Torsional Vibration Energy Research Articles

Рассеяние энергии в муфтах переменной жесткости со змеевидной пружиной при крутильных колебаниях

The paper presents results of the theoretical research of the structural vibration damping in the variable stiffness couplings with a serpentine spring, which are rather widely used in the drives of the heavy engineering and machine tool products exposed to the vibration loads. When performing dynamic calculations of the drives of such machines, it is necessary to know the dissipative characteristics of their components and parts, including the indicated couplings. The paper considers the case of torsional harmonic vibrations characteristic for the coupling drive with a serpentine spring associated with twisting of the shafts connected by this coupling due to the attached parts imbalance. Quantitative characteristics of the torsional vibration energy dissipation in the couplings under consideration were studied and determined using the well-known method for estimating the vibration energy losses due to friction during slipping in the compressed parts’ contact. Mathematical model of the torsional vibration damping in a coupling was developed, which makes it possible to determine its quantitative characteristics in the form of vibration energy dissipation per cycle and the absorption coefficient depending on the coupling design parameters and the vibration process. The proposed model is implemented as an interactive application program in the MATLAB computer environment.

Wearable bistable triboelectric nanogenerator for harvesting torsional vibration energy from human motion

It is ubiquitous for torsional vibration of joint in human motion. However, it is difficult to harvest low-frequency torsional vibration energy from human motion using conventional triboelectric nanogenerators (TENGs). Herein, we propose a wearable bistable triboelectric nanogenerator (WBTENG) with a bistable stiffness feature, which enables high-efficiency torsional vibration energy harvesting from human motion. The prototype of the WBTENG is fabricated to test the electrical performance of the WBTENG. The dependencies of the electrical performance of the WBTENG on dynamic behaviors are investigated. Subsequently, the experiments are carried out to investigate the output voltages under different excitation frequencies, the output power varying with the load resistances and the durability of the WBTENG. In addition, the effect of the excitation amplitude on the electrical output performance of the WBTENG is investigated in detail. The bistable mechanism of the WBTENG is proved to switch the motion pattern between interwell and intrawell oscillations. The peak power is found to reach the highest value of 3.39 mW at 3 Hz with the resistance of 90 MΩ when the WBTENG exhibits interwell oscillation. Moreover, the WBTENG can power a light-emitting diode (LED) array and drive a temperature sensor under human motions. Therefore, the WBTENG can harvest torsional vibration energy efficiently from human motion.

Theoretical modeling and experimental validation of a torsional piezoelectric vibration energy harvesting system

Vibration energy harvesting has been extensively studied in recent years to explore a continuous power source for sensor networks and low-power electronics. Torsional vibration widely exists in mechanical engineering; however, it has not yet been well exploited for energy harvesting. This paper presents a theoretical model and an experimental validation of a torsional vibration energy harvesting system comprised of a shaft and a shear mode piezoelectric transducer. The piezoelectric transducer position on the surface of the shaft is parameterized by two variables that are optimized to obtain the maximum power output. The piezoelectric transducer can work in d15 mode (pure shear mode), coupled mode of d31 and d33, and coupled mode of d33, d31 and d15, respectively, when attached at different angles. Approximate expressions of voltage and power are derived from the theoretical model, which gave predictions in good agreement with analytical solutions. Physical interpretations on the implicit relationship between the power output and the position parameters of the piezoelectric transducer is given based on the derived approximate expression. The optimal position and angle of the piezoelectric transducer is determined, in which case, the transducer works in the coupled mode of d15, d31 and d33.

On the physical interpretation of ab initio normal-mode coordinates for the three C–H stretching vibrations of methanol along the internal-rotation path

Graphical representations are presented for variation along the steepest-descent internal-rotation path in methanol of the normal mode frequencies and their associated eigenvectors in several sets of internal coordinates and in Cartesian atomic displacement vectors di(γ), as determined for the three CH stretching vibrations (ν3, ν2, and ν9) by projected-frequency calculations from the Gaussian suite of programs. The methyl-group CH stretching modes are interesting because the symmetry environment of each C–H bond changes significantly during the internal rotation, i.e., each of the methyl bonds takes turns passing (twice for a complete torsional revolution) through the plane of symmetry of the COH frame of the molecule. No accumulation of geometric phase is observed in any of these plots, and all quantities return to their original values after the internal rotation angle γ increases by 2π. A simple two-vibrational-state, three-parameter model, closely based on earlier models from the literature, can be used to understand nearly quantitatively much of the γ-variation observed in the Gaussian plots, including a number of cusp-like features. In particular, when the three parameters in the model are determined from a fit to the Gaussian projected frequencies for ν2 and ν9 at the top and bottom of the internal rotation path, it is found that the Renner–Teller-like torsion–vibration interaction term is slightly larger in magnitude than the Jahn–Teller-like term, which is consistent with no accumulation of geometric phase in the various plots. Finally, a highly simplified computation is presented to illustrate the changes that will be necessary in order to move from the usual diabatic torsion–vibration treatments in the literature to adiabatic treatments, in which the normal-mode Cartesian displacement vectors given at each point along the internal rotation path by the Gaussian projected frequency calculation are used directly in the torsion–vibration energy level calculation.

An analysis of the vibrational structure of high-resolution UV spectra and long-wave IR Fourier transform spectra in studies of internal rotation in molecules

The methods for analyzing the vibrational structure of high-resolution UV spectra and long-wave IR Fourier transform spectra in studies of internal rotation in α,β-unsaturated carbonyl compounds R4R3C=CR2-COR1 (R1 = F, Cl; R2 = R3 = R4 = H, CH3) are compared. These methods were found to give different experimental values for systems of torsional vibration energy levels up to high quantum numbers, torsional frequencies (0–1 transitions), and anharmonicity coefficients x 11 for trans and cis isomers of the same molecules in the ground electronic state (S 0). It was shown that the experimental technique for analyzing the vibrational structure of UV spectra excludes the hydrolysis of compounds under study. Taking into account Fermi resonance and numerous Deslandres tables constructed for trans and cis isomers provides reliable determination of values necessary for the construction of internal rotation potential functions, because they are multiply repeated in various Deslandres tables. An analysis of the vibrational structure of UV spectra gives more reliable V n internal rotation potential function parameters. The V n parameter values were substantiated by quantum-mechanical calculations performed by other authors.

승용차 동력전달계에 대한 클러치 디스크 특성의 영향 고찰

The clutch with torsional damper is installed on a passenger car with manual transmission, which not only transmits the power generated by engine to the transmission but also absorbs the shock and vibration from the engine. The torsional damper in the clutch dissipates the torsional vibration energy and eliminates the resonance in the driveline but high damping in the damper causes the increase of the vibration level which is against the comfort and durability. In this study, a dynamic model for the passenger car driveline with manual transmission was developed to investigate the vibration and the effects of characteristics of the driveline. With the dynamic model, the vibration characteristics of driveline were examined by the mode analysis and driving simulation, and the effects of hysteresis torque and spring constant were investigated. The vehicle tests with prototype torsional dampers were preformed and the test results showed good agreements with the simulation.

Rotation–torsion–vibration term-value mapping for CH 3OH: Torsion-mediated doorways and corridors for intermode population transfer

Fourier transform infrared spectra of CH 3OH from 930–1650 cm −1 have been analyzed to reveal details of the rotation–torsion–vibration energy manifold of the CO-stretching, CH 3-rocking, OH-bending and CH 3-deformation modes and their torsional combination states. Mapping of the upper-state term values as a function of the rotational quantum number J has shown the locations of numerous substate crossing resonances that give rise to J-localized spectral perturbations and substate mixing and thereby create “doorways” for collision-induced population transfer among the different modes. Other near-degenerate substates are more globally mixed over a wide range of J, corresponding to “corridors” of doorways. Where both partner substates in a doorway resonance have been identified, the perturbations have been analyzed to find estimates of the interaction matrix elements and the degree of mixing between the coupled states. Many of the resonances are between substates of differing torsional quantum number, highlighting the importance of torsion in generating the doorway channels and enhancing intermode vibrational population transfer.

ACTIVE CONTROL SIMULATION OF TORSIONAL VIBRATION FOR TURBINE-GENERATOR SHAFT SYSTEM BASED ON GLOBALLY OPTIMAL CONTROL ALGORITHMS OF QUADRATIC REGULATOR

Global optimal control algorithms of linear quadratic regulator is combined with torsional vibration theory of turbine- generator shaft system, and torsional vibration energy of shaft system and control energy are chosen as performance index of active control. The global optimal control theory with linear quadratic regulator is brought about to control the tortional vibration of the large turbine-generator shaft system. And space state equations on active control of torsional vibration of turbine-generator shaft system are constructed. A solution way on Algebraic Ricatti Equation is proposed to determine the feedback control input matrix. This method is to construct a Hamiltonian matrix and solve its eigenvalue. A simulation program on active control of torsional vibration for discrete system is compiled and simulation analysis on active control of torsional vibration is carried out in a shaft system of 200 MW turbine-generator to examine the active control effectiveness. The results of time domain analysis on active control of torsional vibration show that employing the global optimal control theory of linear quadratic regulator can effectively decrease torsional vibration and control torque input.

Fourier transform spectroscopy of CH 3OH: rotation–torsion–vibration structure for the CH 3-rocking and OH-bending modes

High-resolution Fourier transform spectra of CH 3OH have been investigated in the infrared region from 930 to 1450 cm −1 in order to map the torsion–rotation energy manifolds associated with the ν 7 in-plane CH 3 rock, the ν 11 out-of-plane CH 3 rock, and the ν 6 OH bend. Upper-state term values have been determined from the assigned spectral subbands, and have been fitted to power-series expansions to obtain substate origins and effective B-values for the three modes. The substate origins have been grouped into related families according to systematic trends observed in the torsion–vibration energy map, but there are substantial differences from the traditional torsional patterns. There appears to be significant torsion-mediated spectral mixing, and a variety of “forbidden” torsional combination subbands with |Δ υ t |>1 have been observed, where υ t denotes the torsional quantum number (equivalent to υ 12). For example, coupling of the ( υ 6, υ t )=(1,0) OH bend to nearby torsionally excited ( υ 7, υ t )=(1,1) CH 3-rock and ( υ 8, υ t )=(1,1) CO-stretch states introduces ( υ 6, υ t )=(1,0)←(0,1) subbands into the spectrum and makes the ν 7+ ν 12− ν 12 torsional hot band stronger than the ν 7 fundamental. The results suggest a picture of strong coupling among the OH-bending, CH 3-rocking, and CO-stretching modes that significantly modifies the traditional energy structure and raises interesting and provocative questions about the torsion–vibration identity of a number of the observed states.

A rotation–torsion–vibration treatment with three-dimensional internal coordinate approach and additional FTIR spectral assignments for the CH 3-bending fundamentals of methanol

A theoretical model has been developed to account for certain features of both newly observed and previously reported CH 3-bending subbands between 1450 and 1570 cm −1 in the high-resolution Fourier transform infrared spectrum of CH 3OH [Can. J. Phys. 79 (2001) 435]. The features include (i) an apparent inversion of the rotationless E– A torsional splitting with respect to the ground state, i.e., the A state located above the E state, (ii) a pronounced upward slope in the K-reduced torsion–vibration energy pattern for the subband origins, and (iii) unexpected A 1/ A 2 inversion of the K=2 A and K=3 A J-rotational levels that led to ambiguity in identifying the vibrational mode as ν 4 (A 1) or ν 10 (A 2) . The model is an effective internal coordinate Hamiltonian constructed in G 6 molecular symmetry with the CH 3-bends coupled to each other and to torsion and including a- and γ-type Coriolis coupling. With this model, 33 out of 36 experimental upper-state K-term values for newly assigned ν 4, ν 5 , and ν 10 subbands plus previous ν 4 subbands have together been fitted successfully, employing 9 adjustable parameters and 17 fixed parameters to give a standard deviation of 0.14 cm −1. The P γ Coriolis term appears to be the leading cause of the upward shift in the K-reduced energies. When J-dependence is introduced via a rotational Hamiltonian including b- and c-type Coriolis terms in addition to molecular asymmetry, the observed A 1/ A 2 inversion of the K=2 A and 3 A rotational levels can also be reproduced. Predictions using the fitted K-rotation–torsion–vibration Hamiltonian show an interesting Coriolis-induced crossover and mixing of the ν 5 and ν 10 torsion–vibration energy patterns. These predictions played a role in identifying two of the new ν 5 subbands in the crossing region, thereby helping to validate the model.

Torsional Vibration Frequency and Internal Friction under Tensile Stress in Thin Ribbon Specimens

It is observed that the torsional vibration frequency of thin ribbon specimens markedly increases with the increase of superimposed tensile stress. The square of torsional frequency is nearly linear with the tensile stress. Nevertheless, this phenomenon is not observed in specimens of circular cross section or rectangular cross section with width to thickness ratio of about unity. By means of elastic mechanics analyses, it is shown that the observed phenomenon is associated with the increase of torsional vibration energy induced by tensile stress. Accordingly, the relation between torsional frequency and tensile stress in thin ribbon specimens is derived, which is in agreement with experiments. The corresponding expression of dynamic internal friction is also given.

Fourier Transform Infrared Spectroscopy of the First CO-Stretch Overtone Band of13CH3OH

This paper presents a high-resolution Fourier transform infrared study of the first CO-stretch overtone band of13CH3OH. The spectrum has been recorded at the Justus-Liebig University, Gießsen, Germany on their Bruker IFS 120 HR Fourier transform spectrometer. We have assigned parallel subbands in the torsional staten= 0 forKvalues up to 6. Each individual subband has been fitted to aJ(J+ 1) power series expansion in order to obtain the subband origin and the state-specific energy expansion coefficients for the first CO-stretch overtone state. The average rotational constantBin the CO-stretchvCO= 2 state was found to be 0.768 cm−1, forming a smooth series with that of 0.777 cm−1obtained in thevCO= 1 state and the ground state value of 0.787 cm−1. Modeling of the excited state torsion–vibration energy level structure derived from the subband origins is then discussed and molecular parameters in thevCO= 2 state are proposed. The value obtained for the barrier height to internal rotation is 377.06 ± 0.52 cm−1, nearly indistinguishable from the value 378.65 cm−1reported for the CO-stretchvCO= 1 state. The vibrational energy is found to be 2020.9 ± 1.4 cm−1. The harmonic wavenumber for the CO-stretch vibration in13CH3OH was calculated to be ω = 1029.9 cm−1. The anharmonicity constant of this vibration is ωx= 6.5 cm−1, givingx= 6.3 × 10−3. We have also observed asymmetry-inducedKdoubling for the subbands ofAsymmetry forKvalues from 1 to 3 at sufficiently highJvalues. The size of the splitting coefficients is similar to those observed for the CO-stretch fundamental, with the exception of those for theK= 3Adoublet, where the observed splitting is about 18% larger than that for the ground and CO-stretchvCO= 1 states.

Vibronic spectra and S1 excited electronic state molecular structures for acetyl chloride and acetyl fluoride

Vapor-state absorption spectra have been recorded for acetyl fluoride and acetyl chloride and also for deuterated derivatives with path lengths up to 40 m. The origins of the S1←S0 transitions have been derived, together with the torsional-vibration energy levels in the ground state S0 and excited singlet state S1. Fitting the calculated and observed rotational contours of the vibronic bands has been used to estimate the geometrical parameters in the S1 states. The carbonyl groups in the S1 states are nonplanar. The internal-rotation potentials have been determined for acetyl fluoride and acetyl chloride in the S1 and S0 states. The relative intensities of the torsional transitions in those states indicate that the minima in the potential energy are appreciably displaced along the torsional coordinate in the S0 and S1 states.

Semiclassical inversion of torsional vibration energy levels: Method, and application to acetaldehyde

An RKR-based semiclassical inversion procedure for restricted rotation potentials is developed, tested, and applied to the torsional vibration of acetaldehyde. The method is based on a semiclassical quantization of the problem which in higher-order approximations is shown to yield eigenvalues of extremely high accuracy. Two-phase integral functions are extracted from the torsional eigenvalue spectrum, one of which depends on the potential well and the other on the potential barrier, and these two functions are then subjected to RKR manipulation. The model potential is reproduced within a few per cent in all regions of the potential and the height of the barrier of acetaldehyde, V 3 = 406.1 cm −1, is in excellent agreement with the quantum mechanical results.