基于有限元法的微径铣刀变形分析

文章基于有限元法建立了微径铣刀的欧拉悬臂梁结构动力学模型,求解了不同刀头直径,不同刀头长度和不同刀柄组合的微径铣刀的固有频率,可知随着悬伸长度的减小,固有频率表现出明显的尺度效应。通过计算微径铣刀的振型及变形得知,当悬伸长度相同时,在静态作用力下,随着刀头直径的减小,刀具变形增大;在动态作用力下,刀具变形对微径铣刀的铣削频率和固有频率的平方较敏感,铣削频率离微径铣刀的固有频率越近,刀具变形越大。微径铣刀的动力学变形分析有助于研究微细铣削力、合理选择微细铣削参数、提高铣削过程稳定性,从而获得良好的加工质量。     

Feed rate scheduling model considering transverse rupture strength of a tool for 3D ball-end milling

This paper presents an analytical model of off-line feed rate scheduling to determine desired feed rates for 3D ball-end milling. Off-line feed rate scheduling is presented as the advanced technology to regulate cutting forces through change of feed per tooth, which directly affects variation of uncut chip thickness. In this paper, the uncut chip thickness is calculated by following the movement of the position of the cutter center, which is determined by runout and cutter deflection. Also, since the developed cutting force model uses the cutting-condition-independent coefficients, off-line feed rate scheduling can be effectively performed regardless of continuous change of cutting conditions. Transverse rupture strength of the tool is used to determine the reference cutting force at which resultant cutting forces are regulated through feed rate scheduling. Experiments validated that the presented feed rate scheduling model reduced machining time drastically and regulated cutting forces at the reference cutting force.     

The prediction of dimensional error for sculptured surface productions using the ball-end milling process. Part 2: Surface generation model and experimental verification

This paper presents a surface generation model for sculptured surface productions using the ball-end milling process. In this model, machining errors caused by tool deflections are studied. As shown in Part 1 of this paper, instantaneous horizontal cutting forces can be evaluated from the cutting geometries using mechanistic force models. In this paper, a tool deflection model is developed to calculate the corresponding horizontal tool deflection at the surface generation points on the cutter. The sensitivity of the machining errors to tool deflections, both in magnitude and direction, has been analyzed via the deflection sensitivity of the surface geometry. Machining errors are then determined from the tool deflection and the deflection sensitivity of the designed surface. The ability of this model in predicting dimensional errors for sculptured surfaces produced by the ball-end milling process has been verified by a machining experiment. In addition to providing a means to predict dimensional accuracy prior to actual cutting, this surface generation model can also be used as a tool for quality control and machining planning.     

Numerical simulation and prediction of cutting forces in five-axis milling processes with cutter run-out

Radial cutter runout is a common issue in milling processes and has a direct effect on milling stability due to variations of resulting chip load and forces. This paper presents a new method to effectively model and predict the instantaneous cutting forces in 5-axis milling processes with radial cutter runout based on tool motion analysis. First, the undeformed chip thickness model taking runout effect into account is established under continuous change of cutter axis orientation by means of the sweep traces of cutter edges. Second, the engaged cutting edge is determined and cutting coefficients are subsequently calibrated. Finally, the method of identifying runout parameters from the measured cutting forces is proposed, and mechanistic method is then applied to predict the cutting force. Since this method is completely based on the relative motion analysis of tool-part, it can reduce the prediction errors of cutting forces effectively and is suitable for generic rotation cutters. Several validation examples are given under different cutting conditions to prove its effectiveness and accuracy. The results reveal that the developed method can predict the cutter forces with a high accuracy and has the ability to be used in simulations and optimizations of five-axis machining.     

Cutting force prediction of sculptured surface ball-end milling using Z-map

The cutting force in ball-end milling of sculptured surfaces is calculated. In sculptured surface machining, a simple method to determine the cutter contact area is necessary since cutting geometry is complicated and cutter contact area changes continuously. In this study, the cutter contact area is determined from the Z-map of the surface geometry and current cutter location. To determine cutting edge element engagement, the cutting edge elements are projected onto the cutter plane normal to the Z-axis and compared with the cutter contact area obtained from the Z-map. Cutting forces acting on the engaged cutting edge elements are calculated using an empirical method. Empirical cutting mechanism parameters are set as functions of cutting edge element position angle in order to consider the cutting action variation along the cutting edge. The relationship between undeformed chip geometry and the cutter feed inclination angle is also analyzed. The resultant cutting force is calculated by numerical integration of cutting forces acting on the engaged cutting edge elements. A series of experiments were performed to verify the proposed cutting force estimation model. It is shown that the proposed method predicts cutting force effectively for any geometry including sculptured surfaces with cusp marks and a hole.     

Feedrate scheduling for indexable end milling process based on an improved cutting force model

In CNC machining, an optimal process plan is needed for higher productivity and machining performance. This paper proposes a mechanistic cutting force model to perform feedrate scheduling that is useful in process planning for indexable end milling. Indexable end mills, which consist of inserts and a cutter body, have been widely used in the roughing of parts in the mold industry. The geometry and distribution of inserts compose a discontinuous cutting edge on the cutter body, and tool geometry of indexable end mill varies with axial position due to the geometry and distribution of inserts. Thus, an algorithm that calculates tool geometry data at an arbitrary axial position was developed. The developed cutting force model uses cutting-condition-independent cutting force coefficients and considers run out, cutter deflection, geometry variation and size effect for accurate cutting force prediction. Through feedrate scheduling, NC code is optimized to regulate cutting forces at given reference force. Experiments with general NC codes show the effectiveness of feedrate scheduling in process planning.     

拐角铣削力建模与MATLAB仿真研究

在模具型腔的加工过程中,拐角铣削加工是不可避免的,其中铣削力是影响工件加工质量和刀具寿命的重要因素。以90°拐角铣削加工为例,利用微元法建立了以刀具参数、进给速度和刀具旋转角度为参变量的铣削力模型,基于MATLAB的GUI模块开发了拐角铣削力仿真软件并进行仿真实验。将仿真结果与采用测力仪测量的结果进行比较,结果显示:仿真结果能有效预测拐角铣削力,为实际切削加工提供参考和理论支撑。     

Milling force prediction using a dynamic shear length model

Modelling of cutting forces in milling is often needed in machining automation. In this paper, a new method for the determination of the cutting forces in face milling is presented, which applies a predictive machining theory originally developed for orthogonal cutting to milling operations, with a dynamic shear length model developed and incorporated. The proposed dynamic shear length model is developed based on the analysis for the true tooth trajectories of a milling cutter, taking into account of the characteristic wavy surface effects in milling. The prediction for the cutting forces is carried out at each step of the angular increment of cutter rotation from input data of fundamental workpiece material properties, tool geometry and cutting conditions. Cutting forces at a cutter tooth can be predicted once the shear angle, shear length, shear plane area, and the shear flow stress along the shear length have been determined. The milling force prediction using the dynamic shear length model is verified through milling experimental tests. The sensitivity of the difference between the static and dynamic shear length models with respect to the feed per tooth and the cutter diameter is discussed.     

Milling error prediction and compensation in machining of low-rigidity parts

The paper reports on a new integrated methodology for modelling and prediction of surface errors caused by deflection during machining of low-rigidity components. The proposed approach is based on identifying and modelling key processing characteristics that influence part deflection, predicting the workpiece deflection through an adaptive flexible theoretical force-FEA deflection model and providing an input for downstream decision making on error compensation. A new analytical flexible force model suitable for static machining error prediction of low-rigidity components is proposed. The model is based on an extended perfect plastic layer model integrated with a FE model for prediction of part deflection. At each computational step, the flexible force is calculated by taking into account the changes of the immersion angles of the engaged teeth. The material removal process at any infinitesimal segment of the milling cutter teeth is considered as oblique cutting, for which the cutting force is calculated using an orthogonal–oblique transformation. This study aims to increase the understanding of the causes of poor geometric accuracy by considering the impact of the machining forces on the deflection of thin-wall structures. The reported work is a part of an ongoing research for developing an adaptive machining planning environment for surface error modelling and prediction and selection of process and tool path parameters for rapid machining of complex low-rigidity high-accuracy parts.     

Prediction of cutting force distribution and its influence on dimensional accuracy in peripheral milling

Cutting force has a significant influence on the dimensional accuracy due to tool and workpiece deflection in peripheral milling. In this paper, the authors present an improved theoretical dynamic cutting force model for peripheral milling, which includes the size effect of undeformed chip thickness, the influence of the effective rake angle and the chip flow angle. The cutting force coefficients in the model were calibrated with the cutting forces measured by Yucesan [18] in tests on a titanium alloy, and the model was proved to be more accurate than the previous models. Based on the model, a few case studies are presented to investigate the cutting force distribution in cutting tests of the titanium alloy. The simulation results indicate that the cutting force distribution in the cut-in process has a significant influence on the dimensional accuracy of the finished part. Suggestions about how to select the cutter and the cutting parameters were given to get an ideal cutting force distribution, so as to reduce the machining error, meanwhile keeping a high productivity.     

Tool deflection compensation in peripheral milling of curved geometries

This paper presents compensation of surface error due to cutting force-induced tool deflections in a peripheral milling process. Previous research attempts on this topic deal with error compensation in machining of straight geometries only. This paper is concerned with peripheral milling of variable curvature geometries where the workpiece curvature changes continuously along the path of cut. In the case of curved geometries, both process geometry and the cutting forces have shown to have strong dependence on workpiece curvature and hence variation of surface error along the path of cut. This calls for a different error compensation strategy than the one which is normally used for machining straight geometries. The present work is an attempt to improve accuracy in machining of curved geometries by use of CNC tool path compensation. Mechanistic model for cutting force estimation and cantilever beam model for cutter deflection estimation are used. The results based on machining experiments performed on a variety of geometries show that the dimensional accuracy can be improved significantly in peripheral milling of curved geometries.     

方肩铣刀高速铣削TC4钛合金试验研究及参数优化

利用单因素试验方法,采用镶齿硬质合金涂层方肩铣刀进行钛合金高速铣削试验,研究每齿进给量、铣削宽度、铣削深度、铣削速度对于铣削力的影响。通过对铣削力进行分析,建立方肩铣刀高速铣削的铣削力模型,并采用MATLAB遗传算法以进给方向铣削力Fy最小为目标,对铣削参数进行了优化并给出了最优解集。实验结果表明,使用优化后的参数加工薄壁件可有效减小切削力。     

行星复合铣削及其刀具研究

行星复合铣削方法是复合加工方法的一种实现形式,该加工方法所产生的切削力较普通端铣加工的切削力有大幅度的降低,从而能有效地降低切削热、减少工件变形、提高刀具寿命。行星复合铣削方法切削力大幅度地降低的主要原因是该方法的切削轨迹使其能将厚切削层分解为细小的切削层,而该方法中的立铣刀的螺旋角和半径对实际切削力的影响很小。行星复合铣削方法在刀盘低速旋转时就能实现高速切削,有效地避开了高速旋转刀盘的动平衡问题,结合其切削力小的优势,通过增大刀盘直径并增加立铣刀数量来提高加工效率。行星铣刀采用行星轮系结构,能够达到行星复合铣削方法切削轨迹要求,具有扭矩大、运转可靠等优势。     

Modelling and analysis of micro scale milling considering size effect, micro cutter edge radius and minimum chip thickness

This paper presents mechanisms studies of micro scale milling operation focusing on its characteristics, size effect, micro cutter edge radius and minimum chip thickness. Firstly, a modified Johnson–Cook constitutive equation is formulated to model the material strengthening behaviours at micron level using strain gradient plasticity. A finite element model for micro scale orthogonal machining process is developed considering the material strengthening behaviours, micro cutter edge radius and fracture behaviour of the work material. Then, an analytical micro scale milling force model is developed based on the FE simulations using the cutting principles and the slip-line theory. Extensive experiments of OFHC copper micro scale milling using 0.1 mm diameter micro tool were performed with miniaturized machine tool, and good agreements were achieved between the predicted and the experimental results. Finally, chip formation and size effect of micro scale milling are investigated using the proposed model, and the effects of material strengthening behaviours and minimum chip thickness are discussed as well. Some research findings can be drawn: (1) from the chip formation studies, minimum chip thickness is proposed to be 0.25 times of cutter edge radius for OFHC copper when rake angle is 10° and the cutting edge radius is 2 μm; (2) material strengthening behaviours are found to be the main cause of the size effect of micro scale machining, and the proposed constitutive equation can be used to explain it accurately. (3) That the specific shear energy increases greatly when the uncut chip thickness is smaller than minimum chip thickness is due to the ploughing phenomenon and the accumulation of the actual chip thickness.     

Increasing productivity in sculpture surface machining via off-line piecewise variable feedrate scheduling based on the force system model

Sculpture surface machining is a critical process commonly used in various industries such as the automobile, aerospace, die/mold industries. Since there is a lack of scientific tools in practical process planning stages, feedrates for CNC machining are selected based on the trial errors and previous experiences. In the selections of the process parameters, production-planning engineers are conservative in order to avoid undesirable results such as chipping, cutter breakage or over-cut due to excessive cutter deflection. Currently, commonly used CAD/CAM programs use only the geometric and volumetric analysis, but not the physics of the processes, and rely on experience based cutting tool database and users’ inputs for selection of the process parameters such as feed and speed. Usually, the feeds and cutting speeds are set individual constant values all along the roughing, semi-finishing, and finishing processes. Being too conservative and setting feedrate constant all along the tool path in machining of sculpture surfaces can be quite costly for the manufacturers. However, a force model based on the physics of the cutting process will be greatly beneficial for varying the feedrate piecewise along the tool path.The model presented here is the first stage in order to integrate the physics of the ball-end milling process into the selection of the feeds during the sculpture surface machining. Therefore, in this paper, an enhanced mathematical model is presented for the prediction of cutting force system in ball end milling of sculpture surfaces. This physical force model is used for selecting varying and ‘appropriate’ feed values along the tool path in order to decrease the cycle time in sculpture surface machining. The model is tested under various machining conditions, and some of the results are also presented in the paper.     

基于改进瞬时刚性力模型的机床铣削加工监测

针对用于切削力预测的瞬时刚性力模型所需参数较多且依赖初步切削实验的问题,提出一种不需要切削实验的新型切削力预测方法,实现在实际工厂中监测机床铣削加工过程。在斜角切削模型和正交切削理论的基础上,对传统的瞬时刚性力模型进行改进,减少切削力预测所需的切削参数。改进后的模型仅需在铣削操作开始时从测量的主轴电机扭矩得到的剪切角参数,无需任何额外的传感器就可以实现铣削力预测。在所提模型中,刀具跳动的影响可通过每个切削刃处的旋转半径偏差表示,以精确预测切削力。为验证该模型的有效性,进行切削实验。结果表明：切削力的预测值与实测值吻合较好,在实际加工过程中,无需任何实验铣削或任何额外的力传感器就可以准确了解机床加工状态。     

雕刻表面球形铣削的分段变进给率加工

雕刻表面球形铣削加工中,根据刀头的受力模型,可以计算整个刀具路径上刀头的受力.刀具路径上加工深度变化时,若采用恒进给率,则刀具受力是变化的,为了安全保险起见,往往按最大受力来选择较低的恒进给率,整个加工效率很低.采用变进给率加工,即加工深度小时提高进给率,使刀具在整个路径上受力均匀.本文给出了路径上力的计算仿真方法,以及分段进给率的计算方法,可以指导实际的加工过程,这样既保证了加工过程的安全,又提高了生产率.     

基于改进遗传算法的数控机床加工铣削参数优化方法

对于数控机床加工铣削参数优化多采用常规的可信度近似模型,但该方法易受到材料失效应变系数的影响,导致优化后的加工效率较低,提出基于改进遗传算法的数控机床加工铣削参数优化方法。根据工件的本构模型,对切削刃进行采样抽取,确定最小铣削力波动位置;引入材料失效准则计算材料失效应变系数,基于此,以加工时间最短、加工成本最低和加工能耗消耗最小为目标建立铣削参数优化模型,并采用改进遗传算法求解模型,通过迭代适应度值,输出最佳铣削参数;最后,采用对比实验的形式对所提方法的优化性能进行测试。测试结果表明：应用所提方法对数控机床加工铣削参数进行优化后,能够有效缩短切削时间,提高加工效率。     

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。     

Simplified and efficient calibration of a mechanistic cutting force model for ball-end milling

Accurate evaluation of the empirical coefficients of a mechanistic cutting force model is critical to the reliability of the predicted cutting forces. This paper presents a simplified and efficient method to determine the cutting force coefficients of a ball-end milling model. The unique feature of this new method is that only a single half-slot cut is to be performed to calibrate the empirical force coefficients that are valid over a wide range of cutting conditions. The instantaneous cutting forces are used with the established helical cutting edge profile on the ball-end mill. The half-slot calibration cut enables successive determination of the lumped discrete values of the varying cutting mechanics parameters along the cutter axis whereas the size effect parameters are determined from the known variation of undeformed chip thickness with cutter rotation. The effectiveness of the present method in determining the cutting force coefficients has been demonstrated experimentally with a series of verification test cuts.