Tool Condition Monitoring Based on Nonlinear Output Frequency Response Functions and Multivariate Control Chart

Tool condition monitoring(TCM)is a key technology for intelligent manufacturing.The objective is to monitor the tool operation status and detect tool breakage so that the tool can be changed in time to avoid significant damage to workpieces and reduce manufacturing costs.Recently,an innovative TCM approach based on sensor data modelling and model frequency analysis has been proposed.Different from traditional signal feature-based monitoring,the data from sensors are utilized to build a dynamic process model.Then,the nonlinear output frequency response functions,a concept which extends the linear system frequency response function to the nonlinear case,over the frequency range of the tooth passing frequency of the machining process are extracted to reveal tool health conditions.In order to extend the novel sensor data modelling and model frequency analysis to unsupervised condition monitoring of cutting tools,in the present study,a multivariate control chart is proposed for TCM based on the frequency domain properties of machining processes derived from the innovative sensor data modelling and model frequency analysis.The feature dimension is reduced by principal component analysis first.Then the moving average strategy is exploited to generate monitoring variables and overcome the effects of noises.The milling experiments of titanium alloys are conducted to verify the effectiveness of the proposed approach in detecting excessive flank wear of solid carbide end mills.The results demonstrate the advantages of the new approach over conventional TCM techniques and its potential in industrial applications.

Inverse-designed photonic fibers and metasurfaces for nonlinear frequency conversion[Invited]

Typically, photonic waveguides designed for nonlinear frequency conversion rely on intuitive and established principles, including index guiding and bandgap engineering, and are based on simple shapes with high degrees of symmetry. We show that recently developed inverse-design techniques can be applied to discover new kinds of microstructured fibers and metasurfaces designed to achieve large nonlinear frequency-conversion efficiencies. As a proof of principle, we demonstrate complex, wavelength-scale chalcogenide glass fibers and gallium phosphide three-dimensional metasurfaces exhibiting some of the largest nonlinear conversion efficiencies predicted thus far,e.g., lowering the power requirement for third-harmonic generation by 104 and enhancing second-harmonic generation conversion efficiency by 107. Such enhancements arise because, in addition to enabling a great degree of tunability in the choice of design wavelengths, these optimization tools ensure both frequency-and phase-matching in addition to large nonlinear overlap factors.

BIFURCATION IN A NONLINEAR DUFFING SYSTEM WITHMULTI-FREQUENCY EXTERNAL PERIODIC FORCES

By introducing nonlinear frequency, using Floquet theory and referring to the characteristics of the solution when it passes through the transition boundaries, all kinds of bifurcation modes and their transition boundaries of Duffing equation with two periodic excitations as well as the possible ways to chaos are studied in this paper.

Nonlinear magnitude frequency relation and two types of seismicity systems

nonlinear magnitude frequency equation has been derived in this paper on the assumption that all seismicity systems hold fractal characteristics, and according to the differences of relevant coefficients in the equation, seis-micity systems are classified into two types: type I, the whole earthquake activity is controlled by only one great unified system; type II, the whole earthquake activity is controlled by more than one great system. One type of seismicity system may convert to the other type, generally. For example, a type I system will change to a type II system prior to the occurrence of a strong earthquake in North China. This change can be regarded as an index for earthquake trend estimation. In addition, the difference between b value in nonlinear magnitude frequency equation and that in linear equation and the term dΔM related to the coefficients of nonlinear terms obtained in this paper are proved to be a pair of available parameters for medium short term earthquake prediction.

Influence of porosity distribution on nonlinear free vibration and transient responses of porous functionally graded skew plates

This article deals with the investigation of the effects of porosity distributions on nonlinear free vibration and transient analysis of porous functionally graded skew(PFGS)plates.The effective material properties of the PFGS plates are obtained from the modified power-law equations in which gradation varies through the thickness of the PFGS plate.A nonlinear finite element(FE)formulation for the overall PFGS plate is derived by adopting first-order shear deformation theory(FSDT)in conjunction with von Karman’s nonlinear strain displacement relations.The governing equations of the PFGS plate are derived using the principle of virtual work.The direct iterative method and Newmark’s integration technique are espoused to solve nonlinear mathematical relations.The influences of the porosity distributions and porosity parameter indices on the nonlinear frequency responses of the PFGS plate for different skew angles are studied in various parameters.The effects of volume fraction grading index and skew angle on the plate’s nonlinear dynamic responses for various porosity distributions are illustrated in detail.

Analytical solution to incident angle quasi-phase-matching engineering for second harmonic generation in a periodic-poled lithium niobate crystal

Phase matching or quasi-phase matching(QPM)is of significant importance to the conversion efficiency of second harmonic generation(SHG)in artificial nonlinear crystals like lithium niobate(LN)crystal or microstructured nonlinear crystals like periodic-poled lithium niobate(PPLN)crystals.In this paper,we propose and show that the incident angle of pump laser light can be harnessed as an alternative versatile tool to engineer QPM for high-efficiency SHG in a PPLN crystal,in addition to conventional means of period adjusting or temperature tuning.A rigorous model is established and analytical solution of the nonlinear conversion efficiency under the small and large signal approximation theory is obtained at different incident angles.The variation of phase mismatching and walk-off length with incident angle or incident wavelength are also explored.Numerical simulations for a PPLN crystal with first order QPM structure are used to confirm our theoretical predictions based on the exact analytical solution of the general large-signal theory.The results show that the narrow-band tunable SHG output covers a range of 532 nm–552.8 nm at the ideal incident angle from 0°to 90°.This theoretical scheme,fully considering the reflection and transmission at the air-crystal interface,would offer an efficient theoretical system to evaluate the nonlinear frequency conversion and help to obtain the maximum SHG conversion efficiency by selecting an optimum incident wavelength and incident angle in a specially designed PPLN crystal,which would be very helpful for the design of tunable narrow-band pulse nanosecond,picosecond,and femtosecond laser devices via PPLN and other microstructured LN crystals.

Nonlinear Dynamic Analysis of the Whole Vehicle on Bumpy Road

Through the research into the characteristics of 7-DoF high dimensional nonlinear dynamics of a vehicle on bumpy road, the periodic movement and chaotic behavior of the vehicle were found.The methods of nonlinear frequency response analysis, global bifurcation, frequency chart and Poincaré maps were used simultaneously to derive strange super chaotic attractor.According to Lyapunov exponents calculated by Gram-Schmidt method, the unstable region was compartmentalized and the super chaotic characteristic of ...

Efficient collinear frequency tripling of femtosecond laser with compensation of group velocity delay

This paper demonstrates an approach that negative uniaxial crystal has a relative anomalous dispersion effect which can compensate group velocity delay, and applies this approach to nonlinear frequency conversion of an ultrafast laser field. High efficiency of the third harmonic generation is experimentally fulfilled by adopting a collinear configuration of doubing-compensation-tripling system. Through finely adjusting the incident angle and optical axis direction of the compensation plate, it obtains ultraviolet （UV） output energy of 0.32 mJ centered at 270 nm with spectral bandwidth of 2 nm when input beam at 800 nm was 70 fs pulse duration and 6 mJ pulse energy which was extracted from Ti：sapphire laser system by a diaphragm, corresponding to an 800-to-270 nm conversion efficiency of 5.3% and a factor-of-l.6 improvement in the third harmonic generation of UV band in comparison with a general conventional configuration. Furthermore, when the full energy of 18 mJ from a Ti：sapphire laser system was used and optimized, the UV emission could reach 0.83 mJ.

Identification of Composite-Metal Bolted Structures with Nonlinear Contact Effect

The middle layer model has been used in recent years to better describe the connection behavior in composite structures.The influencing parameters including low pre-screw and high preload have the main effects on nonlinear behavior of the connection as well as the amplitude of the excitation force applied to the structure.Therefore,in this study,the effects of connection behavior on the general structure in two sections of increasing damping and reducing the stiffness of the structures that lead to non-linear phenomena have been investigated.Due to the fact that in composite structure we are faced to the limitation of increasing screw preload which tend to structural damage,so the investigation on the hybrid connection(metal-composite)behavior is conducted.In this research,using the two-dimensional middle layer theory,the stiffness properties of the connection are modeled by normal stiffness and the connection damping is modeled using the structural damping in the shear direction.Nonlinear frequency response diagrams have been extracted twice for two different excitation forces and then proposed by a high-order multitasking approximation according to the response range of the nonlinear finite element model for stiffness and damping of the connection.The effect of increasing the amplitude of the excitation force and decreasing the preload of the screw on the nonlinear behavior of the component has been extracted.The results show that the limited presented novel component model has been accurately verified on the model obtained from the vibration experimental test and the reduction of nonlinear model updating based on that is represented.The comparison results show good agreementwith a maximumof 1.33%error.

A nonlinear model reference adaptive inverse control algorithm with pre-compensator

In this paper, the reduced-order modeling （ROM） technology and its corresponding linear theory are expanded from the linear dynamic system to the nonlinear one, and H∞ control theory is employed in the frequency domain to design some nonlinear system＇ s pre-compensator in some special way. The adaptive model inverse control （AMIC）theory coping with nonlinear system is improved as well. Such is the model reference adaptive inverse control with pre-compensator （PCMRAIC）. The aim of that algorithm is to construct a strategy of control as a whole. As a practical example of the application, the nunlerical simulation has been given on matlab software packages. The numerical result is given. The proposed strategy realizes the linearization control of nonlinear dynamic system. And it carries out a good performance to deal with the nonlinear system.

Influence of surface micro-beams with large deflection on the resonance frequency of a quartz crystal resonator in thickness-shear mode vibrations

We study the dynamic behavior of a quartz crystal resonator （QCR） in thickness-shear vibrations with the upper surface covered by an array of micro-beams （MBs） under large deflection. Through taking into account the continuous conditions of shear force and bending moment at the interface of MBs/resonator, dependences of frequency shift of the compound QCR system versus material parameter and geometrical parameter are illustrated in detail for nonlinear and linear vibrations. It is found that the frequency shift produces a little right （left） translation for increasing elastic modulus （length/radius ratio） of MBs. Moreover, the frequency right （left） translation distance caused by nonlinear deformation becomes more serious in the second-order mode than in the first-order one,

Parametric characteristic of the random vibration response of nonlinear systems

Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of nonlinear engineering systems and structures that can be represented by a Volterra series model.In the present study,the random vibration of nonlinear systems is investigated using Volterra series.Analytical expressions were derived for the calculation of the output power spectral density（PSD） and input-output cross-PSD for nonlinear systems subjected to Gaussian excitation.Based on these expressions,it was revealed that both the output PSD and the input-output crossPSD can be expressed as polynomial functions of the nonlinear characteristic parameters or the input intensity.Numerical studies were carried out to verify the theoretical analysis result and to demonstrate the effectiveness of the derived relationship.The results reached in this study are of significance to the analysis and design of the nonlinear engineering systems and structures which can be represented by a Volterra series model.

Rigorous solution to second harmonic generation considering transmission and reflection of light at air–crystal interface

Considering the transmission and reflection of TE-polarized pump light at the air–crystal interface,the second harmonic generation(SHG)in a lithium niobate(LN)crystal is investigated theoretically and systematically in this work.In previous studies,the theoretical analyses of reflection and transmission of incident wave in the process of nonlinear frequency conversion were not considered in LN crystal on account of the complicated calculations.First,we establish a physical picture describing that a beam of light in TE mode transports in the LN crystal considering transmission and reflection at the crystal surface and generates nonlinear second-order optical polarization in crystal.Then we analytically derive the reflection coefficient and transmission coefficient of pump light by using the dispersion relationships and electromagnetic boundary conditions.We construct the nonlinear coupled wave equations,derive and present the small signal approximation solution and the general large signal solution exactly.Under the transmission model and reflection model,we find that the conversion efficiency of the second-harmonic wave is obviously dependent on transmission coefficient and other general physical quantities such as the length of LN crystal and the amplitude of pump light.Our analytical theory and formulation can act as an accurate tool for the quantitative evaluation of the SHG energy conversion efficiency in an LN crystal under practical situations,and it can practically be used to treat other more complicated and general nonlinear optics problems.

A 515-nm laser-pumped idler-resonant femtosecond BiB_(3)O_(6) optical parametric oscillator

We report on an idler-resonant femtosecond optical parametrical oscillator(OPO)based on BiB_(3)O_(6)(BiBO)crystal,synchronously pumped by a frequency-doubled,mode-locked Yb:KGW laser at 515 nm.The idler wavelengths of OPO can be tuned from 1100 nm to 1540 nm.At a repetition rate of 75.5 MHz,the OPO generates as much as 400 mW of idler power with 3.1 W of pump power,the corresponding pulse duration is 80 fs,which is 1.04 times of Fourier transform-limited(FTL)pulse duration at 1305 nm.In addition,the OPO exhibits excellent beam quality with M^(2)<1.8 at 1150 nm.To the best of our knowledge,this is the first idler-resonant femtosecond OPO pumped by 515 nm.

Dynamics Analysis of Active Variable Stiffness Vibration Isolator for Whole-Spacecraft Systems Based on Nonlinear Output Frequency Response Functions

In order to improve the harsh dynamic environment experienced by heavy rockets during different external excitations,this study presents a novel active variable stiffness vibration isolator(AVS-VI)used as the vibration isolation device to reduce excessive vibration of the whole-spacecraft isolation system.The AVS-VI is composed of horizontal stiffness spring,positive stiffness spring,parallelogram linkage mechanism,piezoelectric actuator,acceleration sensor,viscoelastic damping,and PID active controller.Based on the AVS-VI,the generalized vibration transmissibility determined by the nonlinear output frequency response functions and the energy absorption rate is applied to analyze the isolation performance of the whole-spacecraft system with AVS-VI.The AVS-VI can conduct adaptive vibration suppression with variable stiffness to the whole-spacecraft system,and the analysis results indicate that the AVS-VI is efTective in reducing the extravagant vibration of the whole-spacecraft system,where the vibration isolation is decreased up to above 65%under different acceleration excitations.Finally,different parameters of AVS-VI are considered to optimize the whole-spacecraft system based on the generalized vibration transmissibility and the energy absorption rate.

Fiber-based optical frequency comb at 3.3 μm for broadband spectroscopy of hydrocarbons [Invited]

A 125 MHz fiber-based frequency comb source in the mid-infrared wavelength region is presented. The source is based on difference frequency generation from a polarization-maintaining Er-doped fiber pump laser and covers a spectrum between2900 cm^(-1) and 3400 cm^(-1) with a simultaneous bandwidth of 170 cm^(-1) and an average output power up to 70 m W. The source is equipped with actuators and active feedback loops, ensuring long-term stability of the repetition rate, output power, and spectral envelope. An absorption spectrum of ethane and methane was measured using a Fourier transform spectrometer to verify the applicability of the mid-infrared comb to multispecies detection. The robustness and good long-and short-term stability of the source make it suitable for optical frequency comb spectroscopy of hydrocarbons.

Forced vibration control of an axially moving beam with an attached nonlinear energy sink

This paper investigates a highly efficient and promising control method for forced vibration control of an axially moving beam with an attached nonlinear energy sink（NES）.Because of the axial velocity,external force and external excitation frequency,the beam undergoes a high-amplitude vibration.The Galerkin method is applied to discretize the dynamic equations of the beam–NES system.The steady-state responses of the beams with an attached NES and with nothing attached are acquired by numerical simulation.Furthermore,the fast Fourier transform（FFT）is applied to get the amplitude–frequency responses.From the perspective of frequency domain analysis,it is explained that the NES has little effect on the natural frequency of the beam.Results confirm that NES has a great potential to control the excessive vibration.