|
内容記述 |
The natural frequency of a crankshaft twisting vibration is usually calculated by assuming the attached propeller to be a rigid body. The propeller, however, instead of being rigid, is elastic, the vibration of the blades being due to their bending and twisting. The problem of coupling the propeller blade bending vibration with the crankshaft twisting vibration was recently treated, theoretically by J. Meyer in Germany and B. C. Carter in England. They treated the problem by assuming the blade to be homogeneous in section and ascertained their results by model experiments. Further J. Meyer treated briefly the problem in general assuming the area of the blade and its moments of inertia in potential relations with the length of the blade. An example of the areas and their moments of inertia of sections of a three-blade duralmin adjustable pitch propeller are shown in Fig.1. The areas of sections of the blade are approximately in linear relation to its length, but the moments of inertia of areas J^h and J^>fl<, the former being with respect to the minor axis and the latter to the major axis, are not linearly related. The moment of mertia J^h is approximately in linear relation to the initial part, and after reaching maximum gradually decreases, whereas the latter J^>fl< increases from tip to boss in the fourth or fifth power with its length. In the boss they are equalized, because the section there is a circle. The theoretical solution of propeller blade bending vibration of such changes as in J^h and J^>fl<, with its length, is not easy; and by considering the root of the blade, it will be seen that they differ greatly from the characteristic propeller blade section form, so that it may be regarded as part of the propeller boss. We may then assume that the propeller boss forms 29% of the root of the propeller blade, and that it is rigid, and that the elastic propeller blade forms the remaining 71%; and further that in these parts, the areas of the sections and their moments of inertia J^h and J^>fl< are in linear relation to the length of the blade. With these assumptions, namely, that the sectional area and moments of inertia of the blade are in linear relation with its length, the authors examined this problem theoretically and numerical calculations were made with actual datum of an 800HP V type engine and its propeller. In the reports of J. Meyer and B. C. Carter, the area of the blade is assumed homogeneous, the propeller boss neglected, and the blade assumed to extend up to the propeller shaft. The authors calculated also the case in which the blade is assumed to be homogeneous in section, and the propeller boss taken into account, using the actual datum just mentioned. The results of these two cases, namely that of the homogeneous section and that of linear relation to its length, are compaired. The report consists of the following chapters. 1. Introduction. 2. Differential equations that apply generally to problems of coupling the blade bending vibration with the crankshaft twisting vibration. (1) Differential equations, assuming the propeller blade to be rigid, for the case of a V type 12 cylinder engine. (2) Numerical calculation of the natural frequency of twisting vibration of the crankshaft of a V type 12 cylinder engine, will actural datem. (3) General differential equation in connection with problems of the coupling of blade bending vibration with the crankshaft twistsng vibration of a V type 12 cylinder engine. 3. Solutions of the differential equations when the area and the moment of inertia of the area of the propeller blade are in linear relation to its length. 4. Solutions of the differential equations when the area of the propeller blade is homogeneous in section. 5. Numerical calculation of the natural frequencies and their amplitudes of bending and twisting of the case of chapter 4 from actual datum. 6. Numerical calculation of the natural frequencies and their amplitudes of bending and twisting of the case of chapter 3 from actual datum. 7. Conclus on. 8. Appendix. Calculation of the polar moment of inertia of the root of a propeller blade. Tables and Diagrams. In this investigation we obtained the first five natural frequencies in the coupling of the propeller blade bending vibration with the crankshaft twisting vibration for both cases, namely, when the propeller blade section is homogeneous and when the section and its moments of inertia are in linear relation to its length. Two of them are due to the crankshaft twisting vibration of one node and of two nodes, these values being quite equal to that case in which we calculated them by assuming the propeller to be a rigid body. These values moreover do not differ with respect to the above two cases. The remainder are due to the propeller blade bending vibration, that is, due to one node and two node vibrations in y^>fl< direction and one node vibration in y^h direction. The frequencies for the case of homogeneous section are lower than those of the case of linear relation to its length, their ratios being approximately 1.4 (2.0 in only one case). These ratios are reasonable, if we calculate the propeller blade bending vibration only, assuming the root to be rigidly clamped. From these results, we find that in an actual case, with these couplings of the propeller with the crankshaft, there are natural frequencies not only due to the crankshaft twisting vibration but also to the propeller bending vibration, the former being the same as that in which the propeller blade is assumed to be a rigid body. |
SA4148634.pdf (1.9 MB)
