Receptance Coupling Substructure Analysis Research Articles

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.

Investigation of a cutting state-independent method for identifying in-process frequency response functions of the micro milling system

Conveniently obtaining the in-process frequency response functions (FRFs) of micro milling tool is a very difficult task due to the small diameter. This article presents a method to identify the in-process FRFs of micro milling tool based on actual cutting tests, which can be at either stable or chatter cutting state. According to mode superposition principle, the in-process FRFs are predicted by integrating the mode shape with the pole, which includes damping ratio and natural frequency. The in-process mode shape of tool is modeled as being consistent with that corresponding to static state, and thus, it is calculated from the tool’s static state by combining receptance coupling substructure analysis (RCSA) with Timoshenko beam theory. The poles of in-process FRFs are acquired by modal analysis of the response signals from actual micro milling tests. To do this, cutting forces are used as excitation signals, and the velocities of tool are selected as response signals and they are measured from actual micro milling tests. With the aid of editing cepstrum and hampel outlier processing methods, a filtering method is established to remove the harmonic and useless chatter components involved in the response signals. As a result, the finally obtained FRFs are not influenced by the noises in the measured response signals, and the effectiveness of this method is verified by a series of modal tests and micro milling tests.

Receptance coupling substructure analysis based FRF modeling for multi-segment shell with nonlinear joint interface

Multi-segment shell typical of underwater vehicles is currently important underwater equipment. Stealth performance is a key indicator to improve the working capacity of underwater vehicles. Low-noise design is an important means to improve stealthy performance. Accurate and effective identification of its structure Frequency Response Function (FRF) is the premise of low-noise design. However, the multi-section shell joint interface has many connection points, complex transmission path and typical nonlinear characteristics, which challenges the acquisition of its structural FRF. The Receptance Coupling Substructure Analysis (RCSA) is used to segment the multi-stage shell, which can realize the integration of finite element method and experimental method, and provide an effective way to obtain the FRF of multi-segment shell. At the same time, the multi-segment shell is a typical thin-wall structure, and its actual buckling process under impact is a nonlinear (large deformation) process. Therefore, the nonlinear joint interface is constructed based on linear connection, and the RCSA for nonlinear joint interface is studied. On the basis of accurately obtaining the FRF, it is of theoretical and application significance to study the low noise design of shell.

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.

Modeling and prediction for frequency response functions of parameter-varying mechanical systems based on generalized receptance coupling substructure analysis

Most machining systems such as machine tools and robots are parameter-varying mechanical systems, which show different dynamic characteristics under different parameters. Generally, a large number of modal tests are required for parameter-varying mechanical systems to obtain frequency response functions (FRFs) under different system parameters, which reduces efficiency. Receptance coupling substructure analysis (RCSA) provides ideas for solving such problems. In this study, the generalized RCSA (GRCSA) was proposed. The coupling method of two substructures at arbitrary pairs of nodes was derived, and a more general coupling method of multiple substructures at arbitrary pairs of nodes was further elaborated, which provides a complete set of theories and methods for the modeling and prediction of FRF of general parameter-varying mechanical systems. Based on the derivation process and results of the GRCSA, the parameter-varying mechanical systems are classified into three basic categories: variable interface systems, variable spatial attitude systems, and variable substructure systems. Typical cases of three basic categories in engineering practice were selected for studying, and the prediction models for FRFs of various parameter-varying mechanical systems were derived in detail. The calculation methods for FRF matrices of various substructures and the calibration methods for interface parameters are given. The validity of the prediction models was verified by experiments and simulations. The relative errors of the established prediction models under most system variables are less than 1% for the natural frequency, and the maximum relative error of the prediction models is 3.775% for the natural frequency. Finally, based on the prediction models, the FRFs under different system variables were predicted, and the variation laws of the natural frequencies with the system variables were analyzed. The modeling processes based on the GRCSA for the FRFs of typical parameter-varying mechanical systems are general, and can provide references and ideas for the study of frequency response characteristics of other complex parameter-varying mechanical systems.

Simulation tool for chatter prediction of varying tool–machine configurations based on dynamic substructuring

Cutting tools of different type, shape and size are used in milling processes. Every individual tool changes the dynamic behavior of the system and results in varying occurrences of chatter vibrations. This paper presents a simulation tool using a frequency based substructuring method for predicting the process stability without separate measurements of the tool-machine configuration. In particular, frequency response functions of any combined tool-machine configuration is synthesized by the receptance coupling substructure analysis. It enables the calculation of critical machining parameters and maximizing material removal rates by avoiding unstable cutting conditions. Verification is done via finite element analysis of exemplary tool and machine structures.

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.

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.

Improvement of boring operations by means of mode coupling effect

Boring bars are inherently slender tools which are prone to show chatter problems due to their low dynamic stiffness and damping, being this problem their main limitation in productivity. The onset of chatter is mainly related to the dynamic stiffness of the bending mode of the boring bar when the length L to diameter D ratio is higher than 4. Tuned mass dampers (TMD) are effective technical solutions to increase the dynamic stiffness of large ratio boring bars. However, there are many applications where 4–6 L / D ratio tools are required, and the avoidance of chatter without the application of TMDs is interesting due to the high cost of damped tools. This work proposes the use of mode coupling effect to increase the damping and stabilise the machining process avoiding the use of any special device. This effect occurs when the frequency of one of the machine’s modes is similar to the frequency of the dominant mode of the boring bar. As a result, the shape of the critical mode of the boring bar is mixed with the mode originated in the machine, and the damping and stability will be higher than the one that is not subjected to any dynamic coupling. The main contribution of this work is the application of this concept to increase stability in boring operations. This objective has been achieved by optimising the tool length and material by means of a dynamic model based on Receptance Coupling Substructure Analysis (RCSA). The model combines an analytical model of the elastic body of the boring bar with the experimental characterisation of the effect of the rest of the machine. This way, the shape and materials of the boring bar can be optimised to create an increase of damping. The optimisation procedure has been experimentally validated resulting in an increase of cutting stability and demonstrating that not always a shorter bar supposes a higher stability.

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.

Prediction of the dynamic stiffness of boring bars

The productivity of boring operations is limited by chatter vibrations, as an effect of the low dynamic stiffness and damping of these cantilevered structures. The origin of the beforementioned self-excited vibration is mainly related to the dynamic stiffness of the boring bar’s bending mode, which is influenced by the stiffness and damping of the machine tool interface. In this paper a dynamic model is presented, which uses Timoshenko beam theory for the boring bar itself, while the effect of the clamping is experimentally determined applying Receptance Coupling Substructure Analysis (RCSA). The important effect of the boring head at the tool tip is considered on the coupling as well. This way, once the machine interface is characterized, the Frequency Response Functions (FRF) of different boring bars can be predicted.

Estimation of the Frequency Response Function of the Rotational Degree of Freedom

One of the factors that influence the dynamic characteristics of machining systems is the cutting tool. Cutting tools are very diverse, and receptance coupling substructure analysis (RCSA) is essential for analyzing the dynamic characteristics of each tool. For RCSA, a full receptance matrix of the equipment and tools is essential. In this study, rotational degree-of-freedom receptance was estimated and analyzed using translational receptance. Displacement/moment receptance was analyzed according to the distance of the response point using the first-and second-order finite difference methods. The rotation/moment receptance was estimated according to the distance of the response point. Rotation/moment receptance was analyzed using Schmitz’s method and compensation strategies. The limitations of these strategies were analyzed, and the rotation/moment receptance for the beam under free-free boundary conditions was predicted using the second compensation strategy.

Identifying the transient milling force coefficient of a slender end-milling cutter with vibrations

Milling is a complex process during the coupling effect for multiple physical fields, especially for slender end-milling cutters. Because of the weak rigidity of its process system, it is easily affected by the physical behavior such as the milling force. In addition, it produces large vibrations and deformations, which affects the machining quality. To accurately predict the milling force of a slender end-milling cutter, a method to identify the milling force coefficients while considering vibrations is proposed. When considering the small diameter of the milling cutter edge, it is difficult to install sensors to measure the vibration. By combining the measured frequency response function of the cutter handle end and the cutter’s Timoshenko beam finite element model, the interface dynamics parameters between the cutter and the cutter handle are identified. This is based on the receptance coupling substructure analysis, and the cutter edge’s frequency response function is established. When considering the measured milling force data and the state equation of the cutter edge vibration, the real-time vibration of the cutter edge during the milling process is predicted. In addition, the undeformed cutting thickness during the superposition of the cutter edge vibration is obtained. The milling force coefficients are identified based on the undeformed cutting thickness of the coupled vibration, and the influence of the process parameters on the variation of the milling force coefficient is examined. The prediction accuracy and the average milling force coefficient without the vibrations are compared to verify the accuracy.

Mitigation of chatter in thin-wall milling by using double-side support device

This article develops a new method to mitigate chatter vibrations in the thin-wall milling of the structures with half-opened side walls through designing a supplementary device, which can provide double-side support to the weakly rigid positions between cutter and workpiece. It aims to improve the stiffness and damping responses of the side walls without the need to consider the limitation of the workpiece’s geometrical configuration. That is, it is suitable for both the flat and the curved shapes. The typical structural characteristic of the device lies in that as the cutting continues, the supporting positions can be easily adjusted up and down along the axial direction to meet the instantaneous chatter mitigation requirement. Dynamic models of both the curved thin-wall milling process and the workpiece with the supplementary support device are derived by integrating the milling mechanics with the receptance coupling substructure analysis. The in-process modal parameters of the workpiece with the support device, i.e., natural frequency and modal shape, are calculated by comprehensively considering the removal of material and the influence of the supporting position change. Finally, a method that combines the derived models with the dynamic response of the spindle-tool system is used to predict the stability lobe diagrams (SLDs), with which chatter vibrations can be well avoided by reasonably selecting the cutting parameters. A series of thin-wall milling experiments are carried out on typical curved plates to validate the effectiveness of the designed support device together with the proposed methods for mitigating chatter vibrations.

Substructure analysis of vibration-assisted drilling systems

Designing vibration-assisted drilling (VAD) toolholders requires accurately modeling the dynamics of the mechanical structure and its electromechanical coupling with the piezoelectric actuator. The overall dynamics of the VAD toolholder depends on the dynamics of its individual components (e.g., concentrator, piezoelectric disk, drill bit) and the interactions between them. Modelling by substructure analysis therefore provides an efficient framework for studying the effect of each component on the overall dynamics of the VAD system. Nonetheless, the existing substructure analysis methods are only applicable to holders with basic concentrator geometry, which limits their application in designing high-performance holders. In this paper, Receptance Coupling Substructure Analysis (RCSA) is used to combine the dynamic models of the toolholder’s components to determine its vibration response to the electrical excitation of the piezoelectric actuator. This method allows for combining the 3D finite element models of the concentrator with the simplified and analytical models of the rest of the VAD components, enabling the inclusion of complex concentrator designs in modeling without imposing a large computational load. Furthermore, because this method couples the mechanical model of the structure with the electrical model of the piezo-actuator’s impedance, it can be used as a design tool to modify the toolholder’s natural frequencies by tuning the electrical impedance of its piezoelectric components. This possibility effectively converts the piezoelectric components to mechanical members with adjustable structural dynamics, while they also actuate vibrations. Both axial and axial-torsional VAD toolholders are studied in this work, and the accuracy of the presented modelling approach is verified experimentally.

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.

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.

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.

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.