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.     

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.     

THE GEOMETRY, SPECIFICATION AND PREDICTIVE FORCE MODELS FOR PLANE FACED BALL-END MILLING CUTTERS AND OPERATIONS

In this paper the geometry and specification of ball-end milling cutters are studied and discussed followed by an outline of the development of computer-aided predictive models for the three force components, torque and power in plane faced ball-end milling operations, based on the 'Unified-Generalised Mechanics of Cutting Approach'. The models allow for six milling modes, namely; slotting, 'on-centre' end-milling and 'off-centre' end-milling, each machining at the cutter ball-end cutting edge only or at the cutter ball-end and cylindrical periphery cutting edges for two or more flute cutters. The models include all the tool and cut geometrical variables and the cutting speed as well as the tool-workpiece material combination (via the database of basic cutting quantities). The models are verified through extensive numerical simulation studies and a comprehensive experimental testing programme. Good qualitative and quantitative correlation has been found between predicted and measured fluctuating and average force components and torque.     

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.     

A study on calibration of coefficients in end milling forces model

This paper presents an improved approach to calibrate the cutting coefficients in an end-milling model. In order to predict end-milling forces, lots of simulative models are established. In order to use them, coefficients in the models, for example, cutting pressure constants etc., must firstly be calibrated experimentally, and simulative precision and applicability of the models are influenced by them. For simplicity, using average forces to calibrate cutting parameters are widely adopted by lots of researchers. However, the existence of an instruments zero-drift, noise, etc., will have effect on the precision of experimental data, so, it is difficult to directly obtain exact average-cutting forces through experimental data. Aiming at the above problem, the paper investigates milling forces in the frequency domain, discusses the impact of experimental data at different frequencies on cutting force coefficients and the influence of sensitivity of error on experimental data at different frequencies on coefficients is studied. Based on the research, an improved method to calibrate the cutting coefficients is provided. Based on a series of experiments and numerical simulations, the validity of the method is confirmed. At the end of the paper, some useful conclusions are drawn.     

基于ABAQUS/Explicit的AZ31b镁合金微铣削三维仿真研究

传统铣削仿真往往基于宏观建模而忽略了切削刃钝圆半径,对于微切削过程中出现的尺度效应以及最小切削厚度等特有现象无法进行准确描述,与实际加工差距较大。本文利用有限元软件ABQUS/Explicit对AZ31b镁合金材料微铣削过程进行三维变切削厚度仿真,采用ALE自适应技术控制网格畸变过大问题,进而获得了反映尺度效应的微铣削模型,并研究了主轴转速、铣削深度、每齿进给量对于铣削力的相关影响。     

Analysis of cutting force coefficients in high-speed ball end milling at varying rotational speeds

In high-speed ball end milling, cutting forces influence machinability, dimensional accuracy, tool failure, tool deflection, machine tool chatter, vibration, etc. Thus, an accurate prediction of cutting forces before actual machining is essential for a good insight into the process to produce good quality machined parts. In this article, an attempt has been made to determine specific cutting force coefficients in ball end milling based on a linear mechanistic model at a higher range of rotational speeds. The force coefficients have been determined based on average cutting force. Cutting force in one revolution of the cutter was recorded to avoid the cutter run-out condition (radial). Milling experiments have been conducted on aluminum alloy of grade Al2014-T6 at different spindle speeds and feeds. Thus, the dependence of specific cutting force coefficients on cutting speeds has been studied and analyzed. It is found that specific cutting force coefficients change with change in rotational speed while keeping other cutting parameters unchanged. Hence, simulated cutting forces at higher range of rotational speed might have considerable errors if specific cutting force coefficients evaluated at lower rotational speed are used. The specific cutting force coefficients obtained analytically have been validated through experiments.     

An improved cutting force model for micro milling considering machining dynamics

Micro milling, as a versatile micro machining process, is kinematically similar to conventional milling; however, it is significantly different from conventional milling with respect to chip formation mechanisms and uncut chip thickness modelling, due to the comparable size of the edge radius to the chip thickness, and the small per-tooth feeding. Considering tool runout and dynamic displacement between the tool and the workpiece, the contour of the workpiece left by previous tool paths is typically in a wavy form, and the wavy surface provides a feedback mechanism to cutting force generation because the instantaneous uncut chip thickness changes with both the vibration during the current tool path and the surface left by the previous tool paths. In this study, a more accurate uncut chip thickness model was established including the precise trochoidal trajectory of the cutting edge, tool runout and dynamic modulation caused by the machine tool system vibration. The dynamic regenerative effect is taken into account by considering the influence of all the previous cutting trajectories using numerical iteration; thus, the multiple time delays (MTD) are considered in this model. It is found that transient separation of the tool-workpiece occurring at a low feed per tooth, caused by MTD and the existing cutting force models, is no longer applicable when transient tool-workpiece separation occurs. Based on the proposed uncut chip thickness model, an improved cutting force model of micro milling is developed by full consideration of the ploughing effect and elastic recovery of the workpiece material. The proposed cutting force model is verified by micro end milling experiments, and the results show that the proposed model is capable of producing more accurate cutting force prediction than other existing models, particularly at small feed per tooth.     

Dynamic Force Modelling for a Ball-End Milling Cutter Based on the Merchant Oblique Cutting Theory

A new dynamic force model for a ball-end milling cutter is presented in this paper. Based on the principle of the power remaining constant in cuts, the Merchant oblique cutting theory has been successfully used for the differential cutting edge segment of a ball-end milling cutter. A concise method for characterising the relationship of the complex geometry of a ball-end milling cutter and the milling process variables is determined, so that the force coefficients can be decomposed. The geometric property of a ball-end milling cutter and the dynamics of the milling process are integrated into the general model to eliminate the need for the experimental calibration of each cutter geometry and milling process variable. The milling experiments prove that this model can predict accurately the cutting forces in three Cartesian directions.     

Cutting force prediction for ball nose milling of inclined surface

Ball nose milling of complex surfaces is common in the die/mould and aerospace industries. A significant influential factor in complex surface machining by ball nose milling for part accuracy and tool life is the cutting force. There has been little research on cutting force model for ball nose milling on inclined planes. Using such a model ,and by considering the inclination of the tangential plane at the point of contact of the ball nose model, it is possible to predict the cutting force at the particular cutting contact point of the ball nose cutter on a sculptured surface. Hence, this paper presents a cutting force model for ball nose milling on inclined planes for given cutting conditions assuming a fresh or sharp cutter. The development of the cutting force model involves the determination of two associated coefficients: cutting and edge coefficients for a given tool and workpiece combination. A method is proposed for the determination of the coefficients using the inclined plane milling data. The geometry for chip thickness is considered based on inclined surface machining with overlapping of previous pass. The average and maximum cutting forces are considered. These two forces have been observed to be more dominating force-based parameters or features with high correlation with tool wear. The developed cutting force model is verified for various cutting 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.     

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.     

Improved dynamic cutting force model in peripheral milling. Part II: experimental verification and prediction

Cutting trials reveal that a measure of cutter run-out is always unavoidable in peripheral milling. This paper improves and extends the dynamic cutting force model of peripheral milling based on the theoretical analytical model presented in Part I [1], by taking into account the influence of the cutter run-out on the undeformed chip thickness. A set of slot milling tests with a single-fluted helical end-mill was carried out at different feed rates, while the 3D cutting force coefficients were calibrated using the averaged cutting forces. The measured and predicted cutting forces were compared using the experimentally identified force coefficients. The results indicate that the model provides a good prediction when the feed rate is limited to a specified interval, and the recorded cutting force curves give a different trend compared to other published results [8]. Subsequently, a series of peripheral milling tests with different helical end-mill were performed at different cutting parameters to validate the proposed dynamic cutting force model, and the cutting conditions were simulated and compared with the experimental results. The result demonstrates that only when the vibration between the cutter and workpiece is faint, the predicted and measured cutting forces are in good agreement.     

瞬时铣削力建模与铣削力系数的粒子群法辨识

为获得精确的瞬时铣削力模型,对微元铣削力进行分析,建立了微元铣削力模型。依据立铣加工的特点,提出了微元铣削刃参与铣削的判断方法,给出了具体的计算公式。在此基础上,建立了包含剪切效应和犁入效应的瞬时铣削力模型。利用粒子群算法收敛速度快的优点,提出了基于粒子群的单位铣削力系数辨识方法,给出了算法的实现步骤。铣削试验结果表明,该方法能够精确辨识出单位铣削力系数,利用所提出的瞬时铣削力模型获得的铣削力预测值与铣削力实测值的大小和变化趋势基本一致。     

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.     

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%).     

Design and fabrication of a new micro ball-end mill with conical flank face

Micro ball-end milling is an efficient method for the fabrication of micro lens array molds. However, it is difficult to meet the machining quality of micro dimple molds due to the wear and breakage of the milling cutter, which presents large challenges for designing geometric structure and edge strength of micro ball-end mills. In this study, a new configuration of a micro ball-end mill for micro dimple milling is designed and named the micro conical surface ball-end mill. The cutting edge is formed by intersecting the conical surface and the inclined plane. A practical grinding method is proposed based on the kinematic principle of the six-axis computer numerical control (CNC) grinding machine for micro conical surface ball-end mills and is validated by grinding simulations and experiments. Micro dimple milling experiments are conducted on the hardened die steel H13 to investigate the cutting performance of the mill. The milling force, the micro dimple roundness error, and the tool wear morphology are observed and analyzed. The results show that the radial milling force is more stable and the wear resistance is improved for the micro conical surface ball-end mill compared to the traditional micro spiral blade ball-end mill. Therefore, a more stable roundness at the entrance hole of the micro dimple can be obtained by using this design after a number of micro dimples have been milled.     

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。     

CORRELATION-BASED ESTIMATION OF CUTTING FORCE COEFFICIENTS FOR BALL-END MILLING

This article presents a methodology to estimate cutting force coefficients based on the least squares approximation using correlation factor between the estimated and measured cutting forces in order to determine the corresponding tool angular position. This method can be applied on measured cutting force data over any small interval of time that need not contain information of the time instant when the cutting tool enters the workpiece, which has been the main requirement in the conventional method. This allows a quick estimation of the cutting force coefficients regardless of the chosen cutting conditions and tool-workpiece material, which is often the case in industrial machining processes. This proposed method has been validated by comparison of cutting force coefficients obtained using conventional estimation technique for a slot ball-end milling test. Besides being useful for predictive evaluation of forces, such estimation of cutting force coefficients of the cutting force model can be useful for understanding variations in cutting process over the tool life and can assist in online monitoring and process optimization.     

Investigations into high-speed rough and finish end-milling of hardened EN24 steel for implementation of control strategies

High-speed end-milling is used for production of variety of parts, dies, and molds made of hardened EN24 steel which are widely used in power and transport industries. Since desired productivity and quality are important in these industries, different strategies are needed for rough and finish end-milling operations. In this paper, a framework is presented for integrating different requirements of high-speed end-milling. In flat end-milling experiments, slots are machined in hardened EN24 steel using single insert cutter under different sets of cutting parameters for roughing and finishing operations. For rough end-milling, the responses such as material removal volume, tool wear and cutting forces are measured with respect to cutting time. A response surface is developed to predict material removal volume and a set of cutting parameters is selected for a given range of material removal volume using differential evolution (DE) algorithm till the tool wear reaches certain value. The experimental data is also used to develop Bayesian-based artificial neural network (ANN) model. Using this ANN model, reference values for cutting force and cutting time are generated for rough end-milling. Similarly, DE is used to predict a set of cutting parameters for a given range of surface roughness using response surface model. The reference cutting force is obtained for finish end-milling using ANN model. These reference values are useful in the monitoring and implementation of control strategy for the high-speed end-milling operations.