On The Lateral Stability of a Flexible Truck

1983 ◽  
Vol 105 (2) ◽  
pp. 120-125 ◽  
Author(s):  
A. M. Whitman
Keyword(s):  
Asymptotic Expansion ◽  
Geometric Parameter ◽  
Symmetric Function ◽  
Critical Speed ◽  
Numerical Solutions ◽  
Bending Stiffness ◽  
Lateral Stability ◽  
Expansion Parameter ◽  
Entire Structure ◽  
The Stability

Analytic formulae for the critical speed and frequency of an interconnected pair of wheelsets based on an asymptotic expansion in a truck geometric parameter are derived. No restriction is placed on the values of either the shear or bending stiffness; consequently, the entire structure of the stability surface is obtained. The surface is a symmetric function of the two dimensionless stiffnesses and it depends predominantly on their series combination. Expressions are obtained for the local and global extrema and their locations. The frequency varies monotonically from the wheelset kinematic frequency to the rigid truck frequency as a function of stiffness. The results are compared with numerical solutions and found to be accurate in the region of physically obtainable values of the expansion parameter.

A Comparison of the Stability and Curving Performance of Radial and Conventional Rail Vehicle Trucks

1981 ◽  
Vol 103 (3) ◽  
pp. 191-200 ◽  
Author(s):  
D. Horak ◽  
C. E. Bell ◽  
J. K. Hedrick
Keyword(s):  
Shear Stiffness ◽  
Bending Stiffness ◽  
Lateral Stability ◽  
High Shear ◽  
Wear Properties ◽  
Rail Vehicle ◽  
Curving Performance ◽  
Conventional Rail ◽  
The Stability ◽  
Total Shear

This paper compares the lateral stability and steady-state curving performance of radial and conventional rail vehicle trucks. The radial truck has two unique features, it allows direct elastic coupling between the wheelsets and it allows greater total truck shear stiffness for a given bending stiffness. It is shown that the first property allows the radial truck to achieve up to a 40 percent higher critical speed than the conventional truck for equivalent truck total shear and bending stiffness since the direct coupling between the wheelsets allows decoupling of the truck mass from the hunting wheelset masses. The second feature, i.e., greater shear stiffness capability, allows the radial truck to have improved wear properties during the negotiation of tight curves. It is shown that the high shear stiffness property combined with a low bending stiffness reduces the lateral flange force and wheelset angle of attack during flange contact. It is concluded that for routes where the majority of curves are less than 4 deg (greater than 400 m radius) the truck optimized for off-flange performance should have intermediate values of shear stiffness, bending stiffness, and conicity. On the other hand, for routes where the majority of curves are greater than 4 deg, the truck optimized for on-flange performance should have a high shear stiffness and low values of bending stiffness and conicity.

Lateral Stability Behavior of Railway Freight Car System With Elasto-Damper Coupled Wheelset: Part 2—Truck Model

1987 ◽  
Vol 109 (4) ◽  
pp. 500-507 ◽  
Author(s):  
A. K. W. Ahmed ◽  
S. Sankar
Keyword(s):  
Critical Speed ◽  
Lateral Stability ◽  
Stability Behavior ◽  
Railway Freight ◽  
Linearized Stability ◽  
Freight Car ◽  
Lateral Mode ◽  
Lateral Modes ◽  
The Stability ◽  
Railway Freight Car

To investigate the effect of elasto-damper coupled wheelset (EDCW), on the lateral stability behavior of freight cars, a railway freight truck model with two EDCW and pseudo-car body has been developed. The results of linearized stability analysis showed, that for small values of wheelset coupler stiffness, damping has significant influence on the stability behavior of wheelset relative spin as well as wheelset and truck lateral modes. The results further showed that, by utilizing an optimal EDCW coupler parameter, the critical speeds corresponding to truck hunting and wheelset lateral mode can be made equal. In doing so, the truck hunting critical speed on tangent track can be improved by over 100 percent in comparison to truck model with conventional rigid axle wheelsets.

Instability of an Elastic Strip Hanging in an Airstream

1975 ◽  
Vol 42 (1) ◽  
pp. 195-198 ◽  
Author(s):  
S. K. Datta ◽  
W. G. Gottenberg
Keyword(s):  
Small Amplitude ◽  
Critical Speed ◽  
Bending Stiffness ◽  
Elastic Strip ◽  
Approximate Analysis ◽  
Rectangular Strip ◽  
Length Width ◽  
Air Speed ◽  
The Stability

The stability of a long, thin elastic strip hanging vertically in a downward flowing airstream was considered. Experimentally it was observed that the strip remained essentially motionless or at most developed a small amplitude bounded oscillation as the air speed was increased until a critical speed was attained beyond which violent oscillations of the free-ended strip occurred. A linear approximate analysis was performed for this problem which accounted for shape-induced lift and bending stiffness of the strip and which closely predicted critical air speeds for this instability. The critical air speed was studied as a function of the length, width, and thickness of the rectangular strip.

ASSESSMENT OF PINE CROPS GROWTH IN BAIMAK FORESTRY

2020 ◽  
Vol 37 (3) ◽  
pp. 83-90
Author(s):  
T.Z. Mutallapov ◽  
Keyword(s):  
Scots Pine ◽  
Forest Ecosystem ◽  
Distribution Curve ◽  
Comparative Assessment ◽  
Tree Distribution ◽  
Entire Structure ◽  
Structure Changes ◽  
Large Trees ◽  
Different Types ◽  
The Stability

The article presents the results of evaluating the growth of Scots pine in the Baymak forest area. The analysis of forestry and taxation indicators of Scots pine crops on the studied sample areas is carried out, and a comparative assessment of the growth of forest crops growing in different types of forest is given. Increased competition in plantings leads to the natural decline of stunted trees, which is the result of differentiation in the stand. As a result, its structure changes, the number of large trees increases, and, accordingly, the stability of the forest ecosystem increases. In this regard, the appearance of the tree distribution curve by thickness levels also changes. It becomes more "flat", and its competitive load is more evenly distributed over the entire structure of the stand, and competition is weakened.

scholarly journals Steady-state $$\dot{V}{\text{O}}_{2}$$ above MLSS: evidence that critical speed better represents maximal metabolic steady state in well-trained runners

2021 ◽  
Author(s):  
Rebekah J. Nixon ◽  
Sascha H. Kranen ◽  
Anni Vanhatalo ◽  
Andrew M. Jones
Keyword(s):  
Steady State ◽  
Critical Speed ◽  
Lactate Concentration ◽  
Practical Interest ◽  
Blood Lactate Concentration ◽  
Distance Runners ◽  
Severe Intensity ◽  
The Stability ◽  
Trained Runners ◽  
Over Time

AbstractThe metabolic boundary separating the heavy-intensity and severe-intensity exercise domains is of scientific and practical interest but there is controversy concerning whether the maximal lactate steady state (MLSS) or critical power (synonymous with critical speed, CS) better represents this boundary. We measured the running speeds at MLSS and CS and investigated their ability to discriminate speeds at which $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 was stable over time from speeds at which a steady-state $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 could not be established. Ten well-trained male distance runners completed 9–12 constant-speed treadmill tests, including 3–5 runs of up to 30-min duration for the assessment of MLSS and at least 4 runs performed to the limit of tolerance for assessment of CS. The running speeds at CS and MLSS were significantly different (16.4 ± 1.3 vs. 15.2 ± 0.9 km/h, respectively; P < 0.001). Blood lactate concentration was higher and increased with time at a speed 0.5 km/h higher than MLSS compared to MLSS (P < 0.01); however, pulmonary $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 did not change significantly between 10 and 30 min at either MLSS or MLSS + 0.5 km/h. In contrast, $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 increased significantly over time and reached $$\dot{V}{\text{O}}_{2\,\,\max }$$ V ˙ O 2 max at end-exercise at a speed ~ 0.4 km/h above CS (P < 0.05) but remained stable at a speed ~ 0.5 km/h below CS. The stability of $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 at a speed exceeding MLSS suggests that MLSS underestimates the maximal metabolic steady state. These results indicate that CS more closely represents the maximal metabolic steady state when the latter is appropriately defined according to the ability to stabilise pulmonary $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 .

Electrohydrodynamic stability: Taylor–Melcher theory for a liquid bridge suspended in a dielectric gas

2002 ◽  
Vol 452 ◽  
pp. 163-187 ◽  
Author(s):  
C. L. BURCHAM ◽  
D. A. SAVILLE
Keyword(s):  
Surface Tension ◽  
Dielectric Constant ◽  
Electric Fields ◽  
Liquid Bridge ◽  
Numerical Solutions ◽  
Specific Conductivity ◽  
Axisymmetric Deformation ◽  
Aspect Ratios ◽  
The Stability ◽  
Theory And Experiment

A liquid bridge is a column of liquid, pinned at each end. Here we analyse the stability of a bridge pinned between planar electrodes held at different potentials and surrounded by a non-conducting, dielectric gas. In the absence of electric fields, surface tension destabilizes bridges with aspect ratios (length/diameter) greater than π. Here we describe how electrical forces counteract surface tension, using a linearized model. When the liquid is treated as an Ohmic conductor, the specific conductivity level is irrelevant and only the dielectric properties of the bridge and the surrounding gas are involved. Fourier series and a biharmonic, biorthogonal set of Papkovich–Fadle functions are used to formulate an eigenvalue problem. Numerical solutions disclose that the most unstable axisymmetric deformation is antisymmetric with respect to the bridge’s midplane. It is shown that whilst a bridge whose length exceeds its circumference may be unstable, a sufficiently strong axial field provides stability if the dielectric constant of the bridge exceeds that of the surrounding fluid. Conversely, a field destabilizes a bridge whose dielectric constant is lower than that of its surroundings, even when its aspect ratio is less than π. Bridge behaviour is sensitive to the presence of conduction along the surface and much higher fields are required for stability when surface transport is present. The theoretical results are compared with experimental work (Burcham & Saville 2000) that demonstrated how a field stabilizes an otherwise unstable configuration. According to the experiments, the bridge undergoes two asymmetric transitions (cylinder-to-amphora and pinch-off) as the field is reduced. Agreement between theory and experiment for the field strength at the pinch-off transition is excellent, but less so for the change from cylinder to amphora. Using surface conductivity as an adjustable parameter brings theory and experiment into agreement.

scholarly journals The Optimum Design of Stepped Shafts: A Study in Computational Optimization

1982 ◽  
Author(s):  
C. J. Maday
Keyword(s):  
Optimum Design ◽  
Critical Speed ◽  
Numerical Solutions ◽  
Boundary Value ◽  
Minimum Principle ◽  
Problem Formulation ◽  
Rayleigh Quotient ◽  
Computational Optimization ◽  
Stepped Shaft ◽  
Determine Step

Optimum stepped shaft designs are obtained through an application of Pontryagin’s Minimum Principle. Optimum designs are obtained for a given critical speed of specified order. Indexes of Performance to be minimized include mass and rotating inertia. A general problem formulation illustrates how constraints on stress, deflections, and geometric design are taken in account. Numerical solutions are obtained to nonlinear multi-point-boundary-value-problems. A Newton-Raphson algorithm was developed to determine step locations precisely in order to facilitate the convergence of the shooting method used to solve the boundary value problem. Numerical solutions are determined with an assumed critical speed; a Rayleigh quotient calculation is used to verify that the optimum design possesses the assumed value.

A Study of the Lateral Stability of Railroad Vehicles Using a Nonlinear Constrained Multibody Formulation

2001 ◽  
Author(s):  
Davide Valtorta ◽  
Khaled E. Zaazaa ◽  
Ahmed A. Shabana ◽  
Jalil R. Sany
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Theory ◽  
Linear Stability Analysis ◽  
Numerical Study ◽  
Operating Conditions ◽  
Lateral Stability ◽  
Railroad Vehicles ◽  
Contact Formulation ◽  
The Stability

Abstract The lateral stability of railroad vehicles travelling on tangent tracks is one of the important problems that has been the subject of extensive research since the nineteenth century. Early detailed studies of this problem in the twentieth century are the work of Carter and Rocard on the stability of locomotives. The linear theory for the lateral stability analysis has been extensively used in the past and can give good results under certain operating conditions. In this paper, the results obtained using a linear stability analysis are compared with the results obtained using a general nonlinear multibody methodology. In the linear stability analysis, the sources of the instability are investigated using Liapunov’s linear theory and the eigenvalue analysis for a simple wheelset model on a tangent track. The effects of the stiffness of the primary and secondary suspensions on the stability results are investigated. The results obtained for the simple model using the linear approach are compared with the results obtained using a new nonlinear multibody based constrained wheel/rail contact formulation. This comparative numerical study can be used to validate the use of the constrained wheel/rail contact formulation in the study of lateral stability. Similar studies can be used in the future to define the limitations of the linear theory under general operating conditions.

Influence of Interaction Between Torsion and Bending on Long-Term Nonlinear Rotor Dynamics

1999 ◽  
Author(s):  
Jiazhong Zhang ◽  
Bram de Kraker ◽  
Dick H. van Campen
Keyword(s):  
Critical Speed ◽  
Floquet Theory ◽  
Rotor Dynamics ◽  
Steady State Response ◽  
Bending Vibrations ◽  
Bending Vibration ◽  
State Response ◽  
Stability And Bifurcation ◽  
The Stability

Abstract An elementary system with gears and excited by unbalance mass has been constructed for analyzing the interaction between torsion and bending vibration in rotor dynamics. For this system, only the interaction caused primarily by unbalance mass has been investigated. The stability and bifurcation characteristics of the system have been studied by numerical computation based on Hopf bifurcation and Floquet theory. The results show that the interaction between torsion and bending vibrations can affect the stability and bifurcation of the unbalance response, in particular the onset speed of instability. In addition to the above, the interaction also affects the steady-state response. To investigate the influence of unbalance mass, the periodic solution and its stability have been studied near the first bending critical speed of the decoupled system. All the results show that the coupling of torsion and bending vibrations can have a significant influence on the nonlinear dynamics of the whole system.

Sign in / Sign up

Export Citation Format

Share Document