CN111046507A - Method for judging spatial envelope forming interference limit of conical thin-wall high-rib component - Google Patents
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Abstract
The invention relates to a method for judging the spatial envelope forming interference limit of a conical thin-wall high-rib component, which comprises the following steps: s1, determining a judgment principle of space envelope forming interference limit of the conical thin-wall high-rib component; and S2, establishing a spherical coordinate system. The distance from a space point to an original point is r, and an included angle between a connecting line from the original point to the point and a positive z axis is taken as an elevation angle theta to establish a spherical coordinate system; s3, determining a curved surface equation of the conical thin-wall high-rib component and a curved surface equation with a corresponding interference value of d; s4, determining the surface point coordinates of the envelope model and the track point coordinates thereof in the space envelope forming process; s5, determining a characteristic angle judgment criterion of the point of the envelope model in the envelope forming process; and S6, determining the maximum interference surface judgment criterion of the surface points of the envelope model. The method can quickly obtain the interference limit of any conical thin-wall high-rib component, and has strong universality and practicability.
Description
Technical Field
The invention relates to the field of conical thin-wall high-rib component forming, in particular to a method for judging the spatial envelope forming interference limit of a conical thin-wall high-rib component.
Background
The thin-wall high-rib component has light weight, high rigidity, high strength and strong bearing capacity, and is a key bearing part of the aerospace equipment. The method is mainly used for manufacturing structural components such as rocket cabins, oil tanks, airplane fuselages, wings and the like. However, the thin-wall high-rib part has large size and complex shape, and the manufacturing difficulty is high.
At present, the main processing methods comprise milling, precision casting, welding and the like. However, these processes have the defects of low material utilization rate, high processing cost, poor performance of parts, low service life and the like. Although the traditional forging process can produce high-performance parts with high efficiency and low cost, the traditional forging process cannot be directly used for forming thin-wall high-strength parts due to the insufficient tonnage of a forging press and the difficulty in filling materials.
The space envelope forming method is an advanced manufacturing technology for realizing integral forming of the component through continuous local plastic deformation, and is particularly suitable for forming thin-wall components. In the process of space envelope forming, the conical thin-wall high-rib member can be formed by utilizing the rotary motion of the envelope die and the uneven stress of the member. In the process of space envelope forming, an envelope die interferes with the conical thin-wall high-rib component, and the bearing capacity of the component is seriously weakened. If the interference limit value is larger than the critical value, the component is easy to damage under the action of eccentric load and cannot be produced and used.
Disclosure of Invention
The invention aims to solve the technical problem of providing a method for judging the spatial envelope forming interference limit of a conical thin-wall high-rib component, which can quickly obtain the interference limit of any conical thin-wall high-rib component.
The technical scheme adopted by the invention for solving the technical problems is as follows: a method for judging the spatial envelope forming interference limit of a conical thin-wall high-rib component is constructed, and comprises the following steps:
s1, determining the space envelope forming interference limit judgment principle of the conical thin-wall high-rib component: when one point on the surface of the enveloping die is positioned in the solid body of the conical thin-wall high-rib component in the motion process, the point has interference, the interference curved surface where the point is positioned is judged to obtain the interference quantity of the point, and the interference quantity of all the points is compared to obtain the interference limit;
s2, establishing a spherical coordinate system; establishing a spherical coordinate system by taking the vertex of the envelope mold as a coordinate origin o, the central line of a main shaft of the machine tool passing through the coordinate origin as a z-axis, the feeding direction of the envelope mold as the negative direction of the z-axis, the distance from a space point to the origin as r and the included angle between the connecting line from the origin to the point and the positive z-axis as an elevation angle theta
S3, determining a curved surface equation of the conical thin-wall high-rib component and a curved surface equation with a corresponding interference value of d;
s4, determining surface point coordinates of envelope model
And track point coordinates thereof in the process of space envelope forming
S5, determining a characteristic angle judgment criterion of the point of the envelope model in the envelope forming process;
and S6, determining the maximum interference surface judgment criterion of the surface points of the envelope model.
In the foregoing solution, in step S3, the thin-walled high-rib member is composed of planes when the cone angle is 180 °, and an equation of the plane obtained By taking any one reference plane is Ax + By + Cz + D is 0, an equation of a curved surface of the corresponding tapered thin-walled high-rib member is f (x, y, z) is 0, and an equation of an interference curved surface is f (x ', y ', z ') -0; the curved surface equation of the conical thin-wall high-rib component and the curved surface equation when the corresponding interference value is d are calculated as shown in formula (1):
wherein β is one half of the complementary angle of the taper thin-wall high-rib component.
In the above solution, in step S4, the equation for calculating the coordinates of the surface points of the envelope model is shown in formula (2), and the equation for calculating the coordinates of the trace points of the surface points of the envelope model is shown in formula (3):
in the formula (I), the compound is shown in the specification,
the three-dimensional spherical coordinate of the surface point A of the conical thin-wall high-rib component is shown, and gamma is one half of the angle complement of the cone angle of the enveloping mould.
In the formula, ω is an angle between the rotation axis and the positive x-axis at any time.
In the above solution, in step S5, the method for determining the characteristic angle criterion of the point of the envelope model in the envelope shaping process includes:
the characteristic angle comprises an interference extreme angle and an intersection angle; selecting any point N on the surface of the envelope model to obtain a change equation of the interference value along with the rotating shaft, and obtaining two extreme angles omega by the Fermat's theoremj1And ωj2(ii) a Performing interference judgment through the interference value, and removing extreme points outside the ribs to obtain an interference extreme angle; the envelope forming track of the point of the envelope mould and the rib surface fiThe intersection of (x, y, z) 0(i 1, 2, 6) with the characteristic angle ωi1And ωi2(ii) a The equation for calculating the interference extreme angle is shown in formula (4); the calculation equation of the intersection angle of the envelope forming track of the point of the envelope model and the surface of the rib is shown as the formula (5):
wherein (A)i，Bi，Ci，Di) Is the surface f of the ribiThe (x, y, z) ═ 0(i ═ 1, 2, ·, 6) equation parameters.
In the above scheme, in step S6, the method for determining the maximum interference surface criterion of the envelope surface point includes:
selecting a bus where the point of the enveloping model is located, wherein when the bus is in contact with the member, the curved surface of the member where the point is located is a reference curved surface, and further obtaining an interference curved surface equation of the point; substituting the obtained characteristic angle into a formula (3) to obtain a characteristic point, substituting the characteristic point into a formula (1) to obtain an interference surface equation, and comparing the interference surface equations of all the characteristic points to obtain a maximum interference surface and a maximum interference value of the point; and (3) solving the maximum interference value of all points on the surface of the enveloping die, and comparing to obtain the space enveloping forming interference limit of the conical thin-wall high-rib component, wherein if the maximum interference value is less than a critical value, the conical thin-wall high-rib component can be used, otherwise, the conical thin-wall high-rib component cannot be used for production.
The method for judging the spatial envelope forming interference limit of the conical thin-wall high-rib component has the following beneficial effects:
1. the method for judging the interference limit of the space envelope forming of the conical thin-wall high-rib component can quickly obtain the interference limit of any conical thin-wall high-rib component, and has strong universality and practicability.
2. The method provided by the invention realizes accurate calculation from the enveloping die to the conical thin-wall high-rib component, and the interference limit value has high accuracy.
Drawings
The invention will be further described with reference to the accompanying drawings and examples, in which:
FIG. 1 is a schematic diagram of the creation of an envelope model coordinate system;
FIG. 2 is a schematic diagram of an envelope mode interference scenario;
FIG. 3 is a schematic view of a reference curved surface and an interference curved surface of a conical thin-wall high-rib component;
FIG. 4 is a schematic diagram of the movement pattern of surface points in the envelope shaping process of the envelope mold;
fig. 5 is a schematic diagram of characteristic angles of surface points in an envelope shaping process of an envelope mold.
Detailed Description
For a more clear understanding of the technical features, objects and effects of the present invention, embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
As shown in fig. 1-5, the method for determining the spatial envelope forming interference limit of the tapered thin-walled high-rib component of the invention comprises the following steps:
and S1, determining the space envelope forming interference limit judgment principle of the conical thin-wall high-rib component. Under the established space rectangular coordinate system, when one point on the surface of the enveloping die is positioned in the entity of the conical thin-wall high-rib component in the motion process, the point has interference, the interference curved surface where the point is positioned is judged, the interference amount of the point is obtained, and the interference limit can be obtained by comparing the interference amounts of all the points.
And S2, establishing a spherical coordinate system. The vertex of the envelope mold is used as a coordinate origin o, the central line of a machine tool spindle passing through the coordinate origin is used as a z-axis, the feeding direction of the envelope mold is used as the negative direction of the z-axis, and the x-axis bisects one of the ribs to establish a rectangular coordinate system, as shown in fig. 1. Establishing a spherical coordinate system by taking the distance from a space point to an original point as r and the included angle between the connecting line from the original point to the point and a positive z axis as an elevation angle theta
Wherein, when the taper angle is 180 degrees, the length of the thin-wall high-rib component is 140mm, the width is 140mm, the web plate thickness is 2mm, four ribs are respectively arranged in the transverse direction and the longitudinal direction, the rib thickness is 3mm, and the rib height is 20 mm.
And S3, determining a curved surface equation of the conical thin-wall high-rib component and a curved surface equation when the corresponding interference value is d. When the taper angle is 180 °, the surface of the thin-wall high-rib member is composed of planes, the reference plane equation is y-24.33 equals to 0, the corresponding reference surface equation of the tapered thin-wall high-rib member equals to f (x, y, z) equals to 0, and the interference surface equation equals to f (x ', y ', z ') equals to 0, as shown in fig. 3.
S4, determining surface point coordinates of envelope model
And track point coordinates thereof in the process of space envelope forming
And S5, determining the characteristic angle judgment criterion of the point of the envelope model in the envelope shaping process.
And S6, determining the maximum interference surface judgment criterion of the surface points of the envelope model.
Further, in the above step S3, the taper angle of the tapered thin-walled high-rib member is 175 °, and the equation for calculating the reference curved surface of the tapered thin-walled high-rib member and the equation for calculating the corresponding curved surface when the interference value is d are shown in formula (1).
Further, in step S4, in step 1, the enveloping die has a taper angle of 170 °, one point a on the surface of the tapered thin-walled rib is taken, the spherical coordinates are (29.5437,
) Envelope model surface point-sphere coordinates (29.5437,
) The envelope trajectory is derived from the rotation matrix, as shown in fig. 4. The calculation equation of the trace point coordinates of the surface points of the envelope model is shown in formula (2).
In the formula, ω is an angle between the rotation axis and the positive z-axis at any time.
Further, the method for determining the characteristic angle of the point of the envelope model in the envelope shaping process comprises the following steps: the characteristic angle includes an interference extreme angle and an intersection angle. The interference value varies with the rotation axis, and two extreme angles 0.0189 and 3.1819 can be obtained by Fermat's theorem. The envelope forming track of the point of the envelope mould and the rib surface fiThe intersection of (x, y, z) 0(i 1, 2, 6) with the characteristic angle ω312.8272 and ω323.5351, as shown in fig. 5. The equation for calculating the interference extreme angle is shown in the formula (4) As shown. The calculation equation of the intersection angle of the envelope forming track of the point of the envelope model and the rib surface is shown as the formula (5).
Further, the method for determining the maximum interference curved surface of the surface point of the envelope model comprises the following steps: and (3) respectively substituting the two obtained extreme value angles 0.0189 and 3.1819 into a formula (3) to obtain characteristic point rectangular coordinates (7.4928, 22.2555 and 17.9271) (7.4495,23.7333 and 15.9394), substituting the characteristic points into a formula (1) to obtain interference values which are 1.3579 and-0.0408 respectively, and removing external points of the ribs to obtain an extreme value interference value 1.3579. Since the intersection point is located on the reference curved surface, the interference value is 0. Comparing the interference surface equations of all the characteristic points, the maximum interference value of the point can be obtained to be 1.3579. And sequentially solving the maximum interference values of all points on the surface of the envelope model, and comparing to obtain: the maximum interference is 1.6527 when the characteristic angle is 0 at the surface point whose rectangular coordinates are (0,22.6806, 19.9527). The interference limit of space envelope forming of the conical thin-wall high-rib component is larger than one half of the wall thickness, so that the conical thin-wall high-rib component cannot be produced and used.
While the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (5)
1. A method for judging the spatial envelope forming interference limit of a conical thin-wall high-rib component is characterized by comprising the following steps:
s1, determining the space envelope forming interference limit judgment principle of the conical thin-wall high-rib component: when one point on the surface of the enveloping die is positioned in the solid body of the conical thin-wall high-rib component in the motion process, the point has interference, the interference curved surface where the point is positioned is judged to obtain the interference quantity of the point, and the interference quantity of all the points is compared to obtain the interference limit;
s2, establishing a spherical coordinate system; establishing a spherical coordinate system by taking the vertex of the envelope mold as a coordinate origin o, the central line of a main shaft of the machine tool passing through the coordinate origin as a z-axis, the feeding direction of the envelope mold as the negative direction of the z-axis, the distance from a space point to the origin as r and the included angle between the connecting line from the origin to the point and the positive z-axis as an elevation angle theta
S3, determining a curved surface equation of the conical thin-wall high-rib component and a curved surface equation with a corresponding interference value of d;
s4, determining surface point coordinates of envelope model
And track point coordinates thereof in the process of space envelope forming
S5, determining a characteristic angle judgment criterion of the point of the envelope model in the envelope forming process;
and S6, determining the maximum interference surface judgment criterion of the surface points of the envelope model.
2. The method for determining the interference limit in spatial envelope formation of the tapered thin-walled high-rib member according to claim 1, wherein in step S3, the thin-walled high-rib member is composed of planes when the taper angle is 108 °, and if a reference plane is taken, the plane equation is Ax + By + Cz + D is 0, the corresponding curved surface equation of the tapered thin-walled high-rib member is f (x, y, z) is 0, and the equation of the interference curved surface is f (x ', y ', z ') is 0; the curved surface equation of the conical thin-wall high-rib component and the curved surface equation when the corresponding interference value is d are calculated as shown in formula (1):
wherein β is one half of the complementary angle of the taper thin-wall high-rib component.
3. The method for determining the spatial envelope forming interference limit of the tapered thin-wall high-rib component according to claim 2, wherein in the step S4, an envelope model surface point coordinate calculation equation is shown in formula (2), and a trace point coordinate calculation equation of an envelope model surface point is shown in formula (3):
in the formula (I), the compound is shown in the specification,
the three-dimensional spherical coordinate of the surface point A of the conical thin-wall high-rib component is shown, and gamma is one half of the angle complement of the cone angle of the enveloping mould.
In the formula, ω is an angle between the rotation axis and the positive x-axis at any time.
4. The method for determining the spatial envelope forming interference limit of the tapered thin-wall high-rib component according to claim 3, wherein in the step S5, the method for determining the characteristic angle determination criterion of the point of the envelope model in the envelope forming process is as follows:
the characteristic angle comprises an interference extreme angle and an intersection angle; selecting any point N on the surface of the envelope model to obtain a change equation of the interference value along with the rotating shaft, and obtaining two extreme angles omega by the Fermat's theoremj1And ωj2(ii) a Performing interference judgment through the interference value, and removing extreme points outside the ribs to obtain an interference extreme angle; the envelope forming track of the point of the envelope mould and the rib surface fiThe intersection of (x, y, z) 0(i 1, 2, 6) with the characteristic angle ωi1And ωi2(ii) a Equation for calculating interference polar angleAs shown in equation (4); the calculation equation of the intersection angle of the envelope forming track of the point of the envelope model and the surface of the rib is shown as the formula (5):
wherein (A)i，Bi，Ci，Di) Is the surface f of the ribiThe (x, y, z) ═ 0(i ═ 1, 2, ·, 6) equation parameters.
5. The method for determining the spatial envelope forming interference limit of the tapered thin-wall high-rib component according to claim 4, wherein in the step S6, the method for determining the maximum interference surface criterion of the envelope surface points is as follows:
selecting a bus where the point of the enveloping model is located, wherein when the bus is in contact with the member, the curved surface of the member where the point is located is a reference curved surface, and further obtaining an interference curved surface equation of the point; substituting the obtained characteristic angle into a formula (3) to obtain a characteristic point, substituting the characteristic point into a formula (1) to obtain an interference surface equation, and comparing the interference surface equations of all the characteristic points to obtain a maximum interference surface and a maximum interference value of the point; and (3) solving the maximum interference value of all points on the surface of the enveloping die, and comparing to obtain the space enveloping forming interference limit of the conical thin-wall high-rib component, wherein if the maximum interference value is less than a critical value, the conical thin-wall high-rib component can be used, otherwise, the conical thin-wall high-rib component cannot be used for production.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN109214083A (en) * | 2018-09-03 | 2019-01-15 | 武汉理工大学 | Circular test down space envelope profiled envelope mould method for accurately designing |
| CN109271689A (en) * | 2018-09-03 | 2019-01-25 | 武汉理工大学 | Circular test down space envelope profiled envelope mould track Method for Accurate Calculation |
| CN110479840A (en) * | 2019-08-02 | 2019-11-22 | 武汉理工大学 | The high muscle Cylinder shape constructional element envelope roll milling forming method of thin-walled |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109214083A (en) * | 2018-09-03 | 2019-01-15 | 武汉理工大学 | Circular test down space envelope profiled envelope mould method for accurately designing |
| CN109271689A (en) * | 2018-09-03 | 2019-01-25 | 武汉理工大学 | Circular test down space envelope profiled envelope mould track Method for Accurate Calculation |
| CN110479840A (en) * | 2019-08-02 | 2019-11-22 | 武汉理工大学 | The high muscle Cylinder shape constructional element envelope roll milling forming method of thin-walled |
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