The effect of velocity on rigid wheel performance

A simulation model to predict the effect of velocity on rigid-wheel performance for off-road terrain was examined. The soil–wheel simulation model is based on determining the forces acting on a wheel in steady state conditions. The stress distribution at the interface was analyzed from the instantaneous equilibrium between wheel and soil elements. The soil was presented by its reaction to penetration and shear. The simulation model describes the effect of wheel velocity on the soil–wheel interaction performances such as: wheel sinkage, wheel slip, net tractive ratio, gross traction ratio, tractive efficiency and motion resistance ratio. Simulation results from several soil-wheel configurations corroborate that the effect of velocity should be considered. It was found that wheel performance such as net tractive ratio and tractive efficiency, increases with increasing velocity. Both, relative wheel sinkage and relative free rolling wheel force ratio, decrease as velocity increases. The suggested model improves the performance prediction of off-road operating vehicles and can be used for applications such as controlling and improving off-road vehicle performance.     

Prediction of tractive response for flexible wheels with application to planetary rovers

Planetary rovers are typically developed for high-risk missions. Locomotion requires traction to provide forward thrust on the ground. In soft soils, traction is limited by the mechanical properties of the soil, therefore lack of traction and wheel slippage cause difficulties during the operation of the rover. A possible solution to increase the traction force is to increase the size of the wheel-ground contact area. Flexible wheels provide this due to the deformation of the loaded wheel and hence this decreases the ground pressure on the soil surface. This study focuses on development of an analytical model which is an extension to the Bekker theory to predict the tractive performance for a metal flexible wheel by using the geometric model of the wheel in deformation. We demonstrate that the new analytical model closely matches experimental results. Hence this model can be used in the design of robust and optimal traction control algorithms for planetary rovers and for the design and the optimisation of flexible wheels.     

冲角工况下列车车轮损伤机理研究

曲线通过和蛇行运动时将会在轮轨间产生一定的冲角,为探究列车车轮在冲角工况下的损伤机理,利用JD-1轮轨模拟试验机对列车车轮进行滚动接触疲劳试验.结果表明:在冲角工况下车轮试件磨痕的不同区域存在不同的损伤机理,按损伤机理的不同可以将其分为塑性堆积区、疲劳损伤区和磨损区三个区域.在应力发生剧烈变化且应力方向由高应力区指向低应力区的区域将会出现材料的塑性堆积,并且在堆积处产生疲劳裂纹.滚动接触下的疲劳裂纹可以萌生于表面和亚表面,在较强应力作用下,车轮材料的晶粒发生了明显的细化,在横截面上呈现出纤维状组织.     

推广的奇轮的圆色数

图G的圆色数(又称"星色数")xc(G)是Vince在1988年提出的,它是图的色数 的自然推广.本文由奇轮出发构造了一族平面图,并证明了此类图的圆色数恰恰介于2和 3之间,填补了该领域的空白.     

Magnetic molecular wheels and grids - the need for novel concepts in “zero-dimensional” magnetism

Supramolecular chemistry has allowed the production, by self-assembly, of inorganic complexes with a [N × N] square matrix-like configuration of N² metal centers. Interest in these systems is driven by the potential applications in information technology suggested by such a “two-dimensional” (2D), addressable arrangement of metal ions. From the magnetic perspective [N × N] grids constitute molecular model systems for magnets with extended interactions on a square lattice, which have gained enormous attention in the context of high-temperature superconductors. Numerous [2 × 2] grids as well as a few [3 × 3] grids with magnetic metal ions such as Cu(II), Ni(II), Co(II), Fe(II), and Mn(II) have been created. Magnetic studies unraveled a remarkable variety in their magnetic properties, which will be reviewed in this work with emphasis on the underlying physical concepts. An intriguing issue is the connection of [2 × 2] and [3 × 3] grids with “one-dimensional” (1D) rings, as experimentally realized in the molecular wheels. For a [2 × 2] square of spin centers the distinction between a 2D grid and a 1D ring is semantic, but also a [3 × 3] grid retains 1D character: it is best viewed as an octanuclear ring with an additional ion “doped” into its center. Challenging familiar concepts from conventional magnets, the current picture of elementary excitations in antiferromagnetic rings will be discussed, as a prerequisite to understand the complex [3 × 3] grids.     

Turán numbers for odd wheels

The Turán number $\text{ex}(n,G)$ is the maximum number of edges in any $n$-vertex graph that does not contain a subgraph isomorphic to $G$. A wheel$W_n$ is a graph on $n$ vertices obtained from a $C_{n?1}$ by adding one vertex $w$ and making $w$ adjacent to all vertices of the $C_{n?1}$. We obtain two exact values for small wheels:

$\text{ex}(n,W_5)=?\frac{n^2}{4}+\frac{n}{2}?,$

$\text{ex}(n,W_7)=?\frac{n^2}{4}+\frac{n}{2}+1?.$

Given that $\text{ex}(n,W_6)$ is already known, this paper completes the spectrum for all wheels up to 7 vertices. In addition, we present the construction which gives us the lower bound $\text{ex}(n,W_{2k+1})>?\frac{n^2}{4}?+?\frac{n}{2}?$ in general case.     

A Dodecalanthanide Wheel Supported by p‐tert‐Butylsulfonylcalix[4]arene

A dodecaholmium wheel of [Ho₁₂(L)₆(mal)₄(AcO)₄(H₂O)₁₄] ( 1 ; mal=malonate) was synthesized by using p‐tert‐butylsulfonylcalix[4]arene (H₄L) as a cluster‐forming ligand. The wheel consists of three fragments of mononuclear A^3? ([Ho(L)(mal)(H₂O)]^3?), trinuclear B^3? ([Ho(H₂O)₂(mal)(Ho(L)(AcO))₂]^3?), and C³⁺ ([Ho(H₂O)₂]³⁺), and an alternate arrangement of these fragments (A^3?? C³⁺? B^3?? C³⁺? A^3?? C³⁺? B^3?? C³⁺? ) results in a wheel structure. The longest and shortest diameters of the core were estimated to be 17.7562(16) and 13.6810(13) Å, respectively, and the saddle‐shaped molecule possesses a pocketlike cavity inside.     

On product-cordial index sets and friendly index sets of 2-regular graphs and generalized wheels

A vertex labeling f : V → Z2 of a simple graph G = (V, E) induces two edge labelings f+ , f*: E → Z2 defined by f+ (uv) = f(u)+f(v) and f*(uv) = f(u)f(v). For each i∈Z2 , let vf(i) = |{v ∈ V : f(v) = i}|, e+f(i) = |{e ∈ E : f+(e) = i}| and e*f(i)=|{e∈E:f*(e)=i}|. We call f friendly if |vf(0)-vf(1)|≤ 1. The friendly index set and the product-cordial index set of G are defined as the sets{|e+f(0)-e+f(1)|:f is friendly} and {|e*f(0)-e*f(1)| : f is friendly}. In this paper we study and determine the connection between the friendly index sets and product-cordial index sets of 2-regular graphs and generalized wheel graphs.