Theoretical And Experimental Investigation On Elastodynamics Of Three-Ring Gear Transmissions

Three-ring gear transmission is a novel type of planetary transmission with small tooth number difference, which was invented by a Chinese engineer. This new type of transmission has some distinguish advantages, such as large speed-reduction ratio, high load capability, compact volume and simple structure etc, over traditional gear transmissions and planetary trains. Some problems, however, still occur in run, among these problem are severe vibration, high level of noise and heat producing etc, all these problems are big obstacles in its further application and are closely related with the dynamics. On the other hand, three-ring gear transmission is an over-constrained mechanism. Theoretic study on dynamics of over-constrained mechanisms is less at present. So an extensive elastodynamic investigation is pressingly needed in both theory and application. This is just the purpose of this dissertation.Similar to planetary transmissions, two or more inner gears mesh with the same external gear simultaneously. So the tooth numbers of the gears must meet a certain condition, or it would be difficult or even impossible to assemble the transmission: In this dissertation, this condition was analyzed in detail and applied to three representative prototypes.Three-ring gear transmission is an over-constrained mechanism. So the elastic deformations must be taken into consideration in the dynamic model. This dissertation analyzed the elastic deformations and derived the coordinate relation between those deformations.The elastodynamic model of the transmission was established for the first time. In the modeling process, the overall transmission was divided into several subsystems. The dynamic model of the subsystems were built respectively and then assembled into the overall model. This model includes the elastic deformations of the main bearings and parts, and errors of cranks in both length and index.The closed algorithm was analyzed in detail and the faultiness of it was pointed out. A modification to the faultiness was derived afterwards. For compensating the effect of truncated modes on the response, a quasi-static compensation technique was incorporated into the model.A computer simulation was carried out with the modified closed algorithm. The simulating results show that the juxtaposition of two or more mechanisms can considerably reduce the load on the bearing of the housing. The natural frequencies of the transmission were given out for the first time also.The effect of manufacture errors of the cranks on the response was investigated. The result indicates that the errors not only affect the load-sharing but also increase the load on all gears.A comparison was made between the response of the two basic configurations under the same external excitation, and the result shows that the symmetrical is muchbetter than the unsymmetrical in dynamics. This further indicates that the primary factor causing the vibration is the parametric excitation instead of the impact at the dead points.The influence of design parameters on dynamic response was investigated, among these parameters are the stiffness of planetary bearings of input and support shafts, stiffness of bearings of output shaft, stiffness of the mesh gears, the mass of the inner gears, the distance between the input shaft and support shaft, and the driving speed.The parametric study reveals that the response is very high if the driving speed is close to 1/3,1/6,1/9 —of the first order natural frequency of the transmission. This phenomenon is called lower harmonic resonance. The reason for that is explained with perturbation method.In order to verify the theoretic analyses, experimental work was carried out. The experimental results confirmed the existence of lower harmonic resonance.