Theoretical and experimental analysis of an unbalanced and cracked cardan shaft in the vicinity of the critical speed

This paper presents a theoretical and experimental analysis of a coupled lateral and torsional vibrations of two identical rotors interconnected by a flexible Hooke’s joint and modelled as a multibody system with a small misalignment angle. Using energy principle and a Lagrangian transformation, the governing equation of the propeller shaft system is established by considering a nonlinear elastic shaft time-dependent perturbation. To study the sensitivity of the crack for a rotating shaft, the model is enriched by considering the periodical feature of the time-varying stiffness deriving from the crack breathing model. The nonstationary response of a cracked rotor system in the presence of unbalance has been evaluated using orbit patterns and Fast Fourier Transform. The highly oscillated feature of the rotors system is theoretically obtained and experimentally analysed. The analysis demonstrated that the crack parameters in the input shaft tend to inhibit the occurrence of unstable oscillations in lateral deflection, orbit and frequency spectrum of the secondary response. It is also found that the passage of the cracked primary shaft near to an integral multiple of the critical speed leads to the phenomenon of sup-harmonic resonance. Subsequently, the experimental analysis conducted equally indicated that the quantitative relation between the faults and the performance of the transmission is impacted by the time-varying stiffness and is the main cause of the frequency-modulated feature in the Cardan shaft system. Finally, the experimental results were informative for the transient response exploration and comparable to the theoretical findings for validating the proposed twin-rotor model

Stochastic Effect of Grain Elongation on Nanocrystalline Materials Strain and Strain Rate Produced by Accumulative Roll-Bonding and Equal Channel Angular Pressing

Severe plastic deformation techniques are acknowledged to produce elongated grains during fabrication of nanostructured materials. Previous models relating grain size to mechanical properties considered only equivalent radius, thus ignoring other approaches of measuring grain sizes such as semiminor axis, semimajor axis, and major axis radii that determine true grain shape. In this paper, stochastic models of nanomaterials mechanical properties that include the ignored parameters have been proposed. The proposed models are tested with data from nanocrystalline aluminum samples. The following facts were experimentally observed and also revealed by the models. Grain elongates to a maximum value and then decreases with further grain refinement due to grain breakages. Materials yield stress increases with elongation to a maximum and then decreases continuously. The varying approaches of measuring grain radius reveal a common trend of Hall-Petch and Reverse Hall-Petch Relationship but with different critical grain sizes. Materials with high curvature grains have more enhanced yield stress. Reducing strain rates leads to materials with more enhanced yield stress, with critical strain rates values beyond which further reductions do not lead to yield stress enhancement. It can be concluded that, by considering different approaches of measuring grain sizes, reasons for different yield stress for nanomaterials that were observed but could not be explained have been dealt with

Comparison of rumen bacteria distribution in original rumen digesta, rumen liquid and solid fractions in lactating Holstein cows

Microbial diversity in different fractions of rumen content. a, the OTU numbers in original, solid or liquid fraction samples. b, Chao1 index in original, solid or liquid fraction samples. c, Simpson index based on OTUs in original, solid, and liquid fraction samples. HFD: High fiber diet; HED: High energy diet. Data are presented as Mean ± SD. Figure S2. Analysis of similarity (ANOSIM) in different groups. ANOSIM results are presented with box plot when bacteria communities are grouped by diet (a), cows (b), and ruminal content fractions (c) using Bray-Curtis metric based on OTUs. Figure S3. Venn plot for shared OTUs. a, OTUs in HFD and HED. b, OTUs in original, solid and liquid fractions. Figure S4. Ruminal bacteria change in different fractions of rumen content at genera level. LEfSe histogram demonstrating taxonomic differences among different fractions in HFD group (a) and HED group (b) respectively, LDA scores above 2 and P value smaller than 0.05 were shown. LEfSe: linear discriminant analysis (LDA) effect size. Figure S5. Influence of rumen fractions on biomarker taxa abundance. p_: phylum; c_: class; o_: order; f_: family; g_: genus. Data was presented as Mean ± SD. Figure S6. Predominant rumen bacteria at genera level. a, predominant genera higher than 1% in proportion in all samples. b, distribution of predominant genera in each fractions. (DOC 1371 kb

Numerical and experimental diagnosis of complex rotor system by time-frequency techniques

This paper describes the application of Discrete Wavelet Transform (DWT) to identify various types of nonlinear damage caused by, unbalance, rotor-stator contact and a breathing crack in rotating machinery. Multiple faults have been investigated based on numerical and experimental signal analysis using Fast Fourier Transform (FFT) and DWT. A four degree of freedom fully coupled model of the rotor-stator system that includes the nonlinear damage in the rotor vibrations was established using Energy principles. Existence of high system nonlinearity could not allow exhaustive discrimination of rub and crack by classical FFT. Therefore, the DWT was employed. The results provide detailed feature analysis of the fault signals. Practical vibration measurements through a data acquisition system interfaced with Rotor Kit-4 and crack simulator provided the test data. Experimental Time-Frequency analysis gave more realistic faults responses with variable faults features. Irregularity of orbit, harmonic peaks in the presence of rub and crack were unique and distinguished periodic motion from other types of motion. The presence of a crack shifted the critical speed location and exhibited sub-harmonic components, which were more prominent with rub in vibration response. The detailed decomposition signal by DWT method established inherent feature patterns that effectively discriminated the multiple faults

Vibrations of Misaligned Rotor System with Hysteretic Friction Arising from Driveshaft–Stator Contact under Dispersed Viscous Fluid Influences

Dynamic analysis of a combination of misaligned rotors, the disturbance of the Cardan joint and the rotor–stator rubbing within a restricted clearance space in a viscous fluid is complex and can result in persistent vibration anomalies that are often misunderstood. It becomes increasingly important to gain some insights into how the transmission of coupled motion responds dynamically under a variety of conditions. This paper introduces an efficient simulation of the misaligned multi-degree-of-freedom rotor’s model, which was developed to predict the transient dynamic behaviours of a driveshaft deflection. The model accounts for tight clearance as a function of contact deformation according to nonlinear Hertzian contact theory. The paper also examines recent research by considering the influence of parameters such as eccentric masses, applied torques and flexible coupling joint perturbation introduced in the proposed rotor system. The simulation results indicated that the viscous fluid surrounding the driveshaft had sufficient torsional flexibility to dampen the rubbing impact to the driven shaft displacement. In addition, the torsional fluctuations of the flexible coupling abruptly increased, and then significantly impacted the vibration of the submerged driveshaft. Parametric studies involving the interconnected rotor models indicated that the effects of fluid on a close-bounds contact area can create partial disturbance reduction. The high rubbing contact is shown to be lost through the Hooke’s joints during power transmission. The speed-frequency spectrum maps provide valuable information on all the modelled excitations over the frequency of the twice-running speed resonance in a viscous medium. Further, nonlinear characteristics are reconstructed through orbit shapes and can be adopted in the condition monitoring of rotors in engineering practice

Influences of Hydrodynamic Forces on the Identification of the Rotor-Stator-Rubbing Fault in a Rotating Machinery

Mechanical failures of a complex machine such as rotor widely used in severe conditions often require specialized knowledge, technical expertise, and imagination to prevent its rupture. In this paper, a model for analyzing excitation of a coupled lateral-torsional vibrations of a shaft system in an inviscid fluid is proposed. The model considers the recurrent contact of the vibrating shaft to a fixed stator. The simplified mathematical model of the rotor-stator system is established based on the energy principle. The dynamic characteristics of the fluid-rotor system are studied, and the features of rub-impact are extracted numerically and validated experimentally under the effects of the unbalance and the hydrodynamic forces. The main contribution of this article is in extraction and identification of the rub features in an inviscid medium which proved to be complex by the obstruction of the fluid and required the use of appropriate signal processing tools. The results through a synchrosqueezing wavelet transform indicated that the exciting fluid force could significantly attenuate the instability and amplitude of rubbing rotor. The experimental results demonstrated that for half the first critical speed, the subharmonic 1/2×Ω and the irregular orbit patterns provide good indices for rub detection in an inviscid fluid of the rotating shafts. Finally, it is revealed that the instantaneous frequency extraction based on wavelet synchrosqueezing is a useful tool to identify the weak and hidden peak harmonics localised in the time-frequency maps of the fluid-rotor system

Optimization of the mechanical and vibrational damping properties of a hybrid rubber particle and glass fibre railway sleeper composite

In the locomotive industry, the railway structural material is frequently subjected to harsh loads and vibration, and the current durability and vibration-resilience capabilities of the sleepers are insufficient. The aim of this paper is to fabricate a railway sleeper composites with enhanced mechanical and vibrational properties. A full factorial experimental design was followed in the composite fabrication with the rubber particles and fibreglass volume fraction ratio varied between 5 and 20% and 5 to 8% respectively. Modelling and optimisation of the mix design was then carried out using numerical modelling techniques. ANOVA tests were carried out to show the model’s accuracy in predicting tensile strength, compression strength, flexural strength, and vibrational damping, as shown by R ^2 values of 60.69%, 86.60%, 60.05% and 81.41%, respectively. However, the model was not reliable for the composite hardness which had an R ^2 value of 37.87%. The optimisation model developed in the study indicated that rubber particles of size of 150 μ m at volume fraction of 7.48% and fibreglass volume fraction of 8% gave the optimum mechanical and vibrational properties