Discovery of the acetyl cation, CH3CO+, in space and in the laboratory

Using the Yebes 40 m and IRAM 30 m radiotelescopes, we detected two series of harmonically related lines in space that can be fitted to a symmetric rotor. The lines have been seen towards the cold dense cores TMC-1, L483, L1527, and L1544. High level of theory ab initio calculations indicate that the best possible candidate is the acetyl cation, CH3CO+, which is the most stable product resulting from the protonation of ketene. We have produced this species in the laboratory and observed its rotational transitions Ju = 10 up to Ju = 27. Hence, we report the discovery of CH3CO+ in space based on our observations, theoretical calculations, and laboratory experiments. The derived rotational and distortion constants allow us to predict the spectrum of CH3CO+ with high accuracy up to 500 GHz. We derive an abundance ratio N(H2CCO)/N(CH3CO+) ∼ 44. The high abundance of the protonated form of H2CCO is due to the high proton affinity of the neutral species. The other isomer, H2CCOH+, is found to be 178.9 kJ mol−1 above CH3CO+. The observed intensity ratio between the K = 0 and K = 1 lines, ∼2.2, strongly suggests that the A and E symmetry states have suffered interconversion processes due to collisions with H and/or H2, or during their formation through the reaction of H3+ with H2CCO.

Performance Analysis of Drum Brake using Finite Element Method

The principle objective at the back of the task "Examination of Drum Brake Rotor" is to consider and determine the Drum Brake execution underneath overwhelming braking conditions and alongside these traces help within the Drum Brake rotor plan and investigation. ANSYS 11.0 is a universally beneficial Finite Element bundles which can be utilized to decide the temperature, anxiety. ANSYS11.0 is a tool that is adaptable and financially savvy. ANSYS11.Zero utilized in the commercial enterprise to take care of a few mechanical troubles. In this assignment, Axis-symmetric rotor Brake Drum taken into consideration for research. Rib width of 8mm, 10mm and 12mm are made of Cast Iron, Aluminum and Aluminum Composite considered. A Coupled Field Analysis (Transient Thermal Analysis and Structural Analysis) is achieved to gather the temperature conveyance and Von Mises Stress. After exam Coupled subject is Done, the chart plotted among separation and temperature. An undertaking is Made recommend the great mix of materials and rib width for Drum brake rotor, which offers an collection of low temperature and least rotor plate von mises pressure may additionally.

Study on the Dynamic Response of an Unbalanced Rotor System Supported by Ball Bearings

This paper proposed a new four-degree-of-freedom dynamic model of the bearing-rotor system based on ball bearing without Raceway Control Hypothesis, and both the inertia forces of balls and the tilting motions of rotor are fully considering in the calculation of restoring forces and moments of ball bearings. Then the dynamic model are solved by the fourth-step Runge-Kutta method, and the dynamic responses of rotor system including the displacement, velocity and center orbits are obtained, and the influences of rotating speeds, eccentricity and symmetry of rotor are studied and analyzed. The results show that both the varying compliance of ball bearing and rotor eccentric force have a great influence on the dynamic responses and motion patterns of bearing-rotor system, and the titling motion of bearing-rotor should be considered in the analysis of asymmetric rotor or the symmetric rotor under some specific conditions.

Closed-Form Vibration Response of a Special Class of Spinning, Cyclic Symmetric Rotor-Bearing-Housing Systems

Vibration of a spinning, cyclic symmetric rotor supported by flexible bearings and housing is governed by a set of ordinary differential equations with periodic coefficients. As a result, analytical solutions of such systems are generally not available. This paper is to prove that closed-form solutions are available for such systems if the following two conditions are met. First, the rotor has a rigid hub and the rest of the rotor is flexible. Second, elastic mode shapes of the rotor's flexible part only present axial displacement. Under these two conditions, the periodic coefficients will only appear between repeated modes of the spinning rotor and vibration modes of the stationary housing. This unique structure enables a coordinate transformation to convert the governing ordinary differential equations with periodic coefficients into a set of ordinary differential equations with constant coefficients, whose closed-form solution is readily available. Moreover, the coordinate transformation can be derived explicitly. Finally, we demonstrate the closed-form solution through a benchmark numerical model that consists of a spinning rotor, a stationary housing, and two elastic bearings. In particular, the rotor is a circular disk with four evenly spaced radial slots and a central rigid hub. The housing is a square plate with a central rigid shaft and is fixed at four corners. The two elastic bearings connect the rotor and the housing between the hub and shaft. Numerical results confirm that the original equation of motion with periodic coefficients and the closed-form solutions predict the same vibration response.

Ground-Based Response of a Spinning, Cyclic Symmetric Rotor Assembled to a Flexible Stationary Housing Via Multiple Bearings

This paper is to study ground-based response of a spinning, cyclic symmetric rotor assembled to a flexible housing via multiple bearings. In particular, interaction of the spinning rotor and the flexible housing is manifested theoretically, numerically, and experimentally. In the theoretical analysis, we show that the interaction primarily appears in coupled rotor–bearing–housing modes whose response is dominated by the housing. Specifically, let a housing-dominant mode have natural frequency ω(H) and the spin speed of the rotor to be ω3. In rotor-based coordinates, response of the spinning rotor for the housing-dominant mode will possess frequency splits ω(H)±ω3. In ground-based coordinates, response of the spinning rotor will possess alternative frequency splits ω(H)-(k+1)ω3 and ω(H)-(k-1)ω3, where k is an integer determined by the cyclic symmetry of the rotor and the housing-dominant mode of interest. In the numerical analysis, we study a benchmark model consisting of a spinning slotted disk mounted on a stationary square plate via two ball bearings. The numerical model successfully confirms the frequency splits both in the rotor-based and ground-based coordinates. In the experimental analysis, we conduct vibration testing on a rotor–bearing–housing system that mimics the numerical benchmark model. Test results reveal two housing-dominant modes. As the rotor spins at various speed, measured waterfall plots confirm that the housing-dominant modes split according to ω(H)-(k+1)ω3 and ω(H)-(k-1)ω3 as predicted.

Experimental Verification of Ground-Based Response of a Spinning, Cyclic Symmetric, Rotor Assembled to a Flexible Stationary Housing via Multiple Bearings

This paper is to present an experimental study that measures ground-based response of a spinning, cyclic, symmetric rotor-bearing-housing system. In particular, the study focuses on rotor-housing coupled modes that are significantly dominated by housing deformation. In the experiments, a ball-bearing spindle motor, carrying a disk with four evenly spaced slots (i.e., the rotor), is mounted onto a stationary housing. The housing is a square plate supported with steel spacers at four corners and fixed to the ground. Two different ways are used to excite the rotor-housing system to measure frequency response functions (FRFs). One is to use an automatic hammer tapping at the disk, and the other is to use a piezoelectric actuator attached to the housing. Vibration of the rotor and housing is measured via a laser Doppler vibrometer and a capacitance probe. The experiments consist of two parts. The first part is to obtain FRFs when the rotor is not spinning. The measured FRFs reveal two rotor-housing coupled modes dominated by the housing. Their mode shapes are characterized by one nodal line in housing and one nodal diameter in the rotor. The second part is to obtain waterfall plots when the rotor is spinning at various speeds. The waterfall plots show that the housing dominant modes split into primary branches and secondary branches as the spin speed varies. The primary branches almost do not change with respect to the spin speed. In contrast, the secondary branches evolve into forward and backward branches. Moreover, their resonance frequencies increase and decrease at four times of the spin speed. The measured results agree well with the predictions found in the authors’ previous theoretical study [1].

Ground-Based Response of a Spinning, Cyclic Symmetric Rotor Assembled to a Flexible Stationary Housing via Multiple Bearings

This paper is to study free response of a spinning, cyclic symmetric rotor assembled to a flexible housing via multiple bearings. In particular, the rotor spins at a constant speed ω3, and the housing is excited via a set of initial displacements. The focus is to study ground-based response of the rotor through theoretical and numerical analyses. The paper consists of three parts. The first part is to briefly summarize an equation of motion of the coupled rotor-bearing-housing systems for the subsequent analyses. The equation of motion, obtained from prior research [1], employs a ground-based and a rotor-based coordinate system to the housing and the rotor, respectively. As a result, the equation of motion takes the form of a set of ordinary differential equations with periodic coefficients of frequency ω3. To better understand its solutions, a numerical model is introduced as an example. In this example, the rotor is a disk with four radial slots and the housing is a square plate with a central shaft. The rotor and housing are connected via two ball bearings. The second part of the paper is to analyze the rotor’s response in the rotor-based coordinate system theoretically. When the rotor is at rest, let ωH be the natural frequency of a coupled rotor-bearing-housing mode whose response is dominated by the housing. The theoretical analysis then indicates that response of the spinning rotor will possess frequency components ωH ± ω3 demonstrating the interaction of the spinning rotor and the housing. The theoretical analysis further shows that this splitting phenomenon results from the periodic coefficients in the equation of motion. The numerical example also confirms this splitting phenomenon. The last part of the paper is to analyze the rotor’s response in the ground-based coordinate system. A coordinate transformation shows that the ground-based response of the spinning rotor consists of two major frequency branches ωH − (k + 1) ω3 and ωH − (k − 1) ω3, where k is an integer determined by the cyclic symmetry and vibration modes of interest. The numerical example also confirms this derivation.

Parametric Resonances of a Spinning Cyclic Symmetric Rotor Assembled to a Flexible Stationary Housing Via Multiple Bearings

This paper is meant to model free vibration of a coupled rotor-bearing-housing system. In particular, the rotor is cyclic symmetric and spins at constant speed while the housing is stationary and flexible. The rotor and housing are assembled via multiple, linear, elastic bearings. A set of equations of motion is derived using component mode synthesis, in which the rotor and the housing each are treated as a component. The equations of motion take the form of ordinary differential equations with periodic coefficients. Analyses of the equations of motion indicate that instabilities could appear at certain spin speed in the form of combination resonances of the sum type. To demonstrate the validity of the formulation, two numerical examples are studied. For the first example, the spinning rotor is an axisymmetric disk, and the housing is a square plate with a central shaft. The rotor and the housing are connected via two linear elastic bearings. For the second example, the rotor is cyclic symmetric in the form of a disk with four evenly spaced radial slots. The housing and bearings remain the same. In both examples, instability appears as a combination resonance of the sum type between a rotor mode and an elastic housing mode. The cyclic symmetric rotor, however, has more instability zones. Finally, effects of damping are studied. Damping of the housing widens the instability zones, whereas the damping of the rotor does the opposite.

Efficient Techniques for the Computation of the Nonlinear Dynamics of a Foil-Air Bearing Rotor System

The foil-air bearing (FAB) plays a key role in the development of high speed, economical and environmentally friendly oil-free turbomachinery. However, FABs are known to be capable of introducing undesirable nonlinear effects into the dynamic response of a rotor-bearing system. This necessitates a means for calculating the nonlinear response of rotor systems with FABs. Up to now, the computational burden introduced by the interaction of the dynamics of the rotor, air film and foil structure has been overcome by uncoupling these three subsystems, introducing the potential for significant error. This paper performs the time domain solution of a simple rotordynamic system without uncoupling the state variables. This solution is then used as a reference for the verification of two proposed novel methods for reducing the computational burden: (a) use of harmonic balance; (b) use of Galerkin transformation. The applicability and accuracy of these two methods is illustrated on a simple symmetric rotor-FAB system.