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

Chatter stability prediction for multi-robots collaborative milling system

Chatter vibration in milling process is a major obstacle that limits the machining quality and productivity, which may be avoided by using stability lobe diagrams (SLDs). Many traditional models developed to predict chatter stability assume that dynamic parameters of the machine tool remain constant under operational conditions. However, these parameters such as natural frequencies, damping ratios, stiffness, and cutting force coefficients vary depending upon different aspects including spindle speed, tool wear, and machining position, reducing the accuracy of chatter prediction. In this study, a robust chatter prediction method based on conventional analytical milling stability models is presented by employing the Edge theorem and Zero Exclusion condition. In this method, optimal combinations of spindle speeds and machining positions are firstly researched to obtain higher critical depths of cut, based on the conventional stability model, modal fitting technique, Kriging model, and improved particle swarm optimization. At each combination, related nominal modal parameters and cutting force coefficients are identified, and their left and right worst-case deviations are also determined. Critical stable condition for each combination is detected by a graphic approach within the minimum and maximum bounds of uncertainties. Accordingly, a robust stability lobe diagram is obtained with related spindle speeds and critical cutting depths. The proposed method was verified by chatter tests on a real vertical machining center, demonstrating its reliability in chatter prediction compared to the conventional stability lobe diagram.

Regulating the vibration of aerostatic journal spindle based on piezoelectric ceramics

Fuzzy stability analysis of regenerative chatter in milling

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.

This paper presents the effect of experimentally evaluated nonlinearities in a machine joint on the overall machine tool dynamic performance using frequency response functions and stability lobe diagrams. Typical machine joints are very stiff and have weak nonlinearities. The experimental evaluation of the nonlinear joint parameters of a commercial translational guide has been discussed in Dhupia et al., 2007, J. Vibr. Control, accepted. Those results are used in the current paper to represent the connection between the column and the spindle of an idealized column-spindle machine structure. The goal is to isolate and understand the effects of such joints on the machine tool dynamic performance. The nonlinear receptance coupling approach is used to evaluate the frequency response function, which is then used to evaluate the stability lobe diagrams for an idealized machine structure. Despite the weak nonlinearities in the joint, significant shifts in the natural frequency and amplitudes at resonance can be observed at different forcing amplitudes. These changes in the structural dynamics, in turn, can lead to significant changes in the location of chatter stability lobes with respect to spindle speed. These variations in frequency response function and stability lobe diagram of machine tools due to nonlinearities in the structure are qualitatively verified by conducting impact hammer tests at different force amplitudes on a machine tool.

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

Development of a novel boring tool with anisotropic dynamic stiffness to avoid chatter vibration in cutting: Part 1: Design of anisotropic structure to attain infinite dynamic stiffness

The stability lobe diagram (SLD) is commonly used to determine the suitable cutting parameters of the machining system in order to achieve a chatter-free machining process. An improved full-discretization method (FDM) is proposed to predict the SLD based on the hybrid interpolation scheme of the Newton and Lagrange polynomials. In order to solve the SLD, a third-order Newton polynomial is employed to interpolate the state term of the physical space equation of the system. Meanwhile, to investigate the influence of the interpolation order on predicting the SLD, the delayed term is estimated using the Lagrange polynomials of orders one to four successively. Subsequently, after constructing the transition matrix, a series of calculation for the stability prediction are carried out by applying Floquet theory. The calculated results from these constructed methods demonstrate that the FDM with a second-order Lagrange polynomial is optimal, and further has better computational performance compared with some existing discretization methods. Lastly, the influences of the dynamic parameters on chatter stability are analyzed based on the proposed FDM. When the stiffness and damping ratio increase, the limit cutting depth will be enhanced. The increasing natural frequency not only causes an obvious shift of the lobes to the right, but also raises the limit cutting depth to some extent. These theoretical analyses can guide the prediction and improvement of the chatter stability of a machining system.

The frequency response function (FRF) method has been well used to determine the worst spindle speeds and their critical limiting chip width for turning operation by finding the maximum negative real part of the FRF. In this study, a modified FRF concept is adapted for a 2 DOF milling system of planar isotropic dynamics to determine the worst spindle speeds and the critical limiting axial depth of cut in explicit, analytic formulas. Analogous to the formulation of worst spindle speeds, similar expression for the best spindle speeds is also obtained. The modified FRF is obtained by multiplying the original FRF of the structure with a complex scaling factor, corresponding to a scaling and a rotation of its original Nyquist plot. The scaling factor is determined analytically from the system characteristic equation with the radial cutting constant and radial immersion angle as the major system parameters. Through the presented method, it is also shown that the worst spindle speeds for a milling operation can be found without the prior knowledge of modal dynamics and stability lobe diagram. The proposed analytical expressions are confirmed by the existing stability models and experimentally verified.

Dynamic behaviour of spindle system influences chatter stability of machine tool considerably. Self-excited vibrations of the tool results in unstable cutting process which leads to the chatter on the work surface and it reduces the productivity. In this paper, a system of coupled spindle bearing system is employed by considering the angular contact ball bearing forces on stability of machining. Using Timoshenko beam element formulation, the spindle unit is analyzed by including the gyroscopic and centrifugal terms. Frequency response functions at the tool-tip are obtained from the dynamic spindle model. In the second phase, solid model of the system is developed and its dynamic response is obtained from three dimensional finite element analysis. The works on analysis of the stability of milling processes focus on calculating the stability boundary of the machining parameters based on the dynamic models characterizing the milling processes. The stability lobe diagrams are generated from frequency response functions (FRF’s) lead to an stability limit prediction for the system at high speed ranges.

A closed-form approach for identification of dynamical contact parameters in spindle–holder–tool assemblies

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

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.

The paper determines the impact factors of high-speed spindle system including the centrifugal force, gyroscopic moments and the bearing stiffness softening, and builds the general spindle-bearing FEM considering high speeds. Taking a motorized spindle as example, the effect of centrifugal force, gyroscopic effect, the radial stiffness and the coupling factors are analyzed qualitatively and quantitatively. Finally the research shows the variations of bearing radial stiffness, centrifugal force and gyroscopic moments have a significant effect on dynamics of spindle system in high speeds, while modeling the high speed spindle system, above factors must be considered.