Many solutions of beam impact problems have been derived on the basis of the elementary or Timoshenko beam equation. But in a majority of them impact loads are assumed and so the results are only qualitative. Here an infinite beam impacted by an elastic bar is treated without assuming the impact load. Making use of the elementary beam equation and supplying a new assumption of contact between beam and bar, the stresses in them can be analytically obtained. As one case, an analysis by the Timoshenko bending theory is also presented and it is shown that the rotatory inertia and shear deformation have no serious influence on the magnitude of impact stresses. Those theoretical results are compared with experimental ones and good agreement between them is recognized except in a short time range after the impact or at the wave front.

View full abstract

The angle φ between the center line of V-groove and the axis of a rod specimen was called the notch inclination angle, and the variations of notch strengths of mild steels with the variation of φ were studied at room temperature. In impact tensile experiment, the impact strength varied scarcely with φ when φ was near 90°, but it varied suddenly when φ was near φ_s+20°, where φ_s, is an angle corresponding to a shoulder fillet. In static tension experiment, although the notch strengthening appeared at breaking load, the relation between actual breaking stress and φ was similar to that of impact strength qualitatively. Yield strength decreased linearly with the increase of φ when φ was not so close to φ_s. The variation of the elongation percentage and of the contraction percentage of area corresponded to the variation of the impact strength and of the breaking stress, respectively.

View full abstract

The purpose of this investigation was to improve the rotating bending fatigue strength of press-fitted shaft assemblies by varying the geometry of press-fitted portion. Four groups of 50mm-diam. press-fitted specimens were used. As the result, comparing with the fatigue limit of press-fitted plain shaft, maximum increase of the fatigue limit was obtained for the filletted shaft, in which the press-fitted hub had a low protrusion on the face. Taking the reduction of fretting corrosion into consideration, however, the press-fitting of hub overhanging from the shoulder was most preferable with an increase of fatigue limit about 50%. The fatigue limit of the press-fitted plain shaft could be increased by 50% due to press-fitting of hub which had the low protrusion.

View full abstract

The collapse pressure for a pressure vessel which consists of a cylindrical shell, a toroidal shell and a rigid circular plate, is studied in this paper by means of the method of limit analysis. The results of analysis are summarized in a diagram and an approximate design formula. In order to study the practical significance of the theoretical collapse pressure of a pressure vessel, experiments are carried out, and it is found that agrecment exists between the theoretical and the experimental results. Furthermore the obtained theoretical results are compared with those of elastic analysis which was made by one of the authors and other, and almost same tendencies are found in both analysis.

View full abstract

High-temperature vacuum tensile-fatigue tests of α phase Cu-Al alloys with 2% Al, 5% Al and 7% Al were made at room temperature ∼500°C in vacuum (pressure 10^-5 mmHg). And from their results and results of previous papers [Jour. Japan Soc. Test Mat., Vol. 15 (1966), p. 68 ; Jour. Japan Inst. Metals, Vol. 30 (1966), p. 335 ; Memo. Defense Acad., Vol. 6 (1966), p. 145], Al content and temperature dependences of high-temperature vacuum tensile-fatigue in α phase Cu-Al alloys are studied. Obtained results are as follows : (1) The experimental fatigue formula is expressed by log_eN-log_eN_o=-B [log_ew-log_eW], N_o=α⁺c+β⁺and B=α'c+β', α⁺=0.11+10³[c wt%^-1], β⁺=1.5×10³[c], α'=-0.221[wt%^-1] and β'=10, where N is the number of load cycles to cause the failure, w cyclic load, W tensile strength and c Al content (wt%). (2) The tensile strength W is expressed by W=W_oexpA [T-T_o]², W_o=αc+β, A=αc+β and T_o=α^*c, and α=3.00 [kg wt%^-1], β=19.0 [kg], α=0.74×10^-6 [^oK^-2 wt%^-1], β=2.2×10^-6 [^oK^-2] and α^*=40[deg wt%<-1>], where T is the testing temperature.

View full abstract

Tensile-fatigue and tensile tests of drawn tungsten wire (diameter 0.30 mm : JIS-H4461. VWW1-D) at very high temperature (800-2700°C) in vacuum (pressure 10^-5 mmHg) were made using a very high temperature vacuum tensile-fatigue tester of electrical current transite heating type [J. JSMS, Vol. 16 (1967), P. 89]. And temperature-dependences of fatigue and tensile strengths were studied. The main results obtained are as follows : (1) According to the increase of testing temperature, the tendency of necking in the specimen becomes weak and the deformed range increases. (2) Relation between testing temperature T and tensile strength σ_o to cause the fracture is expressed by log₁₀ [σ_o (kg/mm²)]=AT+B, A=-6.7×10^-3oK and B=2.40. (3) Relation among testing temperature T, cyclic stress σ and the number N of stress cycles to cause the failure is expressed by log₁₀N=αT+βlog₁₀[σ (kg/mm²)]+γ, α=-3.56×10^-3oK, β=-3.4×10^-3, and γ=1.45.

View full abstract

Surface strain distributions of rubber cylinders with various shape factors and fillet radii are measured and the relation between these distributions and fatigue rupture is considered. The obtained results are as follows : (1) In the axial strain distribution of the filletted specimen, there exist strain regions of tension and compression and also the strain concentration in both fillets. (2) The maximum surface strain is greater for smaller fillet radius and for larger shape factor but the position of concentration is scarcely influenced by the shape of specimen. (3) In the case of compressive shear, the tensile strain region decreases with the increase of compression and finally wrinkles appear on the compressive side of fillet. (4) The fatigue characteristics of rubber is explained qualitatively by so-called maximum shearing strain theory.

View full abstract

A theory of lifting-lines for a cascade of blades in subsonic shear flow is developed by assuming that the dependence of the local lift force upon the local upstream Mach number in a shear flow is same as that in two-dimensional flow. By comparing numerical examples with experimental results, the physical validity and the limit of applicability of the present theory are discussed. The effect of compressibility upon the mean characteristics of a cascade in shear flow depends upon the root of harmonic mean square of the upstream Mach number (M^*_<-∞>). Experimental correlation is not disappointing, as far as M^*_<-∞> lies within the limit beyond which the small disturbance theory for two-dimensional flow through cascade shows poor validity. Significance of M^*_<-∞> as a criterion for the mean characteristics was also confirmed experimentally.

View full abstract

Recently the mass ratio and natural frequency of the blade in cascade of turbo-jet engin became so small that we made the theoretical and experimental investigation of the flutter problem of cascade by treating it as the oscillation system with two degrees of freedom, and derived many interesting results about the effects of cascade condition on the critical flutter speed and flutter mode. In this 2nd report, using the computational results of the aerodynamic derivatives already shown in the 1st report, the effects of cascade stagger angle, solidity, attack angle (or steady circulation), mass ratio of blade, the ratio of natural frequency of flexural and torsional vibration and position of elastic axis on the critical flutter speed and flutter mode are clarified in the case of cascade with flat plates. And also the effects of camber of blade (or distribution of steady vorticity) and the direction of flexural oscillation on critical flutter speed are shown in a special case.

View full abstract

This paper describes a method of analysis of waterhammer in a pump system including pipelines, bifurcations, surge tanks, reservoirs and pumping stations, where pumps installed in series are operated in parallel. Hydraulic losses are included in the analysis. The analysis is carried out by solving the fundamental equations under boundary conditions by a digital computer. The computer program is composed of several subprograms, by which hydraulic transients in each element of the pump system are computed. Two examples are calculated. One is the waterhammer at a pump installation, where three pumps are operated in parallel and five one-way surge tanks are installed along a discharge line. Computed results are compared with measurements. Another example deals with a pump system, where four main and booster pump sets installed in series are operated in parallel. The water-hammer after power failure in some of pump sets is calculated.

View full abstract

Suction performance of centrifugal pumps can in general be improved by the introduction of an inducer ahead of the main impeller. An inducer is substantially an axial-flow impeller having very steep head-capacity curve and low head coefficient characteristics near normal flow. An ordinary inducer may exert adverse effects on the pump due to the above characteristics. An inducer of special design was investigated with a view to overcoming faults encountered in an ordinary inducer by making full use of characteristics inherent in the axial-flow impeller in low flow range. With the new type of inducer and the addition of an orifice plate placed ahead of it, the values of NPSH at cavitation breakdown points decreased with decreasing flow rates and suction specific speed values of 7000 to 9000 (m³/min, m, rpm) were obtained at low flow rates.

View full abstract

A theoretical study on laminar heat transfer from a disk rotating in uniform forced stream was carried out for the fluid of any Prandtl number in the case when the surface temperature difference is expressed by the quadratic relation : t_ω-t_∞=a_o+a₂r². The results are summarized as follows. (1) The asymptotic solutions for P_r→o and P_r→∞ have an appropriate accuracy in P_r<0.01 and P_r>100. (2) The effect of radial heat conduction in a fluid of low Prandtl number was analized in the case of pure quadratic disk temperature, i.e. t_ω-t_∞=a₂r² and a criterion that the effects of radial heat conduction on the heat transfer coefficient reach 5% was established. According to this criterion, when the ratio of axial stream velocity to rotating velocity of a disk is larger than 0.25, the effect of radial heat conduction in P_r=0.01 may be negligible, even if the rotating Reynolds number decreases to the order of R_ewr=r²ω/ν&cong;10³.

View full abstract

A new method is proposed in this paper for the calculation of temperature distributions of radiant gas which is bounded by two parallel surfaces and has a heat source. Some papers have been published on the calculating method in the case of gray gas with a uniform partial pressure and a uniform heat source. The author tried to calculate the temperature distribution in the case where the absorption coefficient of gas was affected by temperature. This method is also applicable to the case of nonuniform partial pressure and nonuniform heat source. The calculation was conducted by the Monte Carlo method and programmed for electronic digital computation. All examples in this paper were calculated by computer and an increasingly flattened temperature distribution was obtained for the gas in which the absorption coefficient was affected by temperature K (T_g)=KT_m/T_g as compared with that of the gray gas.

View full abstract

The void fraction and the frictional pressure drop were measured for slug and annular twophase upward flow in vertical tubes. On the basis of the experimental results and the assumption of an annular flow model, some predictions are presented for the shear stress at the interface of the gas and liquid phases and for the flow state of the liquid film. The shear stress at the interface, which is affected by both flow states of the gas and liquid, may be expressed as follows : τ_i=(ζ/4) (ρ_gu_s²/2) where ρ_g is the density of the gas and u_s is the slip velocity. The value of the coefficient ζ, defined as above, is calculated from the experimental results and correlated with non-dimensional variables. For the liquid film an equation relating the liquid flow rate and the film thickness is derived from the shear stress distribution in the film by assuming that the film consists of two layers, a laminar sublayer and a turbulent layer. By applying the experimental results to this equation, the eddy diffusivity in the turbulent layer and the velocity distribution in the liquid film are calculated.

View full abstract

This paper describes the derivation of an expression for predicting the frictional pressure drop of steady-state upward two-phase flow based on an annular flow model. The procedure followed is to express the shear stress at the tube wall as a function of the liquid velocity u_δ at the edge of the laminar sublayer and the void fraction α. The effect of the flow characteristics on u_δ is introduced by defining an equivalent mean velocity of the liquid phase u_m^*. The appropriate relation between u_δ and u_m^* is determined from the experimental data in the prior report. As an extension of this analysis, a prediction is also presented for the frictional pressure drop of bubble flow. In addition, the void fraction α is derived from an empirical expression for the mean velocity of the gas phase.

View full abstract

Experimental results of the average heat transfer coefficient are presented for two-component two-phase upward flow in a vertical tube, over a range of values of the liquid flow rate, void fraction and liquid Prandtl number. An empirical equation describing these results is developed. This relation expresses the average Nusselt number as a function of the Prandtl number of the liquid phase and a Reynolds number based on the equivalent mean velocity of the liquid phase (defined in the 2nd report). A theoretical prediction of the heat transfer coefficient is also presented. This is based on assuming the eddy diffusivity for momentum in the liquid film to be equal to that for heat. The results are in good agreement with the experimental data. A discussion of the liquid film resistance to heat transfer is also included for annular flow of single-component two-phase flow.

View full abstract

Spatial four-bar mechanisms are studied with the purpose of utilizing them as generators of functions with one variable. In Part I, the moving closed circuits are first described in connection with the degrees of freedom of spatial mechanisms, and then a number synthesis is made to result in 95 kinds of mechanisms having a single degree of freedom between the driving and driven links. Among them are included many mechanisms whose total number of degrees of freedom is not one. The mechanisms are limited to ones composed of practical pairs, i.e., revolute, prismatic, cylindric, spheric and sphere-groove pairs. A dimensional synthesis is also made with three precision points for a mechanism with two revolute pairs, one cylindric pair and one spheric pair. The equations of the synthesis are given in the form convenient for programming of electronic digital computers.

View full abstract

In Part II, are developed the methods of dimensional synthesis of two spatial four-bar mechanisms, A₁·2·1 mechanism having two revolute and two spheric pairs and A₁·2·2 mechanism having one revolute, one prismatic and two spheric pairs : eight-precision-point synthesis of A₁·2·1 mechanism and four- and six-precision-point syntheses of A₁·2·2 mechanism are introduced. The conditions that both mechanisms are symmetrical are considered and the syntheses to generate symmetrical functions are also introduced : the functions generated by A₁·2·1 and A₁·2·2 mechanisms may coincide with the ideal functions at ten and eight points respectively. Examples of the syntheses are presented, which show that both mechanisms may generate much more precise functions than planar four-or six-bar mechanisms do.

View full abstract

K. Brunell has disussed the basic properties and the design characteristics of the constant diameter cam, especially of the cam whose base curve is given as cycloidal displacement function. However it seems that his discussion is questionable in some points, so in this paper, correcting or supplementing his paper, the properties and the design characteristics of the constant diameter cam will be made clear. Let lift h, dwell angle β and cam base curve ν (θ) : 0&gne;θ&gne;β for follower's rise motion be given, then the cam base curve is given by [numerical formula] Let g be radius of the cam base circle, then the governing criterion is to be such a g that satisfies the following conditions for each θ such that 0&gne;θ&gne;β. g+v (θ)+v" (θ)>0, g+h-v (θ)-v" (θ)>0. If the condition v (θ)+v (β-θ)=h : 0&gne;θ&gne;β holds, the governing criterion becomes g+v (θ)+v" (θ)>0 : 0&gne;θ&gne;β. Moreover we studied the constant diameter cam with cycloidal motion follower and we could express its governing criterion graphically.

View full abstract

There have been presented various boundary conditions for the trailing edge of the lubricant film of journal bearing in the hydrodynamic lubrication theory. They are, however, not so clearly investigated physically in connection with the lubricant film rupture. In this paper, eccentricity ratio and attitude angle are measured, and, at the same time, the generation and growth of the lubricant film rupture are observed by using a transparent journal bearing bushing. The results are investigated with theoretical solutions under various boundary conditions. The shaft center is found to travel along Sommerfeld's theoretical locus in the case of a continuous lubricant film. Then, with occurrence of the lubricant film rupture, the shaft jumps rapidly to the theoretical locus defined with Reynolds' or Gumbel's boundary condition. The theoretical pressure distribution shows that the pressure becomes almost atmospheric in the discontinuous film region. From these results, the conditions of the lubricant film rupture are investigated theoretically.

View full abstract

Das Zahnspiel der Zahnrader spielt eine Rolle auf Schwingung und Gerausch der Zahnrader. Wenn die Betrage des Verzahnungsfehlers und der erzwungenen Kraft im Vergleich mit der Ubertragungsbelastung der Zahnrader groB sind, tritt sog. ZahnstoBerscheinung auf, da der intermittierende Eingriff vorkommt. Infolgedessen wachsen die dynamische Zusatzkraft und das Gerausch sehr an. In dieser Untersuchung werden zuerst der Einflankenwalzfehler, die Eigenfrequenz und die Federkonstante des Zahns gemessen, dann mittels Analog-Rechners wurde die Rechnung vom Schwingungssystem des Versuchsgetriebs durchgefuhrt, das durch einfaches Schwingungs system ersetzt wurde. Die Rechnungsergebnisse wurden im Vergleich mit dem Messungswert dynamischer Zusatzkraft im Betrieb geurteilt. Aus diesen Untersuchungen konnen folgende SchluBfolgerungen gezogen werden. 1) Das Gerausch und die dynamische Zusatzkraft nehmen an der Resonanzfrequenz bemerklich zu. 2) Die Resonanzfrequenz verandert sich durch Verzahungsfehler und statische Belastungen. AuBerdem gibt es die hysteretische Erscheinung im Verlauf der dynamischen Zusatzkrafte auf Drehzahl des Ritzels und wurde die Entstehung der harmonischen Schwingung auch im Versuch gefunden.

View full abstract