Stability improvement and regenerative chatter suppression in nonlinear milling process via tunable vibration absorber

In this paper, a tunable vibration absorber set (TVAs) is designed to suppress regenerative chatter in milling process (as a semi-active controller). An extended dynamic model of the peripheral milling with closed form expressions for the nonlinear cutting forces is presented. The extension part of the cutting tool is modeled as an Euler–Bernoulli beam with in plane lateral vibrations (x–y directions). Tunable vibration absorbers in x–y directions are composed of mass, spring and dashpot elements. In the presence of regenerative chatter, coupled dynamics of the system (including the beam and x–y absorbers) is described through nonlinear delay differential equations. Using an optimal algorithm, optimum values of the absorbers' position and their springs' stiffness in both x–y directions are determined such that the cutting tool vibration is minimized. Results are compared for both linear and nonlinear models. According to the results obtained, absorber set acts effectively in chatter suppression over a wide range of chatter frequencies. Stability limits are obtained and compared with two different approaches: a trial and error based algorithm and semi-discretization method. It is shown that in the case of self-excited vibrations, the optimum absorber improves the process stability. Therefore, larger values of depth of cut and consequently more material removal rate (MRR) can be achieved without moving to unstable conditions.     

Properties of optical phonons in Zn1−x−yMgyBexSe quaternary mixed crystal

Long wavelength optical lattice vibration and dielectric constants of the quaternary mixed crystal Zn_1−x−yMg_yBe_xSe are investigated based on the pseudo-unit-cell mode and Born-Huang procedure. It is found that this material shows a three-mode behavior and the oscillator strength of each mode is mainly controlled by only one component. The theoretical results also show that the linear interpretation method for dielectric constants is reliable. The vibrational frequencies and the oscillator strengths of the ternary mixed crystals Be_xZn_1−xSe, Be_xMg_1−xSe and Mg_xZn_1−xSe are also calculated as special cases of the quaternary mixed crystal for comparing with experiments. The calculation shows agreement with the experimental results.     

Composition and lattice mismatch dependent dielectric constants and optical phonon modes of InAs1−x−ySbxPy quaternary alloys

Based on the pseudopotential formalism under the virtual crystal approximation, the dielectric and lattice vibration properties of zinc-blende InAs_1−x−ySb_xP_y quaternary system under conditions of lattice matching and lattice mismatching to InAs substrates have been investigated. Generally, a good agreement is noticed between our results and the available experimental and theoretical data reported in the literature. The variation of all features of interest versus either the composition parameter x or the lattice mismatch percentage is found to be monotonic and almost linear. The present study provides more opportunities to get diverse high-frequency and static dielectric constants, longitudinal and transversal optical phonon modes and phonon frequency splitting by a proper choice of the composition parameters x and y (0 ⩽ x ⩽ 0.30, 0 ⩽ y ⩽ 0.69) and/or the lattice mismatch percentage.     

Temperature-insensitive transverse load sensing with improved accuracy using stress induced birefringence effects of fiber Bragg grating

Different from the basic sensing theory of the fiber Bragg grating (FBG) sensors based on direct spectral analysis, a new method exploiting the polarization properties of FBG for temperature-insensitive transverse load sensing is proposed. In this paper, the birefringence effects on FBG under transverse load are analyzed. The evolution of the polarization dependent loss (PDL) of FBG with wavelength for the transmitted signals with respect to the transverse load is also studied theoretically and experimentally. We proposed utilizing the PDL evolution of FBG to precisely recover the wavelength spacing between the two peaks of x-mode and y-mode for accurate transverse load measurement. Good agreements between experimental results and numerical simulations had been obtained.     

Feasibility study of nonlinear tuned mass damper for machining chatter suppression

In order to improve the performance of the tuned mass damper (TMD) for machining chatter suppression, a new-type of nonlinear TMD is proposed in this paper. Compared with the common linear TMD, the nonlinear TMD is equipped with an additional series friction-spring element. The capability of the nonlinear TMD in suppressing machining chatter vibration is investigated in this paper. The harmonic balancing method (HBM) is used to estimate the frequency response function (FRF) of the machining system to which the nonlinear TMD is attached. Considering the special nature of the machining stability problem, the optimal design parameters of this nonlinear TMD are those that minimize the magnitude of the real part of the FRF of the nonlinear TMD damped machining system. This paper also demonstrates the performance of the optimally tuned nonlinear TMD for machining stability improvement by calculating the stability diagrams for the milling of the nonlinear TMD damped workpiece. The calculation results show that more than 30% improvement in the critical limiting cutting depth can be obtained, compared to the optimally tuned linear TMD.     

Surface anisotropy energy of thin amorphous magnetic films of (Gd1−xCox)1−yMoy alloys; experimental results

Surface excitations in thin amorphous (Gd_1?xCo_x)_1?yMo_y films obtained by the rf sputtering technique were studied. A microwave spectrometer at X-band was used for magnetic resonance investigation with external magnetic field rotating from perpendicular to parallel resonance orientations. The critical angle and angular dependence of the position of the surface mode and the uniform mode were determined. The Surface Inhomogeneity (SI) model was applied with symmetrical boundary conditions. The surface anisotropy energy term was assumed as a superposition of the uniaxial anisotropy term and a biaxial anisotropy term. The origin of the latter term is not known yet. We also performed the resonance experiment for different temperatures ranging from 180 to 300 K. From the experiment, the uniaxial surface anisotropy constant K′_s1 and the biaxial surface anisotropy constant K′_s2 were found as functions of the temperature; the uniaxial anisotropy energy against temperature changes the sign for y=0.02 from easy axis to easy plane while the biaxial surface anisotropy does not change its character.     

Optical and vibrational properties of CdxHg1-x-y ZnyTe solid solutions

The lattice dynamics of Cd_xHg_1-x-y Zn_yTe solid solutions is studied theoretically and experimentally. The frequencies of the basic optical phonons of Cd_xHg_1-x-y Zn_yTe are calculated in terms of a modified random-element isodisplacement model. As a result, all basic vibrations of the crystal lattice that substantially affect the optical properties of this material in the spectral region corresponding to one-phonon resonance are identified. The optical properties of epitaxial Cd_xHg_1-x-y Zn_yTe layers grown by liquid-phase epitaxy on Cd_1-x Zn_xTe substrates are studied. The calculated and experimental spectral dependences of the dielectric function of Cd_xHg_1-x-y Zn_yTe solid solutions of various compositions are compared at 295 and 78 K, and good agreement between them is reached. The additional lattice vibrations whose frequencies in the phonon density of states are lower than that of the HgTe mode are shown to be caused by the lattice defects of the Cd_xHg_1-x-y Zn_yTe solid solutions.     

Calculations of three-dimensional magnetic excitations in permalloy nanostructures with vortex state

Dynamic susceptibility spectra of the vortex state in nanorings and nanodots are studied using three-dimensional micromagnetic simulations. Spatial maps of the susceptibility have enabled identification of various resonance modes. For an exciting field along the x axis, several resonance peaks appear for a thin dot, including a core mode, whereas only one main resonance peak is detected for a ring corresponding to a volume mode with uniform magnetization perpendicular to the exciting field (x direction). A low-frequency resonance peak related to a surface mode and a high-frequency resonance peak viewed as an edge mode are additionally observed for a thick ring. These three resonance modes (surface, volume and edge modes) which correspond to low, intermediate and high-frequency resonance peaks, respectively, are also captured for an exciting field along the y axis. In addition, a mixed edge and volume mode is revealed at a higher frequency.     

Scattering wave vector dependence of Raman intensity of the v1 internal mode in KH2PO4

The v₁ internal breathing mode of PO₄ tetrahedrons in KH₂PO₄ is observed with the (yx) Raman spectra. It has been found that its intensity depends upon the direction of the scattering wave vector by means of the observations with the z-Δx(yx)y and x-Δz(yx)y scattering geometries. While this mode is very weak in intensity in the x(yx)y spectrum, it becomes very strong as the scattering geometry approaches the z(yx)y one.     

Chatter suppression by parametric excitation: Model and experiments

Chatter vibration leads to challenges in precise machining due to its harmful effect on productivity and surface quality. In this study, a chatter suppression method based on parametric excitation was developed. The effect of parametric excitation on self-excited vibration was investigated based on a model of a van der Pol-Mathieu-Duffing oscillator with a time delay. It reveals that there can be a zero solution for the oscillator under the effect of parametric excitation, while it is impossible to have a stable zero equation without parametric excitation. The stability of a parametrically excited vibration system regarding the regenerative effect in the cutting processes was studied by the averaging method. The stability analysis shows that parametric excitation with an appropriate frequency and large amplitude has a chatter suppression effect no matter whether the waveform is a sinusoidal wave, square wave or triangular wave. To validate the effect of parametric excitation for chatter suppression, experiments were conducted based on a magnetorheological (MR) fluid-controlled boring bar, which can generate high-frequency parametric excitation based on the quick response of the MR fluid. Cutting experiments with an excitation current of different waveforms and diverse frequencies show that chatter can be significantly suppressed by the effect of parametric excitation.     

Multiple chatter frequencies in milling processes

Analytical and experimental identifications of the chatter frequencies in milling processes are presented. In the case of milling, there are several frequency sets arising from the vibration signals, as opposed to the single well-defined chatter frequency of the unstable turning process. Frequency diagrams are constructed analytically and attached to the stability charts of mechanical models of high-speed milling. The corresponding quasiperiodic solutions of the governing time-periodic delay-differential equations are also identified with some milling experiments in the case of highly intermittent cutting.     

Raman spectral of low-lying longitudinal mode of KH2PO4 and KD2PO4 in ferroelectric phase

The origin of the low-lying modes of KH₂PO₄ and KD₂PO₄ in the ferroelectric phase has been clarified by the z(xy)z? Raman scattering experiments. The “S-mode”, which has been usually assigned to the proton tunneling mode in KH₂PO₄ at T<T_c, has been found in the z(xy)z? spectrum of KD₂PO₄ in contrast to the x(xy)y spectrum. It has been found that the frequency of the “S-mode” of KD₂PO₄ is higher than that of KH₂PO₄. These results have shown that the “S-mode” is far from the proton tunneling mode nor the proton/deuteron mode at all. From the present Raman spectroscopy, it is concluded that the “S-mode” is assigned to the libration mode of the PO₄ tertahedrons.     

Free-vibration acoustic resonance of a nonlinear elastic bar

Free-vibration acoustic resonance of a one-dimensional nonlinear elastic bar was investigated by direct analysis in the calculus of variations. The Lagrangian density of the bar includes a cubic term of the deformation gradient, which is responsible for both geometric and constitutive nonlinearities. By expanding the deformation function into a complex Fourier series, we derived the action integral in an analytic form and evaluated its stationary conditions numerically with the Ritz method for the first three resonant vibration modes. This revealed that the bar shows the following prominent nonlinear features: (i) amplitude dependence of the resonance frequency; (ii) symmetry breaking in the vibration pattern; and (iii) excitation of the high-frequency mode around nodal-like points. Stability of the resonant vibrations was also addressed in terms of a convex condition on the strain energy density.     

Comparison of the apparent masses and cross-axis apparent masses of seated humans exposed to single- and dual-axis whole-body vibration

Humans are exposed to whole-body vibration in many types of environment. In almost all cases, the vibration to which the human is exposed comprises multi-axis vibration, such that vibration occurs in all directions simultaneously. Despite the complex nature of vibration to which humans are exposed in the workplace, almost all laboratory studies investigating the biomechanical response of the person have been completed using single-axis simulators. This paper presents a study whereby 15 male subjects were exposed to single-axis whole-body vibration in the x-, y- and z-directions and dual-axis vibration in the xy-, xz-, and yz-directions using a 6 degree-of-freedom vibration simulator. All vibration magnitudes were 0.4 ms⁻² rms in each axis. Acceleration and force was measured in the x-, y-, and z-direction during all trials. Subjects sat in two postures (‘back-on’ and ‘back-off’) on a flat rigid seat. Apparent masses measured using single-axis and dual-axis vibration stimuli showed comparable results; similarly, cross-axis apparent masses (i.e. the ratio of the force in one direction to the acceleration in another direction) were almost identical for the single- and dual-axis vibration stimuli. All results were in agreement with data previously published using single-axis vibration. In most cases, the peaks in the apparent mass and the cross-axis apparent mass occurred at a slightly lower frequency for the dual-axis vibration than for the single-axis vibration. It is hypothesised that this change is due to a nonlinear effect, analogous to that which occurs with increasing vibration magnitude for single-axis vibration.     

Nonlinear vibrations of functionally graded doubly curved shallow shells

Nonlinear forced vibrations of FGM doubly curved shallow shells with a rectangular base are investigated. Donnell’s nonlinear shallow-shell theory is used and the shell is assumed to be simply supported with movable edges. The equations of motion are reduced using the Galerkin method to a system of infinite nonlinear ordinary differential equations with quadratic and cubic nonlinearities. Using the multiple scales method, primary and subharmonic resonance responses of FGM shells are fully discussed and the effect of volume fraction exponent on the internal resonance conditions, softening/hardening behavior and bifurcations of the shallow shell when the excitation frequency is (i) near the fundamental frequency and (ii) near two times the fundamental frequency is shown. Moreover, using a code based on arclength continuation method, a bifurcation analysis is carried out for a special case with two-to-one internal resonance between the first and second doubly symmetric modes with respect to the panel’s center (ω₁₃≈2ω₁₁). Bifurcation diagrams and Poincaré maps are obtained through direct time integration of the equations of motion and chaotic regions are shown by calculating Lyapunov exponents and Lyapunov dimension.     

Regenerative vibration avoidance due to tool tangential dynamics in interrupted turning operations

Linear stability models are often used to predict regenerative vibrations in turning representing continuous operations, simple cutting geometries with constant coefficients and/or dominant modes acting in the feed direction. However, turning of components with interrupted features, such as turbine cases, may lead to large tool overhangs with vibration motions in the cutting speed direction and tool cut-off periods that result in the latter approaches being insufficient. This paper proposes a stability model for chatter in interrupted turning when the dominant vibration is orthogonal to the chip section plane. The method requires the calculation of a dynamic displacement factor that depends on the tool vibration frequency. The simulations of the model are supported by experimental tests for different contact fractions.     

TE, TM modes photorefractive surface waves and their coupling

The nonlinear equations of photorefractive surface waves (PR SWs) with diffusion mechanism are established and calculated numerically for both TE mode and TM mode and their coupling for the first time. The characteristics of TE mode and TM mode are analyzed, such as propagation constants, spatial distribution, penetration depths etc. For relative larger propagation constant, most of the surface wave energy is concentrated on the A_x component of TM mode, and the penetration depth of A_y of TE mode is always larger than that of A_x of TM mode because electro-optical coefficient r₁₃ is always smaller than r₃₃ in general PRC. As a result, the energy of the PR SW is better confined near the surface for TM mode than that for TE mode. When both TE and TM modes PR SWs are present, they will be coupled drastically and the A_x component of TM mode and A_y component of TE mode resonate in the volume of PR medium. As a result, the PR SWs cannot remain decay, and the light energy can not be confined near the surface steadily and the modes are destroyed. The results provide the theoretical instructions and are very significant to generate steady and high density PR SW in practice.     

Anisotropic strain effects on light emission characteristics of CdZnO/ZnO quantum well structures

Anisotropic strain effects by strain relaxation on TE-polarized light emission characteristics of c-plane CdZnO/ZnO quantum well (QW) structures were theoretically investigated by using the multiband effective-mass theory. The CdZnO/ZnO QW structure with anisotropic strain has much larger emission intensity than conventional CdZnO/ZnO QW structure without the strain relaxation. In the case of the strain relaxation along x(or y)-direction, the x(or y)-polarized light emission is observed to be larger than the x(or y)-polarized light emission. In particular, in the case of the strain relaxation along both x- and y-directions, the increase in the spontaneous emission peak is significant. This can be explained by the fact that the internal field is reduced owing to the decrease in the piezoelectric field by the strain relaxation.     

Surface modes in magnetic thin amorphous films of GdCoMo alloys

Surface modes in spin wave resonance in thin amorphous films of (Gd_1-xCo_x)_1-yMo_y alloys were studied. The samples were obtained with rf sputtering technique and a bias voltage was applied. Technological conditions were carefully pre-determined for which surface modes were excited in the resonance experiment. One surface mode was present for samples just after deposition and two modes could be observed in some cases for the same samples kept at room temperature for two or three months. The surface anisotropy constant K_s was determined from the surface inhomogeneity (SI) model with symmetrical or non-symmetrical boundary conditions for one or two surface modes, respectively. The fitted K_s values agree with theoretically predicted ones and they are also compatible with numbers found by experimentalists for monocrystalline, polycrystalline or amorphous films.For all samples we also determined the critical angles θ_c's between the external magnetic field and the normal to the film plane for which the position of the surface mode coincides with the position of the first volume mode. The corresponding critical angles ?_c's for the magnetization differ from π/4 which suggests the presence of surface inhomogeneities of the magnetization distribution.     

光子晶体微腔中高偏振单偶极模的研究

三角晶格排列的光子晶体微腔中的偶极模式是简并的,通过改变其晶格的对称性可以消除模式简并.晶格的整体形变破坏了晶格对称性从而影响光场的分布,同时还改变了电磁场的偏振分布.晶格整体形变使得简并的偶极模式分离成x极和y极偶极模式.通过计算分析发现分离后的模式具有良好的偏振特性,从而为实现单偏振光子晶体激光器提供了一种很好的途径.文中针对光子晶体薄板结构的微腔,主要计算了偶极模中x极偶极模式在不同拉伸时以及不同填充因子情况下的Q值,并分别计算了x关键词： 光子晶体 偶极模 品质因子 偏振度