Increase In Critical Speed Research Articles

Stability and Bautin bifurcation of four-wheel-steering vehicle system with driver steering control.

In this paper, the stability and Bautin bifurcation of a four-wheel-steering (4WS) vehicle system, by considering driver steering control, are investigated. By using the central manifold theory and projection method, the first and second Lyapunov coefficients are calculated to predict the type of Hopf bifurcation of the vehicle system. The topological structure of Bautin bifurcation, a degenerate Hopf bifurcation of the 4WS vehicle system, is presented in parameter space, and it reveals the dynamics of the vehicle system of different choices of control parameters. The influences of system parameters on critical values of the bifurcation parameter are also analyzed. It is shown that with the increase in the frontal visibility distance of the driver control strategy coefficient and the cornering stiffness coefficients of rear wheels, the critical speed increases. Nevertheless, the critical speed decreases with the increase in the distance from the center of gravity of the vehicle to the front axles, Driver's perceptual time delay, and cornering stiffness coefficients of the front wheels.

Analysis of the Performance of Chamfered Finite-Length Journal Bearings under Dynamic Loads

Misalignment is one of the most common challenges that the normal operation of journal bearings faces. This type of problem may be the result of a wide range of reasons, such as bearing wear, shaft deformation, and errors related to the manufacturing and installation process. The main undesirable consequences of the misalignment, such as pressure rise and lubricant film reduction, are concentrated on the bearing edges. Therefore, chamfering the bearing edges reduces such misalignment-related drawbacks. This work presents a novel numerical solution to the problem of finite-length journal bearing considering edge chamfering. This solution involves the determination of the levels of lubricant layer thickness and pressure distribution in addition to the journal trajectory under impact load with the related stability limits. The finite difference method is used in this solution, and the equations of motion are also solved numerically using the Runge–Kutta method. The Results of this novel analysis show that chamfering the bearing edges increases the film thickness and reduces pressure spikes associated with the system operation under the case of 3D misalignment. Furthermore, the chamfered bearing shows a wide stability range under impact loads, where the normal bearing is unstable as the critical speed increases by 26.98%, which has positive consequences on the journal’s trajectory.

Analysis of critical slag entrapment speed at the steel–slag interface

ABSTRACT Based on particle image velocimetry (PIV) technology, the process and flow field characteristics of slag entrapment under the condition of critical slag entrapment are investigated by water model. The change of interface flow field at the slag entrapment process from the occurrence to end of critical slag entrapment is analysed, and the influence of kinematic viscosity of slag on critical slag entrapment velocity is quantitatively analysed. The results show that the kinematic viscosity of slag has an important influence on slag entrapment. The critical blowing flow and critical speed increase with the increasing of the viscosity. Based on the law of conservation of energy and the traditional theoretical calculation models, an improved formula for critical slag entrapment speed is proposed in this study, which further considers the thickness and viscosity of the slag.

Stability of Vibrating Functionally Graded Nanoplates with Axial Motion Based on the Nonlocal Strain Gradient Theory

Considering both the nonlocal scale and material length scale effects, we investigate vibration and stability behaviors of functionally graded nanoplates with axial motion in order to model the two-dimensional nanobelt in nanoengineering. The nonlocal strain gradient theory is applied and the differential nonlocal strain gradient constitutive relation is adopted. Using the physical neutral plane of a functionally graded thin plate, we derive the governing equation of motion for the functionally graded nanoplate with axial motion via Hamilton’s principle, where the kinematic characteristics are introduced into the dynamic behaviors. The governing equation is numerically solved using the Galerkin method. Effects of the nonlocal scale and material length scale parameters, axial velocity, gradient index, biaxial pre-tensions and aspect ratio are discussed. The results demonstrate that complex frequencies of the functionally graded nanoplate with axial motion decrease with an increase of axial velocity in the subcritical region, while the moving nanoplate experiences a divergent instability or flutter instability in the supercritical region. Natural frequency and critical speed decrease with the increase of the nonlocal scale parameter while increase with the increase of the material length scale parameter, reflecting the nonlocal softening and strain gradient hardening mechanisms, respectively. Besides, natural frequency and critical speed increase with the increase of the biaxial pre-tensions and aspect ratio, but decrease with the increase of the gradient index. In particular, the influences of the gradient index and size or weight of functionally graded nanoplates on the critical speed are explored.

Effect of rail pad stiffness on the wheel/rail force intensity in a railway slab track with short-wave irregularity

In this paper, a two-dimensional numerical model is developed to investigate the effect of rail pad stiffness on the wheel/rail force in a slab track with harmonic irregularity. The model consists of a vehicle, nonlinear Hertz spring, rail, rail pad, concrete slab, resilient layer, concrete base, and subgrade. The rail is simulated using the Timoshenko beam element for considering the effects of high-frequency excitation produced by short-wave irregularity. The results obtained from the model are compared with those available in the literature and from the field to prove the validity of the model. Through a parametric study, the effect of variations in rail pad stiffness, vehicle speed, and harmonic irregularity on the wheel/rail force is investigated. For the slab track without any irregularity, the wheel/rail force is at maximum when the vehicle speed reaches the critical speed. As the rail pad stiffness increases, the critical speed increases. When the amplitude of irregularity is high, wheel jumping phenomenon may occur. In this situation, as the vehicle speed and rail pad stiffness are increased, the dynamic wheel/rail force is increased. In the low-frequency range, the wheel/rail force increases as the rail pad stiffness increases. In the high-frequency range, the wheel/rail force increases as the rail pad stiffness is decreased.

Bridge Deck Flutter Control Using Winglets and Static Output Feedback

Control of wind-induced flutter of a bridge deck is studied using static output feedback. Servomotor-actuated winglets provide the control forces. Deck and winglets are modeled as flat plates and their aerodynamic interaction is neglected. Self-excited wind forces acting on deck and winglets are modeled using the Scanlan–Tomko model, with flat plate flutter derivatives (FDs) obtained from Theodorsen functions. Rogers rational function approximation (RFA) is used for time domain representation of wind forces in order to simplify the stability and control analyses. Control input to servomotors is based on direct feedback of vertical and torsional displacements of deck. Feedback gains that are constant, or varying with wind speed, are considered. Winglet rotations being restricted, flutter and divergence behavior is studied using system eigenvalues as well as responses. Results show that variable gain output feedback (VGOF) control using servomotor driven winglets is very effective. It provides the maximum increase in critical speed and maximum attenuation of response, followed by control with gain scheduling, with the former requiring less input power. Control with constant gain is least effective. Control of deck rotation generally appears to improve with wind speed.

Nonlinear Numerical Prediction of a Rotor–Bearing System Using Damped Flexure Pivot Tilting Pad Gas Bearings

ABSTRACTFlexure pivot tilting pad gas bearings with pad radial compliance (FPTPGB-Cs) and metal mesh dampers (MMDs) in parallel (FPTPGB-C-MMDs) have been considered for application to high-speed and high-performance turbomachinery because of their advantages of high effective damping level and adequate compliance with variations in rotor geometry or misalignment. Although the dynamic coefficients of FPTPGB-C-MMDs have been predicted using the linear method, a nonlinear study is urgently needed for their high nonlinear behavior. A nonlinear numerical investigation on the rotor–bearing system supported by FPTPGB-C-MMDs is presented in this study by using the time domain orbit simulation method that couples rotor motion equations, the unsteady Reynolds equation, and pad motion (considering MMDs) equations. The nonlinear predictions are verified by the prediction and experimental results of a published paper.FPTPGB-C-MMDs can effectively suppress the subsynchronous vibrations compared with the rotor system supported by FPTPGB-Cs. The prediction results show that a high damper mesh density has a more positive effect on improving the stability of the rotor system by reducing the subsynchronous vibrations. Investigation shows that MMDs can improve the ability of the rotor system to sustain the effect of destabilizing forces. A high damper mesh density can sustain large destabilizing forces. The simulation results also indicate that low pad radial stiffness or preload leads to high amplitudes of subsynchronous vibrations. A small clearance results in an increase in critical speed and its synchronous amplitude. Moreover, large clearance results in a wide speed range that leads to the occurrence of subsynchronous vibrations with large amplitudes.

Dynamic response to moving masses of rectangular plates with general boundary conditions and resting on variable winkler foundation

The dynamic response to moving masses of rectangular plates with general classical boundary conditions and resting on variable Winkler elastic foundation is investigated in this work. The governing fourth order partial differential equation is solved using a technique based on separation of variables, the modified method of Struble and the integral transformations. Numerical results in plotted curves are then presented. The results show that as the value of the rotatory inertia correction factor Ro increases, the response amplitudes of the plate decrease and that, for fixed value of Ro, the displacements of the plate decrease as the foundation modulus Fo increases for the variants of the classical boundary conditions considered. The results also show that for fixed Ro and Fo, the transverse deflections of the rectangular plates under the actions of moving masses are higher than those when only the force effects of the moving load are considered. For the rectangular plate, for the same natural frequency, the critical speed for moving mass problem is smaller than that of the moving force problem for all variants of classical boundary conditions, that is, resonance is reached earlier in moving mass problem than in moving force problem. When Fo and Ro increase, the critical speed increases, hence, risk is reduced.

The Effect of Pulmonary Rehabilitation on Critical Walk Speed in Patients With COPD: A Comparison With Self-Paced Walks

Walking is frequently used in the exercise rehabilitation of patients with COPD. Walking ability can be characterized by the two-parameter hyperbolic relationship between endurance and speed. One parameter, critical walk speed (s_critical), represents the maximum speed that can be endured indefinitely. The purpose of this study was to: (1) determine the effect of pulmonary rehabilitation on the critical speed and (2) compare the critical speed with the speed chosen during self-paced walking. We estimated critical speed in patients with COPD before and after rehabilitation. Patients completed four high-intensity constant-speed walk tests to intolerance on a 30-m course. The parameters of the hyperbolic relationship were determined using nonlinear regression of endurance on speed. Participants also completed self-paced walks: (1) for as long as they could, (2) at their "usual" and "fast" speeds, and (3) as a 6-min walk test. Twelve participants (FEV(1) [SD], 41 [16] % predicted; FEV(1)/FVC, 41 [12]) completed the study. At baseline, the critical speed (65 [12] m/min) was not significantly different from the self-paced, usual, or 6-min walk speeds (65 [12], 67 [14], and 63 [15] m/min, respectively). There was a significant increase in critical speed (6 [1-10] m/min) and 6-min speed (16 [10-21] m/min) after rehabilitation, without changes in the self-paced, usual, or fast speeds. Patients with COPD increase their critical walk speed after pulmonary rehabilitation. The pace chosen during common walk tasks is closely related to critical speed; this relationship is altered after rehabilitation. ClinicalTrials.gov; No.: NCT00781183; URL: www.clinicaltrials.gov.

Influence of Shear and Gyroscopic Effect of Grinder Spindle on Critical Speed

This study was focused on the theoretical modeling and numerical simulation about the shear effect and gyroscopic effect of spindle system of high-speed grinder. Based on the rotor dynamics, a theoretical model was established using the transfer matrix method. The moment balance equations, and the transition matrix, the state vector, field matrix of spindle system of ultra-high speed grinder were analyzed and calculated. The results showed that shear effect reduced the critical speed in various orders, and its influence on higher orders was more severe than on lower orders. Furthermore, it could be seen that gyroscopic effect increased the critical speed in various orders, and it was sensitive in higher orders. It could be found that the increase of fifth order critical speed reached 16.6% due to gyroscopic effect, while the minimum increase of critical speed was 1.8% due to gyroscopic effect.

Swimming abilities of wild-caught, late-stage larvae of Diplodus capensis and Sarpa salpa (Pisces: Sparidae) from temperate South Africa

Understanding the movement of marine fish larvae in coastal habitats requires an assessment of active swimming abilities. The critical speed ( U-crit) and endurance swimming of late-stage larvae of Diplodus capensis and Sarpa salpa (Family Sparidae), common inshore recreational linefish species, were measured in a laboratory swimming chamber. Postflexion and settlement-stage larvae were collected from the wild in a small bay on the warm temperate coast of South Africa. Larvae were allowed to acclimate in captivity and were tested soon after capture. For the endurance tests a speed of 18 cm s −1 was selected, as this approximated the mean current speed observed in the coastal environment of the area. The mean U-crit value (maximum swimming speed) for D. capensis (19 cm s −1) was similar to that of S. salpa (18 cm s −1), and similarly mean endurance (km swum) for S. salpa (8 km) was similar to that of D. capensis (6 km). The increase in critical speed and endurance swimming abilities with standard length was best described by a linear relationship. At lengths between 12 and 15 mm BL, D. capensis was the better swimmer, whereas S. salpa was the better swimmer between 15 and 16 mm BL. Of all the larvae that swam at critical speed, 90% were in an inertial environment. These swimming speeds exceed the modal current velocities observed in the shallow nearshore of the study region where these larvae occur abundantly. These swimming abilities provide larvae with the potential to influence their dispersal trajectories and ultimately influence their distribution in their nearshore nursery areas.

Vibratory behaviors of Jeffcott system on cylindrical roller bearings

A Jeffcott rotor system on cylindrical roller bearings is studied in detail. Its critical speed is calculated by a new calculation method with roller bearing stiffness and damping. The influences of bearing parameters, such as the roller length, rotor mass, distance between the bearings and the kinematics viscosity of lubrication on the system critical speed are numerically studied, and the influences of an oil film and damping on the critical speed are also studied. Regular curves of the relationship between the geometric parameters and the system critical speed are obtained. The results show that with increasing roller length and radial load, the critical speed increases; and with increasing rotor mass and the distance between the bearings and the kinematics viscosity, the critical speed decreases. This means that an oil film will decrease the critical rotational speed of the rotor system.

Swimming ontogeny of larvae of four temperate marine fishes

Prerequisites for understanding dispersal in pelagic larvae of demersal fishes are data on when swimming abilities of larvae are sufficiently developed to be able to alter passive dispersal trajectories. In laboratory swimming chambers, the development of critical speed and endurance swimming was measured in reared larvae of 4 species of warm-temperate marine and estuarine fishes that spawn pelagic eggs (Sciaenidae, Argyrosom us japonicus; Sparidae, Pagrus auratus, Acanthopagrus australis; Percichthyidae, Macquaria novemaculeata). Size was a better predictor of swimming ability than age. Increase in critical speed with growth was best portrayed by linear or 'flat' curvilinear relationships. Increase in endurance was best portrayed by strongly concave curvilinear relationships. The percichthyid larvae had the highest critical speed initially, but speed increased slowly with growth. The 2 sparids had the greatest increase in speed with growth, and the sciaenid the least. The greatest increase in endurance with growth was found in P. auratus, but performance of M. novemaculeata was only slightly less. The slowest increase in endurance with growth was found in A. japonicus, but, by settlement, its performance was similar to the other species. Until notochord flexion was complete, both speed and endurance were limited. Thereafter, swimming performance improved markedly at a species-specific rate. At settlement, larvae of these species could swim more than 10 km and at speeds of 15 to 20 cm s -1 (=12 to 20 BL s -1 ), which exceeded the average currents in their coastal environment. Following notochord flexion, all larvae swimming at critical speed were in an inertial environment, and this corresponded to when substantial endurance swimming developed. Whether these potential performances are actually realized in the field remains to be determined, but they provide the potential to strongly influence dispersal.

Hyperelastic effects in brittle materials failure

AbstractA fact that has been neglected in most theories of brittle fracture is that the elasticity of a solid clearly depends on its state of deformation. Metals will weaken, or soften, and polymers stiffen as the strain approaches the state of materials failure. It is only for infinitesimal deformation that the elastic moduli can be considered constant and the elasticity of the solid linear. We show by large-scale atomistic simulations that hyperelasticity, the elasticity of large strains, can play a governing role in the dynamics of fracture and that linear theory is incapable of capturing all phenomena. We introduce a new concept of a characteristic length scale ξ for the energy flux near the crack tip and demonstrate that the local hyperelastic wave speed governs the crack speed when the hyperelastic zone approaches this energy length scale. The new length scale ξ, heretofore missing in the existing theories of dynamic fracture, helps to form a comprehensive picture of crack dynamics, explaining super-Rayleigh and supersonic fracture. We further address the stability of cracks, and show agreement of the Yoffe criterion with the dynamics of cracks in harmonic systems. We find that softening hyperelastic effects lead to a decrease in critical instability speed, and stiffening hyperelastic effects leads to an increase in critical speed. The main conclusion is that hyperelasticity plays a critical role in forming a complete picture of dynamic fracture.

ACTIVE WING FLUTTER SUPPRESSION USING A TRAILING EDGE FLAP

The aeroservoelastic behaviour of a thin rectangular wing with a controllable trailing edge flap is investigated. A rather high aspect ratio motivates a numerical model based on linear beam theory for the structural dynamics and strip theory for the unsteady aerodynamic loads. Experimental flutter testing shows good agreement with the numerical stability analysis, and the impact of the trailing edge flap on the dynamics is verified by open-loop testing. The problem of stabilizing the wing utilizing the trailing edge flap is posed, and the design of a fixed-structure feedback controller is performed using numerical optimization. The problem of maximizing closed-loop modal damping with constraints on actuator performance is solved for a sequence of flow speeds and the obtained controller is synthesized using gain scheduling. The fairly large predicted increase in critical speed is experimentally verified with satisfactory accuracy.

Injection Molding Technology for High Speed Optical Disk

Abstract Recently great efforts have been made to increase the data access speed and the data storage density of the optical memory disks such as CD-ROM, DVD, ASMO disk, etc. In the viewpoint of increasing the data access speed of the optical disks, it is of great importance to characterize accurately the vibration phenomena of the rotating disk, which is related to the critical speed and the characteristics of the frequency response. In this paper, towards the goal of increasing the data access speed of the optical disks, we have proposed a novel method for improved characteristics of disk vibration without deteriorating any other specification for the optical memory disks such as geometrical and optical characteristics. A possible idea to improve the vibration characteristics of the optical disk is that the tensile initial stress in the radial direction is to be imposed within the optical disk on purpose. By the synergy effect from the residual (initial) tensile stress frozen within the optical disk combined with the stress induced by the centrifugal force occurring in rotating the optical disk, the stiffness of the disk would increase to have a stronger resistance to the disturbance resulting in increase of critical speed. With such a synergy effect in mind, modifications related to the optical disk substrate design, injection mold design and processing conditions of injection molding were presented and partially evaluated. The computer simulation and experiments indicate that the suggested ideas clearly improve the characteristics of disk vibration without deteriorating any other specification for the optical memory disks.

Laboratory studies of the performance characteristics of mowing mechanisms

Laboratory studies of the effectiveness of rotary cutting mechanisms when cutting singleand groups of grass stems were undertaken. The effect of using static stem supports or ledger plates with clearances of up to 5 mm from the cutting blade was investigated. The effectiveness of cutting with single-toothed and plain discs was also examined. The effect of clamping the tops of grass stems was examined for both types of mechanism. A number of mechanism design parameters was investigated and cutting efficacy was assessed by measuring the stubble length of individual stems, together with the number of stems which were uncut, pulled out of the holder or broken at their base. The critical speed, which is the minimum required for efficient cutting, was also assessed. The use of ledger plates, above and below the cutting blade, resulted in lower criticalcutting speeds than for conventional impact cutting when cutting single stems. For groups of stems, however, the critical speeds when using static elements did not differ significantly from those required for impact cutting. Clamping the tops of the stems resulted in very low critical cutting speeds (5 m/s or less). Critical cutting speed was reduced to below 35 m/s by increasing ledger plate length and byutilizing the whole of the blade length during cutting. Lower cutting speeds were also achieved by using a combination of ledger plate and blade angles which retained stems within the cutting area of the mechanism. If stems were at a distance of 10 mm or more from the ledger plate when contacted by the blade, a cutting speed of at least 35 m/s was required for effective cutting. In practice, the protrusion of the blade from the cutting mechanism should not be less than its height above ground level. Critical cutting speeds exceeded 80 m/s under laboratory conditions if stem inclination waslarge (⩾65°) or blade rake angle exceeded 60°. This is equal to the cutting speeds required under practical conditions. A toothed disc cut groups of stems more effectively than single stems and at a low criticalcutting speed. A plain disc cut effectively only if the tops of the stems were clamped. A minimum critical speed (20–27 m/s) was achieved with a toothed disc with teeth having a 0° rake angle, a 30° clearance angle and a pitch of 8 mm. Tangential wear of the tips of the teeth resulted in a proportional increase in critical speed.

Laboratory studies of the effect of blade parameters and stem configuration on the dynamics of cutting grass

Laboratory experiments were conducted to study the cutting of grass stems with single blades over a range of cutting speeds from 15 to 35 m/s. The blade rake angle was varied from 0 to 45°, using both sharp and blunt cutting edges, and blade thicknesses of 1 to 3 mm were used in a blunt condition. The effect of stem inclination away from the blade was studied over a range of 0 to 60° and the effect of cutting arrays of stems was examined. The blade force and energy during cutting were measured using a piezoelectric transducer. The stem deflection modes were recorded photographically by the use of a camera with an open shutter and the sequential firing of a series of flash guns using electronic control. Blade rake angle was found to have no significant effect on specific cutting force or energy when cutting above the critical speed. At lower speeds, however, increasing the blade angle resulted in an increasing number of uncut stems. The thickness of blunt blades had no significant effect on critical cutting speed or specific cutting force and energy. The bluntest blade (0–15 mm edge radius) required three times the specific cutting energy and twice the specific peak force as a sharp blade (0–325 mm edge radius). The principal effect of the angle of stem inclination was an increase in critical speed from 25 to 60 m/s, as the angle of inclination increased from 0 to 60°. When cutting groups of stems, the critical speed was not dependent on the configuration and number of stems in the group; the specific cutting energy was independent of the group configuration and equal to that when cutting single stems.

The effect of shear and rotary inertia of a rotor at its critical speeds

This paper deals with the eigenfrequencies of flexural vibration of a homogeneous rotor model which includes shear, rotary inertia and the gyroscopic effect. A formula for the critical speeds of this rotor has also been found. It appears that the effect of these factors is smaller when the critical speed increases and the ratio of slenderness of a rotor decreases.

Aeroplane Wing Flutter

FOR all stiffness ratios, there is clearly a marked increase of critical speed when the centre of inertia is as far forward as the flexural centre.