Critical shimmy speed of nonswiveling landing-gear wheels subject to lateral loading

The paper presents a nonlinear model describing vibration of the landing gear relative to the fuselage. The model is intended to analyze the dynamic stability of nonswiveling main-gear wheels. The model is used to show that the lateral component of the fuselage speed has a significant effect on the critical shimmy speed __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 9, pp. 134–142, September 2006.     

Wave effects in a stretched band

Gor'kii Branch, Institute of Mechanical Engineering, Academy of Sciences of the USSR. Translated from Prikladnaya Mekhanika, Vol. 27, No. 9, pp. 87–92, September, 1991.     

Behaviour of tyres driven in soft ground with side slip

A six-component measuring device has been developed, with which forces and moments can be measured on a braked or driven yawing wheel in yielding ground, both in the field and in a test bin. Experimental results on tyres running at a side slip angle are discussed and plotted to show the variety of effects of driving force, slip, side-force and side slip angle. It is shown that with an increasing driving-force at constant slip angle the side-force is considerably reduced. In an approximately calculation, by means of linearized equations of motion of a rear-wheel-drive and a four-wheel-drive vehicle, the behaviour on side slopes and on curves has been studied.As a result it follows that the interaction of the side-force and the driving-force affects markedly the motion of the vehicle. With the four-wheel-drive vehicle on a curve, the radius of curvature and, on the slope, the yaw angle of the vehicle are less than with rear-wheel-drive vehicles.     

汽车摆振动力学机理研究——位移延时反馈及能量传递分析

主要分析了汽车摆振的动力学机理。通过使用解析法从理论上证明了摆振是由位移延时反馈引起的自激振动现象。利用数值分析方法揭示摆振系统的动力学机制及响应行为,验证了解析分析的相关结论。并进一步计算能量输入与能量传递的值,结果表明能量输入可以用来评价汽车摆振的动力学响应。最后根据能量传递规律提出汽车摆振的抑制措施。     

Melting heat and thermal radiation effects in stretched flow of an Oldroyd-B fluid

The incompressible flow of a non-Newtonian fluid with mixed convection along a stretching sheet is analyzed. The heat transfer phenomenon is discussed through thermal radiation. The effects of the melting heat transfer and heat generation/absorption are also taken. Suitable transformations are utilized to attain the nonlinear ordinary differential expressions. The convergent series solutions are presented. The fluid flow, temperature,and surface heat transfer rate are examined graphically. It is observed that the velocity decreases when the relaxation time increases while increases when the retardation time is constant. The results also reveal that the temperature distribution reduces when the radiation parameter increases.     

The modulus of particle networks with stretched strands

Expressions are derived which relate the shear modulus G to interaction forces and geometric structure of a particle network with stretched strands. These relations are compared with corresponding expressions given in literature.     

The buoyancy effects on the boundary layers induced by continuous surfaces stretched with rapidly decreasing velocities

Heat and mass transfer characteristics of the self-similar boundary layer flows induced by continuous surfaces stretched with rapidly decreasing power law velocities U_w x^m, m < –1 are considered for mixed convection flow. The effect of various governing parameters, such as Prandtl number Pr, temperature exponent n, dimensionless injection/suction velocity f_w, and the mixed convection parameter = s Gr/Re² are studied. These parameters have great effects on velocity and temperature profiles, heat transfer coefficient, and skin friction coefficient at the moving surface. Results show that similarity solutions exist only when the condition n = 2m – 1 is satisfied. Critical values of , Nu/Re^0.5 and C_f Re^0.5 are obtained for predominate natural convection for different Prandtl numbers at m = –2, –6 and n = –5, and –13 respectively. Results also show that the effect of buoyancy is more significant for weak than for strong suction. Furthermore, critical Prandtl numbers where f_w profiles have minimums are obtained for m = –2 and –6. Finally, critical values of , C_f Re^0.5 are also obtained for predominate natural convection for both m = –2 and –6.     

Acceleration on stretched meshes with line-implicit LU-SGS in parallel implementation

The implicit lower–upper symmetric Gauss–Seidel (LU-SGS) solver is combined with the line-implicit technique to improve convergence on the very anisotropic grids necessary for resolving the boundary layers. The computational fluid dynamics code used is Edge, a Navier–Stokes flow solver for unstructured grids based on a dual grid and edge-based formulation. Multigrid acceleration is applied with the intention to accelerate the convergence to steady state. LU-SGS works in parallel and gives better linear scaling with respect to the number of processors, than the explicit scheme. The ordering techniques investigated have shown that node numbering does influence the convergence and that the orderings from Delaunay and advancing front generation were among the best tested. 2D Reynolds-averaged Navier–Stokes computations have clearly shown the strong efficiency of our novel approach line-implicit LU-SGS which is four times faster than implicit LU-SGS and line-implicit Runge–Kutta. Implicit LU-SGS for Euler and line-implicit LU-SGS for Reynolds-averaged Navier–Stokes are at least twice faster than explicit and line-implicit Runge–Kutta, respectively, for 2D and 3D cases. For 3D Reynolds-averaged Navier–Stokes, multigrid did not accelerate the convergence and therefore may not be needed.     

Performance prediction of animal drawn vehicle tyres in sand

Four animal drawn vehicle (ADV) tyres of 5.00–19, 6.00–19, 7.00–19 and 8.00–19 sizes were tested in sand under various but controlled conditions in an indoor soil bin. A tyre test carriage with four-bar parallel linkage was developed for accommodating a single wheel of different sizes. Performance tests were conducted at five levels of inflation pressure and load. The sand compaction level was varied in the range of 3.4–4.5 MPa/m and forward speed of the test carriage was maintained at 3.1 km/h. Performance of the tyres 7.00–19 and 8.00–19 was identical and offered less rolling resistance as compared to other tyres. However, their use in camel carts may not be recommended beyond the payload of 6 kN on single wheel with inflation pressure and sand compaction range of 172–379 kPa and 3.4 –4.5 MPa/m, respectively. Based on the experimental results, empirical models were developed to predict the performance of tyres. The accuracy of prediction of the developed empirical models was compared with that of existing semi-empirical approaches. Model with sand mobility number considered relatively simple and convenient to use in the field and yields reasonably good prediction for rolling resistance and sinkage.     

Modeling of the vehicle shimmy system with consideration of clearance of the steering linkage mechanism

The mechanism of vehicle shimmy has been paid much attention in the past decades. In which, the clearance of the steering linkage is usually neglected. Yet the prior research of the authors proved that the clearance can make great effects on the dynamic performance of the linkage. Therefore, based on nonlinear dynamics, a six-DOF dynamic model of vehicle shimmy system with consideration of the clearance was established. In which, the nonlinearity due to clearance of the movement pair in steering mechanism was taken into account. Numerical examples showed that the clearance of the movement pair could make great effects on the dynamic behavior of the vehicle shimmy system, and it is one of the key factors leading to chaos motion of the shimmy system, which provided theoretical basis for vehicle shimmy control.     

The deflection and contact characteristics of some agricultural tyres with zero sinkage

The vertical deflection, contact area, and ground pressure of three agricultural tractor rear tyres (11.2–28, 12.4–28, 13.6–28) were investigated at different normal loads and inflation pressures on a firm surface. A linear mathematical model was evolved to establish relationship among different parameters. The model could be used to represent tyre behaviour under varying operational parameters.     

Relativistic time effects in financial dynamics

Financial time series have a complex dynamic nature. Many techniques were adopted having in mind standard paradigms of time flow. This paper explores an alternative route involving relativistic effects. It is observed that the measuring perspective influences the results and that we can have different time textures.     

Multi-parameter bifurcation study of shimmy oscillations in a dual-wheel aircraft nose landing gear

We develop and investigate a mathematical model of an aircraft nose landing gear with a dual-wheel configuration. The main aim here is to study the influence of a dual-wheel configuration on the existence of shimmy oscillations. To this end, we consider a model that describes the torsional and lateral vibrational modes and the non-linear interaction between them via the tyre-ground contact. More specifically, we perform a bifurcation analysis (with the software package auto) of the model in the two-parameter plane of forward velocity of the aircraft and vertical load on the nose landing gear. This two-parameter bifurcation diagram allows one to identify regions of different dynamics, and the question addressed here is how it depends on two key parameters of the dual-wheel configuration. Namely, we consider the influence of, first, the separation distance between the two wheels and, second, of gyroscopic effects arising from the inertia of the wheels. For both cases, we find that with increasing separation distance and wheel inertia, respectively, the lateral mode becomes more stable and the torsional mode becomes less stable. More specifically, we present associated bifurcation scenarios that explain the transitions between qualitatively different two-parameter bifurcation diagrams. Overall, we find that the separation distance and gyroscopic effects due to wheel inertia may have a significant influence on the quantitative and qualitative nature of shimmy oscillations in aircraft nose landing gears. In particular, the torsional and the lateral modes of a dual-wheel nose landing gear may interact in a quite complicated fashion.     

Interaction of torsion and lateral bending in aircraft nose landing gear shimmy

In this paper we consider the onset of shimmy oscillations of an aircraft nose landing gear. To this end we develop and study a mathematical model with torsional and lateral bending modes that are coupled through a wheel-mounted elastic tyre. The geometric effects of a positive rake angle are fully incorporated into the resulting five-dimensional ordinary differential equation model. A bifurcation analysis in terms of the forward velocity and the vertical force on the gear reveals routes to different types of shimmy oscillations. In particular, we find regions of stable torsional and stable lateral shimmy oscillations, as well as transient quasiperiodic shimmy where both modes are excited.     

Plastic zone correction in a stretched cylinder with an external circumferential crack

The Dugdale hypothesis is adapted to the problem of an external circumferential crack in a stretched cylinder. The lateral surface of the cylinder is stress free and restrained from radial displacements. An external circumferential edge crack in the cylinder which is considered elastic-perfectly plastic is envisaged with the assumption that the plastic zone forms a very thin in-plane layer surrounding the crack. The solution of the problem is reduced to the solution of dual Dini series which, in turn, is reduced to a Fredholm integral equation of the second kind. Solving this integral equation numerically and using the boundedness of the axial stress, the size of the plastic zone correction is obtained.     

Design of manned lunar rover wheels and improvement in soil mechanics formulas for elastic wheels in consideration of deformation

Most of the current lunar rover vehicle wheels are inconvenient for changing broken wheels and have poor shock absorbing in driving, so they cannot be used to carry people on the moon. To meet the demands for manned lunar transportation, a new wheel possessing a woven metal wire mesh tire and using hub-rim combination slide mechanism is designed in this article. The characteristics of the new wheel is analyzed by comparing with the same-size conventional rover wheels after demonstrating the validity of FEM simulation. The new wheel possesses lighter structure and superior shock absorbing. It also provides stronger traction because the deformation of the designed wheel increases the contact area between the tire and lunar terrain. In order to establish an on-line soil parameter estimation algorithm for low cohesion soil, the stress distribution along a driven deformable wheel on off-road terrain is simplified. The basic mechanics equations of the interaction between the wheel and the lunar soil can be used for analytical analysis. Simulation results show that the soil estimation algorithm can accurately and efficiently identify key soil parameters for loose sand.     

Investigation of critical flaws in railway wheels

The fracture of tread-braked monobloc railway wheels is predominantly influenced by the magnitude of the tensile residual stresses in the rim of the wheel. As a consequence of the scatter in fracture toughness and magnitude of the residual stresses, different values of the critical flaw sizes are obtained. A simulation process is adopted which takes into consideration the probability distribution of the stresses and fracture toughness. The flaw size which guarantees a survival probability of 90 per cent will be chosen as the representative value of the minimum critical flaw size. A comparison is made with the critical sizes observed at service failures to illustrate the practical application of the probability distribution approach.