CN109460600A - A kind of aircraft lands are sliding to run section coupling force analysis and method for solving - Google Patents
A kind of aircraft lands are sliding to run section coupling force analysis and method for solving Download PDFInfo
- Publication number
- CN109460600A CN109460600A CN201811280726.XA CN201811280726A CN109460600A CN 109460600 A CN109460600 A CN 109460600A CN 201811280726 A CN201811280726 A CN 201811280726A CN 109460600 A CN109460600 A CN 109460600A
- Authority
- CN
- China
- Prior art keywords
- aircraft
- tire
- shock absorber
- equation
- rocker arm
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 238000000034 method Methods 0.000 title claims abstract description 60
- 230000008878 coupling Effects 0.000 title claims abstract description 29
- 238000010168 coupling process Methods 0.000 title claims abstract description 29
- 238000005859 coupling reaction Methods 0.000 title claims abstract description 29
- 238000004458 analytical method Methods 0.000 title claims abstract description 19
- 238000007906 compression Methods 0.000 claims abstract description 91
- 230000006835 compression Effects 0.000 claims abstract description 90
- 238000004088 simulation Methods 0.000 claims abstract description 24
- 239000006096 absorbing agent Substances 0.000 claims description 86
- 230000035939 shock Effects 0.000 claims description 86
- 239000011295 pitch Substances 0.000 claims description 14
- 238000005096 rolling process Methods 0.000 claims description 13
- 238000004364 calculation method Methods 0.000 claims description 10
- 238000013016 damping Methods 0.000 claims description 10
- 238000006243 chemical reaction Methods 0.000 claims description 3
- 230000008569 process Effects 0.000 abstract description 13
- 238000000342 Monte Carlo simulation Methods 0.000 abstract description 6
- 230000001133 acceleration Effects 0.000 description 5
- 230000008901 benefit Effects 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 230000002411 adverse Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000011156 evaluation Methods 0.000 description 1
- 238000012804 iterative process Methods 0.000 description 1
- 238000005457 optimization Methods 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 238000011426 transformation method Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B64—AIRCRAFT; AVIATION; COSMONAUTICS
- B64F—GROUND OR AIRCRAFT-CARRIER-DECK INSTALLATIONS SPECIALLY ADAPTED FOR USE IN CONNECTION WITH AIRCRAFT; DESIGNING, MANUFACTURING, ASSEMBLING, CLEANING, MAINTAINING OR REPAIRING AIRCRAFT, NOT OTHERWISE PROVIDED FOR; HANDLING, TRANSPORTING, TESTING OR INSPECTING AIRCRAFT COMPONENTS, NOT OTHERWISE PROVIDED FOR
- B64F5/00—Designing, manufacturing, assembling, cleaning, maintaining or repairing aircraft, not otherwise provided for; Handling, transporting, testing or inspecting aircraft components, not otherwise provided for
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/15—Vehicle, aircraft or watercraft design
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/06—Power analysis or power optimisation
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Geometry (AREA)
- Theoretical Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Aviation & Aerospace Engineering (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- General Engineering & Computer Science (AREA)
- Manufacturing & Machinery (AREA)
- Transportation (AREA)
- Automation & Control Theory (AREA)
- Computational Mathematics (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
- Tires In General (AREA)
Abstract
The invention discloses a kind of sliding sections of running of aircraft lands to couple force analysis and method for solving, combine modeling and simulating problem with aircraft six degree of freedom for landing chassis damper/tire coupling compression, it converts the differential equation of each component movement of landing chassis to using damper decrement increment as the non-linear algebraic equation of independent variable, using numerical methods of solving decrement, and then the tire force of full aircraft is solved, it realizes and contacts to earth the simulation analysis of process to aircraft.The present invention can directly extend on the basis of aircraft six degree of freedom simulation model, and without changing its simulation step length, the language Direct Programming such as C++ can be used, and can be effectively applied to aircraft and contact to earth the Monte-Carlo Simulation analysis of process.
Description
Technical Field
The invention belongs to the technical field of control, and particularly relates to a method for analyzing and solving coupling stress of an aircraft landing and running section.
Background
The ground contact process of the aircraft is a short-time and high-dynamic complex motion process, and mainly relates to six-degree-of-freedom motion of the aircraft and coupled compression motion of a landing gear shock absorber and a tire. The problem that the stress of the tire of the aircraft can be obtained only by solving the compression amount of the shock absorber and the tire, and then the motion simulation of the aircraft is carried out. The prior literature does not clearly show a method for solving the coupling between the landing gear shock absorber and the tire compression amount, and the technology is blank in this respect.
Disclosure of Invention
The technical problem solved by the invention is as follows: the method is characterized in that differential equations of motion of all parts of a landing frame are converted into nonlinear algebraic equations with shock absorber compression increment as independent variables, the compression is solved by a numerical method, and then tire stress of the whole aircraft is solved, so that simulation analysis of the aircraft touchdown process is realized. The method can be directly expanded on the basis of a six-degree-of-freedom simulation model of the aircraft without changing the simulation step length, can be directly programmed by adopting languages such as C + + and the like, and can be effectively applied to Monte Carlo simulation analysis of the ground contact process of the aircraft.
The purpose of the invention is realized by the following technical scheme: a method for analyzing and solving coupling stress of an aircraft landing run segment comprises the following steps: (1) building a tire force model; (2) establishing a shock absorber axial force model; (3) the airplane wheel and the tire are arranged on the wheel shaft and used as a whole to establish an equation of motion of the airplane wheel and the tire; (4) replacing the rocker arm landing gear with a geometric relationship structure; (5) taking the wheel axle and the rocker arm as a whole, and establishing a motion equation of the wheel axle and the rocker arm according to the geometric relationship structure in the step (4); (6) calculating the swing angle of the rocker arm and the coordinates of the wheel axle in the coordinate system of the aircraft according to the geometric relation structure in the step (4); calculating the height of an axle and the compression amount of a tire according to the geometric relationship of the main landing frame after the aircraft pitches and rolls;
(7) obtaining a main landing frame algebraic equation according to the tire force model in the step (1), the shock absorber axial force model in the step (2), the wheel and tire motion equation in the step (3) and the wheel axle and rocker arm motion equation in the step (5), wherein the main landing frame algebraic equation is regarded as a main landing frame unary nonlinear equation, and the increment delta S of the shock absorber compression is an unknown number in the main landing frame unary nonlinear equation;
(8) giving out a shock absorber motion trend judgment condition, and judging a solving interval of the shock absorber compression increment delta S in the primary landing frame unary nonlinear equation;
(9) solving a primary nonlinear equation of the main landing frame by adopting a variable capacitance difference secant method to obtain the actual compression amount of the shock absorber, and obtaining the tire stress after obtaining the tire compression amount according to the actual compression amount of the shock absorber;
(10) and adding the tire stress and the moment into a six-degree-of-freedom equation of the aircraft to simulate.
In the method for analyzing and solving the coupling stress of the landing and running section of the aircraft, in the step (1), the tire force model is obtained by the following formula:
N＝N(δ)；
f＝cN；
wherein N is the tire force, with the vertical tire compression face up, as a function of the tire compression δ; f is the rolling friction force of the tire; and c is the rolling friction coefficient.
In the method for analyzing and solving the coupling stress of the landing and running section of the aircraft, in the step (2), the shock absorber axial force model is obtained by the following formula:
F＝fa+ff+fd；
wherein ,faFor the force of the air spring present in the shock absorber, ffIs the friction force present in the shock absorber, fdIs the damping force present in the shock absorber and F is the shock absorber axial force.
In the method for analyzing and solving the coupling stress of the landing and running section of the aircraft, in the step (3), the motion equation of the wheels and the tires is obtained by the following formula:
wherein T is the force of the wheel axle to the wheel and the tire; n is tire force; m isWheelMass of wheels and tires; h is the altitude of the axle.
In the method for analyzing and solving the coupling stress of the landing and running section of the aircraft, in the step (4), the section AB is a cantilever beam and is fixedly connected with the aircraft body; the CE section is connected to the middle part of the AD section, the CE section and the AD section are combined into a rocker arm, the rocker arm is hinged with the cantilever beam at the point A, and the D is a wheel shaft; the BC section is a shock absorber, is hinged with the cantilever beam at the B and is hinged with the rocker arm at the C; one end of the rocker arm is rotatably connected with the wheel shaft, and the middle part of the rocker arm is hinged with the shock absorber; when the shock absorber compresses, point C moves to point C1Position, point D moved to D1Location.
In the method for analyzing and solving the coupling stress of the landing and running section of the aircraft, in the step (5), the motion equation of the wheel shaft and the rocker arm is obtained by the following formula:
wherein ,JRocker armIs the moment of inertia of the rocker arm ACD; omega is the absolute angular speed of the rocker arm rotating around the axis A; t is the reaction force of the wheel shaft from the wheel and the tire; f is the rolling friction force of the tire; f is the damper axial force.For the pitch angle of the aircraft,is AD1Length of the segment, /)ABLength of AB section, ∠ QAD1Is QA segment and AD1Angle of section ∠ ABC1Is AB segment and BC1The angle of the segments.
In the method for analyzing and solving the coupling stress of the landing and running section of the aircraft, in the step (6), the swing angle of the rocker arm and the coordinates of the wheel axle in the coordinate system of the aircraft are obtained through the following formulas:
Δ＝∠BAC-∠BAC1；
∠HAD1＝∠HAD+Δ；
XD＝XA+lADsin∠HAD1；
YD＝YA-lADcos∠HAD1；
wherein, Delta is swing angle of the rocker arm, XD、YDIs the coordinates of the axle in the aircraft coordinate system; xA、YAIs the coordinate of axis a in the aircraft coordinate system;for aircraft pitch angle,/ADIs the length of the AD segment.
The axle height and tire compression are obtained by the following equations:
δ＝max{0,hland-(hL-rcosφ)}；
wherein ,is the pitch angle of the aircraft; phi is the aircraft roll angle; xG、YGIs the coordinate of the aircraft centroid in the aircraft coordinate system; h isvIs the altitude of the aircraft centroid, and h is the tire axis altitude; h islandIs landing site altitude; r is the tire radius; l0The distance between the left and right tire shafts in an uncompressed state; δ is the tire compression amount.
In the method for analyzing and solving the coupling stress of the landing and running section of the aircraft, in the step (7), the algebraic equation of the main landing frame is as follows:
the primary landing pad unary nonlinear equation is: f (Δ S) ═ 0.
In the method for analyzing and solving coupling stress of landing and running section of aircraft, in step (8), in the k-th simulation, the increment Δ S of the shock absorber compression amount is preset to be 0, namely the shock absorber compression amount is kept unchanged from the value of the k-1-th step, and when the value is not changed from the value of the shock absorber compression amount to the value of the shock absorber compression amount, the step (k-1) is carried outWhen the damping force is applied, the compression amount of the damper tends to increase, and the damping force is increased at delta S epsilon (0, S)max-Sk-1]Solving a primary landing frame one-element nonlinear equation in an interval; wherein f isf＝|cffa|≠0；
When in useAt this time, the shock absorber compression amount tends to decrease at Δ Sec [ -Sk-10) solving a primary landing frame one-element nonlinear equation in an interval; wherein f isf＝|cffa|≠0；
If the two conditions are not satisfied, the compression amount of the shock absorber is kept unchanged at the value of the k-1 step, and the equation is not solved, namely, the delta S is equal to 0.
In the method for analyzing and solving the coupling stress of the landing and running section of the aircraft, in step (9), a secant method is adopted to solve the following formula for a primary landing frame nonlinear equation:
the number of iteration steps; delta SjFor solving the equation, the value of the independent variable in the j step is Delta Sj+1For solving the equation, the independent variable value of the (j + 1) th step, Delta Sj-1And f is a function calculation formula on the left side of the primary landing frame unary nonlinear equation.
The calculation method of the tolerance epsilon is as follows:
j∈[1,20]:ε＝0.01
j∈(21,40]:ε＝0.1
j∈(41,60]:ε＝1.0
j∈(61,80]:ε＝10
j∈(81,100]:ε＝100
j is the current iteration number;
when f (Δ S)j)<Stopping iteration when epsilon and solving the equation into delta Sk＝ΔSjAnd after the solution is successful, the actual compression amount of the shock absorber is as follows:
Sk＝Sk-1+ΔSk
obtaining the actual compression quantity S of the shock absorberkThen, according to the actual compression quantity S of the shock absorberkAnd obtaining the tire stress after obtaining the tire compression.
Compared with the prior art, the invention has the following beneficial effects:
the method solves the problem of solving the tire compression amount and the normal force of the landing and running section quickly and accurately, meets the requirement of Monte Carlo simulation on rapidity, and does not need to rely on commercial software for the landing frame model solution.
Drawings
Various other advantages and benefits will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. Also, like reference numerals are used to refer to like parts throughout the drawings. In the drawings:
FIG. 1 is a schematic diagram of tire and wheel forces provided by an embodiment of the present invention;
FIG. 2 is a schematic view of an alternative geometry for a rocker arm landing gear system provided by an embodiment of the present invention;
FIG. 3 is a schematic view of a rocker arm landing gear system provided by an embodiment of the present invention;
FIG. 4 is a schematic illustration of the relationship between the friction force and the increment of compression for a shock absorber provided by an embodiment of the present invention;
FIG. 5 is a graphical illustration of the compression versus time curves for a shock absorber provided in accordance with an embodiment of the present invention;
FIG. 6 is a graph illustrating compression versus time for a tire provided in accordance with an embodiment of the present invention;
FIG. 7 is a graphical illustration of angular acceleration and time curves for a rocker arm provided in accordance with an embodiment of the present invention;
FIG. 8 is a schematic view of the maximum compression spread of the shock absorber provided by the embodiment of the present invention;
FIG. 9 is a schematic view of the maximum compression spread of a tire provided by an embodiment of the present invention.
Detailed Description
Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art. It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict. The present invention will be described in detail below with reference to the embodiments with reference to the attached drawings.
The embodiment provides a method for analyzing and solving coupling stress of an aircraft landing run-off section, which comprises the following steps:
(1) building a tire force model;
(2) establishing a shock absorber axial force model;
(3) the airplane wheel and the tire are arranged on the wheel shaft and used as a whole to establish an equation of motion of the airplane wheel and the tire;
(4) replacing the rocker arm landing gear with a geometric relationship structure;
(5) taking the wheel axle and the rocker arm as a whole, and establishing a motion equation of the wheel axle and the rocker arm according to the geometric relationship structure in the step (4);
(6) calculating the swing angle of the rocker arm and the coordinates of the wheel axle in the coordinate system of the aircraft according to the geometric relation structure in the step (4); calculating the height of an axle and the compression amount of a tire according to the geometric relationship of the main landing frame after the aircraft pitches and rolls;
(7) obtaining a main landing frame algebraic equation according to the tire force model in the step (1), the shock absorber axial force model in the step (2), the wheel and tire motion equation in the step (3) and the wheel axle and rocker arm motion equation in the step (5), wherein the main landing frame algebraic equation is regarded as a main landing frame one-dimensional nonlinear equation, and the increment delta S of the shock absorber compression amount is an unknown number in the main landing frame one-dimensional nonlinear equation;
(8) giving out a shock absorber motion trend judgment condition, and judging a solving interval of shock absorber compression increment delta S in a primary landing frame unary nonlinear equation;
(9) solving a primary nonlinear equation of the main landing frame by adopting a variable capacitance difference secant method to obtain the actual compression amount of the shock absorber, and obtaining the tire stress after obtaining the tire compression amount according to the actual compression amount of the shock absorber;
(10) and adding the tire stress and the moment into a six-degree-of-freedom equation of the aircraft to simulate.
Tire force model
Fig. 1 is a schematic diagram of tire and wheel forces provided by an embodiment of the present invention. As shown in fig. 1, the tire force N is upward perpendicular to the tire compression and is a function of the amount of tire compression δ, as shown in equation (1), and is typically given in the form of an interpolation table. The tire rolling friction force f and the tire force N have a linear relation, as shown in formula (2), wherein c is the rolling friction coefficient.
N＝N(δ) (1)
f＝cN (2)
3 shock absorber axial force model
Presence of air spring force f in shock absorberaAnd a friction force ffAnd a damping force fdAre respectively S,Where S is the amount of compression of the shock absorber and the shock absorber axial force F is calculated as equation (3).
F＝fa+ff+fd(3)
fa＝fa(S)(4)
Wherein the air spring force faPositive and there is also a large spring force when the shock absorber compression S is zero, cfIs the damper coefficient of friction.
Frictional force ffDamping force fdImpeding damper motion, damper linear velocityGreater than zero ff and fdAt a positive value, the linear velocity of the damperLess than zero ff and fdTaking a negative value.
4 wheel and tire equations of motion.
The wheel and the tire are arranged on the wheel shaft and can be seen as a whole, and the motion equation is shown as the formula (7).
Wherein T is the force of the wheel axle to the wheel and the tire, and the direction is downward; n is the tire force, the direction is upward; m isWheelMass of wheels and tires; h is the altitude of the axle. From the formula:
equation of motion for 5 axles and rockers
The rocker arm landing gear is schematically shown in fig. 2. Wherein the AB section is a cantilever beam and is fixedly connected with the aircraft body. The CE section is fixedly connected to the middle of the AD section, the CE section and the AD section are combined to form a rocker arm, the rocker arm is hinged to the cantilever beam at the point A, and the D is a wheel shaft. The BC section is a shock absorber and is hinged with the cantilever beam at the B section and is hinged with the rocker arm at the C section. The rocker arm is rotatably connected with the wheel shaft at the end D, the rocker arm is hinged with the shock absorber at the point C, and when the shock absorber is compressed, the point C moves to the point C1Position, point D moved to D1Location. The dotted lines in the figure are auxiliary lines for describing the geometrical relationship of the components. The line through point a, which is perpendicular to the axis of the aircraft fuselage, intersects the horizontal line at point H. A line passing through the point A and vertical to the horizontal line intersects with the horizontal line at a point H. The line of the wheel passing shaft vertical to the upper horizontal line intersects with the upper horizontal line at J1And (4) point.
Equation of motion for axles and rockers as in formula (9)
Namely:
wherein JRocker armIs the moment of inertia of the rocker arm ACD; ω is the absolute angular velocity of the rocker arm about axis A, defined herein as positive when counterclockwise in FIG. 2; t is the reaction force of the wheel shaft from the wheel and the tire; f is the rolling friction force of the tire; f is the damper axial force.Is the aircraft pitch angle.
7 landing gear correlation geometry
After the shock absorber is compressed, the coordinates of the wheel axle in the aircraft coordinate system (the origin of the aircraft coordinate system is at the head of the aircraft, and the three axes x, y and z point to the rear, upper and left directions of the aircraft respectively) are changed, so that the tire compression amount is influenced. Taking the main landing frame as an example, a related geometric relation calculation formula is given. The front landing frame is similar to the main landing frame, the geometrical relationship is relatively simple, and a calculation formula of the geometrical relationship of the front landing frame is not given in the text.
(1) Coordinate calculation of rocker swing angle and wheel axle in aircraft coordinate system
As can be seen from fig. 2, the calculation methods of the swing angle of the rocker arm, the coordinates of the wheel axle in the coordinate system of the aircraft are shown in equations (11) to (17).
Δ＝∠BAC-∠BAC1(12)
∠HAD1＝∠HAD+Δ (14)
XD＝XA+lADsin∠HAD1(16)
YD＝YA-lADcos∠HAD1(17)
Wherein Delta is swing angle of rocker arm, XD、YDIs the coordinates of the axle in the aircraft coordinate system; xA、YAIs the coordinate of axis a in the aircraft coordinate system;for aircraft pitch angle,/ADIs the length of the line segment AD.
(2) Wheel axle height, tire compression calculation
The geometrical relationship of the main landing frame after the pitching and rolling of the aircraft is schematically shown in figure 3. As shown in FIG. 3, G is the aircraft center of mass position and the initial position of the midpoint of the line connecting the two main landing gear axes is O1The pitch back position is O2The position after rolling is O3。GLIs the midpoint position of the left main wheel shaft, GRIs the position of the middle point of the right main wheel shaft. The dashed lines in fig. 3 are auxiliary lines for describing the geometric relationship. P1、P2、P3、P4、P5For each foot of the auxiliary line, each line segment is represented by a letter of origin and end, and the length of each line segment is represented by l, is a calculated intermediate quantity, e.g.Represents a line segment O1P5Length of (d).
The invention adopts a coordinate transformation method and directly provides calculation formulas of parameters such as wheel axle altitude, tire compression amount and the like from a space geometric relation.
δ＝max{0,hland-(hL-rcosφ)} (25)
wherein Is the pitch angle of the aircraft; phi is the aircraft roll angle; xG、YGIs the coordinate of the aircraft centroid in the aircraft coordinate system; h isvIs the altitude of the aircraft centroid, and h is the tire axis altitude; h islandIs landing site altitude; r is the tire radius; l0The distance between the left and right tire axles (uncompressed state); delta is the amount of tire compression
8 landing frame coupling compression quantity solving method
Aiming at solving the problem of landing frame shock absorber/tire coupling compression, a differential equation of motion of each component of a landing frame is converted into a nonlinear algebraic equation taking shock absorber compression increment as an independent variable, criterion conditions are given, the shock absorber compression motion trend is judged, the algebraic equation is solved by a numerical method under different conditions, and finally, the shock absorber compression and the tire compression which meet the landing frame component motion equation and the geometric coupling relationship are solved, so that the tire stress of the whole aircraft is solved, and the simulation analysis of the aircraft in the grounding process is realized.
8.1 differential equation to nonlinear algebraic equation
Algebraic equation of main landing gear
The term is derived from equation (10):
substituting equations (2) and (8) into the above equation yields the algebraic equation for the primary landing gear motion:
8.2 independent variable selection of nonlinear algebraic equation and method for solving each quantity in independent variable selection
In the k-th step of the simulation, the increment of the compression amount of the shock absorber is assumed to be Δ S*(Note: the corner mark in this section)*Representing the temporary quantities used in solving the nonlinear algebraic equations), the parameters in equation (27) are calculated as follows:
1) compression amount S of the shock absorber:
S＝Sk-1+ΔS (29)
2) linear velocity of damper
Step is simulation step length which is the same as the six-degree-of-freedom simulation step length of the aircraft.
3) Calculating the axial force f of the shock absorber according to the formulas (4), (5) and (6)a、ff、fdAnd f can be determined according to the sign of Delta Sf and fdThe sign of (a).
4) From the geometrical relationships, the coordinates Xd, Yd of the wheel axle in the coordinate system of the aircraft can be calculated from (11), (12), (13) (14), (15), (17).
5) Calculating the altitude h of the wheel shaft according to the formula (18-24), and calculating the second derivative of the wheel shaft by using a difference method
In the geometric relationship, the altitude h of the aircraft centroidVAircraft pitch angleThe aircraft roll angle phi comes from the six-degree-of-freedom motion equation of the aircraft and adopts the value of the k step.
6) Calculate the angle ∠ HAD of the rocker arm according to equation (15)1And calculating the second derivative thereof by using a difference method
ω＝[(∠QAD1)-(∠QAD1)k-1]/step (33)
7) The tire compression amount δ is calculated from equation (25).
8) The tire force N and the rolling friction force f are calculated from the equations (1) and (2).
It can be seen that given the increase in shock absorber compression Δ S, each of the quantities in equation (27) can be solved, and thus this equation can be considered as a one-dimensional nonlinear equation with the shock absorber compression increase Δ S as an argument.
f(ΔS)＝0 (35)
Damper motion trend determination
Equation (35) includes the damper friction force ffThe relationship between the frictional force of the shock absorber and the increment of the compression amount thereof is schematically shown in FIG. 4 according to equation (5).
As can be seen from equation (5) or fig. 4, the friction force jumps when Δ S is equal to 0. Therefore, a jump occurs at the left end of the equation (35) when Δ S is equal to 0, which adversely affects the convergence of the numerical solution of the algebraic equation. In order to ensure that the equation (35) is successfully solved in an iterative manner, the motion trend of the shock absorber is judged firstly, and then the solution is carried out under three conditions.
In the k-th simulation, the respective forces and parameters are calculated first assuming that the increment Δ S of the shock absorber compression amount is 0, that is, the shock absorber compression amount is temporarily kept constant from the value in the k-1 th step. In contrast, although the amount of compression of the damper remains constant, the damper friction is calculated here as follows:
ff＝|cffa|≠0 (36)
equation (36) is used only for judging the damper movement tendency.
When in use
When the damping force is applied, the compression amount of the damper tends to increase, and the damping force is increased at delta S epsilon (0, S)max-Sk-1]Solving an equation (35) for the interval;
when in use
At this time, the shock absorber compression amount tends to decrease at Δ Sec [ -Sk-10) interval solving equation (35);
if the two conditions are not satisfied, the compression amount of the shock absorber is kept unchanged at the value of the k-1 step, and the equation is not solved, namely, the delta S is equal to 0.
Solution of unary nonlinear equation
The unitary equation (35) can be solved using a secant method:
limiting the value range of the independent variable in the iterative process when the value is delta Sj+1And when the range exceeds the limited range, correction is needed, and an iteration initial value is reasonably selected.
(1) When at Δ S ∈ (0, S)max-Sk-1]When the interval is solved, the iteration initial value is positive, and the magnitude is 0.01 mm; if Δ S is given by the formula (37)j+1<0, then corrected using the following equation:
ΔSj+1＝ΔSj/2(38)
if is represented by formula (3)7) Given as Δ Sj+1>Smax-Sk-1Then, the correction is made using the following equation:
(2) when at Δ S ∈ [ -Sk-10) during interval solution, the iteration initial value is negative, and the magnitude is 0.01 mm;
if Δ S is given by the formula (37)j+1>0, then the correction needs to be made using the following equation:
ΔSj+1＝-ΔSj/2 (40)
if Δ S is given by the formula (37)j+1<-Sk-1Then, the correction needs to be made using the following formula:
when in useThe iteration is stopped, epsilon is a tolerance, and a smaller positive number is taken. The invention provides a variable capacitance difference secant method solving method which comprises the following steps:
j∈[1,20]:ε＝0.01
j∈(21,40]:ε＝0.1
j∈(41,60]:ε＝1.0 (42)
j∈(61,80]:ε＝10
j∈(81,100]:ε＝100
j is the current iteration number.
f(ΔSj)<Stopping iteration when epsilon and solving the equation into delta Sk＝ΔSjAfter the solution is successful
Sk＝Sk-1+ΔSk(43)
Obtaining the actual compression quantity S of the shock absorberkThen, force and parameter need to be recalculated to be the true value of the simulation k step, which mainly comprises fa,k、ff,k、fd,k、Nk、fk、δk、Xdk,Ydk,Zdk、And solving the tire compression amount to obtain the tire stress.
Typical working condition simulation of aircraft touchdown process simulation
In the process of grounding of the landing frame of the aircraft, the aircraft is regarded as a whole, and the tire force N is taken askAnd rolling friction force fkAnd the force and moment to the mass center of the aircraft are added into the six-degree-of-freedom motion equation of the aircraft, so that the six-degree-of-freedom motion equation of the aircraft can be solved, and the simulation analysis of the touchdown process of the landing frame system is realized.
By adopting the method provided by the text, the typical working condition is selected, the simulation analysis is carried out on the grounding process of the aircraft, and the simulation step length is 1 ms. The simulation results are shown in fig. 5 to 7.
As can be seen from fig. 5 to 7: the tire is sprung up once and makes a second contact with the ground. Both the shock absorber compression and the tire compression undergo a process from zero to maximum rebound and settling. The angular acceleration of the rocker arm and the vertical acceleration of the wheel axle have large instantaneous values, so that the angular acceleration and the vertical acceleration have certain influence on the compression motion of the landing gear and cannot be ignored during accurate modeling.
Monte Carlo simulation of touchdown procedure
Monte Carlo simulation of six-degree-of-freedom motion and landing frame compression process in the ground contact process of the aircraft can be realized based on the model and the method. The simulation results are shown in fig. 8 to 9.
According to the Monte Carlo simulation result, comprehensive evaluation or scheme optimization design can be carried out on the ground contact performance of the aircraft.
The above-described embodiments are merely preferred embodiments of the present invention, and general changes and substitutions by those skilled in the art within the technical scope of the present invention are included in the protection scope of the present invention.
Claims (10)
1. A method for analyzing and solving coupling stress of an aircraft landing run-off section is characterized by comprising the following steps:
(1) building a tire force model;
(2) establishing a shock absorber axial force model;
(3) the airplane wheel and the tire are arranged on the wheel shaft and used as a whole to establish an equation of motion of the airplane wheel and the tire;
(4) replacing the rocker arm landing gear with a geometric relationship structure;
(5) taking the wheel axle and the rocker arm as a whole, and establishing a motion equation of the wheel axle and the rocker arm according to the geometric relationship structure in the step (4);
(6) calculating the swing angle of the rocker arm and the coordinates of the wheel axle in the coordinate system of the aircraft according to the geometric relation structure in the step (4); calculating the height of an axle and the compression amount of a tire according to the geometric relationship of the main landing frame after the aircraft pitches and rolls;
(7) obtaining a main landing frame algebraic equation according to the tire force model in the step (1), the shock absorber axial force model in the step (2), the wheel and tire motion equation in the step (3) and the wheel axle and rocker arm motion equation in the step (5), wherein the main landing frame algebraic equation is regarded as a main landing frame unary nonlinear equation, and the increment delta S of the shock absorber compression is an unknown number in the main landing frame unary nonlinear equation;
(8) giving out a shock absorber motion trend judgment condition, and judging a solving interval of the shock absorber compression increment delta S in the primary landing frame unary nonlinear equation;
(9) solving a primary nonlinear equation of the main landing frame by adopting a variable capacitance difference secant method to obtain the actual compression amount of the shock absorber, and obtaining the tire stress after obtaining the tire compression amount according to the actual compression amount of the shock absorber;
(10) and adding the tire stress and the moment into a six-degree-of-freedom equation of the aircraft to simulate.
2. The aircraft landing run segment coupling stress analysis and solution method of claim 1, wherein: in step (1), the tire force model is obtained by the following formula:
N＝N(δ)；
f＝c N；
wherein N is the tire force, with the vertical tire compression face up, as a function of the tire compression δ; f is the rolling friction force of the tire; and c is the rolling friction coefficient.
3. The aircraft landing run segment coupling stress analysis and solution method of claim 1, wherein: in step (2), the damper axial force model is obtained by the following formula:
F＝fa+ff+fd；
wherein ,faFor the force of the air spring present in the shock absorber, ffIs the friction force present in the shock absorber, fdIs the damping force present in the shock absorber and F is the shock absorber axial force.
4. The aircraft landing run segment coupling stress analysis and solution method of claim 1, wherein: in step (3), the wheel and tire equations of motion are obtained by the following equations:
wherein T is the force of the wheel axle to the wheel and the tire; n is tire force; m isWheelMass of wheels and tires; h is the altitude of the axle.
5. The aircraft landing run segment coupling stress analysis and solution method of claim 1, wherein: in the step (4), the section AB is a cantilever beam and is fixedly connected with an aircraft body; the CE section is connected to the middle part of the AD section, the CE section and the AD section are combined into a rocker arm, the rocker arm is hinged with the cantilever beam at the point A, and the D is a wheel shaft; the BC section is a shock absorber, is hinged with the cantilever beam at the B and is hinged with the rocker arm at the C; one end of the rocker arm is rotatably connected with the wheel shaft, and the middle part of the rocker arm is hinged with the shock absorber; when the shock absorber compresses, point C moves to point C1Position, point D moved to D1Location.
6. The aircraft landing run segment coupling stress analysis and solution method of claim 5, wherein: in step (5), the motion equation of the wheel shaft and the rocker arm is obtained by the following formula:
wherein ,JRocker armIs the moment of inertia of the rocker arm ACD; omega is rocker armAbsolute angular velocity of rotation about axis a; t is the reaction force of the wheel shaft from the wheel and the tire; f is the rolling friction force of the tire; f is the damper axial force.For the pitch angle of the aircraft,is AD1Length of the segment, /)ABLength of AB section, ∠ QAD1Is QA segment and AD1Angle of section ∠ ABC1Is AB segment and BC1The angle of the segments.
7. The aircraft landing run segment coupling stress analysis and solution method of claim 5, wherein: in the step (6), the rocker swing angle and the coordinates of the wheel axle in the coordinate system of the aircraft are obtained through the following formulas:
Δ＝∠BAC-∠BAC1；
∠HAD1＝∠HAD+Δ；
XD＝XA+lADsin∠HAD1；
YD＝YA-lADcos∠HAD1；
wherein, Delta is swing angle of the rocker arm, XD、YDIs the coordinates of the axle in the aircraft coordinate system; xA、YAIs the coordinate of axis a in the aircraft coordinate system;for aircraft pitch angle,/ADIs the length of the AD segment.
The axle height and tire compression are obtained by the following equations:
δ＝max{0,hland-(hL-rcosφ)}；
wherein ,is the pitch angle of the aircraft; phi is the aircraft roll angle; xG、YGIs the coordinate of the aircraft centroid in the aircraft coordinate system; h isvIs the altitude of the aircraft centroid, and h is the tire axis altitude; h islandIs landing site altitude; r is the tire radius; l0In an uncompressed stateDistance between left and right tire axles; δ is the tire compression amount.
8. The aircraft landing run segment coupling stress analysis and solution method of claim 7, wherein: in step (7), the main landing leg algebraic equation is:
the primary landing pad unary nonlinear equation is: f (Δ S) ═ 0.
9. The aircraft landing run segment coupling stress analysis and solution method of claim 7, wherein: in step (8), in the k-th simulation, the increment Δ S of the shock absorber compression amount is preset to be 0, that is, the shock absorber compression amount is maintained to be constant with the value of the k-1-th simulation, and when the shock absorber compression amount is not changed with the value of the k-1-th simulationWhen the damping force is applied, the compression amount of the damper tends to increase, and the damping force is increased at delta S epsilon (0, S)max-Sk-1]Solving a primary landing frame one-element nonlinear equation in an interval; wherein f isf＝|cffa|≠0；
When in useAt this time, the shock absorber compression amount tends to decrease at Δ Sec [ -Sk-10) solving a primary landing frame one-element nonlinear equation in an interval; wherein f isf＝|cffa|≠0；
If the two conditions are not satisfied, the compression amount of the shock absorber is kept unchanged at the value of the k-1 step, and the equation is not solved, namely, the delta S is equal to 0.
10. The aircraft landing run segment coupling stress analysis and solution method of claim 7, wherein: in step (9), the following formula is solved for the primary landing frame unary nonlinear equation by adopting a secant method:
the number of iteration steps; delta SjFor solving the equation, the value of the independent variable in the j step is Delta Sj+1For solving the equation, the independent variable value of the (j + 1) th step, Delta Sj-1And f is a function calculation formula on the left side of the primary landing frame unary nonlinear equation.
The calculation method of the tolerance epsilon is as follows:
j∈[1,20]:ε＝0.01
j∈(21,40]:ε＝0.1
j∈(41,60]:ε＝1.0
j∈(61,80]:ε＝10
j∈(81,100]:ε＝100
j is the current iteration number;
when f (Δ S)j)<Stopping iteration when epsilon and solving the equation into delta Sk＝ΔSjAnd after the solution is successful, the actual compression amount of the shock absorber is as follows:
Sk＝Sk-1+ΔSk
obtaining the actual compression quantity S of the shock absorberkThen, according to the actual compression quantity S of the shock absorberkAnd obtaining the tire stress after obtaining the tire compression.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201811280726.XA CN109460600B (en) | 2018-10-30 | 2018-10-30 | Coupling stress analysis and solving method for landing running section of aircraft |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201811280726.XA CN109460600B (en) | 2018-10-30 | 2018-10-30 | Coupling stress analysis and solving method for landing running section of aircraft |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN109460600A true CN109460600A (en) | 2019-03-12 |
| CN109460600B CN109460600B (en) | 2023-06-09 |
Family
ID=65608939
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201811280726.XA Active CN109460600B (en) | 2018-10-30 | 2018-10-30 | Coupling stress analysis and solving method for landing running section of aircraft |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN109460600B (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112173158A (en) * | 2020-09-25 | 2021-01-05 | 中国直升机设计研究所 | Landing/ship-borne load calculation method for wheeled landing gear helicopter |
| CN115019563A (en) * | 2022-08-04 | 2022-09-06 | 西安羚控电子科技有限公司 | Unmanned aerial vehicle landing route planning method and planning system |
| CN117010497A (en) * | 2023-05-26 | 2023-11-07 | 中国民用航空飞行学院 | Navigation aircraft landing gear shock absorber navigation field knowledge modeling method |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102015452A (en) * | 2008-05-09 | 2011-04-13 | 扬·宾内贝泽尔 | Ground-bound device for take off, landing and taxiing of aircrafts |
| US20150151835A1 (en) * | 2013-12-04 | 2015-06-04 | Isaiah W. Cox | Load Transfer in a Powered Aircraft Drive Wheel |
| CN107506533A (en) * | 2017-08-03 | 2017-12-22 | 中国航空工业集团公司西安飞机设计研究所 | A kind of quasistatic undercarriage kinetic model construction method |
| CN107798153A (en) * | 2016-08-31 | 2018-03-13 | 中仿智能科技（上海）股份有限公司 | Determination method of the undercarriage to aircraft active force during being risen and fallen on sliding jump deck |
| CN108388733A (en) * | 2018-02-27 | 2018-08-10 | 清华大学 | Four-wheel layout undercarriage modeling method based on frictional ground force and device |
-
2018
- 2018-10-30 CN CN201811280726.XA patent/CN109460600B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102015452A (en) * | 2008-05-09 | 2011-04-13 | 扬·宾内贝泽尔 | Ground-bound device for take off, landing and taxiing of aircrafts |
| US20150151835A1 (en) * | 2013-12-04 | 2015-06-04 | Isaiah W. Cox | Load Transfer in a Powered Aircraft Drive Wheel |
| CN107798153A (en) * | 2016-08-31 | 2018-03-13 | 中仿智能科技（上海）股份有限公司 | Determination method of the undercarriage to aircraft active force during being risen and fallen on sliding jump deck |
| CN107506533A (en) * | 2017-08-03 | 2017-12-22 | 中国航空工业集团公司西安飞机设计研究所 | A kind of quasistatic undercarriage kinetic model construction method |
| CN108388733A (en) * | 2018-02-27 | 2018-08-10 | 清华大学 | Four-wheel layout undercarriage modeling method based on frictional ground force and device |
Non-Patent Citations (1)
| Title |
|---|
| 刘刚，郑宏涛，李洋: "水平着陆飞行器着陆架***耦合压缩触地过程仿真分析", 《宇航总体技术》 * |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112173158A (en) * | 2020-09-25 | 2021-01-05 | 中国直升机设计研究所 | Landing/ship-borne load calculation method for wheeled landing gear helicopter |
| CN115019563A (en) * | 2022-08-04 | 2022-09-06 | 西安羚控电子科技有限公司 | Unmanned aerial vehicle landing route planning method and planning system |
| CN117010497A (en) * | 2023-05-26 | 2023-11-07 | 中国民用航空飞行学院 | Navigation aircraft landing gear shock absorber navigation field knowledge modeling method |
| CN117010497B (en) * | 2023-05-26 | 2024-03-26 | 中国民用航空飞行学院 | Navigation aircraft landing gear shock absorber navigation field knowledge modeling method |
Also Published As
| Publication number | Publication date |
|---|---|
| CN109460600B (en) | 2023-06-09 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN109460600A (en) | A kind of aircraft lands are sliding to run section coupling force analysis and method for solving | |
| CA3112372C (en) | Vehicle-mounted motion simulation platform based on active suspension, and control method thereof | |
| CN107506533B (en) | Quasi-static landing gear dynamic model construction method | |
| CN110405762B (en) | Biped robot attitude control method based on spatial second-order inverted pendulum model | |
| CN111290272B (en) | Attitude stationarity adjusting method based on multi-legged robot | |
| CN101826125A (en) | Method for designing McPherson suspension | |
| CN116661293B (en) | Movement control method and system for wheel-leg type vehicle jumping obstacle | |
| CN108681324A (en) | Mobile robot trace tracking and controlling method based on overall Vision | |
| CN108388733B (en) | Ground friction force-based four-wheel layout undercarriage modeling method and device | |
| Leo et al. | Drop test simulation for an aircraft landing gear via multi-body approach | |
| CN116244836B (en) | ADAMS-based carrier rocket take-off drift safety gap design method | |
| CN111985054A (en) | Method and system for checking slip deflection angle of driving shaft | |
| CN110108162B (en) | Remote automatic throwing drop point correction guidance control method for motion platform | |
| KR101749983B1 (en) | Method for calculating landing gear deflection of air vehicle using position information | |
| CN107967382B (en) | Method for evaluating coupling influence degree of air-breathing aircraft | |
| Azman et al. | Influence of anti-dive and anti-squat geometry in combined vehicle bounce and pitch dynamics | |
| CN103970588A (en) | Mecanum wheel roller outline compensating and amendment modeling and simulating method | |
| CN107798153B (en) | Method for determining acting force of landing gear on airplane in landing and landing processes of ski-jump deck | |
| CN108108527B (en) | Theoretical calculation method for vertical stiffness ratio of aircraft landing gear | |
| Jiehan et al. | The Analysis and Optimization on the Front Suspension System of a Formula Racing Car Based on ADAMS | |
| CN116167249B (en) | Dynamic load calculation method, device and storage medium for asymmetric landing of airplane | |
| Spieck | Simulation of aircraft landing impact under consideration of aerodynamic forces on the flexible structure | |
| CN110160737A (en) | The accurate acquisition methods of elastic pneumatic data based on engineering panel method | |
| Öström et al. | Modeling Aircraft Ground Behavior into a Flight Simulation | |
| CN116738739A (en) | Mechanical analysis and constraint method for jump gesture of two-wheeled foot robot |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |