Surface roughness variation of thin wall milling, related to modal interactions

High-speed milling operations of thin walls are often limited by the so-called regenerative effect that causes poor surface finish. The aim of this paper is to examine the link between chatter instability and surface roughness evolution for thin wall milling. Firstly, the linear stability lobes theory for the thin wall milling optimisation was used. Then, in order to consider the modal interactions, an explicit numerical model was developed. The resulting nonlinear system of delay differential equations is solved by numerical integration. The model takes into account the coupling mode, the modal shape, the fact that the tool may leave the cut and the ploughing effect. Dedicated experiments are carried out in order to confirm this modelling. This paper presents surface roughness and chatter frequency measurements. The stability lobes are validated by thin wall milling. Finally, the modal behaviour and the mode coupling give a new interpretation of the complex surface finish deterioration often observed during thin wall milling.     

Providing stability maps for milling operations

This article presents a new stability prediction tool. The method is based on the dynamic behaviour of both milling tool and workpiece, computed using finite element method. Dynamic behaviour is expressed under the form of transfer functions and used to predict stability lobes at each tool position. The unconditionally stable depth of cut is then stored and displayed on a graphic representation of the machined surface under the form of colour axis, named stability map.An application of the method on a Renault cylinder block is presented as an illustration.     

RCPM—A new method for robust chatter prediction in milling

The reliability of conventional chatter prediction algorithms is limited by the inaccuracy of machining system dynamic models. In this paper, a new probabilistic algorithm for a robust analysis of stability in milling, which performs the stability analysis on an uncertain dynamic milling model, is presented. In this approach, model parameters are considered as random variables, and robust analysis of stability is carried out in order to estimate system's probability of instability for a given combination of cutting parameters. By doing so, probabilistic instead of deterministic stability lobes are obtained, and a new criterion for system stability based on level curves and gradient of the probabilistic lobes can be applied to identify optimal robust stable cutting conditions. Experimental validation consisted of different phases: firstly, machining system dynamics were estimated by means of pulse tests. Secondly, cutting force coefficients were determined by performing cutting tests. Eventually, chatter tests were performed and the experimental stability lobes were compared with the predicted robust stable regions.     

Chatter avoidance in the milling of thin floors with bull-nose end mills: Model and stability diagrams

The milling of thin parts is a high added value operation where the machinist has to face the chatter problem. The study of the stability of these operations is a complex task due to the changing modal parameters as the part loses mass during the machining and the complex shape of the tools that are used. The present work proposes a methodology for chatter avoidance in the milling of flexible thin floors with a bull-nose end mill. First, a stability model for the milling of compliant systems in the tool axis direction with bull-nose end mills is presented. The contribution is the averaging method used to be able to use a linear model to predict the stability of the operation. Then, the procedure for the calculation of stability diagrams for the milling of thin floors is presented. The method is based on the estimation of the modal parameters of the part and the corresponding stability lobes during the machining. As in thin floor milling the depth of cut is already defined by the floor thickness previous to milling, the use of stability diagrams that relate the tool position along the tool-path with the spindle speed is proposed. Hence, the sequence of spindle speeds that the tool must have during the milling can be selected. Finally, this methodology has been validated by means of experimental tests.     

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.     

Chatter milling modeling of active magnetic bearing spindle in high-speed domain

A new dynamical modeling of Active Magnetic Bearing Spindle (AMBS) to identify machining stability of High Speed Milling (HSM) is presented. This original modeling includes all the minimum required parameters for stability analysis of AMBS machining. The stability diagram generated with this new model is compared to classical stability lobes theory. Thus, behavior's specificities are highlighted, especially the major importance of forced vibrations for AMBS. Then a sensitivity study shows impacts of several parameters of the controller. For example, gain adjustment shows improvements on stability. Side milling ramp test is used to quickly evaluate the stability. Finally, the simulation results are then validated by HSM cutting tests on a 5 axis machining center with AMBS.     

Investigation of surface integrity in high speed end milling of a low alloyed steel

Understanding the effects of cutting speed, feed rate and cutting depth on surface integrity is very important for the control of workpiece quality. This paper presents a global experimental study of surface integrity in the case of high speed end milling. In the global term, we include measurements of residual stresses, surface roughness and cutting forces. Our observations and conclusions are mainly concentrated on the effect of depth of cut with a set of constant parameters, such as cutting speed, feed rate, and tool/material couple. This set of constants has been determined using the theory of stability lobes. All experiments have been performed with an electro-spindle equipped with magnetic bearings. The results lead to a good understanding of the influence of cutting conditions on surface integrity in high speed milling of a low alloyed steel. The discussion examines a specific point where the residual stress and residual stress gradient are lowest and also the origin of the residual stress value.     

Modeling and simulation of milling processes including process damping effects

Especially in high speed milling of aluminum alloys in the aviation industry, chamfered milling tools have proven themselves. Due to the chamfer, an extended contact between the tool and the workpiece at the flank face is evoked, which leads to additional process damping forces opposed to tool vibrations. Hence, the cutting process shows improved stability characteristics. This article presents an approach for the identification and modeling of these process damping effects in transient milling simulations. For this purpose, a simulation- and experiment-based procedure for the identification of required simulation parameters depending on the tool chamfer geometry is introduced and evaluated. Finally, the identified parameters are used for transient simulations of milling processes with extended stability due to the tool chamfer. The suitability of the proposed identification method and simulation model for milling with process damping is finally proved by a comparison between simulations and experiments.     

Continuous model for analytical prediction of chatter in milling

A novel analytical approach for prediction of chatter in milling process is presented. Existing approaches use lumped-parameter models to define the dynamics of tools/workpieces. In this paper a continuous beam model is employed for prediction of milling operations dynamics. The tool boundary conditions are elastic support at the tool/holder/spindle interface and free support at the other end. Employing the continuous model eliminates the need for tool tip frequency response function (FRF) measurements in tool-tuning practice, especially in micro-milling, where FRF measurement is practically very difficult. Tool/holder/spindle interface parameters, once identified, can be used for other tool lengths. The impact hammer test is used to identify stiffness and damping parameters of the tool/holder/spindle interface. Using the new analytical approach and picking single-frequency solution (SFS), stability lobes are obtained for a slotting operation. The resulting lobes are compared to those obtained by the well-proven lumped-parameter model. In addition to a good general agreement between the two approaches, the continuous model prediction is more conservative for critical depth of cut, which is attributed to its ability to consider all participating modes in the response and so represents a more accurate representation of the system.     

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.     

Lightweight semi-actively damped high performance milling tool

Long cantilevered high performance milling tools tend to vibrate during machining operation due to process excitation. This impairs the quality of the workpiece surface and limits the achievable material removal rate. An optimisation of the dynamic properties of these tools enables an increased machining performance. This paper introduces a lightweight design of a shell end milling tool with an integrated semi-active damping system based on magnetorheological fluids. The investigations show that this approach allows an adjustment of the dynamic behaviour of the tool. In machining experiments a significant increase of the material removal rates and improved surface quality are achieved.     

On the dynamics of ball end milling: modeling of cutting forces and stability analysis

This paper presents a dynamic force model and a stability analysis for ball end milling. The concept of the equivalent orthogonal cutting conditions, applied to modeling of the mechanics of ball end milling, is extended to include the dynamics of cutting forces. The tool is divided into very thin slices and the cutting force applied to each slice is calculated and summed for all the teeth engaged. To calculate the instantaneous chip thickness of each tooth slice, the method of regenerative chip load calculation which accounts for the effects of both the surface undulations and the instantaneous deflection is used. To include the effect of the interference of the flank face of the tool with the finished surface of the work, the plowing force is also considered in the developed model. Experimental cutting forces are obtained using a five-axis milling machine with a rotary dynamometer. The developed dynamic model is capable of generating force and torque patterns with very good agreement with the experimental data. Stability of the ball end milling in the semi-finishing operation of die cavities is also studied in this paper. The tangential and radial forces predicted by the method of equivalent orthogonal condition are fitted by the equations F_t = K_t(Z)bh_av and F_r = K_r(Z)F_t, where b is the depth of cut and h_av is the average chip thickness along the cutting edge and Z is the tool axis coordinate. The polynomial functions K_t(Z) and K_r(Z) are the cutting force constants. The interdependency of the axial and radial depths of cut in ball end milling results in an iterative solution of the characteristic equation for the critical width of cut and spindle speed. In addition, due to different cutting characteristics of the cutting edge at different heights of the ball nose, stability lobes are represented by surfaces. Comparison of the time domain simulation for the shoulder removal process in die cavity machining with the analytical predictions shows that the proposed method is capable of accurate prediction of the stability lobes.     

Modeling the machining stability of a vertical milling machine under the influence of the preloaded linear guide

The prediction of machining stability is of great importance for the design of a machine tool capable of high-precision and high-speed machining. The machining performance is determined by the frequency characteristics of the machine tool structure and the dynamics of the cutting process, and can be expressed in terms of a stability lobe diagram. The aim of this study is to develop a finite element model to evaluate the dynamic characteristics and machining stability of a vertical milling system. Rolling interfaces with a contact stiffness defined by Hertz theory were used to couple the linear components and the machine structures in the finite element model. Using the model, the vibration mode that had a dominant influence on the dynamic stiffness and the machining stability was determined. The results of the finite element simulations reveal that linear guides with different preloads greatly affect the dynamic behavior and milling stability of the vertical column spindle head system. These results were validated by performing vibration and machining tests. We conclude that the proposed model can be used to accurately evaluate the dynamic performance of machine tool systems designed with various configurations and with different linear rolling components.     

Active vibration control in palletised workholding system for milling

This paper presents the development implementation and testing of an active controlled palletised workholding system for milling operations. The traditional approach to controlling vibration in a machining system is to develop control systems for cutting tools or machine spindles as in the case of milling machines. This work is a deviation from the traditional approach and targets a workholding system for the control of unwanted vibration. Palletised workholding systems, due to their compact design, offer an opportunity to design active control systems that are economical and easier to implement in the case of milling machines. The active control system developed here is based on an adaptive filtering algorithm, the filtered X-LMS, and employs piezo-actuators for dynamic control force. The system has been tested experimentally to demonstrate the reduction in dynamic force due to vibration. Extensive testing has been carried out to validate the performance of the system in terms of parameters of practical importance such as improvement in surface finish and increase in tool life.     

Surface shape prediction in high speed milling

Chatter is one of the main causes affecting the surface quality of machined parts. Since it occurs when a machining process is unstable, it is important to select process parameters that promote stability. However, this condition alone is not sufficient to ensure good surface shape because the dynamics of the machining system as a whole also affects the resulting surface. Thus, even in the absence of chatter, significant movement of the tool or the part may occur causing surface defects. This effect is significant in high speed milling. In order to select optimal machining parameters, a computationally efficient simulator has been developed based on a novel machined surface generation model capable of accurate and reliable prediction of the surface shape. The programme written in MATLAB^® predicts the surface shape from which surface finish, waviness, form and position parameters can be determined. A test bench consisting of a relatively low frequency second order dynamic mode is used to hold a test sample. The results obtained on a machining centre show that the predictions favourably compare with experimental results.     

Dynamic response analysis in end milling using pre-twisted beam finite elements

This paper develops an analytical model for estimating the dynamic responses in end milling, i.e. dynamic milling cutter deflections and cutting forces, by using the finite-element method along with an adequate end milling-cutting force model. The whole cutting system includes the spindle, the bearings and the cutter. The spindle is modelled structurally with the Timoshenko-beam element, the milling cutter with the pre-twisted Timoshenko-beam element due to its special geometry, and the bearings with lumped springs and dampers. Because the damping matrix in the resulting finite-element equation of motion for the whole cutting system is not one of proportional damping due to the presence of bearing damping, the state-vector approach and the convolution integral is used to find the solution of the equation of motion. To assure the accuracy of prediction of the dynamic response, the associated cutting force model should be sufficiently precise. Since the dynamic cutting force is proportional to the chip thickness, a quite accurate alogorithm for the calculation of the variation of the chip thickness due to geometry, run-out and spindle-tool viration is developed. A number of dynamic cutting forces and tool deflections obtained from the present model for various cutting conditions are compared with the experimental and analytical results available in the literature, good agreement being demonstrated for these comparisons. The present model is useful, therefore, for the prediction of end milling instability. Also, the tool deflections obtained using the pre-twisted beam element are found to be smaller than those obtained using the straight beam element without pre-twist angle. Hence neglecting the pre-twist angle in the structural model of the milling cutter may overestimate the tool deflections.     

Tool deflection compensation in peripheral milling of curved geometries

This paper presents compensation of surface error due to cutting force-induced tool deflections in a peripheral milling process. Previous research attempts on this topic deal with error compensation in machining of straight geometries only. This paper is concerned with peripheral milling of variable curvature geometries where the workpiece curvature changes continuously along the path of cut. In the case of curved geometries, both process geometry and the cutting forces have shown to have strong dependence on workpiece curvature and hence variation of surface error along the path of cut. This calls for a different error compensation strategy than the one which is normally used for machining straight geometries. The present work is an attempt to improve accuracy in machining of curved geometries by use of CNC tool path compensation. Mechanistic model for cutting force estimation and cantilever beam model for cutter deflection estimation are used. The results based on machining experiments performed on a variety of geometries show that the dimensional accuracy can be improved significantly in peripheral milling of curved geometries.     

The effect of tool vibrations on the flank surface created by peripheral milling

Tool vibrations have a significant influence on the surface quality with respect to surface location error and roughness. Even chatter-free milling processes can produce a high surface location error since chatter-free does not necessarily mean vibration-free. This article describes a geometric model for predicting the surface formation resulting from peripheral milling processes when tool vibrations are present. This model enables one to predict and minimize the roughness and location error of the flank surface. Comparisons between simulations and experiments show the effectiveness of this modeling approach. An important result of this research is that it has shown that milling at a stability maximum does not generally yield the best surface quality.     

Analytical and experimental investigations on thread milling forces in titanium alloy

This study deals with the thread milling process that is considered a complex machining technique due to its elaborated tool geometry and its tridimensional tool trajectory. It needed advanced research on the threading process which has not been much studied. Previous studies focused on geometrical modeling or mechanistic modeling of the thread milling process. There is a need for a better understanding of parameter effects to accomplish a model that tends to be more realistic and includes local parameters. This investigation does the analysis of thread milling parameters: thread geometry, cutting conditions and tool angles, which can be applied to the tool optimization. The cutting forces and torque were measured and representative values of its variation were calculated and analyzed as response of the experiments. A geometrical analysis and an analysis of variance were employed for determining the influence of the factors and based on the results, it is proposed a physical understanding of the process.     

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.