Critical Rotational Speed Research Articles

Investigation of rotor strength and rotor dynamics for high‐speed high‐power switched reluctance machines

This study proposes an investigation scheme of the rotor strength and rotor dynamic characteristics for high-speed high-power switched reluctance machines (SRMs). The analytical model and finite element analysis model are established to predict the maximum stress and deformation in the rotor. The Mises yield criterion is employed to verify the strength of the rotor at 1.2 times the rated speed. For the rotor dynamics, critical speed, unbalance response, and stability of the shaft system are analysed in detail. In the developed critical speed calculation scheme, the gyroscopic effect and the impact of the rotation speed on the stiffness and damping are considered. Then, the critical speeds acquired by the developed scheme are compared with those derived by using the conventional method. The unbalance response curves at different nodes are adopted for the unbalance response calculation, while the stability of the shaft system is verified by calculating the logarithmic decrement rates. The critical speed measurement experiment is performed on a 160 kW and 18,000 r/min SRM prototype, and the proposed critical speed calculation scheme is proved to be effective and accurate. The effectiveness of the unbalance response calculation method and the stability judgement technique are also verified by experiment.

Vibration suppression of nonlinear rotating metamaterial beams

In this paper, we investigate the nonlinear vibration of a metamaterial structure that consists of a rotating cantilever beam attached to a periodic array of spring–mass–damper subsystems deployed for vibration suppression. The full nonlinear model of the system is developed. The nonlinear response due to a primary resonance excitation is investigated, and the capability of the metastructure to suppress vibration is examined. The mass of the resonators (absorbers) comes at the expense of the host structure’s mass itself, which makes the total mass of the system conservative. Free and forced vibration analyses are performed. We first use the method of multiple scales to analyze the nonlinear behavior of rotating beams. The perturbation solutions are validated against their numerical counterparts. Results show the presence of a critical rotational speed at which the beam undergoes bifurcation and starts to flutter. The addition of the absorbers is observed to slightly reduce this critical speed. Nevertheless, the amplitude of limit-cycle oscillations beyond bifurcation is found to decrease when equipping the rotating beam with local absorbers. The results demonstrate the capability of the metamaterial structure as an efficient damping treatment. Furthermore, we show that careful placement of the absorbers along the cantilever beam (close to the tip) enables further vibration mitigation.

Synchronous Vibration Control for Magnetically Suspended Rotor System Using a Variable Angle Compensation Algorithm

In active magnetic bearings (AMBs) supported rigid rotor systems, the unbalance compensation strategy based on a notch filter was often used to suppress the synchronous unbalance vibration when the rotor operates in the steady-state rotational speed. Whereas the rotor operates in a rotational-speed range including the critical rotational speeds, conventional notch filters should be improved to suppress the unbalance vibration. In most cases, improving the structure of the notch filter, such as a cross-feedback notch filter, phase-shift notch filter, adding the polarity switch or two-stage switch, was considered to make the notch filter work in the rotational-speed range. However, the improved notch filter may affect the stability of the AMBs rotor systems and result in large vibrations when the polarity switch or two-stage switch shifts. To avoid the shortcomings of these methods, a method using a variable angle compensation algorithm was proposed to suppress the synchronous unbalance vibration in finite iterative seeking processes, directly realizing unbalance compensation according to real-time rotor position. Finally, the effectiveness of the method proposed is verified by simulation and experiment results.

Post-resonance backward whirl in accelerating cracked rotor systems

Rotating machinery are known to exhibit backward whirls (BW), which means that the rotating system precesses in the direction opposite to that of its rotation. Since backward whirl is an important characteristic of the dynamic response that almost always points to significant problems and degradations within the system, it is of high interest to study, characterize and predict this phenomenon. To this end, the Campbell diagram is used to predict BW rotational speeds at steady-state operations of rotor systems to precede the critical forward whirl (FW) rotational speeds (i.e., pre-resonance BW). Still, the BW phenomenon in rotor systems that exhibit recurrent passage through critical rotational speeds during startup and coast down operations has not been fully studied and described in the literature. Notably, a recent study of startup and coast down operations found backward whirl orbits appearing immediately after the passage through the critical FW rotational speed (i.e., post-resonance BW). The difference between the well-known pre-resonance BW and this new kind of post-resonance BW phenomenon is further investigated in this paper for rotor systems with an open crack and anisotropic bearings. In addition, Full Spectrum Analysis (FSA) is employed to capture the BW zones in both numerical and experimental data. A finite element model of the cracked rotor-bearing-disk system is employed here to obtain the linear-time-variant (LTV) equations of motion for the considered system. The whirl response is obtained by the numerical integration of the LTV equations of motion. From results obtained from three different rotor configurations it is observed that the post-resonance BW has a different dynamical behavior compared with the pre-resonance BW. Furthermore, the application of the FSA has confirmed the existence of post-resonance BW zones in both numerical and experimental whirl responses. Successful application of the FSA for capturing the post-resonance BW zones of rotational speeds in the experimental response suggests that it has the potential to be a used as a powerful tool for BW-based crack detection.

Research of the internal resonances on a nonlinear dual-rotor based on the energy tracks shifting

The complex coupling characteristics of a dual-rotor system make the mechanism of nonlinear vibrations different from that of a single rotor system. Research of nonlinear vibration of the dual-rotor is beneficial to improve the stability of an aero-engine. Based on nonlinear spring characteristics of rotors, a novel nonlinear dual-rotor dynamics model coupled by the inter-shaft bearing is proposed, and internal resonances on the dual-rotor system are systematically studied. Considering nonlinearities, internal resonance phenomena occurring in the vicinity of the coupling critical rotational speed are systematically analyzed by numerical simulation results such as time histories, Poincare maps, bifurcation maps and largest Lyapunov exponents. Theoretical solutions are calculated based on the improved shooting method and stabilities of theoretical solutions are investigated by using the Floquet theory. The theoretical solutions are consistent with numerical simulation results well. The concepts of the energy track shifting, the energy-Poincare map, stabilities of energy tracks and the energy supplying function are introduced to analyze nonlinear vibration characteristics for the first time. The internal resonance phenomena of the low pressure rotor and the complex nonlinear vibrations of the high pressure rotor are qualitatively analyzed based on the energy viewpoint, and the energy tracks are verified by experiments. Research shows that energy tracks can characterize vibration characteristics well and the energy supplying function provide a possible way to quantify the energy transfer between rotors in the multi-rotor system.

Convective transport around two rotating tandem circular cylinders at low Reynolds numbers

The convective transport around two rotating circular cylinders kept in a tandem configuration to an unconfined flow of an incompressible fluid (Prandtl number, Pr = 0.717) is investigated through two-dimensional numerical simulation. The flow Reynolds number is considered constant at Re = 100. Four different gap spacings between the tandem cylinders such as 0.2, 0.7, 1.5 and 3.0 are chosen for simulation. The cylinders are rotating about their centroidal axes for a range of dimensionless speed $$ \left( {0 \le \Omega \le 2.75} \right) $$ . The rotation to the objects causes the unsteady periodic flow around them to become stabilized and at some critical rotational speed, the vortex shedding stops completely resulting in a steady flow pattern. The critical speed of rotation at which the vortex shedding completely stops is a function of the cylinder spacing. Overall, it is observed that increasing the gap increases the critical rotation rate. The thermal fields are also strongly stabilized as a result of the cylinder rotation. The rotating cylinders actually create a zone in their proximity which acts like a buffer to the convective transport. The conduction mode of heat transfer predominates in these regions causing the heat transfer rate to assume a decaying pattern with increasing the rotational speed at all cylinder spacings.

Vibration Suppression for Magnetically Levitated High-Speed Motors Based on Polarity Switching Tracking Filter and Disturbance Observer

For the unbalance vibration of the rigid rotor system on active magnetic bearings (AMBs) supported high-speed motors in the full rotational speed range, a method based on the polarity switching tracking filter (PSTF) and the disturbance observer (DO) is proposed to achieve vibration suppression. To identify the synchronous unbalance vibration, a positive polarity tracking filter and a negative one are adopted before and after the rigid critical rotational speed range, respectively. The rigid critical rotational speed is in this range whose lower/upper limit is the negative/positive polarity switching frequency. Although the PSTF can effectively reduce the rotor vibration when it rotates at subcritical rotational speed range and supercritical range, the vibration increases evidently and even destabilize the system within the rigid critical rotational speed range. It means that the PSTF cannot suppress the rotor unbalance vibration in the full rotational speed range. However, this vibration during the rigid critical rotational speed range can be considered as a kind of disturbance and the DO is adopted to observe it, then the vibration identified is compensated in the control current to reduce the rotor unbalance vibration in the rigid critical rotational speed range. Therefore, the method based on the PSTF and the DO can suppress the unbalance vibration in the full rotational speed range. Finally, simulation and experiment results demonstrate that the method proposed can effectively suppresses the synchronous unbalance vibration of the AMBs-rigid rotor system in the full rotational speed range.

Using DEM to investigate how shell liner can induce ball segregation in a ball mill

Sometimes it is desirable to segregate the ball load in a mill so as to allow for the possibility of larger balls dealing with coarser particles at the feed end and finer product being ground more efficiently at the discharge end. The Hardinge mill with cylindrical and conical sections has been used to achieve segregation quite effectively. The cylindrical section tends to retain the biggest balls while the smaller balls drift to the conical section. However, this is a complex design and we use the discrete element method (DEM) model to investigate if simply altering liner configuration on an ordinary cylindrical mill can lead to similar success. The study involves simulating a mill with 4 sections. Each section can be configured with distinct liner profiles. Three ball size classes are tracked for evidence of segregation at 75% and 60% of critical mill rotation speed. The ball distributions in the various segments at the end of 80 mill revolutions suggest that varying axial liner profile configuration can affect ball segregation, particularly for the mill running at 75% of critical speed. The convenience of using computer simulations to avoid costly plant trials is highlighted.

Influence of bit design on the stability of a rotary drilling system

This paper extends the RGD model originally proposed by Richard et al. (J Sound Vib 305(3):432–456, 2007, https://doi.org/10.1016/j.jsv.2007.04.015) to investigate drilling-induced vibrations, by considering idealized drag bits characterized either by multiple angular offsets between the blades or by a combination of full and partial blades, a departure from the symmetric bit of the RGD model consisting of multiple continuous blades. The RGD model is built on a two-degrees of freedom discrete representation of the drillstring combined with a rate-independent bit/rock interaction law. By relaxing the original constraints on the bit geometry, the coupled state-dependent delay differential equations governing the angular and axial motions of the bit now contain multiple state-dependent time delays. A linear stability analysis leads to explicit expressions for the critical rotational speed(s) defining two different regimes of stability of the coupled dynamics. Stability maps indicate that both groups of bits have a better axial stability than their RGD counterparts. It is also found that multiple critical rotation speeds exist for certain bit geometries, in contrast to the single axial stability boundary of the original RGD model. Time simulations confirm the predictions of the linear stability analysis and show evidence of the existence of different types of quasi-periodic responses before the establishment of a limit cycle characterized by both axial and torsional stick-slip events.

Prediction of Cuttings Transport Behavior under Drill String Rotation Conditions in High-Inclination Section

Cuttings are likely to accumulate and eventually form a cuttings bed in the highly-deviated section, which usually lead to high friction and torque, slower rate of penetration, pipe stuck and other problems. It is therefore necessary to study cuttings transport mechanism and improve hole cleaning efficiency. In this study, the cuttings-transport behaviors with pipe rotation under turbulent flow conditions in the highly deviated eccentric section were numerically simulated based on Euler solid–fluid model and Realizable [Formula: see text]–[Formula: see text] model. The resulted numerical results were compared with available experimental data in reported literature to validate the algorithm, and good agreement was found. Under the conditions of drill string rotation, cuttings bed surface tilts in the direction of rotation and distributes asymmetrically in annulus. Drill string rotation, drilling fluid flow rate, cuttings diameter, cuttings injection concentration and drilling fluid viscosity affect the axial velocity of drilling fluid; whereas drilling fluid tangential velocity is mainly controlled by the rotational speed of drill string. Increase in value of drill string rotation, drilling fluid flow rate or hole inclination will increase cuttings migration velocity. Notably, drill string rotation reduces cuttings concentration and solid–fluid pressure loss, and their variations are dependent on inclination, cuttings injection concentration, cuttings diameter, drilling fluid velocity and viscosity. However, when a critical rotation speed is reached, no additional contribution is observed. The results can provide theoretical support for optimizing hole cleaning and realizing safety drilling of horizontal wells and extended reach wells.

The Dynamics of a Rotor System of a 1100 MW Turbine Unit

The calculations data of the critical rotational speeds of the shaft line on yielding supports with the support yield in the vertical and horizontal directions of the modernized turbine unit K-1000-60/1500-2 (after modernization, the turbine unit type is designated as K-1100-60/1500-2M) have been presented. 1000 MW turbine units comprising a high-pressure cylinder and three low-pressure cylinders have been in operation at nuclear power plants since 1984. The design models of shafting are based on technical and improved theories of variable cross-section rods on elastic-damper supports, taking into account the coupling of vibrations in two planes, inertia of rotation, gyroscopic moments and aerodynamic forces on the disks. Additionally, the stress condition of the most dangerous sections of welded rotors has been investigated in case of a sudden short circuit in the generator. The conditions of the shafting for the cases of two- and three-phase short circuits were considered. The calculations of the critical rotational speeds of the shaft line and of the strength of the rotors in case of a short circuit were performed using software packages developed in the IPMash of the NAS of Ukraine, Joint-Stock Corporation “Turboatom”. The calculation data show that no dangerous resonance vibrations of the shaft line of the upgraded К-1100-60/1500-2М turbine unit are detected and the strength of the shaft line in case of a sudden short circuit in the generator is in conformity with the requirements of regulatory and technical documents.

A Evaluation of the Dynamic Strength of the Shaft Line with Welded Rotors of Low Pressure Cylinders of the K-220-44-1 Turbine

To assess the danger of resonance vibrations, the calculations data of the critical rotational speeds and strength in case of a sudden short circuit in the generator of the shaft line of the upgraded K-220-44-1 turbine unit have been presented. The turbine unit comprising a high-pressure cylinder and two low-pressure cylinders has been in operation at nuclear power plants since the early 1970s. The shaft-line consists of a high-pressure all-forged rotor, two low-pressure welded rotors, an intermediate part and a generator rotor. For the rotors of the turbine unit constituting the shafting, rod models with concentrated masses and elastic-damping support were used. Recommendations on the choice of vertical compliance of supports for computational studies are given. Estimates of the critical speeds of the shafting are obtained without taking into account the lubricant layer of the support bearings. The dynamic state of the shafting is considered for two-phase and three-phase short circuits in the generator. The maximum twisting moments in the rotors' necks under the support bearings are estimated, and the safety factors for the limiting table torque in the plasticity state are determined. The calculations were performed using software packages developed in the A. Podgorny Institute of Mechanical Engineering Problems of NASU, Joint Stock Corporation "Turboatom". The calculation data show that no dangerous resonance vibrations of the shaft-line of the upgraded K-220-44-1 turbine unit are detected and the strength of the shaft-line in case of a sudden short circuit in the generator is in conformity with the requirements of regulatory and technical documents.

New s-process Mechanism in Rapidly Rotating Massive Population II Stars

Abstract We report a new mechanism for the s-process in rotating massive metal-poor stars. Our models show that above a critical rotation speed, such stars evolve in a quasi-chemically homogeneous fashion, which gives rise to a prolific s-process. Rotation-induced mixing results in primary production of 13C, which subsequently makes neutrons via during core He burning. Neutron capture can last up to (∼3 × 105 yr) with the peak central neutron density ranging from ∼107 to 108 . Depending on the rotation speed and the mass loss rate, a strong s-process can occur with production of elements up to Bi for progenitors with initial metallicities of [Z] ≲ −1.5. This result suggests that rapidly rotating massive metal-poor stars are likely the first sites of the main s-process. We find that these stars can potentially explain the early onset of the s-process and some of the carbon-enhanced metal-poor (CEMP-s and CEMP-r/s) stars with strong enrichment attributed to the s-process or a mixture of the r-process and the s-process.

Elastoplastic deformation of a rotating hollow cylinder with a rigid casing

A rotating hollow cylinder with fixed ends is considered, the inner surface of which is free of stresses, and the outer one is fixed from radial movements. It is assumed that the cylinder is made of an ideal isotropic elastoplastic material, and the deformations in it are small and represent the sum of elastic and plastic deformations. Stresses are associated with elastic deformations by Hooke's law. Plastic deformations are determined using the Tresca - Saint-Venant condition and the plastic flow rule associated with it. The cylinder rotation speed first monotonically increases to a maximum value, and then decreases to zero. By using the elastic solution, the dependence is found for the critical rotation speed at which the plastic flow begins. It is established that, depending on the thickness of the cylinder and the Poisson's ratio, plastic flow can begin, either on the inner or on the outer surface of the cylinder. In addition, 3 plastic regions appear in the cylinder at the loading stage, and 4 plastic regions appear at the unloading stage. These regions correspond to two faces and two edges of the Treska prism. For each plastic region, an exact analytical solution of the determining system of equations is found. The system of conditions at the boundaries between the regions providing continuity of the obtained solutions throughout the cylinder is given. Two cases are considered, i.e. the case with a plastic flow which starts first on the inner, and then on the outer surface of the cylinder. Analytical expressions are obtained for rotational speeds at which new regions appear. The relationship between the nucleation rates of the secondary and primary plastic flow is established. The value of the maximum rotation speed sufficient for a complete transition of the cylinder to the state of the secondary plastic flow was also found. It has been revealed that the adding of a rigid casing can significantly increase the resource of an exploited part.

A modified transfer matrix method for bending vibration of CFRP/Steel composite transmission shafting

The bending vibration of transmission shafting directly influences dynamic performance of mechanical systems. The adoption of carbon fiber-reinforced plastics (CFRP) hollow shaft in the long-span transmission shafting can effectively reduce bending vibration. This paper aims to modify the transfer matrix method (TMM) for the CFRP/Steel composite transmission shafting system based on lamination theory and layer-wise beam theory. The dynamic kinetic equations of the steel and CFRP segments of the composite transmission shafting were modeled; then the bending vibration was solved by combining the boundary conditions of the CFRP/Steel composite transmission shafting. The experimental tests have been carried out in the CFRP/Steel composite transmission shafting to obtain the critical speed of rotation. Moreover, the results of modified TMM were compared with experimental tests, finite element method, and simply supported beam model. The comparison results show that the modified TMM proposed in this paper can effectively calculate the bending vibration characteristics of the CFRP/Steel composite transmission shafting system.

Design Consideration and Characteristic Investigation of Modular Permanent Magnet Bearingless Switched Reluctance Motor

In order to increase structure compactness, critical rotor speed, and output torque of existing 12/12 bearingless switched reluctance motor (BSRM) with axial-biased permanent magnet, an improved modular permanent magnet BSRM is comprehensively investigated. First, basic structure and operation principle for torque and suspending force are briefly introduced. Second, magnetic design, including torque and suspending force, is taken into account. In addition, basic size estimation, self-starting capability, maximum suspending force, and selection of secondary air-gap are comprehensively considered in design. Third, several characteristics, such as torque, suspending force, etc., are deeply analyzed. Finally, a prototype motor is manufactured based on the above-mentioned analysis and design method. And the implemented experiment results show that the improved structure has good performance.

Effect of roughness on sealing performance of oil seals with surface texture

PurposeThis paper aims to obtain the film thickness, friction torque and pumping rate and analyze the effects of roughness and surface micro-dimple texture (circular, square and equilateral triangle) on the performance of the oil seal.Design/methodology/approachOn the basis of elastohydrodynamic lubrication and the pumping mechanism of rotating shaft seal, this paper establishes a numerical model of hybrid lubrication of oil seal in sealing area. The model is coupled with fluid mechanics, rough peak contact mechanics and deformation analysis.FindingsThe results show that surface texture significantly improves the lubrication properties of the oil seal. The oil seal with the square texture has the largest oil film thickness, while the equilateral triangle texture has a better effect on the pumping rate.Originality/valueTo get closer to the real working environment of the oil seal, based on the surface roughness, this paper studies the effect of the texture shapes applied to the oil seal lip surface on the performance of the oil seal. The critical roughness and rotational speed values with zero pumping rate are obtained, which provides a theoretical basis for the correct selection of oil seals.

Effects of Design Parameters on the Multiphysics Performance of High-Speed Permanent Magnet Machines

In the design of high-speed permanent magnet machines (HSPMMs), comprehensive effects of design parameters on the various properties of electromagnetic loss, rotor stress, rotor critical speed, and temperature distribution must be analyzed to obtain the optimal design. The aim of this paper is to examine the effects of design parameters, such as the pole number, stator slots number, number of conductors per slot, permanent magnet (PM) thickness, PM pole arc coefficient, air gap length, rotor diameter, core length, and sleeve thickness, on multiphysics performance based on a high-power HSPMM. A reasonable design is determined according to the above-mentioned analysis that satisfies all specified multiphysics constraints. The theoretical results are confirmed by the experimental results on a prototype in terms of electromagnetic, mechanical, and thermal characteristics such as back electromotive force, no-load loss, full-load current, overspeed experiment, and temperature distribution.

Vibration characteristics of filament wound composite tubes applied to the intermediate shaft in ship propulsion system

In this study, the CFRP shafts made up of T700-SC multilayered composites have been designed to replace the steel shaft of a ship. An important design variable to be considered when designing composite material intermediate shafts is the natural frequency for resonance avoidance at critical rotational speed and torsional strength for axial load. In order to satisfy these, strength and modal analysis were performed. In order to minimize the deformation of the shape due to the residual stress after mandrel removal, it was laminated by axial symmetry. The fibers orientation angle has a great influence on the natural frequency of the drive shaft. The carbon fiber should be closely oriented at [Formula: see text] to improve the modulus of elasticity in the direction of length of the intermediate shaft and to increase the natural frequency. Also, the optimum fiber orientation for maximum torsional strength should be close to [Formula: see text]. The stacking pattern and the stacking order were finally decided considering the results of the finite element analysis (FEA).

Tribological performances of graphite–MoS2 coating at various high temperatures

The tribological performances of the graphite–MoS2 coating deposited on the disc specimen, whose material is GCr15 steel, are experimentally investigated under high temperatures. Effects of graphite content, applied load, rotational speed and test temperature on the coefficient of friction and wear scar width of the coating are evaluated. The graphite–MoS2 coating with 20 wt% graphite addition exhibits the relatively small coefficient of friction and wear scar width at 200 ℃. At or beyond 400 ℃, the coating's lubricating effect is severely deteriorated with the testing time. At 200 ℃, there exists a critical applied load of 10 N and a critical rotational speed of 1250 rpm beyond which the MoS2 coating with 20 wt% graphite content is worn through and brings out a large coefficient of friction. The test results indicate that adding 20 wt% to 33 wt% graphite to MoS2 coating leads to an obvious reduction of the coefficient of friction and wear scar width for the coating at 200 ℃.