Internal meshing cylindrical gear pair with constant meshing characteristics constructed tooth pair

An internal meshing cylindrical gear pair with a constant meshing characteristics constructed tooth pair, comprising an external cylindrical gear with a constructed tooth pair and an internal cylindrical gear with a constructed tooth pair as a pair based on conjugate curves, wherein a normal tooth profile curve Γs1 of the external cylindrical gear with a constructed tooth pair and a normal tooth profile curve Γs2 of the internal cylindrical gear with a constructed tooth pair are continuous combined curves ΓL with the same curve shape, and the continuous combined curves ΓL comprise a combined curve ΓL1 of an odd power function curve and a tangent at an inflection point thereof;

• the continuous combined curve is formed by two continuous curves, a connection point of the two continuous curves is an inflection point or a tangent point of the continuous combined curve, and the inflection point or the tangent point of the continuous combined curve is a designated point located on a meshing force action line of the internal meshing cylindrical gear pair with a constructed tooth pair;
• and the normal tooth profile curves are swept along given conjugate curves to obtain tooth surfaces of the external cylindrical gear with a constructed tooth pair and the internal cylindrical gear with a constructed tooth pair;
• wherein when the continuous combined curve ΓL is the combined curve ΓL1 of the odd power function curve and the tangent at the inflection point thereof, the continuous combined curve ΓL is formed by an odd power function curve ΓL12 and a tangent ΓL11 at an inflection point of the odd power function curve;
• a rectangular coordinate system is established at the tangent point of the continuous combined curve, and an equation of the combined curve ΓL1 of the odd power function curve and the tangent at the inflection point thereof is as follows:
• {
• Γ
• L
• ⁢
• 11
• ∶
• x
• 10
• =
• t
• ,
• y
• 10
• =
• 0
• ⁢
• (
• t
• 1
• ≤
• t
• <
• 0
• )
• Γ
• L
• ⁢
• 12
• ∶
• x
• 10
• =
• t
• ,
• y
• 10
• =
• at
• 2
• ⁢
• n
• -
• 1
• ⁢
• (
• 0
• ≤
• t
• ≤
• t
• 2
• )
• ,
• wherein a parameter tis an independent variable of the equation;
• t1 and t2 are value ranges of the continuous curve;
• a is a coefficient of the equation;
• n is a degree of the independent variable and is a positive integer;
• and x10 and y10 are x-axis and y-axis coordinate values of the combined curve in the rectangular coordinate system, respectively.