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Research.
2 Study on the vibration characteristics of the gear transmission system The main excitation of the vibration of the gear transmission system is the meshing stiffness, gear error and unstable load with time. It is a parameter self-excited vibration system. The vibration of the gear transmission includes radial, circumferential and Axial vibration, experimental and theoretical studies have shown that in the spur gear transmission system, the radial vibration and axial vibration of the gear are generated by the vibration of the circumferential vibration. The equation of motion of the system can generally be described as: micro angular displacement; M is the equivalent mass of the gear pair, M=MiM2/(M+M2): MiM2 is the equivalent mass of the driving wheel and the passive wheel respectively, Mi=i'i2 are respectively two The transmission inertia of the gear; rbirb2 is the base circle radius of the two gears; C is the damping coefficient; K(t, x) is the gear meshing stiffness, which is a periodic function of time, K(t, x) = Ek; W is the tooth surface Normal static load, W=Ki/bi; Ki is the torque transmitted by the driving wheel; F(t,x) is the forced external force generated by error and modification, F(t,x)=EK/e/; At the same time, the number of pairs of teeth is meshed, K is the meshing stiffness of the pair of teeth, and e/ is the combined error of the pair of teeth. "From, the deformation of each sheet is independent. The calculation of the helical gear load distribution based on this model is ignored. The further interaction between the pieces is to simplify the helical teeth into a rigid or elastically clamped cantilever plate. Since the geometry of the cantilever plate is quite different from that of the gear teeth, the conclusions obtained are rarely used to study the load distribution. In this way, the deformation caused by the load and the root bending moment Monch and Roy are used to freeze the epoxy resin gear. The distribution of photoelastic experiments was carried out. Conry and Seireg calculated the load distribution on the contact line of the helical gear by linear programming technique. The tooth deformation was divided into bending deformation, contact deformation, support deformation, etc., calculated by material mechanics and Hertz deformation formula. The deformation components. Mathis and Simon studied the load distribution and deformation of the helical gear with three-dimensional finite element. Nicmann and Bathge and Nicmann and Winter used the total length variation of the contact line to estimate the stiffness fluctuation of the gear. Umezawa of Tokyo University of Technology used a finite-difference model of gears to theoretically analyze the load distribution of the helical gear along the contact line. After a series of studies on the load distribution and meshing stiffness characteristics of a pair of finite tooth width gears, The magnitude of the end face coincidence degree X and the axial surface coincidence degree X determine the magnitude of the gear meshing stiffness fluctuation (ie, the calculated vibration amplitude). Since Umezawa is a skew tooth deformation formula summarized by a finite difference model of an equivalent cantilever beam, His research can not consider the influence of the size of the gear structure in the solution, and must be comprehensively studied Mutual influence of wheel geometry and structural parameters on gear transmission vibration In addition, after determining the dynamic load history acting on the gear, it is established to accurately predict the dynamic stress of the gear structure and the centrifugal stress and analysis model of the high-speed gear structure to ensure the reliability of the gear device. The ground work also has a very important significance. In the past, the dynamic stress calculation of gear structure mostly used the analysis of the overall gear structure. Due to the limitation of computer memory, the three-dimensional finite element model of the gear structure is to remove the tooth part. Dynamic stress response of various parts of gear structure such as root, rim and spoke. Since cylindrical gears and bevel gears are typical cyclic symmetry, various theoretical methods for solving the natural vibration characteristics and dynamic response of cyclic symmetrical structures are applied to gears. In the transmission. Using finite element and cyclic symmetry, Ramamurti studied the static stress and dynamic stress of spur gear by establishing a substructure model with one tooth. Yin Zeyong studied the static contact stress and centrifugation of an aviation gear train using three-dimensional finite element and cyclic symmetry conditions. The theoretical model of the stress gear after introducing the cyclic symmetry condition to study the centrifugal stress, natural vibration characteristics, dynamic response and dynamic stress of the gear structure is an effective way to analyze the dynamic characteristics of the gear. For example, the automotive transmission system and the spindle drive system of the machine tool. High-speed light-load, but frequently started and stopped gear transmission system, people have begun to study the nonlinear dynamics of the gap caused by the flank clearance in recent years. Cai and Hayashi have established the nonlinear equation of the nonlinear motion of the spur gear transmission. The rise of research will make the dynamics simulation of the gear unit closer to the actual state of the gear.
Gear device and structure various damping vibration and noise reduction technology, power modification and dynamic sensitivity method research gear shaping technology, including three-form maintenance technology of thermal elastic deformation of gear device The research of forecasting has important significance for key gears such as aviation and yemei ship. 4 The dynamic performance optimization design of gear transmission has been until the early 1990s. The optimized design of gear transmission is basically static optimization design because of its optimized design. Both the objective function and the constraint function are static performance indicators, that is, the vibration characteristics generated when the gear is working are not considered. With the advancement of science and technology and the rapid development of mechanical transmission, people have higher and higher requirements for the dynamic performance of the gear transmission. The gear transmission system required to be designed has less vibration and noise, that is, the dynamic characteristics are better than the current static design optimization design of the gear transmission. It is relatively mature, but the dynamic performance optimization design is not much research. It is also in the initial stage of the dynamic performance optimization design of the gear transmission, which can be roughly divided into consideration of instantaneous The optimization design of beam dynamic response and the optimization design of pseudo-dynamic performance (referred to as dynamic performance optimization design) The difference between the latter and the former is that the constraint function is not the instantaneous dynamic response constraint function, but the dynamic performance index in a meshing period. Maximum or cumulative value. Due to the immature research on the optimal design of instantaneous constrained dynamic response at home and abroad, and the practical difficulties, it is mainly used to study the dynamic performance optimization design. The actual design of gear train dynamic performance optimization design is often used. Mathematical Programming Method Criterion Method Structure Perturbation Method, Inverse Perturbation Method, Gradient Projection Method Based on Sensitivity Analysis.
Due to the emergence of genetic algorithms, people began to use this random global optimization algorithm without sensitivity analysis to carry out dynamic optimization design of mechanical systems. The work in this area has been reported, but the genetic algorithm for gear train dynamic performance optimization design is not much, the author will discuss this in another paper. 5 Conclusion From the above discussion, we can see the analysis of gear transmission vibration And the optimization design research of dynamic performance has been paid more and more attention to the design of mechanical products. It should pay more attention to its dynamic performance instead of the traditional static performance. Only in this way, the designed gear transmission is closer to its The actual working state is more reliable.
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