Investigation on chatter stability of robotic rotary ultrasonic milling

In recent years, industrial robots with higher flexibility and lower cost have become a hot topic in the manufacturing field. In terms of practical machining applications, they are mainly employed in the situations with low cutting forces such as deburring, chamfering and polishing. However, the weak stiffness of robot induces milling chatter easily. Severe chatter not only damages the dimensional accuracy of parts, but also decreases machining efficiency and tool life. Thus, it is urgent to seek a new method to suppress robotic milling chatter. In this paper, robotic rotary ultrasonic milling (RRUM) technology is used to restrict machining vibration. Meantime, an analytical model of stability is developed. Robotic milling system is considered as a three degrees of freedom (3-DOF) model. After that, based on analysis of dynamic chip thickness, a linear force model is developed through defining an angle γ affected by ultrasonic vibration. Then, the semi-discretization method (SDM) is applied to obtain stability lobe diagrams. The analysis result indicates that stability region of RRUM is improved by 133% compared with robotic conventional milling (RCM). Finally, verification experiments are carried out to prove the rationality and effectiveness of these stability lobe diagrams.     

A model-based adaptive controller for chatter mitigation and productivity enhancement in CNC milling machines

Seeking a higher level of automation, according to Intelligent Manufacturing paradigm, an optimal process control for milling process has been developed, aiming at optimizing a multi-objective target function defined in order to mitigate vibration level and surface quality, while preserving production times and decreasing tool wear rate. The control architecture relies on a real-time process model able to capture the most significant phenomena ongoing during the machining, such as cutting forces and tool vibration (both forced and self-excited). For a given tool path and workpiece material, an optimal sequence of feedrate and spindle speed is calculated both for the initial setup of the machining process and for the continuous, in-process adaptation of process parameters to changes the current machining behavior. For the first time in the literature, following a Model-Predictive-Control (MPC) approach, the controller is able to adapt its actions taking into account process and axes dynamics on the basis of Optimal Control theory. The developed controller has been implemented in a commercial CNC of a 3-axes milling machine manufactured by Alesamonti; the effectiveness of the approach is demonstrated on a real industrial application and the performance enhancement is evaluated and discussed.     

高速铣削颤振识别和稳定性预测

颤振是刀具与工件之间剧烈的自激振动,是影响工件表面质量与刀具磨损的重要因素。通过高速铣削试验,对加工过程中铣削力与振动信号进行分析,给出了一种通过监测加工过程中信号功率谱能量比变化来识别颤振的方法。试验结果表明:颤振发生时信号功率谱最主要的特性是在主轴转动频率、切削频率及其谐波两边等间距处会出现相应的颤振频率,当主颤振频率处的能量超过一定的阈值时,加工系统颤振,否则,无颤振。建立了颤振动力学模型,通过试验获得了铣削系统频响函数和铣削力系数,绘制了铣削加工稳定性曲线。结合提出的颤振识别方法,验证了动力学模型的准确性,可为实际加工中合理选择加工参数和颤振监测提供参考。     

Optimal robust control of drug delivery in cancer chemotherapy: A comparison between three control approaches

During the drug delivery process in chemotherapy, both of the cancer cells and normal healthy cells may be killed. In this paper, three mathematical cell-kill models including log-kill hypothesis, Norton–Simon hypothesis and E_max hypothesis are considered. Three control approaches including optimal linear regulation, nonlinear optimal control based on variation of extremals and H_∞-robust control based on μ-synthesis are developed. An appropriate cost function is defined such that the amount of required drug is minimized while the tumor volume is reduced. For the first time, performance of the system is investigated and compared for three control strategies; applied on three nonlinear models of the process. In additions, their efficiency is compared in the presence of model parametric uncertainties. It is observed that in the presence of model uncertainties, controller designed based on variation of extremals is more efficient than the linear regulation controller. However, H_∞-robust control is more efficient in improving robust performance of the uncertain models with faster tumor reduction and minimum drug usage.     

An intelligent sensor for detection of milling chatter

In this paper, a new real-time sensor system has been developed to detect chatter in milling operations. In the developed sensor system, a pattern recognition technique based on an unsupervised neural network using the adaptive resonance theory (ART) is adopted for detection of milling chatter. The features on the cutting force spectrum are fed into the sensor system to classify the milling process with or without chatter. The experimental results indicate that the proposed sensor system can accurately detect milling chatter regardless of the variation in cutting conditions.     

Active regenerative chatter suppression during boring manufacturing process

Machining performance such as that of the boring process is often limited by chatter vibration at the tool–workpiece interface. Among various sources of chatter, regenerative chatter in cutting systems is found to be the most detrimental. It limits cutting depth (as a result, productivity), adversely affects surface finish and causes premature tool failure. Though the machining system is a distributed system, all current active controllers have been designed based upon a simplified lumped single degree of freedom cutting process model. This is because it was found that in the majority of cutting processes, there exists only one dominating mode. However, such simplification does have some potential problems. First, since the system itself is a distributed system, theoretically it consists of infinite number of vibration modes. When the controller is designed to control the dominating mode(s) only, the energy designed to suppress the particular mode(s) may excite the rest of the structural modes, which unavoidably causes the so-called spillover problem. Second, the success of the control design of such simplified single degree of freedom system relies on the availability of accurate model parameters (such as the effective mass, stiffness and damping), which is unfortunately very hard to acquire. This is because the global properties are varying with the metal removal process and the movable components of machine tool. In this paper, an active controller designed from wave point of view is used to absorb chatter vibration energy in a broad frequency band to improve machining performance of a non-rotating boring bar. In contrast to most of the current active chatter control design, the wave controller is designed based on the real distributed cutting system model. The main advantage of such a control scheme to chatter suppression is its robustness to model uncertainties. The control scheme also eliminates the control spillover problem.     

Chaos control and synchronization via a novel chatter free sliding mode control strategy

In this paper, we propose a novel chatter free sliding mode control (SMC) strategy for chaos control and synchronization to the nonlinear uncertain chaotic systems. A new sort of dynamical sliding mode surface with both integral and differential operators is introduced to divert the discontinuous sign function switch term into the first derivative of the control input; hence a chatter free control input is obtained for the chaotic systems with uncertainties. Based on the Lyapunov stability theory and SMC technique, stability analysis is performed and a theorem serving as designing the chatter free sliding mode control input is also proposed. In the simulation part, first, the results regarding chaos control and synchronization are given to show that the proposed strategy can control the states of the uncertain chaotic systems to desired states with fast speed. In order to show the advantage of eliminating chatter in control input of our method, we give the simulation results performed by traditional SMC and the method proposed recently. Simulation results indicate that this novel chatter free sliding mode control strategy is very effective to chaos control and synchronization.     

Nonlinear regenerative chatter in turning

Chatter is a topic of immense engineering importance because its occurrence in machining results in poor surface finish, promotes tool wear and hampers productivity. In this paper, a single degree of freedom, delay differential equation model is presented. The central idea of the model is the study of regenerative chatter effect, which qualitatively explains the nonlinear dynamics in machining. Stability charts are derived for the linearized case in a two dimensional phase plane (μ, Ω) with the bifurcation parameter μ representing the dynamic variation of the chip thickness, and the critical rotational speed Ω. The governing nonlinear equations are integrated in time by Adams Predictor corrector Method. Phase portraits are drawn between the instantaneous tool position x₁ and the relative tangential velocity x₂. It has been shown that in the absence of a cubic nonlinearity, the chatter response appears to be more chaotic.     

Optimal control for chatter mitigation in milling—Part 1: Modeling and control design

Active structural methods constitute a promising way to mitigate chatter vibrations in milling. This paper presents an active system integrated into a spindle unit. Two different optimal control strategies are investigated. The first one only considers the dynamics of the machine structure in the controller design and minimizes the influence of cutting forces on tool tip deviations. The second one takes explicitly the process interaction into account and attempts to guarantee the stability of the overall closed-loop system for specific machining conditions. The modeling and formulation used for both strategies are presented in this first part. A simulation allows the comparison of their respective working principle. The validation of the proposed concept in experimental conditions is described in the second part.     

Computations of optimal cylinder flow control in weakly conductive fluids

A nonlinear adjoint-based optimal control approach of cylinder wake by electromagnetic force has been investigated numerically in the paper. A cost functional representing the balance of the regulated quantities with different weights and interaction parameter N (Lorentz force) has been constituted, where the regulated quantities related with flow and force are taken as targets of regulation and the Lorentz force, (as interaction parameter N), is taken as a control input. Based on the cost functional and Navier-Stokes equations, the corresponding adjoint equations have been derived and the sensitivity of the cost functional is found to be a simple function of the adjoint stream function in the adjoint field. For the different regulations, the forms of optimal control rules are similar while the adjoint equations are different. The receding-horizon predictive control setting is employed to discuss the optimal control problems. Under the action of optimal N(t), the flow separation is suppressed fully, so that the oscillations of drag and lift are suppressed and the total drag coefficient decreases dramatically. For the different regulations, the control effects have some differences due to the different values of optimal inputs corresponding to the different adjoint flow fields.     

Prediction of chatter in high-speed milling by means of fuzzy neural networks

This paper develops a new method for predicting chatter vibration in high-speed end milling using a fuzzy neural network model. Firstly, an experimental system is established. The system consists of an NC jig grinding machine with control device, a force sensor, a charge amplifier, and an FFT (fast Fourier transform) analyser. Over 10 groups of the typical experimental data are obtained under different milling tool wear states and cutting conditions. Then, because the experimental system is a nonlinear dynamic system with some fuzzy factors and too complicated to simplify it into an exact mathematical model, it is substituted by fuzzy neural networks, which are trained by using the above data. Lastly, for verifying the effectiveness of predicting self-excited chatter with the above model, some more experiments are performed. The comparison between the calculated and experimental results confirms that the method proposed in this paper could correctly predict the chatter vibration in high-speed milling. Therefore, the models of the method are reasonable and practical, and the accuracy is very high, which is significant for grasping the stable domain of high-speed milling in both theory and practice.     

Proportional-integral based fuzzy sliding mode control of the milling head

A-axis (that is, the milling head) is an essential assembly in the five-axis CNC machine tools, positioning precision of which directly affects the machining accuracy and surface qualities of the processed parts. Considering the influence of nonlinear friction and uncertain cutting force on the control precision of the A-axis, a novel fuzzy sliding mode control (FSMC) based on the proportional-integral (PI) control is designed according to the parameters adaptation. Main idea of the control scheme is employing the fuzzy systems to approximate the unknown nonlinear functions and adopting the PI control to eliminate the input chattering. Simulation analyses and experimental results illustrate that the designed control strategy is robust to the uncertain load and the parameters perturbation.     

Approximate dynamic programming-based approaches for input-output data-driven control of nonlinear processes

We propose two approximate dynamic programming (ADP)-based strategies for control of nonlinear processes using input-output data. In the first strategy, which we term ‘J-learning,’ one builds an empirical nonlinear model using closed-loop test data and performs dynamic programming with it to derive an improved control policy. In the second strategy, called ‘Q-learning,’ one tries to learn an improved control policy in a model-less manner. Compared to the conventional model predictive control approach, the new approach offers some practical advantages in using nonlinear empirical models for process control. Besides the potential reduction in the on-line computational burden, it offers a convenient way to control the degree of model extrapolation in the calculation of optimal control moves. One major difficulty associated with using an empirical model within the multi-step predictive control setting is that the model can be excessively extrapolated into regions of the state space where identification data were scarce or nonexistent, leading to performances far worse than predicted by the model. Within the proposed ADP-based strategies, this problem is handled by imposing a penalty term designed on the basis of local data distribution. A CSTR example is provided to illustrate the proposed approaches.     

Fixed‐structure robust controller design for chatter mitigation in high‐speed milling

Chatter is an instability phenomenon in high‐speed milling that limits machining productivity by the induction of tool vibrations, inferior machining accuracy, noise, and wear of machine components. In this paper, a fixed‐structure active chatter control design methodology is proposed, which enables dedicated shaping of the chatter stability boundary such that working points of higher machining productivity become feasible while avoiding chatter. The control design problem is cast into a nonsmooth optimization problem, which is solved using bundle methods. Using this approach, fixed‐structure dynamic (delayed) output feedback controllers can be synthesized. Distinct benefits of this approach are the a priori fixing of the controller order, the limitation of the control action, and the fact that no finite‐dimensional model approximations and online chatter estimation techniques are required. All these benefits are important in milling practice. Representative examples illustrate the power of the proposed methodology in terms of increasing the chatter‐free depth of cut, thereby enabling significant increases in machining productivity. Copyright © 2014 John Wiley & Sons, Ltd.     

Probability‐weighted nonlinear stochastic optimal control strategy of quasi‐integrable Hamiltonian systems with uncertain parameters

The nonlinear stochastic optimal control problem of quasi‐integrable Hamiltonian systems with uncertain parameters is investigated. The uncertain parameters are described by using a random vector with λ probability density function. First, the partially averaged Itô stochastic differential equations are derived by using the stochastic averaging method for quasi‐integrable Hamiltonian systems. Then, the dynamical programming equation is established based on stochastic dynamical programming principle. By minimizing the dynamical programming equation with respect to control forces, the optimal control forces can be derived, which are functions of the uncertain parameters. The final optimal control forces are then determined by probability‐weighted average of the obtained control forces with the probability density of the uncertain parameters as weighting function. The mean control effectiveness and mean control efficiency are used to evaluate the proposed control strategy. The robustness of the proposed control is measured by using the ratios of the variation coefficients of mean control effectiveness and mean control efficiency to the variation coefficients of uncertain parameters. Finally, two examples are given to illustrate the proposed control strategy and its effectiveness and robustness. Copyright © 2014 John Wiley & Sons, Ltd.     

Visual analysis of a cold rolling process using a dimensionality reduction approach

The rolling process is a strategical industrial and economical activity that has a large impact among world-wide commercial markets. Typical operating conditions during the rolling process involve extreme mechanical situations, including large values of forces and tensions. In some cases, these scenarios can lead to several kinds of faults, which might result in large economic losses. Thereby, a proper assessment of the process condition is a key aspect, not only as a fault detection mechanism, but also as an economic saving system. In the rolling process, a remarkable kind of fault is the so-called chatter, a sudden powerful vibration that affects the quality of the rolled material. In this paper, we propose a visual approach for the analysis of the rolling process. According to physical principles, we characterize the exit thickness and the rolling forces by means of a large dimensional feature vector, that contains the energies at specific frequency bands. Afterwards, we use a dimensionality reduction technique, called t-SNE, to project all feature vectors on a visual 2D map that describes the vibrational states of the process. The proposed methodology provides a way for an exploratory analysis of the dynamic behaviors in the rolling process and allows to find relationships between these behaviors and the chatter fault. Experimental results from real data of a cold rolling mill are described, showing the application of the proposed approach.     

Fractional order and BICO disturbance observers for a run-of-mine ore milling circuit

Grinding mill circuits are hard to control due to poor plant models, large external disturbances, uncertainties from internal couplings, and process variables that are difficult to measure. This paper proposes a novel fractional order disturbance observer (FO-DOB) for a run-of-mine (ROM) ore milling circuit. A fractional order low pass filter (Q-filer) is used in the DOB to offer an additional degree of freedom in tuning for set-point tracking performance and disturbance rejection performance. Another disturbance observer is introduced in which a Bode ideal cut-off (BICO) filter is used for the Q-filter. A full non-linear plant model is used for evaluation of the performance gained over the ubiquitous PI controller. The simulation results show that the FO-DOB and BICO-DOB schemes are useful additional tools for ROM ore milling circuit control implementations.     

Modeling and adaptive force control of milling by using artificial techniques

The contribution discusses the use of combining the methods of neural networks, fuzzy logic and PSO evolutionary strategy in modeling and adaptively controlling the process of ball-end milling. On the basis of the hybrid process modeling, off-line optimization and feed-forward neural control scheme (UNKS) the combined system for off-line optimization and adaptive adjustment of cutting parameters is built. This is an adaptive control system controlling the cutting force and maintaining constant roughness of the surface being milled by digital adaptation of cutting parameters. In this way it compensates all disturbances during the cutting process: tool wear, non-homogeneity of the workpiece material, vibrations, chatter, etc. The basic control principle is based on the control scheme (UNKS) consisting of two neural identifiers of the process dynamics and primary regulator. An overall procedure of hybrid modeling of cutting process used for creating the CNC milling simulator has been prepared. The experimental results show that not only does the milling system with the design controller have high robustness, and global stability, but also the machining efficiency of the milling system with the adaptive controller is 27% higher than for traditional CNC milling system.     

Model-based expert system to automatically adapt milling forces in Pareto optimal multi-objective working points

The objective of this paper is to present an open and modular expert rule-based system in order to automatically select cutting parameters in milling operations. The knowledge base of the system presents considerations of stability, machine drives efficiency and restrictions while adaptively controlling milling forces in suitable working points. Moreover, a novel classical cost function has been conceived and constructed to Pareto-optimise cutting parameters subjected to multi-objective purposes, namely: tool-life, surface roughness, material remove rate and stability rate parameter. Different Pareto optimal front solutions can be obtained modulating the weighting factors of the cost function. Additional rules have been added in order to manually and/or automatically modulate this cost function. Furthermore, a database which relates weighting factors, cutting conditions and cost function variables is produced for learning purposes. Chatter detection and suppression system automatically feedback to the system to take into account non-modelled disturbances. Finally, since the knowledge of the system is basically obtained from mathematical models, the possibility of combining experience and knowledge from expert engineers and operators is included. In this way, best practice from mathematical modelling and expert engineers and operators is joined in one system obtaining a full, automated system combining the best of each world.As a result, the expert rule-based system selects Pareto optimal cutting conditions for a broad range of milling processes, sorting out automatically different problems such as chatter vibrations, incorporating model reference adaptive control (MRAC) of forces. This procedure is intuitive, being executed in the same way as a human expert would do and it provides the possibility to interact with expert engineers and operators in order to take into account their experience and knowledge. Finally, the expert system is designed in modular form allowing incorporating new functionalities in rule based forms to them or just adding new modules to improve the performance of the milling system.     

时变非线性不确定系统H∞鲁棒模型预测控制

针对输入受限的时变不确定非线性系统,提出一种H∞鲁棒模型预测控制策略。假设线性化系统矩阵一致有界,将非凸的无穷时域优化问题转化为带有单个线性矩阵不等式(LMI)约束的凸优化问题,降低控制量求解难度。结合滚动优化原理与H∞控制方法在线极小化性能指标,使得闭环系统满足控制性能和约束。在LMI框架下给出H∞NMPC的求解方法及其鲁棒稳定性充分条件。仿真实验对比验证了该策略的有效性。