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.

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

Measuring 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.

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.

Dynamics Modeling of Clamping System Considering Characteristics of the Clamping Contact Surface

The dynamic characteristics of the clamping system, which is composed of workpiece and chuck, have important effects on the stability of turning process. However, in current researches on cutting stability, the influence of the characteristics of clamping contact surface on the clamping system was rarely considered. In order to improve the prediction accuracy of stable cutting limits in turning process, the role of clamping contact surface in deciding the dynamics of the clamping system was analyzed in this paper. Then, the dynamics model of clamping system was established considering the characteristics of clamping contact surface between workpiece and chuck. The dynamics parameters of the clamping system were obtained with receptance coupling substructure analysis method. The frequency response function of clamping system at different cutting position was presented, which is a foundation for analyzing the cutting stability.

Predicting Tool Point FRF by RCSA in High Speed Milling

Tool point frequency response function (FRF) is the key parameters to predict the milling stability in high-speed milling. Receptance coupling substructure analysis (RCSA) is described to predict the tool point FRF. The major difficulties in RCSA are the identification of joint connection parameters and the obtaining of FRFs of substructure. This paper separation of the milling system into three substructures: the machine-spindle-holder taper, the extended holder-tool shank, and the tool extended portion. Develop the connection model compose of linear and rotational springs and dampers. Determine the substructure FRF by measurement and Euler-Bernoulli beam model. Tool point FRF is obtained by coupling the substructure FRFs through the connection model by RCSA.

Identification of Toolholder-Spindle Joint Based on Receptance Coupling Substructure Analysis

Stiffness identification of toolholder-spindle joint is a basic work for machine tool dynamic research. In this paper, an identification method based on receptance coupling substructure analysis is described. Once the frequency response functions of the toolholder, the spindle and the toolholder-spindle assembly are obtained, the analytical stiffness could be calculated. The method is verified efficiency through dynamic response experiment. Identified stiffness results under different drawbar forces are also discussed.