CN112816163A - Method for determining vertical rigidity of large-opening structure of cabin body of rectangular fuselage - Google Patents
Method for determining vertical rigidity of large-opening structure of cabin body of rectangular fuselage Download PDFInfo
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Abstract
The invention belongs to the field of aviation structure design, and particularly relates to a method for determining vertical rigidity of a large-opening structure of a cabin body of a rectangular fuselage. The method comprises the following steps: the rigidity ratio of a rectangular machine body with a large opening structure and the rigidity ratio of a rectangular machine body without the large opening structure and the length, width and wall thickness of a rectangular section of the rectangular machine body are given; the two rectangular bodies have the same structure except the large opening structure; and solving an expression of the area of the upper boundary beam and an expression of the area of the lower boundary beam by taking the rigidity ratio and the length, width and height of the rectangular section as parameters and taking the minimum area of the upper boundary beam and the minimum area of the lower boundary beam as constraint conditions.
Description
Technical Field
The invention belongs to the field of aviation structure design, and particularly relates to a method for determining vertical rigidity of a large-opening structure of a cabin body of a rectangular fuselage.
Background
The large opening structure cuts off the force transmission path of the airplane structure, which is a difficult point of airplane design. The conventional large opening of the circular fuselage is based on a small number of design references, while the rectangular opening is a special cabin opening, is a novel structural form, and lacks design experience in model design and introduction of the structure of the type in the design information of the airplane.
In order to minimize the impact of the large opening area on the fuselage and to meet the requirements of continuous rigidity and coordinated deformation, the opening area must be reinforced. However, technical information on the reinforced design of the fuselage large opening is rarely published, so that the design technique and experience are relatively lacking.
Disclosure of Invention
The purpose of the invention is as follows: the design principle and method of the vertical bending stiffness of the rectangular large-opening structure of the airplane are provided for the first time, the analytical expression of the vertical stiffness ratio is deduced, and the dilemma that no theoretical basis exists for strengthening the design of the rectangular large-opening structure of the airplane is solved.
The technical scheme is as follows:
a method for determining the vertical rigidity of a large-opening structure of a cabin body with a rectangular fuselage comprises the following steps:
the vertical rigidity ratio xi and the rectangular section length, width and wall thickness of the rectangular machine body are given to the expected rectangular machine body with the large opening structure and the rectangular machine body without the large opening structure; the two rectangular bodies have the same structure except the large opening structure;
and determining the sum of the area of the upper side beam and the area of the lower side beam according to the length, the width and the wall thickness of the rectangular section so as to compensate the vertical rigidity of the rectangular machine body with the large opening structure to be xi times of the vertical rigidity of the rectangular machine body without the large opening structure.
Further, determining the sum of the upper side beam area and the lower side beam area according to the length, the width and the wall thickness of the rectangular section, and the method comprises the following steps:
taking the rigidity ratio and the length, the width and the height of the rectangular section as parameters, taking the minimum sum of the area of the upper boundary beam and the area of the lower boundary beam as a constraint condition, and solving an expression of the area of the upper boundary beam and an expression of the area of the lower boundary beam;
the expression of the area of the upper boundary beam is as follows:
the expression for the area of the lower boundary beam is:
wherein ,
k is an area ratio, FupIs the area of the upper side rail, FdownThe area of the lower boundary beam is shown, and the width of the rectangular section is shown as b; h is the height of a rectangular section; delta0Equal to δ is the wall thickness.
Further, the sum of the upper side beam area and the lower side beam area is determined according to the length, the width and the wall thickness of the rectangular section, and the method further comprises the following steps:
drawing a group of stiffness ratio curves under the aspect ratio of the rectangular section according to the expression of the stiffness ratio; the stiffness ratio curve represents the vertical bending stiffness ratio and the section area A of the opening reinforcing structure under different area ratios of the upper and lower boundary beams1Area ratio A of the cross section of the model without the opening0The corresponding relationship of (a);
searching a stiffness ratio curve corresponding to the minimum area ratio on the stiffness ratio curves;
finding out A corresponding to the stiffness ratio in the stiffness ratio curve corresponding to the minimum area ratio1/A0；
According to the corresponding A1/A0And calculating the sum of the areas of the upper and lower boundary beams according to the minimum area ratio.
Further, the calculation formula of the sum of the areas of the upper and lower boundary beams is as follows:
p＝A1/A0。
further, the expression of the stiffness ratio is:
ξ denotes the stiffness ratio, EIyRigidity of a rectangular body having a large opening structure; e0Iy0Rigidity of a rectangular body having no large opening structure, E is modulus of elasticity of a rectangular body having a large opening structure, E0Modulus of elasticity, I, of a rectangular fuselage of largely open constructionyMoment of inertia, I, of a rectangular fuselage with a large open structurey0Is the moment of inertia of a rectangular fuselage without a large opening structure.
Further, the method further comprises:
establishing a model of a rectangular machine body with a large opening structure;
establishing a model of a rectangular machine body without a large opening structure;
determining an expression of the rigidity of the rectangular fuselage with the large opening structure and an expression of the rigidity of the rectangular fuselage without the large opening structure according to the parameters of the model;
and transforming the ratio of the two expressions to obtain an expression of the area of the upper side beam and an expression of the area of the lower side beam.
Further, in the coordinate system of the model of the rectangular body having no large opening structure, the origin o of the coordinate is the geometric center point of the cross section, the z-axis is positive when pointing upward along the height direction of the cross section, and the y-axis is positive when pointing to the right side along the width direction of the cross section.
Further, in the coordinate system of the model of the rectangular body having the large opening structure, the origin o of coordinates is the geometric center point of the cross section, the z-axis is positive when pointing upward in the direction of the height of the cross section, and the y-axis is positive when pointing to the right in the direction of the width of the cross section.
Has the advantages that:
the present invention studies the concept of introducing a stiffness ratio, i.e. the stiffness ratio of a large opening structure to a complete fuselage structure. The rigidity ratio is equal to 1 which is a design critical value, which shows that the rigidity of the reinforced large opening structure of the fuselage is consistent with the rigidity of the complete fuselage structure; a stiffness ratio greater than 1 indicates that the reinforced structural stiffness is greater than the stiffness of the complete fuselage structure; a stiffness ratio of less than 1 indicates that the stiffened structural stiffness does not achieve the stiffness of the complete fuselage structure.
Drawings
FIG. 1 is a schematic view of a large-opening structure calculation model;
FIG. 2 is a diagram of a computational model without large openings;
FIG. 3 is a graph of stiffness ratio at h/b of 0.1;
FIG. 4 is a graph of stiffness ratio at h/b of 1;
FIG. 5 is a graph of stiffness ratio at h/b of 2;
FIG. 6 is a graph of stiffness ratio at h/b of 5;
FIG. 7 is a graph of stiffness ratio at h/b of 10.
Detailed Description
The invention provides a method for determining vertical rigidity of a large-opening structure of a cabin body of a rectangular fuselage, which comprises the following steps:
(1) building model of large opening structure of rectangular machine body
For a rectangular large opening structure, reinforcing beams are generally arranged at four corners, and a cross-sectional view of a typical reinforced fuselage large opening structure is shown in fig. 1. The origin of coordinates o is the geometric center of the cross-section, the z-axis is positive when pointing upward along the height of the cross-section, and the y-axis is positive when pointing to the right along the width of the cross-section.
In fig. 1:
b-rectangular opening section width;
h is the height of the section of the rectangular opening;
delta-rectangular opening cross-sectional wall thickness;
Fup-left and right side roof rails centralize area;
Fdown-left and right side sill convergence area;
(2) calculation model without large opening
The model of a rectangular fuselage without openings is schematically shown in fig. 2. The origin of coordinates o is the geometric center of the cross-section, the z-axis is positive when pointing upward along the height of the cross-section, and the y-axis is positive when pointing to the right along the width of the cross-section.
In fig. 2:
b-rectangular cross-sectional width;
h-rectangular section height;
δ0-fuselage cell wall thickness without openings.
(3) Calculating the vertical bending rigidity of the large-opening structure
And defining the bending rigidity of the model around the y axis as the vertical bending rigidity.
Due to the fact thatSymmetry, centroid coordinate yc＝0
Static moment S of the model about the y-axisyComprises the following steps:
the cross-sectional area A of the large opening structure is as follows:
A＝(b+2h)δ+2(Fup+Fdown)
centroid coordinate zcComprises the following steps:
the moment of inertia of the cross section to the centroid principal axis y is:
will zcSubstituting the expression into the above formula can obtain:
the vertical bending rigidity of the large-opening structure is EIy
In the above formula. And E is the elastic modulus of the material.
(4) Calculating the vertical bending stiffness of a non-opening structure
The moment of inertia of the model winding mandrel in fig. 2 was calculated as:
the vertical bending rigidity of the non-opening structure is E0Iy0
In the above formula. E0The elastic modulus of the material with no opening structure.
(4) Vertical bending stiffness ratio
The rigidity ratio xi of the large-opening structure and the body structure without the large opening is as follows:
generally, aircraft designs all use aluminum alloy series materials, so E ═ E0
Xi is 1, which shows the rigidity EI of the large-opening structural modelyRigidity E with respect to the unopened fuselage model0Iy0Rather, when the structure is designed, how to strengthen the structure under the condition of meeting the requirement of vertical rigidity can be determined according to the expression of xi.
When the stiffness ratio expression is determined, the problem is solved in the following two ways:
one is to adopt the step (5), namely a graph method;
the other method adopts the step (6) -formula determination method
(5) Determining boundary beam area by graph method
In general, a structure in which a rectangular cross-sectional machine body lower wall panel is opened is considered to have a wall thickness that matches a wall thickness before the opening and to be reinforced only by adjusting the areas of the upper and lower side sills, and therefore, δ is considered to be δ0。
A series of different upper and lower boundary beam section area values are set according to a rigidity ratio formula xi expression, and a series of data are calculated by using excel software to make a rigidity ratio curve as shown in figure 3.
In the figure: a. the1Area of opening reinforcement structure, A0Is the area of the model without the opening, and has:
A1＝(b+2h)δ+2(Fup+Fdown)
A0＝2(b+h)δ0
Fup/Fdownshowing different upper and lower boundary beam area ratios.
The corresponding stiffness ratio curves are shown in figures 3-7 according to the value of the cross-sectional dimension b/h of the rectangular large-opening fuselage.
Designing proper reinforcement xi, rootFinding the corresponding A according to the stiffness ratio curve1/A 0The value of the ratio, denoted as p, corresponds to the axis of abscissa on the graph;
by
The following can be obtained:
according to F corresponding to pup/FdownProportional curve, which can be derived from Fup+FdownThe total area expression determines the values of the upper and lower rocker areas, respectively.
For example: search Fup/FdownWhen the curve is 2:8
Search Fup/FdownWhen the curve is 5:5
It can be seen from the vertical stiffness ratio curve that the lower the area ratio of the upper edge beam to the lower edge beam, the better the stiffness compensation effect under the same area condition.
(6) Formulaic determination of upper and lower side beam area expression
The rigidity ratio expression is used, and the area ratio of the upper boundary beam to the lower boundary beam is set as follows:
solving the equation yields:
wherein ：
in general, the optimal solution for k is such that Fup+FdownAnd taking the corresponding value when the minimum value is obtained.
Example 1
A rectangular fuselage section with a width b of 3000mm, a height h of 1500mm and a wall thickness δ02mm, the boundary beam needs to be arranged at four angular points for strengthening the lower wall due to the large opening of the cabin body, and when the vertical bending rigidity is consistent with the rigidity of the model without the opening, the area F which needs to be compensated by the boundary beamupAnd FdownHow is it determined?
The method comprises the following steps:
1) from the data of the size of the structure,
when the vertical bending rigidity of the reinforced model is required to be consistent with that of the model before opening, xi is 1;
if F is foundup/FdownThe curve 2:8 gives p 1.02.
Then the areas of the upper and lower boundary beams are respectively:
if F is foundup/FdownAs a 5:5 curve, we can get: p is 1.10
Then the areas of the upper and lower boundary beams are respectively:
the second method comprises the following steps:
when the vertical bending rigidity of the reinforced model is required to be consistent with that of the model before opening, xi is 1; if it is
Solving the equation yields:
if it is
Solving the equation yields:
the calculation errors (2509.4, 2544) obtained by the two methods are 2% at most, which are caused by reading precision of a chart, effective digits reserved by calculation and the like, and the errors can be ignored in engineering.
Claims (8)
1. A method for determining the vertical rigidity of a large-opening structure of a cabin body with a rectangular fuselage is characterized by comprising the following steps:
the vertical rigidity ratio xi and the rectangular section length, width and wall thickness of the rectangular machine body are given to the expected rectangular machine body with the large opening structure and the rectangular machine body without the large opening structure; the two rectangular bodies have the same structure except the large opening structure;
and determining the sum of the area of the upper side beam and the area of the lower side beam according to the length, the width and the wall thickness of the rectangular section so as to compensate the vertical rigidity of the rectangular machine body with the large opening structure to be xi times of the vertical rigidity of the rectangular machine body without the large opening structure.
2. The method of claim 1, wherein determining the sum of the upper and lower sill areas from the rectangular cross-section long wide wall thickness comprises:
taking the rigidity ratio and the length, the width and the height of the rectangular section as parameters, taking the minimum sum of the area of the upper boundary beam and the area of the lower boundary beam as a constraint condition, and solving an expression of the area of the upper boundary beam and an expression of the area of the lower boundary beam;
the expression of the area of the upper boundary beam is as follows:
the expression for the area of the lower boundary beam is:
wherein ,
k is an area ratio, FupIs the area of the upper side rail, FdownThe area of the lower boundary beam is shown, and the width of the rectangular section is shown as b; h is the height of a rectangular section; delta0Equal to δ is the wall thickness.
3. The method of claim 1, wherein determining the sum of the upper and lower sill areas from the rectangular cross-section long wide wall thickness further comprises:
drawing a group of stiffness ratio curves under the aspect ratio of the rectangular section according to the expression of the stiffness ratio; the stiffness ratio curve represents the vertical bending stiffness ratio and the section area A of the opening reinforcing structure under different area ratios of the upper and lower boundary beams1Area ratio A of the cross section of the model without the opening0The corresponding relationship of (a);
searching a stiffness ratio curve corresponding to the minimum area ratio on the stiffness ratio curves;
finding out A corresponding to the stiffness ratio in the stiffness ratio curve corresponding to the minimum area ratio1/A0；
According to the corresponding A1/A0And calculating the sum of the areas of the upper and lower boundary beams according to the minimum area ratio.
4. The method of claim 3, wherein the sum of the areas of the upper and lower boundary beams is calculated by the formula:
p＝A1/A0。
5. the method of claim 1, wherein the stiffness ratio is expressed as:
ξ denotes the stiffness ratio, EIyRigidity of a rectangular body having a large opening structure; e0Iy0Rigidity of a rectangular body having no large opening structure, E is modulus of elasticity of a rectangular body having a large opening structure, E0Modulus of elasticity, I, of a rectangular fuselage of largely open constructionyIs provided withMoment of inertia, I, of a rectangular fuselage of large-opening constructiony0Is the moment of inertia of a rectangular fuselage without a large opening structure.
6. The method of claim 5, further comprising:
establishing a model of a rectangular machine body with a large opening structure;
establishing a model of a rectangular machine body without a large opening structure;
determining an expression of the rigidity of the rectangular fuselage with the large opening structure and an expression of the rigidity of the rectangular fuselage without the large opening structure according to the parameters of the model;
and transforming the ratio of the two expressions to obtain an expression of the area of the upper side beam and an expression of the area of the lower side beam.
7. The method of claim 6, wherein in the coordinate system of the model of the rectangular fuselage without the large opening structure, the origin of coordinates o is the geometric center point of the cross-section, the z-axis is positive pointing up along the height direction of the cross-section, and the y-axis is positive pointing to the right along the width direction of the cross-section.
8. The method of claim 6, wherein in a coordinate system of a model of a rectangular fuselage having a large opening structure, the origin of coordinates o is the geometric center point of the cross-section, the z-axis is positive when pointing up along the height direction of the cross-section, and the y-axis is positive when pointing to the right along the width direction of the cross-section.
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