Research On Time-varying Meshing Stiffness Of Marine Bevoloid Gear System

Based on the urgency of my country’s construction of a marine power and the development of marine technology,it is necessary to continuously update and iterate on naval architecture.Marine engineering is an indispensable part of ship research,which is related to the power handling performance of ships.The gear system,as an important part of the transmission device,has important theoretical and practical application value for the continuous research on its inherent characteristics and dynamics.As a new type of gear,beveloid gear has the advantages of compensating axis error,smooth transmission,eliminating backlash,etc.It is widely used in occasions where there is a high demand for transmission accuracy and stability.However,the current research on calculating the time-varying meshing stiffness of beveloid gear pairs is still insufficient.It is urgent to propose a method that can quickly and accurately calculate the stiffness of beveloid gears.In order to facilitate the analysis of the contact process of the beveloid gear,this paper firstly establishes the expression of the tooth profile of the beveloid gear.By using the method of meshing with the standard rack,and then performing space conversion,the expression of the space contact line between the beveloid gear and the rack is indirectly derived.The tooth profile surface of the beveloid gear is enveloped and drawn.The formed tooth surface proves the correctness of the derivation process.Next,assuming that a pair of beveloid gears meshing with the same rack,the contact line equation of the parallel shaft beveloid gear pair is derived.Based on the slicing method,analytical algorithms for calculating the stiffness of helical gears,spur beveloid gears and helical beveloid gears are proposed.For helical gears and spur beveloid gears,the Ishikawa formula was used to calculate the deformation of the gear tooth slices,and then the meshing stiffness was calculated.For helical beveloid gears,the energy principle is used to calculate the deformation of gear tooth slices,and the stiffness calculation method of helical beveloid gears is deduced.Next,change the parameters of the helical beveloid gear and analyze the influence of different parameters on the stiffness.The analytical method is verified by the finite element method and the experimental method respectively.The finite element simulation method is used to calculate the stiffness of the helical gear and the helical beveloid gear.The possible causes of the error are analyzed by comparing with the analytical method.The stiffness measurement test was designed for the helical beveloid gear.Besides,the two-dimensional CAD drawings of the non-standard parts were drawn,which laid the foundation for the subsequent processing.Based on the test results of others,the calculation process of gear stiffness was modified and the rotational stiffness of the reducer was analyzed.Finally,the overall stiffness of the reducer was calculated,which was compared with the test results to prove the correctness of the analytical calculation results.Using the meshing stiffness solution method proposed in this paper,the timevarying meshing stiffnesses of helical gears,spur beveloid gears and helical beveloid gears are calculated respectively.Comparing the analytical results and finite element results of helical gears and helical beveloid gears,the calculation results of the two methods are at the same order of magnitude and can be mutually verified.For the helical beveloid gear,the test results and the analytical calculation results are compared.It shows the test results can prove the correctness of the analytical calculation method.