CN111680361B - Airship scaling model design method based on similarity theory - Google Patents
Airship scaling model design method based on similarity theory Download PDFInfo
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Abstract
The invention discloses a method for designing an airship scaling model based on a similarity theory, which takes a set airship structural member as a prototype object, designs the scaling model of statics corresponding and dynamic characteristics based on the similarity theory, and provides an equation analysis method combined with finite element analysis.
Description
Technical Field
The invention relates to the technical field of airship model design, in particular to a method for designing an airship scaling model based on a similarity theory.
Background
At present, the low-speed near space aircraft mainly comprises a balloon, an airship, an unmanned aerial vehicle, a solar airplane and the like, wherein the large airship is one of development emphasis of the low-speed near space aircraft, is mainly used for high-resolution earth observation, information collection, communication guarantee, investigation and monitoring, missile early warning, strategic delivery, environment and meteorological data detection and the like, and has very strong military and civil values. Because the large airship is large in size, the ground test is usually replaced by a scaling model test, and the purpose of the scaling model test is to acquire reliable mechanical property information and analysis experience of the full-size model at the early stage of structural design on one hand and develop an effective experimental method on the other hand. The mechanical data obtained by the scaling model not only can predict the mechanical characteristics of the full-size model, but also can be used for correcting the numerical model of the full-size model, so that the scaling model test is more focused on the problems of similarity relation between the scaling model and the full-size structure, external load boundary simulation, weight influence, deformation and strain measurement method, test error analysis, correlation between a judgment test result and an analysis result, applicability of a test system and the like.
Therefore, how to improve the accuracy of the similarity relationship between the scaling model and the full-size structure, and to achieve scaling and reduce model errors is a problem that needs to be solved by those skilled in the art.
Disclosure of Invention
In view of the above, the invention provides a method for designing an airship scaling model based on a similarity theory, which takes a set airship structural member as a prototype object, designs the scaling model of the statics corresponding and dynamic characteristics based on the similarity theory, and provides an equation analysis method combined with finite element analysis, and designs a scaling model with a certain proportion according to the established similarity relationship, so that the scaling model keeps higher similarity with the prototype in the aspects of statics corresponding and dynamic characteristics, and can be popularized for the scaling model design of large airships.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
the airship scaling model design method based on the similarity theory comprises the following specific steps:
step 1: obtaining a cyst similarity relationship by adopting a dimension analysis method;
step 2: obtaining a keel similarity relationship by adopting a finite element method;
step 3: calculating a pull rope similarity relationship;
step 4: the similar relationship of the airship is obtained by combining the similar relationship of the bag body, the similar relationship of the keel and the similar relationship of the pull rope;
step 5: and calculating a scaling model parameter according to the whole similarity relation of the airship, and constructing an airship scaling model according to the scaling model parameter.
Preferably, the specific implementation process of the step 1 is as follows:
step 11: determining that the natural frequency expression of the capsule body is omega=f (l, rho, E, P, v and F), wherein omega is frequency, l is size, rho is material surface density, E is material line tensile elastic modulus, P is capsule body internal pressure, v is Poisson's ratio, F is static load, and the dimensions are respectively expressed as follows:
[ω]＝T -1
[l]＝L
[ρ]＝ML -2
[E]＝FL -1
[P]＝FL -2
[F]＝F；
step 12: taking l, ρ and E as basic quantities, and carrying out dimensionless treatment:
step 13: according to the similarity criteria of the capsulesAnd obtaining the capsule similarity relationship with the dimensionless result:
where λ represents a similarity coefficient.
Preferably, the specific implementation process of the step 2 is as follows:
step 21: dispersing the circular structure into units by a finite element method, and establishing a corresponding stiffness equation;
dispersing the keels into n Euler beam units, fixedly connecting the beam units, and obtaining the stiffness equation of the ith round pipe under a local coordinate system according to the finite element method, wherein the stiffness equation is as follows:
wherein e represents a local coordinate system,is the beam unit stiffness matrix of the ith and the round tube under the local coordinate system, and is +.>Is the node displacement vector of the ith and the round tube under the local coordinate system, +.>The node force vector of the ith and the round tube under the local coordinate system is obtained;
step 22: obtaining a similarity relation of each unit by adopting an equation analysis method according to the stiffness equation;
step 23: according to the uniqueness of the node displacement vector and the node force vector when the integral stiffness equation is assembled, the similarity coordination relation between the units is supplemented;
step 24: the similar relation and the similar coordination relation of the whole units acquire a keel similar relation;
preferably, in the step 3, only the axial stretching deformation of the pull rope is considered, so as to obtain a similar relationship of the pull rope:
where Δ represents the axial deformation of the stretch, and a represents the axial direction.
Preferably, in the step 4, the similarity coefficients of the bag body, the keel and the pull rope in rigidity, mass and external load are unified, and the whole similarity relationship of the airship is obtained.
Compared with the prior art, the invention discloses a design method of the airship scaling model based on the similarity theory, which is used for respectively deducing the similarity relation among the capsule body, the keel and the pull rope of the airship composition structure, wherein the similarity relation of the keel is deduced by an equation analysis method combined with finite element analysis, then the scaling model is designed according to the established similarity relation, the equation analysis method combined with finite element analysis can be better suitable for designing the scaling model of a complex structure, and the similarity relation of the substructure of the scaling model can be quickly established by utilizing the existing unit stiffness equation in the finite element analysis. The invention can improve the degree of freedom of the scale model design, can be used for guiding the scale model design and test of the large airship structure, and provides technical support for the scheme design and optimization.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required to be used in the embodiments or the description of the prior art will be briefly described below, and it is obvious that the drawings in the following description are only embodiments of the present invention, and that other drawings can be obtained according to the provided drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a design method of an airship scale model based on a similarity theory.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The embodiment of the invention discloses an airship scaling model design method based on a similarity theory, which comprises the following specific steps:
s1: obtaining a cyst similarity relationship by adopting a dimension analysis method;
s11: determining that the natural frequency expression of the capsule body is omega=f (l, rho, E, P, v and F), wherein omega is frequency, l is size, rho is material surface density, E is material line tensile elastic modulus, P is capsule body internal pressure, v is Poisson's ratio, F is static load, and the dimensions are respectively expressed as follows:
[ω]＝T -1
[l]＝L
[ρ]＝ML -2
[E]＝FL -1
[P]＝FL -2
[F]＝F；
s12: taking l, ρ and E as basic quantities, and carrying out dimensionless treatment:
s13: according to the similarity criteria of the capsuleAnd obtaining a bag body similarity relationship with a dimensionless result:
wherein λ represents a similarity coefficient;
s2: obtaining truss similarity relations by adopting a finite element method;
s21: dispersing the circular structure into units by a finite element method, and establishing a corresponding stiffness equation;
the keels are discretized into n Euler beam units, the beam units are fixedly connected, and the stiffness equation of the ith round tube under a local coordinate system is obtained according to a finite element method:
wherein e represents a local coordinate system,is the local coordinate of the ith round tubeThe unit stiffness matrix of the beam is tied down,for the node displacement vector of the ith round tube under the local coordinate system, < + >>The node force vector of the ith round tube under the local coordinate system is obtained;
s22: obtaining the similarity relation of each unit by adopting an equation analysis method according to the stiffness equation;
in the case of an isotropic material,
wherein, subscripts '1' and '2' represent nodes at two ends of an ith circular tube, u represents axial displacement of the nodes, v represents transverse disturbance of the nodes, θ represents a corner of the nodes, and P u Representing the axial concentrated load borne by the node, P ν Represents the transverse concentrated load born by the node, M θ Representing bending moment;
e in formula (5) i A i And E is i I i Respectively replaced by a thin-walled circular tube matrix [ k ] of laminated composite material ij ] 6×6 K in (k) 11,i And k 44,i Then the following system of equations is developed:
bringing the similarity coefficient of each physical quantity into formula (6) to obtain a similarity relationship
S23: according to the uniqueness of the node displacement vector and the node force vector when the integral stiffness equation is assembled, the similar coordination relation among all units is supplemented;
in the stiffness equation assembly process of the integral structure, the unit stiffness equation is expressed as follows in the integral coordinate system:
wherein q i,6×1 And P i,6×1 Respectively representing the node displacement vector and the node force vector of the ith circular tube (keel) under the integral coordinates, T i,6×6 Representing a coordinate transformation matrix;
the round tubes are rigidly connected, so that the displacement vector and the node force vector of the nodes at the same position of the adjacent round tubes satisfy uniqueness, meanwhile, the similarity has invariance in space, namely, the similarity coefficients of the same dimension physical quantity in the coordinate system conversion are the same, and the two points are obtained
P i,6×1 The similarity coefficients of the neutral force and the moment are respectively unified as lambda F And lambda (lambda) M And the characteristic quantity u represents the deformation of the whole structure to obtain
Substituting the formula (9) and the formula (10) into the formula (8) and comparing with the formula (4) to obtain
The space relative position of each unit in the representation scaling model is kept unchanged, so that the similarity coefficient of the lengths of all round tubes is the same, and lambda is used uniformly L Characterization, i.e
Similar coordination conditions can be obtained from formulas (9) - (12):
s24: the similarity relationship and the similarity coordination relationship of the whole units obtain a keel similarity relationship;
the combined type (7) and the formula (13) take the round pipe parameters and similar coordination conditions as model design parameters, and only the displacement deformation characteristic value of the whole rigid frame is reserved as the investigation response to obtain
According to finite element theory, obtaining a characteristic equation of the rigid frame dynamics characteristic problem, | (K-omega) 2 M) |=0, where K and M respectively represent a stiffness matrix and a quality matrix of the whole rigid frame in the whole coordinate system, and the characteristic quantity ω represents a natural circle frequency, and since the natural frequency ω as a response quantity of the whole structure cannot be scattered to each unit, the characteristic equation of the whole rigid frame is supplemented by using a similar coordination condition, so as to obtain a similar relationship of the dynamic characteristic problem of the keel:
the combined type (14) and the formula (15) obtain the similar relationship of the statics/dynamic characteristics of the keels:
s3: calculating to obtain a pull rope similarity relationship;
only the axial stretching deformation of the pull rope is considered, and the similar relationship of the pull rope is obtained:
wherein Δ represents the axial deformation of the stretch;
s4: carrying out simultaneous connection according to the bag body similarity relationship, the truss similarity relationship and the stay rope similarity relationship to obtain the whole similarity relationship of the airship;
unifying similar coefficients of the bag body, the keel and the stay rope in rigidity, mass and external load:
1) The similar coefficients of the transverse rigidity of the bag body and the keel are consistent, and the similar coefficients of the axial rigidity of the pull rope and the keel are consistent, namely
Wherein "1", "2", "3" respectively represent the capsule body, the keel and the pull rope;
2) The quality of the pull rope is negligible, and the quality similarity coefficient of the bag body, the keel and the inflatable three parts in the bag body is mainly ensured to be consistent, namely
Wherein, the subscript "4" represents the air charge in the bladder;
3) The bag body, the keel and the pull rope have consistent external load similarity coefficient, namely
Combining the formulas (17) - (19) to obtain the integral similar relation of the airship;
s5: and calculating the scaling model parameters according to the overall similarity relation of the airship, and constructing the airship scaling model according to the scaling model parameters.
Examples
And calculating the scaling model parameters by utilizing the similarity relation, firstly determining the scaling model parameters of the capsule body, then calculating the common rigidity similarity coefficient and the mass similarity coefficient of the simultaneous substructures, and finally designing the scaling model of the keel, the stay rope and the air additional mass according to the two similarity coefficients.
The similarity coefficient of the 1/5 scale model related parameters of the airship structural member is shown in table 1, and specifically comprises the following steps:
1) The material and the skin thickness of the capsule body in the scaling model are the same as those of the prototype, the external dimension is reduced according to 1/5, and the internal pressurizing is improved by 5 times;
2) The outer diameter of the round tube in the scaling model is 9.4mm, the thickness is 2.08mm, the same single-layer material as the prototype is adopted, the single-layer thickness is about 0.14mm, and the layering angle sequence is (+ -45) 2 /(0/90) 4 /0 3 ；
3) The section area of the pull rope in the scaling model is 1/5 of that of the prototype;
4) The density of the air filled in the scaled model is 5 times that of the prototype, the air density can be kept unchanged during the test, and a counterweight sheet with quite additional mass is added on the surface of the bag body.
Table 1 1/5 scaling model similarity coefficients
| Parameters (parameters) | External dimension | Quality of | Bending stiffness | Static load | Balloon pressurization | Displacement of static response | Natural frequency (natural frequency) |
| Similarity coefficient | 1/5 | 1/25 | 1/125 | 1/5 | 5 | 1/5 | 5 |
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (2)
1. The airship scaling model design method based on the similarity theory is characterized by comprising the following specific steps of:
step 1: obtaining a cyst similarity relationship by adopting a dimension analysis method;
the specific implementation process of the step 1 is as follows:
step 11: determining the natural frequency expression of the capsule body as omega=f (l, rho, E, P, v and F), wherein omega is frequency, l is size, rho is material surface density, E is material line tensile elastic modulus, P is capsule body internal pressure, v is Poisson's ratio, F is static load, and performing dimensional representation;
step 12: taking l, ρ and E as basic quantities, and carrying out dimensionless treatment on the natural frequency of the capsule body:
step 13: according to the similarity criteria of the capsulesAnd obtaining the capsule similarity relationship with the dimensionless result:
wherein λ represents a similarity coefficient;
step 2: obtaining a keel similarity relationship by adopting a finite element method;
the specific implementation process of the step 2 is as follows:
step 21: dispersing the circular structure into units by a finite element method, and establishing a corresponding stiffness equation;
the keels are discretized into n Euler beam units, the beam units are fixedly connected, and the stiffness equation of the ith round pipe under the local coordinate system is obtained according to the finite element method:
wherein e represents a local coordinate system,for the beam unit stiffness matrix of the ith round tube under the local coordinate system,/for the beam unit stiffness matrix of the ith round tube>For the node displacement vector of the ith round tube under the local coordinate system, < + >>The node force vector of the ith round tube under the local coordinate system;
step 22: obtaining the similarity relation of each unit by adopting an equation analysis method according to the stiffness equation;
in the case of an isotropic material,
wherein, subscripts 1 and 2 represent nodes at two ends of an ith circular tube, u represents axial displacement of the nodes, v represents transverse disturbance of the nodes, θ represents rotation angle of the nodes, and P u Representing the axial concentrated load borne by the node, P ν Represents the transverse concentrated load born by the node, M θ Representing bending moment;
e in formula (5) i A i And E is i I i Respectively replaced by a thin-walled circular tube matrix [ k ] of laminated composite material ij ] 6×6 K in (k) 11,i And k 44,i Then the following system of equations is developed:
bringing the similarity coefficient of each physical quantity into formula (6) to obtain a similarity relationship,
step 23: according to the uniqueness of the node displacement vector and the node force vector when the integral stiffness equation is assembled, the similarity coordination relation between the units is supplemented;
in the stiffness equation assembly process of the integral structure, the unit stiffness equation is expressed as follows in the integral coordinate system:
wherein q i,6×1 And P i,6×1 Respectively representing a node displacement vector and a node force vector of the ith circular tube under the integral coordinates, T i,6×6 Representing a coordinate transformation matrix;
P i,6×1 the similarity coefficients of the neutral force and the moment are respectively unified as lambda F And lambda (lambda) M And the characteristic quantity u represents the deformation of the whole structure to obtain
Substituting the formula (9) and the formula (10) into the formula (8) and comparing with the formula (4) to obtain
The space relative position of each unit in the representation scaling model is kept unchanged, so that the similarity coefficient of the lengths of all round tubes is the same, and lambda is used uniformly L Characterization, i.e
Similar coordination conditions can be obtained from formulas (9) - (12):
step 24: integrating the similarity relationship and the similarity coordination relationship of each unit to obtain a keel similarity relationship;
the combined type (7) and the formula (13) take the round pipe parameters and similar coordination conditions as model design parameters, and only the displacement deformation characteristic value of the whole rigid frame is reserved as the investigation response to obtain
According to finite element theory, obtaining a characteristic equation of the rigid frame dynamics characteristic problem, | (K-omega) 2 M) |=0, where K and M respectively represent a stiffness matrix and a quality matrix of the whole rigid frame in the whole coordinate system, and the characteristic quantity ω represents a natural circle frequency, and since the natural frequency ω as a response quantity of the whole structure cannot be scattered to each unit, the characteristic equation of the whole rigid frame is supplemented by using a similar coordination condition, so as to obtain a similar relationship of the dynamic characteristic problem of the keel:
the combined type (14) and the formula (15) obtain the similar relationship of the statics/dynamic characteristics of the keels:
step 3: calculating a pull rope similarity relationship;
step 4: obtaining the overall similar relationship of the airship according to the similar relationship of the bag body, the similar relationship of the keel and the similar relationship of the pull rope;
unifying similar coefficients of the bag body, the keel and the stay rope in rigidity, mass and external load:
1) The similar coefficients of the transverse rigidity of the bag body and the keel are consistent, and the similar coefficients of the axial rigidity of the pull rope and the keel are consistent, namely
Wherein subscripts 1, 2, 3 respectively represent a capsule body, a keel and a pull rope;
2) Ensuring the consistency of the mass similarity coefficients of the bag body, the keel and the inflatable three parts in the bag body, namely
Wherein subscript 4 represents the air charge within the bladder;
3) The bag body, the keel and the pull rope have consistent external load similarity coefficient, namely
Combining the formulas (17) - (19) to obtain the integral similar relation of the airship;
step 5: and calculating a scaling model parameter according to the whole similarity relation of the airship, and constructing an airship scaling model according to the scaling model parameter.
2. The airship scaling model design method based on the similarity theory according to claim 1, wherein in the step 3, only axial stretching deformation of the pull rope is considered, and the pull rope similarity relationship is obtained:
where Δ represents the axial deformation of the stretch, and a represents the axial direction.
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