considering such cutting parameters as feed rate, depth of cut, and tool geometry. However, the change in the moving direction of the cutter, which has a major effect on cutting forces, is often neglected by previous researchers. This work aims to establish the theoretical basis to show how cutting forces along a curve can be predicted. Two case studies are used to illustrate the proposed cutting force prediction strategy.