CN100441326C - Geometric model of new elongater for skew rolling tubular products - Google Patents

Abstract

The present invention relates to a hot rolling pipe elongating technology which can be directly applied to a skew rolling pipe elongating device. For overcoming the defects of the existing skew rolling pipe elongating device and realizing the optimized skew rolling, the present invention provides a new geometric model of the skew rolling pipe elongating device. The hot rolling pipe elongating technology is basically characterized in that rollers are arranged in a convergent form, i.e., the rolling angle psi is less than 0; in the Cartesian coordinate system, the offset y0 is not zero, and the signs of the feed angle beta and the offset y0 can not be the same. By using four equations sets provided by the present invention to carry out the optimization calculation, the new geometric model of the skew rolling pipe elongating machine is obtained, and the goals of lightening the expansion of deformation zone metal and raising the rolling speed are achieved.

Description

A kind of new oblique milling tubing elongator

Technical field

The present invention relates to a kind of hot rolling tubing elongation technology, this technology can directly apply to oblique milling tubing extension device.

Background technology

Modern common oblique milling tubing elongator has:

1) Diescher pipe mill

2) Assel pipe mill (roller trio skew rolling elongator)

3) ACCU ROLL pipe mill

4) roller trio skew rolling planetary rolling machine (PSW)

The phenomenon that any oblique milling process produces deformed area metal " cripling " is inevitable, this in order to alleviate " cripling ", with the raising mill speed, people have done a lot of discussions for many years, but produce little effect, helplessly developed the pipe mill (as Diescher pipe mill, ACCU ROLL pipe mill) of oblique-axial rolling combination, not only frame for movement is huge for this class pipe mill, simultaneously because the operation of rolling of oblique-axial rolling combination causes the milling train adjustment complicated.The roller trio skew rolling planetary rolling machine of early eighties exploitation in last century and the four roller oblique milling planetary rolling machines of developing recently are a kind of planetary cross-country power mechanisms, and roll is the convergence type and arranges, so metal " cripling " phenomenon is subjected to controlling significantly, but because the complicated shortcoming that also causes some to be difficult to accept of frame for movement.

Geometrical model according to above-mentioned four kinds of pipe mills utilizes the technical scheme of this patent to carry out Practical Calculation, just know these four kinds of pipe mills at operation of rolling deformed area metal " cripling " the serious and not high reason of mill speed.Show the geometrical model of above-mentioned four kinds of diagonal rolling pipe mills among Fig. 2 respectively.

A common feature of common oblique milling elongator geometrical model is that roll axis (Z axle) is adjusted centre of gyration O ₁Point all on the x of coordinate system shown in Figure 1 axle, does not have side-play amount on the y axle.What their geometrical models were different is roll off angle ψ=0 of Diescher pipe mill; Roll off angle ψ＞0 of Assel and ACCU ROLL pipe mill, roll are radial pattern and arrange; Roll off angle ψ＜0 of PSW, roll are the convergence type and arrange.

Below by results of calculation the disadvantage that above-mentioned several oblique milling elongator geometrical model exists is described.Resonable degree for more several oblique milling elongator oblique milling processes is set as follows identical design conditions:

Calculate the deformed area from begin to subtract wall again the section of tube reducing start at, up to subtract wall, tube reducing is ended simultaneously, calculate asynchronous region length 120mm, begin to subtract wall hollow billet exradius r=82.92mm on the section of tube reducing again, subtract wall tube reducing r=76.68mm at the end again, wall thickness reducing amount 6.24mm, feed angle β=8 °, roll axis is adjusted centre of gyration point O ₁Distance (being the amount of movement of roll axis on the x axle) x to the datum level of crossing the rolled piece axis ₀=290mm, side-play amount y ₀=0.

The geometrical model different according to various skew rolling mills, different design conditions are:

The Diescher pipe mill, roll off angle ψ=0,

The Assel pipe mill, ψ=4 °,

ACCU ROLL pipe mill, ψ=15 °,

PSW，ψ＝-55°。

Result of calculation is listed in table 1

The Rcos ξ of common oblique milling tubing elongator and Rcos ε value table 1

The result of calculation of table 1 shows, only with regard to alleviating deformed area metal " cripling ", that best is PSW, be in particular in that Rcos ε value successively decreases from deformed area inlet to outlet, and lapse rate is also very big, like this, along with tube wall thickness from the inlet to exporting attenuation gradually, the metal lateral flow reduces significantly, has obviously alleviated metal " cripling " phenomenon to " cripling " responsive tenuity.So so, be because PSW has adopted the very big negative roll off angle of absolute value (being ψ＜0), cause rolled piece direction of rotation and roll speed vector forward angle ε to become big gradually from inlet to outlet.It is least rational that the roll axis of ACCU ROLL is arranged, its Rcos ε value increases progressively to outlet from the deformed area inlet, and its reason is its roll off angle ψ＞0; Assel also is ψ＞0, but the absolute value of ψ little than ACCU ROLL, so the roll axis of Asaeel is arranged reasonable a little than ACCU ROLL; The ψ of Diescher=0, its roll axis is arranged also more a shade better than Assel.

The common fault of common oblique milling elongator is, the rolled piece axial velocity is too small, and deformed area metal " cripling " serious (except the PSW) can not be realized pure oblique milling process, thus be because their geometrical model determines like this, side-play amount y not only ₀=0, and roll off angle ψ＞0.The ψ of PSW＜0, the absolute value of ψ is very big, thereby deformed area metal " cripling " is not serious, can realize pure oblique milling process, but the rolled piece axial velocity is too little.

Summary of the invention

The objective of the invention is to overcome the deficiency and the shortcoming of existing diagonal rolling pipe mill, propose a kind of new oblique milling tubing elongator.

The present invention proposes to describe four Mathematical Modelings of oblique milling process, be optimized calculating by them and obtain new oblique milling tubing elongator geometrical model, meeting the purpose that realizes alleviating deformed area metal " cripling " and raising mill speed on the oblique milling tubing elongator of new geometrical model.Use preceding two Mathematical Modelings, can also reasonably distribute deflection, design oblique milling elongator roll and Mannesmann piercing mill, hot tube expanding machine roll, top, they also are the Mathematical Modelings of accurately adjusting roll simultaneously; Use latter two Mathematical Modeling, can calculate the axial and rotary speed of rolled piece accurately.

A kind of new oblique milling tubing elongator, the improvement by to the geometrical model of existing oblique milling tubing elongator proposes to realize the optimized a kind of new oblique milling tubing elongator of oblique milling, it is characterized in that: roll is the convergence type and arranges, be roll off angle ψ＜0, in coordinate system oxyz, side-play amount y ₀≠ 0, and feed angle β and side-play amount y ₀Can not jack per line, that is: a or b,

A, amount of movement x ₀＞0, roll is the convergence type and arranges roll off angle ψ for negative, and feed angle β is for bearing skew y ₀Amount is for just;

B, amount of movement x ₀＞0, roll is the convergence type and arranges roll off angle ψ for negative, and feed angle β is being for just, side-play amount y ₀For negative.

Described a kind of new oblique milling tubing elongator utilizes following (1) Mathematical Modeling, at known rolled piece curved surface β, ψ, r, x ₀, y ₀, z condition under, can try to achieve roll curved surface θ, X, Y, R, Z parameter;

Get a z value, just can obtain one corresponding to roller radius R of this point with at coordinate system O ₁The coordinate figure of X, Y, Z among the XYZ is got several z values and is just obtained several corresponding R values and X, Y, Z, value, and several R values and Z, X, Y value have just constituted about coordinate system O ₁The roll curved surface of XYZ;

$\left(1\right)\left\{\begin{array}{c}z=z\\ \mathrm{tg\&theta;}=\frac{{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="C20041008231800161.png,C20041008231800171.png"\; state="\{\{state\}\}">y</figure-callout>}}_0\cos \mathrm{\&beta;}-z\sin \mathrm{\&beta;}}{{\mathrm{<figure-callout\; id="0"\; label="x"\; filenames="C20041008231800161.png,C20041008231800171.png"\; state="\{\{state\}\}">x</figure-callout>}}_0\cos \mathrm{\&beta;}+\mathrm{ztg\&psi;}}\\ \left(\begin{array}{c}X\\ Y\\ Z\end{array}\right)=\left(\begin{array}{ccc}\cos \mathrm{\&psi;}& \sin \mathrm{\&beta;}\sin \mathrm{\&psi;}& -\cos \mathrm{\&beta;}\sin \mathrm{\&psi;}\\ 0& \cos \mathrm{\&beta;}& \sin \mathrm{\&beta;}\\ \sin \mathrm{\&psi;}& -\sin \mathrm{\&beta;}\cos \mathrm{\&psi;}& \cos \mathrm{\&beta;}\cos \mathrm{\&psi;}\end{array}\right)\left(\begin{array}{c}r\cos \mathrm{\&theta;}-x_0\\ r\sin \mathrm{\&theta;}-y_0\\ z\end{array}\right)\\ R=\sqrt{X^2+{\mathrm{<figure-callout\; id="2"\; label="Y"\; filenames="C20041008231800171.png"\; state="\{\{state\}\}">Y</figure-callout>}}^2}\end{array}\right.$

Wherein:

β---feed angle,

ψ---roll off angle,

R---rolled piece exradius on the different rolled pieces cross section,

x ₀---roll axis is adjusted swivel point along the amount of movement on the x axle of coordinate system oxyz,

y ₀---roll axis is adjusted swivel point along the side-play amount on the y axle of coordinate system oxyz,

Z---metal and roll contact point be the coordinate figure on the z axle (rolled piece axis) in coordinate system oxyz,

θ---rolled piece cross section circle is gone up the parameter of the parametric equation of rolled piece cylindrical,

X---metal and roll contact point are at coordinate system O ₁Coordinate figure among the XYZ on the X-axis,

Y---metal and roll contact point are at coordinate system O ₁Coordinate figure among the XYZ on the Y-axis,

R---different rolls cross section topping roll radius,

Z---metal and roll contact point are at coordinate system O ₁Among the XYZ on the Z axle (roll axis)

Coordinate figure;

Counterclockwise feed angle β that forms and roll off angle ψ get "+" number, and feed angle β that forms and roll off angle ψ get "-" number clockwise.

Described a kind of new oblique milling tubing elongator utilizes following (2) Mathematical Modeling, at known roll curved surface β, ψ, R, Z, x ₀, y ₀Under the parameter condition, can try to achieve rolled piece curved surface θ ', r, X ₀, Y ₀, Z ₀, x, y, z parameter;

Get a Z value, just can obtain a coordinate figure corresponding to rolled piece radius r value z in coordinate system oxyz of this point, just draw several corresponding r value and z values for several Z values, several r values and z value have just constituted the rolled piece curved surface about coordinate system oxyz.

Wherein:

β---feed angle,

ψ---roll off angle,

R---different rolls cross section topping roll radius,

x ₀---roll axis is adjusted swivel point along the amount of movement on the x axle of coordinate system oxyz,

y ₀---roll axis is adjusted swivel point along the side-play amount on the y axle of coordinate system oxyz,

Z---metal and roll contact point be the coordinate figure on the z axle (rolled piece axis) in coordinate system oxyz,

θ '---the parameter of different rolls cross section topping roll profile circle parametric equation,

R---rolled piece exradius on the different rolled pieces cross section,

X ₀---roll axis is adjusted swivel point along coordinate system O ₁Amount of movement on the X-axis of XYZ,

Y ₀---roll axis is adjusted swivel point along coordinate system O ₁Side-play amount on the Y-axis of XYZ,

Z ₀---roll axis is adjusted swivel point along coordinate system O ₁Amount of movement on the Z axle of XYZ

X---metal and the roll contact point coordinate figure on the x axle in coordinate system oxyz,

Y---metal and the roll contact point coordinate figure on the y axle in coordinate system oxyz,

Z---metal and roll contact point be the coordinate figure on the z axle (rolled piece axis) in coordinate system oxyz;

Counterclockwise feed angle β that forms and roll off angle ψ get "+" number, and feed angle β that forms and roll off angle ψ get "-" number clockwise.

Described a kind of new oblique milling tubing elongator utilizes described (3) Mathematical Modeling, at known roll curved surface or roll curved surface β, ψ, r, x ₀, y ₀, under the z, θ parameter condition, can try to achieve the forward angle ξ of roll speed direction and rolled piece axis; Calculate and compare the Rcos ξ value of different parameters,, constituted a kind of new oblique milling tubing elongator corresponding to the bigger geometric parameter less of Rcos ξ with Rcos ε;

$\left(3\right)\left\{\begin{array}{c}z=z\\ \text{tg\&theta;=}\frac{{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="C20041008231800161.png,C20041008231800171.png"\; state="\{\{state\}\}">y</figure-callout>}}_0\cos \mathrm{\&beta;}-z\sin \mathrm{\&beta;}}{x_0\cos \mathrm{\&beta;}+\mathrm{ztg\&psi;}}\\ \cos \mathrm{\&xi;}=\frac{\left|\begin{array}{cc}r\cos \mathrm{\&theta;}-x_0& r\sin \mathrm{\&theta;}-{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="C20041008231800161.png,C20041008231800171.png"\; state="\{\{state\}\}">y</figure-callout>}}_0\\ \sin \mathrm{\&psi;}& -\sin \mathrm{\&beta;}\cos \mathrm{\&psi;}\end{array}\right|}{\sqrt{{\left|\begin{array}{cc}r\sin \mathrm{\&theta;}-y_0& z\\ -\sin \mathrm{\&beta;}\cos \mathrm{\&psi;}& \cos \mathrm{\&beta;}\cos \mathrm{\&psi;}\end{array}\right|}^2+{\left|\begin{array}{cc}z& r\cos \mathrm{\&theta;}-x_0\\ \cos \mathrm{\&beta;}\cos \mathrm{\&psi;}& \sin \mathrm{\&psi;}\end{array}\right|}^2+{\left|\begin{array}{cc}r\cos \mathrm{\&theta;}-x_0& r\sin -{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="C20041008231800161.png,C20041008231800171.png"\; state="\{\{state\}\}">y</figure-callout>}}_0\\ \sin \mathrm{\&psi;}& -\sin \mathrm{\&beta;}\cos \mathrm{\&psi;}\end{array}\right|}^2}}\end{array}\right.$

Wherein:

The roll speed direction on ξ---metal and the roll contact point and the forward angle of rolled piece axis,

β---feed angle,

ψ---roll off angle,

R---rolled piece exradius on the different rolled pieces cross section,

x ₀---roll axis is adjusted swivel point along the amount of movement on the x axle of coordinate system oxyz,

y ₀---roll axis is adjusted swivel point along the side-play amount on the y axle of coordinate system oxyz,

Z---metal and roll contact point be the coordinate figure on the z axle (rolled piece axis) in coordinate system oxyz,

θ---rolled piece cross section circle is gone up the parameter of rolled piece cylindrical parametric equation;

Counterclockwise feed angle β that forms and roll off angle ψ get "+" number, and feed angle β that forms and roll off angle ψ get "-" number clockwise;

Obtain the roll speed direction on metal and the roll contact point and the forward angle ξ of rolled piece axis, just can obtain on the contact point metal in the speed of rolling direction;

The more little mill speed of angle ξ is just big more, and the geometrical model difference of milling train, the size of angle ξ are also different; The geometrical model difference of milling train, the size of roller radius R are also different.Can be by the product " R cos ξ " of roller radius R and cos ξ symbol value as skew rolling mill geometrical model mill speed, " R cos ξ " is big more, and mill speed is just high more, and this index of mill speed is just excellent more.

Described a kind of new oblique milling tubing elongator utilizes following (4) Mathematical Modeling, at known rolled piece curved surface or roll curved surface (β, ψ, r, x ₀, y ₀, z, θ parameter) under the condition, can try to achieve the forward angle ε of roll speed direction and rolled piece rolling tangential direction; Calculate and compare the Rcos ε value of different parameters,, constituted a kind of new oblique milling tubing elongator corresponding to the less geometric parameter bigger of Rcos ε with Rcos ξ;

Wherein:

The roll speed direction on ε---metal and the roll contact point and the forward angle of rolled piece direction of rotation,

β---feed angle,

ψ---roll off angle,

R---rolled piece exradius on the different rolled pieces cross section,

x ₀---roll axis is adjusted swivel point along the amount of movement on the x axle of coordinate system oxyz,

y ₀---roll axis is adjusted swivel point along the side-play amount on the y axle of coordinate system oxyz,

Z---metal and roll contact point be the coordinate figure on the z axle (rolled piece axis) in coordinate system oxyz,

θ---rolled piece cross section circle is gone up the parameter of the parametric equation of rolled piece cylindrical;

Counterclockwise feed angle β that forms and roll off angle ψ get "+" number, and feed angle β that forms and roll off angle ψ get "-" number clockwise.

The more little rolled piece rotary speed of forward angle ε of roll speed direction on metal and the roll contact point and rolled piece direction of rotation is just big more, and the metal lateral flow is just many more, and deformed area metal " cripling " is just serious more, and just the oblique milling state is just poor more.Outside the Pass the size of rolled piece rotary speed and angle ε have, still relevant with roller radius R, therefore also should represent the quality of skew rolling mill geometrical model oblique milling state by product " the R cos ε " value of roller radius R and cos ε, the more little oblique milling state of R cos ε is just good more.

The beneficial effect that the present invention has compared with prior art is:

Be optimized to calculate and obtain a kind of new oblique milling tubing elongator, the purpose that on new oblique milling tubing elongator, realizes alleviating deformed area metal " cripling " and improve mill speed.

In addition, use preceding two in above-mentioned four mathematics equation group, can reasonably distribute deflection, instruments such as design oblique milling elongator roll and Mannesmann piercing mill, hot tube expanding machine roll, top; They also are the Mathematical Modelings of accurately adjusting roll simultaneously; Use latter two Mathematical Modeling, can calculate the axial and rotary speed of rolled piece accurately.

Description of drawings

Fig. 1 coordinate system that Mathematical Modeling is set up of deriving;

The geometrical model of the common oblique milling elongator of Fig. 2, i.e. Diescher pipe mill, Assel pipe mill, ACCU ROOL pipe mill and psw geometrical model;

A kind of new oblique milling tubing elongator a roll off angle Ψ of Fig. 3 is for negative, and feed angle β is negative, side-play amount y ₀For just; B roll off angle Ψ is for negative, feed angle β for just, side-play amount y ₀For negative.

In Fig. 1 derived the coordinate system of Mathematical Models, the rolled piece axis was on the z of coordinate system oxyz axle, and roll axis is at coordinate system O₁On the Z axis of XYZ. Coordinate system O₁XYZ is by seat Mark is that oxyz gets through twice rotation and twice translation. For the first time rotation is around x axle rotation β The angle, "+" got at the β angle that is rotated counterclockwise formation, get "-" that turns clockwise and form; Second Inferior rotation is that "+" got, dextrorotation in the Ψ angle that is rotated counterclockwise formation around y axle rotation Ψ angle Turn to get "-" of formation. Twice translation is to move x along x axle and y axle respectively₀And y₀Value. First Inferior rotation forms corner β angle, is exactly feed angle; The corner Ψ that for the second time rotation forms rolles over exactly Roll the angle.

The specific embodiment

Describe the specific embodiment of the present invention in detail below in conjunction with drawings and Examples.

At first draft a kind of new oblique milling tubing elongator: feed angle β=8 °, roll axis is adjusted centre of gyration point O ₁To the distance of the datum level of crossing the rolled piece axis, i.e. the amount of movement x of roll axis on the x axle ₀=290mm, roll off angle ψ=-20 °, side-play amount y ₀=-80mm.

Calculate the identical of existing oblique milling tubing elongator in other design conditions and the background technology, that is: calculate the deformed area from begin to subtract wall again the section of tube reducing start at, up to subtracting wall, tube reducing end of a period, calculate asynchronous region length 120mm, begin to subtract wall hollow billet exradius r=82.92mm on the section of tube reducing again, subtract wall tube reducing r=76.68mm at the end again, wall thickness reducing amount 6.24mm.These conditions have been described the rolled piece curved surface of deformed area, therefore use equation group (1) (if the known roll curved surface meets the tendency with equation group (2)), calculate the related parameter that has of curved surface, utilize then equation group (3) and equation group (4) calculate respectively roll speed direction and rolling direction forward angle ξ and with the forward angle ε of rolled piece direction of rotation, and calculate Rcos ξ value and Rcos ε value, thereby judge the resonable degree of oblique milling process.List in table 2 according to aforementioned calculation condition result of calculation.

Table 2

Make a general survey of result of calculation, compare with table 1, a kind of new oblique milling tubing elongator is more superior than the geometrical model of above-mentioned common several elongators: Rcos ξ value is bigger than common elongator, is more than three times of PSW, is about 1.6 times (if proper transformation β, Ψ and y of other common elongator ₀Value also can produce better effect); Rcos ε is the same with PSW to successively decrease to exporting from deformed area inlet, and this illustrates the present invention than common elongator mill speed height not only, and has the stronger ability of controlling deformed area metal " cripling ".

Claims (5)

1. new oblique milling tubing elongator is characterized in that: roll is the convergence type to be arranged, i.e. roll off angle ψ＜0, and in coordinate system oxyz, side-play amount y ₀≠ 0, and feed angle β and side-play amount y ₀Can not jack per line, that is: a or b,

A, amount of movement x ₀＞0, roll is the convergence type and arranges roll off angle ψ for negative, and feed angle β is for bearing skew y ₀Amount is for just;

B, amount of movement x ₀＞0, roll is the convergence type and arranges roll off angle ψ for negative, and feed angle β is being for just, side-play amount y ₀For negative.

2. a kind of new oblique milling tubing elongator according to claim 1 is characterized in that, utilizes the Mathematical Modeling of the following stated, at known rolled piece curved surface β, ψ, r, x ₀, y ₀, z condition under, can try to achieve roll curved surface θ, X, Y, R, Z parameter;

$\left\{\begin{array}{c}z=z\\ \mathrm{tg\&theta;}=\frac{y_0\cos \mathrm{\&beta;}-z\sin \mathrm{\&beta;}}{x_0\cos \mathrm{\&beta;}+\mathrm{ztg\&psi;}}\\ \left(\begin{array}{c}X\\ Y\\ Z\end{array}\right)=\left(\begin{array}{ccc}\cos \mathrm{\&psi;}& \sin \mathrm{\&beta;}\sin \mathrm{\&psi;}& -\cos \mathrm{\&beta;}\sin \mathrm{\&psi;}\\ 0& \cos \mathrm{\&beta;}& \sin \mathrm{\&beta;}\\ \sin \mathrm{\&psi;}& -\sin \mathrm{\&beta;}\cos \mathrm{\&psi;}& \cos \mathrm{\&beta;}\cos \mathrm{\&psi;}\end{array}\right)\left(\begin{array}{c}r\cos \mathrm{\&theta;}-x_0\\ r\sin \mathrm{\&theta;}-y_0\\ z\end{array}\right)\\ R=\sqrt{X^2+Y^2}\end{array}\right.$

Wherein:

β---feed angle,

ψ---roll off angle,

R---rolled piece exradius on the different rolled pieces cross section,

x ₀---roll axis is adjusted swivel point along the amount of movement on the x axle of coordinate system oxyz,

y ₀---roll axis is adjusted swivel point along the side-play amount on the y axle of coordinate system oxyz,

Z---metal and roll contact point be the coordinate figure on the z axle (rolled piece axis) in coordinate system oxyz,

θ---rolled piece cross section circle is gone up the parameter of the parametric equation of rolled piece cylindrical,

X---metal and roll contact point are at coordinate system O ₁Coordinate figure among the XYZ on the X-axis,

Y---metal and roll contact point are at coordinate system O ₁Coordinate figure among the XYZ on the Y-axis,

R---different rolls cross section topping roll radius,

Z---metal and roll contact point are at coordinate system O ₁Coordinate figure among the XYZ on the Z axle (roll axis);

Counterclockwise feed angle β that forms and roll off angle ψ get "+" number, and feed angle β that forms and roll off angle ψ get "-" number clockwise.

3. a kind of new oblique milling tubing elongator according to claim 1 is characterized in that, utilizes following Mathematical Modeling, at known roll curved surface β, ψ, R, Z, x ₀, y ₀Under the parameter condition, can try to achieve rolled piece curved surface θ ', r, X ₀, Y ₀, Z ₀, x, y, z parameter;

$\left\{\begin{array}{c}Z=Z\\ \begin{array}{c}{X}_0=-x_0\cos \mathrm{\&psi;}-y_0\sin \mathrm{\&beta;}\sin \mathrm{\&psi;}\\ Y_0=-y_0\cos \mathrm{\&beta;}\\ Z_0=-x_0\sin \mathrm{\&psi;}-y_0\sin \mathrm{\&beta;}\cos \mathrm{\&psi;}\end{array}\\ {\mathrm{\&theta;}}^{\&prime;}=\mathrm{\&pi;}+\mathrm{arc}\left(\mathrm{tg}\frac{Y_0\cos \mathrm{\&beta;}+(Z-Z_0)\sin \mathrm{\&beta;}}{X_0\cos \mathrm{\&beta;}-(Z-Z_0)\mathrm{tg\&psi;}}\right)\\ \left(\begin{array}{c}x\\ y\\ z\end{array}\right)=\left(\begin{array}{ccc}\cos \mathrm{\&psi;}& 0& \sin \mathrm{\&psi;}\\ \sin \mathrm{\&beta;}\sin \mathrm{\&psi;}& \cos \mathrm{\&beta;}& -\sin \mathrm{\&beta;}\cos \mathrm{\&psi;}\\ -\cos \mathrm{\&beta;}\sin \mathrm{\&psi;}& \sin \mathrm{\&beta;}& \cos \mathrm{\&beta;}\cos \mathrm{\&psi;}\end{array}\right)\left(\begin{array}{c}R\cos {\mathrm{\&theta;}}^{\&prime;}\\ R\sin {\mathrm{\&theta;}}^{\&prime;}\\ Z\end{array}\right)+\left(\begin{array}{c}{x}_0\\ y_0\\ 0\end{array}\right)\\ r=\sqrt{x^2+y^2}\end{array}\right.$

Wherein:

β---feed angle,

ψ---roll off angle,

R---different rolls cross section topping roll radius,

x ₀---roll axis is adjusted swivel point along the amount of movement on the x axle of coordinate system oxyz,

y ₀---roll axis is adjusted swivel point along the side-play amount on the y axle of coordinate system oxyz,

Z---metal and roll contact point be the coordinate figure on the z axle (rolled piece axis) in coordinate system oxyz,

θ '---the parameter of different rolls cross section topping roll profile circle parametric equation,

R---rolled piece exradius on the different rolled pieces cross section,

X ₀---roll axis is adjusted swivel point along coordinate system O ₁Amount of movement on the X-axis of XYZ,

Y ₀---roll axis is adjusted swivel point along coordinate system O ₁Side-play amount on the Y-axis of XYZ,

Z ₀---roll axis is adjusted swivel point along coordinate system O ₁Amount of movement on the Z axle of XYZ,

X---metal and the roll contact point coordinate figure on the x axle in coordinate system oxyz,

Y---metal and the roll contact point coordinate figure on the y axle in coordinate system oxyz,

Z---metal and roll contact point be the coordinate figure on the z axle (rolled piece axis) in coordinate system oxyz;

Counterclockwise feed angle β that forms and roll off angle ψ get "+" number, and feed angle β that forms and roll off angle ψ get "-" number clockwise.

4. a kind of new oblique milling tubing elongator according to claim 1 is characterized in that, utilizes the Mathematical Modeling of the following stated, at known roll curved surface or roll curved surface β, ψ, r, x ₀, y ₀, under the z, θ parameter condition, can try to achieve the forward angle ξ of roll speed direction and rolled piece axis;

$\left\{\begin{array}{c}z=z\\ \mathrm{tg\&theta;}=\frac{y_0\cos \mathrm{\&beta;}-z\sin \mathrm{\&beta;}}{x_0\cos \mathrm{\&beta;}+\mathrm{ztg\&psi;}}\\ \cos \mathrm{\&xi;}=\frac{\left|\begin{array}{cc}r\cos \mathrm{\&theta;}-x_0& r\sin \mathrm{\&theta;}-y_0\\ \sin \mathrm{\&psi;}& -\sin \mathrm{\&beta;}\cos \mathrm{\&psi;}\end{array}\right|}{\sqrt{{\left|\begin{array}{cc}r\sin \mathrm{\&theta;}-y_0& z\\ -\sin \mathrm{\&beta;}\cos \mathrm{\&psi;}& \cos \mathrm{\&beta;}\cos \mathrm{\&psi;}\end{array}\right|}^2+{\left|\begin{array}{cc}z& r\cos \mathrm{\&theta;}-x_0\\ \cos \mathrm{\&beta;}\cos \mathrm{\&psi;}& \sin \mathrm{\&psi;}\end{array}\right|}^2+{\left|\begin{array}{cc}r\cos \mathrm{\&theta;}-x_0& r\sin -y_0\\ \sin \mathrm{\&psi;}& -\sin \mathrm{\&beta;}\cos \mathrm{\&psi;}\end{array}\right|}^2}}\end{array}\right.$

Wherein:

The roll speed direction on ξ---metal and the roll contact point and the forward angle of rolled piece axis,

β---feed angle,

ψ---roll off angle,

R---rolled piece exradius on the different rolled pieces cross section,

x ₀---roll axis is adjusted swivel point along the amount of movement on the x axle of coordinate system oxyz,

y ₀---roll axis is adjusted swivel point along the side-play amount on the y axle of coordinate system oxyz,

Z---metal and roll contact point be the coordinate figure on the z axle (rolled piece axis) in coordinate system oxyz,

θ---rolled piece cross section circle is gone up the parameter of the parametric equation of rolled piece cylindrical;

Counterclockwise feed angle β that forms and roll off angle ψ get "+" number, and feed angle β that forms and roll off angle ψ get "-" number clockwise.

5. a kind of new oblique milling tubing elongator according to claim 1 is characterized in that, utilizes the Mathematical Modeling of the following stated, at known roll curved surface β, ψ, r, x ₀, y ₀, under the z, θ parameter condition, can try to achieve the forward angle ε of roll speed direction and rolled piece rolling tangential direction;

$\left\{\begin{array}{c}z=z\\ \mathrm{tg\&theta;}=\frac{y_0\cos \mathrm{\&beta;}-z\sin \mathrm{\&beta;}}{x_0\cos \mathrm{\&beta;}+\mathrm{ztg\&psi;}}\\ \cos \mathrm{\&epsiv;}=\frac{-\left|\begin{array}{cc}r\sin \mathrm{\&theta;}-y_0& z\\ -\sin \mathrm{\&beta;}\cos \mathrm{\&psi;}& \cos \mathrm{\&beta;}\cos \mathrm{\&psi;}\end{array}\right|\mathrm{tg\&theta;}+\left|\begin{array}{cc}z& r\cos \mathrm{\&theta;}-x_0\\ \cos \mathrm{\&beta;}\cos \mathrm{\&psi;}& \sin \mathrm{\&psi;}\end{array}\right|}{\sqrt{{\left|\begin{array}{cc}r\sin \mathrm{\&theta;}-y_0& z\\ -\sin \mathrm{\&beta;}\cos \mathrm{\&psi;}& \cos \mathrm{\&beta;}\cos \mathrm{\&psi;}\end{array}\right|}^2+{\left|\begin{array}{cc}z& r\cos \mathrm{\&theta;}-x_0\\ \cos \mathrm{\&beta;}\cos \mathrm{\&psi;}& \sin \mathrm{\&psi;}\end{array}\right|}^2+{\left|\begin{array}{cc}r\cos \mathrm{\&theta;}-x_0& r\sin -y_0\\ \sin \mathrm{\&psi;}& -\sin \mathrm{\&beta;}\cos \mathrm{\&psi;}\end{array}\right|}^2}\sqrt{{\mathrm{tg}}^2\mathrm{\&theta;}+1}}\end{array}\right.$

Wherein:

The roll speed direction on ε---metal and the roll contact point and the forward angle of rolled piece direction of rotation,

β---feed angle,

ψ---roll off angle,

R---rolled piece exradius on the different rolled pieces cross section,

x ₀---roll axis is adjusted swivel point along the amount of movement on the x axle of coordinate system oxyz,

y ₀---roll axis is adjusted swivel point along the side-play amount on the y axle of coordinate system oxyz,

Z---metal and roll contact point be the coordinate figure on the z axle (rolled piece axis) in coordinate system oxyz,

θ---rolled piece cross section circle is gone up the parameter of the parametric equation of rolled piece cylindrical,

Counterclockwise feed angle β that forms and roll off angle ψ get "+" number, and feed angle β that forms and roll off angle ψ get "-" number clockwise.

Images