US 2024/0125374 A1 · A NON-ORTHOGONAL ELLIPTICAL TOROIDAL WORM GEAR PAIR

Abstract

The present invention belongs to the field of mechanical transmission technology, and proposes a non-orthogonal elliptical toroidal worm gear pair, including an involute cylindrical gear and an elliptical toroidal worm formed by a primary envelope of the involute cylindrical gear; both adopt spatial non-orthogonal transmission, and the shaft angle satisfies the self-locking condition and the restriction condition of minimum tooth top width; the toroidal generatrix of the elliptical toroidal worm is elliptical, which can increase the number of meshing teeth and the total length of instantaneous contact line. A non-orthogonal elliptical toroidal worm gear pair proposed in this invention has the characteristics of toroidal worm drive and can realize the whole facewidth of the gear to participate in the meshing drive. It can be used in the fields of precision continuous indexing transmission, continuous lapping of cylindrical gear tooth flank, and has good popularization application value and industrialization prospect.

A non-orthogonal elliptical toroidal worm gear pair, which is characterized in that the non-orthogonal elliptical toroidal worm gear pair comprising an involute cylindrical gear and an elliptical toroidal worm spreading from a single-envelope of the involute cylindrical gear;

the involute cylindrical gear includes involute spur gear and involute helical gear;
the tooth flank of the involute spur cylindrical gear is the involute cylindrical surface formed by the involute stretching along the axial direction, the tooth flank of the involute helical gear is the involute helicoid formed by the involute doing spiral movement along the axial direction, the involute is generated by the generating line doing pure rolling on the base circle;
the involute cylindrical gear is ground and shaped by the hard tooth flank wear-resistant material;
the equations of the left flank of the involute cylindrical gear are as follows:
{
x
1
⁢
L
=
r
b
⁢
cos
⁡
(
u
-
σ
0
-
α
1
⁢
λ
)
+
r
b
⁢
u
⁢
sin
⁡
(
u
-
σ
0
-
α
1
⁢
λ
)
y
1
⁢
L
=
-
r
b
⁢
sin
⁡
(
u
-
σ
0
-
α
1
⁢
λ
)
+
r
b
⁢
u
⁢
cos
⁡
(
u
-
σ
0
-
α
1
⁢
λ
)
z
1
⁢
L
=
α
1
⁢
ρ
1
⁢
λ
+
α
2
⁢
h
L
where, x1L is the x coordinate of each point on the left tooth surface, y1L is the y coordinate of each point on the left tooth surface, z1L is the z coordinate of each point on the left tooth surface;
rb is the radius of the base circle of the involute gear;
u is the rolling angle formed by the dominant involute tooth profile;
a σ0 is half of the base circular angle corresponding to the transverse base thickness of the involute cylindrical gear;
hL is the axial parameter of the tooth flank;
ρ1 is the helical parameter;
λ is the angle at which the involute makes a spiral motion along the axial direction;
α1 is the parameter taking the value of 0 or 1, α2 is the parameter taking the value of 0 or 1;
the equations of the right flank of the involute cylindrical gear are as follows:
{
x
1
⁢
R
=
r
b
⁢
cos
⁡
(
u
-
σ
0
+
α
1
⁢
λ
)
+
r
b
⁢
u
⁢
sin
⁡
(
u
-
σ
0
+
α
1
⁢
λ
)
y
1
⁢
R
=
r
b
⁢
sin
⁡
(
u
-
σ
0
+
α
1
⁢
λ
)
-
r
b
⁢
u
⁢
cos
⁡
(
u
-
σ
0
+
α
1
⁢
λ
)
z
1
⁢
R
=
α
1
⁢
ρ
1
⁢
λ
+
α
2
⁢
h
R
where, x1R is the x coordinate of each point on the right flank, y1R is the y coordinate of each point on the right flank, z1R is the z coordinate of each point on the right flank;
hR is the right flank axial parameter;
when the tooth flank equations of the above involute cylindrical gear satisfies α1=0 and α2=1, the corresponding left and right tooth flank equation is the tooth flank equation of the involute spur cylindrical gear;
similarly, when α1=1 and α2=0, the corresponding left and right tooth flank equation is the tooth flank equations of the involute helical cylindrical gear;
the reference surface of the elliptical toroidal worm described in the present invention is an elliptical toroidal surface, the generatrix of the elliptical toroidal surface is the intersection line between the inclined section and the reference cylinder within the working length of the worm, the inclined section passes through the axis of rotation of the elliptical toroidal worm and the angle with the horizontal plane is the shaft angle ε;
the equation satisfied by the generatrix of the elliptical toroidal surface is as follows:
y
2
(
r
⁢
csc
⁢
ε
)
2
+
x
2
r
2
=
1
where, r is the radius of the base circle of the involute indexing cylinder, x is the x-coordinate of any point on the generatrix, y is the y-coordinate of any point on the generatrix;
the elliptical toroidal worm and involute cylindrical gear adopt spatially non-orthogonal transmission, and the shaft angle is determined according to the self-locking condition;
the facewidth of the involute cylindrical gear is related to the working length of the elliptical toroidal worm and the shaft angle, and in order to achieve the full facewidth of the involute cylindrical gear to participate in the mesh, the following relationship should be satisfied:
b=L sin ε
where, b is the facewidth of the involute cylindrical gear, L is the working length of the elliptical toroidal worm gear;
the tooth flank of the elliptical toroidal worm is made of the involute spur gear's involute cylindrical surface or involute helical gear's involute helicoid as the tool generatrix surface according to the envelope method, and the corresponding transmission coordinate system is established according to the position relationship between the involute cylindrical gear and the elliptical toroidal worm mesh transmission;
the details are as follows:
the equation of the tooth flank of the involute cylindrical gear is obtained by the coordinate transformation and the principle of tooth conjugate meshing of the elliptical toroidal worm;
the transmission subsets are ground and shaped with hard tooth material, so the equations of the tooth surface on the upper side of the elliptical toroidal worm are as follows:
{
x
2
⁢
L
=
(
x
1
⁢
L
⁢
cos
⁢
φ
1
-
y
1
⁢
L
⁢
sin
⁢
φ
1
-
a
)
⁢
cos
⁢
φ
2
+
[
(
x
1
⁢
L
⁢
sin
⁢
φ
1
+
y
1
⁢
L
⁢
cos
⁢
φ
1
)
⁢
cos
⁢
ε
+
z
1
⁢
L
⁢
sin
⁢
ε
]
⁢
sin
⁢
φ
2
y
2
⁢
L
=
[
(
x
1
⁢
L
⁢
sin
⁢
φ
1
+
y
1
⁢
L
⁢
cos
⁢
φ
1
)
⁢
cos
⁢
ε
+
z
1
⁢
L
⁢
sin
⁢
ε
]
⁢
cos
⁢
φ
2
-
(
x
1
⁢
L
⁢
cos
⁢
φ
1
-
y
1
⁢
L
⁢
sin
⁢
φ
1
-
a
)
⁢
sin
⁢
φ
2
z
2
⁢
L
=
-
(
x
1
⁢
L
⁢
sin
⁢
φ
1
+
y
1
⁢
L
⁢
cos
⁢
φ
1
)
⁢
sin
⁢
ε
+
z
1
⁢
L
⁢
cos
⁢
ε
x
1
⁢
L
=
r
b
⁢
cos
⁢
τ
+
r
b
⁢
u
⁢
sin
⁢
τ
y
1
⁢
L
=
-
r
b
⁢
sin
⁢
τ
+
r
b
⁢
u
⁢
cos
⁢
τ
z
1
⁢
L
=
α
1
⁢
ρ
1
⁢
λ
+
α
2
⁢
h
L
τ
=
u
-
σ
0
-
α
1
⁢
λ
h
L
=
r
b
(
i
12
-
cos
⁢
ε
)
+
a
⁢
cos
⁡
(
u
-
σ
0
-
φ
1
)
⁢
cos
⁢
ε
-
sin
⁡
(
u
-
σ
0
-
φ
1
)
⁢
sin
⁢
ε
u
=
-
r
b
2
⁢
cos
⁡
(
τ
-
φ
1
)
⁢
sin
⁢
ε
+
ρ
1
2
(
τ
+
σ
0
)
⁢
sin
⁡
(
τ
-
φ
1
)
⁢
sin
⁢
ε
-
ρ
1
⁢
a
⁢
cos
⁡
(
τ
-
φ
1
)
⁢
cos
⁢
ε
-
r
b
⁢
ρ
1
(
i
12
-
cos
⁢
ε
)
+
r
b
⁢
a
⁢
sin
⁢
ε
(
r
b
2
+
ρ
1
2
)
⁢
sin
⁡
(
τ
-
φ
1
)
⁢
sin
⁢
ε
where, a is the spread center distance, φ1 is the rotation angle of the involute cylindrical gear, φ2 is the rotation angle of elliptical toroidal worm, i12 is the reciprocal of the transmission ratio of the worm gear pair, σ0 is half of the base circular angle corresponding to the transverse base thickness of the involute cylindrical gear, u is the rolling angle formed by the dominant involute tooth profile;
similarly, the equations of the lower side tooth surface of the elliptical toroidal worm are as follows:
{
x
2
⁢
R
=
(
x
1
⁢
R
⁢
cos
⁢
φ
1
-
y
1
⁢
R
⁢
sin
⁢
φ
1
-
a
)
⁢
cos
⁢
φ
2
+
[
(
x
1
⁢
R
⁢
sin
⁢
φ
1
+
y
1
⁢
R
⁢
cos
⁢
φ
1
)
⁢
cos
⁢
ε
+
z
1
⁢
R
⁢
sin
⁢
ε
]
⁢
sin
⁢
φ
2
y
2
⁢
R
=
[
(
x
1
⁢
R
⁢
sin
⁢
φ
1
+
y
1
⁢
R
⁢
cos
⁢
φ
1
)
⁢
cos
⁢
ε
+
z
1
⁢
R
⁢
sin
⁢
ε
]
⁢
cos
⁢
φ
2
-
(
x
1
⁢
R
⁢
cos
⁢
φ
1
-
y
1
⁢
R
⁢
sin
⁢
φ
1
-
a
)
⁢
sin
⁢
φ
2
z
2
⁢
R
=
-
(
x
1
⁢
R
⁢
sin
⁢
φ
1
+
y
1
⁢
R
⁢
cos
⁢
φ
1
)
⁢
sin
⁢
ε
+
z
1
⁢
R
⁢
cos
⁢
ε
x
1
⁢
R
=
r
b
⁢
cos
⁡
(
τ
)
+
r
b
⁢
u
⁢
sin
⁡
(
τ
)
y
1
⁢
R
=
r
b
⁢
sin
⁡
(
τ
)
-
r
b
⁢
u
⁢
cos
⁡
(
τ
)
z
1
⁢
R
=
α
1
⁢
ρ
1
⁢
λ
+
α
2
⁢
h
R
τ
=
u
-
σ
0
+
α
1
⁢
λ
h
R
=
r
b
(
i
12
-
cos
⁢
ε
)
+
a
⁢
cos
⁡
(
u
-
σ
0
+
φ
1
)
⁢
cos
⁢
ε
sin
⁡
(
u
-
σ
0
+
φ
1
)
⁢
sin
⁢
ε
u
=
-
r
b
2
⁢
cos
⁡
(
τ
+
φ
1
)
⁢
sin
⁢
ε
+
ρ
1
2
(
τ
+
σ
0
)
⁢
sin
⁡
(
τ
+
φ
1
)
⁢
sin
⁢
ε
-
ρ
1
⁢
a
⁢
cos
⁡
(
τ
+
φ
1
)
⁢
cos
⁢
ε
-
r
b
⁢
ρ
1
(
i
12
-
cos
⁢
ε
)
+
r
b
⁢
a
⁢
sin
⁢
ε
(
r
b
2
+
ρ
1
2
)
⁢
sin
⁡
(
τ
+
φ
1
)
⁢
sin
⁢
ε
the above tooth equations are determined by two parameters φ1 and u, other parameters are known, and upper tooth surface and lower tooth surface of elliptical toroidal gear vice can be obtained by MATLAB numerical analysis and 3D modeling software in the range of φ1 and u, and then they are stitched with the top toroidal surface and root toroidal surface of elliptical toroidal worm to generate the 3D solid model of non-orthogonal elliptical toroidal worm gear pair, and finally the non-orthogonal elliptical toroidal worm gear pair is obtained.

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A non-orthogonal elliptical toroidal worm gear pair

Life of this patent

A non-orthogonal elliptical toroidal worm gear pair

Life of this patent

Abstract

Claims1