Tool Point Frequency Response Research Articles

Case study of vibration in a mobile milling machine

Many industries rely on heavy-duty machinery such as cranes, pipelines, motors, which are subject to wear and tear. Milling of such parts using conventional machine tools presents many drawbacks and is impossible in some cases. In such situations, mobile machine tools can be used to machine directly on site. However, mobile machines are flexible, and are prone to detrimental vibrations during cutting operations. Vibrational stability in the surfacing process has been extensively studied in conventional milling. However, the focus of this article is an original study on a mobile milling machine used for on-site surfacing operations. An experimental investigation into the vibrational behavior of the machine is carried out and a sensorless method is used to detect the onset of chatter. Machine flexibility is discussed using a tool-point frequency response function and references from the literature. Milling operations are carried out over a range machining parameter to determine an experimental stability limit. Internal sensors for spindle motor consumption and spindle motor encoder are monitored during the machining process. A threshold is established for determining the appearance of chatter using only the machine’s internal sensors.

Research on the stability analysis of milling of thin-walled parts based on the dynamic characteristics

Chatter in thin-walled parts is easy to occur in the process of machining, so the analysis of the stability of thin-walled parts has always been a research hotspot. In this paper, considering the influence of cutter eccentricity on milling force first, the coefficients of milling force were able to be identified by combining the milling force model with genetic algorithm. The results show that this method can obtain the milling force coefficients only by one experiment, and the accuracy is higher. Then the tool point Frequency Response Function (FRF) for a given combination can be calculated by using the Receptance coupling substructure analysis (RCSA) method that uses Timoshenko beam theory. Finally, the milling system can be divided into three types by aspect ratio. That is, when aspect ratio is less than 0.03, the system is considered to be a rigid tool-flexible workpiece system, but aspect ratio is between 0.03 and 0.2, the system is considered to be a flexible tool-flexible system, then aspect ratio is greater than 0.2, the system is considered to be a flexible cutter-rigid workpiece system.

DYNAMICAL CONTACT PARAMETER IDENTIFICATION OF SPINDLE-HOLDER-TOOL ASSEMBLIES USING SOFT COMPUTING TECHNIQUES

In industry, the capability to predict the tool point frequency response function (FRF) is an essential matter in order to ensure the stability of cutting processes. Fast and accurate identification of contact parameters in spindle-holder-tool assemblies is very important issue in machining dynamics analysis. This work is an attempt to illustrate the utility of soft computing techniques in identification and prediction contact parameters of spindle-holder-tool assemblies. In this paper, three soft computing techniques, namely, genetic algorithm (GA), simulated annealing (SA), and particle swarm optimization (PSO) were used for identification of contact dynamics in spindle-holder-tool assemblies. In order to verify the proposed identification approaches, numerical and experimental analysis of the spindle-holder-tool assembly was carried out and the results are presented. Finally, a model based on the adaptive neural fuzzy inference system (ANFIS) was used to predict the dynamical contact parameters at the holder-tool interface of a spindle-holder-tool assembly. Accuracy and performance of the ANFIS model has been found to be satisfactory while validated with experimental results.

Robust Chatter Stability Prediction of the Milling Process considering Uncertain Machining Positions

Milling stability is a function of the tool point frequency response functions (FRFs), which vary with the movements of the moving parts within the whole machine tool work volume. The position-dependent tool point FRFs result in uncertain prediction of the stability lobe diagram (SLD) for chatter-free machining parameter selection. Taking the variations of modal parameters to represent the variations of tool point FRFs, this paper introduces the edge theorem to predict the robust milling chatter stability. The application of the edge theorem requires the minimum and maximum modal parameters within the machining space defined by the machining position and machining allowance information. Then, radial basis function artificial neural networks (RBFANNs) are used to predict the position-dependent modal parameters in X and Y directions based on the sample information of machining positions and related modal parameters at the tool point. Moreover, sample machining spaces are determined based on the aforementioned sample positions, and the trained RBFANNs are used to obtain corresponding sample extreme modal parameters. On this basis, RBFANNs for predicting the position and machining allowance-dependent extreme modal parameters can also be trained, and they are combined with the edge theorem and zero exclusion condition to calculate robust pairs of the spindle speed (n) and limiting axial cutting depth (aplim) and then plot the robust SLD (RSLD). A case study was performed on a real three-axial vertical machining center, and the plotted RSLD considering position variations was compared with the traditional SLD. Results of the chatter tests show that the RSLD can provide more reliable (ap, n) pairs to guarantee the milling stability, validating the feasibility of the proposed robust milling chatter stability prediction method.

An improved rapid prediction method of the milling tool point frequency response function

During the prediction of the tool point frequency response function (FRF) based on receptance coupling substructure analysis (RCSA), in allusion to the problems that the existing tool model cannot simulate the contour of the tool precisely and the large amount of calculation for joint parameter identification during the calculation of the rotational FRF of the spindle, the joint model and the optimization algorithm affect the identification accuracy when acquiring the rotational FRF of the spindle. This study proposes a rapid prediction method for the tool point FRF on the basis of RCSA. The method divides the spindle-holder-tool system into two parts: the spindle-holder-partial shank and the remaining tool. On this basis, this study proposes a method of accurately establishing the model of the remaining tool with a 3D scanner and improves the calculation method of the rotational FRF of the spindle-holder-partial shank assembly through the reverse RCSA and finite difference method directly through the modal impact testing on the cutting tool. This study provides the experiments on a vertical machining center and compares the predicted FRF and the measured FRF on the tool point. The result indicates that the predicted FRF curve is consistent with the measured FRF curve with the relative error of natural frequency within 4.0%. This study confirms that the method is feasible, effective, and convenient.

Prediction of Tool Point Frequency Response Functions within Machine Tool Work Volume Considering the Position and Feed Direction Dependence

A chatter vibration in milling process results in poor surface finish and machining efficiency. To avoid the chatter vibration, the stability lobe diagram (SLD) which is the function of tool point frequency response functions (FRFs) is adopted to predict the chatter-free machining parameters. However, the tool point FRF varies with the changes of machining positions and feed directions within machine tool work volume. Considering this situation, this paper presents a method to predict the position and feed direction-dependent tool point FRF. First, modal parameters of the tool point FRFs obtained at some typical positions and feed directions are identified by the modal theory and matrix transformation method. With the sample information, a back propagation (BP) neural network whose inputs are the position coordinates and feed angle and outputs are the modal parameters can be trained with the aid of the particle swarm optimization (PSO) algorithm. Then, modal parameters corresponding to any position and feed direction can be predicted by the trained BP neural network and used to reorganize the tool point FRFs with the modal fitting technique. A case study was performed on a real vertical machining center to demonstrate the accurate prediction of position and feed direction-dependent tool point FRFs. Furthermore, the position and feed direction-dependent milling stability was researched and origin-symmetric distributions of the limiting axial cutting depths at each machining position were observed.

Evaluating tool point dynamics using output-only modal analysis with mass-change methods

This paper discusses the evaluation of tool point dynamics using output-only modal analysis methods. As compared to the traditional experimental modal analysis procedures that rely on the input and the output, both being known, output-only methods discussed herein can evaluate modal parameters using only the measured response of the tool subjected to unknown impact-based excitations. Since the input is not known, the estimated shapes are unscaled. To correctly scale shapes, we use the mass-change method. We present analytical models to guide the optimal selection of the mass to be added as well as to guide its placement on the tool. Analytical models systematically characterize errors in scaling the eigenvector and errors due to uncertainties in the estimation of the natural frequencies. The model suggests placement of the mass to be added at the anti-node(s) for the mode(s) of interest. These models guide experiments on two tools – a slender boring bar, and an end mill. Tool point frequency response functions (FRFs) reconstructed with the natural frequencies, damping ratios, and scaled mode shapes evaluated with the output-only mass-change method are compared with and found to be in good agreement with FRFs obtained from the traditional experimental modal analysis procedures. Since output-only methods require one less transducer, and since these methods are robust to uncertainties and inconsistencies in the input, output-only methods promise advantages from the industrial point of view.

Modal interactions for spindle, holders, and tools

This paper describes the interaction between vibration modes associated with the machine-spindle and those associated with the holder-tool when the holder-tool combination is inserted in the milling machine spindle. It is shown that when the bending natural frequency of the holder-tool is near a machine-spindle natural frequency, there is a combined two mode frequency response (similar to a dynamic absorber) for the assembly that exhibits increased dynamic stiffness over those situations when the interaction is absent. Experimental results are provided. The variation in tool point frequency response with tool extension length is then used to calculate the corresponding stability maps. These maps are evaluated to determine the effect of interactions between machine-spindle and holder-tool modes on milling stability. Conclusions are presented.

Prediction of Stability Lobe Diagrams in High-Speed Milling by Operational Modal Analysis

Self-excited regenerative vibration or chatter limits the primary requirements like productivity, surface finish and dimensional accuracy of high-speed machining. It is the most critical factor that severely affects the tool-life and life of the machine tool. Out of several methods followed for suppressing and avoiding chatter, machining conditions chosen with stability lobe diagram is the most reliable way. Stability lobe diagrams are typically generated by knowing specific cutting force coefficients and tool point frequency response functions (FRFs). Inaccurate use of tool point FRFs significantly affects the stable regions of stability lobe diagrams. As tool-point FRFs are influenced by gyroscopic effect, centrifugal force, thermal change in bearing dynamics, etc. during machining, it is important to consider the effect of these factors on tool point FRFs in order to generate accurate stability lobe diagrams. The present work covers a new approach for estimating tool point FRFs during machining operations, employing cutting tool vibration signals. For measuring the vibration at the tip of end mill at different spindle speeds, a non-contact laser vibrometer is used. In order to remove the tooth pass frequency and its harmonics from the measured signals, a comb filter is employed. The filtered signal is subjected to Operational Modal Analysis (OMA) in order to derive tool point FRFs. With the estimated FRFs at different spindle speeds, the stability lobe diagrams are drawn for high-speed milling machine. Comparative study of stability lobe diagrams, drawn with static modal analysis and Operational Modal Analysis, have shown that the cutting conditions chosen from stability lobe diagram derived with OMA, are found to be more realistic for avoiding chatter during high-speed milling applications.

Effects of a drawbar design and force on multipurpose aerostatic spindle dynamics

The tool point frequency response function (FRF), or receptance, is an important dynamic condition for machining processes, especially milling and finishing, as it enables users to calculate the most appropriate operating conditions, namely spindle speed and depth of cut, for achieving the best spindle performance. In this paper, we evaluate the effects of the drawbar on the tool point FRF of a multipurpose aerostatic spindle using a new procedure. The drawbar was considered to be nested inside the shaft and the receptance of the assembly was predicted based on a multiple-point receptance coupling approach. We coupled the tool holder and the tool to the receptance, so two types of contact parameter were considered simultaneously. We determined the contact parameters between the shaft and the tool holder, and between the tool holder and the tool, and included the values obtained when coupling with different combinations of tool holder and tool. We also evaluated the shaft-tool holder contact parameter for three different axial pulling forces. Moreover, we investigated the aerostatic bearing dynamics, including the stiffness and damping factor, in three different cases of supplied air pressure. Finally, we estimated the FRF of the tool under several aerostatic bearing and drawbar conditions and calculated stability lobe diagrams based on the estimated FRF. These results show that considering the drawbar improves the estimate of the tool point FRF and, subsequently, the stability lobe diagram. The effect of varying the length and density of the drawbar on the tool point FRF was also investigated.

Analyzing the Dynamic Characteristics of Milling Tool Using Finite Element Method and Receptance Coupling Method

This study aims to investigate the dynamic characteristics of a milling machine with different head stocks by using finite element (FE) method and receptance coupling analysis (RCA). For this purpose, five full finite element machine models, including vertical column, reformed head stock and feeding mechanism were created. With these models, the tool point frequency response functions were directly predicted. Another approach was the application of the receptance coupling method, in which the frequency response of the assembly milling tool was calculated from the receptance components of the individual substructures through the coupling operation with the interfaces of the feeding mechanism. Results show that a whole machine model with reformed stock has superior dynamic behavior when compared with the original design, by an increment of 10% in the dynamic stiffness. The receptance coupling method was verified to show an accurate prediction of the frequency response functions of the spindle tool when compared with the results obtained from the full FE models. Overall, the proposed methodology can help the designer to efficiently and accurately develop the machine tool structure with excellent mechanical performance.

Prediction of the Frequency Response Function of a Tool Holder-Tool Assembly Based on Receptance Coupling Method

Regenerative chatter has a fatal influence on machine performance in high-speed milling process. Basically, machine condition without chattering can be selected from the stability lobes diagram, which is estimated from the tool point frequency response function (FRF). However, measurements of the tool point FRF would be a complicated and time-consuming task with less efficiency. Therefore prediction of the tool point FRF is of importance for further calculation of the machining stability. This study employed the receptance coupling analysis method to predict the FRF of a tool holder-tool module, which is normally composed of substructures, tool holder and cutter with different length. In this study, the angular components of FRFs of the substructures required for coupling operation were predicted by finite element analysis, apart from the translational components measured by vibration experiments. Using this method, the effects of the overhang length of the cutter on the dynamic characteristics have been proven and successfully verified by the experimental measurements. The proposed method can be an effective way to accurately predict the dynamic behavior of the spindle tool system with different tool holder-tool modules.

The role of tool presetting in milling stability uncertainty

This paper describes the relationship between presetter tool extension length and diameter measurements, the tool point frequency response function (FRF), and milling stability. Three scenarios are considered: 1) the tool extension from the holder face is controlled during setup and measured by the presetter for validation; 2) the tool extension length from the holder face is not controlled during setup and measured to update the tool information in the part program; and 3) the measured extension length is used to update the stability boundary prediction and corresponding operating parameters in the part program. Example presetting results are provided to establish the associated measurement uncertainty. Next, the receptance coupling substructure analysis (RCSA) technique is used within a Monte Carlo simulation to establish the tool point FRF uncertainty as a function of the tool extension length and diameter uncertainty. Finally, the distribution in the tool point FRF is propagated to uncertainty in the milling stability limit. Each of the three scenarios is evaluated to understand their implications for milling stability.

A method of measuring the frequency response function of the tool point based on the surface of feeding system

In the existing method of predicting the frequency response function of the tool point, the effect of lathe feed system is considered in the tool point frequency response function. The junction surface affects the tool point frequency response function, and the junction surface include: bearing–lead screw, lead screw–nut, working bench-guide rail, tool holder–turning tool. The lathe machining system is divided into four substructures, and the lead screw–nut junction surface and workbench-guide rail junction surface have a significant effect in the tool point frequency response function, so we mainly considered the impact of these junctions surface. Through the junction surface stiffness and junction surface damping to obtain a small response at the junction surface. And the frequency response function of the substructure is obtained by hammering method and Timoshenko beam model. Finally, the frequency response function of the substructure end is coupled with the vibration response of the lead screw–nut and workbench-guide rail by the response coupling method, and finally we get the tool point frequency response function. The CA6140 lathe was used as the experimental object, and the frequency response function of the tool point is predicted by above method. The experimental results show that the predicted tool point frequency response function has a high degree of coincidence. The method proposed in this paper can quickly get the frequency response function of the tool point which laid a foundation for the accurate prediction of static and dynamic characteristics of machine tool.

Tool point frequency response function prediction using RCSA based on Timoshenko beam model

In advanced manufacturing, tool point frequency response function (FRF) is the most extensive requirement in avoiding the unstable condition of a machine tool, especially in generating a stability lobe diagram which is widely used in predicting the milling stability for chatter avoidance. However, compared with the analytical method that uses a Euler-Bernoulli beam model for calculating the tool point FRF, the analysis based on a Timoshenko beam model mathematically or analytically is seldom provided. Experimental validation is also not sufficient. In this paper, an approach of tool point frequency response prediction based on Timoshenko beam model is presented, using receptance coupling substructure analysis. This approach employs the combination of experimental result and numerical beam analysis. The proposed receptance calculate theory allows to better estimate the matrix of receptance related to rotation. Based on this theory, an unknown tool point FRF can be predicted by an already known tool point FRF. In the meantime, no additional experiment is required after a single experiment to compute tool holder frequency response. Prediction method has been verified by experiments. The results show the effectiveness and reliability of the proposed method in tool point frequency prediction and effective manufacturing.

Tool Point Frequency Response Prediction for Micromilling by Receptance Coupling Substructure Analysis

One of the challenges in micromilling processing is chatter, an unstable phenomenon which has a larger impact on the microdomain compared to macro one. The minimization of tool chatter is the key to good surface quality in the micromilling process, which is also related to the milling tool and the milling structure system dynamics. Frequency response function (FRF) at micromilling tool point describes dynamic behavior of the whole micromilling machine-spindle-tool system. In this paper, based on receptance coupling substructure analysis (RCSA) and the consideration of rotational degree-of-freedom, tool point frequency response function of micromilling dynamic system is obtained by combining two functions calculated from beam theory and obtained by hammer testing. And frequency response functions solved by Timoshenko's and Euler's beam theories are compared. Finally, the frequency response function is identified as the modal parameters, and the modal parameters are transformed into equivalent structural parameters of the physical system. The research work considers the difference of theoretical modeling between the micromilling and end-milling tool and provides a base for the dynamic study of the micromilling system.

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 contact stiffness of shrink-fit tool-holder joint based on fractal theory

Shrink-fit holders are used widely in high-speed machining because of their high concentric and rigid clamp performance. In this paper, a method to determine the contact stiffness and contact force of shrink-fit tool-holder joint is proposed. The relationship between the contact stiffness and the normal contact load is deduced based on Hertz contact theory and fractal geometry theory. The contact force at the interface is obtained through finite element contact analysis. The identified contact stiffness is incorporated into the finite element model of the tool-holder assembly, which is used to predict the tool point frequency response function of the assembly. The predicted frequency response function agrees with that of the experiment, which verifies the proposed identification method. The effect of radial interference, tool insertion length, and rotational speed on contact behaviors between the shrink-fit tool-holder connection is determined, which is informative for the application and design of the tool-holder assembly.

Modeling and Measurement of Micro End Mill Dynamics using Inverse Stability Approach

Micro-milling applications require high precision and dimensional accuracy. Chatter vibrations arising from unstable cutting conditions cause poor surface finish and damage to the cutting tools. Tool point frequency response functions (FRF); needed to generate stability diagrams, cannot be determined experimentally due to very small tool size. In this study an analytical model for tool point FRF of micro end mills is presented. An inverse algorithm is proposed to correct geometric representation and damping of the tool. The model and the correction methodology presented improve productivity and part quality in micro-milling through accurate prediction of chatter stability limits, enabling better cutting parameter selection.

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.