CN115122667B - Automatic forming von Kamen type composite material inclined grid structure and forming tool thereof - Google Patents
Automatic forming von Kamen type composite material inclined grid structure and forming tool thereof Download PDFInfo
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- XAGFODPZIPBFFR-UHFFFAOYSA-N aluminium Chemical compound [Al] XAGFODPZIPBFFR-UHFFFAOYSA-N 0.000 claims description 4
- 229910052782 aluminium Inorganic materials 0.000 claims description 4
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- 229920000647 polyepoxide Polymers 0.000 claims description 2
- 239000000463 material Substances 0.000 abstract description 2
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Classifications
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
- B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
- B29C70/00—Shaping composites, i.e. plastics material comprising reinforcements, fillers or preformed parts, e.g. inserts
- B29C70/04—Shaping composites, i.e. plastics material comprising reinforcements, fillers or preformed parts, e.g. inserts comprising reinforcements only, e.g. self-reinforcing plastics
- B29C70/28—Shaping operations therefor
- B29C70/30—Shaping by lay-up, i.e. applying fibres, tape or broadsheet on a mould, former or core; Shaping by spray-up, i.e. spraying of fibres on a mould, former or core
- B29C70/32—Shaping by lay-up, i.e. applying fibres, tape or broadsheet on a mould, former or core; Shaping by spray-up, i.e. spraying of fibres on a mould, former or core on a rotating mould, former or core
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
- B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
- B29C33/00—Moulds or cores; Details thereof or accessories therefor
- B29C33/38—Moulds or cores; Details thereof or accessories therefor characterised by the material or the manufacturing process
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
- B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
- B29C33/00—Moulds or cores; Details thereof or accessories therefor
- B29C33/42—Moulds or cores; Details thereof or accessories therefor characterised by the shape of the moulding surface, e.g. ribs or grooves
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
- B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
- B29C53/00—Shaping by bending, folding, twisting, straightening or flattening; Apparatus therefor
- B29C53/56—Winding and joining, e.g. winding spirally
- B29C53/58—Winding and joining, e.g. winding spirally helically
- B29C53/60—Winding and joining, e.g. winding spirally helically using internal forming surfaces, e.g. mandrels
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
- B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
- B29C53/00—Shaping by bending, folding, twisting, straightening or flattening; Apparatus therefor
- B29C53/80—Component parts, details or accessories; Auxiliary operations
- B29C53/82—Cores or mandrels
- B29C53/821—Mandrels especially adapted for winding and joining
- B29C53/825—Mandrels especially adapted for winding and joining for continuous winding
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
- B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
- B29C70/00—Shaping composites, i.e. plastics material comprising reinforcements, fillers or preformed parts, e.g. inserts
- B29C70/04—Shaping composites, i.e. plastics material comprising reinforcements, fillers or preformed parts, e.g. inserts comprising reinforcements only, e.g. self-reinforcing plastics
- B29C70/28—Shaping operations therefor
- B29C70/54—Component parts, details or accessories; Auxiliary operations, e.g. feeding or storage of prepregs or SMC after impregnation or during ageing
-
- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F42—AMMUNITION; BLASTING
- F42B—EXPLOSIVE CHARGES, e.g. FOR BLASTING, FIREWORKS, AMMUNITION
- F42B15/00—Self-propelled projectiles or missiles, e.g. rockets; Guided missiles
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- Engineering & Computer Science (AREA)
- Mechanical Engineering (AREA)
- Chemical & Material Sciences (AREA)
- Composite Materials (AREA)
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- General Engineering & Computer Science (AREA)
- Moulding By Coating Moulds (AREA)
Abstract
The invention relates to an automatic forming von Karman type composite material inclined grid structure and a forming tool thereof, wherein the inclined grid structure comprises an upper end frame, a lower end frame and bidirectional spiral ribs, wherein the structural materials of the upper end frame and the lower end frame are composite materials; the upper end frame and the lower end frame and the bidirectional spiral ribs are of an integrated structure; the upper end frame and the lower end frame are both inward flanging structures; the outer contour surfaces of the structures of the upper end frame and the lower end frame are von Karman molded surfaces; the inner contour forms a bidirectional spiral rib, the bidirectional spiral ribs are mutually symmetrical, and the central line of the outer contour surface is a von-Karman molded surface equal-pitch spiral line, or an equal-pitch spiral line, or a short distance line. And automatically laying the skin with equal thickness along the von Karman molded surface closely-arranged spiral lines, and automatically winding the inner layer and the outer layer of the skin along the von Karman molded surface short-range line. The von karman curved bus composite material inclined grid structure can be used for replacing a conical structure, a biconical structure and a biconical hood. The automatic forming von Karman composite material inclined grid structure is formed integrally and automatically and precisely by a special forming tool.
Description
Technical Field
The invention belongs to an automatic forming von Karman type composite material inclined grid structure and a forming tool thereof.
Background
In the rocket structure, the instrument cabin, the last repair cabin, the satellite support, the interstage section, the head cover and other straight bus structures are all made of composite material structures in large quantity, so that a good effect of reducing weight is achieved greatly. The von karman type curved bus composite material inclined grid structure has not been applied to rocket structures. The von Karman type bent bus composite material inclined grid structure has the characteristics of large inner envelope and parallel lower bus tangent line and rotating shaft, and can be used for replacing a conical straight bus composite material inclined grid structure which cannot meet the inner envelope requirement and is butted with a column section. The curvature characteristics of von karman type curved bus are superior to those of curved bus such as circle and ellipse, and the mesh structure of the non-skin von karman type composite material can be used for replacing a biconical structure which has the inner envelope requirement and is butted with the column section. The von Karman type curved bus structure has good aerodynamic appearance, and can obviously reduce aerodynamic resistance and load born by rocket. Half-cap separated von-karman honeycomb hoods have been used in our aerospace field. The whole hood thrown von-karman composite lattice structure has not been designed for use. Compared with the von Karman type honeycomb structure, the von Karman type composite material grid structure has low skin rib height and small internal occupied space, and can be used for small-diameter carrier rockets; mounting the instrument on its skin is also more convenient and reliable than honeycomb. The carrier rocket head cover mainly bears the external pressure effect, the characteristic of anisotropy of the composite material grid structure can be fully utilized by the von Karman composite material oblique grid structure, and the grid is arranged in the bearing direction by utilizing the characteristic of curvature change of the von Karman head cover, so that the external pressure bearing efficiency is improved. The von Karman type composite material inclined grid structure combines the optimal aerodynamic shape with a high-strength light structure, and has good engineering application value.
Disclosure of Invention
The invention solves the technical problems that: an automatically formed von Karman composite oblique lattice structure and a forming tool thereof are provided. The automatic forming von Kamen composite material inclined grid structure and the forming tool thereof have reasonable design and realize the lightening of the structure. The automatic forming von Kamen type composite material inclined grid structure and the forming tool thereof have low manufacturing cost and are suitable for automatic batch production of composite material grid storage boxes.
The solution of the invention is as follows: automatic molding von willebrand type composite material inclined grid structure is characterized in that: comprises an upper end frame and a lower end frame which are made of composite materials and bidirectional spiral ribs; the upper end frame and the lower end frame and the bidirectional spiral ribs are of an integrated structure; the upper end frame and the lower end frame are of inward turning structures; the outer contour surfaces of the structures of the upper end frame and the lower end frame are von Karman molded surfaces; the inner profile is provided with bidirectional spiral ribs which are mutually symmetrical, and the central line of the outer profile surface is a von-Karman profile equal-pitch spiral line, or an equal-pitch spiral line, or a short distance line.
Preferably, the sections of the bidirectional spiral ribs are all trapezoids which are congruent with each other, the trapezoids are perpendicular to the central line of the outer contour surface of the bidirectional spiral rib, the central line of the trapezoids points to Feng Ka, and the direction of the rotation axis of the door profile and the central point of the lower bottom of the trapezoids are scanned along the central line of the outer contour surface of the bidirectional spiral rib to form the bidirectional spiral rib.
Preferably, the composite material is a carbon fiber/epoxy resin composite material.
Preferably, it is used to replace a cone structure, a double cone structure, or a double cone nose cap in rocket structures.
Preferably, for a diagonal grid structure instead of a conical structure, the bus bar equation for the outer profile of the structure is determined by:
s1, outer radius R of upper end frame of to-be-formed inclined grid structure 1 Outer radius R of lower end frame 2 Substituting into the bus equation of the von Karman profile, determining the parameter phi in the bus equation of the von Karman profile, and recording the result as phi Upper part ；
S2, phi to be solved Upper part Substituting the distance h between the upper end frame and the lower end frame of the to-be-formed inclined grid structure intoObtaining the distance x of the upper end frame from the vertex of the von Karman profile Upper part ；
S3, mixing the above x Upper part And the sum of the sum and the H is the height H in the bus equation of the Von-Karman molded surface, so that the bus equation of the Von-Karman molded surface of the inclined grid structure to be molded is obtained.
The constant pitch helix trajectory equation is:
k is a constant, and the constant pitch spiral track equation is then determined by determining the value of k, and the value is determined by the following formula:
the helix angle alpha of the spiral line is the included angle between the line tangent of the von Karman profile and the tangent of the spiral line;
The value range of the helix angle alpha of the spiral line of the right-hand coordinate system is (0 degrees, 90 degrees), and the value range of x is [ x ] Upper part ,x Upper part +h]Can select the best according to the specific bearing condition of the structureAnd (5) value conversion. The left hand coordinate system spiral line and the right hand coordinate system spiral line are symmetrical to form the center line of the outer contour surface of the bidirectional spiral rib.
Preferably, in order to lead the bidirectional spiral rib to orthogonally obtain a structure with high external pressure bearing capacity in the middle part of the structure, the structure is formed by the following formulaCalculate phi as phi In (a) And substituting alpha=45° into a k value calculation formula and rounding to obtain a k value, thereby obtaining the required equal-pitch spiral line.
After the k value is determined, the formula:
combination->At [ x ] Upper part ,x Upper part +h]And (3) taking the x value to calculate the corresponding phi value, thereby calculating the helix angle of the equal-pitch helix at any position between the upper end surface and the lower end surface of the inclined grid structure of the von Karman type composite material.
The equal helix angle spiral trajectory equation is:
determination of tan alpha Etc The equal helix angle spiral track equation is uniquely determined along with the value of (1); alpha Etc The range of values (0 DEG, 90 DEG).
Preferably, the start point and the end point of the equal-pitch spiral are the same as the start point and the end point of the equal-pitch spiral, so that
Von karman composite inclined grid structure upper end surface phi abutting cylindrical section instead of conical structure Upper part A lower end face phi Lower part(s) Pi. From the fourth equation of the constant pitch spiral trajectory, von Karman's equation can be calculatedAngle difference between upper and lower end points of constant pitch spiral on the surface:
according to Δθ=k (1-cos φ Lower part(s) )-k(1-cosφ Upper part )＝k+kcosφ Upper part ；
Obtaining tan alpha by solution Etc The helix angle of each of the helix angle helices is alpha Etc 。
The geodesic trajectory equation is:
determination of sin alpha 2 The value of (2) then uniquely determining the geodesic trajectory equation; alpha 2 The range of the values is as followsThe optimal value can be selected according to the specific bearing condition of the structure.
Preferably, in order to make the starting point and the ending point of the short distance line identical to those of the constant-pitch spiral line, the following steps are adopted
According to Δθ=k (1-cos φ Lower part(s) )-k(1-cosφ Upper part )＝k+kcosφ Upper part ；φ Lower part(s) ＝π；
Solving to obtain sin alpha 2 ，α 2 Is the helix angle of the short-range line at the lower end of the structure;
at alpha 2 After determination, the method is characterized by the Kraro relation R 1 sinα 1 ＝R 2 sinα 2 =rsin90° =const, the spiral angle of any position of a short-range line between the upper end face and the lower end face of the von Karman type composite material oblique grid structure can be calculated.
Preferably, for an auto-formed von-karman composite inclined grid structure instead of a bipyramid, the bus equation is solved by solving the following three equation sets:
wherein:
wherein:
wherein:
h 1 、h 2 the heights of the upper cone and the lower cone in the double cones are respectively R Upper part Is the radius of the upper end face of the upper cone in the double cone, R In (a) Radius of the lower end face of the upper cone in the double cones, R Lower part(s) The radius of the lower end face of the lower cone in the double cone is a known quantity; r is the radius at the lower end phi=pi of the von Karman profile and x 1 For von Karman's profile apex to upper cone upper face distance, x 2 The distance from the lower end phi=pi of the von-karman profile to the lower end face of the lower cone is an unknown quantity to be solved.
The outer contour surface center line equation of one spiral rib in the short-range line bidirectional spiral rib is as follows:
the inclined grid structure also comprises a skin, and the skin is formed by combining automatic winding of short-range wires and automatic laying of dense spirals with equal thickness.
The equation of the closely-spaced spiral line with equal thickness and automatic laying is as follows:
adjusting phi 0 The values result in skin plies of different helix angles.
An automatic forming composite material inclined grid von Kamen hood is divided into two parts, wherein the lower part is a hood body, and the upper part is a sphere gap tangent to the hood body; the cover body and the ball gap are respectively formed, and the ball gap is sleeved at the upper end of the cover body from top to bottom outside the cover body; the cover body is of the inclined grid structure.
When the bidirectional spiral rib in the oblique grid structure of the cover body is a spiral line with equal pitch, the spiral angle at the phi=pi position at the lower end of the cover body is marked as alpha, and the k value is determined by the following method:
The automatic forming tool for forming the von Kamen type composite material inclined grid structure comprises a core mold, a male mold and a female mold; the male die is a split male die, a pair of bidirectional spiral rib grooves corresponding to the bidirectional spiral ribs in claim 1 are formed on the split male die at certain angles, and the outer contour surface of the split male die is a von-Karman molded surface with corrected expansion geometric parameters; the central line of the rib groove is a von-Karman profile spiral line with the geometric parameters of the expansion quantity modified.
The external contour surface of the split male die is a von Karman molded surface with corrected expansion geometric parameters, and the correction method is that the external radius R of an upper end frame of the structure 1 Outer radius R of structural upper end frame 2 The distance h between the upper end frame and the lower end frame of the structure is subtracted by the corresponding expansion caused by high-temperature curing to obtain R respectively 1 correction 、R 2 correction 、h Correction The forming device male die outer contour conical surface bus equation is as follows:
H correction Is determined by the following means:
s1, R is 1 correction 、R 2 correction Substituting into the bus equation of the von Karman profile, determining the parameter phi in the bus equation of the von Karman profile, and recording the result as phi Upper correction ；
S2, phi to be solved Upper correction Combining the distance h between the upper end frame and the lower end frame of the to-be-formed inclined grid structure Correction Substituted intoObtaining the distance x of the upper end frame from the vertex of the von Karman profile Upper correction ；
S3, mixing the above x Upper correction And h Correction The sum is H Correction 。
The central line of the rib groove is a von-Karman profile spiral line with the geometric parameters of expansion amount modified; the correction method is to obtain the corrected von Karman profile spiral line by utilizing the characteristic that the angle difference delta theta between the upper end point and the lower end point of the medium-pitch spiral line is unchanged in the expansion curing process on the basis of correction of the male die outer contour cone bus equation.
The corrected rib and groove central line equations are respectively as follows:
1) Male mould von-karman profile constant pitch helix trajectory equation:
2) Male die von karman profile equi-helical angle spiral trajectory equation:
3) Male mold von karman profile geodesic trajectory equation:
the start point and the end point of the spiral line of the mold surface of the three male molds von Karman are coincident.
The bidirectional spiral rib with the central line of the outer contour surface being a short distance line is formed by adopting automatic continuous winding, and the equal-pitch spiral rib and the equal-spiral angle spiral rib are formed by adopting automatic laying.
Automatic winding is realized through an ellipsoidal head, the winding track is accurately calculated, the simulation winding of the short-range wire bidirectional spiral rib is realized, and the accurate calculation of the automatic continuous winding track is realized by solving an equation set consisting of the following seven equations:
a＝k′b
y＝acosφ 1 ＝R 1
c＝R 2 sinα 2
φ 2 ＝90°-α′
Wherein: k' is the length-axis ratio of the ellipsoidal head, and the value range is 1, 2.5; phi (phi) 1 The initial angle of the elliptical cross section of the ellipsoidal head is; a is an ellipsoidal head semi-major axis; b is an ellipsoidal head short half shaft; alpha' is the included angle between the tangent of the ellipsoidal bus and the tangent of the ellipsoidal short-range line; θ 1 Is the circumferential initial angle; phi (phi) 2 The end angle of the elliptical cross section of the ellipsoidal head is; θ 2 Is a circumferential termination angle;
the large ends of the von Karman profiles are transited by cylindrical spiral lines;
the cylindrical spiral equation is:
preferably, the bidirectional spiral rib groove is formed by machining a cutter with the cross section of the bidirectional spiral rib perpendicular to the central line of the inclined rib groove, wherein the central line of the cutter points to the direction of the rotating shaft of the outer surface of the male die, and the cutter is along the central line of the inclined rib groove.
The split male die is an aluminum split male die, and a hard die forming tool is formed.
The split male die is an aluminum backing plate and a silicon rubber grid male die to form a soft die forming tool, the silicon rubber grid male die is formed by casting through a silicon rubber male die casting die, and the soft die forming device and the hard die forming device share a core die.
Compared with the prior art, the invention has the beneficial effects that:
the structure of the invention has the advantages of reasonable design, low cost, light weight and the like, and the manufacturing tool of the structure has the advantages of low manufacturing cost, suitability for automatic mass production of the structure and the like.
(1) The von Karman type bent bus composite material inclined grid structure has the characteristics of large inner envelope and parallel lower bus tangent line and rotating shaft, and can be used for replacing a conical straight bus composite material inclined grid structure which cannot meet the inner envelope requirement and is butted with a column section. The curvature characteristics of von karman type curved bus are superior to those of curved bus such as circle and ellipse, and the mesh structure of the non-skin von karman type composite material can be used for replacing a biconical structure which has the inner envelope requirement and is butted with the column section. The von Karman type curved bus structure has good aerodynamic appearance, can obviously reduce aerodynamic resistance and load born by a rocket, and the von Karman type curved bus composite material inclined grid hood can replace von Karman type honeycomb structure hood and double cone composite material inclined grid hood, so that the optimal aerodynamic appearance is combined with a high-strength light structure.
(2) The von Karman type curved bus composite material is obliquely arranged in a grid structure, and the rigidity of the structure is improved by adding grid reinforcing ribs; and meanwhile, the structural bearing efficiency is improved in a mode of increasing grid reinforcing ribs. The von Karman composite material oblique grid structure can fully utilize the characteristic of anisotropy of the composite material grid structure and utilize the characteristic of change of curvature of the von Karman hood to arrange the grid in the bearing direction, so that the bearing efficiency is improved.
(3) The mesh reinforcing ribs of the mesh structure of the equal-pitch spiral ribs and the equal-pitch spiral ribs of the von Karman composite material are automatically formed in an automatic laying mode, so that the production efficiency and the structure quality consistency are improved.
(4) According to the von Karman type composite material short-range line spiral rib grid structure, the center line of the grid reinforcing rib is the short-range line on the von Karman type surface, the winding track of the grid reinforcing rib is accurately calculated, and by utilizing an ellipsoidal head, automatic continuous winding of the reinforcing rib and the skin is realized, so that the production efficiency is high, and the von Karman type composite material short-range line spiral rib grid structure is suitable for batch production.
(5) The von Karman profile aluminum alloy grid male die can be accurately corrected, and is suitable for grid structures with high dimensional accuracy requirements.
(6) The von karman profile is a non-deployable complex profile, and the constant pitch helix, and the short range line on the von karman profile are spatially complex curves. The silicon rubber grid male die formed by the method has double curvatures, good adhesion with the ellipsoidal surface of the core die and good continuity of the spiral rib grooves.
(7) The silicon rubber grid male die is formed by casting through a three-dimensional casting die, each silicon rubber grid male die is only one tenth to one fifth of the circumference, the grid processing amount is greatly reduced, the processing time of a five-coordinate machine tool can be greatly reduced, the processing cost and the compression processing period are reduced, and the product quality is not influenced; thereby reducing the cost and accelerating the development progress. The structural geometry is not as accurate as that of hard die forming, but can meet the use requirement.
(8) The von karman type curved bus composite material oblique grid structure skin is formed in an automatic winding forming mode, so that the effects of enhancing the shearing resistance of the skin and rib interface, reducing the folds of the outer layer of the skin, optimizing the layering angle and gradually changing the thickness of the skin can be achieved.
(9) The inclined grid structure of the von Karman type curved bus composite material meets the requirement of production, has good structural integrity, good forming process and high production efficiency, and realizes low cost and light weight.
Drawings
FIG. 1 is a von Karman composite lattice structure replacing a conical straight busbar lattice structure;
FIG. 2 is a schematic view of helix angle of a curved bus revolution surface spiral line;
FIG. 3 shows a comparison of three helices of a von Karman lattice structure instead of a cone structure;
FIG. 4 is a cross-sectional view of a constant pitch spiral von Karman composite mesh structure;
fig. 5 is an equi-helical angle spiral von karman grid structure (only spiral grid shown);
fig. 6 is a short Cheng Xianfeng karman grid structure (only a geodesic grid is shown);
FIG. 7 is a cross-sectional view of an automated placement von Karman composite grid structure forming tooling;
FIG. 8 is a schematic illustration of a von Karman composite mesh structured aluminum alloy mesh male mold;
FIG. 9 is a female mold of a von Karman composite lattice structure;
FIG. 10 is a schematic illustration of an aluminum alloy pad of von Karman composite lattice construction;
FIG. 11 is a perspective casting mold of a von Karman grid structured silicone rubber grid male mold;
FIG. 12 is a perspective casting mold grid bottom plate of a silicone rubber grid male mold;
FIG. 13 is a schematic view of a von Karman composite mesh structured silicone rubber mesh male mold;
FIG. 14 is a large end-to-end entangled fiber tow trajectory of a von Karl lattice structure;
fig. 15 is a cross-sectional view of a von karman short Cheng Xianwang lattice structure wound end-to-end;
FIG. 16 shows the helix angle of a closely spaced helix and the tow width;
FIG. 17 is a schematic illustration of a von Karman lattice structured closely packed spiral lay of equal thickness;
FIG. 18 is a double cone structural size requirement;
FIG. 19 is a comparison of three helices on a sphere;
FIG. 20 is a comparison of three helices on an ellipsoid;
FIG. 21 is a non-skinned von Karman composite lattice structure in place of a biconical structure;
FIG. 22 shows a comparison of three helices of a von Karman grid hood;
FIG. 23 is a von Karman short-range wire mesh headcap (only short-range wire mesh shown);
FIG. 24 is a von Karman constant pitch helix mesh headcap (only helix mesh shown);
FIG. 25 is a von Karman's equi-helical pitch helix mesh headcap (only the helix mesh is shown);
FIG. 26 is a von Karman short Cheng Xianwang headgear large end-to-end entangled fiber tow trajectory;
FIG. 27 is a view of the butt joint of von Karman mesh hood body and tip structure;
fig. 28 is a view of a von karman grid hood body molding tooling mandrel and a silicone male mold.
In the figure: 1 die 2 die one 3 bolt 4 upper die 5 blanking cover 6 bolt 7 convex positioning sleeve 8 concave positioning sleeve 9 die two 10 internal thread cylindric lock
Detailed Description
The invention is further illustrated below with reference to examples.
The invention will be described in further detail with reference to the drawings and examples.
1) Spiral angle calculation of spiral line on curved bus rotary surface
As shown in fig. 2, the helix angle α of the helix is defined as the angle between the tangent of the generatrix of the surface of revolution and the tangent of the helix. Taking any point A (x, y, z) on the spiral line, and polar coordinates A (x, r, theta). Let the parameter equation of bus with t as parameter be:
the tangent line of the bus is:
the x-axis is used as a rotation axis to form a rotation surface.
The tangential direction vector of the bus line at the point A is as follows:
let the parameter equation of the spiral line taking t as the parameter be:
the direction vector of the spiral tangent at point a is:
the helix angle α at point a satisfies the following relationship:
the above formula is only given a positive sign due to the symmetry of the spiral line on the surface of revolution.
2) Von Karman type composite material inclined grid structure replacing conical grid structure and tool
2.1 Von Karman-structured bus equation and chord height calculation of relative cone thereof
Von willebrand structural bus equation is:
wherein:
r is the radius of the lower end and H is high.
The upper end of the replaced conical composite material inclined grid structure is 727.602mm in diameter, the lower end of the replaced conical composite material inclined grid structure is 950mm in diameter and 415mm in height, and the half cone angle beta of the conical section is=15° (in this example).
Solving this equation to obtain Φ= 1.707675763; bringing it into the equation:
solving this equation yields x= 546.1514266;
the required von-karman structural bus equation is:
wherein:
namely: x= 480.5757133 (1-cos phi) (15)
In order to reduce the cost, the shaping tool core mould is still a cone section (because the shaping tool core mould is replaced by a cone section structure, the shaping tool core mould is not required to be designed into a von Karman type structure by utilizing the characteristic that the curvature change of the structure except for the end head of the von Karman type structure is small, and the cone core mould of the cone section structure is adopted), the von Karman type structure bus causes the non-uniform thickness of the shaping tool male mould, and the product is heated unevenly during solidification and heating, so that the shaping quality is affected. The chord heights of the von Karman hood and the corresponding cone segments in the middle are calculated (the von Karman structure is formed by using a conical mandrel instead of the cone segments by calculation and the combination example is feasible, the forming quality of the structure is not affected, and the production cost is indeed reduced).
When phi= 124.626626 °,
at this time
Corresponding cone segment mid-radius 419.4005426.
The radius difference was 16.25622423 and the chord height was 15.702307mm.
The maximum chord heights of the von Karman hood and the corresponding cone segments are calculated.
Order theThe method can be solved as follows: phi= 127.6878416 °
x＝480.5757133*(1-cos(127.6878416))＝774.3800611
Here 20.72863451mm below the middle of the structure.
When phi= 127.6878416 °
Corresponding cone segment radius 424.9547636, radius difference 16.4057574 and chord height 15.8467448mm. Has little influence on the curing quality. The core mould of the corresponding cone section can be used, and only the male mould can be changed.
Von karman structural profiles are formed by von karman busbar revolution, whose profile parameter equation:
wherein f (φ) = 480.5757133 (1-cos φ) (18)
2.2 von-Karman type constant-pitch spiral rib composite material inclined grid structure design
Let von. Karman's structural profile constant pitch helix equation be:
substituting into (8) to obtain:
the solution is as follows:
in order to make the bidirectional spiral ribs orthogonal near the middle of the structure, the following adjustment calculation is performed:
in the middle phi= 124.626626, substituting the above and letting alpha=45°,
obtaining: k= 1.146209659
Namely: θ= 1.146209659 (1-cos φ) (24)
In the above method, theta is an radian system, and in order to facilitate three-dimensional modeling of the structure, theta is converted into an angle system:
θ is k= 65.6729759 when the angle is made.
The maximum chord height phi= 127.6878416 °, substituting the above and letting alpha=45°, converting the radian system into an angle system (1.127261195 x 180/pi= 64.58730888), k= 64.58730888,
to compare the thermal expansion correction effect, the rounding was 65. When k=65, Φ= 126.485473 °
x＝480.5757133*(1-cos(126.485473))＝766.3351415
961.1514266-766.3351415＝194.816285，
Here 12.68375mm below the middle of the structure.
When phi= 126.485473 °
Corresponding cone radius 422.7991337.
The radius difference was 16.3830214 and the chord height was 15.8247835mm.
The normal constant pitch helix equation on von karman profile at 12.68375mm below the middle of the structure is:
the constant pitch helix on the von karman profile is shown in the right-hand curve of fig. 3. The inclined grid structure of the von Karman type equal-screw-distance spiral rib composite material replacing the conical grid structure is shown in fig. 4, the ribs are 8mm in height, 6mm in width, 7.5 degrees in draft angle, 1.2mm in skin, 8mm in thickness at the upper end frame and 40mm in width.
Von karman composite inclined lattice structure with upper end surface phi= 1.707675763 and lower end surface phi=pi is substituted for the conical lattice structure. From the fourth equation above, the angular difference between the upper and lower end points of the constant pitch helix on the von karman profile can be calculated:
Δθ＝65(1-cos180°)-65(1-cos97.842614°)＝56.13059348°
2.3 Von-type equal helix angle spiral bar composite material inclined grid structure design
Let von. Karman's structural profile equal helix angle spiral equation be:
substituting into (8) to obtain:
the solution is as follows:
the upper limit is integrated with phi=pi and phi= 1.707675763,
and let the integrated value Δθ= 56.13059348 °
And (3) solving to obtain: tan α= 0.896512192, α= 41.87661382 °.
The equi-helical angle spiral equation on the von karman structural profile is:
the equi-helical angle spiral on the von karman profile is shown in the middle curve of fig. 3. The von karman type equal helix angle spiral bar composite material inclined grid structure replacing the conical grid structure is shown in fig. 5. The helical rib composite material oblique grid structure rib structure parameters of the equal helical angle helical rib composite material are the same as those of the equal helical angle helical rib structure parameters, and only the equal helical angle helical grid is shown.
2.4 Von Karman type short-range wire spiral bar composite material inclined grid structure design
The spiral line on the rotation surface conforming to the relation of the clairet (Chairaut) is a short-range line.
Clero (charaut) relation:
r 1 sinα 1 ＝rsin90°＝const (31)
wherein: r is (r) 1 Is any one of busesRadius of the point; alpha 1 Helix angle for this point; r=const is the pole bore radius of the geodesic spiral wound wire.
The formula (7) shows that:
multiplying both sides by R 2 ＝g 2 (t) (1)
And (3) solving to obtain:
substituting the formulas (18) and (19) into the above formula:
The upper limit is integrated with phi=pi and phi= 1.707675763,
and let the integrated value Δθ= 56.13059348 °
And (3) solving to obtain: sin α= 0.5916313655, α= 36.27286047 °, this angle being the helix angle of the short-range line at the lower end of the structure.
c＝r 2 sinα 2 ＝475sin36.27286047°＝281.0248984
c＝r 1 sinα 1 ＝363.801sinα 1 ＝281.0248984
And (3) solving to obtain: sin alpha 1 ＝0.772468735，α 1 ＝50.57609969°The angle is the helix angle of the short range line at the upper end of the structure.
The equation for the short-range line on the profile of von karman is:
the short-range line on the von karman profile is seen in the left-hand curve of fig. 3. The von karman style short-range wire spiral bar composite inclined grid structure replacing the conical grid structure is shown in fig. 5. The structural parameters of ribs of the inclined grid structure of the short-range wire spiral rib composite material are the same as those of the equal-screw-distance spiral rib structure, and only the short-range wire grid is shown.
The arc lengths of the short-range, equi-helical-angle, and equi-pitch helical lines on the von-karman profile across the same end points shown in fig. 3 were 599.117mm, 601.027mm, 604.157mm, respectively, were calculated. Meanwhile, as can be seen in fig. 3, since the bus bars of the von karman profiles are curved bus bars, the spiral lines on the three von karman profiles have larger difference, so that only the short-range spiral ribs on the von karman profiles can be automatically wound, and the other two spiral ribs can be formed only by an automatic laying mode.
2.5 von-Karman profile and constant-pitch spiral rib expansion amount correction and structure forming tool
Von karman hood expansion calculation. The expansion is calculated as follows:
Δl＝l 0 ×(α m -α c )×(T gel -t) (38)
wherein: Δl—die swell; l (L) 0 -product size;
α m -the coefficient of thermal expansion of the mold material; alpha c -the coefficient of thermal expansion of the product;
T gel -resin gel point temperature; Δα= (α) m -α c ) The difference in thermal expansion coefficient is calculated as the difference between the thermal expansion coefficients of the aluminum alloy and the steel alloy and the thermal expansion coefficient of the carbon material.
The difference in thermal expansion coefficient in the diameter direction was Δα=10.7.
Structurally, it isEnd diameter expansion amount: 727.602 ×10.7X10X10 -6 ＝0.856
Diameter of upper end of die: 727.602-0.856= 726.746
Diameter expansion amount of the lower end of the structure: 950×10.7X10X10 -6 ＝1.118
Diameter of lower end of die: 950-1.118 = 948.882
The difference in thermal expansion coefficients in the height direction is: Δα=24-4=4.
Structural height expansion amount: 415×20×110×10 -6 ＝0.913
Height of the die: 415-0.913= 414.087
Computing corresponding von Karman cover bodies
Solving this equation yields Φ= 1.707676467, which is taken into the equation:
solving this equation yields x= 544.9506681;
the die was 414.087mm high, 726.746mm in diameter at the upper end and 948.882mm in diameter at the lower end.
The expansion-corrected von karman hood bus equation is:
Wherein:
the structure is as follows: θ=k (1-cos Φ), k=65 (43)
And (3) a mold: θ '=k "(1-cos φ') (44)
The structure is as follows:φ 2 ＝180°
and (3) a mold:φ′ 22 ＝180°
Δθ＝θ 2 -θ 1 ＝θ′ 22 -θ′ 1 (45)
formula (43), formula (44) and phi 1 、φ 2 、φ′ 1 、φ′ 2 Substituting formula (45), it can be calculated:
k”＝65.00005314
the constant pitch helix equation on the von-karman profile corrected for expansion is:
the cross section of the aluminum alloy male die, the male die and the female die are respectively shown in figures 7, 8 and 9. Compared with a corresponding conical section structure tool, the von Karman type tool with the constant-pitch spiral rib inclined grid structure is characterized in that the outer contour of a male die, the constant-pitch spiral rib groove of the male die, the inner contour of a female die and the conical section structure are different, and the rest of the tool can be used in the prior art. The outer contour generatrix of the male die is represented by a formula (41) and a formula (42), and the equal-pitch spiral rib groove of the male die is formed by processing a special cutter with a rib section along an equal-pitch spiral line of a formula (46). The internal contour bus of the female die is shown as a formula (13) and a formula (14). The von Karman profile aluminum alloy grid male die can be accurately corrected, and is suitable for grid structures with high dimensional accuracy requirements.
To further reduce the cost, a silicone rubber male mold is designed. The aluminum alloy backing plate is shown in fig. 10, and is mounted on the mandrel shown in fig. 7 instead of the aluminum alloy male die. The silicon rubber grid male die is shown in fig. 13, and is adhered to the aluminum alloy backing plate, so that the space position of the grid rib groove on the silicon rubber grid male die is the same as that of the grid rib groove on the aluminum alloy grid die, and the same structure is formed as that of the aluminum alloy grid die. The three-dimensional casting mold of the silicon rubber grid male mold is shown in fig. 11, the grid bottom plate of the three-dimensional casting mold of the silicon rubber grid male mold is shown in fig. 12, and the von Karman profile is a non-expandable curved surface, so that the molding difficulty of the silicon rubber grid mold is high, and the three-dimensional casting is needed. And selecting a proper tangent plane, so that the distances between the four angles of the silicon rubber grid die and the tangent plane are approximately equal, the three-dimensional casting is flattened as much as possible, and the smooth fluidity of the cambered surface is fully utilized to ensure the casting quality of the silicon rubber male die. The von karman profile is a non-deployable complex profile, and the constant pitch helix, and the short range line on the von karman profile are spatially complex curves. The silicon rubber grid male die formed by the method has double curvatures, and is good in fit with the ellipsoidal surface of the core die and good in continuity of the spiral rib grooves. Each silicon rubber grid male die is only one fifth of the circumference, the grid processing amount is greatly reduced, and the processing time of a five-coordinate machine tool can be greatly reduced, so that the processing cost and the compression processing period are reduced, the cost is reduced, and the grinding progress is quickened. The structural geometry is not as accurate as that of hard die forming, but can meet the use requirement.
2.6 Von-karman type equi-helical angle helical rib expansion correction
Referring to the methods described in 2.3) and 2.5), the equi-helical angle spiral equation on the von-karman profile corrected for the amount of expansion can be calculated as:
2.7 Von Karman type short-range line spiral rib expansion correction
Referring to the methods described in 2.4) and 2.5), the shortpath equation on the von-karman profile corrected for the amount of expansion can be calculated as:
2.8 Design of winding track of upper end socket
Radius of upper end of cone section
c=asinα' = 218.0248984 (as described in 2.4) (52)
(see the method described in 2.4) (53)
φ 2 ＝90°-α′ (54)
Let k=1.2, the values of the parameters obtained by solving the equation set are shown in the following table:
and calculates the value of the following formula:
2×(θ 2 -θ 1 )-7×18°＝-3.317376818°≈-3.32° (56)
z＝bsinφ 1 ＝102.8091576
the middle uses cylindrical spiral line to transition 8.06 degrees.
Cylindrical spiral equation:
θ=8.06°, where z= 91.05467799.
Von willebrand winding, 20 spiral tendons:
(18°×7-3.32°+56.13°+56.13°-0.94°)×2＝468°
468°+18°＝486°，486°-360°＝126°，126°/18°＝7
the winding can be continuous. See fig. 14, 15.
2.9 Von-karman-profile closely spaced spiral equations and closely spaced equal thickness placements
As shown in fig. 16, the width of the fiber bundles at the time of automatic laying is set to d, and n fiber bundles are total. At R 0 The circumference of the part is: 2 pi R 0 =nd, perimeter at R: 2pi r=nd R 。
In order to automatically lay the central line of the fiber tows along the closely-arranged spiral lines on the conical surface, the following steps are:
d＝d R cosα (58)
Thereby making it
R 0 ＝Rcosα (59)
β=0 +.>Is->
Namely:
bringing formula (18), formula (19) and formula (61) into formula (8):
the closely spaced spiral equations on the von karman face are:
can be taken outAdjusting phi 0 The values result in skin plies of different helix angles.
As shown in fig. 17, the closely-spaced spiral lines are used for automatically laying the skin fiber bundles of the curved bus composite structure, so that the skin with equal thickness can be obtained.
The skin is formed in a paving and winding integrated mode, the outermost layer skin and the innermost layer skin are automatically wound and formed, so that the shearing resistance between the skin and ribs is increased, folds on the outer surface of the structure are reduced, and the middle layers of the skin are different in phi 0 The dense spiral is laid with equal thickness, so as to achieve the purpose of equal thickness of the skin.
The automatic winding and forming mode can achieve the similar braiding effect between rib nodes and between ribs and the skin, so that the shearing capacity of interfaces between ribs and between grids and the skin is enhanced, and a short-range wire spiral rib grid structure is preferably selected for forming in an automatic winding mode. The equal-pitch spiral rib grid structure is simple in design because the calculation of the equal-pitch spiral line equation does not need integration. The helical rib grid structure with the orthogonal equal helix angles is well stressed by external pressure. A constant pitch helix, the helix angle decreasing with decreasing radius; an equal helix angle helix, the helix angle not changing with the change of radius; the nanowire helix angle increases with decreasing radius. The characteristics of each spiral rib grid structure and the spiral angle change characteristics of each spiral line are combined, and different spiral rib grid structures are selected according to engineering actual requirements.
3) Von Karman type composite material inclined grid structure replacing bipyramid
The double cone structure size requirement is shown in fig. 18.
Typical curved generatrices include circles, ellipses, hyperbolas, parabolas, cycloids, von-karman curves, and the like. The bus equations are respectivelyy＝ax 2 、When the x coordinate axis of the bus bar is coincident with the rotation axis, the ellipse, the hyperbola and the von Karman curve can pass through given three points; whereas circles, parabolas, cycloids cannot pass through a given three-point, the x coordinate axis needs to be offset a distance from the axis of rotation to pass through the given three-point.
The circular bus equation by giving three points can be set as:
solving the equation to obtain:
The circular bus equation is:
from this, phi can be calculated 1 When the angle between the tangent line of the bus and the axis is 20.19 DEG, the included angle is 20.19 DEG
There are 2) the method described in connection with the circular bus parametric equation, three kinds of spiral lines on the sphere with the same end point can be obtained, see fig. 19.
The elliptical bus equation by giving three points can be set as:
solving the equation to obtain:
The elliptic bus equation is:
from this, phi can be calculated 1 When= 37.57226867 °, the included angle between the tangent line of the bus and the axis is 22 °.
The method 2) is combined with an elliptic bus parameter equation, so that three spiral lines on an elliptic surface with the same endpoint can be obtained, and the three spiral lines are shown in fig. 20.
The remaining curved bus parametric equations and the three spiral lines on the revolution surface formed by the curved buses can be all obtained by the same method, and will not be described in detail.
Given a three-point von-karman grid structure bus equation, the following equation is satisfied:
wherein:
wherein:
wherein:
R、x 1 、x 2 for unknowns, solving the equation to obtain: x is x 1 ＝437.2448422mm，x 2 75.48403095mm, r= 1406.545135mm. Taking x after finishing 1 ＝437.2mm，x 2 ＝75.3mm，R＝1406.5mm。
By giving a three-point von-karman grid structure bus equation:
wherein:
the arc of phi= 2.698933903 (0.859pi) is substituted into the arc, so that the tangent of the tangent line of the bus at the lower end of the grid structure of the von Karman composite material with the axis is 0.2476677873, namely the angle of the tangent line of the bus with the axis is 13.91 degrees, which is smaller than the angle value of the circular bus and the elliptic bus, and the lower end of the structure is more parallel to the axis, which is more beneficial to axial force transmission, thereby being beneficial to butt joint with the column section.
Curvature calculation:
the upper end of the structure is 437.2mm from the von Karman cone tip. Phi= 1.114769991 (0.355 pi) radians. The structural median face is 937.2mm from von Karman cone apex. Phi= 1.771762345 (0.564 pi) radians.
Phi is calculated from 0.35 pi to 0.86 pi, and the curvature is calculated every 0.05 pi, and the values are as follows:
0.0003068711225，0.0002946813551，0.0002958739336，0.0003096719477，0.0003372552273， 0.0003818648089，0.0004495429159，0.0005508529452，0.0007046814009， 0.0009475511678,0.001361227071
The radius 2581.56mm of the circular generatrix and the curvature 0.0003873626799. The circular bus curvature starts to be smaller than von karman bus at slightly greater than 0.6pi. At the part with phi less than 0.6 pi, the structural profile is changed from a spherical shape to a von Karman shape, so that the curvature of the profile is reduced, and the bearing capacity is improved. At the part with phi larger than 0.6pi, the included angles between the tangent line and the axis of the von Karman type structural bus are smaller than those of the circular bus, which is favorable for axial force transmission and is favorable for butt joint with the column section.
Substituting the elliptic parameter equation into equation (79) to obtain an elliptic curvature radius:
and the same applies to obtain the calculation formulas of the curvatures and the radii of curvatures of hyperbolas, parabolas and cycloids.
The more upward curvature is calculated to be elliptical, hyperbolic, parabolic and cycloidal, the better the linearity is than the von Kaplan curve. According to the curvature characteristics of each busbar and the included angle between the tangent line of the busbar at the lower end and the axis, a von Karman grid structure is selected.
The original double-cone structure has a strict rigidity requirement. Hollow circular section moment of inertia:
from the above equation, the smaller the diameter, the smaller the moment of inertia. The short-range line helix angle increases with decreasing radius as described in 2), which is advantageous for increasing the small end stiffness and for large end openings. Meanwhile, the curvature of the short distance line is smaller than that of a spiral line with equal pitch and equal spiral angle, and the force transmission is direct and good in manufacturability. Therefore, a von willebrand type short-range wire spiral bar composite material grid structure is selected, and the short-range wire equation is as follows:
The short-range line helix angle changes from bottom 15 ° to upper end to 32.74 °, and from equation (58), the upper end stiffness is improved by cos15 °/cos32.74 ° =1.148 times over the equal helix angle helical rib.
The non-skinned von karman composite lattice structure replacing the biconical structure is shown in fig. 21.
4) Composite oblique grid von Kamen hood
Composite diagonal mesh von karman hoods were designed to replace the biconical composite mesh hoods. Proximate to engineering practice, von-karman hood lower end radius 500, height 1400, at which time its bus equation is:
wherein:
4.1 Design of von Kamen hood bulb
For the convenience of process shaping, the fairing is divided into two parts, the lower part is a von Karman cover body, and the upper end is a sphere gap which is matched with the von Karman cover body. The von Karman cover body and the sphere are respectively formed, and the sphere is sleeved at the upper end of the von Karman cover body from top to bottom outside the von Karman cover body.
Make the ball lack inWhen tangent to the von Karman mask.
Let the projection of the segment on the xoy plane be:
and (3) solving to obtain:
and (3) solving to obtain: r= 128.9327909
4.2 Composite material short-range line spiral rib inclined grid von Karman head cover
Short Cheng Xianji holes are on von Kamen hood profileWhere it is located.
arcsin(110.2663301/500)＝12.74°
The short-range line is from phi=pi to phiAnd the grid at the position of the short-distance pole hole is avoided, and a space is reserved for a shaft of the forming tool during forming. / >To->Between (a) and (b)Von Karman cover body and the ball segment are integrally formed.
The short-cut lines on the von karman hood profile are shown in the left-hand curve of fig. 22. The composite material short-range wire spiral ribs are obliquely arranged on the grid von Karman hood, as shown in figure 23. Only a geodesic grid is shown.
With the methods described in 2.2) and 2.3), von Karman hood constant pitch helix and constant pitch helix were obtained.
4.3 Composite material constant-pitch spiral rib inclined grid von Karman hood
The constant pitch helix on the von karman hood profile is shown in the right curve of fig. 22. The composite constant pitch helical ribs are inclined to grid von Karman hood see FIG. 24. Only a constant pitch helical mesh is shown.
4.4 Composite material equi-helical angle spiral rib inclined grid von Karman head cover
The constant pitch helix on the von karman hood profile is shown in the middle curve of fig. 22. The composite material with the helical ribs of equal helix angles obliquely arranged on the net von Karman hood is shown in figure 25. Only the equi-helical angle spiral mesh is shown.
4.5 Closely spaced spirals on von karman hood
Can be taken outAdjusting phi 0 The values result in skin plies of different helix angles.
From the method described in 2.8), the trajectory of the composite material stubs helical ribs diagonal to the grid von-karman hood large end relative to the wound fiber tows can be calculated, see fig. 26.
To->The von Karman cover body and the ball segment are integrally formed and sleeved at the upper end of the von Karman cover body, as shown in fig. 27.
In order to realize the opposite winding of the large ends of the composite material short-range wire spiral ribs inclined grid von and the Karman hood, a hood body molding tool mandrel and a silicon rubber male die are designed, as shown in fig. 28. The method for designing and shaping the silicone rubber male mold is described in 2.5).
5) Instead of the von-karman profile spiral length calculation of the conical lattice structure.
To facilitate automatic winding and automatic laying of the composite fiber tows, the helical length on the von-karman profile was calculated.
Let von karman bus tangent and X-axis clip angle be γ, combine (13), (15), (16):
the included angle between the tangential line of von Karman bus and the tangential line of the spiral line on the von Karman molded surface is alpha,
the helical length on von-karman profile is:
the length of the stubs on von karman profile is:
from 2.4) c=r 'sinα' =475sin36.27286047+= 281.0248984:
α′＝36.27286047° (101)
the constant pitch helix length on von-karman profile is:
from k= 1.146209659 in formula (22) and 2.4), it can be seen that:
the constant pitch helix length on von-karman profile is:
from 2.3 it is known that α= 41.87661382 ° (105)
The closely spaced helices on the von karman profile are of length:
from formula (60):
cosα＝R 0 /R (107)
the geodesic, equi-helical angle helix, and equi-pitch helix arc lengths for the same endpoints of fig. 3 can be calculated to be 599.117mm, 601.027mm, 604.157mm, respectively. The closely spaced spiral arc length of fig. 17 is 937.291mm.
Note that: due to the problem of formula version display, the applicationIf the display appearsWhich is essentially the parameter phi.
Although the present application has been described with respect to the preferred embodiments, it is not intended to be limited thereto, and any person skilled in the art can make any possible variations and modifications to the technical solution of the present application by using the methods and technical matters disclosed above without departing from the spirit and scope of the present application, so any simple modifications, equivalent variations and modifications to the above embodiments according to the technical matters of the present application fall within the scope of the technical matters of the present application.
The application is not described in detail in the field of technical personnel common knowledge.
Claims (26)
1. Automatic molding von willebrand type composite material inclined grid structure is characterized in that: comprises an upper end frame and a lower end frame which are made of composite materials and bidirectional spiral ribs; the upper end frame and the lower end frame and the bidirectional spiral ribs are of an integrated structure; the upper end frame and the lower end frame are of inward turning structures; the outer contour surfaces of the structures of the upper end frame and the lower end frame are von Karman molded surfaces; the inner contour is formed into a bidirectional spiral rib, the bidirectional spiral ribs are mutually symmetrical, and the central line of the outer contour surface is a von-Karman molded surface equal-pitch spiral line, or an equal-pitch spiral line, or a short distance line;
For a canted mesh structure instead of a conical structure, the bus bar equation for the outer profile of the structure is determined by:
s1, outer radius R of upper end frame of to-be-formed inclined grid structure 1 Outer radius R of lower end frame 2 Substituting the bus equation of von-karman profile to determine parameters in the bus equation of von-karman profileΦThe result of the solution is recorded asΦ Upper part ；
S2, to be solvedΦ Upper part Substituting the distance h between the upper end frame and the lower end frame of the to-be-formed inclined grid structure into
Obtaining the distance x of the upper end frame from the vertex of the von Karman profile Upper part ；
S3, mixing the above x Upper part And the sum of the sum and the H is the height H in the bus equation of the Von-Karman molded surface, so that the bus equation of the Von-Karman molded surface of the inclined grid structure to be molded is obtained.
2. The diagonal grid structure according to claim 1, wherein: the sections of the bidirectional spiral ribs are all trapezoids which are congruent with each other, the trapezoids are perpendicular to the central line of the outer contour surface of the bidirectional spiral rib, the central line of the trapezoids points to Feng Ka, and the central point of the lower bottom of the trapezoids is scanned along the central line of the outer contour surface of the bidirectional spiral rib to form the bidirectional spiral rib.
3. The diagonal grid structure according to claim 1, wherein: the composite material is a carbon fiber/epoxy resin composite material.
4. The diagonal grid structure according to claim 1, wherein: is used for replacing a conical structure, a double conical structure or a double conical hood in a rocket structure.
5. The diagonal grid structure according to claim 1, wherein: the constant pitch helix trajectory equation is:
k is a constant, and the constant pitch spiral track equation is then determined by determining the value of k, and the value is determined by the following formula:
the helix angle alpha of the spiral line is the included angle between the line tangent of the von Karman profile and the tangent of the spiral line;
the value range of the helix angle alpha of the spiral line of the right-hand coordinate system is (0 degrees, 90 degrees), and the value range of x is [ x ] Upper part ,x Upper part +h]The left hand coordinate system spiral line and the right hand coordinate system spiral line are symmetrical to form the center line of the outer contour surface of the bidirectional spiral rib.
6. The diagonal grid structure according to claim 5, wherein: in order to lead the bidirectional spiral rib to orthogonally obtain a structure with high external pressure bearing capacity in the middle part of the structure, the structure is formed byCalculatingΦIs marked asΦ In (a) And substituting alpha=45° into a k value calculation formula and rounding to obtain a k value, thereby obtaining the required equal-pitch spiral line.
7. The diagonal grid structure according to claim 5 or 6, wherein: after the k value is determined, the formula:
Combination->At [ x ] Upper part ,x Upper part +h]The corresponding value of x is calculatedΦAnd (3) calculating the value of the spiral angle of any position of the equal-pitch spiral line between the upper end surface and the lower end surface of the inclined grid structure of the von Karman type composite material.
8. The diagonal grid structure according to claim 1, wherein: the equal helix angle spiral trajectory equation is:
determination of tan alpha Etc The equal helix angle spiral track equation is uniquely determined along with the value of (1); alpha Etc The range of values (0 DEG, 90 DEG).
9. The diagonal grid structure according to claim 8, wherein: in order to make the starting point and the ending point of the equal-spiral angle spiral line identical to those of the equal-pitch spiral line, let
According to Δθ=k (1-cosΦ Lower part(s) )-k(1-cosΦ Upper part )＝k+kcosΦ Upper part ；Φ Lower part(s) ＝π；
Obtaining tan alpha by solution Etc The helix angle of each of the helix angle helices is alpha Etc 。
10. The diagonal grid structure according to claim 1, wherein: the geodesic trajectory equation is:
determination of sin alpha 2 The value of (2) then uniquely determining the geodesic trajectory equation; alpha 2 The range of the values is as follows
11. The diagonal grid structure according to claim 10, wherein: in order to make the starting point and the ending point of the short distance line identical to those of the constant-pitch spiral line, make
According to Δθ=k (1-cos Φ Lower part(s) )-k(1-cosΦ Upper part )＝k+kcosΦ Upper part ；Φ Lower part(s) ＝π；
Solving to obtain sin alpha 2 ，α 2 Is the helix angle of the short-range line at the lower end of the structure;
at alpha 2 After the determination, the spiral angle of any position of the short distance line between the upper end surface and the lower end surface of the inclined grid structure of the von Karl composite material can be calculated by the Krelet relation.
12. The diagonal grid structure according to claim 4, wherein: for an automatically formed von-karman composite oblique grid structure replacing a bipyramid, the bus equation is obtained by solving the following equation set consisting of three equations:
wherein:
wherein:
wherein:
h 1 、h 2 the heights of the upper cone and the lower cone in the double cones are respectively R Upper part Is the radius of the upper end face of the upper cone in the double cone, R In (a) Radius of the lower end face of the upper cone in the double cones, R Lower part(s) The radius of the lower end face of the lower cone in the double cone is a known quantity; r is von Karman profile lower endΦRadius at =pi, x 1 For von Karman profile vertex toDistance x of upper end face of upper cone 2 For von Karman's profile lower endΦThe distance from pi to the lower end face of the lower cone is an unknown to be solved.
13. The diagonal grid structure according to claim 12, wherein: the outer contour surface center line equation of one spiral rib in the short-range line bidirectional spiral rib is as follows:
14. the diagonal grid structure according to claim 1, wherein: the novel spiral constant-thickness automatic laying device also comprises a skin, wherein the skin is formed by combining automatic winding of short-range wires and automatic laying of close-packed spirals with equal thickness.
15. The diagonal grid structure according to claim 14, wherein: the equation of the closely-spaced spiral line with equal thickness and automatic laying is as follows:
adjustment ofΦ 0 The values result in skin plies of different helix angles.
16. An automated molding composite diagonal mesh von-karman hood, characterized by: the device is divided into two parts, wherein the lower part is a cover body, and the upper part is a sphere which is tangential with the cover body; the cover body and the ball gap are respectively formed, and the ball gap is sleeved at the upper end of the cover body from top to bottom outside the cover body; the cover is an inclined grid structure according to any one of claims 1 to 15.
17. A hood according to claim 16 wherein: when the bidirectional spiral rib in the oblique grid structure of the cover body is a spiral line with equal pitch, the lower end of the cover body is provided withΦThe helix angle at pi is noted as α, and the k value is determined by:
18. the automatic forming tool for forming the von Kamen type composite material inclined grid structure comprises a core mold, a male mold and a female mold; the method is characterized in that: the male die is a split male die, a pair of bidirectional spiral rib grooves corresponding to the bidirectional spiral ribs in claim 1 are formed on the split male die at certain intervals, and the outer contour surface of the split male die is a von Karman molded surface with corrected expansion geometric parameters; the central line of the rib groove is a von-Karman profile spiral line with the geometric parameters of expansion quantity modified.
19. The forming tool of claim 18, wherein: the external contour surface of the split male die is a von Karman molded surface with corrected expansion geometric parameters, and the correction method is that the external radius R of the upper end frame of the structure 1 Outer radius R of structural upper end frame 2 The distance h between the upper end frame and the lower end frame of the structure is subtracted by the corresponding expansion caused by high-temperature curing to obtain R respectively 1 correction 、R 2 correction 、h Correction The forming device male die outer contour conical surface bus equation is as follows:
H correction Is determined by the following means:
s1, R is 1 correction 、R 2 correction Substituting the bus equation of von-karman profile to determine parameters in the bus equation of von-karman profileΦThe result of the solution is recorded asΦ Upper correction ；
S2, to be solvedΦ Upper repairPositive direction Combining the distance h between the upper end frame and the lower end frame of the to-be-formed inclined grid structure Correction Substituted intoObtaining the distance x of the upper end frame from the vertex of the von Karman profile Upper correction ；
S3, mixing the above x Upper correction And h Correction The sum is H Correction 。
20. The forming tool of claim 18, wherein: the central line of the rib groove is a von-Karman profile spiral line with the geometric parameters of expansion amount modified; the correction method is to obtain the corrected von Karman profile spiral line by utilizing the characteristic that the angle difference delta theta between the upper end point and the lower end point of the medium-pitch spiral line is unchanged in the expansion curing process on the basis of correction of the male die outer profile cone bus equation.
21. The forming tool of claim 20, wherein: the corrected rib and groove central line equations are respectively as follows:
1) Male mould von-karman profile constant pitch helix trajectory equation:
2) Male die von karman profile equi-helical angle spiral trajectory equation:
3) Male mold von karman profile geodesic trajectory equation:
the start point and the end point of the spiral line of the mold surface of the three male molds von Karman are coincident.
22. The forming tool of claim 18, wherein: the bidirectional spiral rib with the central line of the outer contour surface being a short distance line is formed by automatic continuous winding, and the equal-pitch spiral rib and the equal-helix-angle spiral rib are formed by automatic laying.
23. The forming tool of claim 22, wherein: automatic winding is realized through an ellipsoidal head, winding tracks are accurately calculated, simulated winding of the short-range wire bidirectional spiral ribs is realized, and accurate calculation of automatic continuous winding tracks is realized by solving an equation set consisting of the following seven equations:
a＝k′b
y＝acosφ 1 ＝R 1
c＝R 2 sinα 2
φ 2 ＝90°-α′
wherein: k' is the length-axis ratio of the ellipsoidal head, and the value range is 1, 2.5;Φ 1 the initial angle of the elliptical cross section of the ellipsoidal head is; a is an ellipsoidal head semi-major axis; b is an ellipsoidal head short half shaft; alpha' is the included angle between the tangent of the ellipsoidal bus and the tangent of the ellipsoidal short-range line; θ 1 Is the circumferential initial angle;Φ 2 the end angle of the elliptical cross section of the ellipsoidal head is; θ 2 Is a circumferential termination angle;
the large ends of the von Karman profiles are transited by cylindrical spiral lines;
the cylindrical spiral equation is:
24. the forming tool of claim 18, wherein: the bidirectional spiral rib groove is formed by machining a cutter with the cross section of the bidirectional spiral rib perpendicular to the central line of the inclined rib groove, wherein the central line of the cutter points to the direction of the outer surface rotating shaft of the male die, and the cutter is along the central line of the inclined rib groove.
25. The forming tool of claim 18, wherein: the split male die is an aluminum split male die, and a hard die forming tool is formed.
26. The forming tool of claim 18, wherein: the split male die is an aluminum backing plate and a silicon rubber grid male die to form a soft die forming tool, the silicon rubber grid male die is formed by casting through a silicon rubber male die casting die, and the soft die forming device and the hard die forming device share a core die.
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