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.     

Dynamics of regenerative chatter and internal resonance in milling process with structural and cutting force nonlinearities

In this paper, internal resonance and nonlinear dynamics of regenerative chatter in milling process is investigated. An extended dynamic model of the peripheral milling process including both structural and cutting force nonlinearities is presented. Closed form expressions for the nonlinear cutting forces are derived through their Fourier series components. In the presence of the large vibration amplitudes, the loss of contact effect is included in this model. Using the multiple-scales approach, analytical approximate response of the delayed nonlinear system is obtained. Considering the internal resonance dynamics (i.e. mode coupling), the energy transfer between the coupled x–y modes is studied. The results show that during regenerative chatter under specific cutting conditions, one mode can decay. Furthermore, it is possible to adjust the rate at which the x-mode (or y-mode) decays by implementation of the internal resonance. Therefore, under both internal resonance and regenerative chatter conditions, it is possible to suppress the undesirable vibration of one mode (direction) in which accurate surface finish is required. Under the steady-state motion, jump phenomenon is investigated for the process with regenerative chatter under various cutting conditions. Moreover, the effects of structural and cutting force nonlinearities on the stability lobes diagram of the process are investigated.     

A modal disturbance estimator for vibration suppression in nonlinear flexible structures

This paper presents a control strategy for the suppression of vibration due to unknown disturbance forces in large, nonlinear flexible structures. The control action proposed, based on the modal approach, consists of two contributions. The first is the well-known Independent Modal-Space Control, which increases system damping and improves its behavior close to the resonance frequencies. The second is a disturbance estimator, which calculates the modal components of the external forces acting on the system and compensates for them using actuator forces. The system modal coordinates, required by both logics, are estimated through a modal state observer.The proposed control logic is tested on a flexible boom. The paper reports the numerical and experimental results both for the linear and nonlinear (large motion) boom configuration.     

Tuneable vibration absorber design to suppress vibrations: An application in boring manufacturing process

Dynamic vibration absorbers are used to reduce the undesirable vibrations in many applications such as electrical transmission lines, helicopters, gas turbines, engines, bridges, etc. Tuneable vibration absorbers (TVA) are also used as semi-active controllers. In this paper, the application of a TVA for suppression of chatter vibrations in the boring manufacturing process is presented. The boring bar is modeled as a cantilever Euler–Bernoulli beam and the TVA is composed of mass, spring and dashpot elements. In addition, the effect of spring mass is considered in this analysis. After formulation of the problem, the optimum specifications of the absorber such as spring stiffness, absorber mass and its position are determined using an algorithm based on the mode summation method. The analog-simulated block diagram of the system is developed and the effects of various excitations such as step, ramp, etc. on the absorbed system are simulated. In addition, chatter stability is analyzed in dominant modes of boring bar. Results show that at higher modes, larger critical widths of cut and consequently more material removal rate (MRR) can be achieved. In the case of self-excited vibration, which is associated with a delay differential equation, the optimum absorber suppresses the chatter and increases the limit of stability.     

Origin and suppression of back conversion in a phasematched nonlinear frequency down-conversion process

Back conversion is an intrinsic phenomenon in nonlinear frequency down-conversion processes. However, the physical reason for its occurrence is not well understood. Here, we theoretically reveal that back conversion is the result of a π-phase jump associated with the depletion of one interacting wave. By suppressing the idler phase jump through a deliberate crystal absorption, the back conversion can be inhabited, thus enhancing the conversion efficiency from the pump to the signal. The results presented in this Letter will further the understanding of nonlinear parametric processes and pave the way toward the design of highly efficient down-conversion systems.     

Auxiliary mass throw in a tuned and damped vibration absorber

Dynamic vibration absorbers should be tuned and optimally damped to control the amplitudes of vibration of the primary mass over the whole range of exciting frequencies. The lighter the auxiliary mass the greater is the amplitude of its excursions relative to the primary mass. In the case of the tuned system the maximum steady state throw of the auxiliary mass can be easily calculated from the formulas given. These are most elegantly derived by use of a frequency locus technique. It is shown that is the system is also optimally damped the throw of the auxiliary mass has its minimum value which depends only on the mass ratio.     

Facile synthesis and characterization of Co nanoplatelets with tunable dimensions via solution reduction process

Plate-like Co nanoparticles with different sizes were synthesized by solution reduction process. The size of Co nanoplatelets can be tuned by varying the concentration of CoCl₂·6H₂O and the dosage of N₂H₄·2H₂O. The Co nanoplatelets with the different size all exist in both fcc and hcp crystal structures. The normal direction of the nanoplatelets is perpendicular to the (002) planes of hcp phase or to the (111) planes of fcc phase. The saturation magnetizations of the samples are lower than the corresponding bulk value. The coercivities of the samples vary with the phase content and the particle size. The shape control mechanism was discussed.     

Broadband and tunable terahertz absorption via photogenerated carriers in undoped silicon

Terahertz absorbers based on doped silicon have achieved broadband and high-efficiency absorption due to their high concentration of carriers.However,their tunable performance is obviously insufficient.Here,we propose a new scheme for active terahertz absorption based on undoped silicon with a metamaterial antireflection layer,which realizes both strong absorption and ultrahigh modulation depth.Benefiting from the weak absorption and high transmission of undoped silicon for 1064-nm continuous wave,uniformly distributed carriers across the entire thickness of the absorber are excited,and efficient free carrier absorption of the terahertz wave is obtained.We use only a 500-μm thick absorber and achieve absorption greater than 90%in the range of 0.58 to 1.92 THz,with a peak value of 99%.More important,the absorber can be switched between two working states of nonabsorption and high-efficiency absorption by changing the pump power,which means the modulation depth reaches 100%.This simple and high-performance implementation scheme provides a new idea for the design of terahertz tunable absorbers.     

Nonresonant excitation and nonlinear suppression of parasitic transverse modes in free-electron masers

Excitation of transverse parasitic modes at the frequency of the operating mode in free-electron masers is considered. The influence of parasitic field on the starting current of the autooscillator with a low-quality cavity as well as the phenomenon of suppression of the total parasitic field by the operating one in the regime of its saturation are investigated.     

Electro-optically tunable self-focusing and self-defocusing in KTP crystals by a cascaded second-order process

We report the transformation of a linear electro-optically tunable non-phase-matched second-order nonlinear process into a cascaded second-order nonlinear process in a bulk KTP crystal to generate the effect of electrooptically tunable Kerr-type nonlinearity. By applying an electric field on the x–y plane, parallel to the z-axis of the crystal, phase mismatch is created, which introduces a nonlinear phase shift between the launched and reconverted fundamental waves from the generated second harmonic wave. Due to the nonuniform radial intensity distribution of a Gaussian beam, a curvature will be introduced into the fundamental wavefront, which focuses or defocuses the incident beam while propagating through the crystal.     

Stability and instability of nonlinear guided waves in saturable media

The stability of stationary TE_m thin film-guided waves in asymmetric planar waveguides with a self-focusing saturable nonlinear cladding was investigated numerically. The results indicate that the TE₀ wave is unstable to propagation on the negatively sloped branch of the nonlinear dispersion curve.     

Self-focusing and nonlinear acceleration process in laser produced plasma

Ruby laser intensities exceedingI ^* - 10¹⁴ W/cm² create a predominant acceleration of dense plasma due to nonlinear collisionless interaction resulting mainly from collective effects. Recoil causes confinement of the plasma interior in the form of a superlinearly increased radiation pressure. Similar nonlinear forces produce self-focusing in plasmas at a threshold laser power of only 10⁵ to 10⁶ W. The resulting filaments have intensitiesI ^*, from which their diameter can be determined in agreement with measurements of Korobkin and Alcock. These high intensities should allow some observed properties of laser produced plasmas (keV ions, linear increase of the ion charge) to be interpreted on the basis of the nonlinear acceleration described.     

线性与非线性光晶格中偶极孤立子的稳定性

利用变分法研究了线性和非线性交叉光晶格中偶极玻色-爱因斯坦凝聚(BEC)体系中物质波孤立子的稳定性.选用柱对称高斯型试探波函数,得出参数的Euler-Lagrange方程和体系的有效作用势能,根据有效势能是否具有局域最小值判断体系是否具有稳定孤立子解.结果表明,由于存在接触相互作用的空间调制,在排斥和吸引偶极相互作用下,均能形成稳定的孤立子解.给出了参数空间中存在稳定解的区域和物质波波包宽度随时间的变化曲线.     

Combustion parameters identification and correction in diesel engine via vibration acceleration signal

Using closed loop control of the internal combustion engine is beneficial to reducing emission and fuel consumption. Accurate combustion parameters are the foundation of effective closed loop control. Some combustion parameters, including the start of combustion, the location of maximum pressure rise rate and the location of peak pressure can be identified from the vibration signals. Empirical Mode Decomposition (EMD) method is introduced to reconstruct the vibration acceleration signal, from which the combustion parameters are identified. However, there are angle deviations between the combustion parameters extracted from the reconstructed vibration acceleration signal and those from the cylinder pressure. Algorithms to correct the angle deviations are introduced. A system deviation value is used to correct the extracted start of combustion with an error bound being within 0.6 °CA. Two algorithms are proposed to correct the deviation between the predicted location of maximum pressure rise rate and that from the cylinder pressure. Test results show that the two algorithms are able to correct the deviation within 0.3 °CA error bound. The location of peak pressure can be predicted with the knee point following the peak value in the reconstructed vibration acceleration signal. The predicted result is then corrected using a linear regression of the location of peak pressure versus the knee point within 0.5 °CA error bound. A real-time monitoring framework is utilized for calculating the combustion parameter prediction.     

Molecular dynamics simulations of structural disordering and forming defects in a milling process for selenium

In our previous paper, structural changes of selenium powders ground by a planetary ball mill at various rotational speeds were investigated for the nanostructural modification of particles using mechanical grinding process. The experimental results indicated that the amorphisation of Se by grinding accompanies lattice strain, and the lattice strain arises from impact energy which is more than an energy related to intermolecular interaction. In this paper, molecular dynamics simulations of selenium have been carried out under compressing conditions of various pressure strengths for obtaining information of the lattice strain at atomic level. Then, dynamical behaviour of atomic configuration has been discussed in this process. The structural disordering and formation of the structural defects were estimated by deviations of bond length and angle and the number of created defects before and after compressing from simulated results. The disordering took place during compressing at various pressure strengths, and the disordered atoms return to their initial positions at lower pressure. Stable disordered state and defects after the compression can however remain by compression at more than a certain pressure strength mainly associated with binding energy of selenium.     

Stability and vibration of a helical rod with circular cross section in a viscous medium

The stability and vibration of a thin elastic helical rod with circular cross section in a viscous medium are discussed. The dynamical equations of the rod in the viscous medium are established in the Frenet coordinates of the centreline with the Euler angles describing the attitudes of the cross section as variables. We have proved that the Lyapunov and Euler conditions of stability of a helical rod in the space domain are the necessary conditions for the asymptotic stability of the rod in the time domain. The free frequencies and damping coefficients of torsional and flexural vibrations of the helical rod in the viscous medium are calculated.     

Generating terahertz radiation via optical rectification in nonlinear crystals: Theory and experimental results

Key principles of terahertz radiation generation via laser pulse optical rectification are reviewed. The development of theoretical concepts is considered in connection with recent experimental results. The usability of resonant effects and metamaterials for the further development of this technique of generation is analyzed.