Tool Tip Frequency Response Function Research Articles

Milling Stability Modeling by Sample Partitioning with Chatter Frequency-Based Test Point Selection

This paper describes a sample partitioning approach to retain or reject samples from an initial distribution of stability maps using milling test results. The stability maps are calculated using distributions of uncertain modal parameters that represent the tool tip frequency response functions and cutting force model coefficients. Test points for sample partitioning are selected using either (1) the combination of spindle speed and mean axial depth from the available samples that provides the high material removal rate, or (2) a spindle speed based on the chatter frequency and mean axial depth at that spindle speed. The latter is selected when an unstable (chatter) result is obtained from a test. Because the stability model input parameters are also partitioned using the test results, their uncertainty is reduced using a limited number of tests and the milling stability model accuracy is increased. A case study is provided to evaluate the algorithm.

Prediction of pose- and position-dependent tool-tip dynamics in high-speed dry gear hobbing

High-speed dry gear hobbing is an advanced and efficient machining technology for automotive gears. Frequent changes in the hob mounting angle (tilt angle) and shifting position result in variations in the tool-tip frequency response function (FRF), which inevitably modify the hobbing stability boundary. To construct an accurate stability boundary for high-speed dry gear hobbing, the primary objective is to predict the tool-tip FRF related to different combinations of hob tilt angles and shifting positions, that is, pose- and position-dependent tool-tip FRF. This study proposes a novel tool-tip FRF prediction strategy that combines multi-output Gaussian Process regression (MOGPR) and Receptance Coupling Substructure Analysis (RCSA). First, the FRFs at the tips of the hob-mounting base were estimated through a series of impact tests under a limited combination of hob tilt angles and shifting positions, and the corresponding modal parameters were identified. The MOGPR model was then leveraged to reveal the mapping relationships between the modal parameters, hob tilt angles and shifting positions. Based on this, the hob-mounting base pose- and position-dependent FRFs can be obtained using the modal fitting technique. Subsequently, the pose-and position-dependent tool-tip FRFs were obtained by coupling the receptances of the hob-toolbar assembly with the fitted hob-mounting base FRFs through the RCSA. Finally, a series of impact tests were conducted to verify the effectiveness of the proposed method. The prediction of pose- and position-dependent tool-tip dynamics can provide a foundation for accurately modeling hobbing stability.

Dynamic Modeling for Chatter Analysis in Micro-Milling by Integrating Effects of Centrifugal Force, Gyroscopic Moment, and Tool Runout.

During micro-milling, regenerative chatter will decrease the machining accuracy, destabilize the micro-milling process, shorten the life of the micro-mill, and increase machining failures. Establishing a mathematical model of chatter vibration is essential to suppressing the adverse impact of chatter. The mathematical model must include the dynamic motions of the cutting system with the spindle-holder-tool assembly and tool runout. In this study, an integrated model was developed by considering the centrifugal force induced by rotational speeds, the gyroscopic effect introduced by high speeds, and the tool runout caused by uncertain factors. The tool-tip frequency-response functions (FRFs) obtained by theoretical calculations and the results predicted by simulation experiments were compared to verify the developed model. And stability lobe diagrams (SLDs) and time-domain responses are depicted and analyzed. Furthermore, experiments on tool-tip FRFs and micro-milling were conducted. The results validate the effectiveness of the integrated model, which can calculate the tool-tip FRFs, SLDs, and time responses to analyze chatter stability by considering the centrifugal force, gyroscopic effect, and tool runout.

Chatter failure comparison for high-speed milling of aerospace GH4099 with silicon nitride ceramic end mills: A laboratory scale investigation

Chatter generated in the high-speed cutting process can seriously limit the machining efficiency and affect the surface machining quality, which urgently needs to be controlled. Aiming at brittle ceramic end mills that are very sensitive to vibration, a strategy based on the modal experimental method is proposed to construct effective and accurate stability lobe diagram (SLD) for chatter prediction and failure analysis in this work. Firstly, the tool tip frequency response function (FRF) of four kinds of self-developed ceramic end mills and commercial cemented carbide end mills with the same structure are established by means of hammering modal experiments, and the modal parameters are solved and identified. Then, based on our established high-speed milling chatter prediction model, the milling force coefficients are obtained by linear regression analysis and calculation, thereby the milling SLDs of five end milling tools are developed. Finally, a series of high-speed side milling experiments are carried out using consistent cutting conditions. The results show that the constructed SLDs can effectively predict the chatter failure region and milling stability for five kinds of end mills, and four ceramic milling tools exhibit more excellent chatter suppression performance according to frequency domain analysis of vibration signals and the observation of workpiece surface vibration marks, in which the S4 ceramic milling tool presents the most significant high-speed milling stability.

Efficient Prediction of Stability Boundaries in Milling Considering the Variation of Tool Features and Workpiece Materials.

Theoretical stability analysis is a significant approach to predicting chatter-free machining parameters. Accurate milling stability predictions highly depend on the dynamic properties of the process system. Therefore, variations in tool and workpiece attributes will require repeated and time-consuming experiments or simulations to update the tool tip dynamics and cutting force coefficients. Considering this problem, this paper proposes a transfer learning framework to efficiently predict the milling stabilities for different tool-workpiece assemblies through reducing the experiments or simulations. First, a source tool is selected to obtain the tool tip frequency response functions (FRFs) under different overhang lengths through impact tests and milling experiments on different workpiece materials conducted to identify the related cutting force coefficients. Then, theoretical milling stability analyses are developed to obtain sufficient source data to pre-train a multi-layer perceptron (MLP) for predicting the limiting axial cutting depth (aplim). For a new tool, the number of overhang lengths and workpiece materials are reduced to design and perform fewer experiments. Then, insufficient stability limits are predicted and further utilized to fine-tune the pre-trained MLP. Finally, a new regression model to predict the aplim values is obtained for target tool-workpiece assemblies. A detailed case study is developed on different tool-workpiece assemblies, and the experimental results validate that the proposed approach requires fewer training samples for obtaining an acceptable prediction accuracy compared with other previously proposed methods.

Prediction of the Posture-Dependent Tool Tip Dynamics in Robotic Milling Based on Multi-Task Gaussian Process Regressions

Chatter vibration is one of the main factors that limit the productivity and quality of the robotic milling process. To predict the robotic milling stability, it is essential to obtain the tool tip frequency response function (FRF). The tool tip dynamics of a robot heavily depend on its postures and used tools. A state-of-art methodology of combining the regression model with the Receptance Coupling Substructure Analysis (RCSA) method is proved to be effective in predicting tool tip FRFs of machine tools for different positions and tools. However, for the milling robot, the cross coupling FRFs have an obvious influence on the dynamic property of the milling robot, thereby greatly affecting the milling stability boundary. It is of great challenge to directly integrate the effect of the cross coupling FRFs into the state-of-art approach to predict the tool tip dynamics. To tackle this challenge, in this paper, we propose an approach to predict the posture-dependent tool tip dynamics for different tools in robotic milling considering the cross coupling FRFs. First, a more comprehensive RCSA procedure is adopted to include the cross coupling FRFs. Then, the impact test is designed to measure the required FRF matrix. By fitting the measured FRF matrix with the multiple-degree-of-freedom (MDOF) model, the number of modal parameters is significantly reduced. Next, the Multi-Task Gaussian Process (MTGP) regression model is employed to mine the physical correlations between different modal parameters. Compared to the ordinary Gaussian Process regression model, the number of required regression models in MTGP is reduced and the prediction performance is improved in terms of accuracy and robustness. Furthermore, the effectiveness of the proposed approach is validated by the impact test and milling experiment on an industrial robot.

Calibration rod selection strategy in RCSA-based method for reliable calculation of milling tool-tip FRFs in rotating conditions

The measurement of milling tool-tip frequency response functions (FRFs) in rotating conditions is challenging in practice. Methods based on the receptance coupling substructure analysis (RCSA) can obtain rotating tool-tip FRFs using normal modal test devices; thus, they have received extensive attention in the research community. The typical RCSA framework first adopts a calibration rod for measuring rotating FRFs. Then, it analytically calculates the desired tool-tip FRFs through the RCSA theory. As the calculation process involves matrix inversion, high-quality FRF data is required. However, experimentally measured FRFs in rotating structures contain severe noise, leading to an unreliable calculation. This paper presents a novel error analysis model to investigate the propagation mechanism of measurement errors in the typical RCSA framework. Results show that measurement errors would cause errors in the length of the coupled substructure while introducing scaling effects. The calibration rod is found to be vital for RCSA calculation reliability. The patterns of the calculation error are opposed when adopting a short or long calibration rod. Then, a calibration rod selection strategy is proposed. The strategy makes full use of the high measurement quality near the resonance in rotating FRFs and achieves the dominant mode frequency matching between the clamped rod and the clamped tool by adjusting the rod length. Simulations validate the error analysis model and the calibration rod selection strategy. Experimental results also show that the optimal selection of the calibration rod could improve the calculation reliability of rotating tool-tip FRFs in the typical RCSA framework.

Physics-informed Bayesian machine learning case study: Integral blade rotors

This paper provides a physics-informed Bayesian machine learning (PIBML) description and case study. The PIBML approach applies three physics-based models to establish the initial beliefs before testing to determine the probability of milling stability (or prior). These include: receptance coupling substructure analysis (RCSA) prediction for the tool tip frequency response functions; finite element software prediction of the mechanistic force model coefficients; and a spindle speed-dependent power law model for process damping. Testing was then performed to identify optimal stable machining conditions using an expected improvement in material removal rate criterion. The prior probability of stability was updated using the test results to determine the posterior probability of stability. The test results were compared to the parameter recommendations provided by the endmill manufacturer. A demonstration integral blade rotor was machined at the optimal stable machining conditions for 304 stainless steel and 6061-T6 aluminum. The disagreement between manufacturer recommendations and milling performance in both materials tested emphasizes the need for broad implementation of PIBML approaches to increase machining productivity and efficiency.

Dynamic force and stability prediction for milling using feed rate scheduling software and time-domain simulation

This paper describes: 1) the use of feed rate scheduling software to predict the radial depth of cut variation for three-axis milling toolpaths and; 2) the use of the radial depth profile in a time-domain simulation to predict dynamic cutting forces. The time-domain simulation, which also includes the tool tip frequency response functions and force model (which relates the cutting force components to the chip geometry) as inputs, enables dynamic force profiles to be predicted and parameter combinations that cause chatter to be identified. A ramp geometry is selected that provides constantly varying radial depth and force predictions are completed at multiple axial depths for comparison to measured forces. Both stable and unstable (chatter) milling conditions were observed with good agreement between time-domain simulation and measurement results. The value of combining the feed rate scheduling software and time-domain simulation is demonstrated.

A machining digital twin for hybrid manufacturing

Hybrid manufacturing consisting of metal additively manufactured preforms and computer numerical control (CNC) machining has been established to be an effective method for high material use rates. However, hybrid manufacturing introduces unique challenges. Near-net shape designs are typically selected, which result in a smaller margin for part placement within the stock and stringent requirements for work coordinate system identification. Additionally, less stock material reduces the preform stiffness, which limits the material removal rates during machining. This paper demonstrates a digital twin for CNC machining of a wire arc additively manufactured preform that implements: 1) structured light scanning for stock model identification and tool path generation; 2) a fused filament fabrication apparatus to attach temporary fiducials and scan targets to the preform that enable coordinate system definition for both the CAM and CNC machine; 3) preform and tool tip frequency response function measurements to enable stable milling parameter selection; and 4) post-manufacturing measurements of geometry, surface finish, and structural dynamics to confirm designer intent. These efforts define key components of the machining digital twin for hybrid manufacturing.

Chatter stability analysis in Micro-milling with aerostatic spindle considering speed effect

The regenerative chatter is one of the fundamental obstacles in high-speed micro-milling process, which causes tool wear and poor surface quality. In order to predict the chatter stability of micro-milling with aerostatic spindle more accurately, the effects of rotating speed on the dynamic stiffness and damping coefficients of aerostatic journal bearing are investigated firstly. The frequency response functions (FRFs) of aerostatic spindle under different rotating speeds are calculated considering the speed effect of aerostatic bearing, centrifugal force and gyroscopic moment. A method for calculating the stability lobe diagram (SLD) of micro-milling considering the speed effect is proposed in this paper. The speed-dependent SLD is simulated based on tool tip FRFs under different rotating speeds and is verified by micro-milling of aluminum 7075. In addition, the effects of supply air pressure and air film thickness on the SLD are investigated comprehensively. The results provide guidance to improve the chatter stability and cutting efficiency in micro-milling with aerostatic spindle.

Receptance coupling substructure analysis and chatter frequency-informed machine learning for milling stability

This paper describes a milling stability identification approach that simultaneously considers: physics-based models for the tool tip frequency response functions and stability predictions; the binary result from a milling test (automatically labeled as stable or unstable based on frequency content); chatter frequency when an unstable result is obtained; and user risk tolerance. The algorithm applies probabilistic Bayesian machine learning with adaptive, parallelized Markov Chain Monte Carlo sampling to update the probability of stability with each milling test. The result is a robust solution for rapid convergence to optimized milling parameters for maximum metal removal rate using all available information.

Time-domain simulation and testing for dynamic force and stability prediction in milling: Collaboration with feed rate scheduling software

This paper describes: 1) the use of feed rate scheduling software to predict the radial depth of cut variation for three-axis milling toolpaths and; 2) the use of this radial depth profile in a time-domain simulation to predict dynamic cutting forces. The time-domain simulation, which also includes the tool tip frequency response functions and force model (which relates the cutting force components to the chip geometry) as inputs, enables dynamic force profiles to be predicted and parameter combinations that cause chatter to be identified. A ramp geometry is selected that provides constantly varying radial depth and force predictions are completed at multiple axial depths for comparison to measured forces.

Semi-supervised graph convolutional network to predict position- and speed-dependent tool tip dynamics with limited labeled data

The tool tip frequency response function (FRF), as one of the essential inputs to calculate the stability lobe diagram (SLD), varies with the position and speed of changes in the moving components within the machine tool work volume. How to predict the position- and speed-dependent tool tip dynamics accurately has become one of the most challenging tasks in obtaining SLDs while avoiding chatter. However, traditional finite element analyses or kinematic modelling-based methods are costly and time consuming. Data-driven machine learning methods require large amounts of labeled data to train a model, but labeled industrial data are limited and extremely valuable in real manufacturing industries.To minimize experimentation, an improved semi-supervised graph convolutional network (GCN) is proposed to predict position- and speed- dependent tool tip dynamics with limited labeled data. First, the inverse stability solution is applied to identify dominant modal parameters under cutting conditions to obtain labeled samples. Subsequently, both the limited labeled samples and large amounts of unlabeled samples are converted into graph data to train a GCN regression model integrated with a multilayer perceptron. To avoid overfitting under limited data conditions, the conventional GCN is extended by stacking a transposed GCN, which is utilized to reconstruct the initial node features. The results demonstrate an improved prediction performance by adding the unsupervised reconstruction error into the loss function. Compared with other machine learning methods, our proposed method has superior performance in predicting tool tip dynamics with only 20% of the labeled samples. Finally, the SLDs were reconstructed with predicted FRFs, and the accuracy of the SLDs was validated through chatter tests.

Multi-Point Substructure Coupling Method to Compensate Multi-Accelerometer Masses in Measuring Rotation-Related Frequency Response Functions

AbstractTool-tip frequency response functions (FRFs) are often required in milling vibration analysis. Receptance coupling substructures analysis (RCSA) affords an efficient analytical way for different tool-tip FRFs prediction with only one modal test. The coupling theory includes both translational and rotational degrees-of-freedom, so rotation-related FRFs are essential to know in the test. The finite-differential technique is generally used to measure these special FRFs due to the avoidance of specialist equipment. The technique uses several translational accelerometers spatially placed close to each other to approximate the rotational vibration. However, the added sensor masses lead to a frequency shift of the test structure, and the phenomenon would aggravate as the sensors increase. The polluted measurement data would subsequently decrease the tool-tip FRFs prediction accuracy. Addressing this problem, this paper introduces a multi-point substructure coupling method to simultaneously compensate the multi-accelerometer masses in a single experimental setup. The proposed method considers the installed accelerometers as multiple point masses and then uses inverse coupling calculation to isolate their effect. The compensation procedure is first effectively validated in simulation and experiment, and then, it is integrated into an RCSA-based application of predicting different tool-tip dynamics. Experimental results show that the compensated FRF data can improve prediction accuracy, especially when predicting tools shorter than the tested tool.

Optimization and Tuning of Passive Tuned Mass Damper Embedded in Milling Tool for Chatter Mitigation

Milling tools with a large length–diameter ratio are widely applied in machining structural features with deep depth. However, their high dynamic flexibility gives rise to chatter vibrations, which results in poor surface finish, reduced productivity, and even tool damage. With a passive tuned mass damper (TMD) embedded inside the arbor, a large length–diameter ratio milling tool with chatter-resistance ability was developed. By modeling the milling tool as a continuous beam, the tool-tip frequency response function (FRF) of the milling tool with TMD was derived using receptance coupling substructure analysis (RCSA), and the gyroscopic effect of the rotating tool was incorporated. The TMD parameters were optimized numerically with the consideration of mounting position based on the maximum cutting stability criterion, followed by the simulation of the effectiveness of the optimized and detuned TMD. With the tool-tip FRF obtained, the chatter stability of the milling process was predicted. Tap tests showed that the TMD was able to increase the minimum real part of the FRF by 79.3%. The stability lobe diagram (SLD) was predicted, and the minimum critical depth of cut in milling operations was enhanced from 0.10 to 0.46 mm.

Efficient joint identification and fluted segment modelling of shrink-fit tool assemblies by updating extended tool models

In milling, the dynamic behavior of the tool center point is crucial for estimating surface quality of the workpiece as well as the process stability behavior. Experimental-analytical receptance coupling can be used for predicting the tool tip dynamics but requires accurate analytical modelling of the holder-tool assembly. This includes the reliable identification of the holder-tool joint properties as well as the correct modelling of the fluted segment of end mills. However, the modelling effort associated with accurately representing the dynamic behavior of the fluted segment is significant. In addition, the joint identification requires a reference tool tip frequency response function of the tool assembly clamped in the machine spindle. This is inefficient and can also lead to incorrect estimation of joint properties. This paper provides an efficient method for joint identification and fluted section modelling using an offline, free–free excitation approach. The objective of this paper is to enable a direct comparison of the dynamic behavior of the freely constrained analytical tool assembly model with that of the real freely constrained tool assembly. The comparison of displacement to force frequency response at certain points on the tool assembly allows for the identification of tool model parameters such as the joint properties and effective diameter of the fluted segment. The comparability is realized by extending the analytical holder-tool beam model to include the receptance model of the standard spindle-holder interface. In this study, as an example, a thermal shrink-fit holder-tool beam model is extended to include an HSK-A63 interface. Subsequently, frequency response functions at two points on the real freely constrained tool assembly are measured in order to identify the joint stiffness and effective diameter of the fluted segment using the corresponding proposed formulations. The updated holder-tool model is then coupled with a 4-axis milling machine and validated. Despite the reduced modelling effort, a good prediction accuracy could be achieved for different holder-tool combinations.

A Robust RCSA-Based Method for the In Situ Measurement of Rotating Tool-Tip Frequency Response Functions

AbstractMeasuring rotating tool-tip frequency response functions (FRFs) is difficult because of the fluted tip geometry. The methods based on receptance coupling substructure analysis (RCSA) can obtain rotating tool-tip FRFs with a few tests. Existing RCSA-based methods require at least one smooth rod for measurement and then mathematically calculate the desired rotating tool-tip FRFs. However, involving the inverse of the experimentally obtained FRFs matrix, these methods are susceptible to the measurement noise in the rotating structure. In addition, the inconsistency between the holder–tool and holder–rod connections is another uncertainty which impacts accuracy. This paper presents a robust RCSA-based method to obtain rotating tool-tip FRFs. It is found that tool-tip FRFs can be calculated from another point FRFs on the same assembly. Then, one point on the smooth cylindrical shank of the tool is selected for measurement. The measured FRFs, along with those from the theoretical tool model, calculate the rotating tool-tip FRFs. Compared with the previous methods, the proposed one does not require inverting the measured FRFs matrix, inherently avoiding amplification of measurement noise. Since the tool replacement is no longer required, in situ measurement is achieved to ensure the same holder–tool connection throughout the procedure. The proposed method is first validated in a numerical case and then verified experimentally by a commercial hammer and laser vibrometer. Both results show that the method is insensitive to the measurement noise and can obtain rotating tool-tip FRFs with considerable accuracy.

Optimal design of spindle-tool system for improving the dynamic stability in end-milling process

This paper presents an optimum design approach of a spindle-tool system to improvise the dynamic stability of end-milling. Initially, the tool-tip frequency response function is obtained by analyzing the spindle-tool assembly with the finite element model. The chatter-free regions are maximized using an optimization methodology by considering the spindle and tool parameters as design variables. A simulated experimental dynamic data consisting of the average stable depth of cut is obtained for different combinations of design variables by the method of design of experiments (DOE) and analysis of variance technique is applied to find the influence of design parameters on the outputs. Based on the obtained results, the data is generalized with the help of a neural network model that works as an estimator of the average stable depths for the optimization module. The average stable depth of cut over a range of operating speeds is maximized by selecting optimal tool and spindle parameters.

Rapid prediction of posture-dependent FRF of the tool tip in robotic milling

Abstract During the robotic milling process, vibration is one of the main factors that affect the machining accuracy and surface quality due to the low stiffness of the robot structure. The robotic milling stability is a function of the frequency response function (FRF) at the tool tip, which is posture-dependent within the workspace. This paper introduces an approach for rapidly predicting the tool tip FRF for industrial robotic milling at any posture. In this method, the models of the one degree-of-freedom (DOF) robot and two DOF robot are extended to a six DOF industrial robot to calculate the FRF at the holder tip based on the FRF acquisition tests at the arranged postures and a standardization process. Considering the coupling effects between the holder and the tool, the tool tip FRF at any posture of the milling robot is calculated using the receptance coupling substructure analysis (RCSA) method. Accordingly, the proposed method is applied to an industrial robot, and the feasibility of this method for predicting the posture-dependent FRF at high frequency in the workspace is validated though the impact tests. Moreover, the stability lobe diagram is calculated and the chatter tests are performed to validate its accuracy. At last, the robot structural modes are observed at the low-frequency dominant modes, whose frequencies are around 10 to 20 Hz.