Calculation of vibration characteristics of gearbox


For the simple model equations established, the eigenvalues ​​and eigenvectors can be directly obtained, that is, the main modes and natural frequencies of each order are obtained. The method of matrix triangulation can also be used to solve the problem of generalized eigenvalues ​​into standard eigenvalue problems, and the natural frequencies and mode shapes of each order are obtained. For the multi-degree-of-freedom system, the low-frequency eigenvalues ​​and eigenvectors can be easily obtained by using the extreme value principle of Rayleigh quotient. However, the fundamental frequency given by the Rayleigh quotient method is too large, and a small approximate fundamental frequency value can be given. The matrix iterative method is to first solve the eigenvector and then solve the eigenvalue. For the common eigenvalue problem, the initial vector is appropriately selected, iterated, and finally the eigenvalue is obtained. In addition, there is a transfer matrix method, which divides a complex or continuous system into a finite number of links or unit segments, and then uses the transfer matrix to obtain the natural frequencies and eigenvectors of the system. The actual engineering structure is a continuous distribution of elastic bodies. Only some structurally simple elastic bodies can be solved by analytical methods. For complex elastic bodies such as gearboxes, numerical methods such as finite difference method and finite element method are used to solve.
When analysing individual parameters in a model, it is often necessary to use a finite element calculation method. When establishing the analysis model of the gear system, the coupling effects of the various parts are considered separately. This is a method of artificially dividing a system into several components and establishing a dynamic model called dynamic substructure. After calculating the various parameters and solving the various models of the established gear system, we must also consider the interface of each substructure and the connection (coordination) conditions between them, and finally analyze and calculate the vibration characteristics of the entire gearbox. The analytical model we have established in the past does not consider the substructure analysis model of the bearing and the box. The marine gearbox generally adopts a sliding bearing. The basic composition of the sliding bearing is the bearing bush and the bearing housing. The dynamic bearing supports the gear shaft and its bearing bush. And the bearing seat can be considered together with the box body, and the connection between the journal and the bearing bush can be added with an elastic element and a damping element of suitable rigidity. The analytical model of the gearbox can only be established using the finite element method.
Considering the error caused by various parameters in the simplified calculation model when building the model, the accumulated error of the various errors of large complex structures will be difficult to control, and the coupling of each part is not easy to achieve. : Can you use the finite element method for analysis and solving? The answer is yes. The key is to solve the related problems in finite element modeling. These problems include the handling of gear teeth stiffness, the finite element simulation of bolted joints, the solid modeling of complex gears, the finite element modeling of herringbone gears, and the rational application and solution of various elements in finite element modeling. Counting problems and so on.
Since the meshing rigidity of the gear is varied, the Zhangjiagang mill assumes that the gear is elastically connected at the meshing position in the analysis model, and also considers the contact damping problem. According to the relevant research, from the results, the meshing stiffness of the gear has little effect on the natural vibration mode of the whole system, but it has a great influence on the magnitude of the excitation force. For calculating the dynamic characteristics of the whole rotor system, it is not necessary to deeply and meticulously explore the change of the meshing stiffness value during the meshing process, which brings great convenience to simplifying the modality of the solution system.
Therefore, when establishing the analysis model of the gear system, the coupling effect of each part is considered separately. This is a method of artificially dividing a system into several components and establishing a dynamic model called dynamic substructure. After calculating the various parameters and solving the various models of the established gear system, we must also consider the interface of each substructure and the connection (coordination) conditions between them, and finally analyze and calculate the vibration characteristics of the entire gearbox. The analytical model we have established above does not consider the substructure analysis model of the bearing and the box. The ship gearbox generally adopts a sliding bearing. The basic composition of the sliding bearing is the bearing bush and the bearing seat. The bearing bush and the bearing seat can be considered together with the casing by dynamic pressure supporting the gear shaft. The connection between the journal and the bearing bush can be added. Stiff elastic and damping elements. For the solution of the analysis model of the gear box, only the finite element method can be used. The determination of the natural vibration characteristics of the gear is inseparable from the finite element method. Therefore, in addition to the test method, the finite element method should be used as the basic method.



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