Modelling the dynamics of industrial robots for milling operations

Using industrial robots as machine tools is targeted by many industries for their lower cost and larger workspace. Nevertheless, performance of industrial robots is limited due to their mechanical structure involving rotational joints with a lower stiffness. As a consequence, vibration instabilities, known as chatter, are more likely to appear in industrial robots than in conventional machine tools. Commonly, chatter is avoided by using stability lobe diagrams to determine the stable combinations of axial depth of cut and spindle speed. Although the computation of stability lobes in conventional machine tools is a well-studied subject, developing them in robotic milling is challenging because of the lack of accurate multi-body dynamics models involving joint compliance able of predicting the posture-dependent dynamics of the robot. In this paper, two multi-body dynamics models of articulated industrial robots suitable for machining applications are presented. The link and rotor inertias along with the joint stiffness and damping parameters of the developed models are identified using a combination of multiple-input multiple-output identification approach, computer-aided design model of the robot, and experimental modal analysis. The performance of the developed models in predicting posture-dependent dynamics of a KUKA KR90 R3100 robotic arm is studied experimentally.     

Rapid prediction of posture-dependent FRF of the tool tip in robotic milling

During the robotic milling process, vibration is one of the main factors that affect the machining accuracy and surface quality due to the low stiffness of the robot structure. The robotic milling stability is a function of the frequency response function (FRF) at the tool tip, which is posture-dependent within the workspace. This paper introduces an approach for rapidly predicting the tool tip FRF for industrial robotic milling at any posture. In this method, the models of the one degree-of-freedom (DOF) robot and two DOF robot are extended to a six DOF industrial robot to calculate the FRF at the holder tip based on the FRF acquisition tests at the arranged postures and a standardization process. Considering the coupling effects between the holder and the tool, the tool tip FRF at any posture of the milling robot is calculated using the receptance coupling substructure analysis (RCSA) method. Accordingly, the proposed method is applied to an industrial robot, and the feasibility of this method for predicting the posture-dependent FRF at high frequency in the workspace is validated though the impact tests. Moreover, the stability lobe diagram is calculated and the chatter tests are performed to validate its accuracy. At last, the robot structural modes are observed at the low-frequency dominant modes, whose frequencies are around 10 to 20 Hz.     

Prediction of in-process frequency response function and chatter stability considering pose and feedrate in robotic milling

Chatter occurs easily during robotic milling owing to the low structural stiffness of industrial robots and can degrade the machining quality or even cause robot failure. The accurate frequency response function (FRF) of the robot is essential for predicting chatter stability and selecting the appropriate process parameters. However, the FRF of a robot is affected by multiple factors, such as pose, operating state, and external excitation. In this study, an in-process FRF prediction method considering robot pose and feedrate was developed and used to predict chatter stability. Firstly, the static FRFs were obtained from the experimental modal analysis for different robot poses and used to train a Gaussian process regression (GPR) model. Subsequently, the static FRF predicted using GPR and the modal parameters identified by operational modal analysis (OMA) were used to calculate the in-process FRFs of the robot in the operation state. After removing the harmonic components of the vibration signals using a matrix notch filter, OMA was conducted using the least-squares complex frequency. Furthermore, the FRF of the robot was transformed from the robot flange coordinate system into the engagement coordinate system using the kinematics model and the tool path. The dynamic milling model, considering tool and robot modes was used for predicting stability. Finally, the proposed method was demonstrated by time-domain simulation of the robot-tool system and milling tests, and the effects of the running state and feed direction on chatter stability considering robot mode were analyzed.     

Suppression of nonlinear regenerative chatter in milling process via robust optimal control

During the milling process, self-excited vibration or chatter adversely affects tool life, surface quality and productivity rate. In this paper, nonlinear cutting forces of milling process are considered as a function of chip thickness with a complete third order polynomial (instead of the common linear dependency). An optimal control strategy is developed for chatter suppression of the system described through nonlinear delay differential equations. Counterbalance forces exerted by actuators in x and y directions are the control inputs. For optimal control problem, an appropriate performance index is defined such that the regenerative chatter is suppressed while control efforts are minimized. Optimal control law is determined based on variation of extremals algorithm. Results show that under unstable machining conditions, regenerative chatter is suppressed effectively after applying the optimal control strategy. In addition, optimal controller guarantees robust performance of the process in the presence of model parametric uncertainties.     

Research on the directionality of end dynamic compliance dominated by milling robot body structure and milling vibration suppression

The end dynamic characteristics dominated by the milling robot's body structure play a crucial role in vibration control and chatter avoidance in robotic milling. As the excitation source, the milling force may exist in any direction under different process parameters. Consequently, investigating the directional distribution of the end dynamic characteristics becomes essential for studying the direction-dependent dynamic response of a milling robot. In this paper, firstly, the directionality of the end modal vibration is proved based on the body structure mode shape of the milling robot. Subsequently, combined with the multi-body dynamics model of milling robots, the distribution of the end dynamic compliance with the excitation direction in the robot mode is modeled and found to be double-sphere, which is verified experimentally. A convenient method for acquiring the double-sphere dynamic compliance (DSDC) is given and its portability is shown. Then, two application cases of the DSDC in milling vibration suppression are given. In Case 1, based on the DSDC, the milling vibration amplitude is found to be distributed as an eccentric ellipse with a non-orthogonal basis with the feed angle in a robot mode, wherein a feed direction selection method for reducing milling vibration without traversal calculation is given with experimental validation. Case 2 shows that according to the guidance of the DSDC, the tuned mass damper can significantly suppress the milling vibration. It is worth noting that the directionality of the end modal vibration and DSDC constitute fundamental dynamic properties of milling robots, which may provide a new theoretical basis for the research related to the robotic end dynamic characteristics (such as frequency response function identification, mode coupling chatter mechanism and its suppression, etc.), which are well worth exploring.     

A state-of-the-art review on robotic milling of complex parts with high efficiency and precision

Milling refers to a class of material processing methods that relies on a high-speed rotating milling cutter removing extra material to get desired shapes and features. Being distinct from conventional material removal techniques, like CNC machining, robotic milling has the benefits of lower cost, higher flexibility, better adaptability, etc. Therefore, robotic milling has attracted a large amount of researchers’ interest and become an important material-removing way in the machining of complex parts. Trying to present a comprehensive and systematic review on the robotic milling of complex components, this paper elaborates the history and state of the art on stiffness, dynamics, posture planning, chatter, and compensation in the robotic milling process. Furthermore, future potential research topics about robotic milling are also discussed.     

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.     

Global stability predictions for flexible workpiece milling using time domain simulation

This paper describes the use of peak-to-peak (PTP) force diagrams for machining stability prediction and validates its suitability for milling processes where the workpiece is considerably more flexible than the machine-tool system. These diagrams result from numerous executions of a time domain simulation which includes both the tool and workpiece dynamics and a mechanistic force model. The applicability of the PTP force diagram is validated experimentally through peripheral milling tests of thin-walled structures. Measured and simulated cutting forces are compared. It is shown that the PTP diagrams offer the global stability information which is provided by the traditional lobe diagram, while preserving the detailed, local information provided by time domain simulation.     

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。     

基于Web的铣削过程颤振稳定域远程仿真系统研究

文章在分析数控加工铣削过程颤振稳定域仿真技术,介绍MATLABWebServer应用程序体系结构与开发原理的基础上,研究开发了基于Web的数控加工铣削过程颤振稳定域远程仿真系统;该系统实现了MATLAB语言与HTML语言的结合应用,为数控加工过程切削参数的合理、有效地选择提供了一种网络化远程仿真工具和方法,整个系统的主要功能在实际数控加工中得到了相应的验证。     

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.     

Position-oriented process monitoring in milling of thin-walled parts

Improving machining performance of thin-walled parts is of great significance in aviation industry, since most aviation parts are characterized by large size, complex shape, and thin-walled structure. Machining process monitoring is the essential premise to improve the machining performance. In order to improve the machining quality and efficiency, this paper presents a position-oriented process monitoring model based on multiple data during milling process, and corresponding solution is provided. Through obtaining the internal data set of the numerical control (NC) system during machining, it is possible to correlate the cutting position with monitoring signals including cutting force, acceleration, and spindle power. Then, process optimization is realized to improve the machining quality and efficiency based on the monitoring results. Machining tests are conducted on aircraft structural part as well as blade part, and the experimental results show this method provides a significant insight into the machining process of thin-walled part and contributes to the process optimization. By using feedrate optimization, time consumption for the rough milling process of one titanium alloy part reduced from 19.1 h to 14.4 h and the number of cutter consumption dropped from 5 to 3. And according to the result of position-oriented process monitoring, the machining strategies were optimized to reduce vibration and avoid chatter, thereby improving the machining quality.     

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.     

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.     

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.     

Knowledge graph and function block based Digital Twin modeling for robotic machining of large-scale components

Robotic machining is a potential method for machining large-scale components (LSCs) due to its low cost and high flexibility. However, the low stiffness of robots and complex machining process of LSCs result in a lack of alignment between the physical process and digital models, making it difficult to realize the robotic machining of LSCs. The recent Digital Twin (DT) concept shows potential in terms of representing and modeling physical processes. Therefore, this study proposes a robotic machining DT for LSCs. However, the current DT is not capable of knowledge representation, multi-source data integration, optimization algorithm implementation, and real-time control. To address these issues, Knowledge Graph (KG) and Function Block (FB) are employed in the proposed robotic machining DT. Here, robotic machining related information, such as the machining parameters and errors, is represented in the virtual space by building the KG, whereas the FBs are responsible for integrating and applying the algorithms for process execution and optimization based on real-world events. Moreover, a novel adaptive process adjustment strategy is proposed to improve the efficiency of the process execution. Finally, a prototype system of the robotic machining DT is developed and validated by an experiment on robotic milling of the assembly interface for an LSC. The results demonstrate that the robotic machining is successfully optimized and improved by the proposed method.     

Hybrid statistical modelling of the frequency response function of industrial robots

Models that predict the Frequency Response Function (FRF) of six degree-of-freedom (6-dof) industrial robots used for machining operations such as milling are usually built using Experimental Modal Analysis (EMA) of vibration data obtained from modal impact hammer tests performed at a finite number of points in the robot's workspace corresponding to specific arm configurations. While modal impact hammer tests are not constrained by the operating conditions of the robot, such as specific arm configurations allowed by part fixturing, they are limited by the number of workspace points that can be practically sampled and the associated robot downtime. Alternatively, the process of determining robot FRFs from on-line machining process data (e.g., forces and vibration) through Operational Modal Analysis (OMA) enables a denser sampling of the robot's workspace without requiring robot downtime. However, OMA may require several long tool paths and one or more complex part setups to enable sampling of a sufficiently large number of locations/arm configurations. This paper presents an efficient hybrid statistical modelling methodology that combines the two approaches, thus enabling possible optimization of sampling density and robot downtime, to efficiently determine the robot FRFs as a function arm configuration. The approach consists of first calibrating a Gaussian Process Regression (GPR) model with FRF data derived from EMA conducted at a small number of discrete locations in the robot's workspace. Then, FRFs calculated from OMA of milling forces and tool tip vibration data derived from robotic milling tests are used to update the initial GPR model using Bayesian inference and efficient hyperparameter updating. The proposed hybrid robot FRF modelling method is experimentally validated and shown to yield accurate predictions of the robot FRF while being computationally efficient.     

An expert system for hydro/aero-static spindle design used in ultra precision machine tool

A novel expert hydro/aero-static spindle design system strategy is presented in this paper. It is based on the comprehensive principles of machine design, machining dynamics and metal cutting mechanics. The transmission and lubrication types of the spindle are decided by a selection system, which utilize a dedicated logical choice algorithm in the light of the specifications of both workpiece material and desired cutting condition. Hydro/aero-static spindles are designed by this system from its dynamics perspective. The chatter vibration of the spindle is automatically improved by optimizing the structural parameters of the spindle. Meanwhile, the predicted Frequency Response Function (FRF) of the spindle based on the rotor dynamics is integrated to the chatter vibration stability law. Consequently, the expert design system enables the structure of machine tools to be designed efficiently with a higher precision. The proposed system was demonstrated through an aerostatic spindle design for micro-array structures machining.     

Robotic path compensation training method for optimizing face milling operations based on non-contact CMM techniques

Currently, the use of industrial robots in the machining of large components in metallic materials of significant hardness is proliferating. The low rigidity of industrial robots is still the main conditioning for their use in machining applications, where the forces developed in the process cause significant deviations on the cutting tool path. Although there are already methodologies that facilitate the pose study of the robot mechanical behaviour, predicting deviation values of the cutting tool path and facilitating the selection of process variables, robotic cell users still request new methods able to allow them to optimize the use of these production systems. On the other hand, non-contact measurement technologies have burst into many fields of knowledge, their use is becoming consolidated, and they allow the digitization of complex surfaces. This research presents the development of a new method of robotic machining trajectory compensation that allows optimizing the manufacture of flat surfaces using an industrial anthropomorphic robot. The new training method determines the actual deviations of the cutting tool after the machining process, and checks if these are within the admissible range of flatness error. This method is a novel iterative technique that incorporates the algorithm that uses the measured deviations and a reduction factor fr to calculate the offset that modifies the coordinate value of the programmed path points outside the admissible range and generates a new machining path to be tested. The method has been tested on a pre-industrial scale for aluminium machining, and the algorithm has carried out two iterations to generate a compensated robotic milling path within a flatness tolerance range of 300 µm, improving the error deviation by 37% comparing to the initial path.     

Estimation of stability lobe diagrams in milling with continuous learning algorithms

The productivity of milling processes is limited by the occurrence of chatter vibrations. The correlation of the maximum stable cutting depth and the spindle speed can be shown in a stability lobe diagram (SLD). The stability is different for different width of cut and can change with the axis positions. Today it is already a great effort to estimate the SLD only for one position. Many experiments are necessary to measure the SLD or derive a detailed mathematical model to calculate the SLD. Moreover not only the cutting depth, but also the cutting width should be represented in the SLD. This paper presents a new approach to assess the process stability based on measured acceleration signals. The multidimensional stability lobe diagram (MSLD) are derived during the production using two new continuously learning algorithms. In this paper the application of a continuous learning support vector machine and a continuous neural network is shown. The support vector machine and the neural network are extended to make them capable for continuous learning and time-variant systems. A new trust criterion is introduced, which gives information about the prediction quality of the output for the selected input region. The learned MSLDs are evaluated against analytically calculated MSLDs and the learning algorithms can reproduce the analytical results very well.