Varying Workpiece Dynamics in Milling Stability Analysis

Dynamic stability of a milling process with varying workpiece dynamics is investigated. The milling tool moves along the workpiece with a prescribed feed rate, whereby the contact point shifts. Furthermore, the workpiece dynamics is affected by material removal. The resultant varying workpiece dynamics is taken into account by parametric model order reduction including modal truncation. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On a thermomechanical milling model

This paper deals with a new mathematical model to characterize the interaction between machine and workpiece in a milling process. The model consists of a harmonic oscillator equation for the dynamics of the cutter and a linear thermoelastic workpiece model. The coupling through the cutting force adds delay terms and further nonlinear effects. After a short derivation of the governing equations it is shown that the complete system admits a unique weak solution. A numerical solution strategy is outlined and complemented by numerical simulations of stable and unstable cutting conditions.     

基于端铣刀动态铣削力/力矩的新型混联机床逆向动力学仿真研究

混联机床是近年来并联机床发展的一个重要的趋势,清华大学和齐齐哈尔第二机床厂联合开发了一种新型混联机床.本文针对该机床进行了考虑铣削过程的新型混联机床的逆向动力学仿真研究,得到了端铣刀铣削参数对驱动力的影响规律.     

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)     

The Study of Psychoacoustic Effects of Noise Emitted by the Machine Tools Structure

The main sources of noise at work, in industrial environments, are machine tools: namely, mechanical transmission structure composed of gears, bearings, electric motors drive and the cutting process. Generated vibrations are transmitted through structures, carcasses or directly to environment, developing a complex acoustic field around machine tools. In terms of occupational medicine, the noise is generated by a combination of vibrations producing sounds with different characteristics and that are produced in the workplace [2]. It is important to identify the dominant noise source, the cause of exceeding the admissible limits (87dB) and noise transmission mode to make an objective correlation with effects on humans [1]. Hearing loss can occur immediately at extreme sound levels, but, in general, the problem is noise exposure over time. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Using ARMA models to forecast workpiece roundness error in a turning operation

The paper describes the methodology for developing autoregressive moving average (ARMA) models to represent the workpiece roundness error in the machine taper turning process. The method employs a two stage approach in the determination of the AR and MA parameters of the ARMA model. It first calculates the parameters of the equivalent autoregressive model of the process, and then derives the AR and MA parameters of the ARMA model. Akaike's Information Criterion (AIC) is used to find the appropriate orders m and n of the AR and MA polynomials respectively. Recursive algorithms are developed for the on-line implementation on a laboratory turning machine. Evaluation of the effectiveness of using ARMA models in error forecasting is made using three time series obtained from the experimental machine. Analysis shows that ARMA(3,2) with forgetting factor of 0.95 gives acceptable results for this lathe turning machine.     

Vibration surveillance during milling of flexible details with a use of the optimal control

The paper concerns vibration surveillance during ball end milling of curved flexible details. Here is explained dynamic analysis of non-stationary vibrating system, from which are separated subsystems: modal, structural and connective. An assessment of coincidence of the calculation model results with those from investigation on milling machine is performed. Ball end milling of flexible details is observed very frequently in case of modern machining centres. It is obvious that tool-workpiece relative vibration plays principal role during cutting process. The most important task is to create a FE-model of machined flexible detail and obtain its good correlation with the results of experimental modal analysis. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Discrete Interpolation of G01 Codes in 2D Machining under Bounded Accelerations

In this paper, a new algorithm is proposed to interpolate G01 codes in 2D milling. Without resorting to smooth curve approximation, the algorithm makes full use of the acceleration bounds to change directions with optimal velocities at the cutter location points designated by the G01 codes, and then makes global lookahead and optimization to generate time-optimal interpolation of the G01 codes. The algorithm is realized and tested on NC wood carving machine, showing that when compared with the classical equal-velocity corner-turning method, the current method can reduce the machining time by 14?C115 %, while maintaining better details than the classical method.     

Machine learning for global optimization

In this paper we introduce the LeGO (Learning for Global Optimization) approach for global optimization in which machine learning is used to predict the outcome of a computationally expensive global optimization run, based upon a suitable training performed by standard runs of the same global optimization method. We propose to use a Support Vector Machine (although different machine learning tools might be employed) to learn the relationship between the starting point of an algorithm and the final outcome (which is usually related to the function value at the point returned by the procedure). Numerical experiments performed both on classical test functions and on difficult space trajectory planning problems show that the proposed approach can be very effective in identifying good starting points for global optimization.     

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.     

New steps in the amazing world of sequences and schedules

In this paper we consider classical shop problems:n jobs have to be processed onm machines. The processing timep _i,j of jobi on machinej is given for all operations (i, j). Each machine can process at most one job at a time and each job can be processed at most on one machine at a given time. The machine orders are fixed (job-shop) or arbitrary (open-shop). We have to determine a feasible combination of machine and job orders, a so-called sequence, which minimizes the makespan. We introduce a partial order on the set of sequences with the property that there exists at least one optimal sequence in the set of minimal elements of this partial order independent of the given processing times. The set of minimal elements (set of irreducible sequences) can be in detail described in the case of the two machine open-shop problem. The cardinality is calculated. We will show which sequences are generated by the well-known polynomial algorithms for the construction of optimal schedules. Furthermore, we investigate the problemO∥C _max on an operation set with spanning tree structure. Supported by Deutsche Forschungsgemeinschaft, Project ScheMA     

Multi-modal method for chatter stability prediction and control in milling of thin-walled workpiece

Chatter stability in milling can be predicted by analytical methods or numerical methods. The system should be considered as multi-modal in milling of thin-walled workpiece. This paper proposes a numerical difference method based on Adams-Bashforth scheme. Moreover, multi-modal scheme of numerical methods is proposed. Analytical methods and numerical methods are verified by performing a series of milling trials. The experimental results are consistent with the predicted critical stability boundaries. Moreover, a new method for analyzing the computational time of analytical methods and numerical methods, which is based on the time complexity modeling, is presented. Computational time can be expressed as exact mathematical expression. By using the expression, the rate of increase of computational time can be derived.     

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.     

Enhancement of the micro mechanical basis for local approach cleavage models

The present study is concerned with the investigation of the micro mechanisms of micro defect nucleation in bainitic steels in order to provide an enhanced basis for probabilistic cleavage models. By a micro mechanical modelling of the cleavage initiation process the effects and the interactions of the relevant parameters can be identified. For this purpose Representative Volume Elements (RVE) of the micro structure are utilised, accounting for both, the grain structure as well as the brittle particles at the grain boundaries. The RVE's are loaded based on the local mechanical field quantities determined numerically at the cleavage origins of different fracture mechanics specimens. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Transient Finite Element Simulation of the Temperature Field during Cryogenic Turning of Metastable Austenitic Steel AISI 347

The process chain in manufacturing often consists of many steps. As part of current researches the possibility of combining two process steps, turning and hardening, is investigated to optimize the manufacturing time and to decrease the energy consumption of the process. For metastable austenitic steels, deformation induced hardening during turning can be used to achieve surface hardening [1] and thus to increase the wear resistance [2] as well as the fatigue strength [3], by applying high passive forces onto the workpiece. This enables an austenite-martensite phase transformation, for which it is necessary to maintain low process temperatures, typically below room temperature. Thus, cryogenic coolants are applied [4]. For a better understanding of the influence of cutting parameters on the process temperatures and thus martensite formation, knowledge of the exact temperature distribution in the workpiece and in the contact zone between workpiece and tool is essential. Since the experimental determination of the temperature field is hardly possible, an inverse determination of the process temperatures via transient finite element simulation is performed. The present finite element approach only takes thermal loads into account. The simulations are performed in the finite element program FEAP (Finite Element Analysis Program) with an Eulerian mesh, which requires special consideration of the rigid body rotation of the workpiece. In order to prevent unphysical oscillations in the solution, introduced by the convective time derivative, a streamline upwind / Petrov–Galerkin stabilization scheme is utilized. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear process machine interaction in tool grinding

The manufacturing of high performance cutting tools, like drills and chamfers, is done by a deep grinding process. This tool grinding process shows nonlinear relations between predefined process parameters, as cutting depth, feed speed and cutting speed, and the process characteristics, as process forces, surface properties and stability. Within an interdisciplinary research project a process model is built up to represent the process machine interaction and to predict process forces, deformation of the workpiece and geometry errors caused by this deformation. In this paper, the process model and the coupling of the included submodules will be described. The focus is thereby on the explanation of the contact module and the implementation in the dynamical model. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Size dependent buckling analysis of functionally graded micro beams based on modified couple stress theory

Buckling analysis of functionally graded micro beams based on modified couple stress theory is presented. Three different beam theories, i.e. classical, first and third order shear deformation beam theories, are considered to study the effect of shear deformations. To present a profound insight on the effect of boundary conditions, beams with hinged-hinged, clamped–clamped and clamped–hinged ends are studied. Governing equations and boundary conditions are derived using principle of minimum potential energy. Afterwards, generalized differential quadrature (GDQ) method is applied to solve the obtained differential equations. Some numerical results are presented to study the effects of material length scale parameter, beam thickness, Poisson ratio and power index of material distribution on size dependent buckling load. It is observed that buckling loads predicted by modified couple stress theory deviates significantly from classical ones, especially for thin beams. It is shown that size dependency of FG micro beams differs from isotropic homogeneous micro beams as it is a function of power index of material distribution. In addition, the general trend of buckling load with respect to Poisson ratio predicted by the present model differs from classical one.     

Determining optimal replacement time for metal cutting tools

Traditional tool life models do not take into account the variation inherent in metal cutting processes. As a consequence, the real tool life rarely matches the predicted values. To compensate for this uncertainty, tools are usually replaced prematurely, which leads to unnecessarily high tool costs. In some cases, however, wear-out occurs earlier than predicted, which imposes a risk of workpiece damage or rework and can lead to other extra charges. To balance these costs, this paper proposes an age replacement model. It is assumed that penalty costs are incurred each time a tool fails before the planned replacement. The probability of such an event is determined from the tool reliability function, which models the wear-out by a mixture of Weibull distributions, while failures due to external stresses are accounted for by a homogeneous Poisson process. The optimal replacement time is then determined from a total time on test (TTT) plot. The adequacy of the proposed approach for practical application is tested and confirmed in a case study on turning of Inconel 718 with cubic boron nitride (CBN) tools.     

On scheduling an unbounded batch machine

A batch machine is a machine that can process up to c jobs simultaneously as a batch, and the processing time of the batch is equal to the longest processing time of the jobs assigned to it. In this paper, we deal with the complexity of scheduling an unbounded batch machine, i.e., c=+∞. We prove that minimizing total tardiness is binary NP-hard, which has been an open problem in the literature. Also, we establish the pseudopolynomial solvability of the unbounded batch machine scheduling problem with job release dates and any regular objective. This is distinct from the bounded batch machine and the classical single machine scheduling problems, most of which with different release dates are unary NP-hard. Combined with the existing results, this paper provides a nearly complete mapping of the complexity of scheduling an unbounded batch machine.     

A two-scale simulation framework for Internal Traverse Grinding

We present a hybrid framework which aims at the modelling and simulation of Internal Traverse Grinding of hardened 100Cr6/AISI 52100 by using electro plated cBN grinding wheels. We focus on the thermo-mechanical loading conditions on the workpiece that results from the interaction of workpiece and tool. The modelling framework basically consists of three components, namely representative plane strain adaptive finite element simulations on a meso-scale, capturing the proximity of a single cBN grain when cutting through the workpiece bulk. Secondly, we incorporate a kinematic simulation on the process level to gain detailed simulation-based information on the transient grain-bulk-interaction. The third component of the framework consists of a macro-scale process model that uses the superposed results of the former two components as thermo-mechanical boundary conditions. Using this framework, we target the prediction of metallurgical effects, such as white layers, on the workpiece on the macro scale in the near future. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)