Browse Topic: Mathematical analysis
The current effort presents novel investigations of rotor-wake–surface interactions for the Dragonfly lander, NASA's rotorcraft lander to explore Titan. The numerical framework couples unsteady RANS with blade-element and virtual disk rotor models and a coupled Lagrangian particle tracking method to examine rotor–ground interactions and brownout. Simulations span a range of complexity, from isolated rotor benchmarks and rotor pairs to full eight-rotor configurations without a fuselage and the eight-rotor configuration with a simplified Dragonfly fuselage. To quantify model fidelity and near-ground shear, blade-resolved simulations of the isolated rotor are performed using Spalart–Allmaras and Reynolds Stress turbulence models with vorticity confinement, demonstrating that virtual blade models under-predict tip-vortex strength and local inflow distortion but reproduce wall shear reasonably well, whereas blade-resolved RSM solutions yield higher peak shear levels relevant to brownout prediction. These findings improve understanding of planetary rotorcraft aeromechanics and sediment transport in ground-effect while supporting ongoing efforts to assess environmental risks for Dragonfly operations and inform multi-rotor VTOL design for terrestrial applications.
This study presents a structured evaluation framework for reasonably foreseeable misuse in automated driving systems (ADS), grounded in the ISO 21448 Safety of the Intended Functionality (SOTIF) lifecycle. Although SOTIF emphasizes risks that arise from system limitations and user behavior, the standard lacks concrete guidance for validating misuse scenarios in practice. To address this gap, we propose an end-to-end methodology that integrates four components: (1) hazard modeling via system–theoretic process analysis (STPA), (2) probabilistic risk quantification through numerical simulation, (3) verification using high-fidelity simulation, and (4) empirical validation via driver-in-the-loop system (DILS) experiments. Each component is aligned with specific SOTIF clauses to ensure lifecycle compliance. We apply this framework to a case of driver overreliance on automated emergency braking (AEB) at high speeds—a condition where system intervention is intentionally suppressed. Initial numerical analysis suggested that the scenario narrowly satisfies the acceptance criteria. Applying the proposed framework to this scenario reveals that significant safety risks can persist even when the system functions according to its design intent. Our findings demonstrate that foreseeable misuse can be formally modeled, simulated, and empirically validated within the SOTIF framework. The proposed approach enables system developers to quantify behavioral risk and assess human-centered edge cases with greater rigor. This work contributes to operationalizing SOTIF for behavioral safety assurance and lays the foundation for future research on risk mitigation through adaptive HMI and context-aware alerts.
Waiting for a wound to heal is incredibly frustrating. First, it must clot; then an immune system response is needed; followed by scabbing and scarring — and that’s not even getting into the pain part.
Bearings are essential mechanical components that support external loads and facilitate rotational motion. With the increasing demand for high-performance applications in industries such as semiconductors, aerospace, and robotics, the need for accurate and robust performance evaluation has intensified. Traditionally, bearing performance has been assessed using static or quasi-static theoretical approaches. However, these methods are limited in their ability to capture time-dependent behaviors, which are critical in real-world applications. In this study, a rigid body dynamics analysis was proposed to evaluate the time-dependent behavior of bearings. The methodology was first applied to a deep groove ball bearing, and the results were compared with those obtained from bearing theory to validate the approach. Subsequently, the method was extended to an automotive wheel bearing, and the time-dependent contact angles and ball loads were analyzed under axial and radial loading conditions. The results demonstrate that the proposed approach provides reliable predictions and enables performance evaluation beyond the capabilities of conventional static theory.
This study focuses on the numerical analysis of weather-strip contact sealing performance with a variable cross-sectional design, addressing both static and dynamic behaviors, including the critical issue of stick-slip phenomena. By employing finite element modeling (FEM), the research simulates contact pressures and deformations under varying compression loads, DCE (Door Closing Efforts) requirements, typical in automotive applications. The analysis evaluates how changes in the cross-sectional shape of the weather-strip affect its ability to maintain a consistent sealing performance, especially under dynamic vehicle operations. The study also delves into stick-slip behavior, a known cause of noise and vibration issues, particularly improper/ loosened door-seal contact during dynamic driving condition. This study identifies key parameters influencing stick-slip events, such as friction coefficients, material stiffness, surface interactions, sliding velocity, wet/dry condition. Numerical simulations are used to predict stick-slip tendencies, and potential improvements, such as optimizing material properties or altering geometric profiles, are proposed. The results demonstrate that optimizing the variable cross-section can significantly enhance sealing performance, leading to better noise, vibration, and harshness (NVH) characteristics. Additionally, adjustments to material properties and geometric profiles are shown to reduce stick-slip effects, contributing to quieter and more reliable weather-strip systems in automotive applications. The findings of this study offer valuable insights for the design of more effective weather-strip systems in modern vehicles
This research investigates the potential of salt gradient solar ponds (SGSPs) as a sustainable and effective solution for thermal energy storage. The study examines the design, construction, and performance of SGSP systems that incorporate coal cinder, comparing their performance with traditional SGSPs without coal cinder. A combination of experimental and numerical approaches is used to evaluate the thermal characteristics and energy efficiency of these systems. The findings indicate that the salt gradient solar pond with coal cinder (SGSP-CC) achieves notably higher temperatures across the Upper Convective Zone (UCZ), Non-Convective Zone (NCZ), and Lower Convective Zone (LCZ), with measured temperatures of 42.57°C, 56.8°C, and 69.86°C, respectively. These represent increases of 7.53%, 12.01%, and 15.49% over those in the conventional SGSP (SGSP-C). Additionally, the energy efficiency gains in the UCZ, NCZ, and LCZ for the SGSP-CC are noteworthy, with increases of 38.06%, 39.61%, and 42.73%, respectively, compared to the SGSP-C. The numerical simulations align closely with the experimental data, showing deviations of less than 5% in both temperature distribution and energy efficiency across all zones. This research highlights the potential of SGSPs with reflectors for improved thermal storage efficiency.
The engineering model determining the onset of Vortex Ring State (VRS) was applied to eVTOL aircraft, and the effect of different landing trajectories and aircraft drag was investigated. Next, the new model to compare the VRS susceptibility according to the different blade geometries and trajectories is proposed by extending Ahlin & Brown's model to incorporate the two-dimensional thrust and inflow distribution on the rotor disc. For validation, two different trajectories crossing the boundary of the onset of the VRS were simulated, and the results were compared with the Vorticity Transport Method (VTM). Furthermore, the disturbance distribution of moderately and highly twisted blades are compared. The extended model can capture the physical phenomena by the distribution of the disturbances and reflect the effect of blade geometries and trajectories. It is essential to investigate the model further through a correlation analysis using experiments or numerical analysis.
This paper investigates an output-based approach for tiltrotor whirl flutter bifurcation analysis. The approach uses free decay output data for a quantity of interest at various forward speeds to estimate the system's recovery rate to equilibrium while capturing its variation with amplitude. The recovery rate is then extrapolated to predict the bifurcation diagram, which gives the limit-cycle oscillation amplitude for the quantity of interest as a function of the forward speed. The approach is demonstrated using output data from transient simulations of a notional tiltrotor model with polynomial structural nonlinearities. The approach accurately predicts the tiltrotor whirl flutter speed and limitcycle oscillation amplitudes while only requiring two free decays. This approach can facilitate whirl flutter bifurcation analyses of tiltrotor systems exhibiting nonlinear dynamics.
Helicopters in high-speed forward flight often generate High-Speed Impulse (HSI) noise, presenting a major challenge for noise control and narrowing the range of helicopter use. This paper proposes a novel method for active noise reduction by adjusting the rotor diameter length, effectively delaying HSI noise onset and reducing HSI noise impact. Utilizing the CLORNS solver and the Ffowcs Williams-Hawkings (FW-H) equation, this approach was tested on the AH-1G rotor through simulation analysis. The study simulated the rotor's dynamic diameter length changes, analyzing the effect of crucial parameters on the sound field. Results indicate that this method significantly controls the production of rotor high-speed pulse noise, achieving a noise reduction of up to 2dB at critical operational points. This research aids in formulating specific rotor noise control laws and expands the range of scenarios for helicopter usage.
This paper investigates a sliding-window matrix pencil method for predicting flutter points and limit-cycle oscillation amplitudes of nonlinear aeroelastic systems that experience whirl flutter. The approach applies the matrix pencil method to a short time window that slides along the free decay of a quantity of interest, quantifying the variation in the system's recovery rate to equilibrium with amplitude. The recovery rates at each amplitude and various forward speeds are extrapolated to predict the critical forward speed of zero recovery rate at those amplitudes. This process yields a set of limit-cycle oscillation solutions that can be visualized as a bifurcation diagram. The approach is demonstrated using output data from transient simulations of a propeller-nacelle test case with hardening structural nonlinearities. The impact of each parameter in the sliding-window matrix pencil method is first characterized via sensitivity analyses. Next, the bifurcation diagram is predicted using the recovery rates for the optimal parameter values. The results are compared with direct time marching and with the extrapolation of recovery rates estimated from envelope functions. The proposed method accurately captures the bifurcation diagram using two pre-flutter transient simulations with no need for envelope functions. This approach shows promise for output-based bifurcation analysis of nonlinear aeroelastic systems exhibiting limit-cycle oscillations associated with whirl flutter.
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