Deformation Vibrations Research Articles

Analysis of Heavy Motor Vehicle Chassis Frame with Different Materials Equipped with CNG Cylinders of Composite Materials Using CAE Tools

Abstract: The transport sector now has a significant impact on both the economies of developed and developing nations The frame, also known as the chassis, is the main part of the vehicle because it has the highest design stress. This is vehicle support as all components are only supported on the chassis. Using the chassis as a platform, the front and rear suspensions are connected without dropping. At the same time, it can also be used for sudden stops, bumpy roads, and high-speed driving. It has sufficient rigidity to withstand impact, deflection, bending, vibration and shape deformation caused by causes. Scientific data obtained from various studies to date, weight, stress and strength, deformation, etc. have proven to be ideal for many factors. This can be done by changing the section and material of the chassis frame. The material chosen for this project is AISI4130 for LPO 1613 CNG BS-IV OBDII Front Engine Bus for Delhi Integrated Intermodal Transport System (DIMTS). Create 3D models in CAE Solid-works and analyze them with ANSYS 19.2. Automotive composite CNG cylinders are the best combination of the latest technology using carbon fiber reinforced seamless aluminum inner liner

Active vibration control of composite laminates with MFC based on PID-LQR hybrid controller

Due to the high vibration sensitivity, the flexible composite structure is prone to vibration and structural deformation, thus it is necessary to study active vibration control to improve its performance. Based on the idea of the PID control and LQR control, a PID-LQR hybrid controller is proposed in this article. It is proved that the hybrid controller has better control performance by simulating the structural vibration response under various excitation conditions. Finally, the effectiveness of the hybrid controller is verified by the active control experiment, and the vibration response is reduced by about 31.55% after control.

Nonlinear 2D-DQ volume-preservative global–local dynamic analysis of composite sandwich plates with soft hyperelastic cores and viscoelastic Winkler-Pasternak foundations

Nonlinear large amplitude vibration and dynamic deformations of sandwich plates with composite face sheets and hyperelastic cores that encounter large thickness changes during the vibration are investigated here for the first time. Moreover, a new global–local zigzag hyperelastic plate theory that considers the incompressibility and large transverse deformability of the core, and employs transverse normal strains whose order is higher than that of the in-plane strains is proposed. The plate is resting on a viscoelastic Winkler-Pasternak substrate, exposed to various spatial and time distributions of loads, and experiencing a diversity of edge conditions. The governing equations of motion are obtained by using Hamilton’s principle, von Kármán’s assumptions, and the series expansion of the volume-preserving strain energy density function. A 2D differential quadrature (2D-DQ) technique is employed for the spatial discretization of a structure with both constitutive and kinematic nonlinearities, for the first time. The time-dependent combination of the nonlinear coupled motion equations and boundary conditions is treated by an iterative/updating Runge-Kutta time-marching technique and the effects of the thickness and aspect ratio of the plate, viscoelastic and shear parameters of the foundation, types of the edge conditions, constitutive parameters of the composite materials, fiber orientation angle, and magnitude and distribution pattern of the loads on the resulting dynamic lateral deflections are studied. Results reveal that while the vibration frequencies and amplitudes of the face sheets are quite different, the damping is more remarkable when stiffer cores are utilized. Moreover, the effects of the higher vibration modes are more apparent in looser edge conditions, smaller fiber angles, and special excitation frequencies.

Experimental investigation on vortex-induced vibration characteristics of a segmented free-hanging flexible riser

Different from the traditional marine riser, the vertical lifting pipeline in the deep-sea mining system can be regarded as a free-hanging flexible riser with an unconstrained bottom end. Likewise, problems in terms of vortex-induced vibration (VIV) and flexible deformations can arise during operation. This paper presents experimental tests on a segmented free-hanging marine riser used for deep-sea mining, focusing on the vortex-induced vibration. The riser was formed by connecting pipe sections using flanges, with the top fixed and a lumped mass block added at the bottom to simulate the lifting pump and buffer station, resulting in weakly constrained boundary conditions. By employing the modal superposition principle and the wavelet time-frequency method, we comprehensively investigated the response characteristics of the typical pipe sections and the coupled oscillation of the riser's vibration modes. During the experiment, two important phenomena that differed from previous VIV tests were observed. Firstly, at low reduced velocities (Ur ≤ 7.77), the dominant frequency no longer conformed to the doubling principle in both directions but remained consistent. Secondly, the weak constraint effect of the concentration of mass at the bottom disrupts the formation of vortex shedding, thereby reducing the bending response of the CF direction of the bottom pipe sections. Meanwhile, the drag force enhances the bending response of the IL direction. Additionally, the middle and bottom pipe sections of the riser exhibited obvious mode competition, with the dominant mode often followed by several subordinate modes with considerable vibration energy.

Evaluation of static and dynamic responses considering thickness stretching effect for layered composite and sandwich arches using exponential shear and normal deformation theory

Present theory investigates the dimensionless vibration frequencies, deformations, and stresses for multilayered and sandwich arches using exponential shear and normal deformation theory (ESNDT). Present studies consider the effect of [1+(z/R)]radius of curvature while selecting the displacement field of arches under the action of uniform load. It includes the effects of transverse shear (γxz≠0) and transverse normal deformation(εz≠0)i.e., effect of thickness stretching. The governing relations are obtained using the Navier's method, and Hamilton's virtual work principle. The proposed layered arches are completely free from shear correction, and its top and bottom surfaces is satisfies zero traction free end conditions. Present study obtained very accurate natural frequencies for layered sandwich arches than other theories because, available literature not considered the thickness stretching effect i.e.,(εz=0). Hence, the present scientific investigation accounts the effect of thickness stretching i.e.,(εz≠0). However, the non-availability of exact elasticity results of bending and dynamic responses for layered sandwich arches. Present theory is obtained vibration frequencies, displacements, and stresses of layered composite and sandwich arches; the results are compared and validates through prior published literature.

Vibration and deformation suppression in mirror milling of thin-walled workpiece through a magnetic follow-up support fixture

Large thin-walled workpieces have large deformation and vibration during end milling due to their weak rigidity, which can lead to degradation of the surface quality of workpiece. To this end, this paper proposes a new method to suppress vibration and deformation during mirror milling of thin-walled workpieces by using a magnetic follow-up support fixture. The main idea is to design a fixture that can clamp around the milling area of the workpiece in real time, follow the tool motion and continuously provide a controlled air pressure force to the opposite side of the milling area without providing the mirroring support fixture that occupies a large space to the opposite side of workpiece. First, to accurately characterize the motion of the fixture, a mathematical model of the axial magnetic force considering the lateral offset is developed. On this basis, to efficiently investigate the capability of the fixture in improving the dynamic characteristics and dynamic response of workpiece, the finite element method (FEM) is used to analyze the frequency response functions (FRF) and the mode shapes of workpiece under the action of the fixture. Then, the vibration amplitude and deformation of workpiece on the milling path are simulated and studied by considering the variation of the air pressure and the position of the fixture. Finally, the prototype of the fixture is developed and then the effectiveness and feasibility of the proposed method are verified under the experimental tests with different machining parameters.

Dynamic behavior of EPS amended lightweight soil under cyclic loading

The dynamic behavior of expanded polystyrene (EPS) particle amended lightweight soil was explored using consolidated undrained dynamic and monotonic triaxial tests conducted on samples of lightweight soil with different mixing ratios. The dynamic stress, dynamic strain, and dynamic pore pressure time history curves, and shear strength criterion were studied. As a kind of structural soil, the dynamic strain time history curves of lightweight soil could be divided into three stages as the vibration compaction, vibration deformation and vibration failure stages according to the cumulative deformation rate of dynamic strain, but the vibration compaction stage was not obvious. The dynamic strain accumulation for lightweight soil was mainly single amplitude in compressive region. The deformation rate during the vibration failure stage for the lightweight soil was larger than that of the remolded soil owing to its increased stiffness and brittleness with added cementation. Unlike that of the remolded soil, dynamic pore pressures fluctuated markedly in lightweight soil tests. The dynamic pore pressure development of lightweight soil was found to relate to the mixing ratios of its components and the confining pressures. For lightweight soil samples with high EPS particle mixing ratio, the dynamic pore pressures remained in the positive range, increasing unsteadily with some fluctuation. However, for lower EPS content samples in different confining pressures, the dynamic pore pressure showed decreasing trends into the negative range, again changing unsteadily with fluctuation, showing a trend of suction and soil skeletal dilation. Based on analysis of results, it was determined that, general pore pressure, limit equilibrium and yield criterias were not suitable to describe the dynamic behavior of lightweight soil, while the dynamic strain criterion was suitable. Excluding the plastic deformation range, the single amplitude dynamic compression strain of 5% was recommended as the dynamic strain criterion to determine dynamic strength of lightweight soil.

FTIR Study of Enriched Bituminous Ukhaa-Khudag Coal

In the present work we pay an attention to the molecular structural changes between raw coal and its enriched, dense productions. Bituminous Ukhaa-Khudag coal in the form of an enriched, dense coal product is currently used as an energy source by Mongolian consumers for everyday need. There are three types of samples from one source: it is a raw coal (sample 1) and two of industrial prod- ucts as an enriched, dopant (organic based) added coal (sample 2) and simply enriched coal (sample 3). The raw coal general characterization is given through the elemental analysis, thermogravimetry analysis, moreover functional groups were identified by Fourier Transform infrared spectroscopy. The differences in the FTIR spectra of the samples were done.Some details are as follows: hydroxyl group vibrations are existing, rather weak in agreement of TG result; vibrations of aliphatic group were rarely in the long wave near region, carbonate minerals in the region of 1300-900 cm−1 are visible but overlapped, and an isolated out-of-plane deformational vibration (around 800 cm−1) or two-adjacent (800-750 cm−1) or three-adjacent (around 700 cm−1) of sp2-hybrid bonded aromatic CHx-groups were still presenting.After the processing hydroxyl group bands were affected in enriched coals, sample 2 and 3. In the spectrum of the sample 2 the long wave bands were intensively blurred.Industry processing retains an amount of water in the productions. Water excess influenced absorbance bands were able to be removed via the drying processing, however, the affection to the spectral struc- ture in sample 2 was unrecoverable.

Active vibration control and experimental investigations of the composite parabolic shell with variable cross-section under thermal load

The accurate dynamic equation of the parabolic shell with variable cross-section is developed in this paper. The geometric nonlinearity is used to amend the expression of the strain. Considering the large overall motion and solar heat flux, the flexible deformations and freedom vibrations of the parabolic shell are analyzed by the proposed method. Meanwhile, the strain rate feedback control law with piezoelectric layer is presented to improve the dynamic performance of the parabolic shell during the motion process. The experiments with parabolic shell are studied to verify the correctness of the proposed method and control strategy. It is found that the results obtained by the proposed method agree very well with the experiments. Furthermore, the numerical results show that high-frequency vibration and flexible deformation can be effectively improved by the Macro Fiber Composite (MFC). And the optimized controller gain coefficient is also discussed at the end of this paper. This paper demonstrates the importance of the piezoelectric layer for the improvement of the dynamic response of flexible parts.

Transportation and deformation of high-speed aluminum nanoparticles in inert gas with molecular dynamics study

In addition to complex deformation, high-speed nanoparticles in gas are also accompanied by significant size and interfacial effects. In this work, we simulate the transportation behavior of high-speed aluminum nanoparticles in helium gas with the classical molecular dynamics method. The evolution of aerothermodynamic quantities of solid particles and liquid particles is revealed, and different temperature rise effects are found. Furthermore, the melting of aluminum particles induced by high aerodynamic drag force is discovered, and the melting threshold conditions are proposed. In low-density (0.002 g/cm3) and high-density (0.02 g/cm3) gas, the initial velocity at which particles start to melt is 6 and 4 km/s, respectively. During the deformation of solid particles, the evolution of dislocation motion is discussed, and the evolution of the development characteristics of the molten layer is given. During the deformation of the liquid particles, vibration deformation and bag deformation modes are observed. The threshold conditions for deformation mode transitions are also given. Only in high-density gas, bag deformation occurs when the initial velocity of particles (D > 5 nm) exceeds 6 km/s. The local mechanical quantity of gas is used to explain the variation of the drag force of the particles. Moreover, the drag force model is corrected according to temperature and deformation effects. Within a certain period, the model results overestimate the drag force, and the error with the simulation results is about 25%. This provides a model reference for high-speed nanoparticle dynamics and two-phase flow problems.

In English

We investigated influence of multiwalled carbon nanotubes (CNT) on spectral characteristics of composites “rubber-carbon nanotubes”on the base of butadiene-nitrile rubber at 0–10 % of CNTs. IR reflectance maxima of composites were measured in the spectral area of the rubber CH deformation and valence vibrations. IR absorption spectra of composites “rubber-carbon nanotubes” after vulcanization includes some giant two-polar oscillations. IR absorption spectrum of composites “rubber-carbon nanotubes” at 1 % of CNTs without vulcanization includes the alone two-polar oscillation. Two-photon interference is a result of quantum entanglement of dipole-active vibrations and photon splitting according to Hong-Ou-Mandel (HOM) quantum effect. Two-photon maximal entanglement saturation is called as Bell states. HOM quantum effect is perspective for high-coherent optical quantum computers on composites “rubber-carbon nanotubes”.

Modelling and prediction on the modal and harmonic response of helix tube in large-scale spiral-wound heat exchangers

Spiral-wound heat exchangers (SWHEs) have been widely used in chemical production processes. As the equipment becomes larger, the SWHEs start facing the problem of failure caused by the flow-induced vibration (FIV) phenomenon. To assure the safety and reliability of the SWHEs, it is important to understand clearly the natural modes of spirally wound coils in different sizes and their response under external excitation. Therefore, a 3D model of the helix tube is established and the helix tubes are fully investigated. The effects of different geometrical parameters on the frequency and vibration amplitude of the helix tubes are performed at each mode, by using the finite element (FE) method. Then, the vibration amplitude analysis of the helix tube under harmonic excitation is carried out, and the dangerous frequency band of the equipment under different geometrical parameters is obtained, which is mainly around 10 Hz to 40 Hz in current domain. Moreover, sensitivity analysis is presented to have a more in-depth investigation into the effects of vibration deformation and frequency, which shows that the biggest influence factor is the helix angle. Finally, machine learning is used to predict dangerous frequency, then case studies are presented to verify the validity of the regression method in which the random forest (RF) model and extreme gradient boosting (XGBoost) have the smallest error, less than 10%. The results are very important for designing SWHEs on large scale to meet the requirement of industry development.

A geotechnical seismic isolation system based on marine sand cushion for attenuating ground shock effect: Experimental investigation

In this paper, an experimental study is introduced on the feasibility of applying a geotechnical seismic isolation system based on marine sand cushion (GSI-MSC) to resist explosion-induced ground shocks. The isolation system is characterised by low cost, easy availability, and slippage limitations, and it is particularly suitable in the protection of engineering structures during emergencies. Laboratory experiments on a steel tank structure were performed using a self-developed explosion shock and vibration simulation platform. The attenuation effects of the isolation system on ground motion, superstructural vibration and structural deformation were analysed. The results showed that GSI-MSC can reduce the intensity of ground shock, decrease the amplification effect of structural vibration, and weaken structural deformation. The attenuation effects were significantly enhanced with an increase in sand cushion thickness. The isolation mechanism was revealed from the perspective of spectrum analysis. The decreased lateral stiffness and reduced damping ratio improved the soft layer effect and internal energy dissipation of the sand cushion. This in turn led the GSI-MSC to exhibit a better harmonic attenuation effect over a wider range of high frequencies, beginning at a lower threshold. After isolation, the principal frequency of the ground motion decreased while the amplitude of high-frequency harmonics decreased, resulting in the weakening of the superstructural dynamic response. This indicated that the isolation system has a more stable attenuation effect on the low-period structures.

Deformation Information Extraction from Multi-GNSS Coordinate Series Based on EWT-ICA-R

Global navigation satellite system (GNSS) has been widely used in many deformation monitoring fields in recent years and can achieve centimeter-level or even sub-centimeter-level real-time monitoring accuracy through the carrier phase double-differenced technique. However, this technique cannot eliminate or weaken multipath errors, which become the main error source for GNSS deformation monitoring. Therefore, extracting deformation information from coordinate series mixed with multipath errors has become a key issue for further improving the accuracy of GNSS deformation monitoring. In this paper, we propose an approach to overcome this issue called empirical wavelet transform-independent component analysis with reference (EWT-ICA-R). The specific process is as follows. First, EWT is employed to model the multipath errors from a priori GNSS coordinate series, and the model is input to ICA-R as a reference signal. Then, the GNSS deformation monitoring series mixed with multipath errors and deformation information is decomposed into sub-series of different scales using EWT, and these sub-series are input to ICA-R as multi-channel signals. Finally, ICA-R is used to calculate the input signals together to obtain the multipath errors in the GNSS deformation monitoring series and then subtract the multipath errors from the GNSS deformation monitoring series to obtain accurate deformation information. Experiments show the following: (1) For the vibration deformation experiments, the correlation coefficients between the deformation information extracted by the proposed method and the real values reached 0.981, 0.981, and 0.885 in the E, N, and U directions, respectively, and the corresponding root mean square errors decrease to 0.694 mm, 0.694 mm, 1.852 mm, respectively. (2) For the slow-deformation experiment, the correlation coefficients in the three directions were all higher than 0.98, and the corresponding root mean square errors decrease to 1.345 mm, 1.546 mm, and 3.866 mm, respectively. The experiments verified the feasibility of the proposed method to accurately extract deformation information, which makes it possible to obtain sub-millimeter GNSS deformation information and provide effective technical support for deformation monitoring in related fields.

Biocompatible Poly(Vinyl Alcohol)-Copper Oxide-Graphene Oxide (PVA-CuO-GO) Nanocomposites: Synthesis, Structural and Optical Properties

Motivated by the unique combination of copper oxide (CuO) and GO (graphene oxide) nano-fillers with optimized composition in the PVA (poly vinyl alcohol) polymer, the studies in this paper have been directed towards the synthesis and characterization of (PVA-CuO-GO) polymer nanocomposites. The polymer nanocomposites, i.e., PVA-CuO-GO have been prepared by melt blending technique considering GO and CuO with variable wt.% (ranging from 0.5 to 3 wt.%). The composite was made in the shape of a dumble-like structure. To get the structural information, optical properties, surface morphology and available functional groups in the composites and their mechanisms, XRD (x-ray diffraction), UV-Vis-NIR spectrophotometer, photoluminescence (PL), FESEM (field emission scanning electron microscope) and FTIR (Fourier transform infrared) techniques have been used, respectively. From XRD data, the effect of wt.% of nano-fillers on crystalline size and micro-strain has been studied. The average crystalline size and micro-strain were calculated as ∼32 nm and ∼0.0250, respectively. From UV-Vis-NIR spectrophotometer data, tauc plots have been studied which tells that the increment in wt.% of nano-fillers causes the optical band gap to increase. On increasing the concentration of nano-fillers from 0.5 to 3 wt.%, the bandgap was increased from 2.5 to 2.8 eV. This tuning of bandgap can be supposed as fine tuning in near UV region. According to PL results, all the composites show a wide emission band in the UV-Vis region with the maximum at 487 nm when excited by 415 nm wavelength. Further, the luminescence intensity has been found to decrease with the addition of wt.% of the loading. The smoothness of the surfaces of the composites has also been studied with EDAX analysis. According to FTIR spectra, the available functional groups were found as: C–O, C–H stretch, C–H asymmetric stretch, C=O carbonyl stretch and C–H bending and deformation vibrations. In view of the characterizing results, the synthesized polymer nanocomposites can be used in several kinds of optoelectronics applications.

ANALYSIS OF MODELS AND PARAMETERS OF SENSORS BASED ON BREGG GRIDS AND THE INFLUENCE OF PHYSICAL PARAMETERS ON THE SPECTRAL CHARACTERISTICS OF GRIDS

The results of the project have a wide practical application in various industries, such as medical institutions and healthcare facilities, large industrial enterprises, in the automotive industry, food, agricultural and livestock industries, as well as in industrial technology, the metallurgical industry; oil and gas industry. In phase interferometric sensors (PID) based on arrays, the optical element itself acts as a sensitive element, which leads to a significant reduction in cost. The OB segment between two gratings is a Fabry-Perot interferometer. Under the influence of deformation and acoustic vibrations, the phase difference of signals from two adjacent Bragg gratings changes. Interferometric sensors are most sensitive to changes in the length of a fiber segment under the influence of external factors. The principle of operation of distributed fiber-optic measuring complexes based on PID in the simplest case (in the case of one PID) is shown in Figure 3.6 and is as follows [4]. Each of the Bragg gratings RB1 and RB2 of the sensor reflects the pulse coming to it from the pulsed laser at the same Bragg wavelength. In this case, the time delay between the reflected pulses is equal to twice the propagation time of light in the sensitive element of the sensor – a fiber enclosed between the gratings. The reflected pulses enter the compensating interferometer (CI), which, in turn, also bifurcates each of them. The delay introduced into the propagation of pulses by the arm 2 of the CI with respect to arm 1 ensures the overlap in time of the pulse reflected from the grating RB1 at the output of arm 2 and the pulse reflected from the grating RB2 at the output of arm 1 and their phase shift by ϕ 0 =π/2.

Biodegradation of pretreated polyethylene film by Pseudomonas aeruginosa AMB‐CD‐1

AbstractA comparative study evaluated the acid, alkali, and heat‐treated polyethylene biodegradation efficiency of Pseudomonas aeruginosa AMB‐CD‐1. The polyethylene (PE) pieces were separately treated with heat (50°C), acid (1N HCl), and alkali (1N NaOH) and then washed with water before use. All the treated samples were analyzed through thermogravimetric analysis. In addition, weight and temperature changes during the decomposition reactions were also measured and determined. In these treatments, the PE films of heat‐treated and acid‐treated low‐density polyethylene (LDPE) indicated more significant weight loss at 120°C (48.99% and 40.75%, respectively) as compared to their control or untreated PE and alkali‐treated LDPE (21.84% and 24.68%, respectively). A biodegradation assay was then conducted with treated and untreated LDPE films with P. aeruginosa AMB‐CD‐1 strain. Fourier transform infrared spectroscopy analysis revealed that the heat or acid‐pretreated samples with isolate AMB‐CD‐1 displayed peaks at 2922.84, 2923.97, and 1450.31, 874.22 cm−1 for C–H stretching deformation vibration, CH2 scissoring vibration, –CHO stretching, and strong alkyl structure, respectively. Furthermore, the new peaks with a significant difference at 2500–2000 cm−1 (O═C═O, O–H stretching vibration: carboxylic acid) and 1500–1000 cm−1 (–CHO and C═O stretching) were noticed in the infrared spectral range of LDPE degradation. Modifications in the functional group provided evidence that biodegradation had impacted the chemical structure of the LDPE film. Additionally, it was demonstrated that pretreating LDPE films with heat or acid could speed up their biodegradation.

Three-dimensional simulation effects of trailing-edge actuation on a morphing A320 wing by means of hybrid turbulence modelling

PurposeThis study aims to investigate the effects of electroactive morphing on the Airbus A320 Reduced Scale prototype of the H2020 N° 723402 European Research project smart morphing and sensing (SMS) for aeronautical configurations [1],[2].Design/methodology/approachThe flow regimes correspond to low subsonic take-off conditions. The morphing is applied through the vibration and slight deformation of the near trailing edge region; respecting the way, this actuation has been applied on the experimental prototype using micro fibre composite actuators. Optimal frequency range has been used, associated with low amplitudes of deformation with the Arbitrary Lagrangian Eulerian methodology. This study used an adapted turbulence modelling with the organised eddy simulation (OES) as well as a hybrid approach delayed detached eddy simulation – with embedded OES (DDES–OES), able to sensitise and keep up the coherent structures development.FindingsThe morphing at an optimal frequency (300 Hz) and amplitude (0.7 mm), applied on a length (3.5 cm) near the trailing edge, has been studied at Reynolds number 1 million and incidence of 10°. The effects on the main flow instabilities and on the turbulent vortex structures are analysed using proper orthogonal decomposition. A modification of the wake structures and a formation of organised rows of vortices along the shear layer are obtained. This leads to a quasi-two-dimensional wake, benefits on the aerodynamic performance and a decrease of the frequency peaks in the spectrum, corresponding to an attenuation of the coherent structures.Originality/valueThis study provides a fundamental understanding of how the actuation modifies the coherent and turbulent vortex structures around the wing and in the wake.

A Nonlinear Dynamic Model for Characterizing the Downhole Motions of the Sidetracking Tool in a Multilateral Well

It is of practical interest to investigate the mechanical behaviors of a sidetracking tool system and to describe the sidetracking tool’s vibration mechanical response, as this can provide an important basis for evaluating and optimizing the tool structure and effectively controlling the profile of the sidetracking window. In this article, three nonlinear dynamic models with ten, six, and two degrees of freedom, respectively, are established using the Lagrange method to characterize the behavior of the sidetracking tool. It should be noted that in these models, the axial, lateral, and torsional vibration of the tool system are fully coupled. The process of the sidetracking tool mills in the casing-pipe wall is divide into three typical stages, i.e., the window mill, pilot mill, and watermelon mill grinding the casing, respectively. The dynamic response of the three stages is studied to more effectively analyze the influence of the sidetracking tool vibration deformation on the window width. The Runge–Kutta method, which is easy to implement, is applied to solve the supposed nonlinear dynamic model, and some useful findings are as follows. The effects of sidetracking tool vibrations at different stages on window widening size are illustrated quantitatively. The vibration trajectory pattern of the sidetracking tool is different from that of the conventional drilling tool due to the influence of the whipstock, which changes from the general whirling motion pattern to the X reciprocating pattern, and the vibration amplitude decreases. Due to the influence of the tool’s lateral amplitude, the window profile is widened. The widened window size of the window mill and the pilot mill are 3.30 mm and 2.74 mm, respectively, and the extended window size of the watermelon mill is 0.07 mm, while the maximum window width formed by the sidetracking tool is 374.34 mm. This work proposes, for the first time, the coupled vibration model of the sidetracking tool system, which is helpful to better understand the nonlinear dynamic effects of the sidetracking tool, laying the foundation for the optimization of the sidetracking parameters.

Highly Stable Vibration Measurements by Common-path off-axis Digital Holography

Measurements of vibration and dynamic deformation with high resolution and accuracy by non-destructive techniques are of great interest in many branches of engineering. We report a non-destructive method based on digital holographic interferometry for high-precision micro-vibration measurement of a 3D object. Herein, a new and simple configuration of a common-path off-axis digital holographic system, with high mechanical stability and compact in size, is proposed. The simplicity, compactness, and high stability of the proposed setup are provided by employing a wedge plate in-line with the test object to create a clean reference beam. The object and reference beams propagate the same path, without the need for any specialized optical component or arrangement, and these beams allow to interfere on the faceplate of the image sensor to form a digital hologram. The feasibility of the proposed system is demonstrated by measuring the vibration of the objects driven by different excitation signals. A series of digital holograms of a vibrating object is recorded by the use of a high-speed image sensor. The result of the reconstruction of the recorded holograms is an array of complex numbers containing the complete amplitude and phase profile of the object, which in turn provides displacement and vibration information. Due to its simple geometry and significant outcomes, the proposed system could be established as a powerful tool for a wide range of optical imaging and measurement investigations.