Hybrid model- and signal-based chatter detection in the milling process

Chatter causes machining instability and reduces productivity in the metal cutting process. It has negative effects on the surface finish, dimensional accuracy, tool life and machine life. Chatter identification is therefore necessary to control, prevent, or eliminate chatter and to determine the stable machining condition. Previous studies of chatter detection used either model-based or signal-based methods, and each of them has its drawback. Model-based methods use cutting dynamics to develop stability lobe diagram to predict the occurrence of chatter, but the off-line stability estimation couldn’t detect chatter in real time. Signal-based methods apply mostly Fourier analysis to the cutting or vibration signals to identify chatter, but they are heuristic methods and do not consider the cutting dynamics. In this study, the model-based and signal-based chatter detection methods were thoroughly investigated. As a result, a hybrid model- and signal-based chatter detection method was proposed. By analyzing the residual between the force measurement and the output of the cutting force model, milling chatter could be detected and identified efficiently during the milling process.

     

高速铣削时颤振的诊断和稳定加工区域的预报

给出一种通过测量加工过程中的噪声来诊断高速铣削时颤振的方法.先测量环境噪声,然后测量加工噪声.理论分析和试验结果表明,如果加工噪声的主谐振频率接近其中一个环境噪声主谐振频率或者是齿频的整数倍,那么系统无颤振,否则有颤振.建立系统结构和铣削过程动力学特征参数的数学模型.根据测出的颤振频率,通过所建模型可解出系统的固有频率、阻尼比和过程参数,并计算出稳定极限曲线.试验证明,该方法能较好地预报高速铣削时的稳定加工区域.     

Chatter stability of micro end milling by considering process nonlinearities and process damping

The micro end milling uses the miniature tools to fabricate complexity microstructures at high rotational speeds. The regenerative chatter, which causes tool wear and poor machining quality, is one of the challenges needed to be solved in the micro end milling process. In order to predict the chatter stability of micro end milling, this paper proposes a cutting forces model taking into account the process nonlinearities caused by tool run-out, trajectory of tool tip and intermittency of chip formation, and the process damping effect in the ploughing-dominant and shearing-dominant regimes. Since the elasto-plastic deformation of micro end milling leads to large process damping which will affect the process stability, the process damping is also included in the cutting forces model. The micro end milling process is modeled as a two degrees of freedom system with the dynamic parameters of tool-machine system obtained by the receptance coupling method. According to the calculated cutting forces, the time-domain simulation method is extended to predict the chatter stability lobes diagrams. Finally, the micro end milling experiments of cutting forces and machined surface quality have been investigated to validate the accuracy of the proposed model.     

Speed-varying cutting force coefficient identification in milling

Accurate simulation of the machining process is crucial to improve milling performance, especially in High-Speed Milling, where cutting parameters are pushed to the limit.Various milling critical issues can be analyzed based on accurate prediction of cutting forces, such as chatter stability, dimensional error and surface finish. Cutting force models are based on coefficients that could change with spindle speed. The evaluation of these specific coefficients at higher speed is challenging due to the frequency bandwidth of commercial force sensors. On account of this, coefficients are generally evaluated at low speed and then employed in models for different spindle speeds, possibly reducing accuracy of results.In this paper a deep investigation of cutting force coefficient at different spindle speeds has been carried out, analyzing a wide range of spindle speeds: to overcome transducer dynamics issues, dynamometer signals have been compensated thanks to an improved technique based on Kalman filter estimator. Two different coefficients identification methods have been implemented: the traditional average force method and a proposed instantaneous method based on genetic algorithm and capable of estimating cutting coefficients and tool run-out at the same time.Results show that instantaneous method is more accurate and efficient compared to the average one. On the other hand, the average method does not require compensation since it is based on average signals. Furthermore a significant change of coefficients over spindle speed is highlighted, suggesting that speed-varying coefficient should be useful to improve reliability of simulated forces.     

A coupled dynamics,multiple degree of freedom process damping model,Part 2: Milling

Self-excited vibration, or chatter, is an important consideration in machining operations due to its direct influence on part quality, tool life, and machining cost. At low machining speeds, a phenomenon referred to as process damping enables stable cutting at higher depths of cut than predicted with traditional analytical models. This paper describes an analytical stability model for milling operations which includes a process damping force that depends on the surface normal velocity, depth of cut, cutting speed, and an empirical process damping coefficient. Model validation is completed using time domain simulation and milling experiments. The results indicate that the multiple degree of freedom model is able to predict the stability boundary using a single process damping coefficient.     

Prediction of dynamic cutting force and regenerative chatter stability in inserted cutters milling

Currently, the modeling of cutting process mainly focuses on two aspects: one is the setup of the universal cutting force model that can be adapted to a broader cutting condition; the other is the setup of the exact cutting force model that can accurately reflect a true cutting process. However, there is little research on the prediction of chatter stablity in milling. Based on the generalized mathematical model of inserted cutters introduced by ENGIN, an improved geometrical, mechanical and dynamic model for the vast variety of inserted cutters widely used in engineering applications is presented, in which the average directional cutting force coefficients are obtained by means of a numerical approach, thus leading to an analytical determination of stability lobes diagram (SLD) on the axial depth of cut. A new kind of SLD on the radial depth of cut is also created to satisfy the special requirement of inserted cutter milling. The corresponding algorithms used for predicting cutting forces, vibrations, dimensional surface finish and stability lobes in inserted cutter milling under different cutting conditions are put forward. Thereafter, a dynamic simulation module of inserted cutter milling is implemented by using hybrid program of Matlab with Visual Basic. Verification tests are conducted on a vertical machine center for Aluminum alloy LC4 by using two different types of inserted cutters, and the effectiveness of the model and the algorithm is verified by the good agreement of simulation result with that of cutting tests under different cutting conditions. The proposed model can predict the cutting process accurately under a variety of cutting conditions, and a high efficient and chatter-free milling operation can be achieved by a cutting condition optimization in industry applications.     

Stability of milling with non-uniform pitch and variable helix Tools

We study mechanical vibrations in milling with non-uniform pitch and variable helix tools. The process is modeled by a periodic delay differential equation with distributed delay, which takes into account, for example, the nonlinear cutting force behavior, the effect of runout, and the exact delay distribution due to the unequally spaced flutes. We present a new method for the identification of the chatter stability lobes from the linearized system that is based on the multifrequency solution. We give detailed remarks on the truncation of the resulting infinite dimensional matrices and the efficient numerical implementation of the method. Cutting tests for steel milling with a customary end mill with non-uniform pitch and variable helix angle and a conventional end mill with uniform pitch and constant helix angle are performed. The numerical and experimental results coincide well. They reveal a significant increase of the limiting depth of cut for the variable helix tool compared to the conventional tool. Moreover, we show that in contrast to conventional tools, for non-uniform pitch and variable helix tools, an exact model with time-varying coefficients, nonlinear cutting force behavior, and runout is necessary for an accurate prediction of the stability lobes.     

Milling force vibration analysis in high-speed-milling titanium alloy using variable pitch angle mill

Chatter may cause fast wear of tools and poor surface quality of the workpieces at high cutting speed and it will happen on different process parameters; how do we select the suitable cutting speed to suppress the chatter? In this paper, a signal analysis method for milling force and acceleration is adopted to identify chatter, which can obtain the results not only in frequency of chatter but also in the contribution for milling force at different frequencies. Through the milling experiment, the machining vibration behaviors of milling Ti–6Al–4V with variable pitch end mill were investigated. Milling force and acceleration signals obtained from experiment were analyzed and compared at stable and unstable milling processes. The experimental results show that when the chatter occurs, milling forces were found to increase dramatically by 61.9–66.8% compared with that of at stable cutting; machining surface quality became poor and machined surface roughness increases by 34.2–40.5% compared with that of at stable cutting.     

GRADE OF STABILITY IN FUZZY CHATTER STABILITY LOBE MODEL IN MILLING

The machining productivity and part quality are typically limited by the regenerative chatter induced by the dynamic interactions of spindle-holder-tool combination system. The conventional chatter stability model predicts the permissible stable axial depth of cut versus spindle speed by plotting the stability lobe diagram which represents two independent regions as absolutely stable zone and instable zone divided by the critical lobe curve. In fact, it is more reasonable to be a transition stage between the stable and instable zone. This paper introduced the grade of stability (GOS) to improve the conventional chatter stability model and study the transition zone in the stability lobe diagram. The variation of transition zone width with the stability sensibilities for different order lobe curve in milling system was analyzed. Sigmoid function was used as the membership function to develop the fuzzy stability lobe model. Then, the fuzzy stability lobe diagram with an adjustable slope coefficient was implemented to improve the mould steel milling process. The improved fuzzy stability model enhances the reliability of stability lobe diagram and guarantees the chatter-free milling process.     

Chatter reliability prediction of side milling aero-engine blisk

Reliability analysis of a dynamic structural system is applied to predict chatter of side milling system for machining blisk. Chatter reliability is defined as the probability of stability for processing. A reliability model of chatter was developed to forecast chatter vibration of side milling, where structure parameters and spindle speed are regarded as random variables and chatter frequency is considered as intermediate variable. The first-order second-moment method was used to work out the side milling system reliability model. Reliability lobe diagram (RLD) was applied to distinguish reliable regions of chatter instead of stability lobe diagram (SLD). One example is used to validate the effectiveness of the proposed method and compare with the Monte Carlo method. The results of the two approaches were consistent. Chatter reliability and RLD could be used to determine the probability of stability of side milling.

     

A novel chatter stability criterion for the modelling and simulation of the dynamic milling process in the time domain

The modelling of the dynamic processes in milling and the determination of chatter-free cutting conditions are becoming increasingly important in order to facilitate the effective planning of machining operations. In this study, a new chatter stability criterion is proposed, which can be used for a time domain milling process simulation and a model-based milling process control. A predictive time domain model is presented for the simulation and analysis of the dynamic cutting process and chatter in milling. The instantaneous undeformed chip thickness is modelled to include the dynamic modulations caused by the tool vibrations so that the dynamic regeneration effect is taken into account. The cutting force is determined by using a predictive machining theory. A numerical method is employed to solve the differential equations governing the dynamics of the milling system. The work proposes that the ratio of the predicted maximum dynamic cutting force to the predicted maximum static cutting force can be used as a criterion for the chatter stability. Comparisons between the simulation and experimental results are given to verify the new model.     

Chatter prediction utilizing stability lobes with process damping in finish milling of titanium alloy thin-walled workpiece

Machining chatter often becomes a big hindrance to high productivity and surface quality in actual milling process, especially for the thin-walled workpiece made of titanium alloy due to poor structural stiffness. Aiming at this issue, the stability lobes are usually employed to predict if chatter may occur in advance. For obtaining the stability lobes in milling to avoid chatter, this article introduces an extended dynamic model of milling system considering regeneration, helix angle, and process damping into the high-order time domain algorithm which can guarantee both high computational efficiency and accuracy. Via stability lobes, the reasonability and accuracy of the proposed method are verified globally utilizing specific examples in literature. More convincingly, the time-domain numerical simulation is also implemented to predict vibration displacement for partial stability verification. In this extended model, process damping is well-known as an effective approach to improve the stability at low spindle speeds, and particularly, titanium alloy as typical difficult-to-machine material is generally machined at low spindle speeds as well due to its poor machinability. Therefore, the proposed method can be employed to obtain the 3D stability lobes in finish milling of the thin-walled workpiece made of titanium alloy, Ti-6Al-4V. Verification experiments are also conducted and the results show a close agreement between the stability lobes and experiments.     

用广义傅里叶级数法分析棒铣刀颤振问题

采用广义傅里叶级数法分析棒铣刀的颤振问题。在考虑了主轴陀螺效应的基础上，着重分析了切向铣削力参数和径向铣削力参数对铣削系统稳定性的影响，比较了广义傅里叶级数法与基于奈奎斯特稳定性判据的非线性优化法的结果。为了验证广义傅里叶级数法的有效性和准确性，对模型进行了时域仿真。分析结果表明，在考虑了铣刀刀轴陀螺效应之后，影响颤振的因素虽然很多，但铣削力参数（包括切向参数和径向参数）是主要的，铣削力参数对不稳定区的大小和位置都有明显的影响。     

预测铣削稳定性的隐式Adams方法

针对铣削加工过程中产生的振动现象,提出了一种隐式Adams方法（Implicit Adams method,IAM）来预测铣削加工过程的稳定性。考虑再生颤振的铣削加工动力学方程可以表示为时滞线性微分方程,将刀齿周期可分为自由振动阶段和强迫振动阶段,对强迫振动阶段进行离散,运用IAM方法构建状态传递矩阵,利用Floquet理论,判定系统的稳定性,获得系统的稳定性叶瓣图。Matlab软件仿真结果表明,IAM方法是预测铣削稳定性的一种有效方法。随着离散数的增加,IAM方法的收敛速度要快于一阶半离散法（First-order semi-discretization method,1st-SDM）和二阶全离散法（Second-order full-discretization method,2nd-FDM）,离散数较少的IAM方法能达到离散数较多的1st-SDM方法和2nd-FDM方法的局部离散误差。此外,在单自由度和双自由度动力学模型下,三种方法的稳定性叶瓣图显示,IAM方法预测铣削稳定性的预测精度均好于1st-SDM方法和2nd-FDM方法,计算效率远远高于1st-SDM方法,稍高于2nd-FDM方法。切削试验和仿真结果表明,IAM方法的预测精度和可靠度均好于1st-SDM方法和2nd-FDM方法。     

Modeling and Analytical Solution of Chatter Stability for T-slot Milling

T-slot milling is one of the most common milling processes in industry. Despite recent advances in machining technology, productivity of T-slot milling is usually limited due to the process limitations such as high cutting forces and stability. If cutting conditions are not selected properly the process may result in the poor surface finish of the workpiece and the potential damage to the machine tool. Currently, the predication of chatter stability and determination of optimal cutting conditions based on the modeling of T-slot milling process is an effective way to improve the material removal rate(MRR) of a T-slot milling operation. Based on the geometrical model of the T-slot cutter, the dynamic cutting force model was presented in which the average directional cutting force coefficients were obtained by means of numerical approach, and leads to an analytical determination of stability lobes diagram(SLD) on the axial depth of cut. A new kind of SLD on the radial depth of cut was also created to satisfy the special requirement of T-slot milling. Thereafter, a dynamic simulation model of T-slot milling was implemented using Matlab software. In order to verify the effectiveness of the approach, the transfer functions of a typical cutting system in a vertical CNC machining center were measured in both feed and normal directions by an instrumented hammer and accelerators. Dynamic simulations were conducted to obtain the predicated SLD under specified cutting conditions with both the proposed model and CutPro?. Meanwhile, a set of cutting trials were conducted to reveal whether the cutting process under specified cutting conditions is stable or not. Both the simulation comparison and experimental verification demonstrated that the satisfactory coincidence between the simulated, the predicted and the experimental results. The chatter-free T-slot milling with higher MRR can be achieved under the cutting conditions determined according to the SLD simulation.     

插铣过程中稳定域研究现状

切削系统稳定性是插铣技术加工领域中的重要研究内容,插铣切削加工中很多优点的体现必须以无振动稳定切削的实现为前提。稳定域预测的准确与否直接关系到能否有效抑制切削颤振,而切削颤振直接影响工件的表面粗糙度和尺寸精度,刀具磨损和破损以及加工效率等。本文通过求解稳定域的一般步骤,综述稳定域研究现状。通过列举稳定性边界的判别的不同算法,分析和对比各种算法的优缺点,并总结插铣切削过程中稳定性研究存在的问题。     

Chatter prediction based on frequency domain solution in CNC pocket milling

Chatter has been a problem in CNC machining process especially during pocket milling process using an end mill with low stiffness. Since an iterative time-domain chatter solution consumes a computing time along tool paths, a fast chatter prediction algorithm for pocket milling process is required by machine shop-floor for detecting chatter prior to real machining process. This paper proposes the systematic solution based on integration of a stability law in frequency domain with geometric information of material removal for a given set of tool paths. The change of immersion angle and spindle speed determines the variation of the stable cutting depth along cornering cut path. This proposed solution transforms the milling stability theory toward the practical methodology for the stability prediction over the NC pocket milling.     

Vibration analysis in milling titanium alloy based on signal processing of cutting force

In metal cutting processes, the chatter may cause fast wear of tools and poor surface quality of the processed parts; it can happen on different cutting parameters, but how do we identify the chatter and how do we select suitable cutting parameters to avoid chatter at high material removal rate (MRR). In this paper, the signal processing methods such as time domain, frequency domain, and time–frequency domain analysis are introduced. The signals of cutting force that were collected in milling titanium alloy Ti–6Al–4V at variable cutting speeds varied from 80 to 360 m/min; signal analysis methods such as time domain, frequency domain, and time–frequency domain were put forward. Further analysis results reveal that the chatter occur when cutting speeds are 240 and 360 m/min, when the maximum value of cutting forces increase by 61.9–66.8%, the standard deviation increase by 84.1–86.1%, and the surface roughness increase by 34.2–40.5% compared with that of at 80 m/min. Detail signal d2 is employed to monitor cutting stability state from the result of wavelet analysis.     

考虑模态耦合的球头铣刀颤振稳定域建模方法

球头铣刀广泛应用于曲面加工中,因此构造出针对球头铣刀的颤振稳定域叶瓣图意义重大。利用精细积分法对铣削系统二阶动力学方程进行时域数值求解,由切削刃与切触区域不同时刻的关系,确定出时域数值求解方程中所需要的刀刃瞬时切削部位,通过Floquet定理获得了高精度的颤振稳定域叶瓣图,并在三轴数控机床上进行了正确性试验验证。试验结果与预测结果相一致,表明所提供的方法能够为球头铣刀实现无颤振切削加工提供有力的技术支撑。