Receptance Coupling Substructure Analysis Research Articles

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.

Chatter avoidance via structural modification of tool-holder geometry

Chatter is a self-excited vibration that can occur during milling operations causing undesirable consequences such as poor surface finish and increased levels of tool wear. One possible solution to this problem is to optimise the dynamics of the machine by tuning parameters such as tool stickout length, e.g. by using receptance coupling substructure analysis. Unfortunately, experimental limitations of the method, such as the requirement to model interface dynamics and the inefficient optimisation process, have hindered its advancement to the industrial sector.This paper looks to resolve these issues by proposing a new structural modification method for chatter avoidance. Firstly, tool-holder diameter is investigated as a potential tuning parameter: a new experimental dataset demonstrates that this design parameter can have a significant and valuable impact on the chatter stability. Secondly, the direct structural modification method is introduced, allowing the tool-holder diameter to be modelled without any knowledge of the interface behaviour between tool and tool-holder. Thirdly, the inverse structural modification method is proposed, allowing tuning and stability optimisation by solving a single equation. Lastly, a new tunable-mass tool-holder is presented, allowing the dynamics of a milling machine to be tuned for each tool diameter and length range with a single tool-holder. This eliminates the need for manufacturers to purchase a wide range of tool-holders, a significant financial investment.

FREQUENCY RESPONSE PREDICTION FOR ROBOT ASSISTED MACHINING

Robotics is increasing its presence in the machine tool sector. One interesting application for robot assisted machining involves a robot locally increasing the stiffness of a thin walled part to suppress regenerative vibrations and minimize part deformations during machining. Simulating the dynamics improvement achieved when coupling the robot and the part is of high concern, in order to guarantee the appropriate performance of the assisted machining. Receptance Coupling Substructure Analysis (RCSA) technique for High Speed Machining (HSM) dynamics simulation has been expanded to derive the frequency response of the assembled system composed by the coupling of the thin walled part and the robot.

Milling stability prediction of a hybrid machine tool considering low-frequency dynamic characteristics

Stability lobe diagram (SLD) is an important tool to select the spindle speed and axial cutting depth to avoid chatter vibration. For a parallel or hybrid machine tool, the low-frequency dynamic characteristics have a great impact on the SLD and need to be taken into account. One of the major issues related to dynamics analysis is the effective dynamic model of parallel mechanisms, since the stiffness of passive joints varies at different orientations and the structures of components are complex. This paper presents a method to establish an accurate dynamic model and considers the low-frequency characteristics to predict SLD. In this paper, an approach is put forward to get the stiffness and mass matrices of components with variable cross-sections and a structural dynamic model of the parallel mechanism is developed, which innovatively considers the variable stiffness characteristics of the passive joint under different loads. Based on the structural dynamic model, the frequency response function (FRF) of the moving platform is obtained and the results are validated through comparison with those of the hammer test. Using receptance coupling substructure analysis (RCSA) method, the machine-spindle-holder-tool system is divided reasonably and the FRFs at the tool tip are obtained to predict the SLD. It is shown that the low-frequency dynamic characteristics of hybrid machine tools have a great influence on the stability boundary of machine tools, mainly at the low speed region.

Chatter Stability of Micro-Milling by Considering the Centrifugal Force and Gyroscopic Effect of the Spindle

Abstract In the micro-milling process, the minimization of tool chatter is critical for good surface finish quality. The analysis of chatter requires an understanding of the milling tool as well as the dynamics of milling system structure. Frequency response function (FRF) at the micro-milling tool point reflects dynamic behavior of the whole micro-milling machine–spindle–tool system. However, the tool point FRF of micro-milling cannot be obtained directly through the hammering test. To solve the problem, the authors get the FRF of the spindle system based on the rotating Timoshenko beam theory and the receptance coupling substructure analysis (RCSA), and the bearing characteristics are added into the spindle model through structural modification. Then, the centrifugal force and gyroscopic effect caused by the high-speed rotation of the micro-milling spindle are considered to better simulate the real scenario and increase the accuracy of modal parameters. The method has general usage and can be applied to all the micro-milling tools under which only the spindle dimension, bearing characteristics, and contact parameters need to be changed.

TPA and RCSA based frequency response function modelling for cutting forces compensation

In machining process, cutting forces are difficult to measure accurately due to the dynamic characteristic of measurement system. The cutting forces compensation requires the frequency response function (FRF), which cannot be measured in actual production. This paper proposes an effective method for FRF modelling and calculating based on transfer path analysis (TPA) and receptance coupling substructure analysis (RCSA). The measurement system is divided into three substructures: workpiece, table dynamometer with screws, joint surface between two previous substructures. The joint surface is simplified as a spring-damping model with contact stiffness and damping. The FRF of workpiece is obtained by finite element method (FEM), which is adjustable for different workpieces and tool positions. The FRF of dynamometer can be measured only by single impact test. The contact parameters can be identified by a few impact tests, which can be applied to other cutting conditions. The FRF between tool tip and dynamometer output is first derived based on TPA and RCSA. Second, a joint surface parameters identification algorithm as well as its simplified algorithm is presented through a few impact tests. Finally, impact tests and milling tests are implemented for parameters identification, algorithm verification and cutting forces compensation. The experimental results show that the proposed method has sufficient accuracy for the assembly FRF prediction.

Multi-point coupling for tool point receptance prediction

This paper describes a multi-point receptance coupling substructure analysis (RCSA) technique for tool point receptance prediction. The portion of the tool inside the holder is coupled to the portion of the holder that clamps the tool at multiple points along the insertion length. The coupling can be rigid or flexible-damped. The procedure is described analytically and then experimental results are presented. The tool point receptances, or frequency response functions, for four carbide tool blank diameters are tested at multiple extension lengths and compared to predictions for an ER32 collet connection. Stiffness matrices are identified for each of the tool blank diameters and reported. Given the predicted tool point receptances, milling process models can be used to select optimized operating parameters at the process planning stage.

Surface location error prediction and stability analysis of micro-milling with variation of tool overhang length

The stability of micro-milling has an important influence on the machined surface, and choosing proper machining parameters can effectively avoid machining process instability and dynamic error. The frequency response function (FRF) of micro-milling tool point varies with tool overhang lengths, and it affects stability lobe diagram (SLD) of the machining system. During the micro-milling process, the cutting thickness was divided into the shearing zone and the plowing zone. In the shearing zone, the cutting thickness was calculated with considering cycloidal tool path and dynamic cutting thickness. After the micro-milling force model was established, the receptance coupling substructure analysis (RCSA) and experimental modal analysis (EMA) were used to obtain the FRFs at the micro-milling tool point. The 2 three-dimensional diagrams, SLD and surface location error (SLE), were developed comprehensively by means of frequency domain method, and the flank micro-milling experiments were carried out. The validity of the three-dimensional SLD containing tool overhang length and the prediction model of SLE was verified by the experimental results, and surface topography was characterized to show the actual machining state. The experimental results show that, compared with SLE, the change of tool overhang length had more significant influence on SLD, and the chatter remarks were not very obvious on the bottom of the workpiece no matter whether the machining process was stable or not. In unstable region, chatter caused by cutting tool left marks on the machined surface. Under the condition of stable milling, a machined surface with smaller SLE and better topography was obtained. The 2 three-dimensional diagrams can provide good references for the selection of optimal tool overhang length and machining parameters comprehensively.

A Free Interface Component Mode Synthesis Approach for Determining the Micro-End Mill Dynamics

The prediction accuracy of the stability boundary in the machining process depends upon accurate estimation of cutting tool-tip dynamics. Note that the experimental modal analysis using direct impact at miniature end mill (typically 50–500 μm in diameter) is not feasible as it can result in tool failure. Consequently, alternative techniques such as experimental modal analysis using reciprocity theory and frequency-based receptance coupling substructure analysis (RCSA) have been used extensively for determining tool-tip dynamics. The experimental approach based on reciprocity theory assumes that the structure is symmetric (cross frequency response functions (FRFs) are same between two points of interest in a structure). RCSA requires a very fine frequency resolution and matrix inversion, which can lead to computational complexities. In addition, RCSA takes into account the FRFs only at the interface and free end, which can induce errors. Owing to these issues with existing approaches, this paper proposes a free-interface component mode synthesis (CMS) approach for estimation of micro-end mill dynamics. The effect of machine tool compliance including the collet–tool interface has been included for estimation of micro-end mill dynamics via a free-interface CMS approach wherein the experimental and analytical mode shapes are coupled. The predicted micro-end mill dynamics have been compared with RCSA and experimental modal analysis using reciprocity theory. Finally, the stability lobe diagrams for high-speed micromilling of Ti6Al4V has been made using the tool-tip dynamics from CMS, RCSA, and experimental technique using reciprocity theory and validated against experimental measurements for onset of instability.

A practical study of joints in three-dimensional Inverse Receptance Coupling Substructure Analysis method in a horizontal milling machine

Abstract Machine tool components are connected by joints that provide relative motion between contact interfaces. These joints add flexibility to the load path from the tool tip to the foundation and, therefore, the correct determination of joint properties becomes a crucial step if the whole machine performance is to be analyzed. A well suited experimental method to characterize these properties is the Inverse Receptance Coupling Substructure Analysis (IRCSA). In the existing literature, this technique has been widely applied to characterize single two-dimensional connections between two parts, where few measured FRFs are necessary in the implementation. However, a more complex multi-body structure with several joints demands a three-dimensional formulation, where the large number of required FRFs limits the application of IRCSA due to the inherent ill-conditioning of the inverse formulation. The work presented in this paper deals with the mentioned limitation, developing a novel IRCSA approach to characterize completely the linear guideways of an industrial machine tool. To avoid the use of excessive FRFs in the formulation, a procedure to study each joint independently is developed, where an appropriate number of connection points in the contact areas between the rails and the carriages is determined. This way, well-conditioning of the formulation is guaranteed while the required precision is preserved. Furthermore, the presented procedure requires only the measurement of translational degrees of freedom (TDOF), which avoids the need to measure rotational degrees of freedom (RDOF). Comparison of numerically calculated and experimentally measured results has demonstrated the validity of the proposed procedure.

RCSA-based prediction of chatter stability for milling process with large axial depth of cut

Large axial depth of cut is often used in rough milling to improve its machining efficiency or in finish peripheral milling to remove the machining mark. Novel strategy and methodology were proposed in the paper to predict the chatter stability for milling process with large axial depth of cut. The actual tool-point is first determined by the axial depth of cut, the machine-spindle-tool assembly is divided into two components, the machine-spindle-shank and the cutting edge, the tip receptance is obtained using the experiment modal analysis (EMA) method, the tip receptance of the cutting edge component is obtained analytically, and the tool-point dynamics of the machine-tool system is achieved using the receptance coupling substructure analysis (RCSA) technology. The stability lobe diagram (SLD) corresponding to certain tool-point position is obtained using the classical zeroth-order approximation (ZOA) approach, and thus, the SLD of milling process with large axial depth of cut is obtained by considering the actual tool-point position corresponding to different axial depth of cut and the effect of tool-point position on the predicted SLD. The proposed method for obtaining SLD of milling process with large axial depth of cut is verified by cutting test result. As a result, it can be used as a guidance for milling process with large axial depth of cut in shop floor application.

The role of tool presetting in milling stability uncertainty

This paper describes the relationship between presetter tool extension length and diameter measurements, the tool point frequency response function (FRF), and milling stability. Three scenarios are considered: 1) the tool extension from the holder face is controlled during setup and measured by the presetter for validation; 2) the tool extension length from the holder face is not controlled during setup and measured to update the tool information in the part program; and 3) the measured extension length is used to update the stability boundary prediction and corresponding operating parameters in the part program. Example presetting results are provided to establish the associated measurement uncertainty. Next, the receptance coupling substructure analysis (RCSA) technique is used within a Monte Carlo simulation to establish the tool point FRF uncertainty as a function of the tool extension length and diameter uncertainty. Finally, the distribution in the tool point FRF is propagated to uncertainty in the milling stability limit. Each of the three scenarios is evaluated to understand their implications for milling stability.

Receptance coupling model for variable dynamics in fixed-free thin rib machining

An analytical approach for predicting thin rib, fixed-free beam dynamics with varying geometries is presented. The proposed method uses receptance coupling substructure analysis (RCSA) to predict the stepped thickness beam receptances (or frequency response functions) at the fixed-free beam’s free end and at the change in thickness. The assembly receptances are calculated by rigidly connecting receptances that describe the individual stepped beam sections, where the section receptances are computed using the Timoshenko beam model. Comparisons with finite element calculations are completed to verify the technique. It is observed that the RCSA predictions agree closely with finite element results. Experiments are also performed, where the stepped beam thickness is changed by multiple machining passes, and receptance measurements are carried out between passes. The RCSA predictions are compared to experimental results for natural frequency and stiffness. Agreement in natural frequency to within two percent is reported.

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

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

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

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

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

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

Analytical solutions for fixed-free beam dynamics in thin rib machining

Two different analytical approaches for predicting thin rib, fixed-free beam dynamics with varying geometries are presented. The first approach uses the Rayleigh method to determine the effective mass for the fundamental bending mode of the stepped thickness beams and Castigliano’s theorem to calculate the stiffness both at the beam’s free end and at the change in thickness. The second method uses receptance coupling substructure analysis (RCSA) to predict the beam receptances (or frequency response functions) at the same two locations by rigidly connecting receptances that describe the individual stepped beam sections, where the receptances are derived from the Timoshenko beam model. Comparisons with finite element calculations are completed to verify the two techniques. It is observed that the RCSA predictions agree more closely with finite element results. Experiments are also performed, where the stepped beam thickness is changed by multiple machining passes, and receptance measurements are carried out between passes. The RCSA predictions are compared to experimental results for natural frequency and stiffness. Agreement in natural frequency to within a few percent is reported.

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.