Analysis of step bearings with a micropolar lubricant

Squeeze film step bearings lubricated with a micropolar fluid were analysed. It was found that the load capacities increase as the micropolar parameter $\text{}\text{?}\text{gm}{}_1$ increases or as $\text{M =}\text{h}{}^2\text{μ}\text{4γ}$ decreases. The load capacity also decreases as the step height increases.     

Hydrodynamic drag versus roughness for rotating disks

Stylus measurements of the microroughness of rotating disks and their significant correlation with hydrodynamic drag measurements were studied. The roughest disks (R_a ≈ 16 μm) were found to have drag coefficients about 30% greater than those of the smoothest disks (R_a ≈ 0.14 μm). For a Reynolds' number of 1.5 × 10⁶, the following empirical relationship between the drag coefficient C, the average roughness R_a and a parameter designated the peak count wavelength λ_pc was obtained:

$\text{C=}\text{bR}{}_{\mathrm{a}}\text{λ}{}_{\mathrm{pc}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{+ C}{}_{\mathrm{o}}$

where .Other surface parameters and functions were measured in addition to R_a and λ_pc; however, it seems that knowledge of an amplitude-sensitive parameter and a wavelength-sensitive parameter is adequate for characterizing increases in the drag of rotating disks due to surface roughness. R_a is the preferred amplitude-sensitive parameter because it is the most widely used. We propose λ_pc as the wavelength parameter because it is sensitive to the larger profile features rather than to the fine structure.However, there is a need for all workers in the field to standardize on measuring the same parameters so that the results of one group can be easily related to the work of other groups.     

Lubrication of orifice-compensated flexible thrust pad bearings

The effects of the interaction between the restrictor design parameter ($\text{C}{}_{\mathrm{S2}}$), the deformation coefficient ($\text{C}{}_{\mathrm{d}}$) and the Poissons ratio (ν), on the performance characteristics of an orifice-compensated hydrostatic circular thrust pad bearing have been studied. The results are presented for various values of $\text{C}{}_{\mathrm{S2}}\text{,}\text{C}{}_{\mathrm{d}}\text{,}\text{and}\text{ν}$ and are compared with those of capillary-compensated bearings     

The effect of variable permeability on the performance characteristics of porous bearing

An analytical solution for the performance characteristics of a short bearing having an axial and radial permeability of $\text{k}{}_{\mathrm{z}}\text{[1 + cos(}\text{πz}\text{L}\text{)]}$ and $\text{k}{}_{\mathrm{z}}\text{[1 + (}\text{2}\text{π}\text{)]}$, respectively, is obtained. Results are presented which relate the eccentricity ratio and coefficient of friction as functions of load number for various design variables. These results are compared to the results obtained for an isotropic bearing having a permeability of $\text{k}{}_{\mathrm{z}}\text{[1 + (}\text{2}\text{π}\text{)]}$.     

A theory of plastic anisotropy based on a yield function of fourth order (plane stress state)—I

It is shown from various view points that many of the disadvantages of the conventional theory based on a quadratic yield function can be satisfactorily removed by the use of a yield function of fourth order. Incremental equivalent strain $\text{d}\text{?}{}_{\mathrm{eq}}$is defined by $\text{d}\text{?}{}_{\mathrm{eq}}\text{=σ}{}_{\mathrm{ij}}\text{d}\text{?}{}_{\mathrm{ij}}\text{σ}{}_{\mathrm{eq}}$, and cannot generally be expressed simply by the strain increment components d?_ij. In contrast with the conventional theory, coefficients in the yield function f cannot be determined from the r-values only in uniaxial tensile tests, but yield stresses in these tests and for example in an equi-biaxial tension for the same $\text{}\text{?}\text{ge}{}_{\mathrm{eq}}$ are also required. This fact ensures that the $\text{σ}{}_{\mathrm{eq}}\text{?}\text{?}{}_{\mathrm{eq}}$ curve for arbitrary loading is uniquely determined by the uniaxial tension curve in the rolling direction (R.D.), and thus such an intrinsic difficulty of the conventional theory as dependence of the $\text{σ}{}_{\mathrm{eq}}\text{?}\text{?}{}_{\mathrm{eq}}$ curve on types of loading does not arise. Some formulae for the determination of the coefficients in f are given. Relationships between types of earing in axi-symmetrical deep-drawing and the coefficients of f are examined in detail and it is emphasized that only very special cases are included in the conventional yield function and thus use of it is very limited.     

On the dual spherical motions—ISur les mouvements spheriques duaux (lére partie)

In this paper it is shown that if the axes of curvature of the ruled surfaces $\text{U}{}_1\text{(t)}$ in the moving and fixed spaces intersect each other perpendicularly then the dralls (or distribution parameter) of the ruled surfaces, which are generated by the geodesic trihedron U₁, U₂, U₃s of a dual curve $\text{U}{}_1\text{(t)}$, satify the A. Mannheim and R. Hamilton's formulae. Furthermore, the “explicit characterization” of the spherical curve of striction is given in terms of U₃-surface and the skewness of distribution of the generator of U₁-surface.     

The effect of rotational inertia on the squeeze film load between porous annular curved plates

The squeeze film behaviour between rotating annular plates was analysed theoretically for the case when the curved upper plate with a uniform porous facing approached normally the impermeable flat lower plate. Expressions for the pressure and the load capacity were obtained. The load capacity decreased when the speed of rotation of the upper disc increased up to a certain value $\text{B}\text{?}{}_0$ of the curvature parameter $\text{B}\text{?}$. This trend was reversed for $\text{B}\text{?}\text{?}\text{B}\text{?}{}_0$. The load capacity could be increased without altering the speed of rotation by increasing $\text{B}\text{?}$.     

Determination of an improved gear surface of helical gears for pumping actionZur synthese optimaler maschinenelemente — optimale zahnflächen für schraubenpumpen

An improved gear surface of helical gears for pumping action is obtained mainly by theoretical investigation, and partly by test results. This is a further study following the research on gears[1]. A new theory is presented here by selecting characteristic function sequences

$\text{s = Φ}{}_{\mathrm{n}}\text{(t) = 1 ? (1?t)}{}^{\mathrm{n}}\text{, n = 1, 2, 3, … n}{}_0$

which is monotone increasing. The larger n becomes, the larger rate of mass flow $\text{V}\text{and effective work ratio}\text{=}\text{E.W.R.}\text{=}\text{E}$ increases at the same time, thus the optimum tooth profile of gears (consequently the optimal gear surface) can be determined under the assumption that the minimum available cutting pressure angle (θ_ON_O be given in advance.     

Zur geometrie der Joukowsky-transformation und über die kinematische erzeugung von tragflügelprofilenOn the geometry of Joukowski transformation and the kinematical generation of wing profiles

In its first part the paper considers, from an advanced point of view, the essential properties of Joukowski's conformal mapping $\text{J: z}{}^1\text{= z+z?}{}^1$. In general, the point $\text{Z}{}^1\text{(z}{}^1\text{=x}{}^1\text{+iy}{}^1\text{)}$ corresponding to a real point Z (z=x+iy) is uniquely determined, with the exception of the fundamental points situated at the origin O and the circular points $\text{I,}\text{I}$ (Fig. 1). Conversely, a real point $\text{Z}{}^1$ arises from two real points Z, Z′ and two conjugate imaginary points Z″, Z3? are related by the involutary Moebius transformation V: z.z′ = 1.The circle k (1.8), determined by its complex center coordinate M≠0 and radius r≠|m|, is carried by the cubic transformation J into a rational bicircular quartic $\text{K}{}^1$ (1.10), but the same curve is also the mapping of a second circle k′ (1.11), connected with k by V (Fig. 4). The singular foci $\text{M}{}^1$ and $\text{N}{}^1$ correspond to the centers M and N of k and k′. The proper point-pair D, D′ common to k and k′ is mapped onto the proper double point $\text{D}{}^1$ of $\text{k}{}^1$.The second part deals with the kinematic generation, at first by means of an antiparallelogram, of such a quartic $\text{k}{}^1$, determined by $\text{M}{}^1\text{, N}{}^1\text{, D}{}^1$ and an arbitrary simple point $\text{Z}{}^1$. The foci $\text{M}{}^1\text{, N}{}^1$ are the fixed pivots of the four-bar linkage $\text{M}{}^1\text{A}{}_1\text{A}{}_2\text{N}{}^1$, and the position $\text{A}{}_1\text{A}{}_2\text{Z}{}^1$ of the coupler triangle is to be found as the mirror image of the triangle $\text{N}{}^1\text{M}{}^1\text{D}{}^1$ with respect to the perpendicular bisector of $\text{D}{}^1\text{Z}{}^1$ (Figs. 5 and 6). According to the theorem of Roberts, there exist two additional kite linkages generating the same quartic $\text{k}{}^1$. The third fixed pivot $\text{L}{}^1$ corresponds to $\text{D}{}^1$ in the reflection $\text{M}{}^1\text{? N}{}^1$ (Fig. 6).The essential dimensions of all generating linkages are given by formulae (2.2–2.7).     

The high speed size effect in grinding: The role of heat generation

Experimental data on the depth dependence of the specific energy of grinding and of single-point scratching does not agree with the predictions of the ploughing model. In this paper the model is extended to take into account the heat generated beneath the scratching point, the subsequent softening of the material and the influence on the specific energy e and the scratch hardness H_s. For pyramidal points $\text{e = H}{}_{\mathrm{s}}\text{∝ d}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{v}{}_{\mathrm{s}}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$; for spheres $\text{e ∝ d}{}^{\mathrm{<mtext>?</mtext><mtext>3</mtext><mtext>4</mtext>}}\text{v}{}_{\mathrm{s}}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$, whereas H_s shows a different behaviour which depends on the choice of parameters. The dependence on depth d and speed v_s agrees with experimental data on the grinding and scratching of steel.     

A vectorial method using combination theory in the term 2Wi × Vrel to calculate the acceleration of a point in the space kinematics of rigid bodies

This study to calculate the acceleration of a point using combination theory for compound accelerations constitutes a new interpretation of the general relative acceleration equation. The advantages of this new approach are the easy tabulation and the simple order of the solution and the preservation of the physical concepts. Also, the student has the opportunity to distinguish between $\text{2w}{}_{\mathrm{i}}\text{× V}{}_{\mathrm{<mtext>rel</mtext>}}\text{and}\text{2W × V}{}_{\mathrm{P/M}}$, the Coriolis acceleration. This distinction is useful in avoiding an erroneous physical interpretation.     

The graph method of determining the loads in complex gear trains

It is shown in the paper that the power which is transmitted by the respective links of a multiple-path gear train may be easily identified by setting up a graph of the gear train $\text{G}{}_1\text{(ω)}$ for a set of variable angular velocities ω, as well as the mutually conjugate graph, $\text{G}{}_2\text{(M)}$, for a set of torque loads on the respective links. This new method, which is called the graph method, utilizes the principles of signal flow graphs. It is characterized by a good efficiency for determining the power transmitted by any link within the gear train. Moreover, this method makes it possible to determine the value and direction of the circulating power stream flowing through the single or multiplepath closed kinematic chains of a multiple path gear train.     

Box beams subject to torsion

Stress analysis is carried out for the case where a cantilever box beam is subjected to distributed torque and concentrated torque at the tip. Direct stress $\text{σ}{}_{\mathrm{x}}$ acting in a cover plate is assumed to be in the form of $\text{∑}\text{n}\text{σ}{}_{\mathrm{n}}\text{(x)y}{}^{\mathrm{n}}$ where $\text{n}$ is an odd integer and the fundamental equation governing a box beam is introduced, using variational method. The accuracy can be investigated by comparing the values of strain energy by each obtained solution. Since this calculation is very complicated, strain energy formula is simplified by the new device. From the results of theoretical analysis, it became evident that, for the case where approximation improves, there is no necessity for the empirical formula proposed by Kuhn to be used, and that the range affected by the clamped end is about within the breadth of a box beam from the clamped end.     

Modelling of Coulomb damping and wear of vibrating systems

Coulomb damping is often relied upon to control the response of nuclear boiler tube banks acted upon by fluctuating eddy forces from turbulent coolant flow. The required energy dissipation is affected by relative sliding movements between the clamped joints of the tube and support structure. These movements Z are in general related to the centre span deflection y which is coupled to the exciting forces by the relation

$\text{Z=}\text{∑}\text{n=1}\text{∞}\text{α}{}_{\mathrm{n}}\text{y}{}^{\mathrm{n}}$

where the α_n are termed coupling coefficients. Specific models of the damping are developed for direct Coulomb damping (n = 1) and second-order damping (n = 2) under conditions where a constant friction force, i.e. static loading, is assumed to act. The effects of partial slip across the joint are examined, and this gives rise to a damping contribution at amplitudes that lie below the threshold y_p for gross slip at the joint. In general direct Coulomb damping gives rise to a non-linear type of damping and also changes natural frequency with amplitude. Second-order damping tends asymptotically to a constant loss factor $\text{1}\text{Q}{}_{\mathrm{r}}$ at large amplitudes but in general would be comparable with the hysteretic damping.The penalty from frictional damping is the occurrence of an associated wear rate which can be expressed by

$\text{dW}\text{dt}\text{=}\text{k}\text{μ}\text{dξ}{}_{\mathrm{D}}\text{dt}$

where K is the specific wear rate, ξ_D is the energy dissipated as wear and μ the friction coefficient. Since K and μ are defined by environmental and material properties compatible with nuclear environments, the design should be optimized to minimize the energy dissipation.     

Surface roughness and deformation of contact asperities between a rough and a flat surface

Conical asperity models with four kinds of apex angle and sandblasted surfaces were separately deformed by being pressed against a relatively hard flat surface. The real area of contact for the work hardened asperity models increased with decreasing apex angle and that for the sandblasted surfaces also increased with increasing surface roughness. The number of contact points and the separation between a sandblasted and a harder flat surface over the pressure range $\text{8.2 × 10}{}^{\mathrm{?3}}\text{≦}\text{W}\text{L}{}_{\mathrm{x}}\text{L}{}_{\mathrm{y}}\text{p}{}_{\mathrm{m}}\text{≦ 4.4 × 10}{}^{\mathrm{?2}}$ were also measured for comparison with the theoretical results. The experimental results for the sandblasted surfaces agreed with the theory. It is concluded that the real area, the number of contact points and the separation are influenced by the roughness of the softer surface.     

Elastohydrodynamic films in mixed lubrication: An experimental investigation

Experimental investigations were carried out with a Roxana rolling four-ball tester in the mixed lubrication regime. The electrical resistance technique was used in conjunction with ball profiles taken with a stylus apparatus to gain information about the formation of elastohydrodynamic films between rough surfaces and their evolution during running-in. The results show that rough surfaces in general make thinner films than smooth ones, but if $\text{h}{}_0\text{σ}{}_{\mathrm{h}}\text{> 2}$ roughness has a negligible effect.     

A surface roughness parameter in Hertz contact

The influence of surface roughness on the accuracy with which the Hertz theory of elastic contact predicts the contact pressure and contact area between a sphere and a plane is examined theoretically and experimentally. Statistical theories of surface contact suggest that the influence of surface roughness is governed primarily by a single non-dimensional parameter α defined by $\text{α }\text{σR}\text{a}{}_0{}^2$ where σ is the combined roughness of the two surfaces, R is the radius of the sphere and a₀ is the contact radius for smooth surfaces given by the Hertz theory. Experimental measurements of contact area correlate well with this parameter. Provided that the value of α is less than about 0.05, errors in the application of the Hertz theory due to roughness of the surfaces are not likely to exceed about 7%.