Herringbone gear pair with constant meshing characteristics constructed tooth pair
Provided is a herringbone gear pair with a constant meshing characteristics constructed tooth pair. The herringbone gear pair with a constructed tooth pair includes a herringbone gear I with a constructed tooth pair and a herringbone gear II with a constructed tooth pair based on conjugate curves. In the present disclosure, normal tooth profile curves of the herringbone gear pair with a constructed tooth pair are continuous combined curves with the same curve shape, which facilitates machining by the same cutter. A common normal at an inflection point or a tangent point of the continuous combined curve passes through a pitch point of the gear pair, and a position of the inflection point or the tangent point can be adjusted according to an actual demand. A contact ratio of the herringbone gear pair with a constructed tooth pair is designed as an integer.
1 . A herringbone gear pair with a constant meshing characteristics constructed tooth pair, comprising a herringbone gear I with a constructed tooth pair based on conjugate curves and a herringbone gear II with a constructed tooth pair based on conjugate curves, wherein a normal tooth profile curve Γ s1 of the herringbone gear I with a constructed tooth pair and a normal tooth profile curve Γ s2 of the herringbone gear II with a constructed tooth pair are continuous combined curves Γ L with the same curve shape; 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 a common normal at the inflection point or the tangent point of the continuous combined curve passes through a pitch point of the herringbone gear pair; and the normal tooth profile curves are swept along given conjugate curves to obtain tooth surfaces of the herringbone gear I with a constructed tooth pair and the herringbone gear II with a constructed tooth pair;
wherein when the continuous combined curve Γ L is a combined curve Γ L1 of an odd power function curve and a tangent at an inflection point thereof, the continuous combined curve Γ L is formed by an odd power function curve Γ L12 and a tangent Γ L11 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 Γ L1 of the odd power function curve and the tangent at the inflection point thereof is as follows:
{
Γ
L
1
1
:
x
1
0
=
t
,
y
1
0
=
0
(
t
1
≤
t
<
0
)
Γ
L
1
2
:
x
1
0
=
t
,
y
1
0
=
A
t
2
n
-
1
(
0
≤
t
≤
t
2
)
,
wherein x 10 and y 10 are x-axis and y-axis coordinate values of the combined curve in the rectangular coordinate system, respectively; a parameter t is an independent variable of the equation; t 1 and t 2 are value ranges of the continuous curve; A is a coefficient of the equation; and n is a degree of the independent variable and is a positive integer.
2 . The herringbone gear pair with a constant meshing characteristics constructed tooth pair according to claim 1 , wherein a curve equation of the normal tooth profile curve Γ s1 of the herringbone gear I with a constructed tooth pair obtained by rotating the continuous combined curve Γ L around an origin of the rectangular coordinate system by an angle α 1 is as follows:
{
x
0
1
=
x
n
0
cos
α
1
-
y
n
0
sin
α
1
y
0
1
=
x
n
0
sin
α
1
+
y
n
0
cos
α
1
(
n
=
1
,
2
,
3
,
4
,
5
,
6
)
,
wherein x 01 and y 01 are x-axis and y-axis coordinate values of the normal tooth profile curve of the herringbone gear I with a constructed tooth pair in the rectangular coordinate system, respectively.
3 . The herringbone gear pair with a constant meshing characteristics constructed tooth pair according to claim 2 , wherein a curve equation of the normal tooth profile curve Γ s2 of the herringbone gear II with a constructed tooth pair obtained by rotating the normal tooth profile curve Γ s1 of the herringbone gear I with a constructed tooth pair around the origin of the rectangular coordinate system by an angle of 180° is as follows:
{
x
0
2
=
x
0
1
cos
(
180
°
)
-
y
0
1
sin
(
180
°
)
y
0
2
=
x
0
1
sin
(
180
°
)
+
y
0
1
cos
(
180
°
)
,
wherein x 02 and y 02 are x-axis and y-axis coordinate values of the normal tooth profile curve of the herringbone gear II with a constructed tooth pair in the rectangular coordinate system, respectively.
4 . The herringbone gear pair with a constant meshing characteristics constructed tooth pair according to claim 2 , wherein a tooth surface Σ 2 of the herringbone gear II with a constructed tooth pair is obtained by sweeping the normal tooth profile curve Γ s2 of the herringbone gear II with a constructed tooth pair along a given helix, with a tooth surface equation as follows:
{
x
Σ2
=
x
02
cos
θ
-
y
0
2
cos
β
sin
θ
+
(
a
-
r
)
cos
θ
y
Σ2
=
x
0
2
sin
θ
+
y
0
2
cos
β
cos
θ
+
(
a
-
r
)
sin
θ
z
Σ
2
=
±
(
r
θ
cot
β
-
y
0
2
sin
β
)
,
wherein x Σ2 , y Σ2 and z Σ2 are coordinate values of the tooth surface of the herringbone gear II with a constructed tooth pair, respectively; r is a pitch radius of the herringbone gear pair with a constant meshing characteristics constructed tooth pair, and θ is an angle of a given contact line; in the sign “±”, the sign “+” indicates a left tooth surface of the herringbone gear with a constructed tooth pair, and the sign “−” indicates a right tooth surface of the herringbone gear with a constructed tooth pair.
5 . The herringbone gear pair with a constant meshing characteristics constructed tooth pair according to claim 1 , wherein a tooth surface Σ 1 of the herringbone gear I with a constructed tooth pair is obtained by sweeping the normal tooth profile curve Γ s1 of the herringbone gear I with a constructed tooth pair along a given helix, with a tooth surface equation as follows:
{
x
Σ1
=
x
01
+
m
tan
β
y
1
=
y
01
z
Σ1
=
±
m
(
m
1
≤
m
≤
m
2
)
,
wherein x Σ1 , y Σ1 and z Σ1 are coordinate values of the tooth surface of the herringbone gear I with a constructed tooth pair, respectively; β is a helix angle of the gear pair, a parameter m is an independent variable of the equation, and m 1 and m 2 are value ranges of a tooth width; in the sign “±”, the sign “+” indicates a left tooth surface of the herringbone gear with a constructed tooth pair, and the sign “−” indicates a right tooth surface of the herringbone gear with a constructed tooth pair.
6 . The herringbone gear pair with a constant meshing characteristics constructed tooth pair according to claim 1 , wherein a contact ratio of the herringbone gear pair with a constant meshing characteristics constructed tooth pair is designed as an integer, thereby achieving meshing transmission with a constant stiffness.
7 . The herringbone gear pair with a constant meshing characteristics constructed tooth pair according to claim 1 , wherein the herringbone gear I with a constructed tooth pair and the herringbone gear II with a constructed tooth pair are designed to be symmetrical along the tooth width, thereby achieving a constant meshing force action line of the herringbone gear pair.