For high-speed and high-power transmission spur gears used in high-speed railways, ships, helicopters, megawatt wind turbines, and other applications, as well as spur gears used in transmission devices with high comfort requirements such as automobiles, shaping has become an essential component of the spur gear design process. Proper spur gear modification can not only greatly reduce or even avoid dynamic loads, vibration, and noise during the meshing process of spur gears, but also greatly improve transmission accuracy and spur gear strength.
Since Walker published a discussion on involute spur gear tooth modification in 1938, research on tooth profile modification has never stopped. There are dozens of publicly published tooth profile modification formulas, and many companies keep spur gear modification methods and technologies confidential to the public.
Early research on tooth profile modification mainly considered the impact of tooth profile elastic deformation. With the development of technology and the widespread application of computers, there are more and more comprehensive factors to consider in the modification of spur gears. Wang Tong et al. used the finite element method to analyze and calculate the deformation of spur gear shafts. Based on the overall elastic deformation of spur gear shafts and the deformation of gear teeth, a three-dimensional tooth alignment modification study was conducted; Qiu Liangheng et al. studied tooth profile modification based on thermal deformation of spur gears; Luo Biao et al. conducted tooth profile modification design under thermal elastic coupling deformation conditions; Sun Yuehai et al. studied the tooth profile modification of spur gears with errors; Lee et al. included in the modification the elastic deformation of spur gears, shafts, and gearboxes under load, as well as the manufacturing tolerances of spur gears. In recent years, gear modification has deepened towards system optimization and three-dimensional comprehensive modification. Korta et al. optimized and modified the tooth surface using the response surface method, reducing the amplitude of transmission error and the contact stress on the tooth surface; Jia Chao and others completed multi-objective optimization and modification of high-speed internal meshing herringbone spur gears. After the tooth surface modification, the amplitude of load-bearing transmission error decreased, the flash temperature in the meshing in and out areas decreased, and the load distribution on the tooth surface was improved.
The effect of lubrication on spur gear transmission is self-evident, but so far all research on spur gear modification has not considered the role and influence of lubrication. High end spur gears used for high-speed trains, ships, helicopters, megawatt wind turbines, automobiles, etc. generally operate in an elastohydrodynamic lubrication state. Research has shown that the elastohydrodynamic oil film between tooth surfaces has significant stiffness and damping characteristics; Tsuha et al. pointed out that in the state of elastohydrodynamic lubrication, due to the presence and influence of elastohydrodynamic oil film, the Hertz contact stiffness without considering elastohydrodynamic lubrication increases by 2-4 times compared to the contact stiffness of friction pairs. This huge change in contact stiffness is bound to cause significant changes in tooth surface contact deformation, which objectively requires that the influence of lubrication must be taken into account during shaping. However, current research on how to consider the influence of elastohydrodynamic lubrication in tooth profile modification is still blank. Based on the theory of elastohydrodynamic lubrication, the elastohydrodynamic oil film is simplified as a linearized spring and damping. This paper establishes a tribodynamic coupling model for linear contact elastohydrodynamic friction pairs, and uses numerical methods to obtain the stiffness of the tooth surface elastohydrodynamic friction pair during the meshing process of spur gears. The changes in the meshing stiffness and modification amount of spur gears before and after considering elastohydrodynamic lubrication are calculated and compared; A new method is proposed to replace the meshing stiffness of spur gears with the meshing stiffness of tooth surface elastohydrodynamic friction pairs to calculate the amount of tooth profile modification and carry out spur gear modification. The simulation results show that compared to the ISO modification method, the modification effect based on the meshing stiffness of the elastohydrodynamic friction pair is better.