On nonlinear cutting response and tool chatter in turning operation

Tool chatter in turning process is addressed with a new perspective. Turning dynamics is investigated using a 3D model that allows for simultaneous workpiece-tool deflections in response to the exertion of nonlinear regenerative force. The workpiece is modeled as a system of three rotors, namely, unmachined, being machined and machined, connected by a flexible shaft. Such a configuration enables the workpiece motion relative to the tool and tool motion relative to the machining surface to be three-dimensionally established as functions of spindle speed, instantaneous depth-of-cut, material removal rate and whirling. The equations of motion for the model are coupled through the nonlinear cutting force. The model is explored along with its 1D counterpart, which considers only tool motions and disregards workpiece vibrations. Different stages of stability for the workpiece and the tool subject to the same cutting conditions are studied. Numerical simulations reveal diverse, oftentimes inconsistent, tool behaviors described by the two models. Most notably, observations made with regard to the inconsistency in describing machining stability limits raise the concern for using 1D models to obtain stability charts.     

转子动力学横向振动基本方程

针对转子动力学系统横向振动基本方程进行研究.将Euler（欧拉）角表示引入转子动力学系统,可以建立描述转子的非线性旋转运动的精细数学模型.并将该精细模型线性化,建立了描述转子动力的基本方程,通过数值算例分析验证了该方程的正确性和有效性.     

Synchronization effects in rotors partly filled with fluid

In fluid-filled rotors self-excited vibrations occur induced by a surface wave of the fluid. A characteristic property is the instability over the full range of angular velocity above the Eigenfrequency of the system. A possible explanation is the occurrence of synchronization effects between fluid and rotor. The behaviour of rotors partly filled with fluid was mostly studied under the aspect of stability in steady-state conditions. For non-steady-state investigations, discrete models with reduced number of degrees of freedom and reasonable ability to model the system behaviour are desirable due to the complexity of fluid modelling. This paper analyses a simple minimal model and shows synchronization effects between fluid and rotor model. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Synchronization effects in rotors partially filled with fluid-influence on propulsion

In fluid-filled Rotors occur self-excited vibrations induced by surface waves of the fluid. A characteristic property is the instability over an interval of angular velocity above the natural frequency of the system. One explanation is the occurrence of synchronization effects between fluid waves and the critical rotor speed. The behaviour of rotors partly filled with fluid was mostly studied under the aspect of stability in steady-state conditions. For non-steady-state investigations, discrete models with reduced number of degrees of freedom and reasonable ability to model the system behaviour are desirable for observer-based real-time control. This paper analyses a model based on a laval rotor and shows synchronization effects between fluid waves and rotor model and its influence on the rotor propulsion. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling of cutting force prediction in machining high-volume SiCp/Al composites

Variations in cutting forces significantly influence the tool wear and part quality in machining high-volume SiC-particle-reinforced aluminum matrix (SiCp/Al) composites. Properties of the reinforcement SiC particles, such as size and volume fraction, contribute to the change in the cutting forces. This paper presents a cutting force model based on the geometrical and mechanical nature of the tool and workpiece, considering the effect of the SiC reinforcement particles. The cutting force is predicted as three components (F_z, F_x, and F_y) and the resultant cutting force F_τs. The cutting force was considered to generate three deformed zones: (a) shear deformed zone, (b) friction deformed zone on the chip–tool interface, (c) plow deformed zone. The effect of SiC reinforcement particles on friction deformed zone is analyzed emphatically. The friction force from friction deformed zone was obtained by calculating the sliding friction force and rolling friction force. To verify the feasibility and validity of the predicted model of cutting force, cutting experiments were performed with different combinations of cutting speed, feed rate, depth of cut, and tool nose radius. The predicted cutting force values demonstrate good agreement with the measured experimental cutting force values in most cutting conditions. The average percentages of the prediction error were 1.93%, 6.20%, and 10.48% for the F_z, F_x, and F_y components, respectively, thus proving the validity and accuracy of the predicted model of cutting forces.     

Active vibration control of unbalanced flexible rotor–shaft systems parametrically excited due to base motion

Rotor vibrations caused by large time-varying base motion are of considerable importance as there are a good number of rotors, e.g., the ship and aircraft turbine rotors, which are often subject to excitations, as the rotor base, i.e. the vehicle, undergoes large time varying linear and angular displacements as a result of different maneuvers. Due to such motions of the base, the equations of vibratory motion of a flexible rotor–shaft relative to the base (which forms a non-inertial reference frame) contains terms due to Coriolis effect as well as inertial excitations (generally asynchronous to rotor spin) generated by different system parameters. Such equations of motion are linear but time-varying in nature, invoking the possibility of parametric instability under certain frequency–amplitude combinations of the base motion. An investigation of active vibration control of an unbalanced rotor–shaft system on moving bases is attempted in this work with electromagnetic control force provided by an actuator consisting of four electromagnetic exciters, placed on the stator in a suitable plane around the rotor–shaft. The actuator does not levitate the rotor or facilitate any bearing action, which is provided by the conventional suspension system. The equations of motion of the rotor–shaft continuum are first written with respect to the non-inertial reference frame (the moving base in this case) including the effect of rotor internal damping. A conventional model for the electromagnetic exciter is used. Numerical simulations performed on the flexible rotor–shaft modelled using beam finite elements shows that the control action is successful in avoiding the parametric instability, postponing the instability due to internal material damping and reducing the rotor response relative to the rigid base significantly, with sufficiently low demand of control current in comparison with the bias current in the actuator coils.     

Stability and Bifurcations of Rotors in Fluid Film Bearings

To study the nonlinear phenomena of rotors in the sense of bifurcation theory, the mechanical model of a symmetric flexible rotor is investigated which is supported by two identical journal bearings. Two types of journal bearings are considered. While the oil whirl and oil whip oscillations of rotors in plain journal bearings are widely examined, the floating ring bearings cause a quite different vibration behavior with several mode interactions and an area of so-called critical limit cycles leading to a rotor damage. For both types a Hopf bifurcation marks the beginning of the self-excited oscillations in the case of a perfectly balanced rotor. By applying the methods of numerical continuation the occurring limit cycles as well as their stability are determined. The different nonlinear effects with the corresponding bifurcations are explained by describing the global solution behavior of the rotor-bearing systems. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effects of ridge-top and lee-slope fires upon rotor motions in the lee of a steep ridge

Soon after the outbreak of the South Australian Ash Wednesday I bushfire on a ridge in the Adelaide Hills, fires were observed burning up its lee slope in a direction opposite to that of the main fire. To investigate mathematically why this happened, a simple two-dimensional analytical model of a lee rotor (which occurs when airflow over a ridge separates from the lee slope) is developed by applying the first circulation theorem of physical hydrodynamics to a triangular material curve of air parcels in the lee of a ridge. The resultant equation describes how fire-generated buoyancy, frictional driving from above and lee-slope friction affect the average airspeed around a lee rotor.

A comparison between steady-state solutions of the rotor equation with and without a ridge-top fire indicates that the presence of the latter slightly retards any lee rotor which may have existed under neutral pre-fire conditions. The solution of an initial-value problem simulating the growth and decay of a lee-slope fire is next found and its dependence upon the ratio of the frictional relaxation time to the growth time of maximum fire-induced instability across the rotor is investigated and graphed. For growth times greater than 2.5 minutes and reasonable friction coefficients, it turns out that the response of the rotor to the slope fire is almost instantaneous and its maximum speed is more than twice its pre-fire speed. A halving of the friction coefficients even results in the maximum rotor speed being more than the airspeed above it. It is concluded that buoyant enhancement of lee rotors by fires greatly helps the latter to burn up lee slopes and that lee rotors containing intense fires may sometimes even drive the airflow above them.     

基于NARX神经网络方法的汽轮机转子关键部位应力预测

汽轮机启动过程中,对转子进行应力预测具有重要意义.为满足在线预测国产某350 MW超临界汽轮机转子关键部位应力的需要,提出了一种基于具有外部输入的非线性自回归(NARX)神经网络的应力预测方法.根据转子实际尺寸建立二维轴对称有限元模型,确定了相应的边界条件,并对有限元计算结果进行验证,得到了转子在冷启动工况下的温度场和应力场,确定了转子的危险点.再根据冷启动规则,构建了288个典型启动工况,并对每个启动工况分别进行有限元计算,获取了每个工况下机组运行参数以及转子危险点处应力的时间历程数据,进而建立了神经网络训练样本库,并使用NARX神经网络对危险点处应力进行预测.此基于NARX神经网络的预测方法可以准确预测出汽轮机转子危险点处的应力变化趋势,其预测值与有限元仿真结果吻合良好,可以满足转子应力在线预测的需求.     

A “micro” process planning system based on integer programming for prismatic parts produced on horizontal machining centers

An automated process planning system is developed for manufacturing prismatic parts on a Horizontal Machining Center. The goal is to demonstrate the feasibility of using the integer (0–1) programming technique to determine the optimal sequence of machining operations. The final process sequence reflects constraints on tool life. Precedence relationships due to fixturing and/or process requirements are also taken into account. Decision logic for selection of cutting tools and calculation of necessary machining parameters are also developed. Process plans for test workpieces are produced and the effectiveness of the system demonstrated.     

Determining the optimal procurement policy and maximum allowable lifespan for machining tools with stochastically distributed toollife

For high-value added products, machining tools’ lifespan significantly influences the quantity of procurement in machining process. Preemption of tools from the workpiece while processing is continuing is sometime beneficial to safeguard the product from the damage due to tool failure or its malfunction. Also an early discard of a tool is costly for the manufacturing operation. Therefore an optimal strategy for the tool life is sought here to determine the maximum allowable tool lifespan to preempt from the workpiece and to have an appropriate amount of tool stock in the crib to ascertain the proper running of the production schedule and tool inventory. Therefore, an impact of the machining tool lifespan on the production-inventory policy of the system is investigated in this paper. An integrated lifespan related inventory model for machining tools is developed to meet the responding accurate requirement of procurement and inventory. Two numerical examples are presented to illustrate the integrated model. The results show that the practical lifespan adoption of machining tools has significant impact on the whole quantity of procurement, and eventually influences the coordinating economic decision making.     

Scheduling of a machining center

A machining center is an advanced NC (Numerical Control) machine that has the capability to perform a variety of operations on a part by automatically changing the cutting tools. Because of its versatile processing capabilities, a machining center is often a production bottleneck, and effective scheduling can result in significant improvement of system performance. The problem, however, is very difficult since many factors such as machine setups, pallets, tool magazine, and possible tool overlapping among different part types, etc., have to be considered. This paper presents an optimization-based approach for the scheduling of a machining center with two pallets. A novel “separable” problem formulation that considers the above mentioned factors is presented. Lagrangian relaxation is applied to decompose the problem into simple subproblems, which are efficiently solved without encountering complexity difficulties. The subgradient method is then used to update the multipliers. Testing results indicate that the approach is effective, and the algorithm provides a valuable tool for solving stand-alone machining center problems. The approach also points out a direction on how to consider machining centers within a job shop environment.     

Prediction of diameter errors in bar turning: a computationally effective model

Machining accuracy can be considerably affected by the deflections of the machine–workpiece–tool system as well as the thermal expansion of material during machining. An improved model for predicting dimensional errors in turning process is presented. This model uses a geometric analysis in the machine frame, in which the elastic deflections of the machine–workpiece–tool system due to the cutting force are studied. In this paper, our workpiece deflection model [A.-V. Phan, G. Cloutier, J.R.R. Mayer, International Journal of Production Research 37 (1999) 4039–4051; G. Cloutier, J.R.R. Mayer, A.-V. Phan, Computer Modeling and Simulation in Engineering 4 (1999) 133–137] earlier developed is employed. As described in Phan et al. (1999), this deflection model is general, accurate and computationally effective thanks to its closed-form solutions derived from the finite element technique. Also, due to the coupling between the cutting force and actual depth of cut, iterative computations are performed to obtain the coupling value of this force which provides further accuracy to the prediction. Finally, via numerical examples, the predicted diameter error on a workpiece, the ratio between the coupled cutting force and its nominal value along the part axis as well as the influence of the cutting force components on the error prediction are computed using the proposed model. The results provide additional insight into the error formation in the turning process.     

Oscillations of Carbon Brushes in Hand‐held Electrical Tools

A series‐universal motor is usually used in hand‐held electrical tools, such as cutting or grinding machines. The corresponding two carbon brushes are preloaded by springs to maintain a proper contact necessary to reduce their wear and erosion. The oscillations of carbon brushes are coupled with the rotor motion. A model including carbon brushes and the main parts of tool rotor is described. By using the method of multibody systems the equations of motion are derived. The one‐sided contact forces and the electrical forces between commutator and brushes are mainly responsible for the nonlinear oscillations of brushes. The contour of contact surface is one of the major parameters of contact force. There exist periods where the brushes are separated from the commutator, i.e. a free flight motion of carbon brush occurs. The measured and simulated results show that a large spring preload and a small brush mass improve the contact and result in reduced free flight periods. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear stability analysis of rotor-bearing systems

High-speed rotors supported by floating ring bearings exhibit beside self-excited vibrations various nonlinear vibration effects, which may cause the damage of the rotor. After deriving the equations of motion of a perfectly balanced turbocharger rotor supported by floating ring bearings, bifurcation analyses are carried out with both rigid and flexible model by applying numerical continuation methods. Thereby, the main focus of the investigation is on the critical bifurcations emanating destructive limit-cycle oscillations of higher amplitudes. Finally, the influence of the shaft elasticity on the critical limit-cycle oscillations is discussed. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Novel approach for modelling of nanomachining using a mesh-less method

In this paper, a mesh-less method, called Smoothed Particle Hydrodynamics (SPH) is used to simulate the nanomachining operation in order to assist with the understanding of the fundamental mechanisms of nano scale material deformation and the characteristics of the post machined surface. An elasto-plastic nano-machining analysis is used to form a nano-groove using a conical tool on a copper specimen. The SPH solutions are validated against nano scale machining experiments conducted using a nanoindenter. The simulated results showed that the normal force is greater than the cutting force in this nano scale machining operation, which is consistent with the experimental results. Both the ploughing and cutting mechanisms were observed in these machining conditions and increased with the increase of the depth of cut. Moreover, the results reveal that the larger negative rake angle reduced the ploughing mechanism and caused higher residual stress and strain along the machined surface. Therefore, the effect of machining parameters on the nano deformation mechanism and the quality of the machined surface can be rapidly assessed using SPH.     

大型近海水平轴风力机转轮的空气动力学性能优化判据

以近海风能工程为研究目标,对具有不同特性参数（设计风速、叶尖线速度和转轮实度）的大容量（1～10 MW）风力机转轮的气动性能与几何特性进行分析与研究．首先提出大型机组转轮气动性能优化判据:在其直径最小的前提下具有尽可能高的年可用风能特性因数以及与之相关的风能利用系数,因而可捕获最多风能,使年发电量最大．接着给出影响它的几个主要气动参数,如转轮设计风速、叶尖线速度以及转轮实度,并分析风力机在近海气象条件下运转时上述两个气动指标随这些参数变化的规律．提供的气动分析方法及结果可作为大型近海风力机转轮气动性能的评价基础．     

Nonlinear dynamics of regenerative cutting processes—Comparison of two models

Understanding the nonlinear dynamics of cutting processes is essential for the improvement of machining technology. We study machine cutting processes by two different models, one has been recently introduced by Litak [Litak G. Chaotic vibrations in a regenerative cutting process. Chaos, Solitons & Fractals 2002;13:1531–5] and the other is the classic delay differential equation model. Although chaotic solutions have been found in both models, well known routes to chaos, such as period-doubling or quasi-periodic motion to chaos are not observed in either model. Careful analysis shows that the chaotic motion from the Litak’s model has sharper spectral peaks, a smaller correlation dimension and a smaller value for the largest positive Lyapunov exponent. Implications to the control of chaos in cutting processes are discussed.     

Modeling and analysis of nonlinear rotordynamics due to higher order deformations in bending

A mathematical model incorporating the higher order deformations in bending is developed and analyzed to investigate the nonlinear dynamics of rotors. The rotor system considered for the present work consists of a flexible shaft and a rigid disk. The shaft is modeled as a beam with a circular cross section and the Euler Bernoulli beam theory is applied with added effects such as rotary inertia, gyroscopic effect, higher order large deformations, rotor mass unbalance and dynamic axial force. The kinetic and strain (deformation) energies of the rotor system are derived and the Rayleigh–Ritz method is used to discretize these energy expressions. Hamilton’s principle is then applied to obtain the mathematical model consisting of second order coupled nonlinear differential equations of motion. In order to solve these equations and hence obtain the nonlinear dynamic response of the rotor system, the method of multiple scales is applied. Furthermore, this response is examined for different possible resonant conditions and resonant curves are plotted and discussed. It is concluded that nonlinearity due to higher order deformations significantly affects the dynamic behavior of the rotor system leading to resonant hard spring type curves. It is also observed that variations in the values of different parameters like mass unbalance and shaft diameter greatly influence dynamic response. These influences are also presented graphically and discussed.     

A new bounding mechanism for the CNC machine scheduling problems with controllable processing times

In this study, we determine the upper and lower bounds for the processing time of each job under controllable machining conditions. The proposed bounding scheme is used to find a set of discrete efficient points on the efficient frontier for a bi-criteria scheduling problem on a single CNC machine. We have two objectives; minimizing the manufacturing cost (comprised of machining and tooling costs) and minimizing makespan. The technological restrictions of the CNC machine along with the job specific parameters affect the machining conditions; such as cutting speed and feed rate, which in turn specify the processing times and tool lives. Since it is well known that scheduling problems are extremely sensitive to processing time data, system resources can be utilized much more efficiently by selecting processing times appropriately.