Solution and Analysis of Chatter Stability for End Milling in the Time-domain

In this paper, the instantaneous undeformed chip thickness is modeled to include the dynamic modulation caused by the tool vibration while the dynamic regenerative effects are taken into account. The numerical method is used to solve the differential equations goveming the dynamics of the milling system. Several chatter detection criteria are applied synthetically to the simulated signals and the stability diagram is obtained in time-domain. The simulation results in time-domain show a good agreement with the analytical prediction, which is validated by the cutting experiments. By simulating the chatter stability lobes in the time-domain and analyzing the influences of different spindle speeds on the vibration amplitudes of the tool under a Fixed chip-load condition, conclusions could be drawn as follows： In rough milling, higher machining efficiency can be achieved by selecting a spindle speed corresponding to the axial depth of cut in accordance with the simulated chatter stability lobes, and in Fmish milling, lower surface roughness can be achieved by selecting a spindle speed well beyond the resonant frequency of machining system.

Impact of Modal Parameters on Milling Process Chatter Stability Lobes

Modals of the machine/tool and machine/part system are the principal factors affecting the stability of a milling process. Based on the modeling of chatter stability of milling process,the influence of modal parameters on chatter stability lobes independently or jointly has been analyzed by simulation. Peak-to-valley specific value,lobe coefficient and the corresponding calculation formula have been put forward. General laws and steps of modal simplification for multimodality system have been summarized.

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.

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.

Modelling and simulation of high-speed milling chatter regeneration based on MATLAB

Considering the deficiency in milling process parameters selection, based on the modelling of dynamic milling force and the deduction of chatter stability limits, the chatter stability lobes simulation program for milling is developed with MAT- LAB. The simulation optimization application software of dynamics was designed using engineering simulation software Visio Basic. The chatter stability lobes for milling, which can be used as an instruction guide for the selection of process parameters, are simulated with frequency response functions （FRFs） gained by hammer test. The validation and accuracy of the simulation algorithm are verified by experiments. The simulation method has been used in a factory with an excellent application effect.

Machining dynamics and chatters in micro-milling:A critical review on the state-of-the-art and future perspectives

Micro-milling technology is widely applied in micro manufacturing,particularly for the fabrication of miniature and micro components.However,the chatters and machining dynamics related issues in micro-milling are often the main challenges restricting its machining quality and productivity.Many research works have rendered that the machining dynamics and chatters in micro-milling are more complex compared with the conventional macro-milling process,likely because of the size effect and rigidity of the micro-milling system including the tooling,workpiece,process variables,materials involved,and the high-speed milling machines,and further their collective dynamic effects.Therefore,in this paper,the state of the art focusing on micro-milling chatters and dynamics related issues over the past years are comprehensively and critically reviewed to provide some insights for potential researchers and practitioners.Firstly,typical applications and the problems caused by the machining dynamics and chatters in micro-milling have been put forward in this paper.Then,the research on the underlying micro-cutting mechanics and dynamics,stability analysis,chatters detection,and chatter suppression are summarized critically.Furthermore,the underlying scientific and technological challenges are discussed particularly against typical precision engineering applications.Finally,the possible future directions and trends in research and development of micro-milling have been discussed.

NOVEL METHOD FOR DYNAMIC OPTIMIZATION OF STABILITY IN HIGH-SPEED MILLING SYSTEM

Considering the self-excited and forced vibrations in high-speed milling processes, a novel method for dynamic optimization of system stability is used to determine the cutting parameters and structural parameters by increasing the chatter free material removal rate （CF-MRR） and surface finish. The method is hased on the theory of the chatter stability and the semi-bandwidth of the resonant region. The objective function of the method is material removal rate（MRR）,the constraints are chatter stability and surface finish, and the optimizing variables are cutting and structural parameters. The optimization procedure is stated. The method is applied to a milling system and CF-MRR is increased 18.86%. It is shown that the influences of the chatter stability and the resonance are simultaneously considered in the dynamic optimization of the milling system for increasing CF-MRR and the surface finish.

Efficient and Stable Optimization of Multi‑pass End Milling Using a Cloud Drop‑Enabled Particle Swarm Optimization Algorithm

Optimization of machining parameters is of great importance for multi-pass end milling because machining parameters adversely or positively affect the time and quality of production.This paper develops a second-order fulldiscretization method(2ndFDM)-based 3-D stability prediction model for simultaneous optimization of spindle speed,axial cutting depth and radial cutting depth.The optimal machining parameters in each pass are obtained to achieve the minimum production time comprehensive considering constraints of 3-D stability,machine tool performance,tool life and machining requirements.A cloud drop-enabled particle swarm optimization(CDPSO)algorithm is proposed to solve the developed machining parameter optimization,and 13 benchmark problems are used to evaluate CDPSO algorithm.Numerical results show that CDPSO algorithm has a certain advantage in computational cost as well as comparable search quality and robustness.A demonstrative example is provided.

Chatter stability of robotic rotary ultrasonic countersinking

In recent years,industrial robots have received extensive attention in manufacturing field due to their high flexibility and great workspace.However,the weak stiffness of industrial robots makes it extremely easy to arouse chatter,which affects machining quality inevitably and generates noise pollution in severe cases.Compared with drilling,the chatter mechanism of robotic countersinking is more complex.The external excitation changes with cutting width and depth in countersinking.This characteristic results in time-varying and nonlinearity of robotic countersinking dynamics.Thus,it is urgent to propose a new method of chatter suppression and provide an accurate stability analysis model.As a new special machining technology,rotary ultrasonic machining has been proved to improve robotic drilling and milling stability effectively.Based on this,robotic rotary ultrasonic countersinking(RRUC)is proposed to improve the robotic countersinking stability in this paper.A three-dimensional stability domain method of RRUC is established.First,the countersinking process was divided intoρparts.The dynamic model of every unit was constructed based on ultrasonic function angle(γ)and dynamic chip area.Then,the stability region of RRUC is obtained based on the semi-discrete method(SDM).Compared with the robotic conventional countersinking(RCC),RRUC improves the stability by 27%.Finally,the correctness and effectiveness of the stability region model are proved by robotic ultrasonic countersinking experiments.

Chatter stability prediction in four-axis milling of aero-engine casings with bull-nose end mill

An analytical model for chatter aero-engine casings is presented in this paper stability prediction in bull-nose end milling of And the mechanics and dynamics variations due to the complex cutter and workpiece geometry are considered by analyzing the effects of the lead angle on the milling process. Firstly, the tool-workpiece engagement region is obtained by using a previously developed method and divided into several disk elements along the tool-axis direction. Secondly, a 3D dynamic model for stability limit calculation is developed and simplified into a 1D model in normal direction considering only the dominant mode of the workpiece. Then the cutting force coefficients, the start and exit angles corresponding to each disk element are determined. And the total stability lobe diagram is calculated using an iterative algorithm. Finally, several experimental tests are carried out to validate the feasibility and effectiveness of the proposed ~rediction approach.

基于数值积分方法的铣削稳定性预测研究

针对立式加工中心铣削颤振现象,用数值积分方法预测铣削加工过程中的稳定性。首先用时滞微分方程表示受颤振影响的单、双自由度铣削动力学模型,对时滞周期进行离散;然后用数值积分方法求解时滞微分方程,依据Floquet判定铣削加工稳定性,获得稳定性叶瓣图;最后为验证数值积分方法求解的正确性,进行参数识别试验获取铣削力系数和模态参数,从求解得到的叶瓣图中选取加工参数进行试验验证。数值仿真结果表明,数值积分方法的计算效率和计算精度优于1st-SDM方法和1st-FDM方法。试验结果表明,数值积分方法的求解结果与试验结果相符,可以指导铣削工艺参数的选取,确保铣削加工稳定。

基于神经网络的薄壁件铣削动力学参数预测

精确预测薄壁件铣削过程中工件的时变动力学参数是选择无颤振切削参数的基础。本文提出了基于三层神经网络的曲面薄壁件铣削时变动力学参数的预测方法。首先利用壳单元将薄壁件进行离散化,将离散单元结点处工件厚度作为输入参数,工件前三阶固有频率作为输出参数,构建三层神经网络。然后将壳单元有限元模型计算结果作为训练样本,训练得到神经网络模型。模态测试实验结果表明,有限元模型对工件固有频率预测的最大误差约为4%;与有限元模型相比,神经网络模型的最大预测误差为0.409%,因此神经网络模型的最大预测误差约为4%。同时,神经网络模型训练时间约为10 s;当预测的切削状态数量为150时,预测时间仅为0.002s。在保证计算精度的前提下,三层神经网络模型可大幅提高计算效率。

Variable-step integration method for milling chatter stability prediction with multiple delays

This paper analyzes the stability of milling with variable pitch cutter and tool runout cases characterized by multiple delays,and proposes a new variable-step numerical integration method for efficient and accurate stability prediction. The variable-step technique is emphasized here to expand the numerical integration method,especially for the low radial immersion cases with multiple delays. First,the calculation accuracy of the numerical integration method is discussed and the variable-step algorithm is developed for milling stability prediction for single-delay and multiple-delay cases,respectively. The milling stability with variable pitch cutter is analyzed and the result is compared with those predicted with the frequency domain method and the improved full-discretization method. The influence of the runout effect on the stability boundary is investigated by the presented method. The numerical simulation shows that the cutter runout effect increases the stability boundary,and the increasing stability limit is verified by the milling chatter experimental results in the previous research. The numerical and experiment results verify the validity of the proposed method.

铍铜合金铣削过程刀具黏附现象对切削颤振影响分析

为了满足高精密铍铜件表面的加工要求,研究刀具表面黏附过程对切削系统和已加工表面的影响,有利于提高加工质量和加工效率。通过建立二自由度切削颤振系统,结合工件材料特性、黏结过程和断续切削过程,采用单因素高速铣削实验方法,解析刀具损伤、切削颤振和已加工表面的内在联系,并通过电镜扫描和白光干涉对刀具表面和已加工表面进行对比分析。切削速度和黏附程度的差异性,极大地影响了切削过程的稳定性,导致已加工表面缺陷的产生。不同黏附环境往往导致了不同的切削状态,尤其是高黏附率环境下的刀具表面黏附有利于维持切削刃形态和减缓加工颤振现象。

Stability analysis of robotic longitudinal-torsional composite ultrasonic milling

Currently,industrial robots are considered as an alternative towards traditional machine tools.Especially for the large-scale parts milling,robotic flexibility and low cost make it possess the irreplaceability.However,the milling chatter caused by its weak rigidity hampers robotic application and promotion severely in aviation industry.Rotary ultrasonic milling(RUM)technology with one-dimensional axial vibration has been proven and approved on avoiding robotic chatter.Based on this,the research of project team demonstrates that longitudinal-torsional composite ultrasonic milling(CUM-LT)involving separation characteristic has a greater advantage than RUM in terms of chatter suppression.Thereby,the CUM-LT as a new means is applied to avoid processing vibration of robotic milling system.And its influence mechanism on stability improvement of weak stiffness processing system is clarified.Meanwhile,the approaches to strengthen separation effect are provided innovatively.Moreover,a new analysis method of robotic CUM-LT(RCUM-LT)stability is proposed on the basis of ultrasonic function angles.The simulation and experimental results indicate that compared with robotic RUM(RRUM),stability regions of separated RCUM-LT(SRCUM-LT)and unseparated RCUM-LT(URCUM-LT)are improved by 124.42%and39.20%,respectively.The addition of torsional ultrasonic energy has a wonderful effect on the milling chatter suppression of low stiffness robots.

铣削过程颤振稳定性分析的研究进展

综述铣削过程颤振稳定性分析的研究概况和进展。颤振建模和稳定性分析是该方法两个关键环节。依据颤振形成的物理条件,将其分为摩擦型颤振、振型耦合型颤振和再生型颤振。从切削过程的非线性和切削系统的非线性两方面,重点介绍再生型颤振的非线性建模的研究成果。稳定性分析方法根据对颤振模型的求解方法,分为频域法、离散法及数值法,概括了各个方法的特点、效果及适用工况。最后介绍了近来兴起的微细铣削研究领域中颤振稳定性分析的研究成果。由于其尺度效应,微细铣削加工具有独特的加工机理和特点,颤振建模中需考虑的因素与传统铣削多有不同,但稳定性分析方法仍大多沿用传统铣削中的方法。

球头刀铣削过程动力学模型

建立了考虑刀杆柔性的球头铣刀铣削振动模型,探讨了交变轴向力对刀杆固有频率的影响。考虑刀具动态变形和工件表面波纹对切削厚度的再生反馈,建立了球头刀铣削动力学模型,对铣削中的动态铣削力和刀杆振动进行了仿真,证明了离线仿真可以对铣削过程动特性做出预测。

轧机颤振建模及理论研究进展

轧机颤振是由系统结构动力学与轧制过程动力学相互耦合导致的一种自激振动,对轧机颤振的研究除了需要合理有效的结构模型,还有赖于对轧制过程的精确表征。现有的轧机结构模型除了考虑三倍频、五倍频及扭振三种基本振动形式和多方向多模态的耦合问题,还有通过张力模型和时滞传递模型耦联而建立的多机架连轧模型。此外,多种非线性因素和非对称特征对轧机颤振的影响也越来越受到重视。Slab分析方法是轧制过程建模最重要和广泛的方法,包括不同变形条件下屈服准则的建立、摩擦模型的确定以及应力分布的计算。基于Slab分析法建立的轧制过程模型包括稳态轧制模型、考虑辊缝波动量的准静态模型以及同时考虑辊缝波动及其波动速度的动态轧制模型。将动态轧制力作为反馈激励源,作用于相应的轧机结构模型,从而可以构建轧制过程与系统结构相耦合的颤振动力学模型,研究系统的稳定性及失稳准则。

正交车铣偏心加工三维颤振稳定性的研究

针对正交车铣复杂运动产生变深度、变厚度的切削特性,基于其加工原理采用解析法提出三维颤振稳定域的理论模型。在模态试验基础上,仿真分析正交车铣偏心加工颤振稳定域叶瓣图,结果表明正交车铣加工产生颤振的条件除了与铣刀几何形状和啮合条件、机床结构的频响应函数、工件材料特性等有关外,主要与铣刀轴转速和切削深度密切相关。在正交车铣切削颤振稳定域试验过程中,切削力频谱分析的结果表明:当刀齿切入频率在力频谱中起主导作用时,切削过程是无颤振和稳定的;当系统结构模态频率在力频谱中起主导作用时,将产生颤振并测得切削力和表面粗糙度值都大于或高于无颤振情况。因此该理论模型及仿真结果可以有效预测正交车铣偏心加工颤振稳定性,为其加工表面质量和加工效率提供理论指导。

铣削建模中多种切削力模型的分析比较

以圆柱螺旋立铣刀为例,分别研究了基于线性切削力模型、指数瞬时切削力模型、指数平均切削力模型以及一般多项式切削力模型的铣削建模及动力学仿真技术。首先,推导出各切削力模型下的切削力系数辨识算法,预测三向切削力并与实验进行对比;然后,根据再生颤振理论及频域法预测技术,推导出各切削力模型下的方向系数矩阵并预测颤振稳定域图。结果表明,线性与指数瞬时切削力模型在铣削力及颤振稳定域预测的精度上高于另外两种模型;指数平均模型在铣削力预测上的相对误差最大,较实验值的最大误差为16%,而一般多项式模型在颤振稳定域预测上的相对误差最大,较线性模型的最大偏差超过50%。