基于RCSA的刀尖频响函数预测方法

为快速获取构建铣床稳定性叶瓣图所需的主轴—刀柄—刀具系统频响函数,提出一种有限元和响应耦合子结构分析法(RCSA)相结合的预测方法。以某型号主轴系统为研究对象,利用有限元法分别计算主轴、刀柄、刀具端点频响函数,再使用RCSA分别耦合主轴—刀柄结合面、刀柄—刀具结合面,最终得到主轴—刀柄—刀具系统刀尖频响函数。将得到的频响函数与理论算法以及完全有限元方法对比,在5000Hz以内,前7阶模态最大误差不超过15%。该方法可以在机床更换刀柄或刀具时只计算对应部分的频响函数,从而实现主轴—刀柄—刀具系统刀尖频响函数的快速预测。     

一种新的预测铣刀刀尖频响函数的方法

为准确快速地预测铣刀刀尖点频响函数,提出一种基于逆响应耦合子结构分析（IRCSA）法辨识刀柄-刀具结合面参数的刀尖点频响函数预测方法。该方法通过建立计算刀柄末端频响函数矩阵和刀尖点频响函数矩阵的数学模型,利用逆响应耦合子结构分析法求取随频率变化的刀柄-刀具结合面参数。通过Cuckoo search算法及有限元分析确定刀尖点频响函数中对刀柄-刀具结合面复刚度矩阵变化最为敏感的固有频率,取该频率对应的结合面参数为刀柄-刀具结合面复刚度矩阵的辨识结果,由此计算出刀尖点频响函数。通过硬质合金圆柱棒、2刃铣刀和4刃铣刀进行验证,对比了所提预测方法、Cuckoo search优化算法预测的刀尖点频响函数与实测值三者之间的差异,实验结果表明该预测方法预测的刀尖点频响函数的固有频率和实测固有频率的误差在5%以内,所用时间约为Cuckoo search优化算法的1%,达到了较高的预测精度,并且更加省时、简便。     

基于RCSA与GA的铣刀刀尖点频响函数预测

基于响应耦合子结构分析法建立了铣刀刀尖点的频响函数预测模型,针对其中主轴—刀柄基座系统频响函数矩阵难以理论计算和实验测试的问题,提出了基于实验模态测试与遗传算法寻优相结合的主轴—刀柄基座系统频响函数矩阵的优化拟合方法。以VMC850E型立式加工中心主轴系统为研究对象,基于上述方法对铣刀刀尖点频响函数进行了预测,并与其实测频响函数进行对比。结果表明:刀尖点的预测频响函数曲线与实测频响函数曲线符合较好,预测频响函数的固有频率与实测固有频率在0~4 000Hz范围内的相对误差小于4.37%。     

考虑夹头与刀具过渡段的主轴系统精确建模

为解决主轴系统刀尖点频响函数预测中的主轴系统子结构划分问题,并提高各子结构建模的精确性,提出基于等转动惯量法对主轴系统中的夹头进行等效建模,基于等平均惯性矩的方法对铣刀的刀齿段和过渡段进行精确建模,以VMC850E主轴系统为研究对象,通过响应耦合子结构法建立主轴系统刀柄—夹头—刀具结合面等效模型,以刀尖点频响函数实验值和理论值误差最小为目标,采用布谷鸟搜索优化算法确定刀柄—夹头、夹头—刀具两个结合面动力学参数.实验结果表明,预测和实测前三阶固有频率之间的误差在1.8％以内,所提方法具有可行性和有效性.     

一种新的铣刀刀齿等效直径确定方法

为确定铣刀刀齿的等效直径,建立了铣刀的等效模型,将铣刀分为刀杆和刀齿两个子结构,基于子结构分析和理论计算的结果建立刀齿等效直径优化的目标函数,采用遗传算法优化确定刀齿的等效直径。以5把不同参数的2刃、3刃和4刃铣刀为研究对象,采用该方法确定刀齿等效直径,据此计算铣刀刀尖点的频响函数,并与等质量法确定的刀齿等效直径所计算的铣刀刀尖点频响函数及其实验值进行对比。分析结果表明,该方法具有更高的计算精度及更好的适用性。     

于频响函数分析的主轴-刀柄-刀具结合面轴向分布参数辨识

针对主轴-刀柄-刀具结合面轴向分布参数的精确辨识问题,提出了一种基于频响函数分析的主轴-刀柄、刀柄-刀具结合面建模及参数辨识的方法。该方法根据主轴系统中各零部件之间的连接关系,将轴承-主轴结合面简化为集中的弹性支撑,建立主轴-刀柄、刀柄-刀具结合面参数沿主轴轴向呈离散分布的结合面模型,并通过Cuckoo search算法辨识结合面参数,确定其在轴向上的分布情况。以4刃铣刀为例,基于所辨识的结合面参数,在ANSYS中建立主轴系统的动力学模型,计算刀尖点频响函数,并与实测值进行比较。结果表明：主轴-刀柄、刀柄-刀具结合面参数在轴向上呈现非线性分布,由其确定的刀尖点频响函数计算值和实测值之间的相对误差在4%以内,达到了较高的建模精度。     

基于频响函数分析的主轴-刀柄-刀具结合面轴向分布参数辨识

针对主轴-刀柄-刀具结合面轴向分布参数的精确辨识问题,提出了一种基于频响函数分析的主轴-刀柄、刀柄-刀具结合面建模及参数辨识的方法。该方法根据主轴系统中各零部件之间的连接关系,将轴承-主轴结合面简化为集中的弹性支撑,建立主轴-刀柄、刀柄-刀具结合面参数沿主轴轴向呈离散分布的结合面模型,并通过Cuckoo search算法辨识结合面参数,确定其在轴向上的分布情况。以4刃铣刀为例,基于所辨识的结合面参数,在ANSYS中建立主轴系统的动力学模型,计算刀尖点频响函数,并与实测值进行比较。结果表明:主轴-刀柄、刀柄-刀具结合面参数在轴向上呈现非线性分布,由其确定的刀尖点频响函数计算值和实测值之间的相对误差在4%以内,达到了较高的建模精度。     

铣刀结合部参数辨识与刀尖点频响函数预测的方法研究

文中应用了一种数值分析和实验相结合的策略对结合部参数进行辨识。针对铣刀结合部,应用响应耦合子结构分析法,对刀具和刀柄之间的结合面参数进行辨识。将辨识结果应用于刀尖点频响函数预测。最后通过实验验证了所提出方法的准确性。     

用半理论法预测主轴系统刀尖点频响函数

采用半理论法,即理论与试验相结合的方法预测主轴系统刀尖点频响函数。首先,介绍半理论法的预测原理;然后,应用半理论法预测主轴系统刀尖点频响函数的流程,包括利用梁理论计算自由-自由状态刀具两端的阻抗矩阵、搭建主轴-刀柄频响函数测试系统、测试装卡短光滑圆柱的主轴-刀柄系统的频响函数、根据半理论法计算刀尖点频响函数和试验验证;最后,以某立式加工中心主轴系统为研究对象,应用该方法对刀尖点频响函数进行预测,并与试验进行对比以证明该方法的有效性。     

高速HSK热装工具系统结合部的参数辨识

HSK工具系统的动态特性直接影响机床的加工效率与质量,获得准确的工具系统结合部参数又是精确预测HSK工具系统动态特性的基础。将热装刀柄-刀具结合部简化为弹簧-阻尼模型,基于Timoshenko梁理论建立了HSK热装刀柄-刀具结合部的有限元模型,采用弹塑性理论辨识结合部的刚度和阻尼,获得了HSK热装刀柄-刀具结合部内沿轴向不同位置的刚度和阻尼。进而建立了HSK热装工具系统的有限元动力学模型,分析工具系统刀尖点的频响函数。最后进行了HSK热装工具系统频响函数的实验测量,与理论频响函数相比较,验证了将结合部等效为弹簧-阻尼的辨识方法的合理性和有效性。     

Sensitivity analysis on ram speed of a direct extrusion process model using a porthole die through CEL method

Prediction of machine tool chatter requires the characterization of dynamic of the machine-tool-workpiece system by means of frequency response functions (FRFs). Uncertainties of the measured FRFs result in uncertainties of the calculated stability diagrams, therefore robustness of stability prediction against parameter perturbations is of high importance. Although there exist methods to determine robust stability in terms of stability radii, these methods either give a conservative estimate of the real uncertainties or are limited to perturbations of a few modal parameters, only. In this paper, a frequency-domain approach is presented to determine robust stability boundaries using the measured FRFs directly without any modal parameter identification. The method is based on an envelope fitting around the measured FRFs combined with some considerations of the single-frequency method. The application of the method is demonstrated in case of a turning operation, where the machine tool structure is characterized by a series of FRF measurements.     

Rapid dynamics prediction of tool point for bi-rotary head five-axis machine tool

Receptance Coupling Substructure Analysis (RCSA), an effective approach to rapidly predict the tool point frequency response function (FRF), generally requires the response of spindle-machine assembly by experiments. This method is feasible for three-axis machine tool because the spindle and its posture are normally unchangeable. But in terms of five-axis milling, the spindle-machine assembly changes continuously. The purpose of this study is to propose new techniques to solve the constantly-changing assembly response in order that RCSA can be used for bi-rotary head five-axis machine tools. Based on receptance matrix determination in coupling direction and single degree of freedom coupling simplification, the swivel model for holder tip receptances is established for swivel motion. According to the concept of oriented frequency response function, the rotational model is derived to calculate the holder tip receptances with rotary motion. By combining the swivel model and the rotational model, the holder tip receptance of arbitrary posture can be calculated by three orthogonal postures. A five-axis machine tool with bi-rotary head is used to conduct FRF tests on different postures. Experimental results show that the models proposed can accurately predict tool point frequency response of any posture and large difference in FRFs among those postures of bi-rotary head is detected.     

Identification of modal parameters of unmeasured modes using multiple FRF modal analysis method

Current modal analysis methods seek to identify the modal parameters of some or all of the modes in the measured frequency range of interest. In many applications however, it will be very useful if modal parameters of some of the out-of-range modes can be identified during modal analysis. Such a goal is obviously theoretically possible since the raw measured frequency response functions (FRFs), upon which modal analysis is performed, do contain adequate information about the out-of-range modes in the form of residue contributions. In this paper, a new method for the estimation of modal parameters using multiple FRFs analysis is presented. In the process of modal identification, the proposed method not only presents accurate modal parameters of the modes which are present in the measurement frequency range, but also quite accurately identifies some of the modes which are not measured. The method calculates the required modal parameters by solving eigenvalue problem of an equivalent eigensystem derived from those measured FRF data. All measured FRFs are used simultaneously to construct the equivalent eigensystem matrices from which natural frequencies, damping loss factors and modeshape vectors of interest are solved. Since the identification problem is reduced to an eigenvalue problem of an equivalent system, natural frequencies and damping loss factors identified are consistent. Applications of the method to both numerically simulated and practically measured FRF data are given to demonstrate the practicality of the proposed method and the results have shown the method is capable of accurately identifying modal parameters of out-of-range modes.     

Identification of bearing dynamics under operational conditions for chatter stability prediction in high speed machining operations

Chatter is a major problem causing poor surface finish, low material removal rate, machine tool failure, increased tool wear, excessive noise and thus increased cost for machining applications. Chatter vibrations can be avoided using stability diagrams for which tool point frequency response function (FRF) must be determined accurately. During cutting operations, due to gyroscopic moments, centrifugal forces and thermal expansions bearing dynamics change resulting in tool point FRF variations. In addition, gyroscopic moments on spindle–holder–tool assembly cause separation of modes in tool point FRF into backward and forward modes which will lead to variations in tool point FRF. Therefore, for accurate stability predictions of machining operations, effects of operational conditions on machine tool dynamics should be considered in calculations. In this study, spindle bearing dynamics are identified for various spindle rotational speeds and cutting forces. Then, for a real machining center, tool point FRFs under operating conditions are determined using the identified speed dependent bearing dynamics and the mathematical model proposed. Moreover, effects of gyroscopic moments and bearing dynamics variations on tool point FRF are examined separately. Finally, computationally determined tool point FRFs using revised bearing parameters are verified through chatter tests.     

FITTING MEASURED FREQUENCY RESPONSE USING NON-LINEAR MODES

The article is devoted to curve fitting of the measured frequency response functions (FRFs) of an actual beam with a non-linear component. A frequency response model, based on the non-linear normal modes (NNMs) approximated by the Ritz–Galerkin method and on a superposition assumption is built up. Identification of NNM is performed by minimising a cost function involving synthetised FRF and measured data and leads to natural frequencies, damping factors, mode shapes as functions of modal amplitudes.     

基于试验频响函数刚体特性参数的计算及其应用

试验频响函数(FRF)正越来越成功、广泛地应用于动态和振动系统的不同领域中。基于模态试验的频响函数,尤其是频响函数中的质量线与刚体特性参数的内在关系,提出了一种简便、易行且精确的进行刚体惯量特性参数的计算方法。进行了相关理论的推导,通过实际试验验证分析了该方法。对大型复杂的结构,采用该方法具有一定的优势。     

An identification method for joint structural parameters using an FRF-based substructuring method and an optimization technique

A new method is proposed to identify the joint structural parameters of complex systems using a frequency response function (FRF)-based substructuring method and an optimization technique. The FRF method is used to estimate the joint parameters indirectly by minimizing the difference between the reference and calculated responses using a gradient-based optimization technique with analytical gradient information. To assess the robustness of the identification method with respect to noisy input data, FRFs contaminated by uniformly distributed random noise were tested in a numerical example. The effects of the random noise and the magnitude of the connection stiffness values on the accuracy of the method were investigated while identifying the joint parameters. When the FRFs were contaminated with random noise, the proposed procedure performed well when used to identify the stiffness values, but the accuracy of identification is deteriorative when used to identify the damping coefficients. The joint parameters of a real bolted structure were also identified by the proposed method. The results show that it can be applied successfully to real structures, and that a hybrid approach using both calculated and measured FRFs in the substructure model can enhance the quality of the identification results.     

Analysis of swept-sine runs during modal identification

Experimental modal analysis of large aerospace structures in Europe combine nowadays the benefits of the very reliable but time-consuming phase resonance method and the application of phase separation techniques evaluating frequency response functions (FRF). FRFs of a test structure can be determined by a variety of means. Applied excitation signal waveforms include harmonic signals like stepped-sine excitation, periodic signals like multi-sine excitation, transient signals like impulse and swept-sine excitation, and stochastic signals like random. The current article focuses on slow swept-sine excitation which is a good trade-off between magnitude of excitation level needed for large aircraft and testing time. However, recent ground vibration tests (GVTs) brought up that reliable modal data from swept-sine test runs depend on a proper data processing. The article elucidates the strategy of modal analysis based on swept-sine excitation. The standards for the application of slowly swept sinusoids defined by the international organisation for standardisation in ISO 7626 part 2 are critically reviewed. The theoretical background of swept-sine testing is expounded with particular emphasis to the transition through structural resonances. The effect of different standard procedures of data processing like tracking filter, fast Fourier transform (FFT), and data reduction via averaging are investigated with respect to their influence on the FRFs and modal parameters. Particular emphasis is given to FRF distortions evoked by unsuitable data processing. All data processing methods are investigated on a numerical example. Their practical usefulness is demonstrated on test data taken from a recent GVT on a large aircraft. The revision of ISO 7626 part 2 is suggested regarding the application of slow swept-sine excitation. Recommendations about the proper FRF estimation from slow swept-sine excitation are given in order to enable the optimisation on these applications for future modal survey tests of large aerospace structures.     

A DUAL FITTING ALGORITHM FOR MODAL PARAMETERS IDENTIFICATION

A dual fitting algorithm (DFA) for modal parameters identification is presented. The method is implemented in three steps: first, the coefficients of the Forsythe orthogonal polynomials for the rational fraction of the frequency response functions (FRFs) are obtained by fitting the experimental FRF data; then the coefficients of the orthogonal polynomials are converted into the coefficients of ordinary power polynomials by the fitting method again; and finally, the poles and residues of the rational fraction of FRFs in ordinary power polynomials are extracted to identify the modal parameters. Some notes to the definition and use of the recurrence formulation for the real half-function Forsythe orthogonal polynomials are introduced. An example is given to show the aspects of the present method.