Analytical Modeling of Chatter Stability in Turning and Boring Operations: A Multi-Dimensional Approach

In this study, an analytical model for the stability of turning and boring processes is proposed. The proposed model is a step ahead from the previous studies as it includes the dynamics of the system in a multi-dimensional form, uses the true process geometry and models the insert nose radius in a precise manner. Simulations are conducted in order to compare the results with the traditional oriented transfer function stability model, and to show the effects of the insert nose radius on the stability limit. It is shown that very high errors in stability, which limit predictions can be caused when the true process geometry is not considered in the calculations. The proposed stability model predictions are compared with experimental results and an acceptable agreement is observed.     

Extension of Tlusty׳s law for the identification of chatter stability lobes in multi-dimensional cutting processes

Chatter vibrations in cutting processes are studied in the present paper. A unified approach for the calculation of the stability lobes for turning, boring, drilling and milling processes in the frequency domain is presented. The method can be used for a fast and reliable identification of the stability lobes and can take into account nonlinear shearing forces, as well as process damping forces. The applicability of Tlusty׳s law, which is a simple scalar relationship between the real part of the oriented transfer function of the structure and the limiting chip width, is extended to milling and any other multi-dimensional chatter problem without neglecting the coupled dynamics. The given analysis is suitable for getting a deep understanding of the chatter stability dependent on the parameters of the cutting process and the structure. Basic examples based on experimental data of real machine tools include the dependence of the stability behavior on the rotational direction in turning, the effect of axial–torsional structural coupling in drilling, and the dynamics of slot milling.     

A study of bifurcation behaviour in oblique turning operation

This paper presents results of linear stability analysis in turning using nonlinear force–feed dynamic model by considering three-dimensional cutting tool geometry. The modified analytical equations for cutting insert with three-dimensional tool geometry are derived by including relative displacements of the tool with respect to a two-degree of freedom work-piece model. The critical stability points obtained as a function of feed are validated against time-domain solutions. Simulation results are shown in the form of limit cycles and bifurcation diagram. Influence of static-feed term on cutting dynamics over a cantilever work-piece is illustrated along with the experimental results.     

Theoretical-experimental modeling of milling machines for the prediction of chatter vibration

Productivity of high speed milling operations can be seriously limited by chatter occurrence. Chatter vibrations can imprint a poor surface finish on the workpiece and can damage the cutting tool and the machine. Chatter occurrence is strongly affected by the dynamic response of the whole system, i.e. the milling machine, the tool holder, the tool, the workpiece and the workpiece clamping fixture. Tool changes must be taken into account in order to properly predict chatter occurrence. In this study, a model of the milling machine-tool is proposed: the machine frame and the spindle were modeled by an experimentally evaluated modal model, while the tool was modeled by a discrete modal approach, based on the continuous beam shape analytical eigenfunctions. A chatter identification technique, based on this analytical-experimental model, was implemented. Tool changes can be easily taken into account without requiring any experimental tests. A 4 axis numerically controlled (NC) milling machine was instrumented in order to identify and validate the proposed model. The milling machine model was excited by regenerative, time-varying cutting forces, leading to a set of Delay Differential Equations (DDEs) with periodic coefficients. The stability lobe charts were evaluated using the semi-discretization method that was extended to n>2 degrees of freedom (dof) models. The stability predictions obtained by the analytical model are compared to the results of several cutting tests accomplished on the instrumented NC milling machine.     

Mechanical design of a new tooling mechanism with on-line controllability of inclination angle

Tool angles are the very important parameters in determining the machining process performance and have significant effects on cutting force, tool wear, tool life, process stability, chip control, etc. This paper presents details of designing a new tooling mechanism which can change on-line the cutting edge inclination angle in turning operations. The mechanism is realised through the use of three specific slopes which work simultaneously to compensate the tooltip deviation due to the change of inclination angles so that the tooltip always stays at one point in space, i.e. its working point. The new tooling mechanism may be used to on-line control and optiimise the machining process.     

超声珩磨颤振单颗磨粒动力学模型的研究

颤振是影响磨削加工稳定性及加工质量的重要因素之一,对于超声珩磨稳定性的研究主要通过动力学模型.在提出对超声珩磨单颗磨粒的基本假设和分析再生型颤振产生机理的基础上,建立了超声珩磨颤振单颗磨粒三维多自由度非线性动力学模型,并简化了轴向和径向超声振动单颗磨粒的动力学模型及其方程,为进一步探求有效的抑振、消振方法提供了依据.     

A computer algorithm for flank and crater wear estimation in CNC turning operations

In order to increase the productivity of turning processes, several attempts have been made in the recent past for tool wear estimation and classification in turning operations. The tool flank and crater wear can be predicted by a number of models including statistical, pattern recognition, quantitative and neural network models. In this paper, a computer algorithm of new quantitative models for flank and crater wear estimation is presented. First, a quantitative model based on a correlation between increases in feed and radial forces and the average width of flank wear is developed. Then another model which relates acoustic emission (AE_rms) in the turning operation with the flank and crater wear developed on the tool is presented. The flank wear estimated by the first model is then employed in the second model to predict the crater wear on the tool insert. The influence of flank and crater wear on AE_rms generated during the turning operation has also been investigated. Additionally, chip-flow direction and tool–chip rake face interfacing area are also examined. The experimental results indicate that the computer program developed, based on the algorithm mentioned above, has a high accuracy for estimation of tool flank wear.     

Finite element analysis of machine and workpiece instability in turning

Chatter is a well-known and self-exited vibration. The stock removal rate is highly affected by this phenomenon. In this paper instability analysis of machining process is presented by dynamic model of turning machine. This model, which consists of machine tool's structure, is provided by finite element method and ANSYS software, so that, the flexibility of machine's structure, workpiece and tool have been considered. The model is evaluated and corrected with experimental results by modal testing on TN40A turning machine in which the natural frequencies and the shape of vibration modes are analyzed. Finally, the stability lobes obtained from this model are plotted and compared with experimental results.     

Machining of free-form surfaces. Part II: Calibration and forces

In the machining simulations of 3D free-form surfaces by ball-end milling, calibration coefficients play very critical role in force predictions. In other words, obtaining the calibration coefficients from calibration tests is a very influential process in the prediction of cutting forces. Accurately obtained calibration coefficients lead to better force predictions. In the literature, the calibration coefficients are assumed to be independent of start and exit angles of the engagement region, thus they are assumed to be identical for any engagement region. Calibration coefficients are obtained from the horizontal slot cutting tests and these tests are repeated for different depth of cuts. In this paper, in order to achieve more accurate force predictions in free-form machining simulations, a new modification algorithm for calibration coefficients is presented. In this research, with theoretical analysis and experimental force signals, it is shown that the inclination angle has a great importance in calibration and in force simulation of 3D free-form machining.     

A predictive surface profile model for turning based on spectral analysis

This article presents a predictive approach of surface topography based on the FFT analysis of surface profiles. From a set of experimental machining tests, the parameters investigated are: feed per revolution, insert nose radius, depth of cut and cutting speed. The first step of the analysis consists of normalizing the measured profiles with the feed per revolution. This results in normalized profiles with a feed per revolution and a signal period equal to 1. The effect of each cutting parameter on the surface profile is expressed as a spectrum with respect to the period length. These effects are quantified and can be sorted in descending order of importance as feed per revolution, insert nose radius, depth of cut and cutting speed. The second part of the paper presents a modeling of the surface profile using the parameters effects and one interaction. The proposed model gives the spectrum of the profile to be predicted. The inverse Fourier transform applied to the spectrum yields the expected surface profile. Measured and simulated profiles are compared for two cutting conditions and results correlate well.     

Mechanics and dynamics of general milling cutters. Part II: inserted cutters

Inserted cutters are widely used in roughing and finishing of parts. The insert geometry and distribution of inserts on the cutter body vary significantly in industry depending on the application. This paper presents a generalized mathematical model of inserted cutters for the purpose of predicting cutting forces, vibrations, dimensional surface finish and stability lobes in milling. In this paper, the edge geometry is defined in the local coordinate system of each insert, and placed and oriented on the cutter body using the cutter's global coordinate system. The cutting edge locations are defined mathematically, and used in predicting the chip thickness distribution along the cutting zone. Each insert may have a different geometry, such as rectangular, convex triangular or a mathematically definable edge. Each insert can be placed on the cutter body mathematically by providing the coordinates of the insert center with respect to the cutter body center. The inserts can be oriented by rotating them around the cutter body, thus each insert may be assigned to have different lead and axial rake angles. By solving the mechanics and dynamics of cutting at each edge point, and integrating them over the contact zone, it is shown that the milling process can be predicted for any inserted cutter. A sample of inserted cutter modeling and analysis examples are provided with experimental verifications.     

Prediction of chip flow direction during machining with self-propelled rotary tools

This paper presents a model for chip flow prediction during tube-end machining process using self-propelled rotary tools. The analysis performed is based on the transformation of the relative kinematic relationships in rotary cutting to that of the conventional cutting with large nose radius. Both relative and absolute chip flow angles are investigated. Tests were performed to measure the absolute chip flow angle, insert self propelled motion, and the deformed chip thickness during machining with self-propelled rotary tool under different cutting conditions. The predicted values of the absolute chip flow angle were in good agreement with that measured experimentally.     

Analysis of compliance between the cutting tool and the workpiece on the stability of a turning process

Chatter is a common vibration problem that limits productivity of machining processes, since its large amplitude vibrations causes poor surface finishing, premature damage and breakage of cutting tools, as well as mechanical system deterioration. This phenomenon is a condition of instability that has been classified as a self-excited vibration problem, which shows a nonlinear behavior characterized by the presence of limit cycles and jump phenomenon. In addition, subcritical Hopf and flip bifurcations are mathematical interpretations for loss of stability. Regeneration theory and linear time delay models are the most widely accepted explanations for the onset of chatter vibrations. On the other hand, models based on nonlinearities from structure and cutting process have been also proposed and studied under nonlinear dynamics and chaos theory. However, on both linear and nonlinear formulations usually the compliance between the workpiece and cutting tool has been ignored. In this work, a multiple degree of freedom model for chatter prediction in turning, based on compliance between the cutting tool and the workpiece, is presented. Hence, a better approach to the physical phenomenon is expected, since the effect of the dynamic characteristics of the cutting tool is also taken into account. In this study, a linear stability analysis of the model in the frequency domain is performed and a method to construct typical stability charts is obtained. The effect of the dynamics of the cutting tool on the stability of the process is analyzed as well.     

Productivity enhancement in dies and molds manufacturing by the use of C continuous tool path

The challenge of die and mold milling is to achieve the specified dimensional and geometrical accuracy, and improve the surface roughness, in order to minimize polishing operations, still necessary to meet the tight tolerances required by the automotive industry and the plastic injection sector. The present study investigates the multi-axis milling of a specific mold steel grade Super Plast ® 300* (SP300) [1], by a ball nose carbide tool coated with Ti(CN). Surface finish analysis given by 3D measurements and data processing techniques shows that micro-geometrical defects generated by C¹ continuous tool path are definitely less serious than those obtained by classical tool paths driven via linear interpolation. Also, polishing time saving is more than 30%. Thus, a substantial productivity enhancement is achieved in dies and molds manufacturing.     

Development of a chip flow model for turning operations

A model is presented which predicts the chip flow direction in turning operations with nose radius tools under oblique cutting conditions. Only the tool cutting edge geometry and the cutting conditions (feed and depth of cut) are required to implement the model. An experimental study has verified the chip flow model and shown that the model's predictions are in good agreement with the experimental results.     

基于灰色关联分析的GH2132线材高精度切削参数优化

目的 通过无心车床车削去除GH2132线材的表面缺陷,分析无心车床加工参数对线材表面粗糙度、尺寸误差和表面显微硬度的响应关系,并建立GH2132线材表面灰色关联度多目标优化模型,确定可行工艺参数域。方法 采用响应曲面中心复合设计,测量车削后GH2132线材的表面粗糙度、尺寸误差和表面显微硬度;利用响应曲面法(Response Surface Method,RSM)分别建立表面粗糙度、尺寸误差和表面显微硬度的单目标预测模型,确定单目标优化最优工艺参数组;基于灰色关联分析(Grey Correlation Analysis,GRA)理论,以表面粗糙度、尺寸误差和表面显微硬度为优化指标进行降维处理,构建车削工艺参数与灰色关联度的二阶回归预测模型;绘制车削工艺参数与灰色关联度值的等值线图,确定可行工艺参数域。结果 对建立的表面粗糙度、尺寸误差和表面显微硬度的单目标预测模型进行方差分析,显著度均小于0.000 1。得到了最小表面粗糙度工艺参数组,切削速度n=373.919 r/min,进给速度vf =0.475 m/min。得到了最小尺寸误差工艺参数组,n=375.636 r/min,vf =0.596 m/min。得到了最大表面显微硬度工艺参数组,n=337 r/min,vf = 0.903 m/min。对于灰色关联度多目标预测模型,误差范围为0.13%~9.4%,确定的可行工艺参数域对应的最小灰色关联度值为0.544 37。结论 基于灰色关联分析的多目标预测模型的准确度较高,主轴转速n对多目标的响应程度大于进给速度vf。通过确定可行工艺参数域,为GH2132线材去除表面缺陷提供工程参考。     

Upper bound analysis of oblique cutting: improved method of calculating the friction area

This paper describes further development of the upper bound analysis of oblique cutting with nose radius tools described previously by Adibi-Sedeh et al. [[1]] by incorporation of an improved method for calculating the friction area at the chip-tool interface. Previously, the friction area was obtained from the shear surface area assuming that the ratio of these areas is the same as in orthogonal machining. Our results showed that this led to overestimation of the effect of friction on the chip flow angle, thereby resulting in smaller changes in the chip flow angle with inclination angle as compared to experimental data. In the new approach, the chip-tool contact length is obtained from the length of the shear surface assuming that the ratio of the lengths is the same as in orthogonal machining and the friction area is calculated using this length. The chip flow angle predicted using the new approach shows much better agreement with experimental data. In particular, the dependence of the chip flow angle on the inclination angle is accurately reproduced. Upper bound analysis of oblique cutting using this new model for the friction area provides an elegant explanation for the relative influence of the normal and equivalent rake angles on the cutting force.     

Investigations on the effects of multi-layered coated inserts in machining Ti-6Al-4V alloy with experiments and finite element simulations

This paper presents investigations on turning Ti-6Al-4V alloy with multi-layer coated inserts. Turning of Ti-6Al-4V using uncoated, TiAlN coated, and TiAlN + cBN coated single and multi-layer coated tungsten carbide inserts is conducted, forces and tool wear are measured. 3D finite element modelling is utilized to predict chip formation, forces, temperatures and tool wear on these inserts. Modified material models with strain softening effect are developed to simulate chip formation with finite element analysis and investigate temperature fields for coated inserts. Predicted forces and tool wear contours are compared with experiments. The temperature distributions and tool wear contours demonstrate some advantages of coated insert designs.     

The significance of normal rake in oblique machining

3D molecular dynamics (MD) simulations of oblique machining of an aluminum workmaterial with a single straight cutting edge were conducted over a wide range of normal rake angles (−45° to +45°) and inclination angles (0° to 45°). Three distinct rake angles, namely, the normal rake angle, α_n, the velocity rake angle, α_v, and the so-called effective rake angle, α_e, associated with oblique machining were considered. Variation of the three components of force (cutting, thrust, and oblique), force ratio (thrust force/cutting force), and specific energy (energy required for unit volume of material removed) with rake angle and inclination angle were determined. Based on the analysis of the simulation results, it is shown that normal rake angle is the angle of significance influencing the mechanics of oblique machining, especially from the point of view of cutting force and specific energy in machining, as reported at the macro scale by many in the literature.     

基于三维测量和混合建模的刀具三维磨损形态研究

刀具磨损部位的三维形态是研究刀具几何参数合理性、分析刀具磨损原因的重要依据。采用三维光学扫描测量技术获取磨损刀具的三维点云数据,利用实体模型与点模型混合处理技术获得刀具磨损区域的三维形态,基于3D模型和点云数据的对比获得磨损前后刀具变化色谱分析图以及偏差分析报告。给出车削硬质合金刀片的三维磨损形态分析步骤,验证方法的可行性和有效性。