Unstable Self-excited Vibrations Research Articles

Nonlinear dynamics of asymmetrically supported supercritical rotor equipped with a dry friction damper

To suppress the excessive transcritical vibration of a supercritical rotor, dry friction damper is a popular choice especially in rotorcraft and aero-engine design. In the current work, we focus on the nonlinear dynamics of asymmetrically supported supercritical rotor equipped with a dry friction damper and the influence of support asymmetry on damper’s performance. Governing equations of the rotor/damper system, which fully consider the nonlinear rub-impact and side dry friction effects, are derived. Typical results of symmetrically supported rotor/damper systems are firstly demonstrated and quantitatively compared with experimental counterparts to confirm the predicting capability of the nonlinear dry friction damper model. Afterward, influences of asymmetric direct stiffness and skew-symmetric cross-coupling stiffness are discussed. It is found that direct stiffness asymmetry deteriorates the transcritical vibration attenuation capability of the damper but reduces the width of transcritical region. For system with a severer direct stiffness asymmetry, a larger pre-tightening force is suggested to be imposed. Besides, unstable self-excited vibration induced by skew-symmetric cross-coupling stiffness is found to be well-limited by the dry friction damper within entire interested rotational speed range. Moreover, during critical speed transition, the self-excited frequency component is completely suppressed.

Numerical Investigation on Torsional Mode Self-Excited Vibration of Guide Vane in a Reversible Pump-Turbine during Pump Mode’s Starting Up

In reversible pump-turbines, guide vane vibrations are considered to have potentially severe consequences of noise and structural damage. Unstable torsional mode self-excited vibrations of guide vanes have been reported at small guide vane openings during transient operations involving pump flow, such as pump starting and closing processes. In this study, coupling simulations were carried out under different operating conditions based on the unsteady computational fluid dynamics (CFD) method with a single-degree-of-freedom (1DOF) oscillator. The results show that the operating conditions, including the initial opening angle and the pressure difference between the runner side and the stay vane side, significantly affect the instability of guide vane torsional mode self-excited vibration. Energy-based analysis indicates that the positive cumulative work done by total hydraulic torque is responsible for unstable torsional mode self-excited vibration. Furthermore, the relatively small phase difference between total hydraulic torque and guide vane angular velocity, and the positive feedback between vibration amplitude and energy accumulation, are considered to be the root causes that eventually induce unstable self-excited vibrations under the operating conditions of small opening angles and high pressure differences.

Analysis of Rail Corrugation Characteristics on High-Speed Rail Based on Transient Finite Element Method

By using the transient finite element method, a three-dimensional wheelset-track coupled rolling contact model for high-speed rail is established, and the rationality and effectiveness of the model are verified by field measurements. Next, the wheel-rail contact stress states and relative slip characteristics are calculated and analyzed to reveal the cause of inner rail corrugation. Then, the vertical vibration acceleration of the rail/wheel is taken as the output variable to study the dynamic responses of the wheelset-track system. Finally, the parameter sensitivity analysis is carried out. The results show that the maximum normal/tangential contact stress between the inner wheel and inner rail is greater than that between outer wheel and outer rail due to the unbalanced load of inner rail caused by the excess superelevation of track structure, which indicates that the unbalanced load of the inner rail may aggravate the development of rail wear, and the rationality of the model established in this paper is verified. The wheel-rail relative slip region on the inner rail side appears periodically, and the distance between the two adjacent slip regions is close to the characteristic wavelength of the measured inner rail corrugation, which illustrates that the periodic variation of slip regions on the inner rail surface plays an important role in the formation of rail corrugation, and the validity of the model is verified. The periodic distribution of wheel-rail relative slip regions on the outer rail surface is not obvious, demonstrating that the outer rail tends to form uniform wear, which is consistent with the fact that the outer rail corrugation is slight in the measured section. The wheelset-track system has been in the process of unstable continuous oscillation in the analysis interval, combined with the analysis results of the wheel-rail relative slip characteristics, it can be concluded that the unstable self-excited vibration of wheelset-track system under the condition of tangential contact force reaching saturation is the main cause of rail corrugation. The dominant characteristic frequencies of vertical vibration accelerations of rail and wheel are all 561 Hz, the corresponding characteristic wavelength (148 mm) is close to the distance (150 mm) between the calculated adjacent slip regions, and is also close to the characteristic wavelengths (125 mm and 160 mm) of inner rail corrugation, which shows that the resonance phenomenon occurs in the wheelset-track system at the above frequency, thus leading to the increase of dynamic responses of wheelset-track system. The fastener vertical stiffness and wheel-rail coefficient of friction have significant effect on the development of rail corrugation, and the running speed determines the occurrence probability of inner/outer rail corrugation by affecting the track superelevation state.

Intelligent chatter detection for CNC machine based on RFE multi-feature selection strategy

Chatter is an unstable self-excited vibration generated during processing. It not only reduces the machining efficiency, machining accuracy, the service life of machine tools and cutting tools, but also results in sound pollution and material waste. To improve the machining stability and product quality of thin-walled workpieces, effective chatter detection of machine tools is essential. This paper presented a signal feature evaluation model and multi-feature recognition system for chatter detection. First, the original signals obtained from the acceleration sensor were processed through local mean decomposition to reduce the noise in the signal. Thereafter, the correlation between the system state and the different features of amplitude domain, frequency domain and nonlinear domain was analyzed. Further, through the feature evaluation model based on recursive feature elimination, the main feature parameters related to machine tool state are obtained, and different recognition algorithms were used to verify the rationality of the fusion features. Finally, an end-to-end chatter detection method and the corresponding software system have been established. Experimental results show that the proposed method can effectively improve the accuracy of vibration detection.

Validation of variable helix milling instability islands

During machining, it is well-known that unstable self-excited vibrations known as regenerative chatter can limit productivity. There has been a great deal of research that has sought to understand regenerative chatter, and to avoid it through modifications to the machining process. One promising approach is the use of variable helix tools. Here, the time delay between successive tooth passes is intentionally modified, in order to improve the boundary of instability. Previous research has predicted that such tools can offer significant performance improvements whereby islands of instability occur in the stability lobe diagram. By avoiding these islands, it is possible to avoid regenerative chatter, at depths of cut that are orders of magnitude higher than for traditional tools. However, to the authors’ knowledge, these predictions have not been experimentally validated, and there is limited understanding of the parameters that can give rise to these improvements. The present study seeks to address this shortfall. A recent approach to analysing regenerative chatter stability is modified, and its numerical convergence is shown to outperform alternative methods. It is then shown that islands of instability only emerge at relatively high levels of structural damping, and that they are particularly susceptible to model convergence effects. The model predictions are validated against detailed experimental data that uses a specially designed configuration to minimise experimental error. To the authors’ knowledge, this provides the first experimentally validated study of unstable islands in variable helix milling, whilst also demonstrating the importance of structural damping and numerical convergence on the prediction accuracy.

Adaptive self-excited vibrations suppression during milling

The problem of the occurrence and rapid suppression of unstable self-excited vibrations arising in the process of milling is considered. It is assumed that tool (cutter) is connected with machine overarm by an elastic suspension, which is used for force sensation. The tool moves evenly along the work surface with a given pressure on it. Pressing of the cutter provides the necessary axial depth of cut. Uniform movement along the work surface provides the required tool feed. Unstable self-excited vibrations or chattering is a deterrent to increase productivity. In this paper we consider the possibility of promptly detecting the onset of unstable auto-oscillations from the amplitude spectrum of the sensor readings of the horizontal forces of interaction between the instrument and the working surface. The amplitude spectrum is obtained using the fast Fourier transform, which allows to determine the beginning of unstable processes in system. Timely change of the axial depth of cut allows to transfer the milling process into the stable zone.

Simulation of chatter in plunge grinding process with structural and cutting force nonlinearities

Prevention of regenerative chatter vibration is one of the most important issues for improving grinding quality. Chatter vibration is an unstable self-excited vibration that the regenerative chatter is its most common type. In this paper, regenerative chatter in plunge grinding process is investigated. A new 3-D nonlinear dynamic model of the plunge grinding process including both structural and cutting force nonlinearities and gyroscopic effects is proposed. The workpiece is modeled as a rotating simply supported beam, which is excited by the wheel. The grinding wheel is regarded as a 1-degree-of-freedom (DOF) spring–mass–damper system moving along the workpiece with constant speed and has a constant rotational speed. Using the method of multiple scales, analytical approximate response of the system is obtained. Using this model, the influences of the angular velocity of workpiece and wheel and the feed velocity on the stability of the grinding process are studied and stability diagram is plotted in the space of these parameters. The results show that with an increase in rotational period of the workpiece, feed velocity for stability of the process decreases.

Analytical solution for nonlinear oscillation of workpiece in turning process

Chatter phenomenon is one of the essential problems in metal machining processes. It causes cutting tool wear and increase of production costs. Chatter vibration is an unstable self-excited vibration that the regenerative chatter is its most common type. In this paper, regenerative chatter in turning process is investigated. A three-dimensional nonlinear dynamic model of the turning process including both structural and cutting force nonlinearities and gyroscopic effects is presented. The workpiece is modeled as a rotating clamped–free beam which is excited by cutting forces. Using the method of multiple-scales, analytical approximate response of the system is obtained. To validate the model its responses are compared with the experimental results. Using this model the influences of tool longitudinal position, workpiece diameter, depth of cut, and rotational speed of workpiece on the stability results are studied. Using these results, turning velocity intervals for stable and unstable cuts are determined.

Investigation into rail corrugation in high-speed railway tracks from the viewpoint of the frictional self-excited vibration of a wheel–rail system

A finite element vibration model of a multiple wheel–rail system which consists of four wheels, one rail, and a series of sleepers is established to address the problem of rail corrugation in high-speed tracks. In the model, the creep forces between the wheels and rail are considered to be saturated and equal to the normal contact forces times the friction coefficient. The oscillation of the rail is coupled with that of wheels in the action of the saturated creep forces. When the coupling is strong, self-excited oscillation of the wheel–rail system occurs. The self-excited vibration propensity of the model is analyzed using the complex eigenvalue method. Results show that there are strong propensities of unstable self-excited vibrations whose frequencies are less than 1,200 Hz under some conditions. Preventing wheels from slipping on rails is an effective method for suppressing rail corrugation in high-speed tracks.

Wind tunnel experiments on unstable self-excited vibration of sectional girders

In this paper, a wind tunnel analysis of two degrees-of-freedom system represented by sectional girders is carried out. Besides an evaluation of the aeroelastic coefficients, the analysis is focused on the influence of the natural frequency ratio on the initiation of unstable vibration, which can be of practical interest. On the phenomenological level, the paper also discusses experimentally ascertained response regimes, with an emphasis on their stability character. The attention is paid to the memory effect in the response described by the hysteresis loop together with the separation curves determining the stability boundaries. The influence of initial disturbance on the stability is examined. Two types of cross-sections were investigated: (i) rectangular one with the aspect ratio 1:5, and (ii) bridge-like cross-section with comparable principal dimensions. For both types of cross-sections, the limits of the stability are significantly affected by an intentionally introduced initial disturbance. This holds especially with regard to the rectangular profile where the separation curves create very narrow sub-domains between a stable and an unstable response, while the bridge-like cross-section demonstrates much stable behaviour.

English

Milling is one of the most common manufacturing processes for automotive components, but its productivity is limited by the onset of regenerative chatter. This is a form of unstable self-excited vibration that occurs when the volume of material removed is too large for a particular spindle speed. This form of chatter is undesirable because it results in premature tool wear, poor surface finish on the machined component and the possibility of serious damage to the machine itself. The chatter stability of a milling process can be determined using well-established theory, provided that the frequency response of the flexible structure can be determined. In practice this usually involves the excitation of a stationery (non-rotating) milling tool with a modal hammer, and measurement of the response of the tool with a co-located accelerometer. However, this measurement is not necessarily accurate due to amplitude dependency factor consideration. There is anecdotal evidence that structural nonlinearity can have a significant effect on the chatter stability of some milling machines. This project develops non-contact electromagnetic actuators to measure the frequency response of milling tools to machine automotive parts. In addition it will describe the practical application of this approach, and discuss its amplitude dependency for current excitation during frequency response function measurement using magnetic force generation.

Hopf bifurcation for delay differential equation with application to machine tool chatter

In the machining process, unstable self-excited vibrations known as regenerative chatter can occur, causing excessive tool wear or failure, and a poor surface finish on the machined workpiece, hence the relevant measures must be taken to predict and avoid this phenomenon of instability. In this paper, we propose a weakly nonlinear model with square and cubic terms in both structural stiffness and regenerative terms, to represent self-excited vibrations in machining. It is proved that Hopf bifurcation exists when bifurcation parameter equals a critical value, a formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are given by using the normal form method and center manifold theorem. Numerical simulations show excellent agreement with the theoretical results.

The influence of feed rate on process damping in milling: modelling and experiments

The performance of milling operations is limited by the onset of unstable self-excited vibrations known as regenerative chatter. Over the past few decades there has been a great deal of research to help predict and explain regenerative chatter. Consequently, high-speed milling operations are now frequently employed, with judicious choice of spindle speeds and depths of cut so as to avoid chatter whilst maintaining high productivity. However, many materials that are increasingly used in aerospace components are difficult to machine at high spindle speeds because of their thermal properties. Examples include titanium and nickel alloys. For these materials, low-speed machining must be employed, and in this regime the role of regenerative chatter is less clearly understood due to the phenomenon of process damping. In the present study, a time domain model of process damping is developed. This model is used to explore the relationship between cutting conditions and the amplitude of chatter vibrations. A qualitative agreement is found between experimental behaviour and the numerical model. In particular, the model predicts a strong relationship between the workpiece feed rate (expressed as a feed per tooth), and the acceptable chatter stability defined by the process damping wavelength. Further work is needed to properly calibrate some of the model parameters.

Fuzzy stability analysis of regenerative chatter in milling

During machining, unstable self-excited vibrations known as regenerative chatter can occur, causing excessive tool wear or failure, and a poor surface finish on the machined workpiece. Consequently it is desirable to predict, and hence avoid the onset of this instability. Regenerative chatter is a function of empirical cutting coefficients, and the structural dynamics of the machine-tool system. There can be significant uncertainties in the underlying parameters, so the predicted stability limits do not necessarily agree with those found in practice. In the present study, fuzzy arithmetic techniques are applied to the chatter stability problem. It is first shown that techniques based upon interval arithmetic are not suitable for this problem due to the issue of recursiveness. An implementation of fuzzy arithmetic is then developed based upon the work of Hanss and Klimke. The arithmetic is then applied to two techniques for predicting milling chatter stability: the classical approach of Altintas, and the time-finite element method of Mann. It is shown that for some cases careful programming can reduce the computational effort to acceptable levels. The problem of milling chatter uncertainty is then considered within the framework of Ben-Haim's information-gap theory. It is shown that the presented approach can be used to solve process design problems with robustness to the uncertain parameters. The fuzzy stability bounds are then compared to previously published data, to investigate how uncertainty propagation techniques can offer more insight into the accuracy of chatter predictions.

Estimates of the bistable region in metal cutting

The classical model of regenerative vibration is investigated with new kinds of nonlinear cutting force characteristics. The standard nonlinear characteristics are subjected to a critical review from the nonlinear dynamics viewpoint based on the experimental results available in the literature. The proposed nonlinear model includes finite derivatives at zero chip thickness and has an essential inflexion point. In the case of the one degree-of-freedom model of orthogonal cutting, the existence of unstable self-excited vibrations is proven along the stability limits, which is strongly related to the force characteristic at its inflexion point. An analytical estimate is given for a certain area below the stability limit where stable stationary cutting and a chaotic attractor coexist. It is shown how this domain of bistability depends on the theoretical chip thickness. The comparison of these results with the experimental observations and also with the subcriticalHopf bifurcationresults obtained for standard nonlinear cutting force characteristics provides relevant information on the nature of the cutting force nonlinearity.

Experimental Study on Self-Excited Vibration Characteristics of a Flexible Weir due to Fluid Discharge.

This paper deals with the characteristics of unstable self-excited vibrations of a rectangular, flexible weir installed in a tank, over which water in the upstream tank discharges into the down-stream one. Experiments were carried out for measuring the vibrational strains of the weir, and the oscillation of the water surface in the up-stream tank with changing inlet velocity of water and discharge height. We examined the vibration characteristics of the weir with changing tank ratio (defined as the down stream tank length/the upstream tank length), and found that the occurrence of unstable vibration depends strongly on the tank ratio. The phase relations of the weir vibration to the upstream tank water oscillation were experimentally investigated.

Experimental Study of Self-Excited Vibrations of a Flexible Weir due to Fluid Discharge

This paper deals with the characteristics of unstable self-excited vibrations of a rectangular, flexible weir installed between two tanks, over which the water in the upper tank discharges into the lower one. Experiments were done for measuring vibrational strains of the weir, oscillation of the overflow water thickness, and the oscillations of the water surface in the upper and lower tanks with changing inlet velocity of water into the upper tank and water discharge height. Four unstable vibration modes were found in our experiments. The 1st unstable vibration mode was sloshing-dominated weir vibration and its vibration frequency was almost equal to the sloshing one for the lower tank. The 2nd one was a high frequency vibration of the weir unrelated to the sloshing oscillation and the 3rd one was a torsional one of the weir with a high frequency different from the 2nd one. The 4th mode was peculiar to the experimental system due mostly to the coupling between the inlet water jet and the weir The phase relations between the weir vibration and overflow water thickness were experimentally investigated.