Receptance Coupling Research Articles

Modular Modeling of a Half-Vehicle System Using Generalized Receptance Coupling and Frequency-Based Substructuring (GRCFBS)

This paper presents an advanced modular modeling approach for vertical vibration analysis of dynamic systems using the Generalized Receptance Coupling and Frequency-Based Substructuring (GRCFBS) method. The focus is on a four-DoF half-vehicle model comprising three key subsystems: front suspension, rear suspension, and the vehicle’s trimmed body. The proposed technique is designed to predict dynamic responses in reconfigurable systems across various applications, including automotive, robotics, mechanical machinery, and aerospace structures. By coupling the receptance matrices (FRFs) of individual vehicle modules, the overall system receptance matrix is efficiently derived in a disassembled configuration. Two generalized coupling methods, originally developed by Jetmundsen and D.D. Klerk, are employed to determine the complete vehicle’s receptance matrix from its subsystems. Validation is achieved by comparing the results with established methods, such as direct solution and modal analysis, demonstrating high accuracy and reliability for complex dynamic systems. This modular approach allows for the creation of reduced-order models focused on key measurement points without the need for detailed system representation. The method offers significant advantages in early-stage vehicle development, providing critical insights into system vibration behavior.

Digital dynamic modeling and topology optimized design of shell face mills

This paper presents digital modeling of shell face mills in milling cylinder heads. The cutter's structural dynamics and its mode shapes are predicted using a Finite Element system. The geometries of the cutter body and inserts are imported from their Computer Aided Design (CAD) models. The insert edge is discretized into small segments to model its varying normal rake and inclination angles, which affect the cutting mechanics. The cutter is dynamically assembled with the target machine tool spindle using the receptance coupling method. A general dynamic cutting force model, which considers the varying edge geometry and inserts’ run-outs, is developed and used to predict cutting forces and chatter stability diagrams. The proposed model is experimentally verified to demonstrate the feasibility of the systematic application of physics-based digital design and analysis of tools for the mass machining of specific parts. The cutter body shape is optimized to increase the stiffness of the bending mode shape that caused chatter via topology optimization, which led to five-fold increase in the absolute stable depth of cut.

Reduced-Order Modeling for Dynamic System Identification with Lumped and Distributed Parameters via Receptance Coupling Using Frequency-Based Substructuring (FBS)

Paper presents an effective technique for developing reduced-order models to predict the dynamic responses of systems using the receptance coupling and frequency-based substructuring (RCFBS) method. The proposed approach is particularly suited for reconfigurable dynamic systems across various applications, like cars, robots, mechanical machineries, and aerospace structures. The methodology focuses on determining the overall system receptance matrix by coupling the receptance matrices (FRFs) of individual subsystems in a disassembled configuration. Two case studies, one with distributed parameters and the other with lumped parameters, are used to illustrate the application of this approach. The first case involves coupling three substructures with flexible components under fixed–fixed boundary conditions, while the second case examines the coupling of subsystems characterized by multiple masses, springs, and dampers, with various internal and connection degrees of freedom. The accuracy of the proposed method is validated against a numerical finite element analysis (FEA), direct methods, and a modal analysis. The results demonstrate the reliability of RCFBS in predicting dynamic responses for reconfigurable systems, offering an efficient framework for reduced-order modeling by focusing on critical points of interest without the need to account for detailed modeling with numerous degrees of freedom.

Correction: Approach to Receptance Coupling Substructure Analysis based on Full Receptance Estimation of Sub-assembly Using the Modal Fitting Method

Correction: Approach to Receptance Coupling Substructure Analysis based on Full Receptance Estimation of Sub-assembly Using the Modal Fitting Method

Approach to Receptance Coupling Substructure Analysis based on Full Receptance Estimation of Sub-assembly Using the Modal Fitting Method

Approach to Receptance Coupling Substructure Analysis based on Full Receptance Estimation of Sub-assembly Using the Modal Fitting Method

The Structure-Dependent Dynamic Performance of a Twin-Ball-Screw Drive Mechanism via a Receptance Coupling Approach

The drive at the center of gravity (DCG) concept-based twin-ball-screw drive mechanism (TBSDM) is vital in automated factories for its robustness and reliability. However, changes in the worktable mass or position result in changes in the center of gravity (CG), significantly affecting the system’s dynamic properties. In this regard, this paper introduces a novel analytical model using improved receptance coupling to analyze vibrations in four modes. A mathematical framework for the twin TBSDM is generated, and the effect of changing the worktable position–mass on each mode is examined. The applicability of the proposed method is verified based on dynamic experiments that were carried out on a TBSDM of a CNC grinding wheel machine tool. After thoroughly analyzing the experimental and theoretical results, it is revealed that changing the worktable position primarily influences the rotational and axial vibrations of the twin ball screw (TBS). Furthermore, changes in the worktable mass significantly affect the coupling vibration among the TBSs and rotors or bearings. Moreover, in terms of performance, the variances between the theoretical and experimental natural frequencies are consistently below 5%. Thus, the proposed method is promising for the improvement of the modeling and analysis of the TBSDM.

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.

A Generalized and Efficient Control-Oriented Modeling Approach for Vibration-Prone Delta 3D Printers Using Receptance Coupling

Delta 3D printers can significantly increase throughput in additive manufacturing by enabling faster and more precise motion compared to conventional serial-axis 3D printers. Further improvements in motion speed and part quality can be realized through model-based feedforward vibration control, as demonstrated on serial-axis 3D printers. However, delta machines have not benefited from model-based controllers because of the difficulty in accurately modeling their position-dependent, coupled nonlinear dynamics. In this paper, we propose an efficient framework to obtain accurate linear parameter-varying models of delta 3D printers at any position within their workspace from a few frequency response measurements. We decompose the dynamics into two sub-models&#x2013;(1) an experimentally-identified sub-model containing decoupled vibration dynamics; and (2) an analytically-derived sub-model containing coupled dynamics&#x2013;which are combined into one using receptance coupling. We generalize the framework by extending the analytical model of (2) to account for differing mass profiles and dynamic models of the printer&#x2019;s end-effector. Experiments demonstrate reasonably accurate predictions of the position-dependent dynamics of a commercial delta printer, augmented with a direct drive extruder, at various positions in its workspace. <i>Note to Practitioners</i>&#x2014;This work aims to equip high-speed 3D printers, like delta machines, with model-based controllers to complement their speed with high-accuracy. Due to the coupled kinematic chains of the delta, complex control methodologies, some of which require real-time state measurements, are often used to achieve satisfactory control performance. Our modeling approach provides an efficient methodology for obtaining accurate linear models without the need for real-time measurements, thus enabling practitioners to design linear model-based feedforward controllers to achieve the high throughput and accuracy desired in additive manufacturing (AM). The models we develop in this paper are intended for use with feedforward vibration compensation methods, which can be beneficial for both industrial-scale AM machines that have high-powered servo motors and feedback controllers, as well as consumer-grade AM machines which use stepper motors in feedforward control.

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.

Model-based analysis of temperature-dependent dynamics in CFRP spindle unit

The application of CFRP to machine tool structures can potentially improve their dynamic characteristics and energy efficiency owing to its highly specific material properties. The different thermal characteristics of CFRP and steel in spindle units likely induce unique thermal deformation, which affects the bearing dynamics. This research proposes a modeling method of CFRP spindle unit dynamics via generalized multipoint receptance coupling with contact characteristics at the spindle-holder interface. The temperature-dependent mechanical properties are analyzed by parameter identification from the model. The translational stiffness and damping of bearings in the CFRP spindle increase with temperature increase at high rotational speed.

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.

Identification of in-process machine tool dynamics using forced vibrations in milling process

An accurate description of machine tool dynamics is essential for health monitoring, chatter prevention, and improvement of manufacturing accuracy. The standard identification approach of experimental modal analysis at the standstill of the machine does not realize the possible variations in the dynamics due to operational conditions. The in-process identification methods in the literature, on the other hand, are associated with implementation difficulties in industrial environments due to the required complex and specially-designed setup, limited excitation forms, or excessive measurement efforts. This paper proposes an industrial-friendly method to estimate the in-process structural dynamics of machine tools, considering practical demands and implementation limits. Knowing that the operational dependency of the dynamics is associated with the machine and spindle structure, the machine–spindle and holder–tool structures are considered two distinguished subsystems. The cross Frequency Response Function (FRF) of the coupled structure, between the tooltip and spindle flange, is determined by measuring forced vibrations during milling operations. The milling forces are considered as excitation input and the process is designed to be stable and chatter-free so that the simulated forces can be accurately used in the identification. Then, the receptance coupling theory is utilized to develop an optimization algorithm. Given the model of the coupled structure, the evolutionary optimization tunes the modal parameters of the machine–spindle dynamics and joint parameters until the predicted cross FRFs match the experimentally determined FRFs. The direct FRF at the tooltip is predicted using identified in-process machine–spindle dynamics through the receptance coupling method. The identified in-process dynamics are used to predict stability diagrams for different tooling systems and, moreover, to design an augmented Kalman filter to estimate cutting forces. Comparison of estimated SLDs and cutting forces with chatter test results and dynamometer measurements validate the outcomes of the proposed identification method. This paper demonstrates that the system dynamics under operational conditions can be successfully identified without requiring costly setup, specially-designed workpieces or operations, and destructive chatter tests.

Stability enhancement and chatter suppression in continuous radial immersion milling

For continuous radial immersion milling operations, the dominant mode shape becomes difficult to determine when stiffness of the tool and workpiece are comparable, and this can pose a great challenge for ensuring machining processes stability. In this paper, we propose a rapid method to obtain time-varying modal parameters of the workpiece by combining experimental measurements with the receptance coupling method. Firstly, the contact parameters between the workpiece and vise were identified by a so-called dynamic coupling matrix. Then the mode shapes and the time-varying natural frequency of the workpiece were determined using the modal parameters of workpiece. Finally, the stability lobe diagrams (SLDs) were computed using the modal parameters and then were validated by undertaking immersion milling experiments. The experiments showed a more conservative and practical SLD for general workpiece under continuous radial immersion, where the workpiece mode had not always dominated the machining process. Based on the proposed method, we also explored two modifications in form of additional cylinder masses and passive support, to suppress chatter. Both modifications were effective in enhancing the minimum boundary of the conservative SLD, and the modification of passive support worked better. Although the modification of the workpiece could improve the stability boundary, it indirectly affected the dynamics of the milling tool through the interaction area between the workpiece and milling tool.

Initial parameters estimation for Euler-Bernoulli beam fitting of measured frequency response functions

In receptance coupling studies, Euler-Bernoulli beam fitting is a powerful method to derive the rotational receptances from a single frequency response function or displacement-to-force receptance measurement. To automatically complete this method, optimization algorithms are used. For optimization process, initial beam parameters including diameter, length and solid damping factor for each mode in the measured displacement-to-force receptance are required to start iterative search. As such, exploring those initial parameters is sort of trial-and-error work and takes quite some time. To speed up and automatize this work, in the current paper, a new practical, general and easy to implement initial parameters estimation procedure, based on the peak-picking method, is proposed. For verification, a nonlinear least squares fitting-based algorithm is applied on measured spindle-holder subassembly displacement-to-force receptances. The results have shown that the estimated initial beam parameters lead to a quick converge in the optimization process and a successful Euler-Bernoulli beam fitting. • A new practical procedure for initial beam parameters estimation is proposed for EulerBernoulli beam fitting. • The proposed procedure remarkably prevents the time-consuming work to determine initial beam parameters. • Its implementations are performed on measured spindle-holder subassembly displacement-to-force receptances. • The proposed procedure certainly improves success probability of optimization algorithms.

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.