# Spur gear meshing

This paper mainly studies spur gears from the perspective of dynamic contact analysis and consults relevant data at home and abroad. The research on spur gear contact is summarized as follows. The contact state of spur gears is very complex, because the radius of curvature at the meshing point changes with the change of meshing position. It is a common research method to simplify the model in the contact analysis of spur gear engagement. The contact mechanics theory put forward by Herz means that the contact mode of a pair of spur gears is replaced by the contact mode of a pair of parallel cylinders, so as to carry out mechanical calculation, which brings great convenience to the calculation, and the calculation error of this method is not large, because the contact area of spur gears is very small compared with the curvature radius of spur gears, and its influence can be ignored.

In 1882, the physicist Hertz published an article on the contact of elastic solids. In this famous article, Hertz discussed the stress and deformation caused by the contact of two incompatible objects, and established the discipline of contact mechanics. In the field of mechanical engineering, contact mechanics is widely used. However, Herz did not consider the friction of the contact surface when studying the contact problem, and assumed that the two objects were ideal elastomers. Therefore, in the 20th century, various researchers and scholars began to further study these problems.

Johnson wrote and published contact mechanics in 1985, which has become a classic book in the academic circles. This book makes a breakthrough in the study of rolling problems between solids, as well as practical engineering problems such as lubrication and thermoelastic contact. In 1990, Kalker wrote and published the book rolling contact of three-dimensional elastic bodies. In this book, the author studied the three-dimensional elastic contact when two objects were in contact, taking into account the Coulomb friction. Another masterpiece of contact mechanics is the paper contact mechanics in tribology published by Goryacheva in 1998, which skillfully links wear, friction and contact mechanics. Therefore, this book is considered by many scholars as the representative of contact mechanics in tribology. The meshing of spur gears is a very typical contact problem. Contact mechanics has been widely used in the study of spur gear contact. The classic one is that the great scholar Tsay proposed an accurate mathematical model of involute spur gear in 1989. Through this model, the problems of spur gear meshing in mathematical simulation can be solved. With the further development of the discipline, this theoretical model is finally applied to the well-known field of numerical simulation to realize the contact analysis of spur gear.

In China, the research and application in this field started relatively late, but in this field, extensive research has been carried out in China recently. In 1987, Liugeng et al. Used the finite element linear programming method to obtain the stress distribution law in the contact area under the meshing state of spur gears, and studied the influence of the helical angle of spur gears on the maximum shear stress in the contact area. In 1989, on the basis of previous studies, caoyuanbiao and others believed that the force on spur gears was not limited to the previous point of view, and spur gear meshing error, contact deformation, manufacturing tolerance and other factors were regarded as another important aspect affecting the force on spur gears, obtained the stress distribution nephogram, and perfected the analysis of contact load. In 1998, the tooth root stress, tooth root deformation and stress distribution on the contact surface were found by yangshenghua using the method of calculation and simulation, and the accuracy of the two methods was analyzed and compared. The finite element method was verified by the numerical calculation method. Nine years later, Xie Zuowei used the same calculation method to simulate and verify the accuracy of the calculation based on Herz theory. Therefore, there is a more scientific solution for spur gear contact.

Lijingcai et al. Used a large number of lattice to replace the contact surface of spur gear on the basis of tooth surface model in 2008. In the research process, the algorithm for automatically solving the initial value of tooth surface contact surface was established, and the accuracy of the algorithm was also proved. In 2009, weiyangang comprehensively analyzed the contact stress of involute spur gears in the meshing process by using the finite element method. In the research of spur gears, he also pointed out that the contact surface temperature is easy to rise. It is of great significance to study and analyze the temperature field distribution on the contact surface of spur gears.

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