Robust chatter stability in micro-milling operations

Micro-milling utilizes miniature end mills to fabricate complex shapes at high rotational speeds. One of the challenges in micro-machining is regenerative chatter, which results in severe tool wear and reduced part quality. The high rotational speeds of micro-milling cause changes in dynamics; and, the elasto-plastic nature of micro-machining operations results in changes to the cutting coefficients. Variations in dynamics and cutting coefficients affect the stability lobes. The tool tip dynamics can be indirectly obtained through mathematical coupling of substructures using the receptance coupling method. The effect of process damping is also considered. The robust chatter stability theorem, which is based on the edge theorem, is employed to provide the robust stability within the minimum and maximum boundaries of changing parameters.     

Theoretical-experimental modeling of milling machines for the prediction of chatter vibration

Productivity of high speed milling operations can be seriously limited by chatter occurrence. Chatter vibrations can imprint a poor surface finish on the workpiece and can damage the cutting tool and the machine. Chatter occurrence is strongly affected by the dynamic response of the whole system, i.e. the milling machine, the tool holder, the tool, the workpiece and the workpiece clamping fixture. Tool changes must be taken into account in order to properly predict chatter occurrence. In this study, a model of the milling machine-tool is proposed: the machine frame and the spindle were modeled by an experimentally evaluated modal model, while the tool was modeled by a discrete modal approach, based on the continuous beam shape analytical eigenfunctions. A chatter identification technique, based on this analytical-experimental model, was implemented. Tool changes can be easily taken into account without requiring any experimental tests. A 4 axis numerically controlled (NC) milling machine was instrumented in order to identify and validate the proposed model. The milling machine model was excited by regenerative, time-varying cutting forces, leading to a set of Delay Differential Equations (DDEs) with periodic coefficients. The stability lobe charts were evaluated using the semi-discretization method that was extended to n>2 degrees of freedom (dof) models. The stability predictions obtained by the analytical model are compared to the results of several cutting tests accomplished on the instrumented NC milling machine.     

Uncharted islands of chatter instability in milling

This paper provides conclusive evidence that isolated islands of chatter vibration can exist in milling processes. Investigations show these islands are induced by the tool helix angle and act to separate regions of period-doubling and quasi-periodic behavior. Modeling efforts develop an analytical force model with three piecewise continuous regions of cutting that describe helix angle tools. Theoretical results examine the asymptotic stability trends for several different radial immersions and helix angles. In addition, new results are shown through the implementation of a temporal finite element analysis approach for delay equations written in the form of a state space model. Predictions are validated by a series of experimental tests that confirm the isolated island phenomenon.     

A comprehensive dynamic cutting force model for chatter prediction in turning

This paper presents a model of the dynamic cutting force process for the three-dimensional or oblique turning operation. To obtain dynamic force predictions, the mechanistic force model is linked to a tool–workpiece vibration model. Particular attention was paid to the inclusion of the cross-coupling between radial and axial vibrations in the force model. The inclusion of this cross-coupling facilitates prediction of the unstable–stable chatter phenomenon which usually occurs in certain cases of finish turning due to process non-linearity. The dynamic force model developed was incorporated into a computer program to obtain time-saving chatter predictions. Experimental tests were performed on AISI 4140 steel workpieces to justify the chatter predictions of the dynamic cutting process model in both the finishing and roughing regimes. Experimental results corroborate the unstable–stable chatter predictions of the model for different cases of finish machining. In addition, experimental results also confirmed the accuracy of chatter predictions for various cases of rough turning.     

Spindle speed ramp-up test: A novel experimental approach for chatter stability detection

Chatter is one of the most limiting factors in improving machining performances. Stability Lobe Diagram (SLD) is the most used tool to select optimal stable cutting parameters in order to avoid chatter occurrence. Its prediction is affected by reliability of input data such as machine tool dynamics or cutting coefficients that are difficult to be evaluated accurately, especially at high speed.This paper presents a novel approach to experimentally evaluate SLD without requiring specific knowledge of the process; this approach is called here Spindle Speed Ramp-up (SSR) test. During this test spindle speed is ramped up, and chatter occurrence is detected by the Order Analysis technique. As result one single test ensures optimal spindle speed identification at one cutting condition, while if few tests are performed the entire SLD could be obtained. Results of the method applied to slotting operation on aluminum are provided and a comparison between different measurements devices is presented. This quick, easy-to-use and efficient test is suitable for industrial application: no knowledge of the process is required, different sensors can be used such as accelerometer, dynamometer or microphone.     

Suppression of regenerative chatter vibration in simultaneous double-sided milling of flexible plates by speed difference

This paper presents a new method to machine flexible plates with high accuracy and high productivity. Precision steel plates are finished conventionally by face milling with electro-magnetic chucks. It is difficult to correct flatness of the flexible plates, because they deform to fit the chuck surfaces when chucked. To solve this problem, the authors have tried simultaneous double-sided milling, but this causes the regenerative chatter vibration. Thus, the new method is proposed and verified to suppress this chatter vibration, in which the regenerative effects on both sides are cancelled out by rotating the two milling cutters at different speeds.     

A general approach to simulating workpiece vibrations during five-axis milling of turbine blades

Workpiece vibrations have a significant influence on the machining process and on the quality of the resulting workpiece surface, particularly when milling thin-walled components. In this paper a simulation system, consisting of an FE model of the workpiece coupled with a geometric milling simulation for computing regenerative workpiece vibrations during the five-axis milling process, is presented. Additionally, a modeling method for visualizing the resulting surface is described. In order to validate the simulation model, turbine blades were machined and the experimental results were compared to the simulation results.     

Theoretical modelling and simulation of cutting forces in face milling with cutter runout

A new approach to theoretical modelling and simulation of cutting forces in face milling is presented. Based on a predictive machining theory, the action of a milling cutter is modeled as the simultaneous actions of a number of single-point cutting tools. The milling forces are predicted from the workpiece material properties, cutter parameters, tooth geometry, cutting conditions and types of milling. The properties of the workpiece material are considered as functions of strain, strain-rate and temperature in the cutting region. It takes into account the effect of the intermittent contact between each milling tooth and the workpiece on the temperature in the cutting region. It also takes into account the effect of cutter runout on the undeformed chip thickness. Milling experiments have been conducted to verify the proposed model. Good agreements between the experimental and simulated results are presented.     

Prediction of chatter in NC machining based on a dynamic cutting force model for ball end milling

Ball end milling is one of the most widely used cutting processes in the automotive, aerospace, die/mold, and machine parts industries, and the chatter generated under unsuitable cutting conditions is an extremely serious problem as it causes excessive tool wear, noise, tool breakage, and deterioration of the surface quality. Due to the critical nature of detecting and preventing chatter, we propose a dynamic cutting force model for ball end milling that can precisely predict the cutting force for both stable and unstable cutting states because our uncut chip thickness model considers the back-side cutting effect in unstable cutting states. Furthermore, the dynamic cutting force model considers both tool runout and the penetration effect to improve the accuracy of its predictions. We developed software for calculating the cutting configuration and predicting the dynamic cutting force in general NC machining as well as single-path cutting. The chatter in ball end milling can be detected from the calculated cutting forces and their frequency spectra. A comparison of the predicted and measured cutting forces demonstrated that the proposed method provides accurate results.     

Modeling of spindle-bearing and machine tool systems for virtual simulation of milling operations

This paper presents a general, integrated model of the spindle bearing and machine tool system, consisting of a rotating shaft, tool holder, angular contact ball bearings, housing, and the machine tool mounting. The model allows virtual cutting of a work material with the numerical model of the spindle during the design stage. The proposed model predicts bearing stiffness, mode shapes, frequency response function (FRF), static and dynamic deflections along the cutter and spindle shaft, as well as contact forces on the bearings with simulated cutting forces before physically building and testing the spindles. The proposed models are verified experimentally by conducting comprehensive tests on an instrumented-industrial spindle. The study shows that the accuracy of predicting the performance of the spindles require integrated modeling of all spindle elements and mounting on the machine tool. The operating conditions of the spindle, such as bearing preload, spindle speeds, cutting conditions and work material properties affect the frequency and amplitude of vibrations during machining.     

Detection of chatter vibration in end milling applying disturbance observer

Suppression of chatter vibration is required to improve the machined surface quality and enhance tool life. For monitoring the chatter vibrations, additional sensors such as acceleration sensors are generally used, which results in high costs and low reliability of the machine tools. In this study, a novel in-process method to detect chatter vibrations in end milling is developed on the basis of a disturbance observer theory. The developed system does not require any external sensors because it uses only the servo information of the spindle control system. Self-excited and forced chatter vibrations are successfully detected.     

Milling force prediction using a dynamic shear length model

Modelling of cutting forces in milling is often needed in machining automation. In this paper, a new method for the determination of the cutting forces in face milling is presented, which applies a predictive machining theory originally developed for orthogonal cutting to milling operations, with a dynamic shear length model developed and incorporated. The proposed dynamic shear length model is developed based on the analysis for the true tooth trajectories of a milling cutter, taking into account of the characteristic wavy surface effects in milling. The prediction for the cutting forces is carried out at each step of the angular increment of cutter rotation from input data of fundamental workpiece material properties, tool geometry and cutting conditions. Cutting forces at a cutter tooth can be predicted once the shear angle, shear length, shear plane area, and the shear flow stress along the shear length have been determined. The milling force prediction using the dynamic shear length model is verified through milling experimental tests. The sensitivity of the difference between the static and dynamic shear length models with respect to the feed per tooth and the cutter diameter is discussed.     

An improved cutting force and surface topography prediction model in end milling

During the milling operation, the cutting forces will induce vibration on the cutting tool, the workpiece, and the fixtures, which will affect the surface integrity of the final part and consequently the product's quality. In this paper, a generic and improved model is introduced to simultaneously predict the conventional cutting forces along with 3D surface topography during side milling operation. The model incorporates the effects of tool runout, tool deflection, system dynamics, flank face wear, and the tool tilting on the surface roughness. An improved technique to calculate the instantaneous chip thickness is also presented. The model predictions on cutting forces and surface roughness and topography agreed well with experimental results.     

Runout effects in milling: Surface finish, surface location error, and stability

This paper investigates the effect of milling cutter teeth runout on surface topography, surface location error, and stability in end milling. Runout remains an important issue in machining because commercially-available cutter bodies often exhibit significant variation in the teeth/insert radial locations; therefore, the chip load on the individual cutting teeth varies periodically. This varying chip load influences the machining process and can lead to premature failure of the cutting edges. The effect of runout on cutting force and surface finish for proportional and non-proportional tooth spacing is isolated here by completing experiments on a precision milling machine with 0.1 μm positioning repeatability and 0.02 μm spindle error motion. Experimental tests are completed with different amounts of radial runout and the results are compared with a comprehensive time-domain simulation. After verification, the simulation is used to explore the relationships between runout, surface finish, stability, and surface location error. A new instability that occurs when harmonics of the runout frequency coincide with the dominant system natural frequency is identified.     

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

Modifying dynamic response of a machine tool is of great importance for chatter mitigation. Tool tip frequency response function (FRF) can be suppressed by capitalizing on the absorber effect due to dynamic interactions among vibration modes of spindle, holder and tool. In this paper, a practical method is presented to modify the system’s FRF by selecting proper dimensions for assembly component without extensive testing. Robustness of the method is demonstrated through simulation and test results. Milling stability tests were also conducted where significant improvements in chatter free Material Removal Rate (MRR) is achieved.     

A chatter free calibration method for determining cutter runout and cutting force coefficients in ball-end milling

The accuracy of cutting force coefficients plays an important role in predicting reliable cutting force, stability lobes as well as surface location error in ball-end milling. In order to avoid chatter risk of the traditional calibration test with an entire-ball-immersed cutting depth, a cylindrical surface milling method is proposed to calibrate the cutting force coefficients with the characteristics of low cutting depth and varying lead angle. A dual-cubic-polynomial function is also presented to describe the non-uniform cutting force coefficients of the ball part cutting edge and the nonlinear chip size effect on cutting force. The variation of the maximum chip thickness versus the lead angle is established with the consideration of cutter runout. According to the dependence of chip thickness on lead angle, a runout identification method is introduced by seeking the critical lead angle at which one of the cutter flutes is just thoroughly out of cut. Then, a lumped equivalent method is adopted for the low cutting depth condition so that the dual-cubic-polynomial model can be calibrated for the chip size effect and the cutting force coefficients respectively. The accuracy of the proposed calibration method has been validated experimentally with a series of milling tests. The stability examinations indicate that the proposed method has an evident chatter-free advantage, compared with that of varying cutting depth method.     

Prediction of chatter stability for multiple-delay milling system under different cutting force models

This paper systematically studies the stability lobe prediction methods for the milling process with multiple delays, which are often induced by cutter runout. Emphasis is put on how to effectively incorporate the instantaneous cutting force model into the prediction procedure of stability lobes. Two original methods are proposed based on the vibration time history of the cutter motion, which is numerically obtained by time domain simulation. A comparison study is made with the existing method taken from the literature and experimental verifications are also carried out to validate both methods.In this study, two different instantaneous cutting force models together with the constant cutting force model are considered in the calculation of the cutting force coefficients during the simulation. The effects of different cutting force models on stability lobes, their consistencies and limitations are highlighted. At the same time, cutting force coefficients calibrated from three tests with different feeds per tooth are also considered in order to show the influences of cutting force coefficient's accuracy. It is found that both types of cutting force models and the calibration accuracy of the cutting force coefficients have great influences on the reliability of the stability lobes.     

Active chatter suppression in turning by band-limited force control

The suppression of chatter vibration is required to enhance the machined surface quality and to increase tool life. In this study, a new, conceptually active approach for chatter suppression in machining is proposed. The hybrid control method developed by applying sensorless force control with a disturbance observer enables the simultaneous and independent control of the position trajectory and band-limited forces. The proposed method is introduced to the carriage of a prototype desktop-sized turning machine, and the ability to suppress chatter is evaluated by end-face cutting tests. The results demonstrate that actively controlling a band-limited force leads to the avoidance of chatter.     

Identification of cutting force characteristics based on chatter experiments

Cutting force coefficients exhibit strong nonlinearity as a function of chip loads, cutting speeds and material imperfections. This paper presents the connection between the sensitivity of the dynamics of regenerative cutting and the cutting force characteristic nonlinearity. The nonlinear milling process is mathematically modelled. The transitions of dynamic cutting process between the stable and unstable zones are considered and experimentally illustrated by applying wavelet transformations on the measurement data.     

Thermal modelling of end milling

Determination of the temperatures during machining is one of the most important challenges for accurate milling simulations. Coupled with excessive shearing, plastic deformation and friction in a small region of cutting, the temperatures in milling may have very significant impact on parts and tools such as dimensional errors, residual stresses and tool wear. Temperature exhibits a non-linear complex-modelling problem in milling process. In this article, for the first time, a novel thermal modelling is introduced for fast and accurate prediction of temperatures in end milling processes. A theoretical modelling approach and experimental validations are presented for various cutting conditions.