Transmission Error Analysis And Optimization Research On Vibration And Noise Of Gear System

Gear transmission is widely used in naval architecture and ocean engineering, traffic and transportation, metallurgy and building materials, engineering machinery for its high load capacity, long life span, high reliability and smooth operation. As an extremely important pivotal fundamental component in equipment manufacturing industry, gear transmission is the most widely used transferring form of power and motion in mechanical system equipment, and to a large extent determines the performance of equipment system, which means that gear transmission has truly vital strategic position. Along with the progress of science and technology, there are requirements of high power, high rotation speed, high precision and light weight for gear transmission. Owing to multiple excitation sources, high excited frequency and great meshing impact, the problems of vibration and noise become more and more prominent gradually. The dynamic characteristic of gear system will directly influence the overall performance and operational reliability of machinery equipment, and it is the restraining factor of precision and low noise for mechanical system. Therefore, coupling analysis of transmission error and optimization research of vibration and noise about gear system has important theoretic meaning and engineering practical value.This paper takes the marine gearbox as research object, and focuses on the problems about dynamic excitation mechanisms of gear system, characteristic of vibrant noise, optimization of dynamic characteristic. Analysis of transmission error about gear system, prediction of vibrant noise based on coupled acoustic-vibration, discrete vibration optimization of mixed multi-variables about transmission system and noise optimum research of multi-frequency and multi-point about structure system are both carried out. A new thinking about reduction of vibration and noise about gear system is provided. The main contents of this paper are as follows:(1) Tooth profile surface equations about the region of tooth flank with no modification, relief zone of tooth tip, modification region of root and root transition arc area are derived via space meshing theory. This paper also formulates the parametric modeling program of the precise tooth surface about helical gear which adopts tip relief, root relief, end relief and longitudinal crowning modification. Based upon existing test parameters, the dynamic meshing behavior of gear pair is calculated and compared with experiment result to verify the model rationality.(2) Synthetically considering the influence of tooth modification(profile modification and longitudinal relief), machining errors and assembly errors, the FEM modeling method of gearing is put forward which includes coupling of multi-factors such as error and modification. Comprehensive effect of these factors to the static transmission error about transmission system is researched. The dynamic model of coupled bend-torsion-axis about transmission system is established via lumped mass method, and on this basis, the dynamic transmission error of gear transmission system is calculated, which provides error excitation force for the analysis about vibration and noise of gear system.(3) Combining with the computing result of dynamic transmission error and modal test data of gear system, the analytical model of coupling vibration about gear system is built, which includes gear pair, transmission shaft, bearing and gearbox. The vibration characteristics such as modal characteristic, vibrant severity and structure-borne noise is researched and compared with the test result of vibration and noise obtained by marine comprehensive performance test bench. This validates the rationality of the analytical method for coupling vibration about gear system.(4) Based on the vibration analysis of gear system, the radiate noise characteristic of coupled acoustic-vibration about gear system is studied. The dynamic reaction force of bearing is solved according to the dynamic model about rigid and flexible coupling system. Treating these forces as acoustic boundary conditions, the prediction model of radiate noise about gearbox is established, which contains structure grid, acoustic grid and field point grid. The sound pressure of case surface and filed point is calculated and compared with test result. Calculating result is in line with test result which means a referencing method for accurate estimation of structure radiate noise is gained.(5) After the setting up of the optimization model of dynamic performance about gearbox transmission system, discrete optimization program of mixed multiple variables is compiled. Adopting the branch and bound algorithm, the variables of optimization design such as tooth number, modulus, helical angle, modification coefficient and tooth width of transmission system are solved, and the vibration acceleration which is the objective function value is then obtained. On this basis, by means that the objective function is to get the minimum sound pressure of multiple fields and multiple frequency bands, the design variable is structural parameter of gear system, this paper establishes the optimization model of noise. Via multi objective optimization algorithm with normal-boundary intersection method, the acoustic optimum of multi-frequency and multi-point is carried out, with its results, obvious optimum effect is acquired.