Aerodynamics of the Maple Seed

Purpose - The paper presents a theoretical framework that describes the aerodynamics of a falling maple (Acer pseudoplatanus) seed. --- Methodology - A semi-empirical method is developed that provides a ratio stating how much longer a seed falls in air compared to freefall. The generated lift is calculated by evaluating the integral of two-dimensional airfoil elements using a preliminary falling speed. This allows for the calculation of the definitive falling speed using Blade Element Momentum Theory (BEMT); hereafter, the fall duration in air and in freefall are obtained. Furthermore, the input-variables of the calculation of lift are transformed to require only the length and width of the maple seed. Lastly, the method is applied to two calculation examples as a means of validation. --- Findings - The two example calculations gave percentual errors of 5.5% and 3.7% for the falling speed when compared to measured values. The averaged result is that a maple seed falls 9.9 times longer in air when released from 20 m; however, this result is highly dependent on geometrical parameters which can be accounted for using the constructed method. --- Research limitations - Firstly, the coefficient of lift is unknown for the shape of a maple seed. Secondly, the approximated transient state is yet to be verified by measurement. --- Originality / Value - The added value of this report lies in the reduction of simplifications compared to BEMT approaches. In this way a large amount of accuracy is achieved due to the inclusion of many geometrical parameters, even though simplicity is maintained. This has been accomplished through constructing a simple three-step method that is fundamental and essentially non-iterative

Replication Data for: Improved Air Gap Permeance Modelling for Single-Slice Magnetic Equivalent Circuit of Skewed Inductions Motors

Replication scripts and data to determine the shape and saturation correction factors for use in NISM and AISM based on a .fem induction motor model. A grid search over the correction factors is performed and the selected factors can be evaluated

Electrical Signature Analysis Data of a Rotor-Eccentric 1.1 kW Induction Motor

Datasets of time values, phase, ground, neutral and line voltages and current measurements of a modified 1.1 kW Cantoni 2SIEL 80-2B induction machine supplied using an Inverto IFC5.5-MP/460 frequency drive and measured using the Pqube 3 Travel power quality analyser. Faulty bearings and eccentric rotor positions are measured. The presence of broken rotor bars has been detected by motor inductance, resistance, and current analysis

A Dataset of Electrical, Thermal, and Radial Shaft Force Measurements of a 1.1 kW Induction Motor with Static Rotor Eccentricity

A dataset is created of terminal voltages, phase currents, stator temperature and radial shaft forces of a rotor-eccentric 1.1 kW induction motor. The induction motor was modified to introduce static rotor eccentricity on the load-end of the motor in a controlled manner by radially displacing the load-side bearing. To achieve this, the motor bearing was externalised and an external flange construction allows a precise introduction of static rotor eccentricity. By changing the flange plate on which the external bearing is mounted, three settings of static eccentricity are introduced: a centric rotor, a rotor with 25% air gap eccentricity at the load side, and a rotor with 50% air gap eccentricity at the load side. Note that while these displacements are present at the load side, the fan-side of the motor remains centric. This means that the average rotor eccentricity is much lower than 25% and 50% of the air gap length. Additionally, the direction of the eccentricity is changed in increments of 90° by rotating the flange plate. The temperature values can be used to infer the actual stator phase resistance as R = R_0 * (1 + k * (T - T_ref)), with the reference phase resistance R_0 = 3.99 ohm at the reference temperature 20°C, and the measured thermal coefficient k = 0.0043609

Replication Data for: Modelling mechanical faults in induction motors using magnetic equivalent circuits and lumped-element shaft-bearing dynamics

A magnetic equivalent circuit induction motor model is combined with a lumped-element rotor dynamics model. Their combination is analysed for (i) rotor position, (ii) rotor acceleration, (iii) unbalanced magnetic pull, (iv) bearing acceleration, and (v) stator currents in the presence of the following mechanical faults: (i) no-fault case, (ii) a stator outer race misalignment, (iii) a rotor mass unbalance, (iv) a bearing outer race spall fault, (v) a bearing inner race spall fault, (vi) a bearing ball spall fault. The dataset is stored as the complete state and input time-series of both models. Additionally, the dq-transformed stator currents are provided

The influence of the unbalanced magnetic pull on fault-induced rotor eccentricity in induction motors

When performing bearing fault measurements, the unbalanced magnetic pull’s (UMP) influence is inadvertently incorporated. The UMP’s influence distorts the measurements used for bearing fault size estimation, leading to inaccurate fault interpretations. In this paper, we combined a magnetic equivalent circuit motor model with a dynamic bearing model to isolate the UMP’s effect, which is unprecedented in the state of the art. The coupled model is used to analyse the dynamic interaction between a mechanical fault and the UMP without neglecting the influence of the rotor slot harmonics nor the magnetic potential losses in the stator and rotor. We compare simulations performed with the UMP and without the UMP in the presence of (i) an outer race bearing fault and (ii) an outer race bearing fault combined with an intrinsic rotor misalignment (IRM). The study finds that the UMP amplifies the rotor eccentricity by a non-negligible amount without accounting for an IRM. Moreover, with the inclusion of an IRM, the rotor vibrations are distorted to the point where bearing fault estimation algorithms could become inoperable. The presence of rotor slot harmonics in the UMP has been identified as a key contributor to the distortion. The findings presented in this article can be used to improve bearing fault size estimation algorithms by isolating the disturbances caused by the UMP. </jats:p

Supplemental Material - The influence of the unbalanced magnetic pull on fault-induced rotor eccentricity in induction motors

Supplemental Material for The influence of the unbalanced magnetic pull on fault-induced rotor eccentricity in induction motors by Philip Desenfans, Zifeng Gong, Dries Vanoost, Konstantinos Gryllias, Jeroen Boydens, and Davy Pissoort in Journal of Vibration and Control</p

A Boundary-Preserving Non-Conformal Mapping for Radial Rotor Eccentricity in Finite Element Simulations of Electrical Machines

Detailed field solutions obtained by the finite element method (FEM) for electrical machines come at a large computational cost. By introducing a novel non-conformal mapping (NCM), which transforms a rotor-centric air-gap domain to a rotor-eccentric air-gap domain, the computational cost and discretization error associated with remeshing are avoided. In contrast to the existing NCM approaches, the proposed solution preserves the boundaries of the air-gap domain concerning a change in rotor eccentricity. Resultingly, the interpolation error at the domain intersections with the FEM stator and rotor models is minimized, limited only by a moving band, which allows the rotation of the rotor. A general validation of a rotor-eccentric induction motor using the novel NCM is performed. Thereafter, a thorough comparison between the NCM and remeshing in terms of mesh quality and computational cost is made. For rotor eccentricities below 90% of the air gap, mesh quality is found to be in line with reference methods. Moreover, due to the efficient mapping and the sole requirement of a single moving band to accommodate rotor rotation, the NCM results in a 50% reduction of the total computation time compared with remeshing and a 12% reduction compared with a recent reference NCM