Gear Precision Modeling And Analysis Of Transmission Precision Based On FE Method

With the development of mechanical equipment towards high precision and high load,there is a higher requirement on the transmission accuracy of the gear transmission system.However,the accuracy of the transmission system is affected by the gear error in the manufacturing process and the stiffness of the supporting system.In order to improve the transmission accuracy of the gear system,it is necessary to know the relationship between the gear error and the stiffness of the support with the transmission accuracy.Finite element method is the most efficient,accurate,intuitive method for gear contact analysis,but the current meshing method and the solving method are unable to meet the quantitative analysis of precision gear contact problem.Therefore,this paper propose a new grid forming method based on the instantaneous contact line,establishing node-to-node precise spur gear contact model;set up the helical gear precision contact model based on the method of spiral rotary replication;embedded gear error and supporting stiffness,researching the accuracy of contact characteristics by the method of quasi static analysis,the specific contents are as follows:To lay the theoretical foundation for the parametric modeling,this paper solve the involute line,the involute line and the addendum circle of gear according to geometry theory.Get the gear transition curve parameter equation based on the conjugate meshing theory of gear and introduce the parameters of involute spiral surface equation for the foundation of establishing the straight gear,helical gear finite element model.The first time introduce the concept of node-to-node modeling method based on the finite element contact theory,which suffers the foundation for the analysis of the relationship between gear error and supporting stiffness with transmission accuracy by quasi static analysis.To make the spur gear FE model exact contact,this paper solve instantaneous meshing point of the end face of gear based on the method of instantaneous contact line,and the get the contact point of involute line by matrix transform.Integrate the point of involute line close to the addendum circle and transition curve of gear.Compare the node to node model and the free meshing grid model to validate the model;Study the relationship between displacements of the contact node with the calculation accuracy by comparing the different node position affect the result of stress.To study the whole cycle transmission precision of spur gear,in this paper,establish the quasi-static finite element model by study the quasi-static mathematical model.Study the influence of tooth profile error,eccentric error,tooth pitch error and support stiffness effect on the transmission precision.Simplify the transmission system support by set up springs between the bearing holes in the gear box;respectively study the influence of bearing and gear box stiffness on transmission accuracy.To establish an exact helical model and get the transmission precision analysis,this paper analyze the advantages of different modeling methods by comparing the analysis of modeling method of instantaneous contact line,rotation stretching method and do sensitivity analysis for the same gear parameters,which provide the theoretical basis for the accurate modeling of helical gear.Study the relationship between the transmission accuracy with brace stiffness and cumulative pitch error of gear.In order to gear precision modeling and analysis of transmission precision,in this paper,establish the FE gear precision contact model and add error of gear and bearing stiffness quantitatively,which can reveal the relationship between the error of gear and bearing stiffness and transmission precision.