Study on the method of analyzing the time-variant internal mesh stiffness of helical gears considering the flexibility of the gear ring

In a 9-speed transmission, as a key participant of a planetary wheel system, the gear ring will be subjected to elastic deformation as a result of the meshing action, affecting the smoothness of the transmission. Firstly, the time-variant stiffness of helical gears is calculated using the potential energy method, the time-variant characteristics of bending rigidity, shear rigidity and compression rigidity are analyzed; secondly, the time -variant gear ring stiffness is computed using the bending beam theory, in which the change in gear ring rigidity is incorporated into the simplified model of the gear ring, and the circumferential displacement, radial displacement and bending angle of the gear ring is used to calculate the gear ring deformation variables and the time-variant stiffness of the internal gear ring; finally, the time-variant stiffness of planetary helical gear is calculated according to parallel connection theory. Finally, based on parallel theory, the comprehensive time -variant mesh stiffness of planetary helical gears was computed, and the ring stiffness influence on the comprehensive time-variant mesh stiffness of planetary helical gears was analyzed in meshing with single and double teeth. The average difference in the zone is 8.9%. The experiment shows that there are two peak values of tooth ring deformation in a meshing period between tooth ring and gear, and the peak value of tooth ring deformation near the meshing point is larger. At low rotational speed, the predicted strain value of the tooth surface of the gear ring has an average difference of 10.6% and 8.6% from the measured value of strain measuring point No. 1 and No. 2.