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.     

Extracting cutter/workpiece engagements in five-axis milling using solid modeler

Predicting cutting forces in milling process simulation requires finding cutter/workpiece engagements (CWEs). The calculation of these engagements is challenging due to the complicated and changing intersection geometry between the cutter and the in-process workpiece. In this paper, a solid modeling based methodology for finding CWEs generated in five-axis milling of free form surfaces is presented. The proposed methodology is an extension of the solid modeler based three-axis CWE extraction method given in [21]. At any given instant of the five-axis tool motion, the velocity vectors along the cutter axis may move in directions that do not lie in the same plane, and therefore the cutter envelopes need to be approximated by spline surfaces. Considering the spline surface approximations, the CWE methodology described in [21] does not work properly for the five-axis milling. Therefore in the proposed method, the in-process workpiece is used instead of the removal volume for extracting the CWEs. A terminology the feasible contact surfaces (FCS), defined by the envelope boundaries, is introduced. To extract the CWEs at a given cutter location, first the BODY entity, obtained by offsetting the FCS with an infinitesimal amount, is intersected with the in-process workpiece. Then, the resultant removal volume is decomposed into faces. Finally, the surface/surface intersections are performed between those faces and the FCS to obtain the CWE boundaries. To be used in the force model, the CWE boundaries are mapped from Euclidean 3D space to a parametric space defined by the engagement angle and the depth-of-cut for a given tool geometry.     

基于Z-MAP方法的球头铣刀铣削力的建模

瞬时刚性切削力的建模是铣削加工物理仿真的基础,然而,球头铣刀的刀齿形状复杂,加工过程中姿态多变,瞬时刚性铣削力的建模难度较大。在考虑刀具姿态调整的情况下,通过齐次坐标变换建立了刀齿的运动轨迹,提出了一种识别刀具和工件瞬时接触区的改进Z-MAP算法,通过计算当前刀齿的参考线与工件的边界面或刀齿扫掠面的交点求出瞬时未变形切屑厚度,并采用非线性回归的方法辨识了切削力系数,在此基础上使用微元积分法建立了瞬时切削力的计算模型。为了验证仿真模型的可靠性,分别进行了垂直加工和倾斜加工试验,试验和仿真结果具有较高的一致性,表明该建模仿真方法是有效的,可以为实际加工中参数的选择和优化提供理论依据。     

螺旋锥齿轮数控加工3维仿真研究

在分析了螺旋锥齿轮数控加工原理后，采用面向对象技术和计算机辅助设计系统中的3维建模功能，提出了CNC铣齿机床、齿轮毛坯和盘铣刀3维几何模型的具体构建方法；利用简化的齿轮毛坯实体模型和盘铣刀实体模型做布尔减运算，来实现模拟工件材料的去除过程；最终给出的加工仿真实例和实际加工结果，验证了加工仿真方法的正确性。所获得的仿真结果可为齿面接触分析、有限元应力分析和齿轮的数控加工等提供了精确的3维实体模型。     

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.     

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.     

Application of a variable flow stress machining theory to helical end milling

A methodology of modeling chip geometry of flat helical end milling based on a variable flow stress machining theory is presented in this article. The proposed model is concerned with the variation of the width of cut thickness. The nonuniform chip thickness geometry is discretized into several segments based on the radial depth of cut. The chip geometry for each segment is considered to be constant by taking the average value of the maximum and minimum chip thickness. The maximum chip thickness for each chip segment is computed based on the current width of cut, feed per tooth and the cutter diameter. The subsequent radial depth of cut is subtracted from the discretized size of the width of cut to obtain the minimum chip thicknesses. The forces for each segment are summed to obtain the total forces acting on the system of the workpiece and the tool. The cutting forces can be predicted from input data of work material properties, cutter configuration and the cutting conditions used. The validation of the proposed model is achieved by correlating experimental results with the predicted results obtained.     

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.     

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.     

Extracting cutting constants via harmonic force components for a general helical end mill

Mechanistic cutting constants serve well in predicting milling forces, monitoring the milling process as well as in helping to understand the mechanistic phenomena of a machining process for a unique pair of workpiece and cutter materials under various types of cutting edge geometry. This paper presents a unified approach in identifying the six shearing and ploughing cutting constants for a general helical end mill from the dynamic components of the measured milling forces in a single cutting test. The identification model is first presented assuming the milling force is measured with a known phase angle of the cutter spindle. When the phase angle of the cutter rotation is not available, as is the case for most milling machines, it is shown that the true phase angle can be identified through the theoretical phase relationship between the different harmonic components of the milling forces measured with an arbitrary phase angle. The numerical simulation and the experimental results for ball and cylindrical end mills are presented to demonstrate and validate the identification methods.     

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.     

Reduced models of grinding wheel topography and material removal to simulate dynamical aspects in grinding

Increasing competition and short product life cycles make it necessary to optimize and evaluate the outcome of manufacturing processes. In tool grinding, models for the final workpiece geometry and cutting forces are of particular interest. To establish a valid general grinding model, we investigated the cutting process and the influence of local grinding wheel engagements on the material removal. We consequently developed models of material removal and grinding wheel topography, which capture the main correlations in grinding. In combination, temporal cutting forces and final workpiece geometry are predictable and are in excellent agreement with experimental data. The introduced models are valid for grinding in general, since they are solely based on the geometry and process parameters, and hence are applicable for manufacturing process optimization.     

Force Modelling for Cylindrical Plunge Cutting

This paper described the development of an analytical model for the cutting forces in multiblade plunge cutting of cylindrical parts. The development uses the relationship between the instantaneous chip area and the local cutting forces at each individual blade to formulate the total resultant forces via kinematic integration along the cutting edges. The model expresses the cutting forces in explicit terms of part material properties, cutter geometry, part geometry, and cutting conditions. Experiments were performed under various cutting conditions to verify the fidelity of the model at different stages of cutter-part engagement. The waveform and amplitude characteristics of the model-predicted forces agree closely with the measurement. The model can facilitate tool geometry design and cutting condition planning in light of the optimisation of cutting forces.     

虚拟加工物理仿真中的误差分析研究

基于虚拟制造的理论与方法,模拟真实加工条件,建立了面向虚拟数控车削加工环境的加工精度分析系统。该系统基于有限元方法,用有限元法计算刀具-工件在切削要素（切削力、夹紧力、切削温度等）作用下的变形,通过求工件-刀具的布尔差集获取切削后的工件轮廓;利用MATLAB优化工具箱,分析工件轮廓,预测零件加工误差。     

Prediction of cutting forces in mill turning through process simulation using a five-axis machining center

Mill turning is a process applied in the milling of a curved surface while the workpiece rotates around its center. Depending on the eccentricity of the tool, when a flat-end mill tool performs a curved trajectory perpendicular to the rotation axis of the tool, its bottom part is engaged in removing material. In order to optimize the process, the cutting force needs to be predicted. Hence, in this work, an approach to simulating the cutting force in mill turning is presented. The case of non-eccentricity of the tool is considered. The undeformed chip geometry is modeling as a function of the tool engagement considering the process kinematics. Experiments were conducted on a five-axis machining center enabling the measurement of the X–Y and Z components of the cutting forces. In order to verify the influence of the bottom part of the tool on the cutting forces, experiments were carried out using three different cutting depths. Numerical cutting simulations and experimental test results are compared to validate the proposed approach.     

Milling Force Model for Aviation Aluminum Alloy:Academic Insight and Perspective Analysis

Aluminum alloy is the main structural material of aircraft,launch vehicle,spaceship,and space station and is pro-cessed by milling.However,tool wear and vibration are the bottlenecks in the milling process of aviation aluminum alloy.The machining accuracy and surface quality of aluminum alloy milling depend on the cutting parameters,material mechanical properties,machine tools,and other parameters.In particular,milling force is the crucial factor to determine material removal and workpiece surface integrity.However,establishing the prediction model of milling force is important and difficult because milling force is the result of multiparameter coupling of process system.The research progress of cutting force model is reviewed from three modeling methods:empirical model,finite element simulation,and instantaneous milling force model.The problems of cutting force modeling are also determined.In view of these problems,the future work direction is proposed in the following four aspects:(1)high-speed milling is adopted for the thin-walled structure of large aviation with large cutting depth,which easily produces high residual stress.The residual stress should be analyzed under this particular condition.(2)Multiple factors(e.g.,eccentric swing milling parameters,lubrication conditions,tools,tool and workpiece deformation,and size effect)should be consid-ered comprehensively when modeling instantaneous milling forces,especially for micro milling and complex surface machining.(3)The database of milling force model,including the corresponding workpiece materials,working condi-tion,cutting tools(geometric figures and coatings),and other parameters,should be established.(4)The effect of chatter on the prediction accuracy of milling force cannot be ignored in thin-walled workpiece milling.(5)The cutting force of aviation aluminum alloy milling under the condition of minimum quantity lubrication(mql)and nanofluid mql should be predicted.     

Swept area modeling and cutter wear study in turn-milling

In turn-milling machining, we found the cutter wear concentrated on a small section around the corner of the cutter and affect the cutter life. In this paper, the idea of swept area is proposed firstly based on the analyses for cutter wear, and it can indicate the cutter wear. Balance of swept area will lead to balanced wear along cutting edge, and expressions of swept areas of infinitesimal elements on the cutting edge are given. Secondly, the cutting depth and cutting angle, which are the key parameters in calculating the swept area, are analyzed based on different contact situations between the cutter and workpiece, and the detailed calculating method is given. Then, the optimization model to balance swept areas along the cutting edge is established, and the cutting parameters including cutter offset and machining length are optimized. Finally, the orthogonal turn-milling machining experiments with different cutting parameters are conducted; the result shows that turn-milling with optimized parameters can actually balance the cutter wear and increase the cutter life.     

Optimization of machining parameters using genetic algorithm and experimental validation for end-milling operations

Optimization of cutting parameters is valuable in terms of providing high precision and efficient machining. Optimization of machining parameters for milling is an important step to minimize the machining time and cutting force, increase productivity and tool life and obtain better surface finish. In this work a mathematical model has been developed based on both the material behavior and the machine dynamics to determine cutting force for milling operations. The system used for optimization is based on powerful artificial intelligence called genetic algorithms (GA). The machining time is considered as the objective function and constraints are tool life, limits of feed rate, depth of cut, cutting speed, surface roughness, cutting force and amplitude of vibrations while maintaining a constant material removal rate. The result of the work shows how a complex optimization problem is handled by a genetic algorithm and converges very quickly. Experimental end milling tests have been performed on mild steel to measure surface roughness, cutting force using milling tool dynamometer and vibration using a FFT (fast Fourier transform) analyzer for the optimized cutting parameters in a Universal milling machine using an HSS cutter. From the estimated surface roughness value of 0.71 μm, the optimal cutting parameters that have given a maximum material removal rate of 6.0×10³ mm³/min with less amplitude of vibration at the work piece support 1.66 μm maximum displacement. The good agreement between the GA cutting forces and measured cutting forces clearly demonstrates the accuracy and effectiveness of the model presented and program developed. The obtained results indicate that the optimized parameters are capable of machining the work piece more efficiently with better surface finish.     

The effects of cutter eccentricity on the cutting force in the ball-end finish milling

Ball-end mill are usually used for finish machining with multi-axis CNC milling centers. Cutter eccentricity (offset magnitude e _c, angular location of the offset vector λ _c) is very important when predicting cutting forces accurately. In the process of cutting force modeling, not only the e _c, but also the λ _c, affects the cutting forces by associating with the rotation angle, the chip thickness, and the entry and exit angles of the cutting forces. The e _c affects the values of the cutting forces, while λ _c causes the delay phenomenon of the cutting forces mainly. Experiment results show that the cutting forces, considering the cutter eccentricity, more especially considering the influence of the λ _c, agree better with the measured cutting forces than the cutting forces without considering the cutter eccentricity.     

MODELING THE PHYSICS OF METAL CUTTING IN HIGH-SPEED MACHINING

ABSTRACT

Physical modeling of metal cutting was carried out to provide an understanding and prediction of machining process details. The models are based on finite element analysis (FEA), using a Lagrangian formulation with explicit dynamics. Requirements for material constitutive models are discussed in the context of high-speed machining. Model results address metal cutting characteristics such as segmented chip formation, dynamic cutting forces, unconstrained plastic flow of material during chip formation, and thermomechanical environments of the work-piece and the cutting tool. Examples are presented for aerospace aluminum and titanium alloys. The results are suited for analysis of key process issues of cutting tool performance, including tool geometry, tool sharpness, workpiece material buildup, and tool wear.