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.     

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.     

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.     

Evaluation of static cutting forces and tool wear in HSM process applied to pocket milling

One of the main operations in the manufacturing of molds and dies is the opening of the initial pocket, from which more complex geometries are machined, in order to obtain the negative shape of the final product. Since this is a rough operation, high cutting forces and significant tool wear are observed. Aiming to reduce such parameters, several strategies of tool entry and internal cut of the pocket have been proposed. In this context, this work aims to evaluate the cutting forces in the different parts of a pocket milling, using three different strategies, which are composed by the tool, cutting conditions, tool entry, and tool trajectory (I: ramp entry with spiral internal cut, II: helical entry with zigzag internal cut, and III: plunge entry). The results obtained for strategies I and II showed an increase in the forces in the direction perpendicular to the face in which flank wear occurred and a sharp increase in force at points where the tool changes trajectory. In strategy III, the occurrence of tool fracture due to chip recut led to very high force values.     

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。     

Improved dynamic cutting force model in ball-end milling. Part I: theoretical modelling and experimental calibration

An accurate cutting force model of ball-end milling is essential for precision prediction and compensation of tool deflection that dominantly determines the dimensional accuracy of the machined surface. This paper presents an improved theoretical dynamic cutting force model for ball-end milling. The three-dimensional instantaneous cutting forces acting on a single flute of a helical ball-end mill are integrated from the differential cutting force components on sliced elements of the flute along the cutter-axis direction. The size effect of undeformed chip thickness and the influence of the effective rake angle are considered in the formulation of the differential cutting forces based on the theory of oblique cutting. A set of half immersion slot milling tests is performed with a one-tooth solid carbide helical ball-end mill for the calibration of the cutting force coefficients. The recorded dynamic cutting forces are averaged to fit the theoretical model and yield the cutting force coefficients. The measured and simulated dynamic cutting forces are compared using the experimental calibrated cutting force coefficients, and there is a reasonable agreement. A further experimental verification of the dynamic cutting force model will be presented in a follow-up paper.     

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.     

钛合金大直径孔螺旋铣削工艺优化研究

本文基于螺旋铣孔技术,采用正交试验和极差值分析方法,在钛合金上进行了19.05mm直径孔的螺旋铣削试验。分析了不同切削参数对轴向切削力、钛合金孔径、粗糙度等的影响,以此为指标优化出最佳工艺参数。在此基础上研究了最佳参数下切削力、加工质量和刀具磨损随加工孔数的变化,发现在大直径孔加工中,螺旋铣孔技术可有效改善加工质量、提高加工效率。     

Experimental study of the effect of tool orientation in five-axis micro-milling of brass using ball-end mills

The effect of tool orientation on the final surface geometry and quality in five-axis micro-milling of brass using ball-end mills is investigated. Straight grooves with a semicircular cross section are cut with different tool inclination and tilt angles, and the resulting surfaces are characterized using an optical profilometer and microscope. Micro-milling cutting forces are recorded synchronously with spindle electric current and cutting motions in order to investigate the correlation between the tool orientation and the achieved surface quality. Results of various cutting experiments and analysis of the final surface geometry show that varying the tool orientation reduces rubbing of the material at the bottom of the grooves, which often occurs in ball-end milling of brass, and improves the final surface quality. The experimental analysis for surface roughness shows that applying a tool inclination angle of 15° can considerably improve the surface roughness at the bottom of the grooves. Analysis of static and averaged peak-to-valley (P-to-V) values of the cutting forces show that the static cutting force values are reduced by half when the tool inclination was increased from 0 to 15°. P-to-V cutting force values in along-the-feed direction were also decreased in the inclined machining.     

Finite element modeling of micro-milling: Numerical simulation and experimental validation

In this study, micro-milling of Inconel 718 was investigated. For this purpose, cutting tests were conducted by using uncoated tools and taking four different feed rates (1.25, 2.5, 3.75, and 5 µm/flute) and a constant cutting velocity (48 m/min) into account. In numerical modeling, thermomechanical behavior was modeled using the modified Johnson–Cook material model. Analyses were also conducted for different cutting tool edge angles (+8°, 0, and ?8°). In the numerical analyses, cutting force, tool stress, and cutting temperature values were estimated depending on tool rotation and cutting tool edge type and compared with experimental results. When the results obtained from the study are considered, it is seen that the experimental cutting force and temperature values are in harmony with the numerical results. Moreover, it is seen that there is an increase in cutting force, cutting temperature, and stress values depending on the feed rate. In addition, in the numerical analyses for different cutting tool edge geometries it was observed that cutting force temperature and tool stress values varied depending on the edge geometries.     

非圆车削的解析测力方法

针对最小相位及非最小相位受控系统,分别提出了相应算法,根据系统输出位置信号及输入的控制力信号,辨识出动态切削力信息。不使用测力传感器,从而消除了附加测力传感器所产生的不利因素,为深入研究数控非圆车削加工特性及动态切削力误差补偿提供了一种新手段。     

切削Ti -6Al -4V硬质合金涂层平头立铣刀的几何参数优化仿真研究

Ti - 6Al - 4V具有热导率低、弹性模量低、加工硬化严重及化学活性高等特点,属难加工材料,一般采用涂层硬质合金刀具加工.刀具几何参数对切削力、切削热、加工表面质量有重要影响.对刀具几何参数优化能够获得最优的刀具切削性能.使用有限元分析软件AdvantEdge建立三维立铣模型,采用单因素试验法模拟分析TiCN/A...     

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.     

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。     

Development and experimental validation of a mechanistic model of cutting forces in micro- ball end milling of full slots

In the present work, a mechanistic model of cutting forces is developed with a novel approach to arrive at the cutting edge geometry as well as the cutting mechanics. The geometry of cutting elements derived and verified using a virtual tool generated in CAD environment is considered. The cutting and edge force coefficients at every discrete point on the cutting edge of micro-ball end mill are established in a novel way from the basic metal cutting principles and fundamental properties of materials, considering edge radius and material strengthening effects. Further, measured edge radius is used in the model. Full slot micro-ball end milling experiments are conducted on a high-precision high-speed machining center using a 0.4 mm diameter tungsten carbide tool and cutting forces are measured using a high-sensitive piezo-electric dynamometer. It is established that the predicted as well as experimental cutting forces are higher at very low uncut chip thickness in comparison with the cutting edge radius in micro-ball end milling also. Amplitudes of cutting forces and instantaneous values with incremental rotation of the tool are compared with predicted values over two revolutions for validation of proposed model.     

A NEW MECHANISTIC MODEL FOR PREDICTING WORN TOOL CUTTING FORCES

An enhanced model for predicting worn tool cutting forces in metal cutting without the need for any worn tool calibration tests is presented in this paper. The new model utilizes a previously developed slip-line field approach in conjunction with a mechanistic force model to predict the shear flow stress and shear angle for a range of cutting conditions with only a minimal number of sharp tool calibration tests. The shear flow stress and shear angle values are then used as inputs into a worn tool force model to predict the cutting forces due to tool flank wear. Predictions of worn tool cutting forces from the new model have been compared to experimental data from both a steel and a ductile iron workpiece. Ductile iron tests are significant because previous shear flow stress and shear angle models require chip measurements which cannot be made with the chips produced by iron workpieces. Model predictions are also compared to literature data obtained using an aluminum workpiece. An excellent comparison between the model predictions and the experimental data is found for all of the materials considered.     

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。     

Tool wear monitoring in ramp cuts in end milling using the wavelet transform

Tool wear identification and estimation present a fundamental problem in machining. With tool wear there is an increase in cutting forces, which leads to a deterioration in process stability, part accuracy and surface finish. In this paper, cutting force trends and tool wear effects in ramp cut machining are observed experimentally as machining progresses. In ramp cuts, the depth of cut is continuously changing. Cutting forces are compared with cutting forces obtained from a progressively worn tool as a result of machining. A wavelet transform is used for signal processing and is found to be useful for observing the resultant cutting force trends. The root mean square (RMS) value of the wavelet transformed signal and linear regression are used for tool wear estimation. Tool wear is also estimated by measuring the resulting slot thickness on a coordinate measuring machine.