The geometric relationship of pitch cone parameters of hypoid gear pair is shown in the figure, and the included angle of two straight lines h1p and H2P ε’ Is the offset angle. According to the definition of offset angle, the offset angles of large and small gears of hypoid gear pair are η and ε ， From the geometric relationship in the figure:
From the geometric relationship in the figure, it can be deduced that the offset angle of the pinion meets the following relationship:
Thus, the offset angle of the big gear can be determined:
Similarly:
According to the analysis diagram, the pitch cone angle of the pinion in the pinion shaft section passing through the pitch point P can be obtained,
Similarly,
So the offset angle of hypoid gear pair
Referring to the figure, the pitch radius 2R, 1R pitch cone distance R1, R2 and pitch cone angle of large and small gears of hypoid gear pair can be obtained δ 1、 δ The functional relationship between 2 is,
Let the intersection distance of the pitch cone of hypoid gear o1h1 = g, O2H2 = Z, and a positive value indicates that the pitch cone vertex is outside the intersection, and vice versa. At the same time, the distance from node P along the wheel axis to intersection O2 is ZG, as shown in the figure, a2o2 = Z P, which can be obtained from the geometric relationship in the figure:
The distance from the intersection of the hypoid gear pair ZG to the hypoid gear pair axis is set to be A1 = 1,
When the distance z from the intersection to the apex of the large wheel pitch cone is obtained, the distance G from the intersection to the apex of the small wheel pitch cone can be expressed by Z value.
The offset angle of hypoid gear can be obtained from the geometric relationship ε’ The parameter relationship is:
Similarly:
The offset angle of hypoid gear pair can be obtained from the above parameter relationship ε And pinion offset angle η The relationship between them is:
