Wheel Size Research Articles

Topography Modeling of Surface Grinding Based on Random Abrasives and Performance Evaluation

The surface morphology and roughness of a workpiece are crucial parameters in grinding processes. Accurate prediction of these parameters is essential for maintaining the workpiece’s surface integrity. However, the randomness of abrasive grain shapes and workpiece surface formation behaviors poses significant challenges, and accuracy in current physical mechanism-based predictive models is needed. To address this problem, by using the random plane method and accounting for the random morphology and distribution of abrasive grains, this paper proposes a novel method to model CBN grinding wheels and predict workpiece surface roughness. First, a kinematic model of a single abrasive grain is developed to accurately capture the three-dimensional morphology of the grinding wheel. Next, by formulating an elastic deformation and formation model of the workpiece surface based on Hertz theory, the variation in grinding arc length at different grinding depths is revealed. Subsequently, a predictive model for the surface morphology of the workpiece ground by a single abrasive grain is devised. This model integrates the normal distribution model of abrasive grain size and the spatial distribution model of abrasive grain positions, to elucidate how the circumferential and axial distribution of abrasive grains influences workpiece surface formation. Lastly, by integrating the dynamic effective abrasive grain model, a predictive model for the surface morphology and roughness of the grinding wheel is established. To examine the impact of changing the grit size of the grinding wheel and grinding depth on workpiece surface roughness, and to validate the accuracy of the model, experiments are conducted. Results indicate that the predicted three-dimensional morphology of the grinding wheel and workpiece surfaces closely matches the actual grinding wheel and ground workpiece surfaces, with surface roughness prediction deviations as small as 2.3%.

Thermo-mechanical response of near-pearlitic steel heated under restriction of thermal expansion

Railway wheels experience high temperatures during operation, especially during severe block braking. The thermal expansion of wheel rim material due to frictional heating is limited by the wheel's geometry and size. This study investigated the impact of this combined mechanical and thermal loading on the mechanical properties and microstructure in the tread surface of an ER7T steel railway wheel.The material response below the austenitisation temperature is comprehensively evaluated through thermal cycling at peak temperatures of 300, 400, 600, and 650 °C, simulating severe block braking cycles with varying degrees of thermal dilatation (25 %, 50 %, 75 %, and 100 %). An initial plastic deformation was observed during the first heating cycle for the two lower temperatures at lower restrictions, followed by a predominantly elastic response. However, at higher restrictions, the material showed time-dependent relaxation during heating, and some plastic deformation was observed during cooling. Notably, even at the lowest level of restriction, similar observations were made at higher peak temperatures. Increasing the restriction resulted in large strains and a wider hysteresis loop. The test bars exposed to the two higher temperatures retained large tensile stresses after cooling. This indicates a risk of a significantly altered residual stress state in the rim of an overheated railway wheel, which could adversely affect its fatigue properties. The study's outcomes will aid in designing and calibrating constitutive material models for severe block braking. Furthermore, it will significantly contribute to research into the thermo-mechanical behaviour of pearlitic/near-pearlitic materials during railway operations and maintenance.

Dissecting the components of error in analogue report tasks

Over the last two decades, the analogue report task has become a standard method for measuring the fidelity of visual representations across research domains including perception, attention, and memory. Despite its widespread use, there has been no methodical investigation of the different task parameters that might contribute to response variability. To address this gap, we conducted two experiments manipulating components of a typical analogue report test of memory for colour hue. We found that human response errors were independently affected by changes in storage and maintenance requirements of the task, demonstrated by a strong effect of set size even in the absence of a memory delay. In contrast, response variability remained unaffected by physical size of the colour wheel, implying negligible contribution of motor noise to task performance, or by its chroma radius, highlighting non-uniformity of the standard colour space. Comparing analogue report to a matched forced-choice task, we found variation in adjustment criterion made a limited contribution to analogue report variability, becoming meaningful only with low representational noise. Our findings validate the analogue report task as a robust measure of representational fidelity for most purposes, while also quantifying non-representational sources of noise that would limit its reliability in specialized settings.

Comparing the advantages and disadvantages of physics-based and neural network-based modelling for predicting cycling power

Models of physical phenomena can be developed using two distinct approaches: using expert knowledge of the underlying physical principles or using experimental data to train a neural network. Here, our aim was to better understand the advantages and disadvantages of these two approaches. We chose to model cycling power because the physical principles are already well understood. Nine participants followed changes in cycling cadence transmitted through a metronome via earphones and we measured their cadence and power. We then developed and trained a physics-based model and a simple neural network model, where both models had cadence, derivative of cadence, and gear ratio as input, and power as output. We found no significant differences in the prediction performance between the models. Both models had good prediction accuracy despite using less input variables than traditional models and using more challenging prediction conditions by enforcing rapid speed changes during cycling. The advantages of the neural network model were that, for similar performance, it did not require an understanding of the underlying principles of cycling nor did it require measurements of fixed parameters such as system weight or wheel size. These same features also give the physics-based model the advantage of interpretability, which can be important when scientists want to better understand the process being modelled.

Meshing principle and numerical study of classic conic worm drive

To explore the meshing mechanism of classic conic worm drive and provide a theoretical basis for creating other types of worm drive, a complete meshing theory on the proposed worm pair and its meshing performance are investigated. A new mathematical model containing a full set of geometric parameters on this drive is established using differential geometry. The formulae for calculating the reference point coordinates in different coordinate systems are attained, and then the blank size of the conical worm wheel is given. To build tooth surface boundaries, the meshing theory based on reference point is applied, which ensures the location of this point on the tooth surface. By solving multivariate nonlinear equation system in MATLAB environment, these conjugate regions and instantaneous contact lines are plotted within the axial section of the conic worm pair, at the same time, these values of sliding angle and induced principal curvature at meshing points are calculated. Finally, a numerical study is performed and the results verify that the conic worm pair has a relatively high tooth surface utilization ratio and favorable conditions for contact stress and lubrication, which is consistent with the practical application.

Application of Finite Element Algorithms for Formula Racing Steering Wheels

The steering wheel of a Formula Student car has an important influence on the driving and handling stability of the car. The steering wheel of the racing car must have good mechanical and stable performance, taking into account lightweight and economic performance. Due to the small riding space of the car, the size of the steering wheel is not required to be too large. In this case, it is very difficult to meet its harsh stress state and control its vibration and noise. Based on the general requirements of the competition rules of the Formula Student racing competition, this paper constructs the geometric model of the steering wheel of the racing car by using the computer 3D design software CATIA. ANSYS software was used to conduct finite element analysis of the mechanical properties of the metal skeleton of the steering disc. Magnesium alloy, a light material with excellent mechanical properties, was selected, and combined with the actual working conditions of the steering disc, especially the force under extreme conditions, the computer simulation results showed that the force distribution and displacement of the steering disc met the design requirements. Considering that the noise and vibration of the steering wheel will have a great impact on the racer, the modal analysis of the steering wheel is carried out by using ANSYS software, and the analysis results show that there is no resonance or instability.

A Grinding Method with an Innovative, Efficient, and Weight-Saving Design for Double Helical Gears

Grinding technology exerts an enormous effect on the surface quality of double helical gears, which are subject to stringent requirements in the aviation industry. This study presents a novel gear-gap-space-borrowing grinding method that diverges from existing techniques. Unlike conventional approaches, this method mitigates the design–manufacturing conflict by exploiting the opposing gear gap space. By borrowing space, the grinding wheel’s size can be enlarged to enhance machinability, diminish the width of the undercut, and align with the lightweight design imperative of double helical gears. The relationship between the grinding wheel diameter and the design parameters of double helical gears is analytically established, leading to the formulation of design rules. These rules facilitate the rapid selection of appropriate grinding wheel sizes for the space-borrowing method. Additionally, through geometric modeling and experimental validation, the optimal gear undercut width and the maximum wheel diameter are determined. The validity and accuracy of the proposed method are verified by simulations and experimental investigations. The study quantitatively evaluates the benefits of this method, including the expansion of the grinding wheel size, the reduction in double helical gear weight, and enhancements in processing efficiency and quality, providing a comprehensive comparison and discussion of these improvements.

Design concepts and control algorithm to minimize the control effort for earth-orbit-raising solar sails

This paper presents novel design concepts and a robust sliding mode control (RSMC) algorithm for a solar sail optimized for an Earth-orbit-raising demonstration mission. The design of the solar sail is focused on minimizing mission difficulty and control effort during the Earth-orbit-rising mission. To this end, a gravity-stabilized long boom and one-sided black-coating film are introduced in the solar sail system, and a reaction wheel is used as a control torque actuator. The strategic combination of these components modifies the attitude control task from 90° back-and-forth pitch motion control for maintaining the proper attitude for receiving solar radiation pressure (SRP) to that of stabilizing the sail attitude perturbed from gravity-stabilized equilibrium. This simplification of the control task can minimize the mission difficulty and control input energy because attitude control is required only for small deviations from the attitude equilibrium, while the one-sided black-coated film with a reflective surface on the opposite side ensures that SRP propulsion effectively pushes the sail toward the orbit-rising direction. Thus, the control torque of the reaction wheel size can be reduced. To validate the Earth-orbit-raising mission performance, a quaternion-based RSMC approach is established for the six degree-of-freedom dynamic model. The simulation results confirm that the proposed solar sail system can stabilize its attitude with minimal control torque energy of the reaction wheels during Earth-orbit-raising missions.

RESEARCH ON 3D MEASUREMENT TECHNOLOGY BASED ON MACHINE VISION

Measurement is an important means for humans to understand and transform the world, and it is the technological foundation for breaking through the forefront of science and solving major problems in economic and social development. The three-dimensional measurement system serves primary national needs, leads national economic development, and ensures national defense security. With the arrival of a new industrial revolution, major industrial countries worldwide have begun to accelerate the strategic deployment of intelligent manufacturing. As an essential component of the construction of smart factories and lighthouse factories, the 3D measurement system will play a vital role in deepening the implementation of the manufacturing power strategy and promoting the high-end, intelligent, and green manufacturing process. In recent years, optical 3D measurement technology represented by surface structured light has developed rapidly and has been widely applied in multiple material processing fields such as forging, casting, and sheet metal. To analyze the manufacturing accuracy of complex parts using surface structured light 3D measurement technology, it is necessary to first scan and reconstruct the overall 3D surface of the part. The reconstructed 3D point cloud data of the part surface should be roughly and precisely matched with the design model. Finally, based on this, data comparison and accuracy analysis should be carried out according to the actual detection requirements of different types of parts. In this process, the accuracy of 3D reconstruction of complex parts and the alignment accuracy between the reconstruction results and the design model directly determine the reliability and accuracy of the final part manufacturing and machining accuracy analysis. This article uses cases to illustrate the application of machine vision in 3D online measurement. The application of three-dimensional measurement technology in online quality inspection and grinding of blades can not only improve the measurement accuracy of online quality inspection of blades but also maintain the relative stability of robot grinding force and improve the grinding effect in robot grinding of aircraft engine blades. Applied to online quality inspection of train wheel hubs, three-dimensional measurement of train wheel adapters and high-speed train wheel size online inspection has been achieved.

Power loss of the chain drive in a race tandem bicycle

Tandem cycling is a paralympic discipline, in which two cyclists ride on one tandem bicycle. Their performance can be improved by minimizing power losses. This study aimed to quantify power loss due to the chain drive of a tandem bicycle and influence of power input, location of power input, and rear chain wheel size. Power loss was determined by the difference between power input applied on the cranks (front or back rider) and power output measured at the rear wheel. Power output values were set from 100 to 400 W, with 50 W increments, and using two gear ratios, 53-11 and 53-13. Power input was generated at the back crank (with only the primary chain—solo bicycle—and with primary and secondary chain attached) and at the front crank (with primary and secondary chain attached). The power loss for the solo bicycle was 2.1% (± 1.5%). A significantly larger power loss was found for the tandem in the back (3.7 ± 2.4%, p < 0.001) and front positions (3.0 ± 1.8%, p < 0.001), with marginal differences between positions at higher power output. Power loss for the tandem was lower with gear 53-13 (2.9% ± 1.7%) compared to 53-11 (4.0 ± 2.8%, p < 0.001, effect size is medium). Therefore, findings suggest that back and front riders experience similar power losses due to the chain drive, but more than on a solo bicycle. Tandem cyclists can reduce their power loss in the chain drive by selecting larger gear ratios. Coaches may consider these findings for selecting and coaching their tandem cyclists.

Experimental Investigation of the Calcified Plaque Material Removal Rate in Coronary Rotational Atherectomy

Abstract Rotational atherectomy (RA) is a minimally invasive procedure to remove the calcified atherosclerotic plaque from arteries to restore blood flow. It uses a high-speed, metal-bonded diamond abrasive grinding wheel to pulverize the calcified plaque into absorbable debris via a catheter through the artery. Although RA has been clinically used for over two decades, procedural complications persist and there remains a lack of consensus on the optimal device parameters. This study aims to investigate the material removal rate (MRR) in coronary RA with respect to grinding wheel sizes and rotational speeds based on a tissue-mimicking phantom. Three grinding wheel sizes, 1.25, 1.5, and 1.75 mm in diameter, and three rotational speeds, 1,20,000, 1,50,000, and 1,80,000 rpm, were investigated. The RA MRR was presented as the luminal area gain and measured by microscopy and image processing. The results show the increase in the grinding wheel size or rotational speed leads to a higher MRR and luminal gain in RA. With a 1.75 mm diameter grinding wheel rotating at 1,80,000 rpm in a 2 mm initial diameter lumen, the max MRR and the luminal gain are 2.49 mm2/three passes and 5.09 mm2, respectively. The MRR decreases as the number of grinding passes increases during RA with the same grinding wheel rotating at a constant speed. This study provides a thorough understanding of the wheel size and speed effects on coronary RA MRR for potential improvements in RA devices and clinical operational guidelines.

Hydrodynamic flexible spindle (HydroFlex) polishing for internal surfaces of complex channels with high aspect ratio

Internal surface finishing of complex channels fabricated by additive manufacturing (AM) is of large consequence to the future functionality of AM components. Conventional fluid-based internal polishing methods struggle to maintain surface finish uniformity and dimensional integrity especially in long, complex channels with correspondingly high aspect ratios. In this study, we introduce a novel hydrodynamic flexible spindle (HydroFlex) polishing process, in which a fixed diamond abrasive wheel is driven by a high-speed flexible spindle and the hydrodynamic force from the flow pattern surrounding the wheel. The performance of HydroFlex polishing in long, complex channels was experimentally investigated. HydroFlex polishing was evaluated in both straight and curved channels with wheel speeds of 50,000, 70,000, and 90,000 rpm and wheel sizes of 1.75, 2.00, and 2.25 mm. Surface finish, grinding forces, dimensional integrity, and surface uniformity were quantitatively compared. This technique improved surface roughness by 88.2% with sub-micron roughness obtained. Channels with varied curvature and length were consistently polished with deviation in roughness and material removal being 7% and 11% indicating uniformity in material removal, and surface roughness improvement regardless of part geometry. Rotational speed and grinding wheel size were found to directly correlate with grinding force and cutting motion. The findings show the potential of HydroFlex polishing being used for uniform, surface roughness improvement in complex, high aspect ratio channels such as those produced by AM processes.

Modeling on the Flatness of Silicon Wafers Ground by the Grind-polishing Wheel

The grind-polishing wheel is a new non-woven structure grinding tool with low elastic modulus and ultra-fine abrasive grains, which can obtain high surface/sub-surface quality ground silicon wafers. To obtain high-shape flatness during grinding with the grind-polishing wheel, a prediction model of the ground silicon wafers’ flatness considering the elastic modulus of the wheel, processing parameters, and abrasive grain size is developed. The grinding experiments under different speed ratios were conducted to verify the prediction model accuracy. It shows that the model can successfully predict the flatness of ground silicon wafers, and the error of the prediction model is less than 13%. The proposed model has some guiding significance for choosing the appropriate character of the grind-polishing wheel and grinding parameters to achieve desirable flatness for silicon wafers.

Enhancing a Three-Mass Vehicle Model with Wheel-Size Effect for Scanning Bridge Frequencies

An advanced miniature vehicle model is proposed by incorporating size of two wheels in a three-mass vehicle model to consider the offset of contact points due to the presence of pavement irregularity. In this proposed vehicle–bridge system, each wheel has its own dimension in addition to the mass related to the degree-of-freedom while it is assumed to be rigid. In the theoretical formulation, the real contact points and contact displacements turn to be unknown parameters. As such, a numerical framework is established by proposing a procedure in the time integration scheme to determine these parameters and deriving explicit coding structure to locate the two wheels on the bridge during simulation. The parametric study investigates the size effect of wheels, effect of vehicle damping, and pitching effect as a result of wheel size on the identification of frequencies. The results show that using larger wheels leads to smaller dynamic responses of the bridge and smaller vertical responses of the vehicle by the present vehicle model. Furthermore, higher accuracy is observed in the proposed vehicle model in comparison with the traditional three-mass vehicle model. The first three bridge frequencies can be identified distinctly under the most severe pavement irregularity.

Data-driven approach for investigating and predicting rutting depth of asphalt concrete containing reclaimed asphalt pavement

The aim of this paper is to investigate and predict the rutting depth of asphalt concrete containing Reclaimed Asphalt Pavement (RAP) content by the data-driven approach with aid of 6 six tree algorithm including Random Forest (RF), Gradient Boosting (GB), Adaptive Boosting (AdaB), Extreme Gradient Boosting (XGB), Light Gradient Boosting (LightGB) and Categorial Gradient Boosting (CatB) using default hyperparameters. A database containing 396 data samples derived from Hamburg Wheel Tracking Test (HWTT) and consisting of 11 input variables such as Corrected Optimum Asphalt Content (COAC), Reclaimed Asphalt Pavement, Nominal Maximum Aggregate Size (NMAS), Flashpoint, m-Value, Mass loss, Specific gravity, Viscosity, Creep stiffness, Temperature, and Number of wheels and 1 output Rutting depth are created. 10 times of 10-Fold CV and four metrics such as R2, RMSE, MAE and MAPE are used to verify the robustness of ML models. XGB model has highest performance with the mean value of R2, RMSE, MAE and MAPE to be equal to 0.9792, 1.0767 mm, 0.7085 mm, 0.1034% respectively. Comparing with other factors like the number of load cycles (number of wheels) and mix design considerations, temperature has a dominant impact on the rutting depth of asphalt pavement (type of binder, NMAS, RAP content). The rutting depth value rises with increasing temperature and COAC. NMAS has a negligible impact on asphalt pavement's resistance to rutting. To increase the rutting resistance when building the asphalt pavement, the chosen asphalt binder has high Viscosity and Flashpoint values. The local interpretation clearly demonstrates each factor's contribution to the rutting depth value in each unique scenario. Engineers can design the rutting resistance of asphalt pavement in advance thanks to the mapping produced by the Partial Dependence Plot 2D under grid contour.

Use of Mobile Sensing Data for Assessing Vibration Impact of E-Scooters with Different Wheel Sizes

With the growing demand of shared electric scooters (e-scooters) for short-distance trips in urban areas, their safety issues have received significant attention from various stakeholders. In general, e-scooter riders encounter more vibrations compared with users of other transportation modes such as bicycles that typically have larger wheels and better suspension systems. Such riding experience may lead to discomfort, affect riders’ health, and increase riding risk. Intuitively, increasing e-scooters’ wheel sizes may provide safer and more comfortable riding experience. However, this assumption has not been well tested. The main objective of this paper is to curtail this gap by quantitatively assessing the impacts riders experienced, through the use mobile sensing data. Specifically, a mobile sensing platform was deployed on e-scooters with different wheel sizes to continuously measure encountered vibrations. Then, the instrumented e-scooters were ridden on routes with different pavement materials. Finally, the collected data were further processed and analyzed to evaluate various riding issues in each riding scenario. The comparative results suggest that e-scooters with larger wheels can efficiently alleviate vibrations during a ride compared with those with smaller wheels. To improve riding experience and safety, it is beneficial to use larger-wheel e-scooters, given other similar riding conditions.

Two Functional Wheel Mechanism Capable of Step Ascending for Personal Mobility Aids

Obstacles such as ramps, steps, and irregular floor surfaces are commonly encountered in homes, offices, and other public spaces. These obstacles frequently limit the daily activities of people who use mobility aids. For this purpose, this study solves a slope minimization problem for personal mobility aids. As a solution approach, a gradient-reduction scheme is proposed, which allows existing mobility aids to reduce the required horizontal forces and vibrations when ascending steps while maintaining their wheel sizes. Practically, an axle-transitional wheel mechanism realizing the gradient-reduction computation model is established, and its step-ascending wheel prototype is developed. Specifically, since the proposed wheel enables integration into existing personal mobility-assisting devices, two functional roles, such as rolling and step ascending, can be used. The developed step-climbing wheel can help the users of mobility aids mitigate the aforementioned limitations. The physical and mental burdens of caregivers and medical staff can also be reduced by making the users of the gradient-reduction scheme more self-sufficient. This study provides details on the axle-transitional wheel mechanism and its step-ascending wheel prototype. The findings are analyzed mathematically, and their functionality is verified through extensive experiments using a prototype.

Generation of Surface Roughness Profiles for Inclusion in Vehicle–Bridge Interaction Analysis and Test Application

Vehicle’s wheels were mostly modeled as a point, which can touch the valleys of pavement roughness, creating unrealistic high-frequency oscillation. This can be avoided by using the disk model for the wheels, which however adds significant complexity to the vehicle–bridge interaction (VBI) analysis. In this paper, a refined roughness formula is generated to account for the wheel size effect such that it can be used by point model. Still, the low-frequency part of the roughness presents some masking effect on the bridge scanning by the test vehicle. To this end, two countermeasures are suggested, i.e. residual response and traffic flows. This study has demonstrated that: (1) the roughness generated by the refined formula can reflect the trace of the disk model; (2) the refined formula facilitates the VBI analysis by using the point model; and (3) the two countermeasures for roughness are effective for improving the scanning of bridge frequencies.

Techno-economic evaluation of a hybrid photovoltaic system with hot/cold water storage for poly-generation in a residential building

There is a growing effort towards the application of solar technologies to meet electrical and thermal demand. However, substantial energy is used in buildings around the world for electricity and thermal comfort. Here we evaluate a novel hybrid solar-powered system for reducing the load on the direct expansion and heat pump unit of a combined heating and air conditioning system while generating electricity. The system combines rooftop photovoltaic (PV) and building-integrated photovoltaic thermal (BIPV/T) systems for electricity generation, while any excess electricity is used to drive a hot and cold water storage system. A residential building in Tehran is used as a case study, and the results are computed via MATLAB, TRNSYS, and Carrier HAP software. The system is shown to outperform both rooftop PV and BIPV/T systems alone, generating at least 50% more electricity while reducing the heating and cooling loads on the machinery by at least 60%. The system also enjoys a payback time of 2.87 years. The impact of thermal comfort setpoints, in addition to inflation and discount rates, are also evaluated via a sensitivity analysis involving several key performance metrics, namely the hot and cold water storage volumes, the size of the desiccant wheel, and the payback time. The cooling load is found to have the greatest influence on the cold water storage volume and the desiccant size, with 80.1% and 41.2% variations for baseline variations of ±20%. With a 57.7% increase, the heating load is found to have the biggest influence on the hot water storage volume. With a 27.1% variation, inflation has the strongest effect on the payback time.

A parametric study of nose landing gear noise in a large-scale aeroacoustic wind tunnel

The nose landing gear (NLG) of an aircraft considerably contributes to the undercarriage noise. In this paper, a large-scale testing program was conducted within the FL-17 5.5 m×4 m aeroacoustic wind tunnel in CARDC to characterize the effects from various parameters on the acoustic performance of a generic NLG model. Those investigated parameters include incoming flow velocity, wheel size, height, angle of attack and yaw angles. The test was majorly comprised of noise source localization and free-field sound pressure level spectra analysis. Two categories of tonal noise were distinguished depending on variation between frequency and incoming flow speed. Effects of the sideline directivity were analyzed, and it was found that the side distribution of OASPL shows a saddle-like trend with the flow/flight direction and the tonal noise changes significantly with directivity angle. Regarding spectral scaling, U∞7 was found to be more appropriate for a large-scale NLG model, while for a compact small-scale NLG model, the traditional U∞6 is still recommended. As to transitional size, a combination of U∞7 and U∞6 showed to be more suitable for scaling within the high and low frequency ranges respectively. Contributions of different elements to NLG noise to different noise sources were discussed, which were found not to be dependent on their relative sizes. Analysis of the wheel diameter showed it does not cause obvious changes to the overall spectra trend but can induce variation of the amplitude and frequency tones. When the wheel is sufficiently small, the upper head of the sliding piston can be directly exposed to the incoming flow and thus generate sharp tonal noise. In terms of NLG height, the main effects on the acoustic performance was found to be associated not with the change in the height itself, but rather with the accompanying changes from other elements. Finally, the effects of angle of attack (α) and yaw angle (β) were analyzed with results showing that the angle of attack could potentially lead to substantial changes in the acoustic performance, while the yaw angle within 0°-8° has minimal effects.