Singularly perturbed dynamics of the tippedisk

The tippedisk is a mathematical-mechanical archetype for a peculiar friction-induced instability phenomenon leading to the inversion of an unbalanced spinning disc, being reminiscent of (but different from) the well-known inversion of the tippetop. A reduced model of the tippedisk, in the form of a three-dimensional ordinary differential equation, has been derived recently, followed by a preliminary local stability analysis of stationary spinning solutions. In the current paper, a global analysis of the reduced system is pursued using the framework of singular perturbation theory. It is shown how the presence of friction leads to slow–fast dynamics and the creation of a two-dimensional slow manifold. Furthermore, it is revealed that a bifurcation scenario involving a homoclinic bifurcation and a Hopf bifurcation leads to an explanation of the inversion phenomenon. In particular, a closed-form condition for the critical spinning speed for the inversion phenomenon is derived. Hence, the tippedisk forms an excellent mathematical-mechanical problem for the analysis of global bifurcations in singularly perturbed dynamics.

Optimization of FSP Process Parameters on AA5052 Employing the S/N Ratio and ANOVA Method

AA5052 bead-on-plate processing has been achieved by the friction stir processing (FSP) technique to examine the manipulation of process parameters. It also improved the base metal surfaces to analyze the microstructure. The tool spinning speed, traverse speed, and axial load were preferred to investigate the effect of friction stir bead-on-plate processing on the tensile strength qualities and microhardness in AA5052. An optical microscope was used to dissect the fabricated processed zones of the microstructure. By using the design of the experiment, the orthogonal array of the L9 Taguchi method was used to construct the processing experiments. The analysis of variance and the signal-to-noise ratio methods were employed to identify the optimum unification of process parameters and the significant benefaction of a specific parameter on the responses. The outcomes showed that the tool spinning speed was the principal factor affecting the characteristics of tensile strength and microhardness, succeeded by the traverse speed and axial load. The intermetallic compound layer had formed during the processing under specified conditions. This examination revealed that the optimum parameters could intensify the mechanical behaviour of AA5052.

Development and Characterization of Biobased Polyamide 56/Polyethylene Terephthalate Composite Fibers

The present research studied the production process and performance of biobased PA56 (polyamide 56) and PET (polyethylene terephthalate) composite fibers through melt side-by-side spinning. The results showed that biobased PA56 and PET composites with strength of 4.0–4.3 CN/dtex were prepared by applying a spinning speed of 4,000–4,050 m/min, draw ratio of 2.50–2.70, first heat roll temperature of 80–90 °C, second heat roll temperature of 160–165 °C, and the addition of 5% compatibilizer between the two components. The fibers and fabric showed high moisture absorption, good air permeability, and excellent antistatic properties. The saturated moisture absorption rate was 11.2%, the air permeability was 9680 g/(m2·d), and the specific resistance was 1080*1010 Ω·m.

Vibration characteristics and stable region of a parabolic FGM thin-walled beam with axial and spinning motion

This paper focuses on the vibration characteristics of the parabolic functionally graded material (FGM) beam considering the axially moving and spinning motion. Based on the Hamilton’s principle, the governing equation of the beam is derived. Then, the Galerkin’s method is employed to solve the equation. The combined influence of axial speed, spinning speed, and geometric parameters on natural frequencies of the beam are investigated. What’s more, the axially moving and spinning motion can lead to a critical axial speed and critical spinning angular speed, respectively. These two critical speeds and stable region affected by different parameters are also discussed.

Designing Courses that Entertain Multi-Goals: Rationale and Practice

The present century is characterized by the speed and influx of information. Given that everyday life both at home and work is flowing at head-spinning speed, the time comes fore as a crucial entity to process mountains of information produced and transmitted to the furthest places in the world with a simple click. In brief, time is a precious treasure that needs to be kept safe and spent wisely. This article reports on a study that explored the possibilities as to how teaching time and the course content could be designed more efficiently in a freshman conversation skills course offered to the prospective English language teachers at a state university in Turkey. The course content was constructed based on an initial needs analysis conducted by their searcher. As a partial requirement of the final exam, the students were asked to prepare a five-minute oral presentation on a quotation or a universal code of values of their choice. The rubric for evaluation and the outline of the oral presentation were both negotiated with the students in detail. Following their presentation, the students were asked to answer two open-ended questions eliciting their opinions about their experiences. The content analysis of the collected data revealed that the students improved research and digital literacy skills. They also established collaboration with their classmates, retained vocabulary items and overcame anxiety issues.

Dynamics and stability analysis of a flexible liquid-filled rotor in a constant thermal environment

In this study, the dynamics and stability of a flexible rotor containing liquid in a constant thermal environment are investigated. According to thermoelastic theory, the thermal axial force exerted on the rotor is calculated by using the analytical method. A spinning Rayleigh beam is used as a simplified model of the rotor. Applying the Hamilton principle, the governing equation of motion for the flexible liquid-filled rotor system is derived. Using the obtained model, the stability prediction model and the critical spinning speed for the rotor system are formulated. To demonstrate the validity of the developed model, the present analysis is compared with the results reported in the previous study, and good agreement is observed from the comparison results. Finally, numerical results based on the obtained model are performed for a better understanding of the parameters including filling parameters, mode number, rotatory inertia and thermal effect on the stability, and critical spinning speed of the rotor system.

Raceway Defect Frequency Deviation of Full-Ceramic Ball Bearing Induced by Fit Clearance in Wide Temperature Ranges

Full-ceramic ball bearings are widely applied in wide temperature ranges due to their excellent thermal shock resistance, and the condition monitoring and fault diagnosis are mainly conducted through the spectrum analysis based on the defect frequencies. However, the outer ring has a spinning motion in the temperature-related fit clearance, which leads to the deviation of raceway defect frequencies, and is not conducive to the fault diagnosis. In this paper, the temperature-related fit clearance is considered in the dynamic model, and defects are added on the inner raceway and outer raceway. The motions of the rings are calculated and analyzed in the frequency domain, and the trends of peak frequencies with temperature are investigated. Simulation and experimental results show that the spinning speed of the outer ring increases with temperature, and the defect frequencies exhibit obvious deviation in wide temperature ranges. In a temperature range of 500 K, the defect frequencies exhibit deviations of over 3%, which is obvious in the defect frequency identification. The results provide insights on the full-ceramic ball bearing dynamics and help with the fault diagnosis and status monitoring of the relevant devices.