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.     

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.     

Study of the parameters in electrical discharge machining through response surface methodology approach

Whereas the efficiency of traditional cutting processes is limited by the mechanical properties of the processed material and the complexity of the workpiece geometry, electrical discharge machining (EDM) being a thermal erosion process, is subject to no such constraints. The lack of correlations between the cutting rate, the surface finish and the physical material parameters of this process made it difficult to use. This paper highlights the development of a comprehensive mathematical model for correlating the interactive and higher order influences of various electrical discharge machining parameters through response surface methodology (RSM), utilizing relevant experimental data as obtained through experimentation. The adequacy of the above the proposed models have been tested through the analysis of variance (ANOVA). Optimal combination of these parameters was obtained for achieving controlled EDM of the workpieces.     

MPM simulations of high-speed machining of Ti6Al4V titanium alloy considering dynamic recrystallization phenomenon and thermal conductivity

Ti6Al4V titanium alloy is often used in the aircraft industry due to its good strength and toughness etc. However, it is very difficult to simulate high speed machining of titanium alloy using the finite element method (FEM). The reason is that the high speed, large deformation and high strain rate of metal material at high temperature etc. will lead to the element distortions and other numerical difficulties. In contrast with FEM, material point method (MPM) has the advantage of simulating extreme large deformation, fracture and impact problems. Therefore, it is specially suitable for dealing with high speed cutting process. In many existing researches about the high speed cutting process using Johnson−Cook constitutive model, the material dynamic recrystallization softening effect under high pressure and high temperature has not been considered. For this, three modified Johnson−Cook constitutive models for Ti6Al4V titanium alloy are adopted and the parameters for these models were obtained by the split Hopkinson pressure bar (SHPB) test considering the critical strain values, high-temperature range and dynamic recrystallization phenomenon. Furthermore, to ensure the numerical accuracy, the transient heat conduction algorithm is employed in MPM implementation. Finally, comparison and discussion are carried out between the experimental and the simulation data, which show that the high speed cutting process can be better simulated using the modified Johnson−Cook constitutive models.     

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.     

Numerical analysis of chip formation during machining for different value of failure strain

Grinding is a very complicated processing. To increase quality of product and minimize the cost of abrasive machining, we should know physical phenomena which exist during the process. The first step to solution of this problem is analysis of machining process with a single abrasive grain. In the papers [1, 2] the thermo-mechanical models of this process are presented, but in this work attention is concentrated on chip formation and his separation from object. The influence of failure strain ε_f on states of strain and stress in surface layer during machining is explained. The phenomena on a typical incremental step were described using step-by-step incremental procedure, with updated Lagrangian formulation. Then, the Finite Element Method (FEM) and Dynamic Explicit Method (DEM) were used to obtain the solution. Application was developed in the ANSYS system, which makes possible a complex time analysis of the physical phenomena: states of displacements, strains and stress. Numerical computations of the strain have been conducted with the use of two methodologies. The first one requires an introduction of boundary conditions for displacements in the contact area determined in modeling investigation, while the second – a proper definition of the contact zone through the introduction of finite elements of TARGET and CONTACT types, without the necessity to introduce boundary conditions. This model includes variational equations of the object's motion and deformation. Examples of calculations for the displacement, strain and stress field in the surface layer zones were presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical analysis of micromachining of C45 steel by single abrasive grain

Grinding is a very complicated processing. To increase quality of product and minimize the cost of abrasive machining, we should know physical phenomena which exist during the process. The first step to solution of this problem is analysis of machining process with a single abrasive grain. In the paper [1] the thermo–mechanical models of this process are presented, but in this work attention is concentrated on chip formation and his separation from object for different velocity of abrasive grain. The phenomena on a typical step time were described using step–by–step incremental procedure, with updated Lagrangian formulation. Then, the finite elements methods (FEM) and dynamic explicit method (DEM) were used to obtain the solution. Application was developed in the ANSYS system, which makes possible a complex time analysis of the physical phenomena – states of: displacements, strains and stress. Numerical computations of the strain have been conducted with the use of two methodologies. The first one requires an introduction of boundary conditions for displacements in the contact area determined in modeling investigation, while the second – a proper definition of the contact zone, without the necessity to introduce boundary conditions in the contact area. Examples of calculations for the intensity of stress in the surface layer zones were presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Vibration control of ultrasonic cutting via dynamic absorber

Ultrasonic machining (USM) is one of the most effective non-conventional techniques. Its application especially to hard-to-machine material (HTM) is growing rapidly. The main operation condition of USM is at resonance where an exciter derives a tuned blade or a tool. In this paper, the coupling of two non-linear oscillators of the main system and absorber representing ultrasonic cutting process are investigated. This leads to a two-degree-of-freedom Duffing’s oscillator in which such non-linear effects can be neutralized under certain dynamic conditions. The aim of this work is the control of the system behavior at principal parametric resonance condition where the system damage is probable. An approximate solution is derived up to the second order for the coupled system. A threshold value of linear damping has been obtained, where the system vibration can be reduced dramatically. The stability of the system is investigated applying both phase-plane and frequency response techniques. The effects of the different parameters of the absorber on system behavior are studied numerically. Comparison with the available published work is reported.     

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.     

Chatter Vibration Surveillance by the Optimal-linear Control of Spindle Speed and Randomly Varying Spindle Speed

Tool-workpiece relative vibration plays principal role during the process of milling with slender ball end mills. Due to certain conditions, a loss of stability and generation of self-excited chatter vibration will appear. The paper is devoted to a new approach towards vibration surveillance of rotating tools in modern milling machines. Dynamic analysis of a slender ball end milling process has been performed and dynamics of controlled structure is described. In order to reduce vibration level, instantaneous change in the spindle speed appears as control command, and thus the method of vibration surveillance by the spindle speed optimal-linear control has been developed. Due to quality of machined surface being worse while milling with high tilting angle of the tool, the other method of milling with randomly varying spindle speed is presented. It allows us to maintain a high efficiency of surveillance without worsening of the machining quality. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An integrated approach to the one-dimensional cutting stock problem in coronary stent manufacturing

This paper presents a two-stage approach for pattern generation and cutting plan determination of the one-dimensional cutting stock problem. Calculation of the total number of patterns that will be cut and generation of the cutting patterns are performed in the first stage. On the other hand, the second stage determines the cutting plan. The proposed approach makes use of two separate integer linear programming models. One of these models is employed by the first stage to generate the cutting patterns through a heuristic procedure with the objective of minimizing trim loss. The cutting patterns obtained from Stage 1 are then fed into the second stage. In this stage, another integer linear programming model is solved to form a cutting plan. The objective of this model is to minimize a generalized total cost function consisting of material inputs, number of setups, labor hours and overdue time; subject to demand requirements, material availability, regular and overtime availability, and due date constraints. The study also demonstrates an implementation of the proposed approach in a coronary stent manufacturer. The case study focuses on the cutting phase of the manufacturing process followed by manual cleaning and quality control activities. The experiments show that the proposed approach is suitable to the conditions and requirements of the company.     

Supervision System of Machining Process States

Due to non‐linear, multidimensional and random character of most processes of machining, an use of analytical methods to process monitoring is difficult, time‐consuming and expensive. An application of algorithms which base on models in real processes is very limited, especially in the case of grinding processes. On the one hand, such methods require realistic and exact models of monitored process, on the other hand, they can characterize restrictive hypothesis concerning the process modeled. Most of model‐basing learning algorithms have an application to linear and steady‐state processes. However, majority of monitored processes are non‐linear, and, additionally, of nonstationary character. The system of monitoring proposed in the paper bases on artificial intelligence methods, which makes it possible to exclude from it a model of the grinding process.     

Regression and ANN models for estimating minimum value of machining performance

Surface roughness is one of the most common performance measurements in machining process and an effective parameter in representing the quality of machined surface. The minimization of the machining performance measurement such as surface roughness (R_a) must be formulated in the standard mathematical model. To predict the minimum R_a value, the process of modeling is taken in this study. The developed model deals with real experimental data of the R_a in the end milling machining process. Two modeling approaches, regression and Artificial Neural Network (ANN), are applied to predict the minimum R_a value. The results show that regression and ANN models have reduced the minimum R_a value of real experimental data by about 1.57% and 1.05%, respectively.     

Cutting of aramide fiber-reinforced plastics by Co2 laser

Comparative characteristics of aramide fiber reinforced plastics (AFRP) made by laser cutting or machining are presented. It is found that the strength of the specimens cut out by laser is 4–25% higher, while the moisture absorption is at least 2 times lower as compared to those cut out by machining. The deviation of the cutting edge size for AFRP 2 mm thick does not exceed 0.4 mm. Calculated and experimental data are given. The possibilities and conditions of cutting the AFRP up to 6 mm thick are determined.Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 3, pp. 375–384, May–June, 1999.     

On the Asymptotic Stability of the Intrinsic and Fractional Bayes Factors for Testing Some Diffusion Models

Random processes, from which a single sample path data are available on a fine time scale, abound in many areas including finance and genetics. An effective way to model such data is to consider a suitable continuous-time-scale analog, X _t say, for the underlying process. We consider three diffusion models for the process X _t and address model selection under improper priors. Specifically, fractional and intrinsic Bayes factors (FBF and IBF) for model selection are considered. Here, we focus on the asymptotic stability of the IBF's and FBF's for comparing these models. Specifically, we propose to employ certain novel transformations of the data in order to ensure the asymptotic stability of the IBF's. While we use different transformations for pairwise comparisons of the models, we also show that a single common transformation can be used when simultaneously comparing all three models. We then demonstrate that, when FBF's are used to compare these models, we may have to employ different, model-specific training fractions in order to achieve asymptotic stability of the FBF's.     

On the role of energy in chip formation

The implicit code ABAQUS/Standard is used to simulate the formation of continuous and segmented chips. Using the described model, the idealized process of friction‐less machining of an elastic ideally‐plastic material is studied. It is shown that Merchant's classical shear angle relation does not hold, as chip formation does not minimize the energy as assumed by Merchant. The model is also used to study segmented chip formation using a realistic material law for the Titanium alloy Ti6Al4V at high cutting speeds.     

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.     

Spindle Speed Variation for the Suppression of Regenerative Chatter

Summary. A phenomenon commonly encountered during machining operations is chatter. It manifests itself as a vibration between workpiece and cutting tool, leading to poor dimensional accuracy and surface finish of the workpiece and to premature failure of the cutting tool. A chatter suppression method that has received attention in recent years is the spindle speed variation method, whereby greater widths of cut are achieved by modulating the spindle speed continuously. By adapting existing mathematical techniques, a perturbative method is developed in this paper to obtain finite-dimensional equations in order to systematically study the mechanism of spindle speed variation for chatter suppression. The results indicate both modest increase of stability and complex nonlinear dynamics close to the new stability boundary. The method developed in this paper can readily be applied to any other system with time-delay characteristics.     

Hierarchic Markov processes and their applications in replacement models

In this paper a new notion of a hierarchic Markov process is introduced. It is a series of Markov decision processes called subprocesses built together in one Markov decision process called the main process. The hierarchic structure is specially designed to fit replacement models which in the traditional formulation as ordinary Markov decision processes are usually very large. The basic theory of hierarchic Markov processes is described and examples are given of applications in replacement models. The theory can be extended to fit a situation where the replacement decision depends on the quality of the new asset available for replacement.