The time variation of contact wire is one of the important characteristics of helical gear transmission. The change of the number of contact lines will cause the change of stiffness and tooth friction, which is the main source of vibration and noise. Kubo and Kiyono research show that with the increase of helical angle of helical gear, the number of contact lines of helical gear increases in the meshing process, which helps to reduce the exciting force and make the operation stable. This is an important reason why the transmission of helical gear is more stable than that of spur gear. With the deepening of research, it is found that the tooth friction is also one of the important excitation sources for the vibration and noise of helical gears. It is particularly important to study the influence of tooth friction on the dynamic characteristics of helical gears, especially for large coincidence helical gears.
Breaking through the limitation that the calculation of time-varying contact line length in Chinmaya Kar and a.r.mohanty’s article published in mechanism and machine theory in 2007 is limited by different meshing plane shapes such as high helical teeth and wide helical teeth and the number of contact lines engaged at the same time, the general algorithm for time-varying contact line calculation of helical gear multi tooth meshing is derived according to the helical gear meshing principle, and the change law of time-varying contact line of helical gear is analyzed. On this basis, considering the friction effect of helical gear under mixed elastohydrodynamic lubrication, the algorithm of time-varying friction and time-varying friction torque on the tooth surface is constructed, the change of time-varying friction and time-varying friction torque on the tooth surface is analyzed, and its change law is given.
A fast algorithm of time-varying contact line length, time-varying friction force and friction torque for helical gear multi tooth meshing is given. The dynamic characteristics of time-varying contact line, time-varying friction force and friction torque are analyzed, and the following conclusions are obtained:
- it breaks through the condition limitation of numerical calculation of contact line length, expands the application scope of numerical calculation of contact line length, and is applicable to the time-varying contact line length calculation of helical gears with wide helical teeth, high helical teeth and spur gears, and the algorithm is convenient, accurate and practical.
- the time-varying contact line length fluctuation is affected by the contact line position at the initial time of meshing in the meshing plane, revealing the condition for the minimum change in the total length of the contact line: at the initial time, when L1 (the shortest distance from the upper end of the contact line to the right end of the meshing area at the initial time of meshing) is equal to the tooth pitch of the end face, When L2 (the shortest distance from the upper end of the contact line to the left end of the engagement area at the start of engagement) and L4 (the shortest distance from the lower end of the contact line to the right end of the engagement area at the start of engagement) are equal, the total length of the contact line remains unchanged.
- after analyzing the fluctuation of tooth friction and tooth friction torque, it is found that the fluctuation of time-varying contact line length is an important reason for the fluctuation of tooth friction and tooth friction torque. Within the selected parameter range, the time-varying contact line length, tooth friction and tooth friction torque fluctuation are the smallest at 20 °, which provides a theoretical basis for helical gear parameter design and engineering optimization.