Receptance Coupling Research Articles

An efficient experimental approach to identify tool point FRF by improved receptance coupling technique

Chatter can be predicted and avoided through the chatter stability lobe, which is computed by dynamic response (frequency response function) at the tool point. Modal impact testing is time-consuming and inefficient, which is not suitable for tool point dynamic prediction. On the contrary, receptance coupling method can efficiently identify the tool point dynamic by combining the full (translational and rotational) receptance matrix of spindle-holder assembly with numerical or analytical model of any attached free-free tool. Generally, it is difficult to directly obtain the rotational receptances of spindle-holder assembly. This paper proposes an efficient experimental method which deduces the rotational receptances from translational receptances on a single experimental setup by improved receptance coupling technique. One main advantage of this method is to further reduce required impact tests and increase efficiency of tool point dynamic prediction. Besides, a wider application of the proposed method can be achieved. The presented approach is experimentally verified and compared with the state-of-the-art methods.

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

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

Compensation of frequency response function measurements by inverse RCSA

This paper describes an analytical approach for compensating accelerometer-based (contact-type) modal testing results for both mass loading and cable energy dissipation (damping). The inverse Receptance Coupling Substructure Analysis (RCSA) approach is implemented, where a lumped parameter model of the accelerometer-cable is decoupled from the measured receptance (or frequency response function) to isolate the structure's receptance. Experimental results are presented for a 12.7mm diameter cantilever rod, a 6.35mm diameter cantilever rod, and clamped-clamped-clamped-free boundary condition thin ribs.

Improving FEM model of low immersion milling process using multi-objective optimization of tool elastic support dynamic properties

The accurate prediction of tool displacement on elastic support is always considered a crucial problem in metal cutting process simulation. Static and dynamic properties of a machine tool structure which are the function of boundary conditions of a tool-tool holder, modal parameters of an end mill, and interface of cutting edge with a workpiece can affect the displacement of the end mill. In this paper, the receptance coupling substructure analysis (RCSA) and multi-objective optimization algorithm, NSGA-II, are combined to determine the elastic support properties. The investigated effective parameters include the tool-tool holder contact length, clamping torque, and the tool length ratio to diameter. In order to evaluate the accuracy of results and simulate the low immersion end milling process, a novel FEM model is created in which the constant stiffness and damping have a linear relationship along the elastic support. The frequency response function-obtained FEM models have good accordance with experimental data. Using this model and linking the FEM model with MATLAB software, cutting forces and tool displacements are simulated. The accuracy of the suggested method is evaluated by simulating two case studies based on different cutting conditions. Comparison between simulation and experimental results indicates that the suggested model can precisely predict the cutting force and tool displacement. The proposed model can be used to simulate the milling processes for various tool boundary conditions in forced and free vibration states, and the consumed time for simulation of process is significantly reduced.

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

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

RCSA-Based Method for Tool Frequency Response Function Identification Under Operational Conditions Without Using Noncontact Sensor

The stability lobe diagrams predicted using the tool frequency response function (FRF) at the idle state usually have discrepancies compared with the actual stability cutting boundary. These discrepancies can be attributed to the effect of spindle rotating on the tool FRFs which are difficult to measure at the rotating state. This paper proposes a new tool FRF identification method without using noncontact sensor for the rotating state of the spindle. In this method, the FRFs with impact applied on smooth rotating tool and vibration response tested on spindle head are measured for two tools of different lengths clamped in spindle–holder assembly. Based on those FRFs, an inverse receptance coupling substructure analysis (RCSA) algorithm is developed to identify the FRFs of spindle–holder–partial tool assembly. A finite-element modeling (FEM) simulation is performed to verify the validity of inverse RCSA algorithm. The tool point FRFs at the spindle rotating state are obtained by coupling the FRFs of the spindle–holder–partial tool and the other partial tool. The effects of spindle rotational speed on tool point FRFs are investigated. The cutting experiment demonstrates that this method can accurately identify the tool point FRFs and predict cutting stability region under spindle rotating state.

Two-points-based receptance coupling method for tool-tip dynamics prediction

ABSTRACTTool-tip frequency response function (FRF) is essential to predict chatter vibration in milling. This key input can be acquired by experimental tests, but a new test has to be performed for every tool clamped on the machine. To avoid such time-consuming procedures, receptance coupling methods have been developed, allowing coupling of the experimental dynamic response of the machine to the numerical model of the tool. Such techniques require joint rotation response, which is hard to experimentally identify. Inversion of receptance coupling technique is usually performed on additional experimental measurements to overcome this issue. This procedure amplifies measurement uncertainties, reducing accuracy of the coupling approach. In this article, a novel receptance coupling technique is presented. Machine and toolkit are connected through two distinct points, eliminating the experimental phase and computation of rotational degrees of freedom (DOFs). Only translation responses are required, acquired by a single test setup. Proposed technique was experimentally validated on different case studies.

Component Mode Synthesis Approach for Micro End Mill Dynamics Considering Machine Tool Compliance

Chatter in machining can be avoided by machining at stable process parameters obtained from the stability lobe diagram. The accuracy of the stability lobe diagram depends on the accurate determination of micro-endmill dynamics. It is not trivial to experimentally determine the tool tip dynamics of a micro-endmill due to relatively small diameters (10μm to 500μm). There are different approaches to estimate the micro-endmill dynamics, however, one of the most widely used techniques is the receptance coupling method. It combines the frequency response functions for the two substructures (machine tool with a portion of shank and the micro-endmill) to determine the tool-tip dynamics. There are certain issues with the receptance coupling which uses only two locations for determining the FRF one at the coupling and other at tip unlike the component mode synthesis which allows use of mode shapes at multiple points in the substructures. Another limitation for receptance coupling method is that the FRF for both substructures must be sampled at same frequency for coupling but the first non-rigid modal frequency for free-free substructure of micro-endmill can exceed 50kHz which would require a high bandwidth sensor with a sampling frequency in excess of 100kHz. Consequently, the component mode synthesis approach has been used to couple the substructures. The mode synthesis approach adopted in the present work contains the position dependent modes along the length of substructures. In order to ensure that the component mode synthesis yields accurate results, a test case of a micro-endmill as a fixed cantilever beam has been analyzed. Note that the actual micro-end mill dynamics is affected by the machine tool compliance which needs to be accounted for. Hence, a component mode synthesis of the two substructures, machine-tool/shank and the micro-endmill is carried out. The mode shapes of machine-tool shank substructure are determined experimentally whereas the micro-endmill mode shapes are determined via finite element method (FEM). The predicted micro-endmill dynamics with machine tool compliance has been experimentally validated.

Rapid dynamics prediction of tool point for bi-rotary head five-axis machine tool

Receptance Coupling Substructure Analysis (RCSA), an effective approach to rapidly predict the tool point frequency response function (FRF), generally requires the response of spindle-machine assembly by experiments. This method is feasible for three-axis machine tool because the spindle and its posture are normally unchangeable. But in terms of five-axis milling, the spindle-machine assembly changes continuously. The purpose of this study is to propose new techniques to solve the constantly-changing assembly response in order that RCSA can be used for bi-rotary head five-axis machine tools. Based on receptance matrix determination in coupling direction and single degree of freedom coupling simplification, the swivel model for holder tip receptances is established for swivel motion. According to the concept of oriented frequency response function, the rotational model is derived to calculate the holder tip receptances with rotary motion. By combining the swivel model and the rotational model, the holder tip receptance of arbitrary posture can be calculated by three orthogonal postures. A five-axis machine tool with bi-rotary head is used to conduct FRF tests on different postures. Experimental results show that the models proposed can accurately predict tool point frequency response of any posture and large difference in FRFs among those postures of bi-rotary head is detected.

Milling stability prediction for flexible workpiece using dynamics of coupled machining system

An efficient machining is limited by the chatter of machining system including spindle and support, which would cause poor surface quality. This paper proposed an improved stability prediction method based on the dynamics of machine tool. Dynamics of the support are considered into the stability prediction of machining process. The spindle was modeled by the receptance coupling substructure analysis method to predict the dynamics at the tool point. The mathematical model of the closed manufacturing system (machine tool, spindle, holder, and tool) was given, as well as the details of joint contacts. The model was used to obtain the system characteristics, and the FRFs of the tool point were obtained from the model in frequency domain. Moreover, the stability limitation for machining system were developed to create the stability lobe diagram with the FRFs of both the spindle and support. Experimental results showed that the depths of improved stability lobes were smaller than those of the original ones, and the improved lobes were more accurate for the stability predictions. The machined surface quality showed that the stable machining system was beneficial to produce good surface. This improved method is helpful for the stability calculation and machining parameter selection especially when milling a thin-walled workpiece or a weak clamping fixture.

Identification of joint dynamics in lap joints

The dynamics of machine tools are greatly dependent on joints, since they add flexibility and damping to structures. In this study, the linear stiffness and damping of a joint in the transverse direction are obtained using two different methods: the inverse receptance coupling method and the new analytical joint identification (AJI) approach. The former approach finds the joint frequency response function by determining the difference between the response of the assembled structure and those of the substructures. However, the only required data for the AJI method are modal parameters of the assembled structure, which can be measured using experimental modal analysis. The accuracy of these methods is first investigated using numerical simulations. Experiments are then conducted on a structure consisting of two beams attached to one another in a lap joint. The proposed methods are utilized to experimentally extract the joint parameters in the transverse direction. Finally, the effects of varying the joint conditions, including surface roughness and the addition of interfacial materials, are investigated.

Receptance coupling of multi-subsystem connected via a wedge mechanism with application in the position-dependent dynamics of ballscrew drives

An accurate model of the feed drive׳s high-order position-dependent dynamics is crucial for the analysis and controller design of a high-performance machine tool. In this paper, a new dynamic substructuring condition-multi-subsystem connected via a wedge mechanism is introduced, which is originated from the ballscrew-nut dynamic coupling interface. Receptance coupling equations were derived for the condition, and a dynamic modeling approach is developed for the ballscrew drive system based on the equations. The developed model accounts for the ballscrew׳s rotational and axial flexibilities and the dynamic couplings among these flexibilities and that of the sliding component. The model explicitly describes the dynamics variation with respect to the table position, and is particularly suitable for sensitivity based analysis. Based on the model, the position-dependent dynamics of an example ballscrew drive was analyzed, by using the frequencies distribution, the modal shape, and especially the sensitivity of the frequency response functions with respect to the table position.

Chatter stability of micro end milling by considering process nonlinearities and process damping

The micro end milling uses the miniature tools to fabricate complexity microstructures at high rotational speeds. The regenerative chatter, which causes tool wear and poor machining quality, is one of the challenges needed to be solved in the micro end milling process. In order to predict the chatter stability of micro end milling, this paper proposes a cutting forces model taking into account the process nonlinearities caused by tool run-out, trajectory of tool tip and intermittency of chip formation, and the process damping effect in the ploughing-dominant and shearing-dominant regimes. Since the elasto-plastic deformation of micro end milling leads to large process damping which will affect the process stability, the process damping is also included in the cutting forces model. The micro end milling process is modeled as a two degrees of freedom system with the dynamic parameters of tool-machine system obtained by the receptance coupling method. According to the calculated cutting forces, the time-domain simulation method is extended to predict the chatter stability lobes diagrams. Finally, the micro end milling experiments of cutting forces and machined surface quality have been investigated to validate the accuracy of the proposed model.

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.

Prediction of coupled torsional–axial vibrations of drilling tool with clamping boundary conditions

Coupled torsional–axial vibrations of the drilling tool play a significant role in the machining dynamics of the drilling process. In this paper, the torsional–axial vibrations of the drilling tool due to the warping deformation of the pretwisted flute are modeled. An enhanced receptance coupling model is developed to predict the coupled torsional–axial vibrations of the drilling tool considering the dynamics of fixture and clamping conditions. Rigid and flexible receptance coupling methods are used, with the simulation results verified through modal experiments. The proposed model is able to provide optimum drilling tool configurations to avoid undesired tool vibrations and improve hole quality.

A hybrid method for dynamic stiffness identification of bearing joint of high speed spindles

Bearing joint dynamic parameter identification is crucial in modeling the high speed spindles for machining centers used to predict the stability and natural frequencies of high speed spindles. In this paper, a hybrid method is proposed to identify the dynamic stiffness of bearing joint for the high speed spindles. The hybrid method refers to the analytical approach and experimental method. The support stiffness of spindle shaft can be obtained by adopting receptance coupling substructure analysis method, which consists of series connected bearing and joint stiffness. The bearing stiffness is calculated based on the Hertz contact theory. According to the proposed series stiffness equation, the stiffness of bearing joint can be separated from the composite stiffness. Then, one can obtain the bearing joint stiffness fitting formulas and its variation law under different preload. An experimental set-up with variable preload spindle is developed and the experiment is provided for the validation of presented bearing joint stiffness identification method. The results show that the bearing joint significantly cuts down the support stiffness of the spindles, which can seriously affects the dynamic characteristic of the high speed spindles.

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.

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.

An improved method for tool point dynamics analysis using a bi-distributed joint interface model

The existing tool point dynamics analysis methods may lead to inaccurate predictions of frequency response function (FRF) in some cases since they ignored the collet geometry. This paper presents an improved method to better predict the contributions of collet geometry to FRF of cutting tool by introducing the effect of collet. The spindle–holder–collet–tool assembly is modeled as two distributed joint interfaces, i.e., collet–holder and collet–tool joint interfaces, rather than the existing single holder–tool joint interface without the effect of collet. Dynamics of the tool and the collet are analyzed using Euler–Bernoulli beam theory, and the tool–collet and holder–collet joint interfaces are separately treated as two distributed zero-thickness damped-elastic layers. The contact stiffness and damping properties of both joint interfaces are identified by minimizing the discrepancy between the measured and predicted tool point FRFs. The tool–collet assembly is supposed to rest on the resilient support provided by the spindle–holder assembly, whose dynamical property is analytically calculated by the receptance coupling substructure analysis (RCSA) method. Wider prediction capacity of the proposed method has been experimentally verified via the comparison with traditional method.

Identification of joint dynamics in 3D structures through the inverse receptance coupling method

Complex structures, such as machine tool centers, are comprised of several components attached through different types of joint. The joints introduce much flexibility and damping to the entire structure, which cannot be ignored in the design stage. Ignoring joint effects and modeling the joints as rigid connections result in deviations between the physical structure dynamics and model dynamics. In order to improve the accuracy of model predictions, joint dynamic properties need to be identified and incorporated into a virtual model. Many studies have investigated joint identification in two-dimensional structures. However, different degrees of freedom (DOFs), including rotational and translational, are coupled in the motions of actual physical structures. An accurate joint model should include translational and rotational frequency response functions (FRFs) and consider the joint’s inertial properties. In this study, the inverse receptance coupling method is utilized to obtain a joint׳s FRFs by using the FRFs of the assembled structure and substructures. Unlike previous studies, which considered only 2 DOFs for the joint element, this study proposes a linear joint model with 6 DOFs at each node to include the effects of translational and rotational FRFs. The proposed model also considers the joint׳s inertial properties and cross FRF terms between translational and rotational DOFs, which have been previously neglected. The joint׳s FRFs are obtained using only translational FRFs of the assembled structure, which makes this method practical in real applications, as there are many limitations regarding the measurement of rotational FRFs. Finite element simulations along with experimental tests are conducted to investigate the applicability of the proposed method for actual physical structures.