Rotor Optimization Research Articles

Assembly accuracy prediction and optimization of aero-engine rotor under the separation condition of assembly and measurement

The measurement and assembly of the aero-engine rotor are separated from each other, which makes it difficult to keep the assembly datum consistent with the measurement datum; the existence of the datum error will cause the characteristic matrix to fail to truly reflect the geometric state of the rotor itself and cause the assembly model to be inaccurate, then ultimately affect the assembly accuracy prediction. Combined with the fact that the geometric characteristics of parts/components are not related to the measurement datum, the datum error elimination method has been proposed which makes the rotor characteristic matrix and assembly model more accurate, thereby improving the prediction effect of assembly accuracy. At the same time, the proposed direct optimization strategy is more efficient than the traditional genetic algorithm. The assembly experiment of the aero-engine rotor shows that the model and method proposed in this paper can better reflect the geometric characteristics of the rotor itself and are beneficial to reduce the coaxiality of the front and rear fulcrum. The related research also has reference significance for other large-scale and high-precision mechanical product assemblies.

Performance based systematic design methodology for development and flight testing of fuel engine powered quadrotor Unmanned Aerial System for industrial applications

This paper presents a systematic study of the design optimization, development, vibration analysis and flight testing of a single power plant variable pitch quadrotor Unmanned Aerial System (UAS) for industrial applications. The use of variable pitch rotors enables the use of a two-stroke internal combustion engine for powering the four rotors through a mechanical transmission. The proposed methodology is described by carrying out the design of a quadrotor UAS with 2–3 kg payload capacity and have endurance in excess of one hour. The study is conducted in a systematic manner. First, the design of rotors is optimized for minimum power consumption during hover as well as forward flight condition using physics based simulation developed and validated for this purpose. From the rotor optimization, an untwisted rotor blade with taper ratio of 0.6 and aspect ratio of 10 appeared to be an optimal choice for the current design. Next, the powerplant selection is carried out based on the optimized rotor designed earlier. Next, two different approaches for mechanical power transmission design is considered: torque tube-bevel gear and belt–pulley system based designs. The transmission system designed using belt and pulley was nearly 14% lighter and showed greater tolerance to manufacturing imperfections. Next, two prototypes are designed and its static and dynamic analysis is carried out to ensure its airworthiness. A Proportional Integral Derivative (PID) based attitude controller is developed using quarternions for attitude stabilization and trajectory tracking to test the flight in simulation and then subsequently on the actual vehicle by implementing it on PixHawk autopilot board. Finally, system integration is carried out to build two prototypes of engine powered quadrotor UAS. Then, vibration data is recorded using the sensors onboard to conduct the vibration analysis and design an efficient vibration isolator. Performance analysis is also, carried out to estimate the speed for best endurance (11 m/s) and best range (27 m/s) for the variable pitch quadrotor designed. The estimated best endurance achieved is 2.2 h and estimated best range is more than 150 km. This design revisits and solves the challenge of developing an agile helicopter without cyclic pitch control which was first explored nearly a century ago.

Near-wake dynamics of a vertical-axis turbine

Cross-flow, or vertical-axis, turbines are a promising technology for capturing kinetic energy in wind or flowing water and their inherently unsteady fluid mechanics present unique opportunities for control optimization of individual rotors or arrays. To explore the potential for beneficial interactions between turbines in an array, as well as to characterize important cycle-to-cycle variations, coherent structures in the wake of a single two-bladed cross-flow turbine are examined using planar stereo particle image velocimetry in a water channel experiment. There are three main objectives in the present work. First, the mean wake structure of this high chord-to-radius ratio rotor is described, compared with previous studies, and a simple explanation for observed wake deflection is presented. Second, the unsteady flow is then analysed via the triple decomposition, with the periodic component extracted using a combination of traditional techniques and a novel implementation of the optimized dynamic mode decomposition. The latter method is shown to outperform conditional averaging and Fourier methods, as well as uncover frequencies suggesting a transition to bluff-body shedding in the far wake. Third, vorticity and finite-time Lyapunov exponents are then employed to further analyse the oscillatory wake component. Vortex streets on both sides of the wake are identified, and their formation mechanisms and effects on the mean flow are discussed. Strong axial (vertical) flow is observed in vortical structures shed on the retreating side of the rotor where the blades travel downstream. Time-resolved tracking of these vortices is performed, which demonstrates that vortex trajectories have significant rotation-to-rotation variation within one diameter downstream. This variability suggests it would be challenging to harness or avoid such structures at greater downstream distances.

Design and Analysis of Dual‐Stator Brushless Doubly‐Fed Generator for Wind Turbine

Brushless doubly‐fed generator (BDFG) is a most promising candidate for the wind turbine due to its simple structure, high reliability, and low converter capacity. To improve space utilization and achieve higher power density, this paper proposes a new dual‐stator BDFG (DS‐BDFG), which provides two separated windings, namely, the power winding (PW) placed in the outer stator and the control winding (CW) placed in the inner stator. A cup‐shaped rotor sandwiched between the inner and outer stators consists of the short‐circuited coil and the salient‐pole core. The coupling between the PW and the CW is realized via the rotor based on the general airgap magnetic field modulation theory for electrical machines. A prototype of the DS‐BDFG with rated PW power of 7.2 kW is designed and optimized. The keys of this paper are the power equation derivation, the determination of pole/slot combinations, and the rotor optimization. The electromagnetic characteristics and unbalanced magnetic force of the DS‐BDFG are analyzed by 2D finite element analysis to verify the reasonableness of the proposed model. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Identification of Bearing Dynamic Parameters and Unbalanced Forces in a Flexible Rotor System Supported by Oil-Film Bearings and Active Magnetic Devices

As the rotational speed of conventional rotor systems supported by oil-film bearings has increased, vibration problems such as oil whip and oil whirl have become apparent. Our group proposed the use of active magnetic bearings (AMBs)/bearingless motors (BELMs) to stabilize these systems. In such a system, measuring the variable stiffness and damping of the oil-film bearings, the current-force and displacement-force parameters of the AMBs/BELMs, and the residual unbalanced force is necessary to satisfy the stability of the rotor system. These parameters are the foundation for the rotor dynamics analysis and optimization of the control strategy. In this paper, we propose a method to simultaneously identify the parameters of the oil-film bearings and AMBs/BELMs along with the residual unbalanced forces during the unbalanced vibration of the rotor. The proposed method requires independent rotor responses and control currents to form a regression equation to estimate all the unknown parameters. Independent rotor responses are realized by changing the PID control parameters of the AMBs/BELMs. Numerical simulation results show that the proposed method is highly accurate and has good robustness to measurement noise. The experimental results show that the unknown parameters identified by the responses generated by different controller parameters are similar. To confirm that the identification results are correct, verification experiments were carried out. The vibration amplitude of the rotor was successfully suppressed by applying a force to the rotor in the opposite direction to the residual unbalanced force. The frequency response characteristics and unbalanced responses of the rotor estimated by the values of the parameters identified show good consistency with the measured results.

The stochastic aeroelastic response analysis of helicopter rotors using deep and shallow machine learning

This paper addresses the influence of manufacturing variability of a helicopter rotor blade on its aeroelastic responses. An aeroelastic analysis using finite elements in spatial and temporal domains is used to compute the helicopter rotor frequencies, vibratory hub loads, power required and stability in forward flight. The novelty of the work lies in the application of advanced data-driven machine learning (ML) techniques, such as convolution neural networks (CNN), multi-layer perceptron (MLP), random forests, support vector machines and adaptive Gaussian process (GP) for capturing the nonlinear responses of these complex spatio-temporal models to develop an efficient physics-informed ML framework for stochastic rotor analysis. Thus, the work is of practical significance as (i) it accounts for manufacturing uncertainties, (ii) accurately quantifies their effects on nonlinear response of rotor blade and (iii) makes the computationally expensive simulations viable by the use of ML. A rigorous performance assessment of the aforementioned approaches is presented by demonstrating validation on the training dataset and prediction on the test dataset. The contribution of the study lies in the following findings: (i) The uncertainty in composite material and geometric properties can lead to significant variations in the rotor aeroelastic responses and thereby highlighting that the consideration of manufacturing variability in analyzing helicopter rotors is crucial for assessing their behaviour in real-life scenarios. (ii) Precisely, the substantial effect of uncertainty has been observed on the six vibratory hub loads and the damping with the highest impact on the yawing hub moment. Therefore, sufficient factor of safety should be considered in the design to alleviate the effects of perturbation in the simulation results. (iii) Although advanced ML techniques are harder to train, the optimal model configuration is capable of approximating the nonlinear response trends accurately. GP and CNN followed by MLP achieved satisfactory performance. Excellent accuracy achieved by the above ML techniques demonstrates their potential for application in the optimization of rotors under uncertainty.

Design optimization of vehicle asynchronous motors based on fractional harmonic response analysis

Abstract. To make vehicles more reliable and efficient, many researchers have tried to improve the rotor performance. Although certain achievements have been made, the previous finite element model did not reflect the historical process of the motor rotor well, and the rigidity and mass in rotor optimization are less discussed together. This paper firstly introduces fractional order into a finite element model to conduct the harmonic response analysis. Then, we propose an optimal design framework of a rotor. In the framework, objective functions of rigidity and mass are defined, and the relationship between high rigidity and the first-order frequency is discussed. In order to find the optimal values, an accelerated optimization method based on response surface (ARSO) is proposed to find the suitable design parameters of rigidity and mass. Because the higher rigidity can be transformed into the first-order natural frequency by objective function, this paper analyzes the first-order frequency and mass of a motor rotor in the experiment. The results proved that not only is the fractional model effective, but also the ARSO can optimize the rotor structure. The first-order natural frequency of asynchronous motor rotor is increased by 11.2 %, and the mass is reduced by 13.8 %, which can realize high stiffness and light mass of asynchronous motor rotors.

A method for preliminary rotor design – Part 1: Radially Independent Actuator Disc model

Abstract. We present an analytical model for assessing the aerodynamic performance of a wind turbine rotor through a different parametrization of the classical blade element momentum (BEM) model. The model is named the Radially Independent Actuator Disc (RIAD) model, and it establishes an analytical relationship between the local thrust loading and the local power, known as the local-thrust coefficient and the local-power coefficient respectively. The model has a direct physical interpretation, showing the contribution for each of the three losses: wake rotation loss, tip loss and viscous loss. The gradient for RIAD is found through the use of the complex step method, and power optimization is used to show how easily the method can be used for rotor optimization. The main benefit of RIAD is the ease with which it can be applied for rotor optimization and especially load constraint power optimization as described in Loenbaek et al. (2021). The relationship between the RIAD input and the rotor chord and twist is established, and it is validated against a BEM solver.

A method for preliminary rotor design – Part 2: Wind turbine Optimization with Radial Independence

Abstract. A novel wind turbine rotor optimization methodology is presented. Using an assumption of radial independence it is possible to obtain an optimal relationship between the global power (CP) and load coefficient (CT, CFM) through the use of Karush–Kuhn–Tucker (KKT) multipliers, leaving an optimization problem that can be solved at each radial station independently. It allows solving load constraint power and annual energy production (AEP) optimization problems where the optimization variables are only the KKT multipliers (scalars), one for each of the constraints. For the paper, two constraints, namely the thrust and blade root flap moment, are used, leading to two optimization variables. Applying the optimization methodology to maximize power (P) or annual energy production (AEP) for a given thrust and blade root flap moment, but without a cost function, leads to the same overall result with the global optimum being unbounded in terms of rotor radius (R̃) with a global optimum being at R̃→∞. The increase in power and AEP is in this case ΔP=50 % and ΔAEP=70 %, with a baseline being the Betz optimum rotor. With a simple cost function and with the same setup of the problem, a power-per-cost (PpC) optimization resulted in a power-per-cost increase of ΔPpC=4.2 % with a radius increase of ΔR=7.9 % as well as a power increase of ΔP=9.1 %. This was obtained while keeping the same flap moment and reaching a lower thrust of ΔT=-3.8 %. The equivalent for AEP-per-cost (AEPpC) optimization leads to increased cost efficiency of ΔAEPpC=2.9 % with a radius increase of ΔR=17 % and an AEP increase of ΔAEP=13 %, again with the same, maximum flap moment, while the maximum thrust is −9.0 % lower than the baseline.

Preliminary design, optimization and CFD analysis of an organic rankine cycle radial turbine rotor

• Optimized design for radial turbine of 220 kW operating with Organic Rankine Cycle. • The objective function has increased the efficiency considering loss models. • 1D optimization based on Controlled Random Search Algorithm (CRSA) • Computational Fluid Dynamics (CFD) applied for preliminary design optimized. • The novelty is the application of optimization methodology in the preliminary design. • The total-total efficiency of the radial turbine increased 2.65% after optimization. The present study describes the development of a preliminary design of a rotor for a radial turbine operating in an organic Rankine cycle. An optimization algorithm is applied to the preliminary design in order to obtain a better configuration of the geometric parameters that provides good quantification of the efficiency in the turbine, a priori, since the application of optimization processes applied to three-dimensional problems consume a lot of computational resources. The strategy makes it possible to obtain an optimized geometry to obtain flow field analyzes by applying computational fluid dynamics techniques. The working fluid R236fa was used for comparison with the literature, as it presents a positive slope of the saturation curve, and thus it is possible to work with lower temperatures. The R245fa working fluid is more suitable to the operating conditions of the proposed cycle, allows an overpressure in the condenser and allows higher levels of system efficiency. The losses at the rotor nozzle were initially modeled using a mean line design approach. The preliminary design was implemented in a commercial code Matlab®, as well as the optimization algorithm, CRSA (Controlled Random Search Algorithm), and the real gas formulations were used based on the NIST REFPROP® database. The present study is presented under three work routes: i) Development of the preliminary design methodology for a radial turbine that operates with ORC producing 50 kW of power, in order to compare with other methodologies presented in the literature. The results were compared with results observed in the literature, and demonstrate agreement between the reference geometry and the thermodynamic parameters. The total-total efficiencies of the reference turbine designs were 76.23% (R236fa) and 79.28% (R245fa); ii) Optimization by CRSA of the preliminary design of a radial turbine developed on the basis of flow coefficient and load coefficient correlations. A three-dimensional analysis of the flow through the blade section using computational fluid dynamics was performed in the final optimized design to confirm the preliminary design and subsequently analyze its characteristics. The optimization focused on the R245fa working fluid. Although several optimized preliminary designs are available in the literature with efficiency levels of up to 90%, the preliminary design choices made will only be valid for machines operating with ideal gases, that is, exhaust gases typical of an air-breathing combustion engine. For machines operating with real gases, such as organic working fluids, the design options need to be rethought and a preliminary design optimization process must be introduced. As an important result observed, an efficiency of 82.4% was obtained in the final design of the radial turbine operating with R245fa after the optimization process.

Utilization of reluctance torque for improvement of the starting and average torques of a brushless wound field synchronous machine

In this paper, the reluctance torque is utilized for improving the starting and average torques of a conventional brushless wound field synchronous machine (BL-WFSM). The conventional BL-WFSMs have an inherent issue of zero-starting torque. The existing BL topologies use expensive rare-earth permanent magnets (RE-PMs) to improve the starting torque; however, the marker price of RE-PMs fluctuates. Therefore, this paper proposes the use of the reluctance torque for improving the starting and average torques of BL-WFSMs. The winding topology and machine layout are adopted, from recently published work. The suggested approach increases the reluctance effect in BL-WFSM by optimizing the rotor shape. The reluctance effect is optimized, to improve the starting and average torques. The Kriging method and a genetic algorithm are used for the rotor optimization. A two-dimensional finite element analysis confirms the improved starting and average torques based on the increase in the reluctance torque.

An Unbalance Optimization Method for a Multi-Stage Rotor Based on an Assembly Error Propagation Model

For the assembly of a multi-stage rotor, such as an aero-engine or gas turbine, the parts need to be assembled optimally to avoid excessive unbalance. We propose a method to optimize the unbalance of a multi-stage rotor during assembly. First, we developed an assembly error propagation model for a multi-stage rotor. The alignment process and distribution of the screw holes of the adjacent rotors was considered for the first time. Secondly, we propose a new assembly datum for unbalance optimization to ensure consistency with the actual conditions of a dynamic balance test. Finally, the unbalance optimization of a multi-stage rotor was achieved using a genetic algorithm, and the corresponding optimal assembly orientations of rotors at different stages were also identified. The results of the simulations showed that the assembly error propagation model had high accuracy and that the genetic optimization process had good convergence. The effect of unbalance optimization was also proven with experiments.

Comparative electromagnetic design of high-speed PMSM with reduced torque ripple for automotive application, part 1 – stator design

This paper concerns the initial motor sizing of a high-speed permanent magnet synchronous motor (HSPMSM), that will be used in educational and research applications. Starting dimensions are chosen from an existing machine topology. In the first part, the motor optimization is performed w.r.t. optimal magnetic loading of the stator, for a fixed rotor topology. The rotor optimization is not included, because further thermal and especially mechanical simulations must be conducted.

Evaluation of novel-objective functions in the design optimization of a transonic rotor by using deep learning

Design optimization of transonic airfoils for rotary blades is a challenging subject that remarkably affects the stage and overall performance of axial-flow compressors. This paper describes a surrogate-based multi-objective optimization process over a transonic rotary blade. This blade works in the first high-pressure stage of a pre-designed industrial axial compressor. It experiences a massive separation behind an impinging shock wave over its suction side, resulting in very low efficiency of the whole stage. The key components of the current approach involve the application of novel-objective functions over the pressure distribution of airfoils, called the location of the shock wave and a flat-roof-top factor, to design supercritical airfoils. Moreover, to ensure the advantages of having an attached boundary layer and a high efficient blade, the area of separated boundary layer is also defined alongside other well-known objective functions related to the polar loss diagram. Notably, a sequential feed-forward multi-layer perceptron is designed to construct a mapping between airfoil geometrical variables and the objective functions. A numerical simulation of the whole compressor has shown an efficiency improvement of about 10% and 0.17% for the first stage and the whole compressor, respectively, and an attached boundary layer with a supercritical pressure distribution when employing the optimized rotor blade at the design stage.

The Design of Low-Cost Synchronous Reluctance Motor with a Surrogate-Assisted Optimization Technique

This paper presents the performance of centrifugal pump coupled with synchronous reluctance motor of 24kW. The 4-pole 36 slots induction motor stator has been used for the prototype. The reduction of torque ripple and power losses is the main aim of research. Different arrangement of rotor flux barrier shapes has been tested through finite element analysis method. The rotor optimization carried out by varying different barrier edge angle, width of flux carriers, flux barriers and shaft diameter. The method of particle swarm optimization has been used by generating samples with surrogate assisted optimization technique for performance improvement of the motor. Distinct flux barrier shapes and designs have been checked through simulation. For the prototype development, final V-shaped best model is chosen. The proposed rotor shows the excellent performance in terms of reduced torque ripple and improved average torque in experimental results. The suggested design also has good thermal and mechanical performances with the capability to use in various industrial applications.

A simple method for modelling fatigue spectra of small wind turbine blades

AbstractSmall‐scale wind turbines have market opportunities in distributed energy generation applications but face future challenges in remaining cost competitive compared with solar photovoltaic systems. High unit costs can be attributed to design conservatism when calculating fatigue loads of key structural components such as the blades. In this study, we use the aeroelastic software FAST to highlight limitations of the International Electrotechnical Commission 61400‐2:2013 small wind turbine design standard for calculating fatigue life using the simplified load model. We present a modified method for calculating the fatigue spectra of small wind turbine blades. An advantage of this method is that it does not require complex aeroelastic simulations or field measurements. This modified method is intended to be implemented early in the blade design stage, such as during rotor optimization simulations, allowing for multiple rotor configurations to be rapidly compared.

Comparative Study of Double-Stator Interior-PM Vernier Machines Based on Electromagnetic-Structural Coupling Analysis

Based on the electromagnetic-structural coupling analysis, this article proposes the comparative study of three double-stator interior- permanent magnet vernier (DS-IPMV) machines, including the spoke-PM, V-shape-PM (V-PM), and H-shape-PM (H-PM) rotor structures. DS cooperation strategies are adopted in the machine design for the performance improvement. Firstly, the rotor optimization of the proposed machines is carried out, with consideration of the tooth-slot cooperation between the rotor and stators. The electromagnetic- structural coupling-simulation is adopted for comprehensive evaluation. Then, the specific performance comparison is carried out, including the magnetic, structural and cost analysis. Consequently, the spoke-PMV machine accommodates the highest torque output, efficiency and cost-effectiveness; meanwhile, the V-PMV machine possesses the highest torque per PM volume with the better ripple performance. Accordingly, prototype experiments are carried out for the validation of the proposed machine design and comparison.

Rotor Topology Optimization of Interior Permanent Magnet Synchronous Motor With High-Strength Silicon Steel Application

This article presents the rotor optimization in an interior permanent magnet synchronous machine (IPMSM) with high-strength non-grain-oriented (NGO) silicon steel material. Different from simple replacement with high-strength NGO, this article presents a customized design to make the best use of rotor iron core material. Specific optimization of the rotor topology is presented, followed with simulation verification by finite element method (FEM). Based on the simulation results, the benefits and limitations of the optimization design with the replacement of high-strength NGO are listed. In order to further overcome the limitations of the presented optimization design, magnetic characteristics of the high-strength NGO laminations subjected to various tensile stresses are measured in the experiment. Finally, experimental results are analyzed, and the conclusions to employ high-strength NGO for IPMSM are summarized.

Simultaneous Magnetic and Structural Topology Optimization of Synchronous Reluctance Machine Rotors

This article presents the simultaneous magnetic and structural topology optimization of a transverse laminated synchronous reluctance machine rotor using a solid isotropic with material penalization (SIMP)-based approach with the globally convergent method of moving asymptotes (GCMMA) optimization algorithm. Magneto-structural single and multi-objective optimization formulations are presented. The single objective formulation maximizes the average torque subject to constraints on torque ripple, Von Mises stress, and compliance. The multiobjective formulation simultaneously maximizes average torque and minimizes compliance subject to constraints on torque ripple and Von Mises stress. In both optimization formulations, the electrical steel densities in the rotor mesh elements are the control variables. Including stress and compliance in the optimization formulation ensures a structurally feasible design. The design-dependent centripetal force contributed by each element in the rotor mesh is considered dependent on its density and mass. An intermediate density material issue is observed where the density of the material in a mesh element does not converge fully to air or electrical steel. This issue is addressed through the use of a thresholding mass function which forces the convergence of the mass but not the density. The two optimization formulations are compared for rotors operating at 4000 and 12 000 r/min. An initial magnetic only topology optimization is used to seed the magneto-structural topology optimization to decrease the computational time. The impact of the magnetic only seed and rotor mesh density on the optimization outcomes is also examined.

Balancing optimization of a multiple speeds flexible rotor

The paper describes a method to perform the dynamic balancing of multiple speeds flexible rotors. The method is integrated with a dual-objective optimization method (DOM) to overcome the shortcomings that classical least squares influence coefficient method (LSM) may induce by generating excessive residual vibrations at specific rotor speeds when a flexible rotor is dynamically balanced. The technique here described involves two consecutive optimization steps. During the first step an optimal correction weight of the parameters population is identified by using a genetic algorithm (GA) applied to an objective function made from the sum of the squares of the residual vibrations. This first optimization step is performed multiple times to obtain a set of optimized correction weights. A second optimization process is then performed by minimizing the maximum value of the residual vibration of the rotor. Each correction weight belonging to the first optimization set is embedded into an equation that represents the residual vibration to obtain the final optimal correction weight. The validity of the proposed method is verified by simulations and experiments related to a double-disc rotor-bearing system. The results show the DOM provides a more effective balancing strategy than the one obtained from using GA and classical LSM.