Non-circular gear transmission, as a new type of gear transmission mode, is derived from cylindrical gear transmission in order to realize variable transmission ratio transmission. It can realize non-uniform rotation between two shafts and other specific motion laws (periodic motion, reciprocating motion, positive and negative motion, etc.) through specific pitch curve function. It is mainly applicable to low-speed and high-torque occasions [1], such as printing press, packaging machine Pumping unit reversing device (as shown in the figure), gear pump, hydraulic motor, flow meter, etc.
With the expansion of the application of non-circular gear and its key role and special requirements in the transmission process, its transmission performance and transmission accuracy can not meet the requirements well, which limits the application of non-circular gear in precision occasions.
The transmission error of gear transmission system is the main factor affecting its transmission performance and transmission accuracy. As for the constant ratio transmission gear, the general method is to establish the theoretical analysis model of the transmission error of the gear transmission system based on the finite element method or numerical analysis method, and analyze the influence trend of the geometric parameters and working conditions parameters on the transmission error of the system, so as to find a method to reduce the transmission error of the gear transmission system. Based on the above analysis methods, scholars at home and abroad have gradually made preliminary exploration and attempt to analyze the transmission error and transmission performance of non-circular gears. Liu Dawei [7-9] proposed that the transmission ratio curve of non-circular gear can be linearly divided by using the idea of differential element method to solve the problem that it is difficult to characterize the time-varying of pitch curve in the process of establishing the dynamic model of non-circular gear transmission system, and systematically analyzed the time-varying transmission law of non-circular gear, laying a certain theoretical foundation for the subsequent analysis of non-circular gear transmission error. David studied the no-load transmission error and instantaneous transmission ratio of non-circular gears, proposed a calculation method of no-load transmission error of non-circular gears, and analyzed the change trend of no-load transmission error and instantaneous transmission ratio. Through establishing the transmission error calculation model of the elliptical gear transmission system, Dong analyzed the influence of the eccentric ratio of the elliptical gear on the transmission pressure angle, instantaneous coincidence, transmission ratio error and transmission error, and verified the correctness of the analysis by using the finite element method. The error artificially introduced in the process of gear processing and installation will be reflected by the eccentric error and center distance error of the gear. Therefore, introducing the eccentric error of the gear into the transmission error calculation model of the gear transmission system, and analyzing the change law of the transmission error and the tooth side clearance has become a new gear transmission error analysis method. The existence of backlash plays an irreplaceable role in the non-circular gear transmission system and is a necessary condition to ensure the reasonable meshing of non-circular gears. The nonlinear change of backlash is the leading factor that causes the gear transmission system to exhibit nonlinear characteristics. Therefore, the eccentric error and backlash of noncircular gears have become one of the key work of researchers of noncircular gears at this stage. The comprehensive eccentricity error composed of eccentricity error and center distance error is equivalent to the instantaneous meshing line of non-circular gear, and the transmission error of non-circular gear transmission system is analyzed. The dynamic backlash of the non-circular gear is measured by setting up the non-circular gear transmission test-bed, and the backlash is controlled by adjusting the relative position relationship between the two teeth in real time through the angular displacement of the driving and driven wheels. Lin and Cai established a nonlinear dynamic model of the meshing of orthogonal curved gear and non-circular gear. By solving the mathematical model, the effects of different meshing frequencies and backlash on the dynamic response of the system were obtained. In view of the stability and accuracy of non-circular gear transmission, Han proposed a helical non-circular gear transmission scheme to reduce meshing impact and achieve backlash adjustment. The backlash of non-circular gear was analyzed by physical contact simulation method, and the effect of axial displacement adjustment on the backlash of non-circular gear pair was obtained.
The above research results have significant guiding significance for the analysis of noncircular transmission error and backlash. However, due to the particularity of noncircular gears, the correctness of applying the above analysis methods to the analysis of noncircular gear transmission error and backlash remains to be verified. Moreover, most of the documents have carried out relevant theoretical analysis, and the correctness of the analysis methods has not been verified through transmission tests. In view of this situation, on the basis of considering the eccentric error of noncircular gears, this paper establishes the bidirectional transmission error and backlash model of noncircular gears based on the meshing line increment method, obtains the method of obtaining backlash in the transmission test through theoretical analysis, and analyzes the influence of load on the transmission error and backlash of noncircular gears in combination with the transmission test.