SHAPE CONTROL METHOD AND SYSTEM FOR THREE-DIMENSIONAL CURVED PROFILE FORMED BY FOUR-DIRECTION DIFFERENTIAL VELOCITY EXTRUSION

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

The present invention claims priority to Chinese Patent Application No. 202411015689.5, filed with the China National Intellectual Property Administration on Jul. 26, 2024, entitled “SHAPE CONTROL METHOD AND SYSTEM FOR THREE-DIMENSIONAL CURVED PROFILE FORMED BY FOUR-DIRECTION DIFFERENTIAL VELOCITY EXTRUSION,” the entire content of which is incorporated herein by reference and constitutes part of the present invention for all purposes.

TECHNICAL FIELD

The present invention relates to the technical field of plastic forming of metals and composite materials, and specifically to a shape control method and system for a three-dimensional (3D) curved profile formed by four-direction differential velocity extrusion.

BACKGROUND

3D curved profiles of metals and composite materials have significant advantages in enhancing the overall strength and stiffness of structures, achieving structural light weighting, saving space, and reducing air resistance. These curved profiles find wide applications and hold important positions in fields such as aerospace, ground transportation, transportation pipelines, and nuclear power industry.

Traditional manufacturing methods for 3D curved profiles include first forming straight profiles by extrusion and then performing bending forming. This conventional forming process of external force-induced bending deformation not only separates the extrusion and bending processes but also easily leads to prominent problems such as cracking, wrinkling, springback, and cross-sectional distortion in the produced curved profiles. Multi-directional differential velocity extrusion technology, which induces bending deformation through the internal velocity ratio of materials, is an integrated extrusion-bending forming process. It not only can overcome many defects of traditional bending forming technologies but also has the advantages of refining grain structure and improving mechanical properties. Although methods of directly forming curved profiles by simultaneously extruding with multiple different extrusion velocities have been proposed, there has been a long-standing lack of precise control methods for the geometric shape and size of 3D curved profiles. It is difficult to achieve precise control over the geometric shape and size of 3D curved profiles formed by multi-directional differential velocity extrusion, and there is an urgent need to establish a precise control method for the shape and dimensions of 3D curved profiles formed by multi-directional differential velocity extrusion.

SUMMARY

In view of the problems existing in the prior art, the present invention provides a shape control method and system for a 3D curved profile formed by four-direction differential velocity extrusion, which can quantitatively regulate the bending radius and deflection angle of 3D curved profiles and realize the precise forming of complex 3D curved profiles.

The technical solutions of the present invention are as follows:

In a first aspect of the present invention, a shape control method for a 3D curved profile formed by four-direction differential velocity extrusion is provided, including steps of:

• • selecting no fewer than six groups of different extrusion velocity combinations within an allowable extrusion velocity range of an extruded material, measuring bending radii of a curved profile corresponding to the different extrusion velocity combinations, and calculating bending radius control factors of the profile corresponding to the different extrusion velocity combinations; and fitting a relationship curve between the bending radii of the curved profile and the bending radius control factors of the profile to obtain a functional relationship between the two;
  • selecting no fewer than six groups of different extrusion velocity combinations within the allowable extrusion velocity range of the extruded material, measuring deflection angles of the curved profile corresponding to the different extrusion velocity combinations, and calculating deflection angle control factors of the profile corresponding to the different extrusion velocity combinations; and fitting a relationship curve between the deflection angles of the curved profile and the deflection angle control factors of the profile to obtain a functional relationship between the two; and
  • calculating four-direction extrusion velocities required for a curved profile to be formed by extrusion according to the two established functional relationships, with a bending radius and a deflection angle of the curved profile to be formed by extrusion as targets.

In some embodiments of the present invention, a first extrusion velocity and a second extrusion velocity are on a same plane and symmetrically distributed, and an angle between the first extrusion velocity and a discharge direction is equal to an angle between the second extrusion velocity and the discharge direction; and

• • a third extrusion velocity and a fourth extrusion velocity are on a same plane and symmetrically distributed; and an angle between the third extrusion velocity and the discharge direction is equal to an angle between the fourth extrusion velocity and the discharge direction.

In some embodiments of the present invention, a dihedral angle between the plane where the first extrusion velocity and the second extrusion velocity are located and the plane where the third extrusion velocity and the fourth extrusion velocity are located is 90°; and ranges of the angles between the directions of the four extrusion velocities and the discharge direction are 90°-180°.

In some embodiments of the present invention, a formula for calculating the bending radius control factors of the profile is as follows:

F r = [ ( 1 - g x ) 2 + ( 1 - g y ) 2 ] × ( 1 / G ) ;

• • where in the formula, F_r represents the bending radius control factor of the profile, g_x represents a first velocity ratio, i.e., a ratio of a smaller value to a larger value in a modulus |{right arrow over (v₁)}| of the first extrusion velocity and a modulus |{right arrow over (v₂)}| of the second extrusion velocity; g_y represents a second velocity ratio, i.e., a ratio of a smaller value to a larger value in a modulus |{right arrow over (v₃)}| of the third extrusion velocity and a modulus |{right arrow over (v₄)}| of the fourth extrusion velocity; and G represents a velocity gradient ratio, i.e., a ratio of a smaller velocity ratio to a larger velocity ratio in the first velocity ratio and the second velocity ratio.

In some embodiments of the present invention, a process for obtaining the functional relationship between the bending radii of the curved profile and the bending radius control factors of the profile is as follows:

• • selecting the no fewer than six groups of different extrusion velocity combinations within the allowable extrusion velocity range of the extruded material, conducting four-direction differential velocity extrusion experiments, and measuring the bending radii of the curved profile corresponding to the different extrusion velocity combinations;
  • calculating the bending radius control factors of the profile according to four-direction extrusion velocities; and
  • fitting the bending radii of the curved profile and the bending radius control factors of the profile to obtain the functional relationship between the bending radii of the curved profile and the bending radius control factors of the profile.

In some embodiments of the present invention, different deflection angle control factors F₀ of the profile are established according to magnitudes of the first velocity ratio g_x and the second velocity ratio g_y, magnitudes of the modulus |{right arrow over (v₁)}| of the first extrusion velocity and the modulus |{right arrow over (v₂)}| of the second extrusion velocity, and magnitudes of the modulus |{right arrow over (v₃)}| of the third extrusion velocity and the modulus |{right arrow over (v₄)}| of the fourth extrusion velocity.

In some embodiments of the present invention, when g_y≤g_x, |{right arrow over (v₁)}|≤|{right arrow over (v₂)}|, and |{right arrow over (v₃)}|≤|{right arrow over (v₄)}|,

• • a formula for calculating the deflection angle control factors is:

F θ = { [ ( 1 - g y ) / ( 1 - g x ) ] × ( ❘ "\[LeftBracketingBar]" v 4 → ❘ "\[RightBracketingBar]" / ❘ "\[LeftBracketingBar]" v 2 → ❘ "\[RightBracketingBar]" ) } 2 ;

• • when g_y≤g_x, |{right arrow over (v₁)}|≤|{right arrow over (v₂)}|, and |{right arrow over (v₄)}|≤|{right arrow over (v₃)}|,
  • a formula for calculating the deflection angle control factors is:

F θ = { [ ( 1 - g y ) / ( 1 - g x ) ] × ( ❘ "\[LeftBracketingBar]" v 3 → ❘ "\[RightBracketingBar]" / ❘ "\[LeftBracketingBar]" v 2 → ❘ "\[RightBracketingBar]" ) } 2 ;

• • when g_y≤g_x, |{right arrow over (v₂)}|≤|{right arrow over (v₁)}|, and |{right arrow over (v₃)}|≤|{right arrow over (v₄)}|,
  • a formula for calculating the deflection angle control factors is:

F θ = { [ ( 1 - g y ) / ( 1 - g x ) ] × ( ❘ "\[LeftBracketingBar]" v 4 → ❘ "\[RightBracketingBar]" / ❘ "\[LeftBracketingBar]" v 1 → ❘ "\[RightBracketingBar]" ) } 2 ;

• • and, when g_y≤g_x, |{right arrow over (v₂)}|≤|{right arrow over (v₁)}|, and |{right arrow over (v₄)}|≤|{right arrow over (v₃)}|,
  • a formula for calculating the deflection angle control factors is:

F θ = { [ ( 1 - g y ) / ( 1 - g x ) ] × ( ❘ "\[LeftBracketingBar]" v 3 → ❘ "\[RightBracketingBar]" / ❘ "\[LeftBracketingBar]" v 1 → ❘ "\[RightBracketingBar]" ) } 2 .

In some embodiments of the present invention, when g_x≤g_y, |{right arrow over (v₁)}|≤|{right arrow over (v₂)}|, and |{right arrow over (v₃)}|≤|{right arrow over (v₄)}|,

• • a formula for calculating the deflection angle control factors is:

F θ = { [ ( 1 - g x ) / ( 1 - g y ) ] × ( ❘ "\[LeftBracketingBar]" v 2 → ❘ "\[RightBracketingBar]" / ❘ "\[LeftBracketingBar]" v 4 → ❘ "\[RightBracketingBar]" ) } 2 ;

• • when g_x≤g_y, |{right arrow over (v₁)}|≤|{right arrow over (v₂)}|, and |{right arrow over (v₄)}|≤|{right arrow over (v₃)}|,
  • a formula for calculating the deflection angle control factors is:

F θ = { [ ( 1 - g x ) / ( 1 - g y ) ] × ( ❘ "\[LeftBracketingBar]" v 2 → ❘ "\[RightBracketingBar]" / ❘ "\[LeftBracketingBar]" v 3 → ❘ "\[RightBracketingBar]" ) } 2 ;

• • when g_x≤g_y, |{right arrow over (v₂)}|≤|{right arrow over (v₁)}|, and |{right arrow over (v₃)}|≤|{right arrow over (v₄)}|,
  • a formula for calculating the deflection angle control factors is:

F θ = { [ ( 1 - g x ) / ( 1 - g y ) ] × ( ❘ "\[LeftBracketingBar]" v 1 → ❘ "\[RightBracketingBar]" / ❘ "\[LeftBracketingBar]" v 4 → ❘ "\[RightBracketingBar]" ) } 2 ;

• • and, when g_x≤g_y, |{right arrow over (v₂)}|≤|{right arrow over (v₁)}|, and |{right arrow over (v₄)}|≤|{right arrow over (v₃)}|,
  • a formula for calculating the deflection angle control factors is:

F θ = { [ ( 1 - g x ) / ( 1 - g y ) ] × ( ❘ "\[LeftBracketingBar]" v 1 → ❘ "\[RightBracketingBar]" / ❘ "\[LeftBracketingBar]" v 3 → ❘ "\[RightBracketingBar]" ) } 2 .

In some embodiments of the present invention, a process for obtaining the functional relationship between the deflection angles of the curved profile and the deflection angle control factors of the profile is as follows:

• • selecting the no fewer than six groups of different extrusion velocity combinations within the allowable extrusion velocity range of the extruded material, conducting four-direction differential velocity extrusion experiments, and measuring the deflection angles of the curved profile corresponding to the different extrusion velocity combinations;
  • calculating the deflection angle control factors of the profile according to four-direction extrusion velocities; and
  • fitting the deflection angles of the curved profile and the deflection angle control factors of the profile to obtain the functional relationship between the deflection angles of the curved profile and the deflection angles control factors of the profile.

In a second aspect of the present invention, a shape control system for a 3D curved profile formed by four-direction differential velocity extrusion is provided, including:

• • a first functional relationship establishment module, configured to: select no fewer than six groups of different extrusion velocity combinations within an allowable extrusion velocity range of an extruded material, measure bending radii of a curved profile corresponding to the different extrusion velocity combinations, and calculate bending radius control factors of the profile corresponding to the different extrusion velocity combinations; and fit a relationship curve between the bending radii of the curved profile and the bending radius control factors of the profile to obtain a functional relationship between the two;
  • a second functional relationship establishment module, configured to: select no fewer than six groups of different extrusion velocity combinations within the allowable extrusion velocity range of the extruded material, measure deflection angles of the curved profile corresponding to the different extrusion velocity combinations, and calculate deflection angle control factors of the profile corresponding to the different extrusion velocity combinations; and fit a relationship curve between the deflection angles of the curved profile and the deflection angle control factors of the profile to obtain a functional relationship between the two; and
  • a solution module, configured to: calculate four-direction extrusion velocities required for a curved profile to be formed by extrusion according to the two established functional relationships, with a bending radius and a deflection angle of the curved profile to be formed by extrusion as targets.

One or more technical solutions of the present invention have the following beneficial effects:

• • According to the shape control method for a 3D curved profile formed by four-direction differential velocity extrusion provided by the present invention, the bending radius and deflection angle of 3D curved profiles can be accurately and quantitatively regulated and predicted according to the functional relationship between the bending radius of the curved profile and the bending radius control factor of the profile, as well as the functional relationship between the deflection angle of the curved profile and the deflection angle control factor of the profile.

According to the shape control method for a 3D curved profile formed by four-direction differential velocity extrusion provided by the present invention, by controlling the extrusion velocities in four directions, 3D curved profiles with different bending radii and deflection angles can be obtained. Meanwhile, the extrusion velocities in the four directions can also be derived according to the required 3D curved profiles with different bending radii and deflection angles, thereby achieving precise shape control over the 3D curved profiles formed by four-direction differential velocity extrusion.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram showing a four-direction differential velocity extrusion forming method in the present invention;

FIG. 2 is a schematic diagram showing a range of an angle α between an extrusion velocity and a discharge direction in four-direction differential velocity extrusion forming in the present invention;

FIG. 3A shows an actual effect of reducing a bending radius r of a curved profile by decreasing g_x and g_y while keeping G=1 in the present invention;

FIG. 3B shows an actual effect of reducing a bending radius r of a curved profile by decreasing g_x and g_y while keeping G=½ in the present invention;

FIG. 3C shows an actual effect of reducing a bending radius r of a curved profile by decreasing g_y and G in the present invention;

FIG. 4 is a relationship curve between a bending radius control factor F_r calculated from experimental values and a bending radius r in the present invention;

FIG. 5A shows an actual effect of reducing a deflection angle θ of a curved profile by increasing g_x and g_y while keeping |{right arrow over (v₄)}|/|{right arrow over (v₂)}| constant, when g_y≤g_x, |{right arrow over (v₁)}|≤|{right arrow over (v₂)}|, and |{right arrow over (v₃)}|≤|{right arrow over (v₄)}| in the present invention;

FIG. 5B shows an actual effect of reducing a deflection angle θ of a curved profile by decreasing g_y while keeping |{right arrow over (v₄)}|/|{right arrow over (v₂)}| constant, when g_y≤g_x, |{right arrow over (v₁)}|≤|{right arrow over (v₂)}|, and |{right arrow over (v₃)}|≤|{right arrow over (v₄)}| in the present invention;

FIG. 5C shows an actual effect of reducing a deflection angle θ of a curved profile by keeping g_x and g_y constant while increasing |{right arrow over (v₄)}|/|{right arrow over (v₂)}|, when g_y≤g_x, |{right arrow over (v₁)}|≤|{right arrow over (v₂)}|, and |{right arrow over (v₃)}|≤|{right arrow over (v₄)}| in the present invention;

FIG. 6 is a relationship curve between a deflection angle control factor F_θ calculated from experimental values and a deflection angle θ in the present invention;

FIG. 7A is a photograph of a 3D curved profile with sections A and B obtained by extrusion after determining extrusion velocities according to r=f(F_r) and θ=f(F_θ) in the present invention; and

FIG. 7B is a photograph of a 3D curved profile with sections C and D obtained by extrusion after determining extrusion velocities according to r=f(F_r) and θ=f(F_θ) in the present invention.

In the figures: 1, extrusion die (including extrusion cylinder); 2, billet; 3, curved profile; 4, first extrusion ram; 5, second extrusion ram; 6, third extrusion ram; and 7, fourth extrusion ram.

DETAILED DESCRIPTION

The present invention will be further described below in conjunction with the accompanying drawings and examples.

Example 1

In a typical embodiment of the present invention, a shape control method for a 3D curved profile formed by four-direction differential velocity extrusion is proposed, including steps of:

• • to ensure that the fitted curve is relatively smooth and has sufficient fitting accuracy, selecting no fewer than six groups of different extrusion velocity combinations within an allowable extrusion velocity range of an extruded material, measuring bending radii of a curved profile corresponding to the different extrusion velocity combinations, and calculating bending radius control factors of the profile corresponding to the different extrusion velocity combinations; and fitting a relationship curve between the bending radii of the curved profile and the bending radius control factors of the profile to obtain a functional relationship between the two;
  • to ensure that the fitted curve is relatively smooth and has sufficient fitting accuracy, selecting no fewer than six groups of different extrusion velocity combinations within the allowable extrusion velocity range of the extruded material, measuring deflection angles of the curved profile corresponding to the different extrusion velocity combinations, and calculating deflection angle control factors of the profile corresponding to the different extrusion velocity combinations; and fitting a relationship curve between the deflection angles of the curved profile and the deflection angle control factors of the profile to obtain a functional relationship between the two; and
  • calculating four-direction extrusion velocities required for a curved profile to be formed by extrusion according to the two established functional relationships, with a bending radius and a deflection angle of the curved profile to be formed by extrusion as targets.

The shape control method is specifically as follows:

• • I. As shown in FIGS. 1 and 2, a billet 2 is placed into an extrusion die (including the extrusion cylinder) 1. Four extrusion velocities {right arrow over (v₁)}, {right arrow over (v₂)}, {right arrow over (v₃)}, and {right arrow over (v₄)} are simultaneously applied to the billet through a first extrusion ram 4, a second extrusion ram 5, a third extrusion ram 6, and a fourth extrusion ram 7. A bending radius r of an extruded curved profile 3 is defined as a bending radius of a profile's centerline, and a deflection angle θ is defined as an angle between the curved profile and a larger velocity corresponding to a smaller velocity ratio in g_x and g_y. The four velocities satisfy the following relationships:
  • (i) as shown in FIGS. 1 and 2, a range of an angle α between directions of the four extrusion velocities and a discharge direction is 90°-180°;
  • (ii) among the four extrusion velocities, and {right arrow over (v₁)} and {right arrow over (v₂)} are on a same plane, an angle between 11 and a discharge direction {right arrow over (v₅)} is equal to an angle between {right arrow over (v₂)} and the discharge direction {right arrow over (v₅)}, and {right arrow over (v₁)} and {right arrow over (v₂)} are symmetrically distributed;
  • (iii) among the four extrusion velocities, and {right arrow over (v₃)} and {right arrow over (v₄)} are on a same plane, an angle between {right arrow over (v₃)} and a discharge direction {right arrow over (v₅)} is equal to an angle between {right arrow over (v₄)} and the discharge direction {right arrow over (v₅)}, and {right arrow over (v₃)} and {right arrow over (v₄)} are symmetrically distributed;
  • (iv) a dihedral angle between a plane where {right arrow over (v₁)} and {right arrow over (v₂)} are located and a plane where {right arrow over (v₃)} and {right arrow over (v₄)} are located is 90°;
  • II. A smaller value is divided by a larger value in moduli |{right arrow over (v₁)}| and |{right arrow over (v₂)}| of two velocities to obtain the velocity ratio gr; a smaller value is divided by a larger value in moduli |{right arrow over (v₃)}| and |{right arrow over (v₄)}| of two velocities to obtain the velocity ratio g; and a smaller value is divided by a larger value in the two velocity ratios g_x and g_y to obtain a velocity gradient ratio G;
  • III. The bending radius r of the curved profile can be reduced by decreasing g_x or g_y while keeping G constant or decreasing; and the bending radius r of the curved profile can be increased by increasing g_x or g_y while keeping G constant or increasing. Thus, a formula for calculating a bending radius control factor of the profile is established as follows:

F r = [ ( 1 - g x ) 2 + ( 1 - g y ) 2 ] × ( 1 / G ) .

No fewer than six groups of different extrusion velocity combinations are selected within an allowable extrusion velocity range of an extruded material, four-direction differential velocity extrusion experiments are conducted, and bending radii of the curved profile corresponding to the different extrusion velocity combinations are measured. According to the established relational expression between a bending radius control factor F_r and g_x, g_y, as well as G, the bending radius control factor F_r is calculated. A functional relationship r=f(F_r) between the bending radius r and the bending radius control factor F_r is established through fitting, thereby enabling accurate regulation of the bending radius of the 3D curved profile.

Taking FIGS. 3A to 3C as examples for further illustration of the specific implementation method, the extrusion velocity combinations were selected when g_x=g_y=½, ⅓, ¼ and G=1, and the bending radius r at this time were 28.1 mm, 20.8 mm, and 18.7 mm, respectively. The extrusion velocity combinations were selected when g_x=½, ⅓, ¼ and G=2, the bending radii r at this time were 17.3 mm, 15.7 mm, and 14.8 mm, respectively, and decreasing both g_x and g_y while keeping G constant could reduce the bending radius r. The extrusion velocity combinations were selected when g_x=½ and g=⅓, ¼, ⅙, the bending radii r at this time were 20.0 mm, 17.3 mm, and 14.7 mm, respectively, and decreasing g_y while reducing G could reduce the bending radius r. By calculating the bending radius control factor F_r, a functional relationship between the bending radius r and the bending radius control factor F_r as shown in FIG. 4 could be established:

r = f ⁡ ( F r ) = 4 ⁢ 4 . 2 - 3 ⁢ 3 . 8 ⁢ F r - 1 ⁢ 4 . 1 ⁢ F r 2 + 4 ⁢ 8 . 5 ⁢ F r 3 - 3 ⁢ 3 . 8 ⁢ F r 4 + 9 . 9 ⁢ F r 5 - 1 . 1 ⁢ F r 6 .

Through the relationship r=f(F_r) expressed by the above formula, the bending radius r of the curved profile can be precisely controlled.

• • IV. According to different combinations of magnitudes of g_x and g_y and magnitudes of |{right arrow over (v₁)}|, |{right arrow over (v₂)}|, |{right arrow over (v₃)}|, and |{right arrow over (v₄)}|, relational expressions between the deflection angle control factor F_θ of the profile and |{right arrow over (v₁)}|, |{right arrow over (v₂)}|, |{right arrow over (v₃)}|, and |{right arrow over (v₄)}|, as well as g_x and g_y can be categorized into the following eight cases.
  • (i) When g_y≤g_x, |{right arrow over (v₁)}|≤|{right arrow over (v₂)}|, and |{right arrow over (v₃)}|≤|{right arrow over (v₄)}|, by increasing g_x or decreasing g_y while keeping |{right arrow over (v₄)}|/|{right arrow over (v₂)}| constant, or keeping g_x and g_y constant while increasing |{right arrow over (v₄)}|/|{right arrow over (v₂)}|, the deflection angle θ of the curved profile is reduced; and by decreasing g_x or increasing g_y while keeping |{right arrow over (v₄)}|/|{right arrow over (v₂)}| constant, or keeping g_x and g_y constant while decreasing |{right arrow over (v₄)}|/|{right arrow over (v₂)}|, the deflection angle θ of the curved profile is increased. Thus, a formula for calculating the deflection angle control factor is established as follows:

F θ = { [ ( 1 - g y ) / ( 1 - g x ) ] × ( ❘ "\[LeftBracketingBar]" v 4 → ❘ "\[RightBracketingBar]" / ❘ "\[LeftBracketingBar]" v 2 → ❘ "\[RightBracketingBar]" ) } 2 .

• • (ii) When g_y≤g_x, |{right arrow over (v₁)}|≤|{right arrow over (v₂)}|, and |{right arrow over (v₄)}|≤|{right arrow over (v₃)}|, by increasing g_x or decreasing g_y while keeping |{right arrow over (v₃)}|/|{right arrow over (v₂)}| constant, or keeping g_x and g_y constant while increasing |{right arrow over (v₃)}|/|{right arrow over (v₂)}|, the deflection angle θ of the curved profile is reduced; and by decreasing g_x or increasing g_y while keeping |{right arrow over (v₃)}|/|{right arrow over (v₂)}| constant, or keeping g_x and g_y constant while decreasing |{right arrow over (v₃)}|/|{right arrow over (v₂)}|, the deflection angle θ of the curved profile is increased. Thus, a formula for calculating the deflection angle control factor is established as follows:

F θ = { [ ( 1 - g y ) / ( 1 - g x ) ] × ( ❘ "\[LeftBracketingBar]" v 3 → ❘ "\[RightBracketingBar]" / ❘ "\[LeftBracketingBar]" v 2 → ❘ "\[RightBracketingBar]" ) } 2 .

• • (iii) When g_y≤g_x, |{right arrow over (v₂)}|≤|{right arrow over (v₁)}|, and |{right arrow over (v₃)}|≤|{right arrow over (v₄)}|, by increasing g_x or decreasing g_y while keeping |{right arrow over (v₄)}|/|{right arrow over (v₁)}| constant, or keeping g_x and g_y constant while increasing |{right arrow over (v₄)}|/|{right arrow over (v₁)}|, the deflection angle θ of the curved profile is reduced; and by decreasing g_x or increasing g_y while keeping |{right arrow over (v₄)}|/|{right arrow over (v₁)}| constant, or keeping g_x and g_y constant while decreasing |{right arrow over (v₄)}|/|{right arrow over (v₁)}|, the deflection angle θ of the curved profile is increased. Thus, a formula for calculating the deflection angle control factor is established as follows:

F θ = { [ ( 1 - g y ) / ( 1 - g x ) ] × ( ❘ "\[LeftBracketingBar]" v 4 → ❘ "\[RightBracketingBar]" / ❘ "\[LeftBracketingBar]" v 1 → ❘ "\[RightBracketingBar]" ) } 2 .

• • (iv) When g_y≤g_x, |{right arrow over (v₂)}|≤|{right arrow over (v₁)}|, and |{right arrow over (v₄)}|≤|{right arrow over (v₃)}|, by increasing g_x or decreasing g_y while keeping |{right arrow over (v₃)}|/|{right arrow over (v₁)}| constant, or keeping g_x and g_y constant while increasing |{right arrow over (v₃)}|/|{right arrow over (v₁)}|, the deflection angle θ of the curved profile is reduced; and by decreasing g_y or increasing g_x while keeping |{right arrow over (v₃)}|/|{right arrow over (v₁)}| constant, or keeping g_x and g_y constant while decreasing |{right arrow over (v₃)}|/|{right arrow over (v₁)}|, the deflection angle θ of the curved profile is increased. Thus, a formula for calculating the deflection angle control factor is established as follows:

F θ = { [ ( 1 - g y ) / ( 1 - g x ) ] × ( ❘ "\[LeftBracketingBar]" v 3 → ❘ "\[RightBracketingBar]" / ❘ "\[LeftBracketingBar]" v 1 → ❘ "\[RightBracketingBar]" ) } 2 .

• • (v) When g_x≤g_y, |{right arrow over (v₁)}|≤|{right arrow over (v₂)}|, |{right arrow over (v₃)}|≤|{right arrow over (v₄)}|, by increasing g_y or decreasing g_x while keeping |{right arrow over (v₂)}|/|{right arrow over (v₄)}| constant, or keeping g_x and g_y constant while increasing |{right arrow over (v₂)}|/|{right arrow over (v₄)}|, the deflection angle θ of the curved profile is reduced; and by decreasing g_y or increasing g_x while keeping |{right arrow over (v₂)}|/|{right arrow over (v₄)}| constant, or keeping g_x and g_y constant while decreasing |{right arrow over (v₂)}|/|{right arrow over (v₄)}|, the deflection angle θ of the curved profile is increased. Thus, a formula for calculating the deflection angle control factor is established as follows:

F θ = { [ ( 1 - g x ) / ( 1 - g y ) ] × ( ❘ "\[LeftBracketingBar]" v 2 → ❘ "\[RightBracketingBar]" / ❘ "\[LeftBracketingBar]" v 4 → ❘ "\[RightBracketingBar]" ) } 2 .

• • (vi) When g_x≤g_y, |{right arrow over (v₁)}|≤|{right arrow over (v₂)}|, |{right arrow over (v₄)}|≤|{right arrow over (v₃)}|, by increasing g_y or decreasing g_x while keeping |{right arrow over (v₂)}|/|{right arrow over (v₃)}| constant, or keeping g_x and g_y constant while increasing |{right arrow over (v₂)}|/|{right arrow over (v₃)}|, the deflection angle θ of the curved profile is reduced; and by decreasing g_y or increasing g_x while keeping |{right arrow over (v₂)}|/|{right arrow over (v₃)}| constant, or keeping g_x and g_y constant while decreasing |{right arrow over (v₂)}|/|{right arrow over (v₃)}|, the deflection angle θ of the curved profile is increased. Thus, a formula for calculating the deflection angle control factor is established as follows:

F θ = { [ ( 1 - g x ) / ( 1 - g y ) ] × ( ❘ "\[LeftBracketingBar]" v 2 → ❘ "\[RightBracketingBar]" / ❘ "\[LeftBracketingBar]" v 3 → ❘ "\[RightBracketingBar]" ) } 2 .

• • (vii) When g_x≤g_y, |{right arrow over (v₂)}|≤|{right arrow over (v₁)}|, |{right arrow over (v₃)}|≤|{right arrow over (v₄)}|, by increasing g_y or decreasing g_x while keeping |{right arrow over (v₁)}|/|{right arrow over (v₄)}| constant, or keeping g_x and g_y constant while increasing |{right arrow over (v₁)}|/|{right arrow over (v₄)}|, the deflection angle θ of the curved profile is reduced; and by decreasing g_y or increasing g_x while keeping |{right arrow over (v₁)}|/|{right arrow over (v₄)}| constant, or keeping g_x and g_y constant while decreasing |{right arrow over (v₁)}|/|{right arrow over (v₄)}|, the deflection angle θ of the curved profile is increased. Thus, a formula for calculating the deflection angle control factor is established as follows:

F θ = { [ ( 1 - g x ) / ( 1 - g y ) ] × ( ❘ "\[LeftBracketingBar]" v 1 → ❘ "\[RightBracketingBar]" / ❘ "\[LeftBracketingBar]" v 4 → ❘ "\[RightBracketingBar]" ) } 2 .

• • (viii) When g_x≤g_y, |{right arrow over (v₂)}|≤|{right arrow over (v₁)}|, |{right arrow over (v₄)}|≤|{right arrow over (v₃)}|, by increasing g_y or decreasing g_x while keeping |{right arrow over (v₁)}|/|{right arrow over (v₃)}| constant, or keeping g_x and g_y constant while increasing |{right arrow over (v₁)}|/|{right arrow over (v₃)}|, the deflection angle θ of the curved profile is reduced; and by decreasing g_y or increasing g_x while keeping |{right arrow over (v₁)}|/|{right arrow over (v₃)}| constant, or keeping g_x and g_y constant while decreasing |{right arrow over (v₁)}|/|{right arrow over (v₃)}|, the deflection angle θ of the curved profile is increased. Thus, a formula for calculating the deflection angle control factor F_θ is established as follows:

F θ = { [ ( 1 - g x ) / ( 1 - g y ) ] × ( ❘ "\[LeftBracketingBar]" v 1 → ❘ "\[RightBracketingBar]" / ❘ "\[LeftBracketingBar]" v 3 → ❘ "\[RightBracketingBar]" ) } 2 .

According to the calculation formulas for the deflection angle control factors in the above eight different cases, no fewer than six groups of different extrusion velocity combinations are selected within the allowable extrusion velocity range of the extruded material, four-direction differential velocity extrusion experiments are conducted, and the deflection angles θ of the curved profile corresponding to the different extrusion velocity combinations are measured. According to the established relational expressions between the deflection angle control factor F_θ and {right arrow over (v₁)}, {right arrow over (v₂)}, {right arrow over (v₃)}, {right arrow over (v₄)}, as well as g_x and g_y, the deflection angle control factors corresponding to the different deflection angles θ are calculated, and a functional relationship θ=f(F_θ) between the deflection angle θ and the control factor F_θ is established through fitting, thereby enabling accurate regulation of the deflection angle of the 3D curved profile.

The following took the case of g_y≤g_x, |{right arrow over (v₁)}|≤|{right arrow over (v₂)}|, and |{right arrow over (v₃)}|≤|{right arrow over (v₄)}| as an example to further illustrate the specific implementation method. As shown in FIGS. 5A to 5C, the extrusion velocity combinations were selected when g_x was ¼, ⅓, and ½, respectively, and |{right arrow over (v₄)}|/|{right arrow over (v₂)}| was kept at 1, the deflection angles θ of the curved profile at this time were 25.9°, 24.8°, and 20.5°, respectively, and increasing g_x while keeping |{right arrow over (v₄)}|/|{right arrow over (v₂)}| constant reduced the deflection angle θ. The extrusion velocity combinations were selected when g_y was ½, ⅓, and ⅙, respectively and |{right arrow over (v₄)}|/|{right arrow over (v₂)}| was kept at 1, the deflection angles θ of the curved profile at this time were 45.0°, 20.0°, and 11.7°, respectively, and decreasing g_y while keeping |{right arrow over (v₄)}|/|{right arrow over (v₂)}| constant could reduce the deflection angle θ. The extrusion velocity combinations were selected when g_x=g_y=½ and |{right arrow over (v₄)}|/|{right arrow over (v₂)}| is 1.5, 2, and 3, respectively, the deflection angles θ of the curved profile are 34.9°, 28.1°, and 20.6°, respectively, and keeping g_x and g_y constant and increasing |{right arrow over (v₄)}|/|{right arrow over (v₂)}| could reduce the deflection angle θ. By calculating the deflection angle control factor, a functional relationship between 0 and F_θ was established as shown in FIG. 6:

θ = f ⁡ ( F θ ) = 63.5 - 25. F θ + 7.7 F θ 2 - 1.3 F θ 3 + 0.1 F θ 4 - 6.1 × 10 - 3 ⁢ F θ 5 + 1.2 × 10 - 4 ⁢ F θ 6 .

Through the relationship of θ=f(F_θ) expressed by the above formula, the deflection angle θ of the curved profile can be precisely controlled.

Further, to verify the precision of the method provided by this patent, with the forming and manufacturing of curved profiles with r=40 mm and θ=45°, r=30 mm and θ=20°, r=20 mm and θ=15° as a target, according to the actual extrusion velocity range of the extruder and the allowable extrusion velocity range of the extruded material, two of the extrusion velocities are set as fixed values, and then according to the functional relationships established in steps 3 and 4 (the following four relational expressions), the extrusion velocities {right arrow over (v₁)}, {right arrow over (v₂)}, {right arrow over (v₃)}, and {right arrow over (v₄)} can be obtained.

F r = [ ( 1 - g x ) 2 + ( 1 - g y ) 2 ] × ( 1 / G ) ; r = f ⁡ ( F r ) = 44.2 - 33.8 F r - 14.1 F r 2 + 48.5 F r 3 - 33.8 F r 4 + 9.9 F r 5 - 1.1 F r 6 ; F θ = { [ ( 1 - g y ) / ( 1 - g x ) ] × ( ❘ "\[LeftBracketingBar]" v 4 → ❘ "\[RightBracketingBar]" / ❘ "\[LeftBracketingBar]" v 2 → ❘ "\[RightBracketingBar]" ) } 2 ; θ = f ⁡ ( F θ ) = 63.5 - 25. F θ + 7.7 F θ 2 - 1.3 F θ 3 + 0.1 F θ 4 - 6.1 × 10 - 3 ⁢ F θ 5 + 1.2 × 10 - 4 ⁢ F θ 6 .

It is specifically as follows:

• • I. when the target component has r=40 mm and θ=45° (in the −x+y quadrant, at an angle with the −x axis), the calculated values of {right arrow over (v₁)}, {right arrow over (v₂)}, {right arrow over (v₃)}, and {right arrow over (v₄)} are 1.00 mm/s, 1.35 mm/s, 1.35 mm/s, and 1.00 mm/s, respectively;
  • II. when the target component has r=40 mm and θ=45° (in the +x+y quadrant, at an angle with the +y axis), the calculated values of {right arrow over (v₁)}, {right arrow over (v₂)}, {right arrow over (v₃)}, and {right arrow over (v₄)} are 1.35 mm/s, 1.00 mm/s, 1.35 mm/s, and 1.00 mm/s, respectively;
  • III. when the target component has r=30 mm and θ=20° (in the +x+y quadrant, at an angle with the +y axis), the calculated values of {right arrow over (v₁)}, {right arrow over (v₂)}, {right arrow over (v₃)}, and {right arrow over (v₄)} are 1.30 mm/s, 1.00 mm/s, 1.95 mm/s, and 1.00 mm/s, respectively; and
  • IV. when the target component has r=20 mm and θ=15° (in the +x-y quadrant, at an angle with the −y axis), the calculated values of {right arrow over (v₁)}, {right arrow over (v₂)}, {right arrow over (v₃)}, and {right arrow over (v₄)} are 1.44 mm/s, 1.00 mm/s, 1.00 mm/s, and 2.78 mm/s, respectively.

Extrusion experiments were conducted according to the calculated {right arrow over (v₁)}, {right arrow over (v₂)}, {right arrow over (v₃)}, and {right arrow over (v₄)}, and the curved profiles shown in FIGS. 7A and 7B were obtained. The bending radii and deflection angles of the curved profiles were measured to determine the errors between the theoretical and experimental values, as shown in Table 1.

For the section A, the target values were r=40 mm and θ=45, the theoretical calculated values were r=39.5 mm and θ=45°, and the actual values obtained by extrusion according to the calculated extrusion velocities were r=40.4 mm and θ=45°. The errors between the theoretical and experimental values of the bending radius and deflection angle were 2.3% and 0%, respectively.

For the section B, the target values were r=40 mm and θ=45°, the theoretical calculated values were r=39.5 mm and θ=45°, and the actual values obtained by extrusion according to the calculated extrusion velocities were r=38.5 mm and θ=45°. The errors between the theoretical and experimental values of the bending radius and deflection angle were 2.5% and 0%, respectively.

For the section C, the target values were r=30 mm and θ=20°, the theoretical calculated values were r=29.7 mm and θ=19.1°, and the actual values obtained by extrusion according to the calculated extrusion velocities were r=29.1 mm and θ=18.5°. The errors between the theoretical and experimental values of the bending radius and deflection angle were 2.0% and 3.1%, respectively.

For the section D, the target values were r=20 mm and θ=15°, the theoretical calculated values were r=20.1 mm and θ=15.2°, and the actual values obtained by extrusion according to the calculated extrusion velocities were r=21.1 mm and θ=15.6°. The errors between the theoretical and experimental values of the bending radius and deflection angle were 4.8% and 2.6%, respectively.

In summary, for the four cases, the error range between the theoretical and experimental results of the bending radius was only 2.0%-4.8%, and the error range between the theoretical and experimental values of the deflection angle was only 0-3.1%, as shown in tables 1 and 2 respectively, indicating that the shape control method for a 3D curved profile formed by four-direction differential velocity extrusion provided in this application has good accuracy.

Table 1 shows the error comparison between theoretical calculated values and experimental values of the bending radius r.

Table 2 shows the error comparison between theoretical calculated values and experimental values of the deflection angle θ.

Example 2

In a typical implementation mode of the present invention, it is to propose a shape control system for a 3D curved profile formed by four-direction differential velocity extrusion, including:

• • a first functional relationship establishment module, configured to: select no fewer than six groups of different extrusion velocity combinations within an allowable extrusion velocity range of an extruded material, measure bending radii of a curved profile corresponding to the different extrusion velocity combinations, and calculate bending radius control factors of the profile corresponding to the different extrusion velocity combinations; and fit a relationship curve between the bending radii of the curved profile and the bending radius control factors of the profile to obtain a functional relationship between the two;
  • a second functional relationship establishment module, configured to: select no fewer than six groups of different extrusion velocity combinations within the allowable extrusion velocity range of the extruded material, measure deflection angles of the curved profile corresponding to the different extrusion velocity combinations, and calculate deflection angle control factors of the profile corresponding to the different extrusion velocity combinations; and fit a relationship curve between the deflection angles of the curved profile and the deflection angle control factors of the profile to obtain a functional relationship between the two; and
  • a solution module, configured to: calculate four-direction extrusion velocities required for a curved profile to be formed by extrusion according to the two established functional relationships, with a bending radius and a deflection angle of the curved profile to be formed by extrusion as targets.

Although the specific embodiments of the present invention have been described in conjunction with the drawings above, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations made on the basis of the technical solutions of the present invention without creative efforts shall still fall within the scope of protection of the present invention.