薄壁筒车削颤振稳定性预测

切削颤振是制约薄壁筒工件加工质量和效率的主要因素之一。采用半离散法对含有时滞项的动力学方程进行稳定性预测分析,结合薄壁筒工件切削振动试验,研究刀具、工件动力学参数匹配关系变化对切削加工稳定性的影响。通过仿真分析得出:随着刀具刚度或固有频率的提升,切削系统稳定性呈上升趋势,但过度提升刀具刚度并不会有效提升切削稳定性;在刀具与工件固有频率接近处,切削系统的稳定性较差;适当调整刀具动态特性参数有利于提高柔性工件切削加工的稳定性;切削过程中,时变的切削位置和工件尺寸会引起切削系统动态特性的变化。根据时变稳定性预测图,从稳定性分析角度解释了一次走刀切削试验中薄壁筒工件表面出现不同加工形貌的原因。     

Model-based chatter stability prediction for high-speed spindles

The prediction of stable cutting regions is a critical requirement for high-speed milling operations. These predictions are generally made using frequency response measurements of the tool/holder/spindle set, obtained from a non-rotating spindle. However, significant changes in system dynamics occur during high-speed rotation. In this paper, a dynamic model of a high-speed spindle-bearing system is elaborated on the basis of rotor dynamics predictions, readjusted with respect to experimental modal identification. Variations in dynamic behaviour according to speed range are then investigated and determined with accuracy. Dedicated experiments are carried out in order to confirm model results. By integrating the proposed speed-dependant transfer function into the chatter vibration stability approach of Budak–Altintas [S. Tobias, W. Fishwick, Theory of regenerative machine tool chatter, The Engineer February (1958)] a dynamic stability lobes diagram is predicted. The proposed method enables a new stability lobes diagram to be established that takes into account the effect of spindle speed on dynamic behaviour. Significant variations are observed and allow the accurate prediction of cutting conditions. Finally, experiments are performed in order to validate chatter boundary predictions in practice. The proposed modelling approach can also be used to qualify a spindle design in a given machining process and can easily be extended to other types of spindle.     

The influence of cryogenic cooling on milling stability

Cryogenic cooling is emerging as an effective process for high performance machining. However, the influence of cryogenic cooling on milling stability is seldom reported. This paper involves experimental study on the effect of cryogenic cooling on milling stability, using a dedicated cryogenic cooling system to applying liquid nitrogen (LN2) jet to the cutting zone. We observe that cryogenic cooling leads to higher stability limit compared with conventional milling operations, which indicates that the cutting efficiency can be improved greatly in LN2 environment as opposed to the conventional one. The stability improvement is explained from the perspective of machining dynamics parameters variation between the two conditions. Cutting force coefficients and modal parameters of spindle-tool system are identified during cryogenic machining, then milling stability lobe diagrams are predicted by time domain and frequency domain methods. On the basis of milling stability analysis, the enhancement of stability boundary is attributed to the significant reduction of cutting force coefficients during cryogenic cooling. Additionally, the experiment result indicates that cryogenic cooling decreases the dominant modal frequency of the spindle-tool system, which shifts the milling stability boundary slightly to lower spindle speed range. The explanations are verified by a plenty of cutting tests.     

Modeling the machining stability of a vertical milling machine under the influence of the preloaded linear guide

The prediction of machining stability is of great importance for the design of a machine tool capable of high-precision and high-speed machining. The machining performance is determined by the frequency characteristics of the machine tool structure and the dynamics of the cutting process, and can be expressed in terms of a stability lobe diagram. The aim of this study is to develop a finite element model to evaluate the dynamic characteristics and machining stability of a vertical milling system. Rolling interfaces with a contact stiffness defined by Hertz theory were used to couple the linear components and the machine structures in the finite element model. Using the model, the vibration mode that had a dominant influence on the dynamic stiffness and the machining stability was determined. The results of the finite element simulations reveal that linear guides with different preloads greatly affect the dynamic behavior and milling stability of the vertical column spindle head system. These results were validated by performing vibration and machining tests. We conclude that the proposed model can be used to accurately evaluate the dynamic performance of machine tool systems designed with various configurations and with different linear rolling components.     

BTA深孔钻削过程中工件振动影响因素的研究

在BTA深孔钻削过程中,工件的振动是导致孔加工质量和精度降低的重要因素。通过实验和MATLAB拟合分析不同的切削参数(进给量f、切削速度v、主轴转速n)对工件振动的影响。分析结果表明,在深孔加工过程中,工件的中间位置振幅最大;随着进给量的和切削速度的增大,工件的振幅增大,振幅增大量先增大后减小;主轴转速的变化对工件的振动影响很小。合理的选择切削参数可以降低工件的振动。     

Investigation of spindle bearing preload on dynamics and stability limit in milling

Many spindle designs offer automatic, speed-dependent preload adjustments to improve the bearing service life. This can result in spindle speed-dependent dynamic properties at the tool tip and errors in process stability predictions. In order to improve stability prediction accuracy for a representative tool and tool holder assembly, the tool tip frequency response functions are measured for different bearing preload values. Using stability models, stability limits are then predicted. Effects of bearing preload on the stability limits are demonstrated via simulations and cutting tests.     

飞机铝合金薄壁件的加工质量研究

在薄壁件切削加工过程中的加工变形和良品率低等问题成为了影响零件的加工精度和生产率的主要因素。因此,研究薄壁件加工中变形误差较大和良品率低等问题在理论研究和实际应用中都具有重大意义。对于铝合金薄壁件主要采用实验研究和限元分析相结合的方法,分析数控加工中薄壁件加工质量的主要影响因素,并论述了加工过程中,从加工工艺方案、装夹方案、刀具的选择和走刀路线等方面控制薄壁件的变形、加强加工过程中其刚度的具体改进措施,以提高薄壁件加工效率和质量。     

基于模态分析的高速铣削主轴转速选择

分析了高速铣削的特点以及切削加工中的振动现象,研究了高速切削和普通切削中的工件振动对加工精度的影响程度,提出了在高速铣削情形下工件振动会影响加工精度的假设。然后采用振动力学中的谐响应方法分析了铣削加工中工件振动的简化模型,研究了工件在刀具作用力下的振动情形;并通过有限元分析软件进行实例仿真,结果表明在高速切削情况下工件的振动会影响要求较高的加工质量。最后,给出了利用模态分析来优化主轴转速的方法,为高速切削情况下减小振动、提高加工质量提供了一种途径。     

Modelling the machining dynamics of peripheral milling

The machining dynamics involves the dynamic cutting forces, the structural modal analysis of a cutting system, the vibrations of the cutter and workpiece, and their correlation. This paper presents a new approach modelling and predicting the machining dynamics for peripheral milling. First, a machining dynamics model is developed based on the regenerative vibrations of the cutter and workpiece excited by the dynamic cutting forces, which are mathematically modelled and experimentally verified by the authors [Liu, X., Cheng, K., Webb, D., Luo, X.-C. Improved dynamic cutting force model in peripheral milling—Part 1: Theoretical model and simulation. Int. J. Adv Manufact Tech, 2002, 20, 631–638; Liu, X., Cheng, K., Webb, D., Longstaff, A. P., Widiyarto, H. M., Jiang, X.-Q., Blunt, L., Ford, D. Improved dynamic cutting force model in peripheral milling—Part 2: Experimental verification and prediction. Int. J. Adv Manufact Tech, 2004, 24, 794–805]. Then, the mechanism of surface generation is analysed and formulated based on the geometry and kinematics of the cutter. Thereafter a simulation model of the machining dynamics is implemented using Simulink. In order to verify the effectiveness of the approach, the transfer functions of a typical cutting system in a vertical CNC machine centre were measured in both normal and feed directions by an instrumented hammer and accelerometers. Then a set of well-designed cutting trials was carried out to record and analyse the dynamic cutting forces, the vibrations of the spindle head and workpiece, and the surface roughness and waviness. Corresponding simulations of the machining processes of these cutting trials based on the machining dynamics model are investigated and the simulation results are analysed and compared to the measurements. It is shown that the proposed machining dynamics model can well predict the dynamic cutting forces, the vibrations of the cutter and workpiece. There is a reasonable agreement between the measured and predicted roughness/waviness of the machined surface. Therefore the proposed approach is proven to be a feasible and practical approach analysing machining dynamics and surface roughness/waviness for shop floor applications.     

A new approach to stability analysis of variable speed machining systems

This paper presents a new method for the stability analysis of variable speed machining systems. By using spindle angular position as the independent variable, the system dynamics are modeled as a linear periodic time-varying system with fixed delay. This representation is proven much easier to analyze and to numerically simulate than the time-varying delay representation, which traditionally uses the real-time as the independent variable. With a finite difference scheme, the infinite dimensional periodic time-varying system is approximated by a finite dimensional periodic time-varying discrete system, which in turn is converted to a time-invariant system by multiplying the time-varying state transition matrix over one period of speed variation. System-relative stability becomes tractable by spectral radius analysis. This approach makes possible the quantitative characterization of system stability as a function of variable speed profiles as well as other system parameters such as stiffness and damping of the cutting process and the tool/workpiece structure. Verifications for the face milling process by numerical simulation and experiment for both constant and variable speed are given.     

An improved prediction of stability lobes using nonlinear thin wall dynamics

With manufactured sections getting much thinner due to weight requirements, there is the vital need for more accurate prediction of stable cutting conditions in machining. The tools used in machining vary in shapes and design hence a more robust model is required to include these varieties. This paper first presents improvements to the well known stability model, by considering the nonlinearity of the cutting force coefficients, and axial immersion angle and their dependency on the axial depth of cut. Secondly, a finite element (FE) and Fourier transform approach to including the nonlinearity of the workpiece dynamics in thin wall machining when predicting stable region is presented. The model and approach are validated extensively using experimental results and a very good agreement has been achieved.     

航空薄壁件铣削加工铣削力预测方法研究

铣削加工中铣削力是导致加工变形的直接原因,而航空薄壁件加工中,加工变形是加工误差产生的主要因素.本文以航空薄壁件铣削加工过程的铣削力为研究对象,通过确定铣削力模型和切削系数参数,建立了刚性和考虑刀具工件变形耦合的柔性预测两种模型.在柔性模型中,采用预扭Timoshenko梁单元的刀具/工件独立建模的方法建立有限元模型,利用Python语言在通用有限元软件Abaqus下迭代求解.实验验证表明预测模型具有很高的准确性和有效性.     

Prediction of chatter in high speed milling including gyroscopic effects

Dynamic stability of machine tools during operations is dependent on many parameters including the spindle speed. In high and ultra high speed machining, the gyroscopic effect on the spindle dynamics becomes more pronounced and can affect the borders of stability of the rotating system. In this paper, a finite element based model of spindle, tool holder and cutting tool is presented which uses Timoshenko beam theory to obtain the frequency response of the system when gyroscopic terms are included. Using this response, the stability of a high speed spindle system in the presence of gyroscopic effect is investigated. It is shown that the gyroscopic effects lower the critical depth of cut in high speed milling.     

纵扭复合超声振动切割铝蜂窝芯表面质量研究

铝蜂窝芯因具有特殊的薄壁网格状结构，传统加工方式往往伴随着变形和毛刺，这是限制铝蜂窝材料应用的关键因素。超声振动加工在减少加工缺陷方面具有很大的潜力。建立有限元模型并进行切削模拟，同时进行铝蜂窝芯切削实验，对铝蜂窝芯在不同振幅和不同主轴转速下切割的表面形貌进行探究，并对不同振幅下圆刀片的磨损程度进行对比。结果表明：与普通切削相比，纵扭复合超声振动切削能够获得更好的表面形貌，更有效地降低切削缺陷数目；随着振幅的增大，切削缺陷数目得到减少，刀具磨损程度得到降低，切削表面的均匀一致性也变得更好，但施加的超声振幅过高也会导致胞壁产生分离；主轴转速增大能够很好地改善胞壁变形和胞壁分离现象。同时，在1 350～2 700 r/min之内存在一个最佳转速，使得切削缺陷数目可以达到最少。     

Dynamic response analysis in end milling using pre-twisted beam finite elements

This paper develops an analytical model for estimating the dynamic responses in end milling, i.e. dynamic milling cutter deflections and cutting forces, by using the finite-element method along with an adequate end milling-cutting force model. The whole cutting system includes the spindle, the bearings and the cutter. The spindle is modelled structurally with the Timoshenko-beam element, the milling cutter with the pre-twisted Timoshenko-beam element due to its special geometry, and the bearings with lumped springs and dampers. Because the damping matrix in the resulting finite-element equation of motion for the whole cutting system is not one of proportional damping due to the presence of bearing damping, the state-vector approach and the convolution integral is used to find the solution of the equation of motion. To assure the accuracy of prediction of the dynamic response, the associated cutting force model should be sufficiently precise. Since the dynamic cutting force is proportional to the chip thickness, a quite accurate alogorithm for the calculation of the variation of the chip thickness due to geometry, run-out and spindle-tool viration is developed. A number of dynamic cutting forces and tool deflections obtained from the present model for various cutting conditions are compared with the experimental and analytical results available in the literature, good agreement being demonstrated for these comparisons. The present model is useful, therefore, for the prediction of end milling instability. Also, the tool deflections obtained using the pre-twisted beam element are found to be smaller than those obtained using the straight beam element without pre-twist angle. Hence neglecting the pre-twist angle in the structural model of the milling cutter may overestimate the tool deflections.     

Providing stability maps for milling operations

This article presents a new stability prediction tool. The method is based on the dynamic behaviour of both milling tool and workpiece, computed using finite element method. Dynamic behaviour is expressed under the form of transfer functions and used to predict stability lobes at each tool position. The unconditionally stable depth of cut is then stored and displayed on a graphic representation of the machined surface under the form of colour axis, named stability map.An application of the method on a Renault cylinder block is presented as an illustration.     

Linear analysis of chatter vibration and stability for orthogonal cutting in turning

The productivity of high speed milling operations is limited by the onset of self-excited vibrations known as chatter. Unless avoided, chatter vibrations may cause large dynamic loads damaging the machine spindle, cutting tool, or workpiece and leave behind a poor surface finish. The cutting force magnitude is proportional to the thickness of the chip removed from the workpiece. Many researchers focused on the development of analytical and numerical methods for the prediction of chatter. However, the applicability of these methods in industrial conditions is limited, since they require accurate modelling of machining system dynamics and of cutting forces. In this study, chatter prediction was investigated for orthogonal cutting in turning operations. Therefore, the linear analysis of the single degree of freedom (SDOF) model was performed by applying oriented transfer function (OTF) and \tau decomposition form to Nyquist criteria. Machine chatter frequency predictions obtained from both forms were compared with modal analysis and cutting tests.     

Estimation of CNC machine–tool dynamic parameters based on random cutting excitation through operational modal analysis

Dynamic properties of the whole machine tool structure including tool, spindle, and machine tool frame contribute greatly to the reliability of the machine tool in service and machining quality. However, they will change during operation compared with the results from static frequency response function measurements of classic experimental modal analysis. Therefore, an accurate estimation of the dynamic modal parameters of the whole structure is of great value in real time monitoring, active maintenance, and precise prediction of a stability lobes diagram.Operational modal analysis (OMA) developed from civil engineering works quite efficiently in modal parameters estimation of structure in operation under an intrinsic assumption of white noise excitation. This paper proposes a new methodology for applying this technique in the case of computer numerically controlled (CNC) machine tools during machining operations. A novel random excitation technique based on cutting is presented to meet the white noise excitation requirement. This technique is realized by interrupted cutting of a narrow workpiece step while spindle rotating randomly. The spindle rotation speed is automatically controlled by G-code part program, which contains a series of random speed values produced by MATLAB software following uniform distribution. The resulting cutting produces random pulses and excites the structure in all three directions. The effect of cutting parameters on the excitation frequency and energy was analyzed and simulated. The proposed technique was experimentally validated with two different OMA methods: the Stochastic Subspace Identification (SSI) method and the poly-reference least square complex frequency domain (pLSCF or PolyMAX) method, both of which came up with similar results. It was shown that the proposed excitation technique combined successfully with OMA methods to extract dynamic modal parameters of the machine tool structure.     

基于ABAQUS软件二次开发的大型曲面薄壁件加工变形预测

针对无法连续模拟大型曲面薄壁件铣削加工变形的问题,利用Python脚本语言对ABAQUS软件的前处理模块进行了二次开发,通过开发的切削力动态加载Python脚本程序,解决了大尺寸曲面薄壁件加工变形的预测问题。实例模拟计算表明,仿真结果符合实际规律,证明利用有限元二次开发技术可以较好地预测大型曲面薄壁件的加工变形,为其在其他领域的应用提供了参考。     

Oscillator-based approach for modeling process dynamics in NC milling with position- and time-dependent modal parameters

Oscillator models provide an efficient approach for simulating the dynamic behaviour of the machine, tool, or workpiece. In their application, however, these models are usually limited to describing the vibration behaviour at one specific position since they do not contain any information about the structure of the machine tool or the workpiece. Additionally, the variation in time dependent parameters caused by the material removal process is not taken into account. In this paper, an adapted model, which takes the position- and time-dependent modal parameters during NC milling into account, is presented and its experimental validation with respect to the machining of thin-walled components is discussed.