Tool Tip Frequency Response Function Research Articles

Design of eddy current dampers for vibration suppression in robotic milling

The milling robot normally has a low stiffness which may easily cause chatter during machining. This article presents a novel eddy current damper design for chatter suppression in the robotic milling process. The designed eddy current dampers are installed on the milling spindle to damp the tool tip vibrations. The structural design and the working principle of the eddy current dampers are explained. The magnetic flux density distribution and the magnetic force generation of the designed eddy current damper are analyzed with the finite element method. The tool tip dynamics without and with eddy current dampers are modeled, and the damping performance of the proposed eddy current dampers in the robotic milling process is verified through both simulations and experiments. The results show that the peaks of the tool tip frequency response function caused by the milling tool modes are damped significantly, and the stable depth of cut is improved greatly with eddy current dampers.

Coupled Model of Rotary-Tilting Spindle Head for Pose-Dependent Prediction of Dynamics

Five-axis machine with rotary-tilting spindle head (RTSH) is always used for sculptured surface machining, and the tool-tip dynamics in various machining postures along the tool path directly affect the machining accuracy and stability. To rapidly evaluate the tool-tip dynamics at different postures during the structural design of tool-spindle-spindle head (TSSH) assembly, this paper proposes a coupled dynamic model of tool-spindle-bearing system (TSBS) and RTSH. The model is a rigid-flexible multibody dynamic model with 36 degrees-of-freedom (DOFs), where in the rotary shaft, swivel shaft and housing are treated as rigid bodies; the tool, tool holder, and spindle shaft are modeled by reduced beams; the bearings and flexible joints are modeled as spring-damping elements. The fully Cartesian coordinates and Lagrangian method are employed to deduce a general parametric dynamic equation. The analytical method for calculating the contact stiffness of bearings and flexible joints is systematically presented, including tool-holder joint, holder-spindle joint, spindle bearings, hirth coupling, and the bearings and locking joints of rotary and swivel shafts. The model is verified by the frequency response functions (FRFs) testing and modal testing at different postures. The experimental results show that the proposed model can be used for accurate and efficient evaluation of the tool-tip FRFs, natural frequencies and mode shapes of TSSH at an arbitrary posture.

High speed tooltip FRF predictions of arbitrary tool-holder combinations based on operational spindle identification

Abstract The chatter vibrations in milling are avoided by selecting spindle speeds and depth of cuts from the stability lobes. However, it has been well observed that the structural dynamics of the spindle system change as a function of speed and even feed. As a result, the measurement of spindle structure's Frequency Response Function (FRF) at zero speed does not lead to an accurate prediction of stability lobes, hence the productive cutting conditions cannot be estimated accurately. In this study, an in-process identification of speed dependent FRF of the spindle structure is proposed. The spindle FRF is either measured during the rotation via impact testing, or FRF is identified from the inverse solution of critical stability limits. The tool-holder is decoupled from the spindle FRF using receptance coupling method, which leads to speed and/or feed dependent spindle shaft FRF. The tool tip FRF is then predicted by coupling the Timoshenko beam based tool-holder to spindle. The proposed method is validated in milling tests. It is shown that the chatter free material removal rates can be more accurately predicted when the spindle speed and feed dependent machine tool dynamics are considered.

Suppressing vibration modes of spindle-holder-tool assembly through FRF modification for enhanced chatter stability

Modifying dynamic response of a machine tool is of great importance for chatter mitigation. Tool tip frequency response function (FRF) can be suppressed by capitalizing on the absorber effect due to dynamic interactions among vibration modes of spindle, holder and tool. In this paper, a practical method is presented to modify the system’s FRF by selecting proper dimensions for assembly component without extensive testing. Robustness of the method is demonstrated through simulation and test results. Milling stability tests were also conducted where significant improvements in chatter free Material Removal Rate (MRR) is achieved.

Posture-dependent stability prediction of a milling industrial robot based on inverse distance weighted method

During robotic milling process, vibration is one of mainly factors that affect machining accuracy and surface quality, due to the low stiffness of robot structure. Robotic milling stability is dependent on the frequency response function (FRF) at tool tip, which is posture-dependent within the work volume. An approach to rapidly predict the industrial robot stability of any posture is presented in this paper. A lot of tool tip positions are arranged to conduct the impacting tests. For each tool tip position, five corresponding robot postures are obtained by determining the redundant freedom and solving inverse kinematics problem. FRFs at the tool tip of all tested robot postures are identified, and modal parameters are acquired. Based on the sample information that contains tested robot postures and corresponding modal parameters, inverse distance weighted (IDW) model is utilized to predict tool tip FRFs at any posture. Consequently, the milling stability lobe diagrams of robot at different postures are available to be obtained. Finally, the approach is proven to be feasible by performing robot milling experiments.

Output-Only Modal Analysis of Micromilling Systems

An output-only modal analysis (OMA) approach is presented to obtain the direct frequency response function (FRF) at the tip of the tool in micromilling setups. White noise input is provided using acoustic excitation and the resulting vibrations are measured using a laser Doppler vibrometer (LDV). Autoregressive (AR) identification is used to extract the natural frequencies and damping ratios of the structural modes of the milling setup, and mass-sensitivity analysis is used to obtain modal stiffness values. The accuracy of the tool tip FRFs that are constructed using OMA is verified by comparing them against the FRFs that are measured using impulse hammer tests. The direct FRF at the tool tip is an essential component in predicting and avoiding excessive and unstable vibrations in milling operations, and the presented approach provides a practical method for the direct measurement of the tool tip FRF in micromilling where the application of traditional hammer tests is not possible.

A new receptance coupling substructure analysis methodology to predict tool tip dynamics

Abstract Tool tip frequency response function (FRF) is essential for chatter stability diagram in machining. But new modal tests are required for different tool-holder-spindle assemblies. To avoid these tests, receptance coupling substructure analysis (RCSA) method has been developed. Previous research proved that the full receptance matrix, which contains rotational and moment contributes, influences the RCSA accuracy. By improving the accuracy and efficiency in acquiring the full receptance matrix, this paper presents a new RCSA methodology to predict the tool tip dynamics when a new tool is selected. To identify the contact dynamics between the tool and tool holder, one required receptance matrix is experimentally measured with a reference tool attached on the machine. Comparing to the classical RCSA technique, an enhanced approach is proposed to better estimate the receptance matrix. Only one impact positon is required in the experiment. The enhanced approach introduces two compensation strategies to process the measuring data from impact test. Each compensation strategy can be chosen to improve the estimation accuracy. The measured receptances, together with the finite element models of the reference tool and the new tool, are used to predict the unknown tool tip FRF. Both numerical simulation and practical experiment are conducted to validate the proposed methodology. The results show that the proposed method is preferred when multiple modes should be considered.

Prediction of tool tip dynamics for generalized milling cutters using the 3D model of the tool body

In general, chatter is the main limitation to proper material removal in milling operations. Stability lobes are good tools to determine chatter-free cutting conditions in terms of spindle speed and cutting depth, which require the frequency response function (FRF) at the tool tip to be known. There are experimental methods to measure the tool tip FRF but this may be time consuming or even impossible for each tool and tool holder combination. Receptance coupling substructure analysis (RCSA) is a widely used approach to predict tool tip dynamics. This paper proposes the use of the RCSA approach with a stereolithographic (STL) slicing algorithm to enable the exact calculation of cross sectional properties such as area and area moment of inertia of the cutting tool from its 3D model opposed to the approximation methods. So that, the effect of flutes on cutting tool structure introduced in an exact manner and the RCSA approach becomes feasible for more complicated tool geometries with varying cross-sectional properties, i.e., tapered ball end mills, end mills with variable flute geometries, and so on. The solid model of the tool can be available by either the tool manufacturer or 3D measurement. Although, at the presence of 3D models, finite element methods (FEM) offer accurate simulation of the dynamic response for solid bodies, they suffer from the compromise between accuracy and computation time, as high number of elements is needed for accuracy. Thus, the use of analytical methods where possible improves the simulation time significantly. The proposed STL slicing algorithm is integrated with a previously developed RCSA method. The experimental results show that the proposed algorithm works more accurate in calculation of the cross-sectional properties and hence free-free response of the tool compared to the existing arc approximation methods. It is also shown that the proposed approach performs better than FEM solutions in terms of the computation time and the compromise between accuracy and computation performance. Finally, the proposed approach in prediction of tool tip dynamics for a robotic machining platform.

Evaluation of machine tools with position-dependent milling stability based on Kriging model

Abstract Machine tool's milling stability is a function of the frequency response function (FRF) at the tool tip, which varies with the position changes of the moving components within the machine tool work volume. The approach to obtain stability lobe diagram avoiding chatter vibrations is generally based on some specific positions, resulting in an incomprehensive and inaccurate chatter prediction. This paper presents a new method to rapidly evaluate the position-dependent milling stability of machine tools. In this method, position combinations of the moving components are arranged to perform the impact testing, and then the corresponding identified FRFs at the tip of machine tool frame-holder base are acquired to identify the modal parameters, with which a Kriging model is developed to describe the relationship between positions and modal parameters. Consequently, based on the modal fitting technique, tip FRFs of machine tool frame-holder base at any position in the whole working space can be reorganized. And such tip FRFs are further adopted to calculate the tool tip FRFs with the identified contact parameters of the holder-tool system using the receptance coupling substructure analysis (RCSA) technique. Then, the milling stability at different positions can be assessed. Furthermore, the proposed method is applied to a vertical machining center, and its accuracy for predicting the milling stability in entire work volume is validated through chatter tests.

Chatter stability prediction for high-speed milling through a novel experimental-analytical approach

Chatter prediction is crucial in high-speed milling, since at high speed, a significant increase of productivity can be achieved by selecting optimal set of chatter-free cutting parameters. However, chatter predictive models show reduced accuracy at high speed due to machine dynamics, acquired in stationary condition (i.e., without spindle rotating), but changing with spindle speed. This paper proposes a hybrid experimental-analytical approach to identify tool-tip frequency response functions during cutting operations, with the aim of improving chatter prediction at high speed. The method is composed of an efficient test and an analytical identification technique based on the inversion of chatter predictive model. The proposed technique requires few cutting tests and a microphone to calculate speed-dependent chatter stability in a wide range of spindle speed, without the need of stationary frequency response function (FRF) identification. Numerical and experimental validations are presented to show the method implementation and assess its accuracy. As proven in the paper, computed speed-dependent tool-tip FRF in a specific configuration (i.e., slotting) can be used to predict chatter occurrence in any other conditions with the same tool.

Improved experimental-analytical approach to compute speed-varying tool-tip FRF

Chatter stability prediction is crucial to improve the performances of modern milling process, and it gets even more important at high speeds, for which very productive cutting parameters can be achieved if the suitable spindle speed is selected. Unfortunately, the available chatter predictive models suffer from reduced accuracy at high speed due to inaccuracies in the input data, especially the machine tool dynamics that is acquired in stationary configurations but could sensibly change with spindle speed. In this paper, an efficient method to identify the speed-varying Frequency Response Functions (FRFs) under operational conditions is presented. The proposed approach is based on the definition of some experimental chatter limits (i.e., chatter frequency and related depth of cut), obtained by a dedicated test, called Spindle Speed Ramp-up. The experimental results are then combined with the analytical stability solution. By minimizing the differences between the experimental and predicted chatter conditions, a dedicated algorithm computes the speed-varying FRFs. Few tests and simple equipment (i.e., microphone) are enough to calculate the FRFs in a wide range of spindle speeds. The proposed technique was validated in real machining applications, the identified tool-tip FRFs are in accordance with expected trend reported in scientific literature. Speed-varying stability lobe diagram reconstructed with the computed FRFs is proven to be accurate in predicting stable cutting parameters.

Receptance coupling based algorithm for the identification of contact parameters at holder–tool interface

To identify stable cutting conditions with a high depth of cut, stability lobe diagrams are used. In order to predict these diagrams, frequency response functions (FRF) at the tool tip are required for every tool, holder and machine combination. To reduce the number of experimental tests, receptance coupling substructure analysis (RSCA) is proposed in the literature. In order to take full advantage of this method, contact parameters between holder and tool must be known. To identify these parameters this paper presents a new method based on free-free measurements. The obtained contact parameters led to good results for various tool lengths. Based on this, an extensive investigation is performed for the ER32 holder interface. Afterwards, the RCSA method is tested. Therefore, different spindle–holder–tool assemblies are modeled for two machine tools. Prediction and measurement of obtained tool-tip FRF shows a good match, especially for the frequency position.

Speed-varying Machine Tool Dynamics Identification Through Chatter Detection and Receptance Coupling

Tool-tip Frequency Response Function (FRF) represents one of the essential inputs to predict chatter vibration and compute the Stability Lobe Diagram (SLD). Tool-tip FRFs are generally obtained for the stationary (non-rotating) condition. However, high speeds influence spindle dynamics, leading to a reduced accuracy of the SLD prediction. This paper presents a comprehensive method to identify speed-varying tool-tip FRFs and improve chatter prediction. First, FRFs for a screening tool is identified by a novel technique based on a dedicated experimental test and analytical stability solution. Then, a tailored receptance coupling technique is used to predict speed-varying tool-tip FRFs of any other tool. Proposed method was experimentally validated: chatter prediction accuracy was demonstrated through chatter tests.

Cumulative Surface Location Error for Milling Processes Based on Tool-tip Frequency Response Function

In milling processes, the desired machined surface cannot be perfectly achieved even in case of chatter-free machining due to the thermally induced errors, the trajectory following errors and the most significant one: the cutting force induced vibration errors. In case of vibration, the error is represented by the so-called Surface Location Error (SLE), which is the distance between the machined and the required surface position. In case of roughing operations, these errors can have a significant impact on the surface position due to the interaction between the subsequent SLEs. The machined surface depends on the previously resulted SLE through the variation of the radial immersion. In this paper, the series of the consecutive SLEs are investigated in a multi-degree-of-freedom model. The dynamical behaviour of the milling tool is described by frequency response functions. The variation of the SLE values is governed by a discrete map, which may lead to an unpredictable final surface position. The parameter range where this unpredictable final SLE occurs is presented together with the traditional stability chart representing the chatter-free domains of cutting parameters. With the proposed methods, the traditional stability chart can be improved, from which chatter-free and CSLE-stable technological parameters can be selected.

Improved RCSA technique for efficient tool-tip dynamics prediction

Chatter prediction requires Frequency Response Function (FRF) at the tool-tip, which can be reliably identified by modal testing. However this procedure is time-consuming and unsuitable for industrial application since measurements must be performed for each tool attached to the machine. Receptance coupling technique can be adopted to speed up FRF identification. This technique computes tool-tip response combining experimental spindle-holder dynamics with numerical/analytical model of the tool. The main drawback is to identify rotational degree of freedom responses that are generally obtained by performing additional calibrations tests. This work presents a new method overcoming this limitation, obtaining rotational responses by a novel inverse formulation that reduces the number of required experiments. The proposed method is based on receptance coupling theory and requires FRF measurements of a single machine setup, thus increasing the efficiency of receptance coupling approach for tool-tip FRF prediction. The proposed technique is proven by experimental validation and the same accuracy of state of the art methods is obtained.

New Continuous Dynamic Coupling for Three Component Modeling of Tool–Holder–Spindle Structure of Machine Tools With Modified Effected Tool Damping

In machine dynamics, the tool point frequency response functions (FRFs) are employed to predict the stable machining conditions. In this paper, a combined analytical–experimental substructuring procedure is proposed to determine the tool point FRFs usable for different holder–tool configurations. Contact interface of holder–spindle and tool–holder is modeled using translational and rotational springs and dampers spread in the length of contact surface. These joint parameters are defined using finite element method. This enables the analyst to introduce the contact stiffness and damping in more detail with taking into consideration the variations of normal pressure in the tool–holder and holder–spindle joints. The dynamic analysis of the holder is done using Timoshenko beam theory by Tchebyshev method. The tool dynamics is modeled based on Euler–Bernoulli beam theory using the method of equivalent diameter. For the purpose of shifting the tool stability lobes to a higher level, tool damping parameter is modified by internal frictional damper and the effect is analyzed by analytical methods and experimental study. After joint parameters are defined continuously by finite element method, a new method for continuous dynamic coupling is presented. The method employs the measured spindle-machine FRFs and analytical models of the tool and holder to predict the tool tip FRFs. In this new method, continuous coupling in two separate domains of response model and modal model is presented. Such structural modeling avoids us to do complex modal tests for a different set of combinations of the holder and tool with specific milling machine. An experimental case study is provided to demonstrate the applicability of the proposed method in dynamic modeling of machine tool.

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.

Tool point dynamics prediction by a three-component model utilizing distributed joint interfaces

In machine dynamics the tool point frequency response functions (FRFs) are employed to predict the stable machining conditions. In this paper, a combined analytical–experimental substructuring procedure is proposed to determine the tool point FRFs for different holder–tool configurations. The method employs the measured spindle-machine FRFs and analytical models of the tool and the holder to predict the tool tip FRFs for different sets of tools and holders mounted on the machine spindle without the need for repeated experimental measurements. Distributed joint interfaces are used to couple the three-component model of the machine. The machine tool tip FRFs with different tool–holder combinations are obtained assuming the clamping conditions at joint interfaces remain unchanged. An experimental case study is provided to demonstrate the applicability of the proposed method in dynamic modeling of machine tool.

Continuous model for analytical prediction of chatter in milling

A novel analytical approach for prediction of chatter in milling process is presented. Existing approaches use lumped-parameter models to define the dynamics of tools/workpieces. In this paper a continuous beam model is employed for prediction of milling operations dynamics. The tool boundary conditions are elastic support at the tool/holder/spindle interface and free support at the other end. Employing the continuous model eliminates the need for tool tip frequency response function (FRF) measurements in tool-tuning practice, especially in micro-milling, where FRF measurement is practically very difficult. Tool/holder/spindle interface parameters, once identified, can be used for other tool lengths. The impact hammer test is used to identify stiffness and damping parameters of the tool/holder/spindle interface. Using the new analytical approach and picking single-frequency solution (SFS), stability lobes are obtained for a slotting operation. The resulting lobes are compared to those obtained by the well-proven lumped-parameter model. In addition to a good general agreement between the two approaches, the continuous model prediction is more conservative for critical depth of cut, which is attributed to its ability to consider all participating modes in the response and so represents a more accurate representation of the system.

A Cutting Performance Based Template for Spindle Dynamics

The stable metal removal rate in milling depends on the dynamic characteristics of the tool-holder-spindle system. We present a methodology for determining the permissible dynamic characteristics based on the intended cutting operation. We produce a template that bounds the tool-tip frequency response function (FRF). Measured FRFs can be compared against the template to check cutting performance. The template can be used in design to match the spindle system to the intended application. The template accounts for lobing effects, multiple modes, process damping, and static stiffness. It accounts for damping variability, producing a safe-side estimate. Experimental results illustrate the template's use.