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.     

Cutting force model considering tool edge geometry for micro end milling process

The analysis of the cutting force in micro end milling plays an important role in characterizing the cutting process, as the tool wear and surface texture depend on the cutting forces. Because the depth of cut is larger than the tool edge radius in conventional cutting, the effect of the tool edge radius can be ignored. However, in micro cutting, this radius has an influence on the cutting mechanism. In this study, an analytical cutting force model for micro end milling is proposed for predicting the cutting forces. The cutting force model, which considers the edge radius of the micro end mill, is simulated. The validity is investigated through the newly developed tool dynamometer for the micro end milling process. The predicted cutting forces were consistent with the experimental results.     

Mechanistic modelling of the milling process using complex tool geometry

Mechanistic models of the milling process must calculate the chip geometry and the cutter edge contact length in order to predict milling forces accurately. This task becomes increasingly difficult for the machining of three dimensional parts using complex tool geometry, such as bull nose cutters. In this paper, a mechanistic model of the milling process based on an adaptive and local depth buffer of the computer graphics card is compared to a traditional simulation method. Results are compared using a 3-axis wedge shaped cut – a tool path with a known chip geometry – in order to accommodate the traditional method. Effects of cutter nose radius on the cutting and edge forces are considered. It is verified that there is little difference (1.4% at most) in the predicted force values of the two methods, thereby validating the adaptive depth buffer approach. The numerical simulations are also verified using experimental cutting tests of aluminium, and found to agree closely (within 12%).     

整体式立铣刀三维建模及切削力预测研究

针对立铣刀三维建模困难及铣削时切削力难以预测等问题,根据微分几何原理建立立铣刀数学模型。基于数学模型将铣刀切削刃离散成斜角切削单元,根据剪切区应力、应变和温度控制方程,由材料本构方程计算流动应力,通过坐标变换关系建立铣削力预测模型。得到的铣削力与已有铣削试验数据一致,验证了铣削力模型的有效性。     

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.     

Mechanistic modeling of cutting forces in micro-end-milling considering tool run out,minimum chip thickness and tooth overlapping effects

This work proposed an improved mechanistic model for prediction of cutting forces in micro-milling process. The combined influences of tool run out, trochoidal trajectory of the tool center, overlapping of tooth, edge radius and minimum chip thickness are incorporated in this model to realize the exact cutting phenomenon. Moreover, an improved undeformed chip thickness algorithm has been presented by considering tool run out, minimum chip thickness and trajectory of all passing teeth for one complete revolution of the tool instead of only the current tooth trajectory. For estimation of tool run out, a model based on the geometry of the two fluted end mill cutter has been developed. Effects of trochoidal trajectory of the tool center and tool run out are found to be significant as each tooth has a different chip load. Further, the effect of minimum chip thickness is found to be significant at lower feed value. The proposed model has been validated by micro-milling experiments on Ti6Al4V-titanium alloys using uncoated flat end mill cutter. The predicted cutting forces were found to be in good agreement with the experimental cutting forces in both feed and cross feed directions.     

Influence of cutting edge radius on surface integrity and burr formation in milling titanium

The influence of the cutting edge micro geometry on cutting process and on tool performance is subject to several research projects. Recently, published papers mainly focus on the cutting edge rounding and its influence on tool life and cutting forces. For applications even more important, however, is the influence of the cutting edge radius on the integrity of the machined part. Especially for titanium, which is used in environments requiring high mechanical integrity, the information about the dependency of surface integrity on cutting edge geometry is important. This paper therefore studies the influence of the cutting edge radius on surface integrity in terms of residual stress, micro hardness, surface roughness and optical characterisation of the surface and near surface area in up and down milling of the titanium alloy Ti–6Al–4V. Moreover, the influence of the cutting edge radius on burr formation is analysed. The experiments show that residual stresses increase with the cutting edge radius especially in up milling, whereas the influence in down milling is less pronounced. The influence of the cutting edge radius on surface roughness is non-uniform. The formation of burr increases with increasing cutting edge radius, and is thus in agreement with the residual stress tests.     

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.     

A FINITE ELEMENT ANALYSIS OF BURR FORMATION IN FACE MILLING OF A CAST ALUMINUM ALLOY

The research discussed in this article focuses on the effects of tool geometry (i.e., rake angle and cutting edge radius) and flank wear upon burr formation in face milling of a cast aluminum alloy. As to tool edge preparation, the use of a tool with variable cutting edge radius was investigated using FEM, and compared for its cutting performance (i.e., burr reduction and tool life) with a conventional tool with uniform cutting edge radius. In order to evaluate 3D face milling through 2D orthogonal cutting simulations, the cross-sections that consist in the cutting speed direction and chip flow direction were selected at different locations along the tool rounded corner. At these cross-sections, the local value of cutting edge radius and their associated tool rake angles as well as the effective uncut chip thickness were determined for 2D cutting simulations. In addition, 3D face milling simulations were conducted to investigate more realistic chip flow and burr generation. Comparisons were made for burrs produced from 3D simulations with a sharp tool, 3D simulations with a worn tool and face milling experiments. Finally, recommendations for cutting tool design are made to reduce burr formation in face milling.     

Modelling, simulation and experimental investigation of cutting forces during helical milling operations

The kinematics of helical milling on a three-axis machine tool is first analysed. An analytical model dealing with time domain cutting forces is proposed in this paper. The cutting force model is established in order to accurately predict the cutting forces and torque during helical milling operations as a function of helical feed, spindle velocity, axial and radial cutting depth and milling tool geometry. The forces both on the side cutting edges and on the end cutting edges along the helical feed path are described by considering the tangential and the axial motion of the tool. The dual periodicity which is caused by the spindle rotation, as well as the period of the helical feed of the cutting tool, has been included. Both simulation and experiments have been performed in order to compare the results obtained from modelling with experiments.     

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.     

ANALYTICAL MODELING OF MICRO END-MILLING FORCES WITH EDGE RADIUS AND MATERIAL STRENGTHENING EFFECTS

The study aims at developing a predictive analytical force model for the micro end-milling operation taking into account the material strengthening as well as the edge radius effects that come into play at the micro level. The mechanistic models for macro end-milling process have been extensively reported in literature and such models predominantly use milling force coefficients which are empirically determined from end-milling experiments. The proposed model for micro end-milling is based on determination of milling force coefficients from fundamental oblique cutting approach. The edge radius effect has been accounted by analyzing the rubbing action similar to the rolling of a cylinder over work surface. Johnson-Cook material model has been modified based on the strain gradient plasticity theory incorporating the increase in material strength with decreasing uncut chip thickness. From the micro orthogonal cutting experiments, a good agreement between the experimental and predicted shear strength values is observed. The force model is validated against measured forces in end-milling experiments carried out on the KERN Evo 5 axis micro machining center. The feed and lateral forces are predicted within 10% deviation on an average.     

Selection of optimum tool geometry and cutting conditions using a surface roughness prediction model for end milling

Influence of tool geometry on the quality of surface produced is well known and hence any attempt to assess the performance of end milling should include the tool geometry. In the present work, experimental studies have been conducted to see the effect of tool geometry (radial rake angle and nose radius) and cutting conditions (cutting speed and feed rate) on the machining performance during end milling of medium carbon steel. The first and second order mathematical models, in terms of machining parameters, were developed for surface roughness prediction using response surface methodology (RSM) on the basis of experimental results. The model selected for optimization has been validated with the Chi square test. The significance of these parameters on surface roughness has been established with analysis of variance. An attempt has also been made to optimize the surface roughness prediction model using genetic algorithms (GA). The GA program gives minimum values of surface roughness and their respective optimal conditions.     

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.     

Research on the modeling of burr formation process in micro-ball end milling operation on Ti–6Al–4V

Burrs generated along the finished edges and surfaces in micro-milling operation have significant impact on the surface quality and operational performance of the finished parts and microstructures. In order to obtain a better recognition of burr generation process, 3-dimensional micro-ball end milling operation FEM models on Ti–6Al–4V have been established. As a result, a newfound type of burr lying on the slot base has been detected. According to their generating locations, burrs discovered in the simulation are classified into four types: entrance burr, exit burr, top burr, and slot base burr. Their formation processes, especially the generation procedure of slot base burr, are carefully investigated and analyzed. Furthermore, the correlation between cutting parameters and top burr sizes in micro-ball end milling is investigated. At last, effective validation experiments for the proposed model are conducted and good agreements are achieved in the morphologies of burrs between the experiments and simulations. It can be concluded that the adoption of a small ratio of axial depth of cut to the mill radius has a significant effect in the reduction of top burr generation in micro-ball end milling operation.     

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.     

Prediction of cutting forces and machining error in ball end milling of curved surfaces -I theoretical analysis

This paper presents a theoretical model by which cutting forces and machining error in ball end milling of curved surfaces can be predicted. The actual trochoidal paths of the cutting edges are considered in the evaluation of the chip geometry. The cutting forces are evaluated based on the theory of oblique cutting. The machining errors resulting from force induced tool deflections are calculated at various parts of the machined surface. The influences of various cutting conditions, cutting styles and cutting modes on cutting forces and machining error are investigated. The results of this study show that in contouring, the cutting force component which influences the machining error decreases with increase in milling position angle; while in ramping, the two force components which influence machining error are hardly affected by the milling position angle. It is further seen that in contouring, down cross-feed yields higher accuracy than up cross-feed, while in ramping, right cross-feed yields higher accuracy than left cross-feed. The machining error generally decreases with increase in milling position angle.     

Cutting forces and their modelling in plunge milling of magnesium-rare earth alloys

Plunge milling is a machining process already recognised as able to afford significant gains in productivity during the roughing phases, especially in the case of deep workpieces. It is generally used for machining hard materials but more rarely for light alloys, especially for magnesium alloys. This paper deals with the study and the modeling of cutting forces in plunge milling of magnesium-rare earth alloys. In this study, the authors consider the case of a dry plunge milling process applied to two wrought Mg-Zr-Zn-RE alloys and one cast Mg-Zr-Zn-RE alloy, that are representative of magnesium-rare earth alloys in aerospace industry. This paper investigates the influence of cutting parameters and the influence of edge radius on cutting forces. An analytical model is set up so as to satisfactorily predict the cutting forces for these three representative magnesium alloys studied using just three instrumented tests. An experimental validation through different plunge milling tests shows good agreement between the model and the measured values in a wide range of cutting conditions.     

基于AdvantEdge仿真的刀具几何参数对钛合金Ti6Al4V切削力的影响研究

利用切削仿真软件Advant Edge对高速切削Ti6Al4V切削过程进行有限元模拟,研究了切削速度为200m/min、切削深度为0.085mm时刀具几何参数(前角γ_o、后角α_o、钝圆半径r_ε)对切削力的影响。通过分析计算求得切削力随刀具几何参数变化的一阶响应面数学模型,实现了利用刀具几何参数对切削力的预测,并通过误差计算和方差分析证明了预测模型的有效性。研究发现,在给定的参数变化范围内,刀具几何参数对_影响作用的大小顺序为前角γ_o钝圆半径r_ε后角α_o;对F_z影响作用的大小顺序为钝圆半径rε前角γ_o后角α_o。