A Model for Analysis of Time-Varying Mesh Stiffness of Helical Gears with Misalignment Errors

A mathematical model is proposed to calculate the time-varying mesh stiffness (TVMS) of helical gears under the condition of gear misalignment by combining the slice method. The proposed method aims to reveal the influences of different misalignment errors (centre distance error, action plane error and off action plane error) on the TVMS of helical gears. The results show that the misalignment error on the plane of action has an enormous influence on mesh characteristics and that it not only changes the contact line and load distribution but also results in a reduced TVMS. Meanwhile, the centre distance error causes the amplitude fluctuation of TVMS and transmission error (TE). The misalignment error on the off plane of action has almost no effect on TVMS and TE. The results can be used for vibration prediction and misalignment fault diagnosis

Prediction and experimental study on structure and radiation noise of subway gearbox

A dynamic finite element model of a coupled gear-rotor-bearing-housing gear system is developed by combining the gearbox transmission model with the housing structure model of subway gearbox with taking stiffness excitation, error exaction and meshing impact exaction as the dynamic excitation. The intrinsic modes and vibration response are computed in the numerical simulation process. Then an acoustic boundary element model of the gearbox is established by using the result of vibration displacement of the nodes on gearbox surface as acoustic boundary conditions. The surface sound pressure of gearbox and radiation noise of field points are solved by the direct boundary element method. In fact the proposed modeling approach not only provides a more comprehensive understanding of the subway gear system, but also can serve as the basis for dynamic and noise optimization of gear system. Finally a vibration and radiation noise experimental study is performed on the subway gear system. The vibration and radiation noise at some concerned locations are monitored and analysed. The comparison analysis shows that computational results are in good agreement with the data of experiment tests

An approach to calculate radiation noise of gear system

A rigid-flexible coupling multi-body dynamic model which contains the structure system and transmission system of gear device is developed taking account of the internal excitations such as the time-varying mesh stiffness, tooth backlash and bearing stiffness and the external torque and speed excitation. Then the dynamic meshing forces of gear pairs and bearing reaction forces are calculated based on the dynamic theory of multi-body system. Afterwards, a vibro-acoustic coupling model of the gear system is established by taking the frequency histories of bearing reaction forces as the boundary conditions, and then the surface sound pressure of gearbox and the radiation noise of outer sound field are calculated. In fact, the proposed model would provide a quicker approach to analyze the radiation noise of the gear system during the design phase. Finally, the radiation noise experimental study is performed on the experimental prototype to verify the rationality of the analysis. The comparison analysis shows that computational results are in good agreement with the data of experiment test

Mathematical models and dynamic contact analysis of involute/noninvolute beveloid gears

This study investigates an approach for parametric modeling and dynamic contact analysis of involute/noninvolute beveloid gears. Firstly, the mathematical models of involute/noninvolute beveloid gear pairs are derived based on the theory of gearing and the generation mechanism. Then the parametric modeling programs of involute/noninvolute beveloid gears are developed to automatically generate exact model via a Matlab code. Subsequently, a numerical example of intersecting axes beveloid gears is presented to evaluate the dynamic stress distribution and dynamic transmission error. Finally, the dynamic contact characteristics of involute and noninvolute beveloid gears are calculated by three-dimensional dynamic contact finite element method, respectively. The results show that the noninvolute beveloid gear pairs can relieve the high dynamic stress and contact shock problem of intersecting axes beveloid gear pairs

Analytical and computational method of structure-borne noise and shock resistance of gear system

An approach to synthetically evaluate structure-borne noise and shock resistance of gear system is proposed. Firstly, dynamic finite element mesh model of gear system which includes shafts, bearings, gears and housing is established by using spring element, tetrahedral element and hexahedral element. Then dynamic finite element analysis model of gear system is gotten by loading the dynamic excitation force which can be calculated via the computation program of gear pair stiffness excitation, error excitation and impact excitation onto the tooth meshing line as boundary conditions. And the dynamic response of gear system is analyzed by using modal superposition method, and the vibration response experimental study of gear system is performed on the gearbox test-bed. The comparative analysis shows that computational results of the vibration response are in good agreement with the data of experiment tests and it could verify the rationality of dynamic finite element mesh model of gear system. Finally, taking acceleration shock excitation load into account on the basis of the dynamic finite element mesh model, the impact response of gear system is solved, and the shock resistance is analyzed based on the strength decision criterion

An approach to calculate radiation noise of gear system

A rigid-flexible coupling multi-body dynamic model which contains the structure system and transmission system of gear device is developed taking account of the internal excitations such as the time-varying mesh stiffness, tooth backlash and bearing stiffness and the external torque and speed excitation. Then the dynamic meshing forces of gear pairs and bearing reaction forces are calculated based on the dynamic theory of multi-body system. Afterwards, a vibro-acoustic coupling model of the gear system is established by taking the frequency histories of bearing reaction forces as the boundary conditions, and then the surface sound pressure of gearbox and the radiation noise of outer sound field are calculated. In fact, the proposed model would provide a quicker approach to analyze the radiation noise of the gear system during the design phase. Finally, the radiation noise experimental study is performed on the experimental prototype to verify the rationality of the analysis. The comparison analysis shows that computational results are in good agreement with the data of experiment test

Modal Analysis and an Experimental Study Into a Marine Gearbox Featuring Confluence Transmission

An approach to calculating vibration modal characteristics of a marine gear system featuring confluence transmission based on the theoretical and the experimental modal analysis is given in view of the fact that it is difficult to accurately determine the modal data of the system because of its complex vibration mechanism. Firstly, a dynamic finite element model of a coupled gear-rotor-bearing-housing system is developed by combining the gearbox transmission model with the gearbox housing model using the modal parameter identification data. Then, the modal frequency and the mode of vibration can be obtained. In fact, the proposed model can provide a faster approach to analysing the mode of the gear system vibration. Finally, experimental testing of the mode of vibration is performed on the experimental prototype to verify the rationality of the theoretical analysis. A comparison of the two sets of results shows that the experimental results are in good agreement with the computational results, with a maximum error of 6.3%

An approach to calculate radiation noise of gear system

A rigid-flexible coupling multi-body dynamic model which contains the structure system and transmission system of gear device is developed taking account of the internal excitations such as the time-varying mesh stiffness, tooth backlash and bearing stiffness and the external torque and speed excitation. Then the dynamic meshing forces of gear pairs and bearing reaction forces are calculated based on the dynamic theory of multi-body system. Afterwards, a vibro-acoustic coupling model of the gear system is established by taking the frequency histories of bearing reaction forces as the boundary conditions, and then the surface sound pressure of gearbox and the radiation noise of outer sound field are calculated. In fact, the proposed model would provide a quicker approach to analyze the radiation noise of the gear system during the design phase. Finally, the radiation noise experimental study is performed on the experimental prototype to verify the rationality of the analysis. The comparison analysis shows that computational results are in good agreement with the data of experiment test

Research on dynamical characteristics of planetary gear system with tooth pitting

The dynamical characteristics research of planetary gear system with tooth pitting is useful for early fault diagnosis and monitor. However, it is an unsolved puzzle to establish the relationship between tooth pitting and dynamical characteristics. In this study, a pitting fault analytical model is proposed to investigate the effects of tooth pitting on the gear mesh stiffness. Then this mesh stiffness with tooth pitting is incorporated into a dynamical model of planetary gear system, and the effects of the tooth pitting on the vibration characteristics is investigated. The simulated results show that the time-varying mesh stiffness is reduced with tooth pitting propagations along width or depth direction. The mesh frequency and its harmonics are mainly frequencies components in the frequency spectrum of dynamic mesh force, but sidebands caused by the tooth pitting are more sensitive than the mesh frequency and its harmonics. The tooth pitting frequency and its harmonics also increase with the rising rotational speed of the sun gear. In addition, both relative statistical indicators of RMS and Kurtosis increase with the growth of tooth pitting size. But the relative indicators have different sensitivity on the vibration signal type. These results could supply some guidance to the condition monitoring and fault diagnosis of planetary gear system, especially to the gear tooth pitting at early stage