It is the aim of this paper to make analyses of torsional rigidity and the stress of a flexible shaft, and make comparisons between theoretical and experimental results. Experiments were conducted with a view to these ends, and the results obtained are summarized as follows: (1) A flexible shaft, when its torsional properties is treated analytically, should not be considered as a group of coil springs, because the contact pressure arises in the side wires of any two layers. (2) An analytical method established by considering the contact pressure between the two layers is useful to determine the torsional properties of flexible shaft. (3) The torsional properties of a flexible shaft depend not so much on the construction of internal layers as on that of the outer layer. (4) In the case of flexible shafts having a constant outside diameter, the torsional rigidity increases and the stresses of side wires decrease with the increase of the number of side wires in the outer layer. (5) The torsional rigidity C and the stress of side wires σ of a flexible shaft can be approximately determined by applying the practical equation proposed by the authors in which the construction of side wires in the outer layer is mainly taken into consideration.
The purpose of this paper is to present, within the framework of our studies on polygonal profile coupling, the measurement of torsional stresses in polygonal profile by application of the principle of sheet analogue. In the first place the analogue is applied to the solution of the problem of the torsional stress distributions in the solid bar with polygonal cross section. The results achieved are compared with the solution hitherto made by the theoretical method of the conformal mapping proposed by Muskhelishvili. It is seen that there is excellent agreement in the result between what is reached by the theoretical method and what is reached by the analogous sheet method. It is thus seen that the sheet analogue method provides a rapid and accurate solution for pure torsion problems. In the second place applying the same technique new results are presented for the torsional stress concentrations in hollow polygonal cross section with circular holes.
This investigation has been conducted to make clear the effect of strain rate on the internal structure and the mechanical properties of rapidly stretched aluminium and aluminium-magnesium alloy. Pure aluminium (99.99% Al) and aluminium-magnesium alloy (4.65% Mg) specimens have been used in this study. The main results obtained are as follows; (1) The yield strength and the tensile strength of pure aluminium in rapid tensile testing are larger than that in static tensile testing. The strain rate gives a remarkable effect on the resistance in deformation of pure aluminium. (2) The yield strength of aluminium-magnesium alloy in rapid tensile testing is larger than that in static tensile testing, but the tensile strength in rapid tensile testing is smaller than in static tensile testing. (3) The yield strength, the tensile strength and the hardness of rapidly pre-stretched pure aluminium are larger than those of statically pre-stretched sort. It is recognized that this fact is mainly due more to the promoted recovery by static pre-stretching at room temperature than to rapid one. (4) An interesting observation worth mentioning in the static tensile testing of the aluminiummagnesium alloy is that after a certain strain is reached the load starts to oscillate, but in the rapid tensile testing, it is not recognized. (5) The yield strength of rapidly pre-stretched aluminium-magnesium alloy is smaller than that of statically pre-stretched sort, and the tensile strength of the rapidly pre-stretched is almost the same as that statically pre-stretched.
The more extensive application of liquid metal coolants to high temperature heat exchange systems today requires the estimation of fatigue properties and creep resistance of metals and alloys in liquid metal environment at elevated temperature. Only a limited amount of work on this subject, however, has hitherto been carried out. This investigation has been started to study the effect of liquid metal environment on the fatigue properties of steels. With a view to securing reliable contact of the specimen with liquid metal and the accuracy of temperature measurement, a fatigue testing machine has been developed of a vertical, cantilever-bending, rotary-loading and fixed specimen type. The molten metal held in a steel container with ceramic coating with the specimen suspended in it is heated in an electric resistance furnace. The preliminary results obtained on the low carbon steel in air, molten lead and zinc at 460°C and 550°C are summarized as follows; (1) The fatigue strength in molten lead of 460°C and 550°C is less than that in air and in higher temperature the difference increases. (2) The fatigue strength in molten zinc is extremely decreased in comparison with that in air because of embrittlement by liquid metal, dissolution of steel into molten zinc and repeated formation and cracking of brittle intermetallic compounds.
Rouse and Zimm have derived theories of viscoelastic properties of random coil polymers in dilute solutions, and Kirkwood and Auer that for rodlike polymers. Comparing these theories with each other in the form of the normalized dispersion curve, we may obtain direct information on the degree of internal freedom of polymer molecules. Many experimental investigations on viscoelasticity of coiling polymers have been made for dilute and for concentrated solutions. Experimental results for dilute solutions show almost quantitative agreement with the theories of Rouse or Zimm, but those for concentrated solutions a systematic disagreement. From these results, it is clear that concentration effect on the viscoelasticity still remains somewhat ambiguous even in the region of dilute solutions. This is not surprising, because all these theories are concerned only with the intrinsic quantities corresponding to infinite dilution without taking account of intermolecular interaction. In this study the dynamic intrinsic viscosity and intrinsic rigidity, therefore, are defined experimentally as follows, [η']=limc→0(η'-ηs)/ηsc, [G']=limc→0G'/c. Considering that, with changing concentration, all relaxation times involved change to some extent as was pointed out by Ferry, we define also the limiting value of the terminal relaxation time as (τ1)0=limc→0τ1(c). The complex rigidities are obtained by means of the torsional crystal method at the frequency of 39.2kc and the temperature of 30.0°C. The relaxation times are derived from the steady shear viscosities measured by a Ubbelohde dilution viscometer. As an example of the random coil conformation, the solutions of the high molecular weight polymethyl methacrylate (Mv=2.1×106) in chloroform were studied. The measured values for G'/c, (G"-ωηs)/c and τ1 were found to be in line with the concentration. The intrinsic rigidities and the limiting relaxation time were determined by extrapolating the experimental data to the zero concentration. The sets of the intrinsic rigidities and the limiting relaxation time thus determined were quantitatively in agreement with the values predicted by the Rouse theory. In the case of the rodlike conformation, poly-γ-methyl-D-glutamate (Mn=1.29×105) which was 100% α-helix in chloroform solutions was investigated. It was found that the measured values approached the theoretical dispersion curves due to Kirkwood and Auer as the concentration was lowered to infinite dilution.
The complex rigidities and the complex dynamic viscosities of the solutions of polyisobutylene (PIB) in cyclohexane and those of the solutions of poly-γ-methyl-D-glutamate (PMDG) in chloroform were measured at frequencies of 19.6kc, 39.2kc, and 117.7kc, respectively. The relaxation times corresponding to the longest mode of chain motion were obtained from the steady shear viscosity measurements. All the measurements were performed within the concentration range about 0.1 to 0.5g/dl and at temperature of 15.0 and 30.0°C. The intrinsic quantities were obtained by extrapolating the measured values to zero concentration, and they were compared with the molecular theories of viscoelastic properties for different conformations in the form of normalized dispersion curves, which were obtained by plotting [G']M/RT, [C"]M/RT, [η']/[η], and [η"]/[η] against the generalized relaxation time (τ1)0/K1=[η]ηsM/RT. The results obtained for PIB in cyclohexane solution show that the experimental values lie between two theoretical dispersion curves by Rouse and Zimm in the four plots for [G'], [G"], [η'] and [η"]. This means that the effect of the hydrodynamic interaction is not negligible (partial free draining) for the system of this random coil polymer. Results obtained for poly-γ-methyl-D-glutamate in helix solvents show qualitative agreement with the Kirkwood-Auer theory for rod-like polymers.