Review and status of tool tip frequency response function prediction using receptance coupling

Abstract. In machining, tool vibrations are one of the main causes of process inaccuracies and poor finishing. To tackle these phenomena, the identification of the tool tip frequency response function (FRF) is essential, since it allows to determine the most suitable cutting conditions for an accurate and stable cut. Nonetheless, the identification of the tool tip FRF is usually achieved through experimental modal methods whose set up and testing phases require specific expertise as well as sensors and devices to be mounted on the machine tool. This paper investigates a methodology to identify tool tip FRF starting from the surface location error (SLE) without the need of additional equipment for the machine tool. The method exploits on-machine sensors (i.e., measuring probe), and it identifies tool tip FRF using a frequency domain cutting force model and the SLEs measured in different cutting tests. The method was experimentally tested to verify its effectiveness and limitations.

A new receptance coupling substructure analysis methodology to improve chatter free cutting conditions prediction

The tool-point frequency response function (FRF) of a spindle–tool system plays a crucial role in predicting machining stability. Among the factors influencing the FRF, the interface characteristics between the spindle and the tool holder are particularly significant, especially when different holder designs are used. This study focused on identifying these interface characteristics for two common tool holder types—BT and BBT—to improve FRF prediction accuracy. The receptance coupling substructure analysis (RCSA) method was employed in conjunction with finite element modeling (FEM) to characterize the spindle–tool holder interfaces without needing extensive experimental tapping tests. Finite element models were developed to generate receptance components for various tool holder–tool assemblies, enabling efficient and accurate coupling within the RCSA framework. The identified interface parameters were applied to predict the tool-point FRFs of the cutter clamped in a BT tool holder with different overhang lengths. The predicted and measured tool compliances differed by 3–4.6%, demonstrating high agreement and reliability. The proposed methodology provides a powerful tool for predictive modeling of dynamic behavior in spindle–tool systems under varying tooling conditions, enhancing process planning and evaluation of the cutting stability in high-precision machining.

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.

An Improved Receptance Coupling Substructure Analysis to Predict Chatter Free High Speed Cutting Conditions

The structural dynamics of a machine tool play a significant role in chatter occurrence, which significantly deteriorates the metal-cutting performance. The receptance coupling substructure analysis (RCSA) is known for eliminating the experimental dependency on repetitive impact hammer testing. However, the identified contact parameters between the holder and tool, which are necessary for RCSA, usually lose accuracy in predicting tool point dynamics when applied to other tool clamping lengths or to combinations with other tools. To this end, a new method based on conventional impact hammer testing and RCSA technique to identify these parameters is proposed. Two descriptions of the proposed method are presented for different tool combinations and different clamping lengths, respectively. This new method eliminates the need for specialized experimental setups. The predicted tool point dynamics, using the identified contact parameters from the proposed method, show deviations below 3% with one exception, indicating that the identifications are accurate for various clamping lengths. The new approach yields significant advancements in the predicted tool point dynamics and stability boundaries compared to a traditional identification method reported in the literature.

Theoretical stability analysis is a significant approach to predicting chatter-free machining parameters. Accurate milling stability predictions highly depend on the dynamic properties of the process system. Therefore, variations in tool and workpiece attributes will require repeated and time-consuming experiments or simulations to update the tool tip dynamics and cutting force coefficients. Considering this problem, this paper proposes a transfer learning framework to efficiently predict the milling stabilities for different tool-workpiece assemblies through reducing the experiments or simulations. First, a source tool is selected to obtain the tool tip frequency response functions (FRFs) under different overhang lengths through impact tests and milling experiments on different workpiece materials conducted to identify the related cutting force coefficients. Then, theoretical milling stability analyses are developed to obtain sufficient source data to pre-train a multi-layer perceptron (MLP) for predicting the limiting axial cutting depth (aplim). For a new tool, the number of overhang lengths and workpiece materials are reduced to design and perform fewer experiments. Then, insufficient stability limits are predicted and further utilized to fine-tune the pre-trained MLP. Finally, a new regression model to predict the aplim values is obtained for target tool-workpiece assemblies. A detailed case study is developed on different tool-workpiece assemblies, and the experimental results validate that the proposed approach requires fewer training samples for obtaining an acceptable prediction accuracy compared with other previously proposed methods.

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

Suppressing vibration modes of spindle-holder-tool assembly through FRF modification for enhanced chatter stability

The milling robot normally has a low stiffness which may easily cause chatter during machining. This article presents a novel eddy current damper design for chatter suppression in the robotic milling process. The designed eddy current dampers are installed on the milling spindle to damp the tool tip vibrations. The structural design and the working principle of the eddy current dampers are explained. The magnetic flux density distribution and the magnetic force generation of the designed eddy current damper are analyzed with the finite element method. The tool tip dynamics without and with eddy current dampers are modeled, and the damping performance of the proposed eddy current dampers in the robotic milling process is verified through both simulations and experiments. The results show that the peaks of the tool tip frequency response function caused by the milling tool modes are damped significantly, and the stable depth of cut is improved greatly with eddy current dampers.

Chatter stability analysis in Micro-milling with aerostatic spindle considering speed effect

Posture-dependent stability prediction of a milling industrial robot based on inverse distance weighted method

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.

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

This paper presents an optimum design approach of a spindle-tool system to improvise the dynamic stability of end-milling. Initially, the tool-tip frequency response function is obtained by analyzing the spindle-tool assembly with the finite element model. The chatter-free regions are maximized using an optimization methodology by considering the spindle and tool parameters as design variables. A simulated experimental dynamic data consisting of the average stable depth of cut is obtained for different combinations of design variables by the method of design of experiments (DOE) and analysis of variance technique is applied to find the influence of design parameters on the outputs. Based on the obtained results, the data is generalized with the help of a neural network model that works as an estimator of the average stable depths for the optimization module. The average stable depth of cut over a range of operating speeds is maximized by selecting optimal tool and spindle parameters.