Centrifugal Loading Research Articles

Three-Dimensional Strains on Twisted and Swept Composite Rotor Blades in Vacuum

This paper presents an investigation of the effects of tip sweep on highly twisted composite rotor blades by acquiring strain data in vacuum. Three parametric test cases were designed for strain measurements, and predictions from a special three-dimensional (3-D) finite element method were used for assessment of data. A set of rotating aluminum beams was also tested as a rudimentary baseline. Three sets of composite rotors (straight, twisted, and twisted–swept) were fabricated and tested, and blade properties carefully characterized. Prediction of 3-D strains was conducted using X3D, a 3-D multibody structural dynamic solver for rotor aeroelasticity. Comparison with measured strains showed overall satisfactory agreements. Under centrifugal loading, strong 3-D strain patterns were observed near the twisted–swept tip. The largest increase in strain magnitude is found to be caused by the twist. Evidence of strong lead-lag bending concentrations due to counteracting axial extension and localized in-plane shear were found in the twisted–swept tip.

Vibration Characteristics of Multi-Stage Blade–Disk–Shaft Integrated Structure with Three-Dimensional Crack

According to the structural parameters of an actual turbofan aeroengine, the dynamics modeling and vibration analysis of multi-stage blade-disk-shaft integrated structure with three-dimensional crack are conducted. Based on the theory of fracture mechanics, the stress intensity factor is considered as a fracture criterion. This paper proposes a three-dimensional (3-d) equivalent notch model which is simpler and more convenient than the traditional crack simulation model. Moreover, its validity is analyzed. Aiming at the harsh working environment of the blades, the penetration crack is considered at the edge and the middle of a blade root, respectively. The influence of the crack on the strength failure of the rotor system is studied. Results show that the appropriate small angle equivalent notch model can be convenient and effective to simulate the fracture cracks, in which 5° is proved to be the best angle. The crack aggravates the vibration of blades obviously. A parametric study is conducted, with a particular focus on the effects of pressure load and centrifugal load on the stress intensity factors and displacement fields.

Free vibration of rotating pretwisted FG-GRC sandwich conical shells in thermal environment using HSDT

The free vibration behavior of rotating pretwisted sandwich conical shell panels with functionally graded graphene-reinforced composite (FG-GRC) face sheets and homogenous core is investigated in uniform thermal environment using finite element method in conjunction with a higher-order shear deformation theory (HSDT). The volume fraction distribution of the graphene in the face sheets is considered to be uniform or layer-wise functionally graded across its thickness. The temperature-dependent effective elastic moduli of the FG-GRC face sheets are computed employing the refined Halpin-Tsai model, while the effective Poison’s ratio, density, and thermal expansion coefficients are obtained using the mixture-rule. The effects of non-linearity arising out of the initial stresses due to thermal and centrifugal loads are incorporated via geometric stiffness based on Green-Lagrange’s strains. The governing equations for sandwich conical shell panels are derived using Lagrange’s equation of motion at moderate rotational speeds. The influence of graphene distribution patterns on the fundamental frequencies of FG-GRC sandwich conical shells under different thermal conditions is studied with emphasis on triggering parameters like pretwist angle, cone length-to-thickness ratio, core-to-face sheets thickness ratio, and dimensionless rotational speed.

Thermo-Structural Analysis of High-Pressure Turbine Blade

Turbine blade tip clearance plays major role in smooth running of axial turbines. The turbine blade clearance contributes 20-40% of total loss in gas turbine. In Rolls Royce MT2 Turbine with 2% tip to span clearance ratio, tip clearance accounts for 40% of total losses. Turbine blade clearance is necessary as the turbine blade operates at very high temperature up to 1700 ºC and very high centrifugal load. Small turbine tip clearance may forbid expansion of turbine blade which will result in turbine tip rubbing with the casing.
 High pressure turbine blade experiences high thermal and centrifugal stress. The objective of this paper is to study the individual and combined effect of these stress. The material used for analysis is cast based nickel alloy IN-738. The melting range of this alloy is 1230-1315 ºC with thermal expansion coefficient of 15.39E-6 per ºC. The turbine blade geometry with height 120 mm is used for analysis. The Mathematical modelling of above geometry shows that the centrifugal force with rotation velocity 100 rad/s produces 0.00252424 mm elongation and combined thermal-centrifugal loading produces 1.46520576 mm elongation.
 The results form ANSYS is used for verification and the elongation due to centrifugal stress is 0.0014885 mm and combined stress produces elongation of 1.2608 mm. The total elongation from analytical method and ANSYS are similar. It shows that the effect due to centrifugal force on turbine blade is less compared to thermal effect. For operating condition of 816 ºC temperature and 100 rad/s rotational velocity, the overall stress contributes around 1.22 % elongation of turbine blade span.

Dynamic Analysis of Sensorless Controlled Industrial Pump Drive

Industrial pumps operating with variable speed provides numerous benefits including valve elimination, wide range of flow rate, single stage higher head and energy saving. The realization of variable speed pump operation is carried out using an induction motor, power electronic switches, current sensors and controller without speed feedback is known as sensorless variable speed control. This paper implements a field-oriented control based sensorless scheme on 150 kW induction motor drive system, which is integrated to centrifugal pump load in Matlab/Simulink environment. The centrifugal pump is modelled mathematically in the same environment for obtaining the identical torque speed characteristics.

Thermo-Mechanical Analysis for an Axisymmetric Functionally Graded Rotating Disc under Linear and Quadratic Thermal Loading

The study presents thermo-mechanical analysis of functionally graded (FG) rotating disc whose material properties, namely, Young’s modulus, density and coefficient of thermal expansion in radial direction are tailored from inner to outer radius using power law form. The disc is considered to be under the influence of internal pressure, centrifugal body force and thermal loading of the form linear as well as quadratic. Response of FG disc under linear and quadratic temperature profile subjected to internal pressure as well as centrifugal body force is analysed. An exact solution for stress in radial and tangential directions, under mechanical and thermal loading is presented. Numerical solutions for stresses under internal pressure with uniform thermal loading are obtained using finite element method and its comparison with analytical results is presented graphically. Results for radial displacement, radial stress and tangential stress are depicted graphically and their interpretation has been discussed.

Thermo-mechanical analysis and estimation of turbine blade tip clearance of a small gas turbine engine under transient operating conditions

Turbine blade tip clearance is one of the significant factors that influence turbine efficiency, Specific Fuel Consumption (SFC), Exhaust Gas Temperature (EGT), and emissions. Controlling these parameters in a small gas turbine engine (SGT) is a challenging task due to small blade height and viscous working environment. SGT are subjected to high-temperature gradients at the combustor outlet, which affects the turbine blade tip clearance. This paper presents the thermo-mechanical analysis of a typical SGT engine to study the blade tip clearance influenced by the deformation of turbine stage components (turbine rotor, nozzle guide vane (NGV) with integral blade shroud) during transient phases. ANSYS Workbench is used to perform transient thermal and structural analyses. The structural analysis is performed taking the material properties to be temperature-dependent. The SGT engine under consideration operates at a design speed of 45,000 rpm. Initially, steady-state thermal analysis and static structural analysis were carried out to understand the structural behaviour of the system under a thermal and centrifugal loading environment. Since different components of the engine assembly operate at different temperatures, the effects of convection and conduction at the interfaces influence the radial clearances between the static and rotating parts of the engine. A one-way coupled transient thermal-structural analysis was performed on a three-dimensional model to capture the actual behaviour of the tip clearance during transient operating conditions. Significant growth of blade and rotor was observed relative to the casing resulting in minimal clearances during these transient operations. Hence, it is important to estimate desired cold clearance, considering transient phenomena, to avoid mechanical blade rub with the shroud. It is observed that high-temperature gradients contribute primarily to the stresses and radial displacement of the rotor compared to centrifugal effects. The turbine rotor takes more time (t = 600 s) to reach steady-state temperatures compared to NGV (t = 120 s) due to the solid mass of the disc. The location and magnitude of maximum and minimum equivalent stress changes with time in NGV and rotor, and they experience maximum stress at the initial time steps compared to steady-state.

Examination of the effect of combined use of Er:YAG laser irradiation and mechanical force loading on bone metabolism using primary human gingival fibroblasts.

Prolonged treatment and painful tooth movement are major problems for patients undergoing orthodontic treatment. Accelerating the movement of teeth leads to shortening of the treatment period, so various studies on the movement of teeth have been conducted in the field of orthodontics. In previous studies, we performed a fiber incision-like fiberotomy using an Er:YAG laser in rats and confirmed acceleration of tooth movement. Therefore, in this study, the effect of Er:YAG laser irradiation on human gingival fibroblasts was investigated in vitro. Human gingival fibroblasts (2.0 × 105 cells) were seeded in a 6-well plate and reached 80% confluence 24h later. A control group not undergoing any irradiation and 3 groups undergoing laser irradiation at 0.6W, 1.0W, and 1.2W were investigated. Laser irradiation was performed 24h after cell seeding. The cells were then recovered 24h later, and the cyclooxygenase-2 (COX-2), interleukin-1β (IL-1β), tumor necrosis factor-α (TNF-α), bone morphogenetic protein-2 (BMP-2), and BMP-4 genes were confirmed by PCR. In addition, a control group not undergoing any procedures, a group undergoing only Er:YAG laser irradiation, a group undergoing only centrifugal loading, and a group undergoing both Er:YAG laser irradiation and centrifugal force loading were investigated. After 24h, cells were collected and PCR was performed. Twenty-four hours after laser irradiation, gene expressions were examined by quantitative RT-PCR, which showed that the gene expressions of COX-2, IL-1β, TNF-α, BMP-2, and BMP-4 increased depending on the amount of irradiation energy, with the largest value at 1.2W. Gene expressions of COX-2, IL-1β, TNF-α, BMP-2, and BMP-4 were significantly higher in the laser with centrifugal load group than in the load group. These results suggest that genes related to bone metabolism are activated in human gingival fibroblasts when mechanical stimulation and laser irradiation are combined. This helps to elucidate the effects of Er:YAG laser irradiation during tooth movement.

Fatigue evaluation of FV520B-I shrouded impeller blade with fatigue crack based on FEA and fracture mechanics

The fatigue life prediction of FV520B-I blade with fatigue crack is a critical study in the fatigue analysis of shrouded impeller. However, the relationship between fatigue crack and fatigue life of FV520B-I blade has not been well studied. In this paper, finite element analysis (FEA) for FV520B-I blade with fatigue crack is conducted; both centrifugal load and aerodynamic load involved, and the stress distribution and the fatigue failure at decisive positions are analyzed. The new correlation between mean stress and fatigue crack is found based on the results of FEA, which is helpful to the development of fatigue life model of FV520B-I blade. Then fatigue test for blade material FV520B-I is performed to determine the fatigue limit. A fatigue life evaluation model for FV520B-I blade is then achieved, by taking fatigue crack as main variable, combining with the comprehensive application of FEA, fatigue test, actual operating parameters and existing fatigue modeling theory. The model is proved to be reliable by comparing the theoretical predicted life with simulated one. Study on fatigue life evaluation method of FV520B-I blade with fatigue crack is novel and essential to improve precision of fatigue life prediction of shrouded impeller in engineering practice.

Geometry-Load Based Hybrid Correction Method for the Pre-Deformation Design of a Steam Turbine Blade

To solve the problem of the slow convergence of the geometry-based correction (GC) method in the design of a steam turbine blade, this paper proposes a geometry-load-based hybrid correction (GLHC) method. In this method, the deformation of the blade caused by the centrifugal load is still corrected by the GC method, while the deformation caused by the aerodynamic load is corrected by the load-based correction (LC) method instead of the GC method. The LC method updates the cold shape of the blade by reversely applying the aerodynamic load to the ideal shape according to the balance between the internal force generated by the deformation of the blade and the aerodynamic load acting on surface of the hot blade shape, thereby reducing the number of iterations by reducing the shape deviation in each step of the iteration. The GLHC method, which combines the GC and LC methods, is used to improve the design process. The efficiency of the GLHC and GC methods are compared with the maximum number of position deviations of the corresponding mesh nodes between the hot blade and ideal blade shapes, which acts as the criterion. The results show that the GLHC method reduces the number of iterations.

A Review of the High-speed Permanent Magnet Rotor Stress Analysis used for Automotive Air-handling Machines

Machines incorporating high-speed electrical machines (HSEM) are becoming increasingly common place in applications including air handling, energy storage and medical devices. They are of increasing interest within the automotive field for air handling applications. HSEM’s use surface-mounted permanent magnet (PM) rotors, manufactured from rare earth metals. However, these PM’s have low tensile strength and are susceptible to failure under the centrifugal load produced at high speed rotation. Retaining sleeves which are an interference fit around the magnets, provide compression and hence resistance to tensile stress. The ability to predict the stresses within the rotor assembly is essential for robust design. This review paper examines existing analytical calculations and finite element analysis (FEA) models. The analytical approaches include both plane stress and plane strain models and the limitations of these are discussed. For relatively long rotors, a generalised plane strain approach is suitable, however it is seldom used. In addition, this latter approach has not been extended to assemblies where the magnets are assembled onto a carrier or shaft. Optimisation of rotors has been addressed in a relatively small number of papers. However, further work is required in this area to ensure that the optimised rotors can be manufactured.

Review of the High-speed Permanent Magnet Rotor Stress Analysis used for Automotive Air-handling Machines

Machines incorporating high-speed electrical machines (HSEM) are becoming increasingly common place in applications including air handling, energy storage and medical devices. They are of increasing interest within the automotive field for air handling applications. HSEM’s use surface-mounted permanent magnet (PM) rotors, manufactured from rare earth metals. However, these PM’s have low tensile strength and are susceptible to failure under the centrifugal load produced at high speed rotation. Retaining sleeves which are an interference fit around the magnets, provide compression and hence resistance to tensile stress. The ability to predict the stresses within the rotor assembly is essential for robust design. This review paper examines existing analytical calculations and finite element analysis (FEA) models. The analytical approaches include both plane stress and plane strain models and the limitations of these are discussed. For relatively long rotors, a generalised plane strain approach is suitable, however it is seldom used. In addition, this latter approach has not been extended to assemblies where the magnets are assembled onto a carrier or shaft. Optimisation of rotors has been addressed in a relatively small number of papers. However, further work is required in this area to ensure that the optimised rotors can be manufactured.

A gravo-aeroelastically scaled wind turbine rotor at field-prototype scale with strict structural requirements

A new sub-scale field-prototype design solution is developed to realize the dynamics, structural response, and distributed loads (gravitational, aerodynamic, centrifugal) that are characteristic of a full-scale large, modern wind turbine rotor. Prior work in sub-scale wind turbine testing has focused on matching aerodynamic/aero-elastic characteristics of full-scale rotors at wind tunnel scale. However, large-scale rotor designs must expand beyond this limited set of scaling parameters for cost-effective prototyping and meet strict requirements for structural safety for field testing. The challenge lies in producing a structural design meeting two competing objectives: novel scaling objectives that prescribe the sub-scale blade to have low mass and stiffness; and traditional structural safety objectives that drive the design to have higher stiffness and mass. A 20% gravo-aeroelastically scaled wind turbine blade is developed successfully that satisfies these competing objectives. First, it achieved close agreement for non-dimensional tip deflection and flap-wise blade frequency (both within 2.1%) with a blade mass distribution constrained to produce target gravitational and centrifugal loads. Second, the entire blade structure was optimized to ensure a safe, manufacturable solution meeting strict strength requirements for a testing site that can experience up to 45 m/s wind gusts. The prototype-scale blade was fabricated and successfully proof-load tested.

Design considerations for variable stiffness, doubly curved composite plates

It is widely acknowledged that laying up composite tapes and fabrics on doubly curved surfaces can introduce wrinkling and overlap defects. It is also not a straightforward task to define fibre angle directions. The latter problem amplifies when considering curvilinear fibre paths on doubly curved surfaces. Herein, we define a new fibre orientation datum curve and use this as a reference for optimisation purposes. A novel implementation of lamination parameters is introduced whereby we constrain the values of lamination parameters based on minimum turning radii of automated fibre placement machines and maximum ply angle change for stiffness optimisation. As an example, this approach is applied to a pre-twisted plate with 68 layers subjected to combined centrifugal and pressure loading. Lamination parameters are used to reduce the complexity and multiplicity of composite laminate design with many layers to a convex and continuous design space using a reduced number of variables. Lamination parameters are varied over the geometry using spline surface interpolation over a grid of control points and the optimal lamination parameter values are found using a gradient based optimiser. The fibre paths for each ply are then designed from the optimal lamination parameter variation using a two-stage optimisation process.

Effects of icariin on adhesion and cytoskeleton of osteoblasts in response to the extreme mechanical environment of hypergravity

Objective To establish a hypergravity loading model with a high-acceleration centrifugal loading device and to investigate the effects of different hypergravity loading and icariin on osteoblast adhesion and cytoskeleton. Methods MC3T3-E1 cells were seeded in the dishes of cell culture at a density of 2×105/cm2. And the experiment was divided into 6 groups: control group (without icariin and loading); simple administration group (only icariin); 10 G loading group (only loading); 10 G administration group (with icariin and loading); 40 G loading group (only loading); 40 G administration group (with icariin and loading). The experimental loading group was loaded with MC3T3-E1 cells using a high-acceleration centrifugal loader. And continuous loading for 3 d, 30 min per d. The control group and the simple administration group were exposed to normal gravity, and the remaining conditions were not different from the experimental group. Icariin was used at a concentration of 10-7 mol/L in all administration groups, and the experiments were carried out according to the method of preventive administration. At the same time, the related molecular biological techniques such as alizarin red staining, alkaline phosphatase (ALP) activity measurement, CCK-8 cell proliferation experiment, cytoskeleton phalloidin staining, qPCR and Western Blot were used to detect the effects of icariin on osteoblasts adhesion protein integrin α5 and integrin β1 and cytoskeleton protein F-actin under hypergravity extreme mechanical environment. Results All models were successfully prepared. The alizarin red staining: The icariin could significantly promote the formation of osteoblastic calcified nodules. And the 10 G loading could also promote the mineralization of osteoblasts and increase the number of mineralized nodules, while the mineralization and the number of mineralized nodules of osteoblasts are significantly reduced in 40 G loading. ALP activity test: The OD values of simple administration group, 10 G loading group and 40 G loading group were 0.246, 0.331 and 0.163, respectively. Compared with 0.207 in the control group, the differences were statistically significant (P<0.05). The 10 G administration group and the 40 G administration group were 0.373 and 0.180, and the differences were statistically significant (P<0.05). The results of CCK-8 proliferation experiments: The OD value of simple administration group were 0.650, which was statistically significant compared with 0.551 of control group (P=0.031). The 10 G loading group and 40 G loading group were 1.193 and 0.245, and their differences with the control group were both statistically significant (P<0.05). The OD value of 10G administration group and the 40 G administration group were 1.300 and 0.310, which were significantly different from the respective loading groups (P<0.05). Phalloidin staining: 10 G loading significantly increased the number of cells, but the changes in cells morphology and skeleton were not obvious. 40 G loading significantly inhibited the increase of the number of cells, meanwhile, made the pseudopods of cells more shorter and even disappeared. 40 G loading made the seriously damage of the cytoskeleton and even cause the cells to death. Icariin had no effect on the cells morphology, but it did has a certain repair effect after the cells loading. The results of qPCR and Western Blot experiments all confirmed that the expressions of integrin α5, integrin β1 and F-actin were up-regulated after icariin treatment. 10 G loading could promote the expression of integrin α5, integrin β1 and F-actin, and 40 G loading significantly inhibited the expression of the mRNA and proteins. Conclusion Both 10 G condition and icariin can promote the development, cell adhesion and the cytoskeleton's stability of osteoblasts, while 40 G has a significant inhibitory effect. Key words: Osteoblast; Hypergravity; Cell adhesion; Cytoskeleton

Examination of the Effect of the Combined Use of Nd: YAG Laser Irradiation and Mechanical Force Loading on Bone Metabolism Using Cultured Human Osteoblasts.

Introduction: In recent years, laser irradiation in the near-infrared ray (NIR) area has been reported to promote bone healing. There are also reports that laser irradiation accelerates orthodontic tooth movement. In this study, we investigated the effect of NIR laser irradiation and mechanical stimulation on osteoblasts. Methods: We seeded osteoblast-like cells and laser irradiation was performed 24 hours after cell seeding. In addition, a control group not receiving anything, a group receiving only Nd: YAG (neodymium-doped yttrium aluminum garnet) laser irradiation, a group receiving only centrifugal loading, and a group receiving both Nd: YAG laser irradiation and centrifugal force loading were set, and after 24 hours and after 48 hours, cells were collected and quantitative real-time polymerase chain reaction (PCR) was performed. Results: 24 hours after laser irradiation, the gene expression of alkaline phosphatase (ALP), the receptor activator of NF-κB ligand (RANKL) and osteoprotegerin (OPG) was significantly higher in the 2.0 W group than in the control group. In addition, the RANKL/OPG ratio was higher in the 2.0 W group than in the control group. Also, in the group using laser irradiation and centrifugal loading in combination, 24 hours after laser irradiation, ALP and OPG showed significantly higher values than those in the centrifugal load only group. Furthermore, the RANKL/OPG ratio also showed high values. Conclusion: These results suggest that osteoblast-like cells activate genes related to bone metabolism by combining mechanical stimulation and laser irradiation. This helps to elucidate the influence of laser irradiation during tooth movement.

Efficacious pitch angle control of variable-speed wind turbine using fuzzy based predictive controller

The Wind energy is more reliable and speedier growing, among the renewable energy resources, due to the world environment challenges as well as increasing demand for energy. The wind turbine system’s stability is cumbersome due to the uneven distribution of wind. Centrifugal and gravitational loads on the blades of a wind turbine creates weariness, resultantly decreases the power output along with the life of the equipment. Therefore, the need for a pitch angle control that can reduce the loading effect in addition to provide maximal power output. This paper proposes the fuzzy based model-predictive controller of pitch angle control to minimize the loading effect on wind turbine by limiting power output and rotor speed to its rated value as well as to maximize the extracted power output as compared to other techniques. The fuzzy logic controller works very efficiently by encountering the system’s non-linearity while model predictive controller helps the system to become more stable and efficient. The superiority of prescribed controller is verified by comparing it with PI controller. The proposed model has been tested in MATLAB/Simulink using a 3MW wind turbine system.

Direct measurement of the damping and stiffening capabilities of cylindrical underplatform dampers

The paper focuses on the cylindrical underplatform damper, a friction damping device widely used in power generation turbines. The first goal of the paper is to estimate the stiffness and damping contribution of cylindrical dampers interposed between adjacent blades vibrating along a typical in-phase mode. For the first time, the damper characterization is performed through the direct measurement of contact forces and platform displacements.Measurements show that the damper does not introduce damping or stiffness if the two platforms, with which the damper is in contact, share the same angles (i.e. blade with symmetrical platform) and are vibrating in-phase. This is an adequate design choice if only the damper sealing function is required, while changes to the disk dynamics are not desired. The damper produces a small stiffening effect only if the two adjacent platforms have different angles. These findings are confirmed by an analytical derivation performed on the basis of a simple yet effective damper model.The damper numerical model requires parameters which may be calibrated, i.e. the cylinder-on-flat tangential contact stiffness. The second goal of the paper is to use the experimental evidence on contact forces and platform displacements to estimate these parameters for different centrifugal loads using a purposely developed technique. These values are compared with those obtained at an identically designed contact interface on a curved flat damper (i.e. cylindrical damper with a flattened side). The differences found in the calibration parameters show that the local stiffnesses depends not only on the local geometry of the contact but also on the damper kinematics.

A parametric study of an unbalanced Jeffcott rotor supported by a rolling-element bearing

Rolling-element bearings are widely used in industrial rotating machines, and hence there is a strong need to accurately predict their influence on the response of such systems. However, this can be challenging due to an interaction between the dynamics of the rotor and the bearing nonlinearities, and it becomes difficult to provide a physical explanation for the nonlinear response. A novel approach, combining a Jeffcott rotor supported by a detailed bearing model with the generalised harmonic balance method, is presented, enabling an in-depth study of the complex rotor–stator interaction. This allows the quasi-periodic response of the rotor, due to variable compliance, to be captured, and the impact of clearance, ring and stator compliance, and centrifugal loading of the bearing on the response to be investigated. A strongly nonlinear response was observed due to the bearing, leading to large shifts in frequency as the excitation amplitude was increased, and the emergence of stable and unstable operating regions. The variable compliance effect generated sub-synchronous forcing, which led to sub-resonances when the ball pass frequency coincided with the frequency of one of the modes. Radial clearance in the bearing had by far the largest influence on the unbalance response, the self-excitation due to variable compliance, and the stability. Introducing outer ring compliance was found to slightly soften the system, and centrifugal loading on the bearing elements marginally increased the system’s region of instability, but neither of these effects had a significant impact on the response for the investigated bearing. When the bearing was mounted on a sufficiently compliant stator, the system was found to behave linearly.

Limit elastic analysis of rotating annular disks having sigmoid-FGM composition based on MROM

Purpose The limit elastic speed of rotating disk is an important design criterion, as it defines the limit before onset of yielding initiates. The purpose of this paper is to establish the limit elastic speeds for S-FG disks and report the stresses induced at such speeds. Design/methodology/approach For S-FGM disk, effective Young’s modulus is calculated using modified rule of mixture and subsequently effective yield stress is also calculated by taking into consideration of stress-strain transfer ratio. The S-FGM disk is subject to centrifugal loading and the stress and deformation characteristics are investigated using variational principle wherein the solution is obtained by Galerkin’s error minimization principle. Based on von-Mises yield criteria, equivalent stress is calculated at different angular speeds till the equivalent stress at any given location in the disk attains the value of effective yield stress at the given location (location of yield initiation). This defines the limit elastic speed for the S-FGM disk (for given n). Findings The limit elastic speed of S-FGM disks for a range of grading index (n) and corresponding stresses within the disk are reported. Results are reported for uniform disks of different aspect ratio and the results reported could be used as practical design data. Practical implications Functional grading of material in structures opens a new horizon to explore the possibility of manufacturing high strength component at low weight. Material grading plays a significant role in achieving desired material properties, and literature review reveals reporting of numerous grading functions to approximate material distribution in structure. Originality/value The work has not been addressed earlier and findings provide a pioneering insight into the performance of S-FG disks.