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In order to model the convenience of the finite element model of the gear transmission system, the gear tooth portion is simplified to the indexing cylinder, and the tight coupling of the gear and the shaft is regarded as a rigid connection, ignoring the influence of the keyway, chamfering and undercutting, and utilizing The rotary meshing method meshes the gear and the gear shaft. The box adopts an extracted neutral surface and is divided into shell units. The bearing is simulated by a rigid spring, and the spring stiffness is obtained by the experimental modal analysis method of the literature.
Gear Train Dynamic Analysis Load and Constraint Processing Stiffness and Error Excited Excitation Force TTsuta describes gear excitation force as the product of gear mesh stiffness and gear error. Yao Wenxi and Mweek et al. studied the calculation method of gear meshing impact force. In this paper, we will consider the gear meshing impact excitation force of the gear and the excitation force caused by the error excitation and the excitation force caused by the gear impact. The nonlinear dynamic equation of the gear system is: m is the system mass matrix; c is the system damping matrix; k(t) is the system stiffness matrix, including the stiffness of the gear transmission system (shaft gear) and the structural system stiffness and joint stiffness, as well as the gear meshing stiffness, which is time-varying; xs is the static relative displacement vector; x is Dynamic displacement vector; e(t) is the gear comprehensive error; Ps is the static load.
The gear box is tightly connected to the gantry by bolts. To simplify the design of the analytical model, the bottom of the box is considered a fixed constraint. Dynamic response optimization design of high-speed heavy-duty gear transmission system Structural analysis and structural optimization of gear transmission system are two processes at different stages and levels in structural design. There are close relations and essential differences between the two. Structural analysis is to determine the final state according to the laws of mechanics under given conditions and parameters. It is the basis of structural optimization design and provides the necessary data for structural optimization design. The structural optimization design should not only rely on the response data obtained from the structural analysis, but also optimize the design points based on the formation of the optimization model, and obtain the optimal structural design. It is the further extension and sublimation of the structural analysis. Structural synthesis. Gear drive system dynamic response optimization design mathematical model design variable selection design variable is the amount that can be changed in the search for optimal design process. The optimal design variables of the drive system are mainly the unit properties of the shell and shell units of the box (ie the shell and shell The thickness of the unit).
MSCNASTRAN optimization is optimized using the default modified feasible direction method. Optimization must define a set of optimization parameters, including defining design variables, describing the relationship between design variables and cell attributes, defining objective functions, and constraints. In the input file (bdf) of MSCNASTRAN, use RAN to represent the application of modal transient response analysis method) to define the type of optimization design analysis; use DESVAR card to define the initial value of the design variable and the boundary value (ie the upper and lower limits of the design variable value) Use DVPREL1 to describe the linear relationship between the unit attribute and the design variable; define the design response with the DRESP1 card or DRESP2 card; use the command DESOBJ(MIN) to call the corresponding DRESP2 defined design response to define the objective function, and use the DESSUB command to call the DSONSTR card to define the constraint. The DOPTPRM card is used to determine the optimal control parameters, and the optimal control parameters such as the number of optimization iterations, the convergence conditions (absolute convergence conditions and relative convergence conditions), and the iteration step size are determined. Objective function value change history 3 Gear transmission system dynamic response optimization design result analysis The card (bdf file) is submitted to the operation. After four iterations, the optimization calculation converges, the objective function declines, and the objective function value decreases from 18792m/ss to 9993m/ss. The value changes by 468 to achieve the purpose of reducing vibration.
The transmission error map drawn after solving the above method is shown. Shown are the flank mesh and the corresponding contact trajectory. Transmission error big wheel convex mesh and meshing trajectory 4 Conclusion In the design and analysis of spiral bevel gear, MATLAB combines the advantages of numerical calculation and optimization analysis with VC, which greatly improves the speed and efficiency of program development. The direct invocation of a large number of math toolkits avoids repetitive work in programming, shortens the cycle and cost of development, reduces the difficulty for developers to implement algorithms, and effectively improves the stability, portability, and visualization of application systems. The values ​​of the four design variables are significantly reduced, and the magnitude of the change is mostly above 20, reflecting the thickness of the small bearing end cap, the thickness of the side of the bearing, the thickness of the left and right side ribs of the lower case, and the thickness of the top of the upper case to the gear system. The vibration has little effect and its thickness is reduced under the conditions of strength and deformation. The values ​​of the remaining design variables all increase, and the variation range is about 10, which reflects that the thickness of each component surface of the gear box has a great influence on the stability and safety of the gear transmission system, indicating that the gear box must be considered when designing the gear transmission. Optimized design of the body to achieve optimal design of the overall dynamic characteristics of the system.
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