Prediction of mechanistic cutting force coefficients using ALE formulation

This paper demonstrated the use of an efficient and accurate numerical tool (i.e., FEA) in simulating the cutting process and determining both the average and instantaneous cutting force coefficients. The main advantage of this approach compared to other available methods is that it eliminates the need for experimental calibrations. In this approach, an Arbitrary Lagrangian Formulation was employed in the finite element method simulations. This formulation has been gaining more recognition in structural analysis for its combined advantages of both Lagrangian and Eulerian formulations in a single model. Based on the work of Kline et al. (ASME J Eng Ind 104:272–278, 10), the tool is discretised along the axis into segments and the cutting forces acting on the cutting edge segment are presented in terms of cutting force coefficients. Cutting force coefficients are obtained using the least squares method and cutting force predictions using evaluated coefficients are shown to match experimental results with satisfactory accuracy.     

Prediction model and simulation of cutting force in turning hard-brittle materials

The removal mechanism of hard-brittle material was studied in this paper. The shear strain and specific shear work of brittle material cutting were analyzed. The cutting force model of hard-brittle material was developed based on the fracture mechanics. Johnson-Cook model was modified and applied to finite element simulation of hard-brittle material cutting. The cutting force of machinable ceramics was predicted by BP neural network. The turning experiments of machinable ceramics were carried out. The influence of processing parameters on cutting force was investigated. The results show that the modified constitutive model well reflects the fracture removal process of brittle material. The simulation results are in well agreement with experimental data and theoretical data. The effects of cutting depth and feed speed on cutting force are larger than those of cutting speed and tool cutting edge angle.     

Identification of instantaneous cutting force coefficients using surface error

Cutting force coefficients are the key factors for efficient and accurate prediction of instantaneous milling force. To calibrate the coefficients, this paper presents an instantaneous milling force model including runout and cutter deformation. Also, forming of surface error is analyzed, and a surface error model considering runout is proposed. Using surface errors of two experiments completed with the same cutting conditions but different axial depth only, cutter deformation is obtained. Then, a new approach for the determination of instantaneous cutting force coefficients is provided. The method can eliminate influences of the other factors except cutter deformation and runout. A series of experiments are designed, and the results are used to identify the parameters. With the evaluated coefficients and runout parameters, the instantaneous milling force and surface error are predicted. A good agreement between predicted results and experimental results is achieved, which shows that the method is efficient, and effect of runout on surface error is not negligible.     

Specific cutting force coefficients modeling of end milling by neural network

In a high precision vertical machining center, the estimation of cutting forces is important for many reasons such as prediction of chatter vibration, surface roughness and so on. The cutting forces are difficult to predict because they are very complex and time variant. In order to predict the cutting forces of end-milling processes for various cutting conditions, their mathematical model is important and the model is based on chip load, cutting geometry, and the relationship between cutting forces and chip loads. Specific cutting force coefficients of the model have been obtained as interpolation function types by averaging forces of cutting tests. In this paper the coefficients are obtained by neural network and the results of the conventional method and those of the proposed method are compared. The results show that the neural network method gives more correct values than the function type and that in the learning stage as the omitted number of experimental data increase the average errors increase as well.     

Investigation of the milling stability based on modified variable cutting force coefficients

The cutting force signal distortion is caused by the dynamic characteristics of cutting force testing system. In order to handle this issue, we propose two improvements in the traditional inverse filtering technology. Firstly, we use three-spline interpolation method instead of the curve fitting method to fit the frequency response function of the test system which basically improves the accuracy of fitting. Secondly, the low-pass filter is added before the inverse filter to eliminate the influence of the high-frequency noise signal on the cutting force signal. We choose the cavity-free surface of outer covering parts of mold of automobile as research objects. The inverse filter dynamic compensation technology has been used to remove the influence of the dynamic characteristics of the test system and the high-frequency noise on the cutting force signal. The effectiveness of the proposed method is verified by relative milling experiments. Based on the experimentally measured forces after dynamic compensation, the modified cutting force coefficients are obtained using the average milling force method. The variation law of the cutting force coefficients with the axial depth, the radial width, and the feed rate is examined. Based on the modified variable cutting force coefficients, the 3D stability of the ball end milling cutter surface has been obtained using full-discretization approach. Combining the results from the cutting experiment and the nonlinear method, the stability prediction based on the modified variable cutting force coefficient can improve the prediction accuracy. The results provide theoretical support for the optimization of the machining process of the cavity-free surface of outer covering parts of mold of automobile.     

Analysis of surface roughness and cutting force components in hard turning with CBN tool: Prediction model and cutting conditions optimization

In this study, the effects of cutting speed, feed rate, workpiece hardness and depth of cut on surface roughness and cutting force components in the hard turning were experimentally investigated. AISI H11 steel was hardened to (40; 45 and 50) HRC, machined using cubic boron nitride (CBN 7020 from Sandvik Company) which is essentially made of 57% CBN and 35% TiCN. Four-factor (cutting speed, feed rate, hardness and depth of cut) and three-level fractional experiment designs completed with a statistical analysis of variance (ANOVA) were performed. Mathematical models for surface roughness and cutting force components were developed using the response surface methodology (RSM). Results show that the cutting force components are influenced principally by the depth of cut and workpiece hardness; on the other hand, both feed rate and workpiece hardness have statistical significance on surface roughness. Finally, the ranges for best cutting conditions are proposed for serial industrial production.     

Modeling of cutting force coefficients in cylindrical turning process based on power measurement

The cutting force is an important physical quantity in metal cutting, and the cutting force coefficients are the basis for establishing the cutting force model. In this paper, the relation between the cutting power and the cutting force coefficients is established. A cutting power model was established with a linear relationship between the spindle power and material removal rate (MRR). The power-based model of the main cutting force coefficients is proposed by extracting the linear equation coefficients of the power-MRR function. The power-based model of feed force coefficients is established as a quadratic polynomial equation between the motor power of the feed axis and feed rate. And the cutting force coefficients and the edge force coefficients of feed force are expressed respectively by the two orders of coefficients of the equation. The thrust force coefficients are indirectly calculated from the relation between tangential cutting force and thrust force with friction angle of tool-chip. The power-based models were verified by a series of cutting tests regarding material properties, cutting parameters, and axial directions. The results show that the cutting force coefficients obtained by measuring the cutting power have good correspondence with that identified by dynamometer.     

一种难加工材料的车削力模型的实验研究

采用了多因素回归正交设计的方法进行了一种难加工材料的车削实验，在给出实验模型和数学推导的基础上，借助于作者设计的计算机软件，高效完成了上述有关工作并建立了该材料切削力的数学模型，为今后的切削加工过程数值模拟以优化切削用量和刀具的结构设计和几伺参数的选择奠定了基础。     

Application of a comprehensive dynamic cutting force model to orthogonal wave-generating processes

The dynamics of a cutting process are very complex in nature. They involve not only the changes of plastic state in the intensive shear zone of the chip formation process but also the elastic behaviour of work material surrounding the plastic deformation zone, especially in the vicinity of the tool nose region. As an extension to the previous developments in formulating the shear angle oscillation in dynamic cutting (D. W. Wu, Development of dynamic shear angle model for wave-generating processes based on work-hardening slip-line field theory. Int. J. Mech. Sci. 29, 407–424, 1987; D. W. Wu, Governing equations of the shear angle oscillation in dynamic orthogonal cutting. Trans. ASME J. of Engng for Indust. 108, 280, 1986), a comprehensive dynamic cutting force model has been developed from the mechanics of the cutting process by taking into account the equilibrium of forces in the primary and secondary plastic deformation zones and the redistribution of the contact stress inside the workpiece in the vicinity of the tool nose region.The model has been tested through a computer simulation for orthogonal wave-generating processes. By reference to existing experimental evidence, the theoretical predictions show generally good agreement with the test results.     

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.     

High-speed milling of CFRP composites: a progressive damage model of cutting force

Three-dimensional Hashin failure criterion and material stiffness degradation model were compiled by VUMAT subroutine. The Abaqus/Explicit solver was performed to establish progressive damage model of cutting force for CFRP high-speed milling, and high-speed milling experiments with different cutting parameters were carried out. Further, the impact mechanism of fiber cutting angle and cutting parameters on cutting force, stress, and material failure during milling was explored, and the material removal mechanism in high-speed milling of CFRP was revealed. The results show that the error between the experimental and simulated of cutting forces is less than 5%, which indicates that the progressive damage model is feasible. The fiber cutting angle has significant influence on cutting force and stress in cutting process, and the cutting direction has a significant influence on cutting force. In addition, cutting parameters play a critical role in cutting force, and the feed per tooth is the most significant factor affecting the cutting force. Simultaneously, the progressive damage model predicts that the shear failure of materials mainly concentrates in the cutting area and extends along the feed direction. Finally, the material removal mechanism of CFRP in high-speed milling was revealed combining cutting force experiment.     

Prediction of cutting force for ball end mill in sculptured surface based on analytic model of CWE and ICCE

Abstract

The force prediction is the precondition of improving equipment utilization ratio and optimizing process for CNC machining. Cutter-workpiece engagement (CWE) and in-cut cutting edge (ICCE) are the keys. In this article, a new analytic method of CWE and ICCE is proposed for ball end milling of sculptured surface and the prediction model of milling force is established. The sculptured surface is discretized into a series of infinitesimal inclined planes corresponding to cutter location points. The geometry relationships of cutter axis, feed direction and inclined plane are defined parametrically. The boundary curves and the boundary inflection points of the CWE are obtained by intersecting spatial standard curved surfaces with rotation transformation of coordinate system. The effective intersection points of the CWE and the cutter edge curve in X_c-Y_ctwo-dimensional plane are the upper and lower boundary points of ICCE. Based on the instantaneous chip thickness considering arbitrary feed direction, the force prediction model for ball end mill of three-axis surface milling is established. Simulation and experiment show that CWE and ICCE calculated by analytic method are well consistent with those of solid method. The predicted cutting forces match well with the measurements both in magnitude and variation trend.     

Behavior of austenitic stainless steels at high speed turning using specific force coefficients

Turning operation has been widely studied, and it is a well-known process. However, still today some limitations exist in the processing of some materials, mainly due to the poor or inexistent characterization. Such is the case of austenitic stainless steels, which in spite of being materials of high economic and technological value, their behavior to machining is still not well understood in some aspects. There are not reliable and updated technological data about austenitic stainless steels at industry. This fact is especially significant when considering technological development conducted by a continuous increment of cutting speeds. Nowadays, there is not a reliable mechanistic model for austenitic stainless steels turning adjusted for high cutting speeds. In this paper, a mechanistic model for cutting force prediction is presented. This model was developed for machining with nose radius tools considering the effect of the edge force due to the rounded cutting edge. In addition, a set of machining tests were carried out to obtain the specific force coefficients expressions for austenitic stainless steels using the mechanistic approach at high cutting speeds. The specific cutting coefficients were obtained applying the force model as an inverse model. This paper presents expressions for shearing and edge cutting coefficients which are valid for a wide range of cutting conditions. Results were validated by comparing the values estimated by the model with the ones obtained by experimentation.     

Prediction of dynamic cutting force and regenerative chatter stability in inserted cutters milling

Currently, the modeling of cutting process mainly focuses on two aspects: one is the setup of the universal cutting force model that can be adapted to a broader cutting condition; the other is the setup of the exact cutting force model that can accurately reflect a true cutting process. However, there is little research on the prediction of chatter stablity in milling. Based on the generalized mathematical model of inserted cutters introduced by ENGIN, an improved geometrical, mechanical and dynamic model for the vast variety of inserted cutters widely used in engineering applications is presented, in which the average directional cutting force coefficients are obtained by means of a numerical approach, thus leading to an analytical determination of stability lobes diagram (SLD) on the axial depth of cut. A new kind of SLD on the radial depth of cut is also created to satisfy the special requirement of inserted cutter milling. The corresponding algorithms used for predicting cutting forces, vibrations, dimensional surface finish and stability lobes in inserted cutter milling under different cutting conditions are put forward. Thereafter, a dynamic simulation module of inserted cutter milling is implemented by using hybrid program of Matlab with Visual Basic. Verification tests are conducted on a vertical machine center for Aluminum alloy LC4 by using two different types of inserted cutters, and the effectiveness of the model and the algorithm is verified by the good agreement of simulation result with that of cutting tests under different cutting conditions. The proposed model can predict the cutting process accurately under a variety of cutting conditions, and a high efficient and chatter-free milling operation can be achieved by a cutting condition optimization in industry applications.     

车削AISI420不锈钢切削力预测模型构建

为了进一步研究AISI420不锈钢的切削机制,在Third Wave Advant Edge中建立车削有限元模型,进行车削加工仿真模拟,并对实验数据进行回归分析,得到三向切削力的预测模型。结果表明:车削力预测模型拟合度较好,回归分析效果显著,有较高的置信度,可为AISI420不锈钢的切削研究提供理论参考。     

Establishment of a cutting force model and study of the stress–strain distribution in nano-scale copper material orthogonal cutting

This article focuses on the establishment of a cutting force calculation model in terms of nano-scale orthogonal cutting, and investigates the stress–strain distribution of single-crystal copper that occurs in terms of nano cutting. The cutting force that occurs during the nano-scale cutting of single-crystal copper, and also its changes under different situations, can be found in this study. The molecular dynamics (MD) model was proposed to evaluate the displacement components of the atom in any temporary situation on the nano-scale cutting. The atom and lattice were regarded as the node and element, respectively. The shape function concept of the finite element method (FEM) is used to calculate the equivalent strain of the nodal atom and element. The equivalent stress–strain relationship equation was acquired by nano-scale thin-film tensile simulation in this study, and was used to further calculate the equivalent stress that occurs under the equivalent strain. Subsequently, a stress–strain distribution during nano-scale orthogonal cutting can be acquired.     

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.