Three-dimensional photoelastic study of the load-carrying capacity/face width ratio of Wildhaber-Novikov gears for automotive applications

Wildhaber-Novikov gears are becoming more and more popular for heavy load applications. They have been tried as speed-reducing gears, in spite of heavy noise generation, in aircraft jet engines, marine engines and agricultural machinery. These circular-arc gears, though stronger than involute geras, have the disadvantage of needing larger face width. Axial face width required can be minimized only at the expense of load-carrying capacity. This is not a serious disadvantage with stationary engines. But in the case of automotive applications, this fact limits the load-carrying capacity of Wildhaber-Novikov gears, since space problem is very critical in these applications and large face widths, therefore, cannot be used for such gear-reduction units. The face width is determined by the helix angle and, therefore, a thorough investigation of the dependence of the load-carrying capacity on helix angle is necessary, if these special types of gears have to make headway into the automotive field. In this experimental investigation, three-dimensional photoelastic technique has been employed to study the load-carrying capacity/face width ratio. Three-dimensional gear models made of epoxy castings (Araldite B) were loaded in a specially built gear-loading fixture and were stress frozen. Gear cutters of Wildhaber-Novikov gears developed at the laboratory were used for the preparation of these three-dimensional gear models. The stress-frozen models were analyzed using the conventional slicing technique to study the contact and bending-stress distribution along the face width. The load-carrying capacity in terms of contact stress and bending stress has been studied for different face widths and helix angles. Twenty-deg pressure angle, 14-mm module gears of alladdendum type of Wildhaber-Novikov gears with different helix angles up to 40 deg were tested. The helical-overlap ratio used was 1.0. The conventional profile parameters were employed for the manufacture of gear cutters of end-mill type. The decrease in contact and bending strength with increase in the helix angle or decrease in the face width, as obtained from this photoelastic method of stress analysis has been compared with existing theoretical results.     

Bending of a uniformly loaded clamped sector plate

The paper involves the expansion of the biharmonic deflection function in a series of non-orthogonal functions satisfying the condition of clamped edges. Each of these non-orthogonal functions is expanded in a series of orthogonal functions which satisfy a certain fourth order differential equation and the boundary conditions implied by the fact that the edges are clamped. This reduces the bending of a uniformly loaded clamped sector plate to the solution of a linear algebraic system of equations. Numerical results for the deflection of the central line are obtained when the semi-sector angle is 15 degrees.     

Luminescent ruthenium tripod complexes: properties in solution and on conductive surfaces

Two luminescent ruthenium complexes containing tripod-type end groups linked through a rigid spacer to a phenanthroline derivative, able to confer an axial geometry to the complexes, are described. One of the compounds is functionalized with thioacetate groups in order to link the metal complex to metallic surfaces. The photophysical and electrochemical behavior of the complexes are studied in solution and on conductive substrates and, furthermore, self-assembled monolayers are investigated in a junction using gold and an indium gallium eutectic, as electrodes, and by time-resolved confocal microscopy. The results show that the complexes form very stable and well-ordered monolayers because of the tripod system, which can anchor the complex almost perpendicular to the surfaces.     

Atomistic simulation of lipid and DiI dynamics in membrane bilayers under tension

Membrane tension modulates cellular processes by initiating changes in the dynamics of its molecular constituents. To quantify the precise relationship between tension, structural properties of the membrane, and the dynamics of lipids and a lipophilic reporter dye, we performed atomistic molecular dynamics (MD) simulations of DiI-labeled dipalmitoylphosphatidylcholine (DPPC) lipid bilayers under physiological lateral tensions ranging from -2.6 mN m(-1) to 15.9 mN m(-1). Simulations showed that the bilayer thickness decreased linearly with tension consistent with volume-incompressibility, and this thinning was facilitated by a significant increase in acyl chain interdigitation at the bilayer midplane and spreading of the acyl chains. Tension caused a significant drop in the bilayer's peak electrostatic potential, which correlated with the strong reordering of water and lipid dipoles. For the low tension regime, the DPPC lateral diffusion coefficient increased with increasing tension in accordance with free-area theory. For larger tensions, free area theory broke down due to tension-induced changes in molecular shape and friction. Simulated DiI rotational and lateral diffusion coefficients were lower than those of DPPC but increased with tension in a manner similar to DPPC. Direct correlation of membrane order and viscosity near the DiI chromophore, which was just under the DPPC headgroup, indicated that measured DiI fluorescence lifetime, which is reported to decrease with decreasing lipid order, is likely to be a good reporter of tension-induced decreases in lipid headgroup viscosity. Together, these results offer new molecular-level insights into membrane tension-related mechanotransduction and into the utility of DiI in characterizing tension-induced changes in lipid packing.     

On the zeros ofζ (1)(s) — a (on the zeros of a class of a generalized Dirichlet series — XVII)

Some very precise results (see Theorems 4 and 5) are proved about thea-values of thelth derivative of a class of generalized Dirichlet series, forl≥l _o =l _o(a) (l _o being a large constant). In particular for the precise results on the zeros ofζ ⁽¹⁾ (s) —a (a any complex constant andl≥l _o) see Theorems 1 and 2 of the introduction.     

Time-dependent flows of rotating and stratified fluids in geometries with non-uniform cross-sections

Unsteady rotating and stratified flows in geometries with non-uniform cross-sections are investigated under Oseen approximation using Laplace transform technique. The solutions are obtained in closed form and they reveal that the flow remains oscillatory even after infinitely large time. The existence of inertial waves propagating in both positive and negative directions of the flow is observed. When the Rossby or Froude number is close to a certain infinite set of critical values the blocking and back flow occur and the flow pattern becomes more and more complicated with increasing number of stagnant zones when each critical value is crossed. The analogy that is observed in the solutions for rotating and stratified flows is also discussed.     

Isotopic sum rules and compliance scheme

It is known that compliance scheme does not provide simple linear isotopic sum rules in λ^?1 similar to the ones in λ in the force constant scheme. The advantage of not having such sum rules in the compliance scheme is discussed in relation to the uniqueness problem of the molecular force field.Incidentally, for the molecules H₂O, D₂O, and HDO, two quadratic relations in terms of the inverse frequency parameters λ^?1 are obtained. These supplement the three obvious product rule relations.     

Uniqueness of methyl fluoride force field

The uniqueness of the general harmonic force field of methyl fluoride is analyzed. The analysis is applicable to other methyl halides as well. Through the compliance scheme, it is seen that by supplementing the data employed by Aldous and Mills (i.e., vibrational frequencies ω_i, Coriolis coupling constants ζ_i and the centrifugal stretching constants D_J, D_JK of CH₃F and CD₃F molecules), with the frequencies of A′ or A″ species of either CH₂DF or CD₂HF, the force field is uniquely determined. The addition of any other extra data including the ¹²CH₃F¹³CH₃F isotopic shifts only makes the determination of the force field parameters more precise.