Stability Lobe Research Articles

Mechanics and dynamics research considering the tool radial runout effect in plunge milling

The tool radial runout effect in milling process has a significant impact on milling mechanics and dynamics, which increases the difficulty of accurate characterization of milling process. According to the cutter-workpiece contact relationship, the instantaneous chip thickness model considering the tool radial runout effect is established, and the prediction model of plunge milling force is obtained by combining the instant rigidity force model. The dynamical model with three degrees of freedom is established according to the characteristics of plunge milling and the time-varying delay effect caused by tool radial runout. The stability lobe diagram of the plunge milling process is obtained by the improved semi-discrete method. The simulation results are in good agreement with the experimental results, which verify the correctness of the model. The results show that the tool radial runout effect can improve the milling stability in a certain speed range. The effect of the tool radial runout on bifurcation frequency is also studied. It is found that the tool radial runout effect can produce period 1 bifurcation frequency in the milling non-stationary process and double the period 2 bifurcation and Hopf bifurcation frequency. The research results can provide theoretical support for accurate characterization and optimization of process parameters in plunge milling process.

Mechanics and dynamics study of helical milling process for nickel-based superalloy

Helical milling is a new high-quality hole-making process which offers many advantages such as better chip transportation and lower cutting forces and cutting temperature than conventional drilling. This paper presents the mechanics and dynamics of helical milling process for nickel-based superalloy. Firstly, according to the kinematics and undeformed chip geometry of helical milling, a cutting force model which considers the variation of the axial depth of cut, the rounded corner effect, and the helix angle of the cutter is established. Next, on the basis of proposed cutting force model, the dynamic cutting forces of helical milling are calculated, and the stability of the operation is simulated with full-discretization method. Finally the cutting force and chatter stability models are validated by verification tests on a nickel-based superalloy GH4169 workpiece. The results show that the simulated cutting forces and chatter stability lobes agree with the measured data well and it is feasible to replace the conventional drilling with helical milling when machining the nickel-based superalloy.

Experimental study on drilling basalt with self-vibratory drilling head

Based on the goal of improving the rock breaking ability when drilling asteroid rock samples under limited energy conditions, this paper proposes a method of drilling rock using self-vibratory drilling head and develops a small self-vibratory drilling head for drilling rock. In order to analyze the dynamic characteristics of drilling rock with self-vibratory drilling head, a rock model hypothesis that the rock consists of a series of micro-segment uniform continuous media is put forward. Base on the hypothesis, the model of drilling rock is constructed, the stability lobes diagram of self-vibratory drilling head drilling basalt is plotted, and the energy mechanism of drilling rock system with self-vibratory drilling head is discussed. The comparison tests of drilling basalt by three kinds of self-vibratory drilling head with different spring stiffness and the conventional method are carried out. The rotational speed is a variable in the comparative tests. The test results show that under the specific rotational speed and spring stiffness, self-excited vibration is produced in self-vibratory drilling head drilling basalt. When self-excited vibration drilling is conducted, although the amplitude fluctuation range of the drilling thrust force is wider than that of conventional drilling, the average drilling thrust force is smaller than the conventional drilling. The amplitude of drilling thrust force increases with an increase in spring stiffness. The method of drilling rock by self-vibratory drilling head is proved to be a potential method for viable drilling of asteroid rock samples.

Bayesian uncertainty quantification and propagation for prediction of milling stability lobe

To predict the stability boundary of cutting operation, it is necessary to establish process force model and dynamic mechanical behavior model. Uncertainty of model parameters may lead to significant differences between predicted and measured stability boundary. In this paper, a novel method for determining boundary of stability in milling, which performs the stability analysis on an uncertain dynamic milling model, is presented. Firstly, the input parameters of milling stability prediction model are considered as random variables. Subsequently, sensitivity analysis is used to determine the most influential parameters, the posterior distributions of all influential parameters are estimated using a Bayesian inference framework, which is built based on an improved Ensemble Markov Chain Monte Carlo (IGWMCMC) algorithm. Compared with the traditional method, IGWMCMC is not affected by affine transformations of space, which can achieve much better convergence on badly scaled problems and the computational costs are cheaper. Finally, the posterior distributions of uncertainties calculated using Bayesian inference are propagated through the computational model. The experimental results verify the reliability of the calculated boundaries of stability lobe diagrams.

Investigation on chatter stability of robotic rotary ultrasonic milling

In recent years, industrial robots with higher flexibility and lower cost have become a hot topic in the manufacturing field. In terms of practical machining applications, they are mainly employed in the situations with low cutting forces such as deburring, chamfering and polishing. However, the weak stiffness of robot induces milling chatter easily. Severe chatter not only damages the dimensional accuracy of parts, but also decreases machining efficiency and tool life. Thus, it is urgent to seek a new method to suppress robotic milling chatter. In this paper, robotic rotary ultrasonic milling (RRUM) technology is used to restrict machining vibration. Meantime, an analytical model of stability is developed. Robotic milling system is considered as a three degrees of freedom (3-DOF) model. After that, based on analysis of dynamic chip thickness, a linear force model is developed through defining an angle γ affected by ultrasonic vibration. Then, the semi-discretization method (SDM) is applied to obtain stability lobe diagrams. The analysis result indicates that stability region of RRUM is improved by 133% compared with robotic conventional milling (RCM). Finally, verification experiments are carried out to prove the rationality and effectiveness of these stability lobe diagrams.

Adaptive sliding mode control of regenerative chatter and stability improvement in boring manufacturing process with model uncertainties

In the machining processes, vibration suppression is crucial in order to achieve the high precision as well as high-quality surface and increase of the material removal rate. In this paper, an adaptive sliding mode control approach is presented to supress the chattering phenomenon in the boring process in the presence of model uncertainties and unmodeled dynamics. The boring bar is modeled as a cantilever Euler–Bernoulli beam, which is actuated by a piezo-actuator located at the bar's end. As a more realistic model, the cutting tool is modeled as an added mass at the bar's end. In order to derive the equations of motion, mode summation method with inclusion the first three modes of vibration is applied. After formulation of the problem, an adaptive sliding mode control scheme is used and an effective control law is derived, which eliminates the chatter vibration. Moreover, a full state observer is designed to estimate three dominant modes of the boring bar. The simulation results demonstrate the effectiveness of the proposed control strategy against the model uncertainties and unmodeled dynamics. Also, it is observed that adaptive sliding mode control acts effectively in improving the stability lobes diagram. Consequently, after implementation of adaptive sliding mode control, more material removal rate can be obtained without stability loss.

Regenerative chatter control in turning process using constrained viscoelastic vibration absorber

This paper focuses on utilization of viscoelastic material to control regenerative chatter in turning process. Self-induced vibrations can lead to the condition called regenerative chatter which produces violent relative vibrations between cutting tool and workpiece and reduces tool life and productivity. The regenerative chatter in turning processes can be controlled by maximizing negative real part of the frequency response function of cutting tool structure. In order to achieve this, a constrained viscoelastic vibration absorber (CVVA) is used. A CVVA consists of a viscoelastic material, such as natural rubber, which is sandwiched between two similar or dissimilar metallic layers. The CVVA is used as a cantilever beam whose fundamental natural frequency is tuned to the natural frequency of the dominant mode of cutting tool/tool holder. The optimum stiffness and damping coefficient of the CVVA are found using a numerical optimization technique and these optimal values are used to find the dimensions of CVVA. The resulting natural frequency of CVVA is verified using finite element simulation software ANSYS. The effectiveness of CVVA in controlling regenerative chatter in a compact CNC lathe is also analysed by constructing stability lobes which are plots of depth of cut vs spindle speed.

Experimental study of stability prediction for high-speed robotic milling of aluminum

It has been fully demonstrated that the regenerative chatter theory is applicable for predicting chatter-free milling parameters for computer numerical control machine tools, but researchers are still arguing whether it is effective for robotic milling processes. The main reason is that the robot’s modes greatly shift, depending on its varying dynamic parameters and joint configurations. More experimental investigations are required to study and better understand the mechanism of vibration in robotic machining. The present paper is focusing on finding experimental support for chatter-free prediction in robot high-speed milling by the regenerative chatter theory. Modal tests are first conducted on a milling robot and used to predict stability lobes by zeroth order approximation. A number of high-speed slotting tests are then carried out to verify the prediction results. Thus, the regenerative chatter theory is proved to be also applicable to robotic high-speed milling. Furthermore, low-frequency modes of the robot structure are investigated by more modal experiments involving a laser tracker and a displacement sensor. The low-frequency modes are identified as the main part of the prediction error of the zeroth order approximation method, which could also be dominant in low-speed robotic milling processes. In addition, robots are different from computer numerical control machines in terms of stiffness, trajectory following error, forced vibration, and motion coupling. These long-period trend terms have to be carefully taken into account in the regenerative chatter theory for robotic high-speed milling.

Stability analysis in milling process based on updated numerical integration method

Abstract With the purpose of fast and accurately predicting the stable lobes of milling system, an updated numerical integration method (UNIM) is proposed to analyze the stability of delay-differential equation (DDE) established based on milling process. Firstly, the solution of DDE is transformed into integral expression which consists of homogeneous and particular terms. The tooth passing period of milling cutter is divided into two sub-periods, including free and forced vibrations. The state map of free vibration between the end and the beginning of time is established. Secondly, the period of forced vibration is divided into several equal time intervals, and the particular term of solution of DDE is approximated based on Hermite numerical integration within the discrete interval. The map of transition matrix is constructed between the current state and the state before the tooth passing period. The stability is analyzed according to the modulus of eigenvalue of transition matrix. Then, the convergence rate of stability analysis based on the UNIM is compared with that respectively based on the zeroth-order SDM, the first-order SDM, the first-order FDM, the second-order FDM, and numerical integration method. The stable lobes of the single and two DOF milling dynamic models are compared respectively based on UNIM and the second-order FDM. Finally, the milling experiment is carried out to verify the effectiveness of the proposed method, and the results show that the stability analysis based on UNIM has high calculation accuracy and speed.

Milling stability prediction of a hybrid machine tool considering low-frequency dynamic characteristics

Stability lobe diagram (SLD) is an important tool to select the spindle speed and axial cutting depth to avoid chatter vibration. For a parallel or hybrid machine tool, the low-frequency dynamic characteristics have a great impact on the SLD and need to be taken into account. One of the major issues related to dynamics analysis is the effective dynamic model of parallel mechanisms, since the stiffness of passive joints varies at different orientations and the structures of components are complex. This paper presents a method to establish an accurate dynamic model and considers the low-frequency characteristics to predict SLD. In this paper, an approach is put forward to get the stiffness and mass matrices of components with variable cross-sections and a structural dynamic model of the parallel mechanism is developed, which innovatively considers the variable stiffness characteristics of the passive joint under different loads. Based on the structural dynamic model, the frequency response function (FRF) of the moving platform is obtained and the results are validated through comparison with those of the hammer test. Using receptance coupling substructure analysis (RCSA) method, the machine-spindle-holder-tool system is divided reasonably and the FRFs at the tool tip are obtained to predict the SLD. It is shown that the low-frequency dynamic characteristics of hybrid machine tools have a great influence on the stability boundary of machine tools, mainly at the low speed region.

Chatter Investigation on Machining of Gray Cast Iron Considering the Damping Effect

In recent years, the study of chatter vibrations has been intensifying in the machining of materials. In this paper an investigation of this phenomena was conducted for gray cast iron (CGI). The chatter vibrations in machining process can considerably compromise the workpiece surface finish, tool wear and in some cases provide severe damage to the machine-tool. Thus there is an imminent need to expand the theory of chatter vibrations for the class of brittle materials. To analyze the vibrations of the process of machining and zones where the process is stable, and where it is unstable, the stability lobes diagram was used. This diagram is constructed at low speed cutting, where the phenomenon of damping arises. The damping is a crucial factor in the process, it increases system stability. This effect was considered in the formulation of chatter vibrations using the indentation model of Wu. For experimental validations the signals of cutting force were acquired and analysis was conducted in frequency domain to identify where the vibrations emerged allied with a roughness analysis of the workpiece. The results demonstrated perfectly the consequences of chatter vibrations in surface finish of grey cast iron and proved that the stability lobes diagram provides good results to detect these vibrations, determining the areas where the material removal should be avoid.

Efficient active chatter mitigation for boring operation by electromagnetic actuator using optimal fractional order PDλ controller

Abstract Due to the factor of limited rigidity of boring bars, small depths of cutting are normally applied for chatter free machining. Stability lobe diagrams can truly represent that limit. However, due to the presence of manufacturing inaccuracies like ovality and eccentricity, these limits are considerably changed. Hence, considering these during modelling the cutting process, stability analysis and controller design is a novel idea, hence implemented in the present work. Dynamic modelling of boring process is presented in detail using a 3-DOF model. Dynamics of such systems is represented using delay differential equations with time periodic coefficients. The system stability is enhanced with active control techniques. The closed loop system considering fractional order PDλ in the loop is a nonlinear time periodic delay differential equation system. Any systematic controller synthesis process for such systems is rarely available in literature. It is observed that a fractional order PDλ controller designed by using combination of pseudo spectral and response optimization techniques is highly efficient in terms of the requirement of low amplitude of the peak force and simplicity of implementation. Transient vibrations can also be quenched in a limited period of time by using this controller. Different control techniques available in literature (H∞ Loop shaping and PD control) are tested and compared to the proposed controller for enhancing the material removal rates and surface finish of the workpiece. By using the active chatter control, the chatter can be efficiently reduced and the material removal rate can be increased. The critical depth of cut is increased from 0.2 mm (open loop) to 0.6 mm (closed loop) with a limited actuator size in the case study.

Modelling the dynamics of industrial robots for milling operations

Abstract Using industrial robots as machine tools is targeted by many industries for their lower cost and larger workspace. Nevertheless, performance of industrial robots is limited due to their mechanical structure involving rotational joints with a lower stiffness. As a consequence, vibration instabilities, known as chatter, are more likely to appear in industrial robots than in conventional machine tools. Commonly, chatter is avoided by using stability lobe diagrams to determine the stable combinations of axial depth of cut and spindle speed. Although the computation of stability lobes in conventional machine tools is a well-studied subject, developing them in robotic milling is challenging because of the lack of accurate multi-body dynamics models involving joint compliance able of predicting the posture-dependent dynamics of the robot. In this paper, two multi-body dynamics models of articulated industrial robots suitable for machining applications are presented. The link and rotor inertias along with the joint stiffness and damping parameters of the developed models are identified using a combination of multiple-input multiple-output identification approach, computer-aided design model of the robot, and experimental modal analysis. The performance of the developed models in predicting posture-dependent dynamics of a KUKA KR90 R3100 robotic arm is studied experimentally.

Dynamics Modeling-Based Optimization of Process Parameters in Face Milling of Workpieces With Discontinuous Surfaces

AbstractFace milling is widely used in machining processes, aimed at providing workpieces with high surface quality. The chatter generated in face milling could lead to tremendous damage to machine tools, poor machined surface quality, and loss of processing efficiency. Most related researches have been focused on the modeling of spindle dynamics and discretization algorithms for chatter prediction. However, few published articles have taken the geometric characteristics of workpieces into consideration, especially for workpieces with discontinuous surfaces in face milling, which leads to poor accuracy of chatter prediction as well as the waste of processing efficiency. To overcome this shortage, a novel dynamic model for the face milling process is built in this paper, considering the cutting insert engagement based on the geometric characteristics of the workpieces and the tool path. The stability lobe diagrams (SLDs) applicable to workpieces with discontinuous surfaces are constructed. A process parameter optimization model is developed to maximize the chatter-free processing efficiency of the face milling process. The sensitivity analysis is utilized to simplify the objective function, and the genetic algorithm is employed to solve the optimization model. The proposed approach is validated by an experimental case study of an engine block, improving the chatter-free material removal rate by 53.3% in comparison to the classic approach.

Research on Cutting Stability of High-Efficiency Micro Turn-Milling Compound Machine Tool Based on Lobes

In order to improve the cutting stability of high-efficiency micro turn-milling machine tools, avoid the chattering problem during the cutting process. In this paper, the chatter problem in the cutting process is studied based on the stable lobes. By analyzing the high-efficiency turn-milling machine tool mechanism and the turn-milling model, the micro turn-milling dynamic dynamic vibration model and the mathematical model of turn-milling chatter are obtained. Then, based on the hammer test method, the transfer function of the tool-workpiece system is obtained, and the turn-milling stable lobes of the high-efficiency micro turn-milling machine tool is constructed. Finally, the research on the stable zone of the turning main spindle parts, the turning back spindle parts and the high-frequency milling part are completed. The experimental research results guide and optimize the selection of cutting parameters for turn-milling process.

Prediction of Regeneration Chatter Stability of Composite Boring Bar

The deep holes cutting process by metal boring bar is usually limited due to the development of chatter vibration. This is because metal boring bar has not only low bending stiffness but also low structural damping. A chatter stability prediction of composite boring bar under regenerative cutting force is presented. Based on the theory of Euler-Bernoulli beam, the regenerative chatter dynamic model of composite boring bar is proposed, and the solution formula of the limited cutting depth and corresponding spindle speed is given. The dynamic stability lobes of the composite boring bar are obtained by numerical calculation. The results indicate that composite boring bar exhibits efficient chatter stability than metal boring bar. Chatter stability is closely related to fiber ply angle. It is demonstrated that when ply angle is 0o, carbon/ epoxy reaches its critical cutting depth, and for graphite/ epoxy boring bar about 25o of ply angle gives its critical cutting depth, It is also demonstrated that stability boundary decreases as the ratio length and diameter increases. Finally, the prediction results of stability are compared with those from the dynamic stiffness and time-domain response, agreement is found.

Vibration analysis of milling process with helix-angle cutter based on Euler method

The chatter vibration is the major limiting factor in increasing the metal removal rates of the machine tools. In this paper, a program for dynamic analysis of thin-walled milling process with helical milling cutter is developed, based on Euler iteration. The program can take into account the characteristics of thin-walled workpiece, the contact separation between workpiece and cutter, the helical angle of cutter teeth and other actual cutting process characteristics. Based on the stability lobe diagram obtained by semi-discrete method, the stability simulation in different cutting parameters around the stable island was carried out. The unstable form of the cutting process was determined by spectrum analysis and Poincare mapping method. The results show that the method is in good agreement with the results of stability Lobe diagram and can capture the stability island in small radial cutting process. This method can well grasp the cutting force and vibration evolution process in cutting process, and provide an effective means for stability analysis of cutting process.

Characteristics of Chatter Stability Lobe in 2-DOF Machining System

A chatter lobe analysis is frequently used to look at the chatter state [1-4]. Even if there is a lot of research on chatter, chatter lobe characteristics are not well defined. In this study, the chatter lobe behavior according to several variables of vibration mode is verified for further clarity. The dynamic variables of the chatter model are defined and their behaviors on chatter lobe boundary are analyzed in detail. In this sense, the chatter model with 2-DOF (2-DOF) was used to analyze chatter stability characteristics [4]. The discussed results are satisfying and these can be used for the prediction of chatter existence in machining processes of 2-DOF systems in several revolution range. These analyses indicate a better agreement for predicting an appropriate stability lobe over a wide detailed range of critical depths of cut in machining operation. The results allow an excellent prediction of chatter according to various static and dynamic variables in machining states. The behavior of chatter dynamic variables in machining were also discussed in detail. All these results can also be applied to other machining processes by establishing a chatter model in a 2-DOF system.

An improved semi-analytical approach for modeling of process damping in orthogonal cutting considering cutting edge radius

Process damping generated between the tool flank face and the wavy finish workpiece surface has a non-negligible effect on cutting dynamics and chatter stability, especially at low cutting speeds, resulting in higher stability limits. In modeling of process damping, the calculation of extruded volume is one of the most critical challenges, especially in machining with honed tools due to the complex and time-variable contact condition between the arc cutting edge and the finite amplitude wave surface. In this study, a semi-analytical method with high computational efficiency is proposed to calculate the extruded volume in cutting with honed tools. Based on this method, we construct the stability lobes under the condition of finite vibration amplitude accurately and efficiently, which overcomes the limitation of analytical methods based on the assumption of small amplitude vibrations and the low computational efficiency of numerical method. The predicted cutting stability is verified against both the experimental results and the time-domain simulation results.

Influence of cutting parameters on force coefficients and stability in plunge milling

Fixed dynamometer is often used to collect cutting force data in plunge milling. The cutting force test signal is distorted because of the dynamic characteristics of the test system consisting of the workpiece and the dynamometer. Then the accuracy of cutting force coefficients based on experimental data analysis is affected. The inverse filtering technique is utilized to compensate for the measurement signal dynamically and verified by experiments. The influence of cutting parameters on cutting force coefficients is investigated by means of the nonlinear instantaneous milling force method. The results demonstrate that the cutting force coefficient has a nonlinear relationship with the feed per tooth and the spindle speed. An improved semi-discrete method is proposed for the machining feature of the plunge milling and utilized to predict the stability of the plunge milling. The measurement signal is analyzed by using the nonlinear method such as phase plane and Poincare section; the accuracy of the prediction of the stability lobe diagram is verified. The results demonstrate that the stability boundary of instantaneous cutting force coefficients is higher than that of the average cutting force coefficients. The research results provide theoretical guidance for the optimization of cutting parameters in the actual machining process.