Finite element method for gear meshing contact unit

The application of the finite element method is divided into three types. The first one is to use the finite element method to find the tooth deformation under a given load. In the analysis of the elastic deformation of the gear teeth, people are mainly concerned with the elastic deformation at the meshing point. In the general finite element analysis, the gear tooth meshing point is often treated as the action point of the meshing force, and thus the calculated deformation is actually the meshing point deformation under the concentrated force. However, due to the elastic deformation, the meshing point actually becomes the meshing contact surface, and the meshing force is a distributed force rather than a concentrated force. Therefore, when the finite element method is used, the distributed force is simplified into a concentrated force and the contact surface is simplified into a contact point. A large error is generated. In order to reduce such an error, a method of compensating by selecting a finite element size corresponding to the contact area is proposed. By finite element analysis of a cylinder having the same curvature, by changing the finite element size of the contact area, The relationship between the finite element analysis results and the Hertz contact deformation is studied to determine the size of the finite element that should be selected in the vicinity of the contact area in order to reduce the above error when the meshing force is processed into a concentrated force. However, this analysis uses a single tooth as the analysis object, so the analysis model cannot consider the influence of adjacent teeth on the simultaneous engagement of multiple pairs of teeth.
The second is to use the finite element method of the contact unit to consider the simultaneous meshing of multiple pairs of teeth and the contact deformation of the teeth, and the meshing analysis of the teeth. It is a numerical method for calculating non-Hertz-type contact problems and is suitable for solving the deformation and stress states of multiple pairs of teeth simultaneously meshing. Since the finite element method of elastic contact problem is based on the theory of elasticity, the results obtained by this analysis actually include various deformations such as bending, shearing, contact compression of the teeth, and multi-tooth can be obtained by this method. The deformation state and the stress state of the mesh are simultaneously engaged, and the gear tooth error can be embedded. Therefore, by using this method for meshing contact analysis, the static transmission error of the gear mesh can be obtained. For example, the meshing contact analysis is performed using the finite element model of the three-dimensional contact problem to obtain the meshing static transmission error. However, if the finite element method of the contact unit is used to deal with the vibration modal analysis of a certain type of marine gearbox, the number of units will be too large, and the contact unit of most software packages cannot perform the vibration mode calculation. The calculation conditions are difficult to solve the solution to this problem.
The third is to consider the elastic liquid dynamic lubrication of the gear meshing tooth surface. In addition to the problem of the second method, the pattern conveyor belt also has a liquid-solid coupling problem, and the existing calculation conditions are also difficult to meet the requirements. Therefore, it is necessary to explore methods suitable for large and complex structures, which will be discussed in another article.
In fact, the meshing damping of the gear teeth is also related to the lubrication state and oiliness of the oil. It involves the viscous hydrodynamic lubrication problem and is also a nonlinear problem, which is difficult to calculate accurately. It is difficult to accurately calculate the quality and moment of inertia of the gear system before the determination of the quality and moment of inertia of the gear system. Only an approximate method can be used. Such finite element analysis software packages can now be used to physically shape and assemble gear components and then calculate their mass and moment of inertia. The result obtained in this way is quite accurate.
After discussing the parameters in the model, the free vibration problem of the model is equivalent to the eigenvalue problem of the matrix, and the problem of solving the forced vibration can be transformed into a modal equation by coordinate transformation, so that the generalized coordinates There is no longer a coupling between them, but to form the modal equation and the corresponding modal stiffness, modal mass, modal damping ratio and modal load vector, the eigenvalue problem must be solved first, and then the modal superposition method is used to finalize Solve.

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