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Yoshikazu SAWARAGI, Taketoshi MATSUDA, Kiyoshi SUGAWARA
1951 Volume 17 Issue 64 Pages
1-5
Published: December 20, 1951
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In this paper the forced vibrations of a system with the restoring force which is expressed as a function of displacement and time is treated theoretically and experimentally. The equation of motion of a single-degree-of-freedom system is expressed as follows : [numerical formula], where m is mass, x is displacement, t is time, c is viscous damping coefficient, A
1, E
1, B
1 are characteristic coefficients of the restoring force, and mrω
2cos (ωt+φ
0) is external force. We solved the equation on the assumption that the steady vibration is approximately expressed as x=x
max cos (ωt-φ
0), and the results were confirmed by suitable experiments. Moreover we discussed on the stability of the solutions theoretically.
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Yoshikazu SAWARAGI
1951 Volume 17 Issue 64 Pages
6-9
Published: December 20, 1951
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The characters of hysteresis loss more or less exist in all machine parts which are used for vibration absorbers, for example, laminated leaf springs and frictional springs in rolling stock and rubbers or vibration absorbers. When the periodic force is applied to a system with such characters, the resonance curves can not be obtained by simple calculations because of the non-linearlity in the differential equations of motion. Then the author developed the graphical solution in this case which was previously proposed by the author concerning to the forced vibrations of the systems with non-linear restoring force. In this paper the author proved by adequate calculations that the graphical solution is practically available for obtaining the resonance curves from the statical hysteresis curves in one degree-of-freedom systems.
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Shujiro KUNII, Yoshikazu SAWARAGI, Setsuo TAKAHASHI
1951 Volume 17 Issue 64 Pages
9-13
Published: December 20, 1951
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On the unstable vibration of a dissipative system with variable flexibility, theoretical analysis discussed in the previous report has been agreeable with experimental results. But in the previous report we treated the unstable vibrations of 1/2 degree and of 2/2 degree, when the coefficient of variable flexibility is small. In this report, applying our method to a system with larger variable flexibility, critical diagrams of instability are determined approximately. It is noticeable that those diagrams are quantitatively different from Erdelyi's or van der Pole's ones, but in fair agreement with Ince's calculated values for non-dissipative system.
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Shujiro KUNII, Yoshikazu SAWARAGI, Setsuo TAKAHASHI
1951 Volume 17 Issue 64 Pages
13-18
Published: December 20, 1951
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In this paper, we investigate the character of the free vibration of a system whose equation of motion is given by the formula : [numerical formula], and compare the results of the calculations with those of the experiments. In our calculations, we assume a sinusoidal solution with half frequency of variable as a periodic one. Adopting the new method of successive approximation, we obtain theoretical expressions for this problem with sufficient accuracy. This enables us to examine the stability of vibration. It is shown that coincidence between our calculations and experiments very satisfactory.
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Yoshikazu SAWARAGI, Setsuo TAKAHASHI
1951 Volume 17 Issue 64 Pages
18-23
Published: December 20, 1951
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On the unstable vibrations of the system with variable flexibility, various discussions have been done over the non-dissipative systems, but the exact treatment is not yet given for the effects of damping on the unstable vibrations. We attempted the experiments about the dissipative system with the sinusoidal variable flexibility, and as the results damping force which is necessary for evasion of unstable vibrations was found out by approxmate analysis. Moreover, the theoretical analysis which is applicable to the larger coeficient of flexibility was successively contrived and was in fair agreement with experimental results.
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Kenkichi MURAKAMI
1951 Volume 17 Issue 64 Pages
23-26
Published: December 20, 1951
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Analytical and graphycal methods have been adopted so far to the solution of equation of vibration which has non-linear terms. Mr. Goro HAYASHI, among these, analyzed the equation which has non-linear damping term remaining its non-linear term as infinite series. I have tried this method to the equation which has non-linear restoration force and successfully applied to a few examples. Original equation is expressed as follows. [numerical formula] f(s)=αs+βs
2+γs
3+δs
4+……… After transforming the equation, we get [numerical formula] Put the Laplace transformation of s (τ) as S (p) and the initial conditions as [numerical formula] Substituting this, we can proceed the caluculation, and reach the conclusion. [numerical formula]
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Toshio NISHIHARA, Yoshikazu SAWARAGI, Yukio OKADA
1951 Volume 17 Issue 64 Pages
26-31
Published: December 20, 1951
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In this report the sub-harmonic resonance of the dissipative system with the restoring force represented by a cubic curve is treated. The authors tried to solve this problems by Fourier series and investigate the stability of the solutions, and then acquired the graphical solution which is useful for actual practice We made an experiment to see the validity of the calculation, that is, we could find how the magnitudes of damping force and external force affect occurrence of sub-harmonic resonance in the non-linear system.
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Tosie TAKAHASI, Atubumi OKUMURA, Hideo HORIE
1951 Volume 17 Issue 64 Pages
31-36
Published: December 20, 1951
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A coupled vibration of propeller blades and shaft, the former in bending and the latter in torsion, was studied analytically. The authors pointed out some mistakes in the boundary conditions used by J. Meyer in the similar problem (D.V.L. Jahrbuch 1938), and obtained rigorous results. The conclusion indicates that the negligence of distributed shaft mass, as done by J. Meyer, leads to some irrationality in the higher modes of vibration.
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Tosie TAKAHASI, Atubumi OKUMURA, Hideo HORIE
1951 Volume 17 Issue 64 Pages
36-39
Published: December 20, 1951
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The experimental proof of the authors' theory on a coupled vibration of propeller blades and shaft was carried out. The model was made of spring steel strip for the blades, and of ebonite bar for the shaft. The resonance-method was adopted for determining the natural frequencies of the system. The blades, put in a coil and magnetic field, were driven by alternating current generated by R-C oscillator. The maximum amplitude at the resonance was detected by a microscope. The results were in good accordance with the theory.
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Tosie TAKAHASI, Atubumi OKUMURA, Hideo HORIE
1951 Volume 17 Issue 64 Pages
39-43
Published: December 20, 1951
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The coupled vibration of propeller blades and shaft, the former in bending, and the latter in torsion, under periodical excitation of torque in the engine part, was analytically studied, and the amplitude and resonance-frequency were made clear. The author concludes that there are serious differences of amplitude and resonance-frequency between the present theory and the usual theory, in which the blades are considered as rigid bodies. The theory will be experimentally verified in the following Report.
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Atsubumi OKUMURA
1951 Volume 17 Issue 64 Pages
43-46
Published: December 20, 1951
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The practical aim of this method is to simplify the process to derive the characteristic equations of structures, which are built up of simple elastic bars or shafts, in their vibration or stability problems. The analyses of the problems of this kind usually become very tedious with the increase of number of connections. Then, the author tries to simplify the process of the analyses in a form of reiterated substitutions in some recurrence formulae. In this 1st report, the method is proposed in some general manner prepareing for applications to practical problems which are to be discussed in the annexed reports.
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Atsubumi OKUMURA
1951 Volume 17 Issue 64 Pages
47-53
Published: December 20, 1951
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As a most simple example of applications, torsional vibration systems are treated to give a clear verification of the method proposed in the 1st report. By this method, the frequency equations of shafting systems which have many concentrated moment of inertias, elastic constraints and gearing connections can be derived by repeated substitution on only one simple recurrence formula. And in addition, it is pointed out that this method covers the problems of branched systems and forced vibrations too, without any difficulty.
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Atsubumi OKUMURA
1951 Volume 17 Issue 64 Pages
53-59
Published: December 20, 1951
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The problems of deep beams have been discussed by L. Prandtl, J. Prescott and many other authors mainly on "Kipperscheinungen" or the phenomena of lateral bucklings. But their analyses start from fundamental equations which were derived individually under the consideration of definite boundary conditions, and have no generality in them. Therefore, in this paper the author tries to generalize the analyses of deep beams. First, most general fundamental equations are proposed which can cover very widely the problems of deep beams without being restricted by any boundary conditions and loading conditions. Second, general solution of these fundamental equations in some simple special cases are shown. Finally in the appendix, starting from these fundamental equations, some vibration problems of deep beams having concentrated inertia mass on them are discussed.
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Teruyoshi UDOGUCHI
1951 Volume 17 Issue 64 Pages
59-65
Published: December 20, 1951
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In the lateral vibration of an elastic bar, the natural frequency varies during the transferring of its support and presents definite numbers of definite maximum and minimum values in accordance with a general rule. In this paper the reality of this rule is first verified by an example of a canti-lever beam. Then the generality of this rule is ascertained by the aid of the solution of the integral equation in the forced vibration of a bar, and the meaning and interpretation of the rule are expressed in view of Rayleigh's principle.
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Yoshikazu SAWARAGI, Shigeru NAKAYAMA, Toshio CHIBA
1951 Volume 17 Issue 64 Pages
65-71
Published: December 20, 1951
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This paper presents the effects of the finite length of the connecting rod on the ranges of unstable vibrations for the torsional vibrations of the shafts systems having a periodically variable moment of inertia and viscous damping force. In studying this problem, we established a differential equation containing a parameter λ, which is the ratio of the crank radius to the length of connecting rod, and a damping parameter δ. We solved this equation by the method of successive approximation, and as the results we obtained the following two remarkable points. First, in the case of no damping, there arise the unstable vibrations in the vicinities of the number of revolutions of shaft 2N
er, 2/3N
er and 1/2N
er in addition to the vicinity of N
er, which corresponds to the ordinary critical speed for torsional vibrations of shaft. Secondly, we pointed out by considering δ that the unstable ranges were reduced and there exists the "ranges of taking along by (Mitnahmebereich
(6))" over the unstable ranges, though it is not too much to say that there is no literature considering the damping parameter δ.
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Tosie TAKAHASI, Noboru FUJIMOTO, Mitio ITIKAWA
1951 Volume 17 Issue 64 Pages
72-77
Published: December 20, 1951
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In the ordinary theory of lateral vibration of beam, the boundary conditions were given, hitherto, at a point or points. But in the practical problems, such as the shaft supported by bearings, or the column built in the foundation, it must be pointed out that the beam can be considered clamped in the elastic support or supports of finite length. The object of the present paper is to give some corrections to the foregoing theory from the above-mentioned point of view. The results may be sumarized as follows : (1) The inertia-and elastic effects of support can be represented by introducing the inertia and elastic terms into the vibrational equation of bar. (2) The well-known formulae for the frequencies of bar under several boundary conditions are entirely included in the present theory as special cases. (3) The increase (or decrease) of stiffness and length of the elastic support raise (or lower) the frequencies, if the total length of beam is kept constant. (4) The Okumura-lkeda's theory, in which the effect of elastic support is treated merely as statical constraints, agrees with the present theory, only if the length of the support is very short, and only when the fundamental vibration is concerned. (5) The results of model experiment are in good accordance with the analysis.
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Noboru FUJIMOTO
1951 Volume 17 Issue 64 Pages
77-78
Published: December 20, 1951
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This paper suggests that some suitable shapes of a thin strip should be chosen when the Young's modulus E is measured by the lateral vibration of a cantilever. The increase in length of strip will cause, at last, the lateral buckling by the weight of itself, on the other hand, the shorter in length, the nearer to a rectangular plate. For the cases above mentioned, the frequencies of strip deviate from the value expected as a cantilever. The experiments are carried out by varying the length of strip from 1 cm to 30 cm by 1 cm step, the thickness being kept constant. As the result of experiments, it can be concluded that the suitable range has been found between l/b=10 and 20, where l and b denote the length and width of the cantilever respectively. The difference of the value E by the order of vibrations shown by Dr. Bock cannot be recognized in the author's experiments.
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Isamu IMACHI
1951 Volume 17 Issue 64 Pages
79-81
Published: December 20, 1951
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The calculated velocities of propagation of lateral waves in bars are discussed under each of the following assumptions : (1) referring to the ordinary beam theory, i. e. neglecting the shearing deformation, rotatory inertia, and all damping effects, (2) introducing the rotatory inertia only, (3) introducing the effective shearing deflection moreover, (3a) same as (3) but considering internal and external viscous resistances, (3b) same as (3) but considering external viscous resistances and internal solid frictions of the type of the constant logarithmic decrement, (4) as a pure shear bar.
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Atuyosi MURAMATU
1951 Volume 17 Issue 64 Pages
81-84
Published: December 20, 1951
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As the methods of measuring Young's Modulas E, ordinarily the so-called static measuring methods, for example, tension test or bending test is used. But in practice, the stresses applied to the materials which constitute machines or structures are scarcely pure static but nearly dynamical. Then I devised and designed newly a measuring apparatus for E by the transverse vibration of cantilever, and made an experiment on several drawn metal wires at room temperature. I observed the relation of E with the annealing temperatures, the carbon percentages and the diameters. Moreover, I compared the static tension test results with the newly devised dynamical test results.
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Tosie TAKAHASHI, Haruaki MURAKAMI, Tetu YAMANOUTI
1951 Volume 17 Issue 64 Pages
84-89
Published: December 20, 1951
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The authors deal analytically and experimentally with the vibration of circular disc supported by an elastic body at its central part. The equation of motion for the central part may be N∇
4w+kw+ρ∂
2w / ∂t
2=0, and for the free part, N∇
4w+ρ∂
2w / ∂t
2=0, where N denotes the flexural rigidity of plate, while ρ and k represent the density and spring constant respectively, and w is the deflection of plate. Applying appropriate boundary conditions, the frequency equation was determined. The influence of several factors on the natural frequency was made clear numerically, and verified by a model experiment.
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Tosie TAKAHASI, Seiken TAJIMA
1951 Volume 17 Issue 64 Pages
89-93
Published: December 20, 1951
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The vibrational equation of plate : [numerical formula] where E=Young's modulus, σ=Poisson's ratio, ρ=density, 2h=thickness varying along the radial direction, w=deflection and t=time, was led to ∇
12 [κ
3 (ζ) ∇
12u (ζ)]-λ
4κ (ζ) u (ζ)=0, under the substitution w=u (ζ) sin nθsin pt, ζ=r/a (a=outer radius of disc), h=h
0κ (ζ), λ
4=3/2×(1-σ
2) ρp
2 : Eh
02/a
4, ∇
12=d
2/dζ
2+ζ
-1d/dζ-n
2ζ
-2. Assuming [numerical formula], the general solution for u was determined, and the frequency equation, under generalized boundary conditions, such as, α
j1u+α
j2u'+α
j3u"+α
j4u'''=0, (j=1, 2, 3, 4) was established. The frequency equation, here given, contains the Prescott's results as a special case. Finally the authors describes an application to a lens-formed section : h=h
0 (1+αζ
2), concave and convex corresponding to the sign of α, where |α| is very small, resulting λ
4=104
·2+113
·8α, for the fundamental frequency of disc clamped at its circunference, and free at the centre.
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Koshiro KUROKI
1951 Volume 17 Issue 64 Pages
94-100
Published: December 20, 1951
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I found a frequency equation of the torsional vibration of a conical bar with circular discs at its both ends, then defined the dimensionless value "s" that indicates the effect of the moment of inertia of the circular disc. In the special cases of "s", i.e. ; for the conical bar with a circular disc at its one end, the natural frequency of fundamental order is found, when the boundary conditions are as follows : (1) both ends are free. (2) one end (with no disc) is fixed. And the change of this natural frequency in connection with "s" and the radius ratio of both ends of the conical part is clearly pointed out. At the same time, the problems of simple conical bar (both ends free ; one end fixed, both ends fixed) are solved.
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Koyu MIYAZAKI
1951 Volume 17 Issue 64 Pages
100-103
Published: December 20, 1951
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In the present paper, the author has mentioned a new solution based on Lagrange's Formula of Interpolation as one of the numerical solutions of linear partial differential equations in the case of having a domain surrounded by an arbitrary closed curve, and has examined whether it is of general practical use by obtaining the answer of the heading problem through applying this new solution to it.
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Koyu MIYAZAKI
1951 Volume 17 Issue 64 Pages
103-106
Published: December 20, 1951
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The existing numerical solutions of linear partial differential equations by means of the difference-methods can be applied only to the cases with simple boundary conditions, but not to the cases with complicated boundary conditions. In the present paper, the author tried to obtain a general numerical solution free from such inconvenience, and applying this new solution to the heading problem, examined whether it is of general practical use by comparing the result with that of Ritz's solution of the same problem.
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Sanae WADA
1951 Volume 17 Issue 64 Pages
106-112
Published: December 20, 1951
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The vibration of a chain, fixed one end to a rotating disc and having a concentrated mass at the other end in the field of centrifugal force, is dealt with as a boundary problem. The analytical results are exactly equal to those of the experiments, and will be shown as follows : a) The larger the intensity of the field becomes, the larger becomes the frequency of a chain. b) The larger the mass ratio M/m of chain m to concentrated mass M becomes, the less becomes the frequency. c) The frequency extends one of a mathematical pendulum in the case of a mass ratio M/m is over twenty. In addition, the author calculated Legendre's polynomials of the 2nd kind from 0th to 7th degree.
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Akira KASHIWAGI
1951 Volume 17 Issue 64 Pages
112-115
Published: December 20, 1951
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The dividing Coefficients a
e1i+a
e2i=1 are taken place in the cases of 1>a
e1i and 1>a
e2i>0, a
e1i<0 and a
e2i>1 or a
e1i>1 and a
e2i<0. Corresponding to the type of vibration, the writer studied to clear their physical meaning by exaning the relation between the dividing coefficient and the curve of amplitude, in comparison with Wydler's theory.
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Hideo YAMADA, Tosimitu TUMURA
1951 Volume 17 Issue 64 Pages
115-119
Published: December 20, 1951
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If a rotating machine has its operating speed above its critical one, it must pass the critical speed when accelerated to operating speed or retarted to a halt. This paper deals with the building up of a vibration of uniformly accelerated or retarded the unbalanced rotor which has linear stiffness and damping. The method of contour integral, by which F. M. Lewis worked analogous problem, is used. The figure shows the maximum amplitude concerning to the damping and acceleration. The experimental formula deduced from the calculated graphs is as follows : R
emax=3·78√q e
-1·16a, a=q
0·379γ
0·7, 10<q<100, 0<γ<0·20 where R
emax is the maximum amplitude measured by the unit of eccentricity, q=N
2/h, N being critical speed and h acceleration, and γ is dimensionless damping. During acceleration the instantaneous speed, at which the vibration amplitude becomes maximum, is higher than the critical speed, and this shift percentage from the critical speed is estimated at 86/√q-34γ.
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Toshio NISHIHARA, Yoshikazu SAWARAGI, Taizo SAWAMURA
1951 Volume 17 Issue 64 Pages
119-124
Published: December 20, 1951
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In case of the sustained oscillations caused by the non-linear characteristics, we can not discuss on the utility of controllers, without the calculations of their amplitude and frequency. From this standpoint, an example of the non-linear characteristics in the relay is treated in this paper. First, we devided the non-linear characteristics into three linear sections and treated this each section by linear vibration theory, then we obtained the sustained oscillations by numerical calculations. Secondly, we approximately represented the characteristics by cubic curve and analytically treated it on the assumption that the sustained oscillations are represented as simple harmonic motions. As the results, we confirmed analytically that the amplitude and frequency of the sustained oscillations caused by the non-linearity are independent of the initial disturbances, and that the frequency is independent of the shape of the characteristics in the relay.
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Toshio NISHIHARA, Yoshikazu SAWARAGI, Taizo SAWAMURA
1951 Volume 17 Issue 64 Pages
124-130
Published: December 20, 1951
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In the case the measuring means in an automatic control system is suffering Coulomb friction, an approximate method formerly was found by Dr. W. Oppelt to decide the stability of the control action. But hitherto the exact method had not been attempted, accordingly we could not estimate the degree of approximation of Oppelt's method. Then the authers applied an exact method to the level-control and pressure control system, and compared Oppelt's results with ours. And we found that Oppelt's method does not bring a serious error. On the other hand, we introduced a new approximate method, which is more simplified and has higher degree of approximation than Oppelt's.
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Yutaka ONO
1951 Volume 17 Issue 64 Pages
130-137
Published: December 20, 1951
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An effect of rails on the vertical oscillations of locomotive is theoretically investigated under the following assumptions : rails are infinitely seamless elastic bars supported by elastic foundation (with distributed spring constant k) and locomotive is an oscillating system with body M, wheel m and spring K between them. This analysis is carried out for both cases of free oscillations, and forced oscillations caused by unbalanced forces of the locomotive engine, at constant speed V. The results obtained are as follows : deflections of rails at loaded points increase as V
2. Periods of vertical oscillations also slightly increase as V
2. Two waves with different velocities propagate along rails. And by introducing the dynamic factors and the effective mass of rail, we can simplify the problems, etc.
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Yutaka ONO
1951 Volume 17 Issue 64 Pages
138-144
Published: December 20, 1951
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Many researches on the longitudinal motion of locomotive while it is running, have already been reported. But the explanations on the velocity with which the locomotive moves longitudinally while running seem insufficient. In this paper, the longitudinal motion of locomotive is regarded as an oscillation which causes a periodical collision between the locomotive and tender. This is a forced oscillation caused by the unbalanced force of engine. Then the velocity of the oscillation can be calculated as a resonant velocity. The results obtained from the calculations concide fairly with practical measurements. Preventions of these oscillations are also discussed.
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Tei MORI
1951 Volume 17 Issue 64 Pages
145-148
Published: December 20, 1951
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I read previously the papers on the theory of the above problem, and in this paper I state how the conclusions of this theory are to be applied to the experimental results of vibration test made on the bogie carriage whose truck springs were designed by the engineers of Keihanshin Electric Railway Co., and on other rolling stock of the same line, especially with respect to up and down motion. Moreover, I investigated the effects on the amplitudes of vibration influenced by the weight of the carriage body and the weight of the rail. Then I have found that we can improve the riding quality of a running carriage by softening the plate oprings, hardening the coil springs, decreasing carriage weight and using heavier rails.
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Tei MORI
1951 Volume 17 Issue 64 Pages
148-154
Published: December 20, 1951
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The investigations on the vibration of a bridge caused by running vehicles, especially by locomotives, have often been published, while those of railway carriages running on a bridge can rarely be found, particularly in the case of carriages which have bogie trucks. I reported previously on the theory of the vibrations of a bogie carriages running on a track, and in this paper, I state how my theory works on the bridge, especially with respect to the up and down motion, and compared their results. Lastly I have found there was no remarkable difference between the amplitudes of the vibration of a carriage running on the bridge and on the ordinary track.
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Tei MORI
1951 Volume 17 Issue 64 Pages
154-158
Published: December 20, 1951
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In the 4th report, I put forward a theory on the vibrations of a bogie railway carriage running on a bridge, assuming that the carriage body was supported by coil springs set on the wheel axles. But in actual construction, there are two kinds of springs, plate and coil, on the wheel axles, so that in this paper, I have studied the modification of the previous theory in the present case. Lastly I compared the maximum amplitudes of vibration calculated by the formula expressed in my reports with experimental data measured by the vibration recorder instabled on the carriage floor, and have found a fair coincidence between them.
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Naoteru ODA
1951 Volume 17 Issue 64 Pages
158-162
Published: December 20, 1951
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A method of looking for the nautral periods of the vertical vibration of cars from the vibration charts of running railway cars is studied. Only the sinious waves are taken out from the charts, the hystogram of periods is plotted, and the mean value of the periods is obtained. Considering this mean value as the natural period of the car, the writer can explain the experimental data of the car well.
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Naoteru ODA
1951 Volume 17 Issue 64 Pages
162-168
Published: December 20, 1951
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One of the most important results of running test of railway cars is that amplitude or acceleration of vibration ξ has complete reproducibility and is a function of the running speed V, the character of the car K and the bed parameter x ; that is, ξ=f (V, K, x). Treating the vibration charts, we cannot infer the vibration characteristics of cars, such as the relation between ξ and V, by means of the incomplete scatter diagrams, which have been used as a conventional method. So the writer plots the complete scatter diagrams of ξ to V by all the waves of vibration charts, and obtaining the curves of regression we can consider the curves as the running characteristics of cars. Requiring the curves of cars by the above method, the writer find out that the resonance speeds are explained well by the natural periods obtained by means of Part 1.
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Naoteru ODA
1951 Volume 17 Issue 64 Pages
168-172
Published: December 20, 1951
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A characteristics of acceleration of running speed, which was reported as an example in Part 2, is discussed statistically. The characteristics manifest that acceleration of both vertical and transversal vibrations increase linearly with running speed, on the contrary to the conventional theory and experimental data. The writer requires the correlation ratios and correlation coefficients between acceleration and running speed. It is proved that these are significant, and that the linearity of the corre lations is not abandoned.
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Tatsuo CHUBACHI
1951 Volume 17 Issue 64 Pages
172-178
Published: December 20, 1951
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In this paper the theoretical equation of motion of tire wheel is obtained, by the consideration of tire deformation and the slip against road, as a method to connect the Kantrowitz's shimmy equation and the usual theory which neglects the tire deformation. This equation leads to the steering characteristics of pneumatic tire. By this aequation the yawing shimmy and the coupled oscillations fo rolling, yawing, tramping etc. are analysed.
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Tadashi MAKI, Takeshi IWASAKI
1951 Volume 17 Issue 64 Pages
178-182
Published: December 20, 1951
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In this paper the authors give the opinnion that the difference between the sliding and statical friction coefficients of the friction clutch causes the longitudinal vibration of the motor-car when the car starts in spite of the normal engine running. And they calculate the period of the clutch transmitting torque which fluctuates because of the above-mendtioned reason.
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Kikusaburo NAGASHIMA, Naoteru ODA
1951 Volume 17 Issue 64 Pages
182-187
Published: December 20, 1951
Released on J-STAGE: March 28, 2008
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The writers studied experimentally the effect of the taper of tire treads on the vibration of railway cars, in cooperation with the Keihanshin Express Electric Railway Co., Ltd. The vibration of running cars was measured in both cases of 1/20-tapered conical tread and cylindrical tread, and the vibration charts are treated statistically. Results obtained are as follows : (1) Acceleration in the case of cylindrical treads are less in both vertical and transversal vibration. (2) In the vertical vibration, difference is a little. (3) But, in the transversal vibration, acceleration is about 7 : 5 when the car speed is over 80 kg/h.
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