Free Vibration Analysis of Two-Stage Planetary Gear With Friction

Considering the effect of teeth surface sliding friction, free vibration of two-stage planetary gears (TPG) is studied theoretically for the first time. The lateral-torsional coupling dynamic model and equation are established with three degrees of freedom: two translations and one rotation. The change rule of natural frequency is discussed with the case of first stage planetary gear’s number 4 and second stage planetary gear’s number 3, 4 and 5. Afterwards three vibration modes are summarized by calculating the free vibration. In order to understand the behavior of friction, the effect of friction on natural frequencies is analyzed for the case of considering friction and not considering friction. Furthermore, the ‘self-coupling’ phenomenon is obtained from the vibration of center component of TPG Meanwhile, the ‘mutual coupling’ is obtained between the first-stage planetary gear (FPG) and the second-stage planetary gear (SPG).

Sound Quality of Aircraft Cabin for VIP and Business Jets

This paper aims to identify the attributes that describe aircraft interior noise, determine most important psychoacoustic models that characterize cabin sounds, and construct a prediction model that can be utilized for VIP and business jets to evaluate subjective perception. In the first part, paired comparison listening tests and free verbalization are conducted with expert subjects who experienced VIP and business aircraft flight. The study generated a list of adjective pairs that describe perception of cabin sounds to be used for semantic differential listening tests. Multi-dimensional scaling is performed on paired comparison data. Results showed that subjects’ decisions can be categorized in loudness and annoyance dimensions which are not necessarily linearly associated. The second part of the study is the development of a sound quality prediction model for aircraft cabin. Semantic differential tests are conducted with potential customers. Objective sound quality metrics are correlated to subjective test responses using principal components regression. This model is found to be most effective explaining pleasantness, comfort, and loudness perception. It is intended to be utilized to modify/redesign noise control treatments and sound signature of an aircraft. All listening tests were conducted inside an aircraft cabin simulator considering the influence of visual content.

Vibration Analysis of Laminated Composite Rectangular Plates With General Boundary Conditions

In this investigation, the free vibration analysis of laminated composite rectangular plates with general boundary conditions is performed with a modified Fourier series method. Vibration characteristics of the plates have been obtained via an energy function represented in the general coordinates, in which the displacement and rotation in each direction is described as an improved form of double Fourier cosine series and several closed-form auxiliary functions to eliminate any possible jumps and boundary discontinuities. All the expansion coefficients are then treated as the generalized coordinates and determined by Rayleigh-Ritz method. The convergence and reliability of the current method are verified by comparing with the results in the literature and those of Finite Element Analysis. The effects of boundary conditions and geometric parameters on the frequencies are discussed as well. Finally, numerous new results for laminated composite rectangular plates with different geometric parameters are presented for various boundary conditions, which may serve as benchmark solutions for future research.

Sound Attenuation in a Flow Duct Periodically Loaded With Micro-Perforated Patches Backed by Helmholtz Resonators

Mitigating the propagation of low frequency noise sources in ducted flows represents a challenging task since wall treatments have often a limited area and thickness. Loading the periphery of a duct with a periodic distribution of side-branch Helmholtz resonators broadens the bandwidth of the noise attenuated with respect to a single resonator and generates stop bands that inhibit wave propagation. However, significant flow pressure drop may occur along the duct axis that could be reduced using micro-perforated patches at the duct-neck junctions. In this study, a transfer matrix formulation is derived to determine the sound attenuation properties of a periodic distribution of MPPs backed by Helmholtz resonators along the walls of a duct in the plane wave regime. In the no-flow case, it is shown that an optimal choice of the MPP parameters and resonators separation distance lowers the frequencies of maximal attenuation while maintaining broad stopping bands. As observed in the no-flow and low-speed flow cases, these frequencies can be further decreased by coiling the acoustic path length in the resonators cavity, albeit at the expense of narrower bands of low pressure transmission. The achieved effective wall impedances are compared against Cremer optimal impedance at the first attenuation peak.

An Analytical and Numerical Investigation of Modulation Sidebands of a Planetary Gear Under Fluctuated External Torque

Certain operating conditions such as fluctuation of the external torque to planetary gear sets can cause additional sidebands. In this paper, a mathematical model is proposed to investigate the modulation mechanisms due to a fluctuated external torque (FET), and the combined influence of such an external torque and manufacturing errors (ME) on modulation sidebands. Gear mesh interface excitations, namely gear static transmission error excitations and time-varying gear mesh stiffness, are defined in Fourier series forms. Amplitude and frequency modulations are demonstrated separately. The predicted dynamic gear mesh force spectra and radial acceleration spectra at a fixed position on ring gear are both shown to exhibit well-defined modulation sidebands. Comparing with sidebands caused by ME, more complex sidebands appear when taking both FET and ME into account. An obvious intermodulation is found around the fundamental gear mesh frequency between the FET and ME in the form of frequency modulations, however, no intermodulation in the form of amplitude modulations. Additionally, the results indicate that some of the sidebands are cancelled out in radial acceleration spectra mainly due to the effect of planet mesh phasing, especially when only amplitude modulations are present.

Research on Vibration Control of Thin Plate Based on Pre-Stressing

The weak dynamic stiffness of thin plate is one of the important factors that limit the use of thin plate. Improving the dynamic stiffness of thin plate is one of the effective methods for the vibration control of thin plate. In this paper, the influence of pre-stress on the vibration characteristics of thin plate is studied. A vibration control method of thin plate based on pre-stress is proposed. The vibration differential equation of quadrate thin plate under pre-stressing is established. Using the Galerkin principle, the natural frequencies corresponding to the shape functions of the quadrate thin plates under pre-stressing in different distribution forms are obtained. By comparison, it is found that pre-stressing on the thin plate can change the dynamic stiffness of thin plate. In particular, tensile stress can increase the dynamic stiffness of thin plate while compressive stress can reduce the dynamic stiffness of the thin plate. The greater the pre-stress, the more obvious the effect. In the end, the requirements of the pre-stress distribution which can improve the dynamic stiffness of thin plate effectively are derived.

Taipei MRT Cabin Soundscape: Route Between Shandao Temple and Taipei Main Station

Soundscape of a specific transportation event conveys not only messages for communication purpose but also becomes a soundmark for the riders. This Taipei MRT cabin soundscape study documents the series of acoustic events during the rides between two stations: Shandao Temple and Taipei Main Station. Taxonomy of sounds, technical data analysis and soundwalks were used as the soundscape data collection methods. Social, mechanical, and indicators sounds were identified as the three main sound classifications. Spectrogram showed the distinguished frequencies and orders of the acoustic events. On train announcements used four languages due to the country’s cultural and social history. This fascinating, unique, and repetitive Taipei MRT cabin soundscape adds to the exuberant soundscape and identity of Taipei.

Acoustical Comfort in Classrooms: Case Study at the University of Brasília

The acoustic conditions in school spaces are fundamental for the success of the learning process. This article aims to present the results of acoustic comfort by the analytical method of 9 classrooms with different geometric characteristics of the University of Brasília. In classrooms the background noise limits are 40 to 50dBA and considering that the teacher’s voice reaches a certain 65 decibels we can highlight that it can be heard clearly by the students. However in an environment with a lot of reverberation of sounds the teacher will have to exert more effort to be understood. The sound perception in a room depends on the intensity and temporal relationship between the direct sound and the indirect sound reflected by the walls of the room, therefore, in the present study were verified two parameters namely the reverberation time and speech intelligibility. The results obtained were compared with the normative parameters of ANSI S12.60: 2010 and it was verified that all rooms are not suitable for teaching-learning activity. To guarantee an environment with better conditions of concentration and learning for the students, acoustic coverings were suggested in order to fit the normative limits.

Sound Absorption Characteristic of Glass and Plastic Bottles: Considerations of Their Dependences on Material Properties

Great number of bottles made by glass, plastic and metal are used to store beverages, liquid ingredients as water, milk, vinegar and also liqueur. Empty bottles after usage are collected for recycling use and resources. Many of them have narrow open mouth and look like typical shape in kinds of Helmholtz resonator. Authors thought that their reuse for functional building parts with sound absorption would be very valuable from points of view of green building and environmental policies, and authors then measured each resonance frequency and sound absorption coefficient of representative, including light-soft-plastic, bottles, with net capacity from 7 to 2000 ml, by setting on the edge of sound tube with diameter of 100 mm. Sound resonances with sound absorption coefficient of 0.3–1.0 at frequencies from 100 to 1000 Hz clearly depending on the capacity could be confirmed. It was also found that measured result was well matched to the numerical calculation based on acoustic impedance change at each section area gradually changed in bottle. It is thought that combination use of recycled bottles with independent resonance frequency is more effective than use of new uniform perforated plates for wide space where we need additional sound absorption in certain frequency range.

Sound Label for Household Appliances

Household appliances and their sound quality are important for our daily life quality. However the appropriate characterization of their sound is a difficult task. Not only product users but also manufacturers can profit from a sound label which characterize the perception of the customers. The purchase decision-making process according to acoustic criteria will be supported by such kind of label. In addition, a label and its components give orientation to the manufacturers during their product development process. Essential aspect for such kind of label is that it should represent the perception of the customers. Therefore psychoacoustical properties, e.g., loudness, sharpness, roughness, tonality, etc., are advantageous for characterization purposes. It would be beneficial to combine these psychoacoustical descriptors into a sound quality label, which is easy to understand. The authors have developed several sound labels for household appliances based on psychoacoustic properties. These sound labels are the result of the listening experiments which were conducted with potential customers. In this paper, various aspects of these investigations are summarized, extended and discussed.