Effect analysis of bearing and interface dynamics on tool point FRF for chatter stability in machine tools by using a new analytical model for spindle–tool assemblies

Self-excited vibration of the tool, regenerative chatter, can be predicted and eliminated if the stability lobe diagram of the spindle–holder–tool assembly is known. Regardless of the approach being used, analytically or numerically, forming the stability lobe diagram of an assembly implies knowing the point frequency response function (FRF) in receptance form at the tool tip. In this paper, it is aimed to study the effects of spindle–holder and holder–tool interface dynamics, as well as the effects of individual bearings on the tool point FRF by using an analytical model recently developed by the authors for predicting the tool point FRF of spindle–holder–tool assemblies. It is observed that bearing dynamics control the rigid body modes of the assembly, whereas, spindle–holder interface dynamics mainly affects the first elastic mode, while holder–tool interface dynamics alters the second elastic mode. Individual bearing and interface translational stiffness and damping values control the natural frequency and the peak of their relevant modes, respectively. It is also observed that variations in the values of rotational contact parameters do not affect the resulting FRF considerably, from which it is concluded that rotational contact parameters of both interfaces are not as crucial as the translational ones and therefore average values can successfully be used to represent their effects. These observations are obtained for the bearing and interface parameters taken from recent literature, and will be valid for similar assemblies. Based on the effect analysis carried out, a systematic approach is suggested for identifying bearing and interface contact parameters from experimental measurements.     

Selection of design and operational parameters in spindle–holder–tool assemblies for maximum chatter stability by using a new analytical model

In this paper, using the analytical model developed by the authors, the effects of certain system design and operational parameters on the tool point FRF, thus on the chatter stability are studied. Important conclusions are derived regarding the selection of the system parameters at the stage of machine tool design and during a practical application in order to increase chatter stability. It is demonstrated that the stability diagram for an application can be modified in a predictable manner in order to maximize the chatter-free material removal rate by selecting favorable system parameters using the analytical model developed. The predictions of the model, which are based on the methodology proposed in this study, are also experimentally verified.     

Modeling and identification of tool holder–spindle interface dynamics

The majority of the chatter vibrations in high-speed milling originate due to flexible connections at the tool holder–spindle, and tool–tool holder interfaces. This article presents modeling of contact stiffness and damping at the tool holder and spindle interface. The holder–spindle taper contact is modeled by uniformly distributed translational and rotational springs. The springs are identified by minimizing the error between the experimentally measured and estimated frequency response of the spindle assembly. The paper also presents identification of the spindle's dynamic response with a holder interface, and its receptance coupling with the holder–tool stick out which is modeled by Timoshenko beam elements. The proposed methods allow prediction of frequency-response functions at the tool tip by receptance coupling of tools and holders to the spindle, as well as analyzing the influence of relative wear at the contact by removing discrete contact springs between the holder and spindle. The techniques are experimentally illustrated and their practical use in high speed milling applications is elaborated.     

Analytical modeling of spindle–tool dynamics on machine tools using Timoshenko beam model and receptance coupling for the prediction of tool point FRF

Regenerative chatter is a well-known machining problem that results in unstable cutting process, poor surface quality and reduced material removal rate. This undesired self-excited vibration problem is one of the main obstacles in utilizing the total capacity of a machine tool in production. In order to obtain a chatter-free process on a machining center, stability diagrams can be used. Numerically or analytically, constructing the stability lobe diagram for a certain spindle–holder–tool combination implies knowing the system dynamics at the tool tip; i.e., the point frequency response function (FRF) that relates the dynamic displacement and force at that point. This study presents an analytical method that uses Timoshenko beam theory for calculating the tool point FRF of a given combination by using the receptance coupling and structural modification methods. The objective of the study is two fold. Firstly, it is aimed to develop a reliable mathematical model to predict tool point FRF in a machining center so that chatter stability analysis can be done, and secondly to make use of this model in studying the effects of individual bearing and contact parameters on tool point FRF so that better approaches can be found in predicting contact parameters from experimental measurements. The model can also be used to study the effects of several spindle, holder and tool parameters on chatter stability. In this paper, the mathematical model, as well as the details of obtaining the system component (spindle, holder and tool) dynamics and coupling them to obtain the tool point FRF are given. The model suggested is verified by comparing the natural frequencies of an example spindle–holder–tool assembly obtained from the model with those obtained from a finite element software.     

Stability limits of milling considering the flexibility of the workpiece and the machine

High speed machining of low rigidity structures is a widely used process in the aeronautical industry. Along the machining of this type of structures, the so-called monolithic components, large quantities of material are removed using high removal rate conditions, with the risk of the instability of the process. Very thin walls will also be milled, with the possibility of lateral vibration of them in some cutting conditions and at some stages of machining. Chatter is an undesirable phenomenon in all machining processes, causing a reduction in productivity, low quality of the finished workpieces, and a reduction of the machine-spindle's working life.

In this study, a method for obtaining the instability or stability lobes, applicable when both the machine structure and the machined workpiece have similar dynamic behaviours, is presented. Thus, a 3-dimensional lobe diagram has been developed based on the relative movement of both systems, to cover all the intermediate stages of the machining of the walls. This diagram is different and more exact than the one that arises out of the mere superposition of the machine and the workpiece lobe diagrams. A previous step of rejecting resonance modes that are not involved in the milling at the bottom zones of the thin walls must be previously performed.

Finally, the proposed method has been validated, by machining a series of thin walls, applying cutting conditions contrasted with the limits previously obtained in the three-dimensional lobe diagram.     

A new analytical–experimental method for the identification of stability lobes in high-speed milling

Increased working speeds and accelerations of high-speed machining produce excitation of oscillations and cause dynamic problems. These problems affect the tool life (tool wear and tool failure), produce shoddy end surface, reduce productivity, produces scrap parts and affect the environment. A chatter’s analytical prediction method was combined with experimental multidegree-of-freedom systems modal analysis to achieve the objective of generating a new method to obtain the stability lobes information. This paper describes the development of this new method which obtains the stability information for some vibration modes that can be used to graph the stability lobes for high-speed milling, and these to help in the selection of parameters for chatter free operations. Some tests were carried out to demonstrate the quality of this method and the accomplishment of the proposed goals.     

Real-time tool wear monitoring in milling using a cutting condition independent method

This paper describes a new method to monitor end milling tool wear in real-time by tracking force model coefficients during the cutting process. The behavior of these coefficients are shown to be independent from the cutting conditions and correlated with the wear state of the cutting tool. The tangential and radial force model coefficients are normalized and combined into a single parameter for wear monitoring. A number of experiments with different workpiece materials are run to investigate the feasibility of tool wear monitoring using this method. We show that this method can be used in real-time to track tool wear and detect the transition point from the gradual wear region to the failure region in which the rate of wear accelerates.     

An inverse estimation scheme to measure steady-state tool–chip interface temperatures using an infrared camera

A new technique is developed to estimate the average steady-state chip–tool interface temperature during turning. An infrared (IR) video camera attached on the carriage of the lathe measures the transient cooling behavior on the rake surface of an insert after the feed motion is halted. This allows the zero heat flux boundary condition, where the transient Laplace heat conduction problem can be solved numerically to obtain the temporal and spatial temperature distribution. With the experimentally determined transient temperature distribution, the one-dimensional ellipsoidal model is used to estimate the average steady-state chip–tool interface temperature during machining. The results on turning gray cast iron (GCI) and AISI 1045 steels with various coated and uncoated K313 carbide inserts are presented.     

Experimental evaluation of strains in the tension–compression using a new tool geometry, X-Die

Sheet-metal forming involves a complex distribution of strains throughout the part. The strains occur due to tension, compression and a mix of both. A geometry has been developed, the X-Die, in order to gain insight into the strain behavior of different materials. The X-Die enables strain paths far into the tension–compression region, thus creating the possibility to extend the experimental base both for definition and for further extrapolation of the forming limit curve (FLC) in the tension–compression region, as well as to evaluate FE-simulation results for the same region.

The experimental results show that the strain signature is impacted by material quality. In qualities such as extra high strength steel (EHSS) and aluminum the strains do not reach as far into the tension–compression region as the strains do in e.g. mild steel. This is due to failure in plane strain tension. Strain paths in materials such as mild steel and high strength steel (HSS) reach far into the tension–compression region before failure. Use of the X-Die provides possibilities to reach farther into the tension–compression region compared with traditional test methods for creating a forming limit diagram (FLD).

Use of the X-Die yields well-defined strain signatures. These clearly defined strain signatures are favorable for comparison with numerical simulations, especially for strain signatures in the tension–compression region.

Furthermore, the experiments using the X-Die indicate that a possible additional forming limit curve, which intersects the original forming limit curve (shear failure), exists so far into the tension–compression region that it is not applicable.

Even though the experiments indicate compression strains >100% (material DX56D), the experiments show potential for an experimentally determined extrapolation of the FLC up to 75% compression strain. The results of the experiments indicate that the X-Die geometry is suitable as a supplementary tool in identifying the strain behavior of different materials far into the tension–compression region and is also a good tool for verification of numerical results in the tension–compression region.     

Identification of strut and assembly errors of a 3-PRS serial–parallel machine tool

In a serial–parallel type machine tool, the parallel spindle platform plays the key role in manipulating three directions of movement. Spatial symmetry of the 3-PRS loops is essential to the machine’s systematic accuracy. Currently, however, there is no effective instrument capable of measuring the symmetrical errors of the corresponding joints and strut lengths during structure assembly. In this study, an experimental method is proposed to identify the mechanism symmetric errors of a 3-PRS serial–parallel machine tool during the test run. It is based on the differentiation of the inverse kinematics equations. The mechanism errors could be derived by an identification model. With the aid of a developed 3D laser ball bar to detect the spatial position and orientation of the spindle platform, and three laser Doppler scales to measure three sliders’ positions simultaneously, the length errors of three struts and the symmetrical errors of the R-joints and S-joints can be identified by the optimization technique. This technique can help shop floor engineers to tune the symmetrical errors of the 3-PRS mechanism during machine assembly.