Critical Value Of Amplitude Research Articles

Correlation of the sound quality and vibration of end of line testing for automatic transmission

This paper introduces a method to quickly and accurately identify the sound quality of automatic transmission in a vehicle by testing the objective vibration parameters on automatic transmission EOL (end of line) test bench. In this study, 50 automatic transmissions serve as the research object, and the vibration parameters of each gear of the transmission are measured on the EOL bench. Then, the transmission is mounted on a vehicle, the vibration parameters and acoustic parameters of corresponding working conditions are measured, and the subjective evaluation of the noise quality of the vehicle is carried out by using a grade scoring method. After this data is collected, the specific vibration parameters and acoustic parameters that are the dominant factors of sound quality are determined by correlation analysis. Based on the multiple linear regression method, the following mathematical models are formulated: the vibration parameters and the subjective evaluation of a vehicle, and the acoustic parameters and the subjective evaluation of a vehicle. Among these models, the mathematical models of the vibration parameters and the subjective evaluation of a vehicle were verified to be more accurate. The consistency between the vibration value in a vehicle and the vibration value on EOL test bench is analyzed and the EOL vibration value is determined to be the most objective evaluation of the data. After batch testing of 100 sets, the effectiveness of this model is within 95%. Finally, the value of critical amplitude of the condition of each gear of transmission is analyzed to form the judgment standard of transmission EOL vibration to ensure better sound quality for the vehicle.

Effect of amplitude of vibration in ultrasonic vibration-assisted single point incremental forming

ABSTRACT In the recent past, ultrasonic vibration-assisted single-point incremental forming has gained the attention of the metal forming researchers’ interest. Being a latest development, the process is not completely established from the point of view of the underlying mechanism and the effect of the process variables on the formability of the component. The amplitude of vibration and frequency of vibration are two ultrasonic process-specific variables which may affect the formability of the component. In this research work, the effect of amplitude of vibration along with forming feed and step-depth have been studied by performing a groove test on AA3003 aluminum sheet. The FFL for the SPIF process is proposed based on the thickness strain of the tensile testing component. The critical value of amplitude of ultrasonic vibration and ultrasonic intensity is identified demarking the ultrasonic softening and ultrasonic hardening zone.

Measurements of heat capacities and turbidities for binary mixtures {water + 2,6-dimethylpyridine} and {water, or heavy water + 2,6-dimethylpiperidine} in the critical regions

The isobaric heat capacities per unit volume in both one-phase and two-phase regions and the turbidities in the one-phase region for the significantly asymmetric binary mixtures of {water + 2,6-dimethylpyridine} and {water, or heavy water + 2,6-dimethylpiperidine} were carefully measured, from which the corresponding critical exponents were obtained and found to be consistent with the 3D-Ising values. The values of the system-dependent critical amplitudes for the heat capacity, the correlation length and the osmotic compressibility were deduced, which together with the values of the critical amplitudes related to the coexistence curves reported previously were used to test some universal critical amplitude ratios. Moreover, the importance of the heat capacity related term in the formalism of the complete scaling theory was confirmed. It was also found that the complete scaling formalism possibly becomes somewhat inapplicable for the significantly asymmetric systems.

The roles of extrinsic periodic information on the stability of stock price

The roles of extrinsic periodic information on the stability of stock price for the case of the stock market crashes are investigated with Heston model. From numerical simulation of the mean escape time (MET), the results indicate that: (i) the varying amplitude of extrinsic periodic information induces and enhances a maximum in curve of the MET versus the mean reversion of volatility or initial position; (ii) there is a critical value of amplitude or frequency of extrinsic periodic information in the behavior of MET versus the long-run variance or amplitude of volatility fluctuations, and when amplitude or frequency takes value below the critical value, the increase in amplitude or frequency enhances the stability of stock price, but restrains it when amplitude or frequency takes value above the critical value.

Monte Carlo simulation with aspect-ratio optimization: Anomalous anisotropic scaling in dimerized antiferromagnets

We present a method that optimizes the aspect ratio of a spatially anisotropic quantum lattice model during the quantum Monte Carlo simulation, and realizes the virtually isotropic lattice automatically. The anisotropy is removed by using the Robbins-Monro algorithm based on the correlation length in each direction. The method allows for comparing directly the value of the critical amplitude among different anisotropic models, and identifying the universality more precisely. We apply our method to the staggered dimer antiferromagnetic Heisenberg model and demonstrate that the apparent nonuniversal behavior is attributed mainly to the strong size correction of the effective aspect ratio due to the existence of the cubic interaction.

Universal critical amplitude ratios in binary mixtures of {benzonitrile + alkane}

Turbidity in the one-phase region and the isobaric heat capacity per unit volume in both one-phase and two-phase regions for the critical solutions of {benzonitrile+n-alkane} were measured, from which the values of the system-dependent critical amplitudes for the correlation length, the osmotic compressibility, the heat capacity and the correction-to-scaling term of the heat capacity were deduced. The previously reported data of the coexistence curves for {benzonitrile+n-alkane} were also reanalyzed with the crossover model to obtain the crossover parameters. Subsequently, these results together with the values of the critical amplitude related to the coexistence curve reported previously were used to calculate some universal critical amplitude ratios, which showed reasonable agreement with the theoretical predictions.

Experimental study of the isochoric heat capacity of isobutanol in the critical and supercritical regions

The one- and two-phase isochoric heat capacities (CV) of isobutanol in the critical and supercritical regions have been measured with a high-temperature and high-pressure nearly constant-volume adiabatic calorimeter. The measurements were made in the temperature range from 324K to 575K for 23 isochores (16 liquid and 7 vapor) from 73.2kgm−3 to 772.2kgm−3. The isochoric heat capacity jump (quasi-static thermograms supplemented by the sensor of adiabatic control) technique have been used to accurately measure of the phase transition parameters (TS, ρS). The total experimental uncertainty of density (ρ), temperature (T), and isochoric heat capacity (CV) were estimated to be 0.06%, 15mK, and 2–3%, respectively. The critical temperature (TC=547.65±0.2K) and the critical density (ρC=272.95±2kgm−3) for isobutanol were determined from the measured saturated properties (CVS, TS, ρS) near the critical point. The measured CV and saturated density (TS, ρS) data near the critical point have been analyzed and interpreted in terms of extended scaling type equations for the selected thermodynamic paths (critical isochore and coexistence curve) to accurately calculate the values of the asymptotical critical amplitudes of heat capacity (A0±) and coexistence curve (B0). The experimentally derived value of the critical amplitude ratio A0+/A0−=0.522 is in good agreement with the value predicted by various scaling theories. The measured thermodynamic properties (CV, TS, ρS) of isobutanol near the critical point were also interpreted in the terms of “complete scaling” theory of critical phenomena. In particularly, the contributions of the “complete” and “incomplete” scaling terms on the coexistence-curve singular diameter were estimated. We determined the values of the asymmetry parameters a3 and b2 of the coexistence curve singular diameter. The strength of the Yang–Yang anomaly Rμ for isobutanol was estimated using asymmetry parameters a3 and the contribution of the second temperature derivative of vapor-pressure and chemical potential in the singularity of two-phase CV2. The measured values of saturated one- and two-phase liquid and vapor isochoric heat capacities (C′V1,C″V1,C′V2,C″V2) and saturated thermal (ρS, TS) properties together with vapor-pressure (PS, TS) data were used to calculate other derived thermodynamic properties such as (KT, ΔHvap, CP, CS, W, (∂P/∂T)′V, (∂V/∂T)′P, (d2PS/dT2), and (d2μ/dT2) of isobutanol at saturation near the critical point.

Wrinkling of Tubes by Axial Cycling

Circular tubes compressed into the plastic range first buckle into axisymmetric wrinkling. Initially, the wrinkle amplitude grows with increasing load, but induces a gradual reduction in axial rigidity that eventually leads to a limit load instability and collapse. For lower D/t tubes, the two instabilities can be separated by strain levels of a few percent. Persistent stress-controlled cycling can cause accumulation of deformation by ratcheting. Here, the interaction of ratcheting and wrinkling is investigated. In particular, it is asked if compressive ratcheting can first initiate wrinkling and then grow it to amplitudes associated with collapse. Experiments on SAF2507 super-duplex steel tubes with D/t of 28.5 have shown that a geometrically intact tube cycled under stress control initially deforms uniformly due to material ratcheting. However, in the neighborhood of the critical wrinkling strain under monotonic loading, small amplitude axisymmetric wrinkles develop. This happens despite the fact that the maximum stress of the cycles can be smaller than the critical stress under monotonic loading. In other words, wrinkling appears to be strain rather than stress driven, as is conventionally understood. Once the wrinkles are formed, their amplitude grows with continued cycling, and as a critical value of amplitude is approached, wrinkling localizes, the rate of ratcheting grows exponentially, and the tube collapses. Interestingly, collapse was also found to occur when the accumulated average strain reaches the value at which the tube localizes under monotonic compression. A custom shell model with small initial axisymmetric imperfections, coupled to a cyclic plasticity model, is used to simulate these cyclic phenomena successfully.

An experimental study on the influence of planar anisotropy on the critical behavior of a Fe17Dy2 single crystal

In order to check the influence of planar anisotropy on the magnetic phase transition which occurs at the Curie temperature, we have made a detailed experimental study on the critical behavior of a high quality Fe17Dy2 single crystal which has a strong planar anisotropy. This study includes deducing various critical exponents from extensive magnetization measurements. The asymptotic and effective critical exponents and their corresponding amplitudes have been derived from the magnetization data measured with the applied field along the easy plane using the conventional methods to analyze phase transitions with and without the inclusion of the “correction-to-scaling” terms originating from the nonlinear irrelevant scaling fields. Inclusion of the correction-toscaling terms could only influence the critical amplitude values. The values of the critical exponents obtained in this way are found to be in excellent agreement with those obtained from the magnetization data taken with the applied field parallel to the hard axis, indicating that the planar anisotropy has not influenced the critical behavior. These results are in agreement with the observations made on Fe17Ho2 and Fe17Er2 single crystals.

Temperature dependence of liquid-liquid interfacial tension and universal critical amplitude ratio: an experimental study

Results of new measurements of the temperature dependence of the liquid-liquid interfacial tension σ of the system cyclohexane/aniline are reported. The system specific value of the critical amplitude σ 0 of the interfacial tension has a value of σ 0 = 38.5 mN m −1. It is combined with the value of the system specific critical amplitude ξ 0 + of the correlation length of local concentration fluctuations to calculate the amplitude ratio R σ, ξ + = [ σ 0( ξ 0 +) 2]/ k B T c ( k B, Boltzmann constant; T c, critical temperature). The experimental value of R σ, ξ + for that system is R σ, ξ + = 0.41. It is at the upper limit of experimental R σ, ξ + values reported in the literature for five one component systems and eight binary mixtures (0.283 < R σ, ξ + < 0.410, mean value 〈 R σ, ξ +〉 = (0.37 ± 0.03); theoretical value, R σ, ξ + = 0.36).

The magnetic phase transition in amorphous rare earth-transition metal alloys

The magnetic phase transition of amorphous RE-TM alloys is investigated by measuring the magnetic moment as function of the temperature and the applied field. The samples are producedby both the melt-spinning technique (Fe30Tb70, Fe33Gd67) and the rf-sputtering technique (Fe67Tb33, Fe51.6Al15.4Tb33). The critical exponents β, γ ', γ and δ, as well as the reduced critical amplitudes J0/JS(0), μh0/(kBTc) and DJ0μh0 are determine d to obtain a complete overview on the behavior of the magnetic phase transition. The critical exponents β, γ' and γ are determined by two independent methods: Modified Arrot plots and the method of scaling plots. As a further method for the determination of the critical exponents β and γ, we have used the method of Kouvel and Fisher. The critical exponent δ is determined from In J versus In(μ0H) plots. The critical exponent values found in general cannot be related definitely to any theoretical prediction, except for Fe30Tb70, for which the critical exponents agree rather well with the values derived for the three dimensional Heisenberg model. Furthermore, the critical amplitude values show significant deviations from the theoretical values as derived for different models.

Critical amplitudes of pure substances

Consequences of theoretical models for the critical amplitudes A, B, Γ, D are considered and calculated values of critical amplitudes for pure substances are presented for the range Zcr=pcrvcr/RTcr=0.22–0.29, as obtained by the proposed expressions.

Finite-amplitude self-oscillations in a rotating Hagen-poiseuille flow

The nonlinear stability of a viscous incompressible flow in a circular pipe rotating about its own axis is investigated. A solution of the initial—boundary value problem for the unsteady three-dimensional Navier—Stokes equations is found by means of the Bubnov—Galerkin method [1–5]. A series of methodological investigations were made. The nonlinear evolution of the periodic self-oscillating regimes is studied, and their characteristic stabilization times, amplitudes, and other integral and fluctuational characteristics are found. The secondary instability of these finite-amplitude wave motions is examined. It is established that the secondary instability is initially weak and linear in character; the corresponding growth times are approximately an order greater than for the primary perturbations. There is the possibility of a sharp, explosive restructuring of the motion when the secondary perturbations reach a certain critical amplitude. A “survival curve” [5] is constructed, which makes it possible to determine the preferred perturbation, distinguishable from the rest if the initial perturbation amplitudes are equal, and the critical amplitude values starting from which the other perturbations may prevail even over the preferred one. The range of these surviving perturbations is obtained. It is shown that as a result of the non-linear interaction of several perturbations at low levels of supercritlcality periodic motion in the form of a single traveling wave is generated.

Detailed magnetization study of an amorphous ferromagnet

Exhaustive magnetization measurements have been carried out on the amorphous ferromagnet ${\mathrm{Fe}}_{40}$${\mathrm{Ni}}_{40}$${\mathrm{P}}_{14}$${\mathrm{B}}_{6}$ in the temperature range 4.2 to 700 K in fields up to 16 kOe. Magnetization at low temperatures is found to decrease in accordance with the predictions of an isotropic nearest-neighbor Heisenberg model. It is observed that in this alloy the rms range of exchange interaction equals roughly the mean nearest-neighbor distance. A theoretical interpretation has been provided for the observation that the spin-wave stiffness constant $D$ is smaller in amorphous than in crystalline ferromagnets. Magnetization data taken in the critical region, besides yielding the values for the Curie temperature and critical exponents as ${T}_{C}=519.9\ifmmode\pm\else\textpm\fi{}0.2$ K, $\ensuremath{\beta}=0.38\ifmmode\pm\else\textpm\fi{}0.01$, $\ensuremath{\gamma}=1.31\ifmmode\pm\else\textpm\fi{}0.02$, and $\ensuremath{\delta}=4.46\ifmmode\pm\else\textpm\fi{}0.04$, satisfy the magnetic equation of state characteristic of a second-order phase transition. The observed exponent values not only obey the static scaling relation but also present a reasonable agreement with the theoretical values deduced from a three-dimensional Heisenberg model. They do, however, exhibit a slight but systematic shift towards the molecular-field values. This observation has been shown to imply an increased effective range of the exchange interaction in the critical region. Long-range forces are found to have a negligible influence on the critical fluctuations of magnetization. Critical amplitude values suggest that the elementary moments involved in the magnetic order-disorder transition are those forming a part of the giant superparamagnetic moments which are found to exist for temperatures well above ${T}_{C}$. Above 575 K, the susceptibility obeys the Curie-Weiss law. A careful analysis of the susceptibility data reveals that the spin polarization of conduction electrons gives a negligible contribution to the distribution of the magnetic moment and that the moments on Ni and Fe atoms remain localized even in the paramagnetic state. No evidence has been found for the indirect exchange between spins on magnetic atoms mediated by conduction-electron spin, as conjectured by Kaneyoshi in amorphous ferromagnets, in the present glassy alloy.

895. Approximation of the apparent secondary emission coefficient in a broad range of target potential variations: G F Semenov and S V Denbnobetskiy,Elektron Tekh Elektronluch Fotoelektr Prib, 2, 1970, 43–46 ( in Russian)

The one- and two-phase isochoric heat capacities (CV) of isobutanol in the critical and supercritical regions have been measured with a high-temperature and high-pressure nearly constant-volume adiabatic calorimeter. The measurements were made in the temperature range from 324 K to 575 K for 23 isochores (16 liquid and 7 vapor) from 73.2 kg m−3 to 772.2 kg m−3. The isochoric heat capacity jump (quasi-static thermograms supplemented by the sensor of adiabatic control) technique have been used to accurately measure of the phase transition parameters (TS, ρS). The total experimental uncertainty of density (ρ), temperature (T), and isochoric heat capacity (CV) were estimated to be 0.06%, 15 mK, and 2–3%, respectively. The critical temperature (TC = 547.65 ± 0.2 K) and the critical density (ρC = 272.95 ± 2 kg m−3) for isobutanol were determined from the measured saturated properties (CVS, TS, ρS) near the critical point. The measured CV and saturated density (TS, ρS) data near the critical point have been analyzed and interpreted in terms of extended scaling type equations for the selected thermodynamic paths (critical isochore and coexistence curve) to accurately calculate the values of the asymptotical critical amplitudes of heat capacity (A0±) and coexistence curve (B0). The experimentally derived value of the critical amplitude ratio A0+/A0−=0.522 is in good agreement with the value predicted by various scaling theories. The measured thermodynamic properties (CV, TS, ρS) of isobutanol near the critical point were also interpreted in the terms of “complete scaling” theory of critical phenomena. In particularly, the contributions of the “complete” and “incomplete” scaling terms on the coexistence-curve singular diameter were estimated. We determined the values of the asymmetry parameters a3 and b2 of the coexistence curve singular diameter. The strength of the Yang–Yang anomaly Rμ for isobutanol was estimated using asymmetry parameters a3 and the contribution of the second temperature derivative of vapor-pressure and chemical potential in the singularity of two-phase CV2. The measured values of saturated one- and two-phase liquid and vapor isochoric heat capacities (C′V1,C″V1,C′V2,C″V2) and saturated thermal (ρS, TS) properties together with vapor-pressure (PS, TS) data were used to calculate other derived thermodynamic properties such as (KT, ΔHvap, CP, CS, W, (∂P/∂T)′V, (∂V/∂T)′P, (d2PS/dT2), and (d2μ/dT2) of isobutanol at saturation near the critical point.