CN104847657A - Multihead taper screw bush pair and forming method of curved surface thereof - Google Patents

Abstract

The invention discloses a multihead taper screw bush pair, comprising a taper screw and a bush pair; the bush pair sleeves the taper screw; a taper screw small end face and a taper screw large end face are located at two ends of the taper screw; a taper screw center line is located on the middle of the taper screw; a curved surface of the taper screw is prepared on the outer surface of the taper screw in a pressing way; a taper bush small end face and a taper bush large end face are located at two ends of the bush pair and are matched with the taper screw small end face and the taper screw large end face; a taper bush center line is located on the middle of the bush pair; a taper bush curved surface is prepared on the outer surface of the bush pair in the pressing way and is matched with the ball curved surface of the taper screw. The multihead taper screw bush pair has the advantages of simple structure, smooth and steady flow, large displacement, small axial size, high carrying capacity and the like, is more smooth and steady in flow, and is greatly reduced in structure size.

Description

The mould-forming method of a kind of bull Conic thread rod lining pair and curved surface thereof

Technical field

The present invention relates to screw pump technology field, in particular to the mould-forming method of a kind of bull Conic thread rod lining pair and curved surface thereof.

Background technique

Screw rod lining pair is the critical component of screw type oil hydraulic pump, at present, the domestic research about screw pump mainly concentrates on post screw pump, and achieve greater advance, and only resting on single head Conic thread rod pump for the research of Conic thread rod pump, the research for bull Conic thread rod pump remains a blank so far.For different occasion of satisfied modern times is to the demand of screw pump, the consecutive variations convergent based on cone spiral motion secondary cavity passes principle and space meshing principle, proposes a kind of new screw pump structure-bull Conic thread rod pump.Bull Conic thread rod lining pair comprises conical screw and taper bush, conical screw positive camber and taper bush negative camber engage each other, form a series of airtight chamber, along with Conic thread rod rotates in lining, working medium is constantly transported to the other end by one end of screw rod lining pair, thus realizes the function of screw pump.

The shortcomings such as existing screw rod lining pair structure is loaded down with trivial details, flow is steady not, discharge capacity is little, axial dimension is excessive, bearing capacity is low.

Summary of the invention

For solving the problem, the object of the present invention is to provide a kind of bull Conic thread rod lining pair.

The invention provides a kind of bull Conic thread rod lining pair, comprising:

Conic thread rod and lining pair, described lining pair its to be sleeved on described Conic thread rod outside;

Conical screw small end face and conical screw large end face, it is positioned at the two ends of described Conic thread rod;

Conical screw center line, it is positioned in the middle part of described Conic thread rod;

The curved surface of conical screw, it is compressed on the outer surface of described Conic thread rod;

Taper bush small end face and taper bush large end face, it is positioned at the two ends of described lining pair and matches with described conical screw small end face and described conical screw large end face;

Taper bush center line, it is positioned at the middle part of described lining pair;

Taper bush curved surface, it is compressed on the outer surface of described lining pair and coordinates with described conical screw type.

Present invention also offers a kind of mould-forming method of bull Conic thread rod lining pair curved surface, it is characterized in that, this mould-forming method comprises the following steps:

Step 101: taper bush curved surface (1) with the outer equal space line of curtate hypocycloid for cross section line style, with small end face (2) for initial planar, small end face geometrical center is true origin, setting up throw of eccentric is e, helical pitch is the circular helix of T, with end face geometric center lines (4) for each end face center, each end face is rotated along circular helix and forms the outer equal space line line style of the series of parallel curtate hypocycloid in small end face (2), and line style rolling circle radius becomes certain linear relationship with end face displacement distance, the smooth surface be made up of these line styles is bull lining curved surface.

The cross section of the determination taper bush curved surface of taper bush Surface Parameters is the outer equal space line of curtate hypocycloid, and the rolling circle radius of taper bush curved surface small end face is r ₁, leading circle radius is R ₁, the rolling circle radius of taper bush curved surface large end face is r ₂, leading circle radius is R ₂, liner head number be N (N=2,3,4 ...), lead circle radius and rolling circle radius meets R _i=Nr _i.

The length of taper bush curved surface rolling circle radius Changing Pattern definition taper bush curved surface is L ₁, the rolling circle radius Changing Pattern of definition taper bush curved surface meets then to be the rolling circle radius of α place cross section be angle of swing

Step 102: conical screw curved surface (5) with the conjugate curve of lining section line for cross section line style, with small end face (6) for initial planar, small end face geometrical center is true origin, setting up throw of eccentric is e, helical pitch is the circular helix of t, with end face geometric center lines (8) for each end face center, each end face is rotated along circular helix and forms the outer equal space line line style of the series of parallel curtate hypocycloid in small end face (6), and line style rolling circle radius becomes certain linear relationship with end face displacement distance, the smooth surface be made up of these line styles is multiple thread screw curved surface.

The cross section of conical screw curved surface is the outer equal space line conjugate curve of curtate hypocycloid, and the rolling circle radius of conical screw curved surface small end face is r ₃, leading circle radius is R ₃, the rolling circle radius of conical screw curved surface large end face is r ₄, leading circle radius is R ₄, screw head number be n (n=1,2,3 ...), lead circle radius and rolling circle radius meets R _i=(n+1) r _i.

The length of conical screw curved surface rolling circle radius Changing Pattern definition conical screw curved surface is L ₂, the rolling circle radius Changing Pattern of definition conical screw curved surface meets then to be the cross section rolling circle radius at β place be angle of swing

Further improve as the present invention, in step 101, the end face curtate hypocycloid equation of taper bush curved surface end face equation taper bush is:

$\left\{\begin{array}{c}{x}_0=(N-1)(r_1+\frac{c_1\mathrm{\α}}{4\mathrm{\π}}T)\sin \mathrm{\θ}-e\sin (n\·\mathrm{\θ})\\ y_0=(N-1)(r_1+\frac{c_1\mathrm{\α}}{4\mathrm{\π}}T)\cos \mathrm{\θ}+e\cos (n\·\mathrm{\θ})\end{array}\right.---\left(1\right)$

In formula, n-screw head number, meets n=N-1

Taper bush curtate hypocycloid derivative equation is obtained to (1) formula differentiate:

$\left\{\begin{array}{c}{x}_0^{\′}=(N-1)(r_1+\frac{c_1\mathrm{\α}}{4\mathrm{\π}}T)\cos \mathrm{\θ}-e\·n\·\cos (n\·\mathrm{\θ})\\ y_0^{\′}=-(N-1)(r_1+\frac{c_1\mathrm{\α}}{4\mathrm{\π}}T)\sin \mathrm{\θ}-e\·n\·\sin (n\·\mathrm{\θ})\end{array}\right.---\left(2\right)$

Order then the outer Equidistant curve equation of taper bush curtate hypocycloid is:

$\left\{\begin{array}{c}x=x_0+a\frac{y_0^{\′}}{\sqrt{h}}\\ y=y_0-a\frac{x_0^{\′}}{\sqrt{h}}\end{array}\right.---\left(3\right)$

Wherein a is the distance that curve outwards offsets, and formula (1), (2), (3) simultaneous are taper bush SECTION EQUATION.

Further improve as the present invention, in step 101, by taper bush small end face, cross-section curve at the uniform velocity rotates around taper bush heart line, at the uniform velocity move forward with helical pitch T again on one side, cross section rolling circle radius and lead circle radius and all linearly increase in moving process; With taper bush center line for z-axis, taper bush curved surface small end face is that xoy plane sets up position fixing system oxyz; With taper bush center line for z ₁axle, taper bush curved surface small end face is x ₁o ₁y ₁plane sets up moving coordinate system o ₁x ₁y ₁z ₁; If moving coordinate system o ₁x ₁y ₁z ₁turning over angle relative to position fixing system oxyz is α, then on taper bush curved surface any point M at system of coordinates o ₁x ₁y ₁z ₁in position coordinate be:

$\left\{\begin{array}{c}{x}_1=x\cos \mathrm{\α}+y\sin \mathrm{\α}\\ y_1=-x\sin \mathrm{\α}+y\cos \mathrm{\α}\\ z_1=\frac{t}{2\mathrm{\π}}\mathrm{\α}\end{array}\right.---\left(4\right)$

Further improve as the present invention, in step 102, conical screw curved surface end face equation conical screw and taper bush are internal messing, meet the internal messing principle of gear, and the conjugate curve formula obtaining the outer equal space line of curtate hypocycloid according to internal messing principle is:

Conical screw does pure rolling in lining, so conical screw angle of rotation with revolution angle meet formula:

Simultaneous (5), (6) formula obtain:

When conical screw engages with taper bush, the point on conical screw and the point on taper bush should meet working pressure angle formula:

Namely formula (7) and (8) simultaneous are obtained conical screw end face line style formula:

Further improve as the present invention, in step 102, the axial equation of conical screw curved surface is by conical screw curved surface small end face, cross-section curve is while at the uniform velocity rotate around conical screw center line, at the uniform velocity move forward with helical pitch t again on one side, cross section rolling circle radius and lead circle radius and all linearly increase in moving process; With conical screw center line for z-axis, conical screw curved surface small end face is that xoy plane sets up position fixing system oxyz; With conical screw center line for z ₁axle, taper bush curved surface small end face is x ₁o ₁y ₁plane sets up moving coordinate system o ₁x ₁y ₁z ₁; If moving coordinate system o ₁x ₁y ₁z ₁turning over angle relative to position fixing system oxyz is β, then on conical screw curved surface any point N at system of coordinates o ₁x ₁y ₁z ₁in position coordinate be:

$\left\{\begin{array}{c}{x}_3=x_2\cos \mathrm{\β}+y_2\sin \mathrm{\β}\\ y_3=-x_2\sin \mathrm{\β}+y_2\cos \mathrm{\β}\\ z_3=\frac{t}{2\mathrm{\π}}\mathrm{\β}\end{array}\right.---\left(10\right)$

Further improve as the present invention, Conic thread rod lining pair meshing condition is for making screw rod-lining pair correct engagement, and above parameter should meet: r ₁=r ₃, c ₁=c ₂, l ₁=L ₂.

Further improve as the present invention, the helical pitch T by taper bush small end face equals lining circular helix pitch.

Further improve as the present invention, the helical pitch t by conical screw curved surface small end face equals screw rod circular helix pitch.

Beneficial effect of the present invention is: with the outer equal space line of curtate hypocycloid for lining curved surface component, with its conjugate curve for screw rod curved surface component, the throw of eccentric numerical value in diverse location cross section is identical, the helical pitch of screw rod lining pair equals the pitch of its axial cylindrical helix, the surface equation obtained is succinct, is conducive to curved surface modeling and processing; In addition, this method generates based on New type conical screw rod lining pair, and the forms of motion of its screw rod lining pair is the planetary motion of parallel axes plane, there is not axial displacement, eliminates the drawbacks such as the wearing and tearing because screw axial displacement brings, leakage; Structure is simple, flow trim, discharge capacity are large, axial dimension is little, bearing capacity advantages of higher, and bull Conic thread rod lining pair flow is more steady, physical dimension also reduces greatly.

Accompanying drawing explanation

Fig. 1 is double end Conic thread rod bush structure schematic diagram;

Fig. 2 is double end taper bush curved surface schematic diagram;

Fig. 3 is double end conical screw curved surface schematic diagram;

Fig. 4 is double end taper bush curved cross section schematic diagram;

Fig. 5 is double end conical screw curved cross section schematic diagram;

Fig. 6 is the implementing procedure figure of the inventive method.

In figure: 1, taper bush curved surface, 2, taper bush small end face, 3, taper bush large end face, 4, taper bush center line, 5, conical screw curved surface, 6, conical screw small end face, 7, conical screw large end face, 8, conical screw center line.

Embodiment

Also by reference to the accompanying drawings the present invention is described in further detail below by specific embodiment.

Embodiment 1, and as Figure 1-5, a kind of bull Conic thread rod lining pair described in the embodiment of the present invention, is characterized in that, comprising: Conic thread rod and lining pair, described lining pair its to be sleeved on described Conic thread rod outside; Conical screw small end face 6 and conical screw large end face 7, it is positioned at the two ends of described Conic thread rod; Conical screw center line 8, it is positioned in the middle part of described Conic thread rod; The curved surface 5 of conical screw, it is compressed on the outer surface of described Conic thread rod; Taper bush small end face 2 and taper bush large end face 7, it is positioned at the two ends of described lining pair and matches with described conical screw small end face 6 and described conical screw large end face 7; Taper bush center line 4, it is positioned at the middle part of described lining pair; Taper bush curved surface 1, it is compressed on the outer surface of described lining pair and matches with described conical screw curved surface 5.

Structure is simple, flow trim, discharge capacity are large, axial dimension is little, bearing capacity advantages of higher, and bull Conic thread rod lining pair flow is more steady, physical dimension also reduces greatly.

Embodiment 2, and as shown in Figure 6, present invention also offers a kind of mould-forming method of bull Conic thread rod lining pair curved surface, this mould-forming method comprises the following steps:

Step 101: taper bush curved surface 1 with the outer equal space line of curtate hypocycloid for cross section line style, with small end face 2 for initial planar, small end face geometrical center is true origin, set up that throw of eccentric is e, helical pitch is the circular helix of T, be each end face center with end face geometric center lines 4, each end face is rotated along circular helix and forms the outer equal space line line style of the series of parallel curtate hypocycloid in small end face 2, and line style rolling circle radius becomes certain linear relationship with end face displacement distance, the smooth surface be made up of these line styles is bull lining curved surface.

The cross section of the determination taper bush curved surface 1 of taper bush curved surface 1 parameter is the outer equal space line of curtate hypocycloid, and the rolling circle radius of taper bush curved surface small end face 2 is r ₁, leading circle radius is R ₁, the rolling circle radius of taper bush curved surface large end face 3 is r ₂, leading circle radius is R ₂, liner head number be N (N=2,3,4 ...), lead circle radius and rolling circle radius meets R _i=Nr _i.

The length of taper bush curved surface rolling circle radius Changing Pattern definition taper bush curved surface 1 is L ₁, the rolling circle radius Changing Pattern of definition taper bush curved surface 1 meets then to be the rolling circle radius of α place cross section be angle of swing

Step 102: conical screw curved surface 5 with the conjugate curve of lining section line for cross section line style, with small end face 6 for initial planar, small end face geometrical center is true origin, set up that throw of eccentric is e, helical pitch is the circular helix of t, be each end face center with end face geometric center lines 8, each end face is rotated along circular helix and forms the outer equal space line line style of the series of parallel curtate hypocycloid in small end face 6, and line style rolling circle radius becomes certain linear relationship with end face displacement distance, the smooth surface be made up of these line styles is multiple thread screw curved surface.

The cross section of conical screw curved surface 5 is the outer equal space line conjugate curve of curtate hypocycloid, and the rolling circle radius of conical screw curved surface small end face 6 is r ₃, leading circle radius is R ₃, the rolling circle radius of conical screw curved surface large end face 7 is r ₄, leading circle radius is R ₄, screw head number be n (n=1,2,3 ...), lead circle radius and rolling circle radius meets R _i=(n+1) r _i.

The length of conical screw curved surface 5 rolling circle radius Changing Pattern definition conical screw curved surface 5 is L ₂, the rolling circle radius Changing Pattern of definition conical screw curved surface 5 meets then to be the cross section rolling circle radius at β place be angle of swing

By on the basis of bull post screw rod lining pair and New type conical screw rod lining pair, propose a kind of curved surface forming method of bull Conic thread rod lining pair, the method with the outer equal space line of curtate hypocycloid for lining curved surface component, with its conjugate curve for screw rod curved surface component, the throw of eccentric numerical value in diverse location cross section is identical, the helical pitch of screw rod lining pair equals the pitch of its axial cylindrical helix, and the surface equation obtained is succinct, is conducive to curved surface modeling and processing; In addition, this method generates based on New type conical screw rod lining pair, and the forms of motion of its screw rod lining pair is the planetary motion of parallel axes plane, there is not axial displacement, eliminates the drawbacks such as the wearing and tearing because screw axial displacement brings, leakage.

Further, in step 101, the end face curtate hypocycloid equation of taper bush curved surface 1 end face equation taper bush is:

$\left\{\begin{array}{c}{x}_0=(N-1)(r_1+\frac{c_1\mathrm{\α}}{4\mathrm{\π}}T)\sin \mathrm{\θ}-e\sin (n\·\mathrm{\θ})\\ y_0=(N-1)(r_1+\frac{c_1\mathrm{\α}}{4\mathrm{\π}}T)\cos \mathrm{\θ}+e\cos (n\·\mathrm{\θ})\end{array}\right.---\left(1\right)$

In formula, n-screw head number, meets n=N-1

Taper bush curtate hypocycloid derivative equation is obtained to (1) formula differentiate:

$\left\{\begin{array}{c}{x}_0^{\′}=(N-1)(r_1+\frac{c_1\mathrm{\α}}{4\mathrm{\π}}T)\cos \mathrm{\θ}-e\·n\·\cos (n\·\mathrm{\θ})\\ y_0^{\′}=-(N-1)(r_1+\frac{c_1\mathrm{\α}}{4\mathrm{\π}}T)\sin \mathrm{\θ}-e\·n\·\sin (n\·\mathrm{\θ})\end{array}\right.---\left(2\right)$

Order then the outer Equidistant curve equation of taper bush curtate hypocycloid is:

$\left\{\begin{array}{c}x=x_0+a\frac{y_0^{\′}}{\sqrt{h}}\\ y=y_0-a\frac{x_0^{\′}}{\sqrt{h}}\end{array}\right.---\left(3\right)$

Wherein a is the distance that curve outwards offsets, and formula (1), (2), (3) simultaneous are taper bush SECTION EQUATION.

Further, in step 101, by taper bush small end face 2, cross-section curve at the uniform velocity rotates around taper bush center line 4, at the uniform velocity moves forward with helical pitch T again on one side, cross section rolling circle radius and lead circle radius and all linearly increase in moving process; With taper bush center line 4 for z-axis, taper bush curved surface small end face 2 sets up position fixing system oxyz for xoy plane; With taper bush center line 4 for z ₁axle, taper bush curved surface small end face 2 is x ₁o ₁y ₁plane sets up moving coordinate system o ₁x ₁y ₁z ₁; If moving coordinate system o ₁x ₁y ₁z ₁turning over angle relative to position fixing system oxyz is α, then on taper bush curved surface any point M at system of coordinates o ₁x ₁y ₁z ₁in position coordinate be:

$\left\{\begin{array}{c}{x}_1=x\cos \mathrm{\α}+y\sin \mathrm{\α}\\ y_1=-x\sin \mathrm{\α}+y\cos \mathrm{\α}\\ z_1=\frac{t}{2\mathrm{\π}}\mathrm{\α}\end{array}\right.---\left(4\right)$

Further, in step 102, conical screw curved surface end face equation conical screw and taper bush are internal messing, meet the internal messing principle of gear, and the conjugate curve formula obtaining the outer equal space line of curtate hypocycloid according to internal messing principle is:

Conical screw does pure rolling in lining, so conical screw angle of rotation with revolution angle meet formula:

Simultaneous (5), (6) formula obtain:

When conical screw engages with taper bush, the point on conical screw and the point on taper bush should meet working pressure angle formula:

Namely formula (7) and (8) simultaneous are obtained conical screw end face line style formula:

Further, in step 102, the axial equation of conical screw curved surface is by conical screw curved surface small end face 6, cross-section curve is while at the uniform velocity rotate around conical screw center line 8, at the uniform velocity move forward with helical pitch t again on one side, cross section rolling circle radius and lead circle radius and all linearly increase in moving process; With conical screw center line 8 for z-axis, conical screw curved surface small end face 6 sets up position fixing system oxyz for xoy plane; With conical screw center line 8 for z ₁axle, taper bush curved surface small end face 6 is x ₁o ₁y ₁plane sets up moving coordinate system o ₁x ₁y ₁z ₁; If moving coordinate system o ₁x ₁y ₁z ₁turning over angle relative to position fixing system oxyz is β, then on conical screw curved surface any point N at system of coordinates o ₁x ₁y ₁z ₁in position coordinate be:

$\left\{\begin{array}{c}{x}_3=x_2\cos \mathrm{\β}+y_2\sin \mathrm{\β}\\ y_3=-x_2\sin \mathrm{\β}+y_2\cos \mathrm{\β}\\ z_3=\frac{t}{2\mathrm{\π}}\mathrm{\β}\end{array}\right.---\left(10\right)$

Further, Conic thread rod lining pair meshing condition is for making screw rod-lining pair correct engagement, and above parameter should meet: r ₁=r ₃, c ₁=c ₂, l ₁=L ₂.

Further, the helical pitch T by taper bush small end face 2 equals lining circular helix pitch.

Further, the helical pitch t by conical screw curved surface small end face 6 equals screw rod circular helix pitch.

The foregoing is only the preferred embodiments of the present invention, be not limited to the present invention, for a person skilled in the art, the present invention can have various modifications and variations.Within the spirit and principles in the present invention all, any amendment done, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (9)

1. a bull Conic thread rod lining pair, is characterized in that, comprising:

Conic thread rod and lining pair, described lining pair its to be sleeved on described Conic thread rod outside;

Conical screw small end face (6) and conical screw large end face (7), it is positioned at the two ends of described Conic thread rod;

Conical screw center line (8), it is positioned in the middle part of described Conic thread rod;

The curved surface (5) of conical screw, it is compressed on the outer surface of described Conic thread rod;

Taper bush small end face (2) and taper bush large end face (7), it is positioned at the two ends of described lining pair and matches with described conical screw small end face (6) and described conical screw large end face (7);

Taper bush center line (4), it is positioned at the middle part of described lining pair;

Taper bush curved surface (1), it is compressed on the outer surface of described lining pair and matches with described conical screw curved surface (5).

2. a mould-forming method for a kind of bull Conic thread rod lining pair curved surface as claimed in claim 1, it is characterized in that, this mould-forming method comprises the following steps:

Step 101: taper bush curved surface (1) with the outer equal space line of curtate hypocycloid for cross section line style, with small end face (2) for initial planar, small end face geometrical center is true origin, setting up throw of eccentric is e, helical pitch is the circular helix of T, with end face geometric center lines (4) for each end face center, each end face is rotated along circular helix and forms the outer equal space line line style of the series of parallel curtate hypocycloid in small end face (2), and line style rolling circle radius becomes certain linear relationship with end face displacement distance, the smooth surface be made up of these line styles is bull lining curved surface,

The cross section of the determination taper bush curved surface (1) of taper bush curved surface (1) parameter is the outer equal space line of curtate hypocycloid, and the rolling circle radius of taper bush curved surface small end face (2) is r ₁, leading circle radius is R ₁, the rolling circle radius of taper bush curved surface large end face (3) is r ₂, leading circle radius is R ₂, liner head number be N (N=2,3,4 ...), lead circle radius and rolling circle radius meets R _i=Nr _i;

The length of taper bush curved surface rolling circle radius Changing Pattern definition taper bush curved surface (1) is L ₁, the rolling circle radius Changing Pattern of definition taper bush curved surface (1), meets then to be the rolling circle radius of α place cross section be angle of swing

Step 102: conical screw curved surface (5) with the conjugate curve of lining section line for cross section line style, with small end face (6) for initial planar, small end face geometrical center is true origin, setting up throw of eccentric is e, helical pitch is the circular helix of t, with end face geometric center lines (8) for each end face center, each end face is rotated along circular helix and forms the outer equal space line line style of the series of parallel curtate hypocycloid in small end face (6), and line style rolling circle radius becomes certain linear relationship with end face displacement distance, the smooth surface be made up of these line styles is multiple thread screw curved surface,

The cross section of conical screw curved surface (5) is the outer equal space line conjugate curve of curtate hypocycloid, and the rolling circle radius of conical screw curved surface small end face (6) is r ₃, leading circle radius is R ₃, the rolling circle radius of conical screw curved surface large end face (7) is r ₄, leading circle radius is R ₄, screw head number be n (n=1,2,3 ...), lead circle radius and rolling circle radius meets R _i=(n+1) r _i;

The length of conical screw curved surface (5) rolling circle radius Changing Pattern definition conical screw curved surface (5) is L ₂, the rolling circle radius Changing Pattern of definition conical screw curved surface (5) meets then angle of swing be place cross section rolling circle radius be

3. the mould-forming method of bull Conic thread rod lining pair curved surface according to claim 2, is characterized in that: in step 101, and the end face curtate hypocycloid equation of taper bush curved surface (1) end face equation taper bush is:

$\left\{\begin{array}{c}{x}_0=(N-1)(r_1+\frac{c_1\mathrm{\α}}{4\mathrm{\π}}T)\sin \mathrm{\θ}-e\sin (n\·\mathrm{\θ})\\ y_0=(N-1)(r_1+\frac{c_1\mathrm{\α}}{4\mathrm{\π}}T)\cos \mathrm{\θ}+e\cos (n\·\mathrm{\θ})\end{array}\right.---\left(1\right)$

In formula, n-screw head number, meets n=N-1

Taper bush curtate hypocycloid derivative equation is obtained to (1) formula differentiate:

$\left\{\begin{array}{c}{x}_0^{\′}=(N-1)(r_1+\frac{c_1\mathrm{\α}}{4\mathrm{\π}}T)\cos \mathrm{\θ}-e\·n\·\cos (n\·\mathrm{\θ})\\ y_0^{\′}=-(N-1)(r_1+\frac{c_1\mathrm{\α}}{4\mathrm{\π}}T)\sin \mathrm{\θ}-e\·n\·\sin (n\·\mathrm{\θ})\end{array}\right.---\left(2\right)$

Order then the outer Equidistant curve equation of taper bush curtate hypocycloid is:

$\left\{\begin{array}{c}x=x_0+a\frac{y_0^{\′}}{\sqrt{h}}\\ y=y_0-a\frac{x_0^{\′}}{\sqrt{h}}\end{array}\right.---\left(3\right)$

Wherein a is the distance that curve outwards offsets, and formula (1), (2), (3) simultaneous are taper bush SECTION EQUATION.

4. the mould-forming method of bull Conic thread rod lining pair curved surface according to claim 2, it is characterized in that: in step 101, by taper bush small end face (2), cross-section curve is while at the uniform velocity rotate around taper bush center line (4), at the uniform velocity move forward with helical pitch T again on one side, cross section rolling circle radius and lead circle radius and all linearly increase in moving process; With taper bush center line (4) for z-axis, taper bush curved surface small end face (2) sets up position fixing system oxyz for xoy plane; With taper bush center line (4) for z ₁axle, taper bush curved surface small end face (2) is x ₁o ₁y ₁plane sets up moving coordinate system o ₁x ₁y ₁z ₁; If moving coordinate system o ₁x ₁y ₁z ₁turning over angle relative to position fixing system oxyz is α, then on taper bush curved surface any point M at system of coordinates o ₁x ₁y ₁z ₁in position coordinate be:

$\left\{\begin{array}{c}{x}_1=x\cos \mathrm{\α}+y\sin \mathrm{\α}\\ y_1=-x\sin \mathrm{\α}+y\cos \mathrm{\α}\\ z_1=\frac{t}{2\mathrm{\π}}\mathrm{\α}\end{array}\right.---\left(4\right).$

5. the mould-forming method of bull Conic thread rod lining pair curved surface according to claim 2, it is characterized in that: in step 102, conical screw curved surface end face equation conical screw and taper bush are internal messing, meet the internal messing principle of gear, the conjugate curve formula obtaining the outer equal space line of curtate hypocycloid according to internal messing principle is:

Conical screw does pure rolling in lining, so conical screw angle of rotation with revolution angle meet formula:

Simultaneous (5), (6) formula obtain:

When conical screw engages with taper bush, the point on conical screw and the point on taper bush should meet working pressure angle formula:

Namely formula (7) and (8) simultaneous are obtained conical screw end face line style formula:

6. the mould-forming method of bull Conic thread rod lining pair curved surface according to claim 2, it is characterized in that: in step 102, the axial equation of conical screw curved surface is by conical screw curved surface small end face (6), cross-section curve is while at the uniform velocity rotate around conical screw center line (8), at the uniform velocity move forward with helical pitch t again on one side, cross section rolling circle radius and lead circle radius and all linearly increase in moving process; With conical screw center line (8) for z-axis, conical screw curved surface small end face (6) sets up position fixing system oxyz for xoy plane; With conical screw center line (8) for z ₁axle, taper bush curved surface small end face (6) is x ₁o ₁y ₁plane sets up moving coordinate system o ₁x ₁y ₁z ₁; If moving coordinate system o ₁x ₁y ₁z ₁turning over angle relative to position fixing system oxyz is β, then on conical screw curved surface any point N at system of coordinates o ₁x ₁y ₁z ₁in position coordinate be:

$\left\{\begin{array}{c}{x}_3=x_2\cos \mathrm{\β}+y_2\sin \mathrm{\β}\\ y_3=-x_2\sin \mathrm{\β}+y_2\cos \mathrm{\β}\\ z_3=\frac{t}{2\mathrm{\π}}\mathrm{\β}\end{array}\right.---\left(10\right).$

7. the mould-forming method of bull Conic thread rod lining pair curved surface according to claim 2, is characterized in that: Conic thread rod lining pair meshing condition is for making screw rod-lining pair correct engagement, and above parameter should meet: $T=\frac{N}{n}\·t,$ r ₁＝r ₃，c ₁＝c ₂， $\mathrm{\α}=\frac{n}{N}\·\mathrm{\β},$ L ₁＝L ₂。

8. the mould-forming method of bull Conic thread rod lining pair curved surface according to claim 2, is characterized in that: the helical pitch T by taper bush small end face (2) equals lining circular helix pitch.

9. the mould-forming method of bull Conic thread rod lining pair curved surface according to claim 2, is characterized in that: the helical pitch t by conical screw curved surface small end face (6) equals screw rod circular helix pitch.