CN111046507B - 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-reinforcement member, which comprises the following steps: s1, determining a space envelope forming interference limit judgment principle of a conical thin-wall high-reinforcement member; s2, establishing a spherical coordinate system. The distance from the space point to the original point is r, and the included angle between the connecting line from the original point to the point and the positive z axis is used as an elevation angle theta, so that a spherical coordinate system is established; s3, determining a curved surface equation of the conical thin-wall high-reinforcement member and a curved surface equation when the corresponding interference value is d; s4, determining the coordinates of the surface points of the envelope model and the coordinates of the track points 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; s6, determining a maximum interference curved surface judgment criterion of the surface points of the envelope model. The interference limit of any conical thin-wall high-rib component can be obtained rapidly by the method, and the method has strong universality and practicability.
Description
Technical Field
The invention relates to the field of forming of conical thin-wall high-strength members, in particular to a method for judging the spatial envelope forming interference limit of a conical thin-wall high-strength member.
Background
The thin-wall high-strength member has light weight, high rigidity, high strength and strong bearing capacity, and is a key bearing part of aerospace equipment. The method is mainly used for manufacturing structural members such as rocket cabins, oil tanks, aircraft bodies, wings and the like. However, the thin-wall high-strength parts have large size, complex shape and large manufacturing difficulty.
The main processing methods at present are milling, precision casting, welding and the like. However, the 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 forging press is not suitable for forming thin-wall high-strength parts due to insufficient tonnage and difficult filling material.
The space envelope forming method is an advanced manufacturing technology for realizing the integral forming of the component through continuous local plastic deformation, and is particularly suitable for forming the thin-wall component. In the space envelope forming process, the tapered thin-wall high-rib component can be formed by utilizing the rotation movement of the envelope mould and the uneven stress of the component. In the space envelope forming process, the envelope mould interferes with the conical thin-wall high-rib component, so that the bearing capacity of the component is seriously weakened. If the interference limit value is larger than the critical value, the component is extremely easy to break 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 interference limit of the space envelope forming of a conical thin-wall high-rib component, which can rapidly obtain the interference limit of any conical thin-wall high-rib component.
The technical scheme adopted 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, which comprises the following steps:
s1, determining a space envelope forming interference limit judgment principle of a conical thin-wall high-reinforcement member: when a point on the surface of the envelope mould moves and is positioned in the entity of the conical thin-wall high-rib member, the point is interfered, an interference curved surface where the point is positioned is judged, the interference quantity of the point is obtained, and the interference quantity of all points is compared to obtain an interference limit;
s2, establishing a spherical coordinate system; taking the vertex of the envelope model as a coordinate origin o, taking the central line of a machine tool spindle passing through the coordinate origin as a z-axis, taking the feeding direction of the envelope model as a z-axis negative direction, taking the distance from a space point to the origin as r, and taking the included angle between the connecting line of the origin to the point and a positive z-axis as an elevation angle theta, so as to establish a spherical coordinate system
S3, determining a curved surface equation of the conical thin-wall high-reinforcement member and a curved surface equation when the corresponding interference value is d;
s4, determining the surface point coordinates of the envelope modelAnd the coordinates of the trace points 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;
s6, determining a maximum interference curved surface judgment criterion of the surface points of the envelope model.
In the above scheme, in the step S3, when the taper angle is 180 °, the thin-wall high-rib member is formed By a plane, any reference plane is taken to obtain a plane equation of ax+by+cz+d=0, the corresponding curved surface equation of the tapered thin-wall high-rib member is f (x, y, z) =0, and the interference curved surface equation is f (x ', y ', z ')=0; the calculation of the curved surface equation of the conical thin-wall high-rib component when the corresponding interference value is d is shown in the formula (1):
wherein beta is one half of the angle complement of the taper angle of the taper thin-wall high-rib component.
In the above scheme, in the step S4, the envelope surface point coordinate calculation equation is shown in formula (2), and the locus point coordinate calculation equation of the envelope surface point is shown in formula (3):
in the method, in the process of the invention,is the three-dimensional spherical coordinates of the surface point A of the conical thin-wall high-rib component, and gamma is one half of the supplementary angle of the cone angle of the envelope mould.
Wherein ω is the angle between the rotation axis and the positive x-axis at any time.
In the above scheme, in the step S5, the method for determining the characteristic angle judgment criterion of the point of the envelope model in the envelope forming process is as follows:
the characteristic angle comprises an interference extremum angle and an intersection angle; selecting any point N on the surface of the envelope model to obtain a change equation of an interference value along with a rotating shaft, and obtaining two extreme value angles omega by the Fermat theorem j1 And omega j2 The method comprises the steps of carrying out a first treatment on the surface of the Carrying out interference judgment through the interference value, and removing extreme points outside the ribs to obtain an interference extreme angle; envelope shaping track of the point of envelope mould and rib surface f i (x, y, z) =0 (i=1, 2, ··, 6) intersects with the characteristic angle ω i1 And omega i2 The method comprises the steps of carrying out a first treatment on the surface of the The interference extremum angle calculating equation is shown in a formula (4); the calculation equation of the intersection angle of the envelope forming track of the envelope mode point and the surface of the rib is shown in the formula (5):
in the formula (A) i ，B i ，C i ，D i ) Is a rib surface f i (x, y, z) =0 (i=1, 2, ··, 6) equation parameters.
In the above scheme, in the step S6, the method for determining the criterion of maximum interference surface of the surface point of the envelope model is as follows:
selecting a bus where the point of the envelope model is located, and when the bus is in contact with a component, the component curved surface where the point is located is a reference curved surface, so as to obtain 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 curved surface equation, and comparing the interference curved surface equations of all the characteristic points to obtain the maximum interference curved surface and the maximum interference value of the point; and (3) obtaining the maximum interference value of all points on the surface of the envelope mould, and comparing to obtain the space envelope forming interference limit of the conical thin-wall high-rib component, wherein if the interference value is smaller than the critical value, the conical thin-wall high-rib component can be used, otherwise, the conical thin-wall high-rib component cannot be produced and used.
The implementation of the method for judging the interference limit of the space envelope forming 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 of the invention realizes the accurate calculation from the envelope mould to the conical thin-wall high-rib component, and has high interference limit value precision.
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 establishment of an envelope coordinate system;
FIG. 2 is a schematic diagram of an envelope interference scenario;
FIG. 3 is a schematic view of a reference surface and an interference surface of a tapered thin-walled high-rib member;
FIG. 4 is a schematic illustration of the pattern of surface point movement during envelope molding;
fig. 5 is a schematic view of the characteristic angle of the surface point in the envelope forming process.
Detailed Description
For a clearer understanding of technical features, objects and effects of the present invention, a detailed description of embodiments of the present invention will be made with reference to the accompanying drawings.
As shown in fig. 1-5, the method for judging the spatial envelope forming interference limit of the conical thin-wall high-rib component comprises the following steps:
s1, determining a space envelope forming interference limit judgment principle of the conical thin-wall high-rib component. Under the established space rectangular coordinate system, when a point on the surface of the envelope mould moves and is positioned in the entity of the conical thin-wall high-rib member, the point is interfered, the interference curved surface where the point is positioned is judged, the interference quantity of the point is obtained, and the interference limit can be obtained by comparing the interference quantity of all the points.
S2, establishing a spherical coordinate system. Taking the envelope model vertex as a coordinate origin o and taking the machine tool spindle central line passing through the coordinate origin as a z axisAnd taking the feeding direction of the envelope mould as the negative direction of the z axis, and dividing one bar by the x axis to establish a rectangular coordinate system, as shown in figure 1. The distance from the space point to the original point is r, the included angle between the connecting line from the original point to the point and the positive z axis is the elevation angle theta, and a spherical coordinate system is establishedWherein, when the taper angle is 180 degrees, the length of the thin-wall high-rib component is 140mm, the width is 140mm, the thickness of the web plate is 2mm, four ribs are respectively arranged in the transverse and longitudinal directions, the thickness of the ribs is 3mm, and the height of the ribs is 20mm.
S3, determining a curved surface equation of the conical thin-wall high-rib member and a curved surface equation when the corresponding interference value is d. When the taper angle is 180 degrees, the surface of the thin-wall high-rib component consists of planes, a reference plane equation is taken as y-24.33=0, a corresponding tapered thin-wall high-rib component reference curved surface equation is f (x, y, z) =0, and an interference curved surface equation is f (x ', y ', z ')=0, as shown in fig. 3.
S4, determining the surface point coordinates of the envelope modelAnd the coordinates of the trace points thereof in the space envelope forming process
S5, determining characteristic angle judgment criteria of the point of the envelope model in the envelope forming process.
S6, determining a maximum interference curved surface judgment criterion of the surface points of the envelope model.
Further, in the step S3, the taper angle of the tapered thin-walled high-rib member is 175 °, and the calculation equation of the curved surface equation when the corresponding interference value is d is shown in the formula (1).
Further, in the step S4, in the step 1, the envelope taper angle is 170 °, a point a on the surface of the tapered thin-walled rib member is taken, and the spherical coordinates are (29.5437，) Envelope surface spherical coordinates (29.5437, < ->) The envelope trajectory is derived from the rotation matrix as shown in fig. 4. The locus point coordinate calculation equation of the envelope surface point is shown in formula (2).
Wherein ω is the 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 forming process comprises the following steps: the characteristic angle includes an interference extremum angle and an intersection angle. The interference value varies with the rotation axis, and two extreme angles 0.0189 and 3.1819 are obtained by the fermat's theorem. Envelope shaping track of the point of envelope mould and rib surface f i (x, y, z) =0 (i=1, 2, ··, 6) intersects with the characteristic angle ω 31 = 2.8272 and ω 32 = 3.5351, as shown in fig. 5. The interference extremum angle calculation equation is shown in formula (4). The calculation equation of the intersection angle of the envelope forming track of the envelope mode point and the surface of the rib is shown in a formula (5).
Further, the method for determining the maximum interference curved surface of the surface point of the envelope model comprises the following steps: substituting the two obtained extremum angles 0.0189 and 3.1819 into formula (3) to obtain feature point rectangular coordinates (7.4928, 22.2555,17.9271) and (7.4495,23.7333,15.9394), substituting the feature point into formula (1) to obtain interference values 1.3579 and-0.0408, and removing the external points of the tendons to obtain extremum interference value 1.3579. Since the intersection point is located on the reference surface, the interference value is 0. And comparing the interference surface equations of all the characteristic points to obtain the maximum interference value of the point as 1.3579. Sequentially solving the maximum interference values of all points on the surface of the envelope mould, and comparing to obtain: the maximum interference is 1.6527 at a feature angle of 0 at a surface point of rectangular coordinates (0,22.6806,19.9527). Because the space envelope forming interference limit of the conical thin-wall high-rib component is more than one half of the wall thickness, the conical thin-wall high-rib component cannot be produced and used.
The embodiments of the present invention have been described above with reference to the accompanying drawings, but the present invention is not limited to the above-described embodiments, which are merely illustrative and not restrictive, and many forms may be made by those having ordinary skill in the art without departing from the spirit of the present invention and the scope of the claims, which are to be protected by the present invention.
Claims (3)
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 a space envelope forming interference limit judgment principle of a conical thin-wall high-reinforcement member: when a point on the surface of the envelope mould moves and is positioned in the entity of the conical thin-wall high-rib member, the point is interfered, an interference curved surface where the point is positioned is judged, the interference quantity of the point is obtained, and the interference quantity of all points is compared to obtain an interference limit;
s2, establishing a spherical coordinate system; taking the envelope model vertex as the origin of coordinatesTaking the central line of a machine tool spindle passing through a coordinate origin asA shaft with an envelope feeding direction of +.>Negative axis, distance from space point to origin is +.>Connecting line from origin to the point and plus +.>The included angle between the axes is elevation angle->Establishing a spherical coordinate system->；
S3, determining a curved surface equation of the conical thin-wall high-reinforcement member and corresponding interference values asA time curve equation;
s4, determining the surface point coordinates of the envelope modelAnd the coordinates of the trace point during the spatial envelope shaping thereof>；
S5, determining a characteristic angle judgment criterion of the point of the envelope model in the envelope forming process;
s6, determining a maximum interference curved surface judgment criterion of the surface points of the envelope model;
in the step S3, the taper angle isThe thin-wall high-strength member consists of planes, and any reference plane is taken to obtain the plane equation of +.>The corresponding curved surface equation of the conical thin-wall high-rib component is +.>The interference surface equation is +.>The method comprises the steps of carrying out a first treatment on the surface of the The calculation of the curved surface equation of the conical thin-wall high-rib component when the corresponding interference value is d is shown in the formula (1):
（1）
in the method, in the process of the invention,is one half of the cone angle complement angle of the cone-shaped thin-wall high-rib component;
in the step S4, the envelope surface point coordinate calculation equation is shown in formula (2), and the locus point coordinate calculation equation of the envelope surface point is shown in formula (3):
（2）
in the method, in the process of the invention,is the three-dimensional spherical coordinates of the surface point A of the conical thin-wall high-rib component, < > and the like>Is one half of the complement angle of the cone angle of the envelope mould;
（3）
in the method, in the process of the invention,is the rotation axis and the positive +.>And an included angle of the axes.
2. The method for determining the interference limit of the space envelope forming of the tapered thin-walled high-rib member according to claim 1, 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 extremum angle and an intersection angle; selecting any point on the surface of the envelope mouldObtaining a change equation of the interference value along with the rotation axis, and obtaining two extreme angles +.>And->The method comprises the steps of carrying out a first treatment on the surface of the Carrying out interference judgment through the interference value, and removing extreme points outside the ribs to obtain an interference extreme angle; envelope shaping track and rib surface of the envelope mould point +.>Intersection and characteristic angle->And->The method comprises the steps of carrying out a first treatment on the surface of the The interference extremum angle calculating equation is shown in a formula (4); the calculation equation of the intersection angle of the envelope forming track of the envelope mode point and the surface of the rib is shown in the formula (5):
(4)
（5）
in the method, in the process of the invention,is tendon surface->Equation parameters.
3. The method for determining the spatial envelope forming interference limit of the tapered thin-walled high-rib member according to claim 2, wherein in the step S6, the method for determining the maximum interference curve criterion of the surface point of the envelope model is as follows:
selecting a bus where the point of the envelope model is located, and when the bus is in contact with a component, the component curved surface where the point is located is a reference curved surface, so as to obtain 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 curved surface equation, and comparing the interference curved surface equations of all the characteristic points to obtain the maximum interference curved surface and the maximum interference value of the point; and (3) obtaining the maximum interference value of all points on the surface of the envelope mould, and comparing to obtain the space envelope forming interference limit of the conical thin-wall high-rib component, wherein if the interference value is smaller than the critical value, the conical thin-wall high-rib component can be used, otherwise, the conical thin-wall high-rib component cannot be produced and used.
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Citations (3)
| 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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| 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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