CN115122667A - Automatic molding von-Karman type composite material inclined grid structure and molding tool thereof - Google Patents
Automatic molding von-Karman type composite material inclined grid structure and molding tool thereof Download PDFInfo
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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
-
- 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
-
- 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
-
- 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
Abstract
The invention relates to an automatic formed 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 a bidirectional spiral rib, wherein the structural material of the upper end frame is made of composite material; the upper end frame, the lower end frame and the bidirectional spiral rib are of an integrally formed structure; the upper end frame and the lower end frame are both of inward flanging structures; the outer contour surfaces of the upper end frame and the lower end frame are von karman profiles; the inner contour forms bidirectional spiral ribs which are mutually symmetrical, and the center line of the outer contour surface of the bidirectional spiral ribs is a von Karman profile equal-pitch spiral line, an equal-helix-angle spiral line or a short-range line. The skin is laid automatically in the same thickness along the von karman profile closely-arranged spiral line, and the inner layer and the outer layer of the skin are wound automatically along the von karman profile short-distance line. The oblique grid structure made of the Von Karman type curved busbar composite material can be used for replacing a conical structure, a biconical structure and a biconical head cover. The automatically formed oblique grid structure of the von Karman composite material is automatically, accurately and integrally formed through a special forming tool in a co-curing mode.
Description
Technical Field
The invention belongs to an automatically-formed von Karman type composite material inclined grid structure and a forming tool thereof.
Background
In the rocket structure, the straight bus structures such as the instrument cabin, the final repair cabin, the satellite support, the stage section, the head cover and the like all adopt a large amount of composite material structures, and a good effect of greatly reducing weight is achieved. And the inclined grid structure of the von Karman type curved busbar composite material is not applied to a rocket structure. The inclined grid structure of the Von Karman type curved busbar composite material has the characteristics of large inner envelope and parallel tangent line of the lower end busbar with the rotating shaft, and can be used for replacing the inclined grid structure of the tapered straight busbar composite material which cannot meet the requirement of the inner envelope and is butted with a column section. The curvature characteristic of the Von Karman type curved bus is superior to that of a round curved bus, an oval curved bus and the like, and the Von Karman type composite material grid structure without skin can be used for replacing a double-cone structure which has an inner envelope requirement and is in butt joint with a column section. The Von Karman type curved bus structure has good pneumatic appearance, and can remarkably reduce the pneumatic resistance and the load born by the rocket. Semi-cover separated von karman type honeycomb structure head covers have been applied to the aerospace field in China. The whole cover is thrown away, and the Karman type composite grid structure is not designed and applied. Compared with the Von.Karman type honeycomb structure, the Von.Karman type composite material grid structure has the advantages that the skin rib height is low, the internal occupied space is small, and the Von.Karman type composite material grid structure can be used for small-diameter carrier rockets; the instrument is more convenient and reliable to install on the skin of the honeycomb structure than the honeycomb structure. The carrier rocket head cover mainly bears the external pressure effect, and the von Karman type composite material inclined grid structure can fully utilize the characteristic of anisotropy of the composite material grid structure and utilize the characteristic of curvature change of the von Karman head cover to arrange grids in the force bearing direction, so that the external pressure bearing efficiency is improved. The inclined grid structure of the von Karman type composite material combines the optimal aerodynamic shape with a high-strength light structure, and has a good engineering application value.
Disclosure of Invention
The invention solves the technical problems that: provides an automatic forming von Karman type composite material inclined grid structure and a forming tool thereof. The automatic forming von Karman type composite material inclined grid structure and the forming tool thereof are reasonable in design and light in structure. The automatic forming Von Karman 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 technical scheme of the invention is as follows: automatic shaping von karman type combined material puts grid structure to one side, its characterized in that: comprises an upper end frame, a lower end frame and a bidirectional spiral rib, wherein the structural material is a composite material; the upper end frame, the lower end frame and the bidirectional spiral rib are of an integrally formed structure; the upper end frame and the lower end frame are both of inward turning structures; the outer contour surfaces of the upper end frame and the lower end frame are von karman profiles; the inner contour is provided with bidirectional spiral ribs which are mutually symmetrical, and the center line of the outer contour surface is a von karman profile equal-pitch spiral line, an equal-helix-angle spiral line or a short-range line.
Preferably, the sections of the bidirectional spiral ribs are all trapezoids which are congruent with each other, the trapezoidal sections are perpendicular to the center line of the outer contour surface of the bidirectional spiral ribs, and the center line of the trapezoidal sections points to the von Kan.
Preferably, the composite material is a carbon fiber/epoxy resin composite material.
Preferably, it is used to replace cone structures, double cone structures, or double cone bonnets in rocket structures.
Preferably, for a diagonal grid structure instead of a tapered structure, the generatrix equation of the outer contour surface of the structure is determined by the following equation:
s1, placing the outer radius R of the upper end frame of the inclined grid structure to be formed 1 Outer radius R of lower end frame 2 Substituting into the busbar equation of the Von karman profile to determine the parameter phi in the busbar equation of the Von karman profile, and recording the solution result as phi On the upper part ；
S2, phi to be solved On the upper part Substituting the distance h between the upper end frame and the lower end frame of the inclined grid structure to be formed into a combination
Obtaining the distance x from the upper end frame to the Von-Karman profile vertex Upper part of ；
S3, mixing the x Upper part of And the sum of H and von is the high H in the von Karman profile bus equation, so that the von Karman profile bus equation of the inclined grid structure to be formed is obtained.
The equation of the constant pitch spiral track is as follows:
k is a constant, and the constant pitch spiral trajectory equation is determined by determining the value of k, which is determined by the following formula:
in the formula, the spiral angle alpha of the spiral line is von, and the included angle between the tangent line of the generatrix of the karman profile and the tangent line of the spiral line is formed;
the value range of the helix angle alpha of the right-hand coordinate system is (0 degree, 90 degrees), and the value range of x is [ x On the upper part ,x On the upper part +h]The optimized value can be selected according to the specific bearing condition of the structure. The left-hand coordinate system spiral line and the right-hand coordinate system spiral line are symmetrical to form the central line of the outer contour surface of the bidirectional spiral rib.
Preferably, in order to enable the bidirectional spiral rib to be orthogonal in the middle of the structure to obtain the structure with high external pressure bearing capacity, the bidirectional spiral rib structure is of a combined structure
Calculate phi as phi In And substituting alpha to 45 degrees into a k value calculation formula and rounding to obtain a k value, thereby obtaining the required helical line with the equal pitch.
After the k value is determined, the k value is determined by the formula:
The equation of the equal helix angle spiral track is as follows:
determination of tan alpha Etc. of The equal helix angle spiral track equation is uniquely determined according to the value of the (D); alpha is alpha Etc. of The value range of (0 °,90 °).
Preferably, the starting point and the ending point of the helix with equal helix angle are the same as the starting point and the ending point of the helix with equal helix angle
Von Karman type composite material inclined grid structure upper end surface phi replacing conical structure and butted with cylindrical section On the upper part Lower end surface phi Lower part Pi. The angular difference between the upper end point and the lower end point of the constant pitch spiral line on the von karman profile can be calculated by a fourth equation of the constant pitch spiral line track equation:
according to Δ θ ═ k (1-cos φ) Lower part )-k(1-cosφ On the upper part )＝k+kcosφ On the upper part ；
Dissolving to obtain tan alpha Etc. of The helix angles of the helix angles are all alpha Etc. of 。
The geodesic trajectory equation is:
determination of sin alpha 2 The geodesic trajectory equation is uniquely determined according to the value of (1); alpha is alpha 2 Has a value range of
The optimized 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 geodesic to be the same as the starting point and the ending point of the uniform pitch helix, the starting point and the ending point of the geodesic are made to be the same as each other
According to Δ θ ═ k (1-cos φ) Lower part )-k(1-cosφ On the upper part )＝k+kcosφ On the upper part ；φ Lower part ＝π；
Solved to obtain sin alpha 2 ，α 2 Is the helix angle of the short-range line at the lower end of the structure;
at α 2 After determination, by the formula R 1 sinα 1 ＝R 2 sinα 2 The spiral angle of the von karman composite material at an arbitrary position of the short-distance line between the upper and lower end faces of the inclined lattice structure can be calculated as Rsin90 ° -const.
Preferably, for the automatically formed von Karman composite inclined grid structure replacing the double cones, the generatrix equation is obtained by solving the equation system consisting of the following three equations:
wherein:
wherein:
wherein:
h 1 、h 2 are respectively twoUpper and lower cone heights in the cone, R On the upper part Is the radius R of the upper end surface of an upper cone in a double cone In Is the radius R of the lower end surface of the upper cone in the double cone Lower part The radius of the lower end face of the lower cone in the double cone is a known quantity; r is the radius at phi ═ pi of the lower end of the von Karman profile, x 1 The distance x from the vertex of the Karman profile to the upper end surface of the upper cone 2 The distance from the position phi pi at the lower end of the karman profile to the lower end face of the lower cone is an unknown quantity to be solved.
The equation of the central line of the outer contour surface of one of the short-range line bidirectional spiral ribs is as follows:
the inclined grid structure further comprises a skin, and the skin is formed by combining short-distance line automatic winding and close-packed spiral equal-thickness automatic laying.
The equation of the close-packed spiral line for the close-packed spiral equal-thickness automatic laying is as follows:
adjustment of phi 0 And obtaining the skin layers with different helix angles by numerical value.
An automatically-formed composite material inclined grid Von & lt & gtKarman head cover is divided into two parts, wherein the lower part is a cover body, and the upper part is a segment tangent to the cover body; the cover body and the segment are respectively formed, and the segment 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 an equal-pitch spiral line, the spiral angle at the position where phi is pi at the lower end of the cover body is recorded as alpha, and the k value is determined in the following way:
the forming tool for automatically forming the von Karman type composite material inclined grid structure comprises a core die, a male die and a female die; 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 & ltu & gt snap door profile with corrected expansion amount geometric parameters; the central line of the rib groove is a von karman profile spiral line with corrected expansion amount geometric parameters.
The outer contour surface of the split male die is a Von-Carmen profile with corrected expansion geometric parameters, and the correction method is that the outer radius R of the upper end frame of the structure 1 Outer radius R of structural upper end frame 2 And subtracting the corresponding expansion amount caused by high-temperature curing from the distance h between the upper end frame and the lower end frame of the structure to respectively obtain R 1 correction 、R 2 correction 、h Correction The forming device male mold outer contour conical surface generatrix equation is as follows:
H correction Is determined by:
s1, adding R 1 correction 、R 2 correction Substituting into the busbar equation of the Von karman profile to determine the parameter phi in the busbar equation of the Von karman profile, and recording the solution 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-molded inclined grid structure Correction Substitution into
Obtaining the distance x from the upper end frame to the Von-Karman profile vertex Upper correction ；
S3, mixing the x Upper correction And h Correction Sum of H Correction 。
The central line of the rib groove is a von karman profile spiral line with corrected expansion geometric parameters; the correction method is based on the correction of the generatrix equation of the outer contour of the male die, and obtains the corrected Von-Karman profile spiral line by utilizing the property that the angle difference delta theta between the upper end point and the lower end point of the medium-pitch spiral line is not changed in the expansion curing process.
The corrected equations of the center lines of the rib grooves are respectively as follows:
1) male die Von, Karman profile equal pitch spiral line track equation:
2) male die von, karman profile equal helix angle spiral trajectory equation:
3) male die Von. Karman profile short-range line trajectory equation:
the starting point and the end point of the spiral line of the three male dies are overlapped.
The bidirectional spiral ribs with short-range lines as the central lines of the outer contour surfaces are formed by automatic continuous winding, and the equal-pitch spiral ribs and the equal-spiral-angle spiral ribs are formed by automatic laying.
The automatic winding is realized through the ellipsoidal head, the simulated winding of the geodesic bidirectional spiral rib is realized through accurately calculating the winding track, and the automatic accurate calculation of the continuous winding track is realized through 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′
in the formula: k' is the length-to-diameter axial ratio of the ellipsoidal head, and the value range is (1, 2.5); phi is a unit of 1 Is the starting angle of the elliptical section of the ellipsoidal head; a is an ellipsoid end socket long half shaft; b is an ellipsoid end socket short semi-axis; alpha' is an included angle between the tangent of the ellipsoid bus and the tangent of the ellipsoid short-range line; theta 1 Is a circumferential starting angle; phi is a 2 Is an ellipsoidal head elliptical section termination angle; theta 2 Is a circumferential end 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 processing a cutter with a bidirectional spiral rib section shape perpendicular to the center line of the oblique rib groove, wherein the center line of the cutter points to the direction of the rotating shaft of the outer surface of the male die and is along the center line of the oblique rib groove.
The split male die is an aluminum split male die to form a hard die forming tool.
The split male die is an aluminum base plate and a silicon rubber grid male die to form a soft die forming tool, the silicon rubber grid male die is formed by pouring a silicon rubber male 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 oblique grid structure made of the Von Karman type curved bus composite material has the characteristics of large inner envelope and parallel tangent lines of the lower end bus and a rotating shaft, and can be used for replacing a tapered oblique grid structure made of the straight bus composite material, which cannot meet the requirement of the inner envelope and is butted with a column section. The curvature characteristic of the Von Karman type curved bus is superior to that of a round curved bus, an oval curved bus and the like, and the Von Karman type composite material grid structure without skin can be used for replacing a double-cone structure which has an inner envelope requirement and is in butt joint with a column section. The von karman type curved bus structure has good pneumatic appearance, can obviously reduce the pneumatic resistance and the load born by a rocket, and can replace the von karman type honeycomb structure head cover and the biconical composite material inclined grid head cover, thereby combining the optimal pneumatic appearance with a high-strength lightweight structure.
(2) The grid structure is obliquely arranged on the Von Karman type curved busbar composite material, and the structural rigidity is improved by adding grid reinforcing ribs; and meanwhile, the bearing efficiency of the structure is improved in a mode of increasing grid reinforcing ribs. The oblique grid structure of the Von Karman type composite material can fully utilize the characteristic of anisotropy of the grid structure of the composite material and utilize the characteristic of curvature change of the Von Karman head cover to arrange the grid in the force bearing direction, thereby improving the bearing efficiency.
(3) The grid structure of the uniform-pitch spiral ribs and the uniform-helix-angle spiral ribs of the von Karman composite material is automatically formed by an automatic laying mode, so that the production efficiency and the structural quality consistency are improved.
(4) Von Karman type combined material short distance line spiral muscle grid structure, its net strengthening rib central line are the short distance line on the Von Karman profile, and net strengthening rib winding orbit utilizes the ellipsoid head through accurate calculation, realizes strengthening rib and the automatic winding in succession of covering, and production efficiency is high, is fit for batch production.
(5) The Von Karman molded surface aluminum alloy grid male die can be accurately corrected and is suitable for grid structures with high requirements on dimensional accuracy.
(6) The von Karman profile is a non-deployable complex profile, and a constant-pitch spiral line, a constant-helix-angle spiral line and a short-range line on the von Karman profile are space complex curves. The silicon rubber grid male die formed by the method has double curvature, is good in fitting property with the ellipsoid profile of the core die, and is good in spiral rib groove continuity.
(7) The silicon rubber grid male die is formed by pouring through a three-dimensional pouring die, each silicon rubber grid male die is only one tenth to one fifth of the circumference, the grid machining amount is greatly reduced, and the machining working hours of a five-coordinate machine tool can be greatly reduced, so that the machining cost and the compression machining 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 the hard die forming, but can meet the use requirement.
(8) The von Karman curved bus composite material obliquely-arranged grid structure skin is formed in an automatic winding forming mode, and the effects of enhancing the shearing resistance of the interface of the skin and ribs, reducing the wrinkles 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 busbar composite material meets the requirements of productization, has good structural integrity, good forming manufacturability and high production efficiency, and realizes low cost and light weight.
Drawings
FIG. 1 is a von Karman-type composite grid structure replacing a tapered straight busbar grid structure;
FIG. 2 is a schematic diagram of the helix angle of a curved generatrix surface of revolution;
FIG. 3 is a comparison of three spiral lines of a von Karman grid structure in place of a tapered structure;
FIG. 4 is a cross-sectional view of a uniform pitch spiral von Karman type composite mesh structure;
FIG. 5 is an equal helix angle spiral von Karman type grid structure (only spiral grid shown);
FIG. 6 is a geodesic von Karman type mesh structure (only geodesic meshes are shown);
FIG. 7 is a cross-sectional view of a forming tool for automatically laying a von Karman type composite grid structure;
FIG. 8 is an aluminum alloy mesh male die of a von Karman type composite material mesh structure;
FIG. 9 is a negative mold of a von Karman-type composite lattice structure;
FIG. 10 is an aluminum alloy backing plate of von Karman type composite grid structure;
FIG. 11 is a three-dimensional casting mold of a silicone rubber mesh male mold with a von Karman-type mesh structure;
FIG. 12 is a three-dimensional casting mold grid base plate of a silicone rubber grid male mold;
FIG. 13 is a silicone rubber mesh male mold of von Karman type composite material mesh structure;
FIG. 14 is a trace of large end-to-end winding of a fiber tow in a von Karman type short range wire mesh structure;
FIG. 15 is an end-to-end winding cross-sectional view of a von Karman-type short-range wire mesh structure;
FIG. 16 is a graph of closely packed helix angle versus tow width;
FIG. 17 is a schematic drawing showing uniform thickness laying of closely-spaced spirals of a von Karman lattice structure;
FIG. 18 illustrates the dimensional requirements for the biconic structure;
FIG. 19 is a comparison of three helices on a spherical surface;
FIG. 20 is a comparison of three helices on an ellipsoid;
FIG. 21 is a skinned von Karman-type composite mesh structure in place of the biconic structure;
FIG. 22 is a comparison of three spiral lines for a von Karman mesh hood;
FIG. 23 is a von Karman short range wire mesh hood (only the short range wire mesh is shown);
FIG. 24 is a von Camator constant pitch spiral mesh hood (only the spiral mesh is shown);
FIG. 25 is a von Camator equal helix angle spiral mesh hood (only the spiral mesh is shown);
FIG. 26 is a trace of large end-to-end winding of a fiber tow on a von Karman short-range wire mesh hood;
FIG. 27 is a diagram of the interfacing of a von Karman mesh hood body with a tip structure;
fig. 28 shows a von karman mesh hood body molding tool core mold and a silicon rubber male mold.
In the figure: 1 die block 2 middle mould 3 bolt 4 upper mould 5 blanking cover 6 bolt 7 convex positioning sleeve 8 concave positioning sleeve 9 middle mould two 10 internal thread cylindric lock
Detailed Description
The invention is further illustrated by the following examples.
The present invention will be described in further detail with reference to the accompanying drawings and examples.
1) Helix angle calculation of helix line on curved generatrix revolution surface
As shown in fig. 2, the helix angle α of the helix is defined as the angle between the tangent to 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). The parameter equation of the bus with t as a parameter is set as follows:
the tangent of the bus is:
the x-axis is used as a rotating shaft to form a rotating surface.
The direction vector of the tangent line of the bus at the point A is as follows:
the parameter equation of the spiral line with t as a parameter is set as follows:
the direction vector of the tangent of the helix at point a is:
the helix angle α at point a satisfies the following relationship:
because of the symmetry of the spiral line on the revolution surface, the above formula only needs to take the positive sign.
2) Von Karman type composite material inclined grid structure and tool for replacing conical grid structure
2.1) Von-Karman-type structure bus equation and calculation of chord height of relative conical section thereof
The busbar equation for the von karman-type structure is:
wherein:
r is the lower end radius and H is high.
The substituted tapered composite inclined lattice structure has an upper end diameter of 727.602mm, a lower end diameter of 950mm, a height of 415mm, and a taper half-cone angle β of 15 ° (for example).
Solving this equation to get phi 1.707675763; it is put into the equation:
solving this equation to get x 546.1514266;
the required von karman bus equation is:
wherein:
namely: x is 480.5757133(1-cos phi) (15)
In order to reduce the cost, the core mold of the forming tool is still in a conical section (because the characteristic that the curvature change of the structure beyond the end head of the Von & Karman structure is small is utilized instead of the conical section structure, the core mold of the forming tool does not need to be designed into the Von & Karman shape, and the conical core mold of the conical section structure is used along), the thickness of the male mold of the forming tool is inconsistent due to the Von & Karman structure bus, and the product is heated unevenly during curing and heating, so that the forming quality is influenced. The chord heights of the von karman cover bodies and the corresponding conical sections in the middle are calculated (the chord heights of the karman cover bodies and the corresponding conical sections are calculated and explained in combination with the examples, the karman type structures are formed by the conical core die, the forming quality of the structures is not influenced, and the production cost is reduced actually).
at this time
Corresponding to cone mid-section radius 419.4005426.
The radius difference was 16.25622423, and the chord height was 15.702307 mm.
And calculating the maximum chord height of the von karman cover body and the corresponding conical section.
Order to
Can be solved to obtain: phi 127.6878416 DEG
x＝480.5757133*(1-cos(127.6878416))＝774.3800611
Here 20.72863451mm below the middle of the structure.
When phi is 127.6878416 DEG
The corresponding cone radius 424.9547636, the radius difference is 16.4057574, and the chord height is 15.8467448 mm. The curing quality is not greatly influenced. The core mould of the corresponding cone section can be used, and only the male mould is changed.
The von karman structure profile is formed by the von karman curve bus rotation, and a profile parameter equation is as follows:
wherein f (phi) 480.5757133(1-cos phi) (18)
2.2) design of oblique grid structure of Von-Karman type constant-pitch spiral rib composite material
The equation of the uniform pitch spiral line on the molded surface of the Karman structure is as follows:
substituting the formula (8) to obtain:
the formula is solved as follows:
to make the bidirectional helical bars orthogonal near the middle of the structure, the following adjustment calculation is performed:
in the middle phi is 124.626626, the above formula is substituted and alpha is 45 degrees,
obtaining: k-1.146209659
Namely: theta is 1.146209659(1-cos phi) (24)
In the above formula, θ is a radian system, and is converted into an angle system for the convenience of three-dimensional modeling of the structure:
and theta is an angle k-65.6729759.
The maximum chord height phi is 127.6878416 degrees, the formula is substituted, alpha is 45 degrees, the radian system is converted into an angle system (1.127261195, 180, pi is 64.58730888), k is 64.58730888,
for comparison of the thermal expansion correction effect, the rounding was 65. When k is 65, phi is 126.485473 DEG
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 is 126.485473 DEG
Corresponding cone radius 422.7991337.
The radius difference was 16.3830214, and the chord height was 15.8247835 mm.
The equation for a constant pitch helix orthogonal on von karman profiles 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 von Karman type equal-pitch spiral rib composite material obliquely-arranged grid structure replacing the conical grid structure is shown in figure 4, ribs are 8mm high and 6mm wide, a draft angle is 7.5 degrees, skins are 1.2mm, upper and lower end frames are 8mm thick and 40mm wide.
The von Karman type composite material replacing the tapered grid structure is obliquely arranged on the upper end surface phi of the grid structure 1.707675763, and the lower end surface phi of the grid structure pi. The angular difference between the upper and lower end points of the constant pitch helix on the von karman surface can be calculated by the fourth equation:
Δθ＝65(1-cos180°)-65(1-cos97.842614°)＝56.13059348°
2.3) design of oblique grid structure of Von-Karman type equal helix angle spiral rib composite material
The equation of the equal helix angle spiral line on the molded surface of the Karman structure is as follows:
substituting the formula (8) to obtain:
the formula is solved as follows:
integrating the above formula with phi pi and phi 1.707675763 as upper and lower limits,
and the integral value Delta theta is 56.13059348 DEG
Obtaining by solution: tan α is 0.896512192, α is 41.87661382 °.
The equation of the equal helix angle spiral line on the molded surface of the Karman structure is as follows:
the isohelix angle spiral on the von karman profile is shown in the middle curve of fig. 3. The von Karman type equal helix angle spiral rib composite material inclined grid structure replacing the conical grid structure is shown in figure 5. The structural parameters of the oblique grid structure rib of the equal helix angle spiral rib composite material are the same as those of the equal pitch spiral rib, and only equal helix angle spiral line grids are shown.
2.4) design of oblique grid structure of Von-Karman type short-range wire spiral rib composite material
The spiral line on the revolution surface which conforms to the relationship of clairo (Chairaut) is a short-range line.
Clairo (Chairaut) relation:
r 1 sinα 1 ＝rsin90°＝const (31)
in the formula: r is 1 The radius of any point on the bus; alpha (alpha) ("alpha") 1 The helix angle for this point; and r is const which is the radius of the polar hole of the geodesic spiral winding type.
The formula (7) shows that:
multiplication of both sides by R 2 ＝g 2 (t) (formula (1))
Obtaining by solution:
substituting the formulas (18) and (19) into the above formula to obtain:
integrating the above formula with phi pi and phi 1.707675763 as upper and lower limits,
and the integral value Delta theta is 56.13059348 DEG
Obtaining by solution: sin α 0.5916313655, α 36.27286047 °, which is 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
Obtaining by solution: sin alpha 1 ＝0.772468735，α 1 50.57609969 deg., which is the helix angle of the short-range wire at the ends of the structure.
The geodesic equation on the profile of the von karman structure is:
the short range line on the von karman profile is shown in the left hand curve of fig. 3. The oblique grid structure of the von Karman type short-range wire spiral rib composite material replacing the conical grid structure is shown in figure 5. The structural parameters of the short-distance linear spiral rib composite material inclined grid structural ribs are the same as those of the equal-pitch spiral rib, and only short-distance linear grids are shown.
The arc lengths of the stub, isopitch helix on the von karman profile shown in figure 3 over the same end points can be calculated to be 599.117mm, 601.027mm, 604.157mm, respectively. Meanwhile, as the buses of the von Karman profiles are curved buses, the difference of spiral lines on the three von Karman profiles is large, only short-distance line spiral ribs on the von Karman profiles can be automatically wound, and other two kinds of spiral ribs can be formed only by an automatic laying mode.
2.5) Von-Karman profile and equal-pitch spiral rib expansion correction and structure forming tool
And calculating the expansion amount of the Karman cover body. The amount of swelling is calculated as follows:
Δl＝l 0 ×(α m -α c )×(T gel -t) (38)
in the formula: Δ l — mold swell amount; l 0 -the size of the product;
α m -the coefficient of thermal expansion of the mould material; alpha is alpha c -the product thermal expansion coefficient;
T gel -resin gel point temperature; Δ α ═ α m -α c ) The difference in thermal expansion coefficient is calculated as the difference between the thermal expansion coefficient of the aluminum alloy or steel alloy and the thermal expansion coefficient of the carbon material.
The difference in coefficient of thermal expansion in the diametrical direction Δ α is 10.7.
Structural upper end diameter expansion: 727.602X 10.7X 110X 10 -6 ＝0.856
Diameter of the upper end of the die: 727.602-0.856 ═ 726.746
Diameter expansion of the lower end of the structure: 950 × 10.7 × 110 × 10 -6 ＝1.118
Diameter of the lower end of the die: 950-1.118-948.882
The difference in thermal expansion coefficient in the height direction is: Δ α -24-4.
Structural height expansion: 415 × 20 × 110 × 10 -6 ＝0.913
Height of the die: 415-0.913 ═ 414.087
Calculate the corresponding von & lt & gtkarman hood height
Solving this equation yields phi 1.707676467, which is substituted into the equation:
solving this equation to get x 544.9506681;
the die height was 414.087mm, the diameter of the upper end was 726.746mm, and the diameter of the lower end was 948.882 mm.
And the von karman cover body bus equation corrected by the expansion amount is as follows:
wherein:
the structure is as follows: θ ═ k (1-cos φ), k ═ 65 (43)
A mould: θ '═ k "(1-cos φ') (44)
The structure is as follows:
φ 2 ＝180°
a mould:
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 equation (45), we can calculate:
k”＝65.00005314
the von karman profile modified by the expansion amount has the following equation:
the cross section, the male die and the female die of the automatic laying aluminum alloy male die are respectively shown in figures 7, 8 and 9. Compared with the corresponding conical section structure tool, the von-clamp-type uniform-pitch spiral rib inclined grid structure tool is only different in male die outer contour, male die uniform-pitch spiral rib grooves and female die inner contour from the conical section structure, and the rest can follow the prior art. The generatrix of the outer contour of the male die is a formula (41) and a formula (42), and the uniform-pitch spiral rib groove of the male die is formed by processing a special cutter with a rib section along a formula (46) uniform-pitch spiral line. The female die internal profile generatrix is expressed by the formulas (13) and (14). The Von Karman molded surface aluminum alloy grid male die can be accurately corrected and is suitable for grid structures with high requirements on dimensional accuracy.
In order to further reduce the cost, a silicon rubber male die is designed. An aluminum alloy shim plate is shown in fig. 10 and is mounted on the mandrel shown in fig. 7 in place of the aluminum alloy male mold. The silicon rubber grid male die is shown in figure 13 and is bonded on the aluminum alloy backing plate, so that the spatial position of grid rib grooves on the silicon rubber grid male die is the same as that of the grid rib grooves on the aluminum alloy grid die, and the silicon rubber grid male die and the aluminum alloy grid die are formed into the same structure. The stereo casting mold of the silicon rubber grid male mold is shown in figure 11, the stereo casting mold grid bottom plate of the silicon rubber grid male mold is shown in figure 12, and because the von-Karman molded surface is an inextensible curved surface, the molding difficulty of the silicon rubber grid mold is higher, and the stereo casting is required to be completed. And selecting a proper cutting plane to ensure that the distances between the four corners of the silicon rubber grid die and the cutting plane are approximately equal, so that the three-dimensional casting is planarized 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 a constant-pitch spiral line, a constant-helix-angle spiral line and a short-range line on the von Karman profile are space complex curves. The silicon rubber grid male die formed by the method has double curvature, is well attached to the ellipsoid surface of the core die, and has good continuity of the spiral rib grooves. Each silicon rubber grid male die is only one fifth of the circumference, the grid machining amount is greatly reduced, and the machining working hours of a five-coordinate machine tool can be greatly reduced, so that the machining cost is reduced, the machining period is shortened, the cost is reduced, and the grinding progress is accelerated. The structure geometric dimension is not as accurate as the hard mould forming, but can meet the use requirement.
2.6) correction of Von-Cammen type constant helix angle helical rib expansion
Referring to the methods of 2.3) and 2.5), the von corrected by the expansion amount can be calculated as follows:
2.7) correction of Von-Karman type short-range wire spiral rib expansion
Referring to the methods of 2.4) and 2.5), the equation of the geodesic on the karman profile can be calculated as follows:
2.8) Upper head winding track design
Radius of upper end of conical section
As described in 2.4 (52) and asin α' 218.0248984 (see fig. 4)
φ 2 ＝90°-α′ (54)
Let k equal to 1.2, the values of the various parameters obtained by solving the system of equations are given in the following table:
and calculates the value of:
2×(θ 2 -θ 1 )-7×18°＝-3.317376818°≈-3.32° (56)
z＝bsinφ 1 ＝102.8091576
the middle is transited by a cylindrical spiral line by 8.06 degrees.
Cylindrical spiral equation:
when theta is 8.06 degrees, Z is 91.05467799 degrees.
Karman winding, 20 helical bars:
(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 surface close-packed helix equation and close-packed uniform thickness lay
As shown in fig. 16, the width of the fiber tow in the automatic placement is d, and n fiber tows are provided in total. At R 0 The circumference of the area is: 2 pi R 0 The circumference at R is: 2 π R ═ nd R 。
In order to automatically lay the center line of the fiber tows along the closely-spaced spiral line on the conical surface, the following steps are carried out:
d＝d R cosα (58)
thereby to obtain
R 0 ＝Rcosα (59)
Namely:
in the formula (8), the formulae (18), (19) and (61):
the closely-spaced spiral equations on von karman's surface are:
is convenient to use
Adjustment of phi 0 And obtaining the skin layers with different helix angles by numerical value.
As shown in FIG. 17, the closely-spaced spiral lines are used for automatically laying the fiber bundles of the curved-bus composite structural skin, and the skin with the same thickness can be obtained.
The skins are formed in a mode of paving and winding in one body, the outermost skin and the innermost skin are automatically wound and formed so as to increase the shearing resistance between the skins and the ribs and reduce the wrinkles of the outer surface of the structure, and the middle layers of the skins are formed in different phi 0 The close-packed spirals are laid in equal thickness to achieve the purpose of skin equal thickness.
The automatic winding forming mode can enable the effect similar to weaving between rib joints and between ribs and the skin to be achieved, so that the shearing resistance of the interfaces between the ribs and between grids and the skin is enhanced, and a short-distance thread spiral rib grid structure is preferably selected to form in the automatic winding mode. The equal-pitch spiral rib grid structure is simple in design because the calculation of the equal-pitch spiral equation does not need integration. The oblique orthogonal spiral rib grid structure with equal spiral angles bears external pressure well. A constant pitch helix, the helix angle decreasing with decreasing radius; the helix angle of the equal helix angle helix does not change along with the change of the radius; the geodesic helix angle increases with decreasing radius. Different spiral rib grid structures are selected according to actual engineering requirements by combining the characteristics of each spiral rib grid structure and the change characteristics of the spiral angles of each spiral line.
3) Von-Karman type composite material inclined grid structure for replacing double cones
The dimensional requirements for the bicone structure are shown in FIG. 18.
Typical curved generatrix has a circleElliptical, hyperbolic, parabolic, cycloidal, von karman curves, etc. The generatrix equations are respectively
y＝ax 2 、
When the x coordinate axis of the bus is coincident with the rotation axis, an ellipse, a hyperbola and a von karman curve can pass through given three points; while circles, parabolas and cycloids cannot pass through given three points, the x coordinate axis needs to be offset by a certain distance relative to the rotating axis so as to pass through the given three points.
The circular generatrix equation by giving three points can be set as:
the circular generatrix equation is:
from this phi can be calculated 1 When the angle is 20.19 degrees, the included angle between the generatrix tangent and the axial line is 20.19 degrees
There are 2) the method combines the circular generatrix parameter equation to obtain three kinds of spiral lines on the spherical surface with the same end point, see fig. 19.
The elliptic bus equation by giving three points can be set as:
the elliptic bus equation is:
from this phi can be calculated 1 When the angle is 37.57226867 degrees, the included angle between the tangent line of the generatrix and the axis is 22 degrees.
There are 2) the method described in conjunction with the ellipse generatrix parameter equation, three helices on the ellipsoid at the same end point can be found, see fig. 20.
The parameter equations of other curved generatrices and the three kinds of spiral lines on the revolution surface formed by the curved generatrices can be obtained by the same method, and the detailed description is omitted.
Karman grid bus equation conforms to the following equation by giving three points von:
wherein:
wherein:
wherein:
R、x 1 、x 2 for the unknowns, solve the equation to obtain: x is the number of 1 ＝437.2448422mm，x 2 75.48403095mm, R1406.545135 mm. Taking x after the whole 1 ＝437.2mm，x 2 ＝75.3mm，R＝1406.5mm。
The busbar equation of the von karman type grid structure by giving three points is as follows:
wherein:
the structure lower extreme face is apart from von, karman conical point 1487.2mm, phi 2.698933903(0.859 pi) radian, substitute this value into the formula, can calculate von karman composite material grid structure lower extreme generating line tangent and the tangent of axis contained angle be 0.2476677873, generating line tangent and axis contained angle be 13.91 promptly, be less than this angle value of round generating line and oval generating line, the structure lower extreme is more nearly parallel with the axis, be favorable to axial biography power more, thereby be favorable to with the butt joint of column section.
And (3) curvature calculation:
the upper end face of the structure is 437.2mm away from the von karman cone apex. Phi is 1.114769991(0.355 pi) radians. The mid-plane of the structure is 937.2mm from the von karman cone apex. Phi is 1.771762345(0.564 pi) radians.
Phi from 0.35 pi to 0.86 pi, 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 of the circular generatrix is 2581.56mm, and the curvature is 0.0003873626799. And the curvature of the round bus is smaller than von karman bus at the position where phi is slightly larger than 0.6 pi. In the part where phi is less than 0.6 pi, the structural profile is changed from a spherical shape to a Von-Karman shape, so that the profile curvature is reduced, and the bearing capacity is improved. In the part where phi is greater than 0.6 pi, included angles between tangent lines of buses of the Von-Karman structure and the axis are smaller than those of circular buses, so that axial force transmission is facilitated, and butt joint with a column section is facilitated.
Substituting an ellipse parameter equation into an equation (79) to obtain the ellipse curvature radius:
in the same way, the calculation formulas of the curvatures and the curvature radiuses of hyperbola, parabola and cycloid can be obtained.
The calculated ellipse, hyperbola, parabola and cycloid have the larger curvature upwards, and the line type is not as good as von Karman curve. The Von-Karman grid structure is selected by comprehensively considering the curvature characteristics of each bus and the included angle between the tangent line of the lower end bus and the axis.
The original double-cone structure has a tighter rigidity requirement. Hollow circular section moment of inertia:
from the above equation, the smaller the diameter, the smaller the moment of inertia. As noted in 2), the stroked helix angle increases with decreasing radius, which facilitates increased small end stiffness and facilitates large end opening. Meanwhile, the curvature of the short-range line is smaller than that of a helical line with equal pitch and equal helix angle, and the force transmission is direct and has good manufacturability. Therefore, a von karman type short-distance wire spiral rib composite grid structure is selected, and the short-distance wire equation is as follows:
the helix angle of the minor axis changes from 15 ° at the bottom to 32.74 ° at the top, and from equation (58), the stiffness of the top is increased by 1.148 times cos15 °/cos32.74 ° compared to the helix with equal helix angle.
A skinnless von karman type composite mesh structure instead of the biconic structure is shown in fig. 21.
4) Composite material inclined grid Von & Karman head cover
The composite material inclined grid Von Karman head cover is designed to replace a biconical composite material grid head cover. The engineering practice is approached, and the radius of the lower end of the von karman cover body is 500, the height is 1400, and the generatrix equation is as follows:
wherein:
4.1) design of Von Karman head cover ball head
In order to facilitate the process forming, the fairing is divided into two parts, the lower part is a Von & Karman cover body, and the upper end is a segment tangent with the Von & Karman cover body. The von karman cover body and the ball segment are respectively molded, and the ball segment is sleeved on the upper end of the von karman cover body from top to bottom outside the von karman cover body.
Make the ball be in short
When the electric heating cooker is tangent to the von Karman cover body.
The projection of the segment on the xoy plane is:
obtaining by solution:
obtaining by solution: r-128.9327909
4.2) composite short-distance wire spiral rib inclined grid Von
Short-range line pole hole Von-Karman head cover profile
To (3).
arcsin(110.2663301/500)＝12.74°
Short range line is from phi to pi
And the space is reserved for the shaft of the forming tool during forming by avoiding the dense grids at the position of the geodesic extreme hole.
To
The von karman cover body and the ball segment are integrally formed.
The geodesic on the profile of the von karman hood is shown in the left curve of fig. 22. The composite material short-distance wire spiral rib is obliquely arranged on the grid von Karman head cover as shown in figure 23. Only a grid of geodesic lines is shown.
With the methods described in 2.2) and 2.3), the constant pitch helix and the constant pitch helix of von Karman headgear can be determined.
4.3) composite constant-pitch spiral rib inclined grid Von
The constant pitch helix on the profile of the von Karman nose cap is shown in the right hand curve of FIG. 22. The composite material constant-pitch spiral ribs are obliquely arranged on the grid von Karman head cover as shown in figure 24. Only a constant pitch helical grid is shown.
4.4) composite Iso-helix angle spiral rib inclined grid Von
The constant pitch helix on the profile of the von Karman nose cap is shown in the middle curve of FIG. 22. The composite material adopts equal helical angle and spiral ribs which are obliquely arranged on a grid von Karman head cover as shown in figure 25. Only the equal helix angle spiral grid is shown.
4.5) closely-spaced spiral lines on Von Karman hood
Is convenient to use
Adjustment of phi 0 And obtaining the skin layers with different helix angles by numerical value.
From 2.8), the trace of the oblique grid von of the short-distance wire spiral rib of the composite material can be calculated, and the trace of the opposite winding fiber tows at the large end of the Karman head cover is shown in FIG. 26.
In order to realize the oblique grid von of the composite material short-distance wire spiral rib, the large end of the clamping door hood is oppositely wound, and a hood body forming tool core mold and a silicon rubber male mold are designed, as shown in figure 28. The design forming method of the silicon rubber male die is described in 2.5).
5) And (4) calculating the length of the spiral line on the Karman profile instead of the von of the conical grid structure.
To facilitate automatic winding and automatic laying of the composite fiber tows, the length of the spiral line on the von karman profile is calculated.
And (3) setting an included angle between the tangent line of the Karman bus and the X axis as gamma, and combining the formulas (13), (15) and (16):
the included angle between the tangent line of the Von-Karman bus and the tangent line of the spiral line on the Von-Karman profile is alpha,
the length of the spiral on the von karman profile is:
the geodesic length on the karman profile is:
from 2.4), c ═ r' sin α ═ 475sin36.27286047 ° -281.0248984, it is known that:
α′＝36.27286047° (101)
the constant pitch helix length on the karman profile is:
as shown in formulas (22) and 2.4), when k is 1.146209659:
the constant pitch helix length on the karman profile is:
from 2.3), α is 41.87661382 ° (105)
The length of the closely-spaced spiral line on the snap profile is:
from the formula (60):
cosα＝R 0 /R (107)
the arc lengths of the geodesic, isopitch helix and isopitch helix of the same end point of fig. 3 can be calculated to be 599.117mm, 601.027mm and 604.157mm respectively. The closely-spaced helix in fig. 17 has an arc length of 937.291 mm.
Note: due to the problem of formula version display, if the display appears in the application
Which is essentially the parameter phi.
Although the present invention has been described with reference to the preferred embodiments, it is not intended to limit the present invention, and those skilled in the art can make modifications and variations of the present invention without departing from the spirit and scope of the present invention.
The invention is not described in detail and is within the knowledge of a person skilled in the art.
Claims (27)
1. Automatic shaping von karman type combined material puts grid structure to one side, its 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, the lower end frame and the bidirectional spiral rib are of an integrally formed structure; the upper end frame and the lower end frame are both of inward turning structures; the outer contour surfaces of the upper end frame and the lower end frame are von karman profiles; the inner contour forms bidirectional spiral ribs which are mutually symmetrical, and the center line of the outer contour surface of the bidirectional spiral ribs is a von Karman profile equal-pitch spiral line, an equal-helix-angle spiral line or a short-range line.
2. The canted grid structure according to claim 1, wherein: the cross sections of the bidirectional spiral ribs are all trapezoids which are equal to each other, the trapezoid cross sections are perpendicular to the outer contour surface central line of the bidirectional spiral ribs and point to the von card, and the central points of the lower bottoms of the door-shaped surface rotating shaft direction and the trapezoid cross sections are swept along the outer contour surface central line of the bidirectional spiral ribs to form the bidirectional spiral ribs.
3. The canted grid structure according to claim 1, wherein: the composite material is a carbon fiber/epoxy resin composite material.
4. The canted grid structure according to claim 1, wherein: used to replace cone structures, double cone structures, or double cone hoods in rocket structures.
5. The canted grid structure according to claim 4, wherein: for a canted mesh structure that replaces a tapered structure, the generatrix equation for the outer contour surface of the structure is determined by:
s1, placing the outer radius R of the upper end frame of the inclined grid structure to be formed 1 Outer radius R of lower end frame 2 Substituting into Von Karman profile bus equation, determining parameter phi in Von Karman profile bus equation, and recording the solution result as phi On the upper part ；
S2, phi to be solved On the upper part Substituting the distance h between the upper end frame and the lower end frame of the inclined grid structure to be formed into a combination
Obtaining the distance x from the upper end frame to the Von-Karman profile vertex On the upper part ；
S3, mixing the x On the upper part And the sum of the sum and the H is the high H in the Von & Karman profile bus equation, so that the Von & Karman profile bus equation of the inclined grid structure to be molded is obtained.
6. The canted grid structure defined in claim 5 wherein: the equation of the constant pitch spiral track is as follows:
k is a constant, and the constant pitch spiral trajectory equation is determined by determining the value of k, which is determined by the following formula:
the spiral angle alpha of the spiral line is von, and the included angle between the tangent line of the generatrix of the karman profile and the tangent line of the spiral line is formed;
the value range of the helix angle alpha of the right-hand coordinate system is (0 DEG, 90 DEG), and the value range of x is [ x [ ] Upper part of ,x Upper part of +h]The left-hand coordinate system spiral line and the right-hand coordinate system spiral line are symmetrical to form the central line of the outer contour surface of the bidirectional spiral rib.
7. The canted grid structure according to claim 6, wherein: in order to ensure that the bidirectional spiral rib is orthogonal in the middle of the structure to obtain a structure with high external pressure bearing capacity, the bidirectional spiral rib is of a combined structure
Calculate phi as phi In And substituting alpha to 45 degrees into a k value calculation formula and rounding to obtain a k value, thereby obtaining the required valueOf helical pitch.
8. The slanted grid structure of claim 6 or 7, wherein: after the k value is determined, the k value is determined by the formula:
9. The canted grid structure according to claim 5, wherein: the equation of the equal helix angle spiral track is as follows:
determination of tan alpha Etc. of The equal helix angle spiral track equation is uniquely determined according to the value of the (D); alpha is alpha Etc. of The value range of (0 °,90 °).
10. The canted grid structure according to claim 9, wherein: in order to make the starting point and the end point of the helix with equal helical angle identical to the starting point and the end point of the helix with equal helical angle, let
According to Δ θ ═ k (1-cos φ) Lower part )-k(1-cosφ On the upper part )＝k+kcosφ Upper part of ；φ Lower part ＝π；
Dissolving to obtain tan alpha Etc. of The helix angles of the helix angles are allα Etc. of 。
11. The canted grid structure defined in claim 5 wherein: the geodesic trajectory equation is:
determination of sin alpha 2 The geodesic trajectory equation is uniquely determined according to the value of (1); alpha is alpha 2 Has a value range of
12. The canted grid structure defined in claim 11 wherein: in order to make the starting point and the end point of the geodesic line identical to the starting point and the end point of the helical line with equal pitch, the order is that
According to Δ θ ═ k (1-cos φ) Lower part )-k(1-cosφ On the upper part )＝k+kcosφ On the upper part ；φ Lower part ＝π；
Solved to obtain sin alpha 2 ，α 2 Is a helix angle of the short-range line at the lower end of the structure;
at α 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 von Karman type composite material inclined grid structure can be calculated according to the Clerod relational expression.
13. The canted grid structure according to claim 4, wherein: for the automatically formed von Karman type composite material inclined grid structure replacing the double cones, a bus equation is obtained by solving an equation system consisting of the following three equations:
wherein:
wherein:
wherein:
h 1 、h 2 respectively the upper and lower cone heights, R, of the double cone Upper part of Is the radius R of the upper end surface of an upper cone in a double cone In Is the radius R of the lower end surface of the upper cone in the double cone Lower part The radius of the lower end face of the lower cone in the double cone is a known quantity; r is the radius at phi ═ pi of the lower end of the von Karman profile, x 1 The distance x from the vertex of the Karman profile to the upper end surface of the upper cone 2 The distance from the position phi pi at the lower end of the karman profile to the lower end face of the lower cone is an unknown quantity to be solved.
14. The canted grid structure defined in claim 13 wherein: the equation of the central line of the outer contour surface of one of the short-range two-way spiral ribs is as follows:
15. the canted grid structure according to claim 1, wherein: the composite material is characterized by further comprising a skin, wherein the skin is formed by combining short-distance line automatic winding and close-packed spiral equal-thickness automatic laying.
16. The canted grid structure according to claim 15, wherein: the equation of the close-packed spiral line for the close-packed spiral equal-thickness automatic laying is as follows:
adjustment of phi 0 And obtaining the skin layers with different helix angles by numerical value.
17. The utility model provides an automatic shaping combined material puts grid von. The lower part is a cover body, and the upper part is a segment tangent to the cover body; the cover body and the segment are respectively formed, and the segment is sleeved at the upper end of the cover body from top to bottom outside the cover body; the housing is a canted grid structure as defined in any one of claims 1 to 16.
18. The hood of claim 17, wherein: when the bidirectional spiral rib in the oblique grid structure of the cover body is an equal-pitch spiral line, the spiral angle at the position where phi is pi at the lower end of the cover body is recorded as alpha, and the k value is determined in the following way:
19. the forming tool for automatically forming the von Karman type composite material inclined grid structure comprises a core die, a male die and a female die; 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 profile with corrected expansion geometric parameters; the central line of the rib groove is a von karman profile spiral line with corrected expansion amount geometric parameters.
20. The forming tool according to claim 19, wherein: the outer contour surface of the split male die is a Von-Carmen profile with corrected expansion geometric parameters, and the correction method is that the outer radius R of the upper end frame of the structure is 1 Outer radius R of structural upper end frame 2 And subtracting the corresponding expansion amount caused by high-temperature curing from the distance h between the upper end frame and the lower end frame of the structure to respectively obtain R 1 correction 、R 2 correction 、h Correction The forming device male mold outer contour conical surface generatrix equation is as follows:
H correction Is determined by:
s1, adding R 1 correction 、R 2 correction Substituting into the busbar equation of the Von karman profile to determine the parameter phi in the busbar equation of the Von karman profile, and recording the solution 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-molded inclined grid structure Correction Substitution into
Obtaining the distance x between the upper end frame and the Von-Karman profile vertex Upper correction ；
S3, mixing the x Upper correction And h Correction The sum of which is H Correction 。
21. The forming tool according to claim 19, wherein: the central line of the rib groove is a von karman profile spiral line with corrected expansion geometric parameters; the correction method is based on the correction of the generatrix equation of the outer contour of the male die, and obtains the corrected Von-Karman profile spiral line by utilizing the property that the angle difference delta theta between the upper end point and the lower end point of the medium-pitch spiral line is not changed in the expansion curing process.
22. The forming tool according to claim 21, wherein: the corrected equations of the center lines of the rib grooves are respectively as follows:
1) male die Von, Karman profile equal pitch spiral line track equation:
2) male die von Karman profile equal helix angle spiral track equation:
3) male die Von. Karman profile short-range line trajectory equation:
the starting point and the end point of the spiral line of the three male dies are overlapped.
23. The forming tool according to claim 19, wherein: the bidirectional spiral ribs with short-range lines as the central lines of the outer contour surfaces are formed by automatic continuous winding, and the equal-pitch spiral ribs and the equal-helix angle spiral ribs are formed by automatic laying.
24. The forming tool according to claim 23, wherein: the automatic winding is realized through the ellipsoidal head, the simulated winding of the geodesic bidirectional spiral rib is realized through accurately calculating the winding track, and the accurate calculation of the automatic continuous winding track is realized through solving an equation set consisting of the following seven equations:
a＝k′b
y＝a cosφ 1 ＝R 1
c＝R 2 sinα 2
φ 2 ＝90°-α′
in the formula: k' is the length-to-diameter axial ratio of the ellipsoidal head, and the value range is (1, 2.5); phi is a 1 Is the starting angle of the elliptical section of the ellipsoidal head; a is an ellipsoid end socket long half shaft; b is an ellipsoid end socket short semi-axis; alpha' is an included angle between the tangent of the ellipsoid bus and the tangent of the ellipsoid short-range line; theta 1 Is a circumferential starting angle; phi is a unit of 2 Is an ellipsoidal head elliptical section termination angle; theta 2 Is a circumferential end angle;
the large ends of the von karman profiles are transited by cylindrical spiral lines;
the cylindrical spiral equation is:
25. the forming tool according to claim 19, wherein: the bidirectional spiral rib groove is formed by processing a cutter with a bidirectional spiral rib section shape, wherein the cutter is perpendicular to the center line of the oblique rib groove, the center line of the cutter points to the direction of the rotating shaft of the outer surface of the male die and is along the center line of the oblique rib groove.
26. The forming tool according to claim 19, wherein: the split male die is an aluminum split male die to form a hard die forming tool.
27. The forming tool according to claim 19, wherein: the split male die is an aluminum base plate and a silicon rubber grid male die to form a soft die forming tool, the silicon rubber grid male die is formed by pouring a silicon rubber male die through a pouring die, and the soft die forming device and the hard die forming device share a core die.
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