CN113962014B - Method for forecasting interstage separation state of heat shield and analyzing safety - Google Patents

Method for forecasting interstage separation state of heat shield and analyzing safety Download PDF

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CN113962014B
CN113962014B CN202110919226.1A CN202110919226A CN113962014B CN 113962014 B CN113962014 B CN 113962014B CN 202110919226 A CN202110919226 A CN 202110919226A CN 113962014 B CN113962014 B CN 113962014B
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heat shield
cabin
representing
separation
acceleration
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CN113962014A (en
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饶炜
董捷
王闯
崔祜涛
田阳
陈正
缪远明
谭志云
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Harbin Institute of Technology
Beijing Institute of Spacecraft System Engineering
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Beijing Institute of Spacecraft System Engineering
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Abstract

A method for forecasting an interstage separation state of a heat shield and analyzing safety relates to the technical field of aerospace, and aims to solve the problem of low safety analysis accuracy rate in a two-stage separation process in the prior art, the relative distance between the heat shield and an entering cabin can be judged through a ray tracing method, and then the safety problem of heat shield separation can be analyzed, and the difference between the separation speed of the heat shield when the heat shield is separated from a constraint mechanism and the separation speed of the heat shield when the heat shield enters the cabin and the actual state calculated by the forecasting method is not more than 0.1 m/s. The method and the device can improve the accuracy of safety analysis in the two-stage separation process.

Description

Method for forecasting interstage separation state of heat shield and analyzing safety
Technical Field
The invention relates to the technical field of aerospace, in particular to a method for forecasting an interstage separation state of a heat shield and analyzing safety.
Background
For safe landing on the Mars surface, all Mars landing tasks employ similar approach, descent, and landing (EDL) methods. These tasks all use an access capsule with a heat shield to protect the lander during high aerodynamic heating of atmospheric access. After the supersonic speed of the access capsule is reached, a parachute system is deployed to slow the landing gear. Once the lander has slowed sufficiently to subsonic speeds, the heat shields are discarded to ensure radar operation.
Before the heat shield is separated and triggered, the separating mechanism is in a locking state, the heat shield and the entering cabin are locked together, after separation and triggering, the heat shield is separated from the entering cabin under the restraint of the separation restraining mechanism, and the restraining mechanism generates restraining force and restraining torque on the two bodies, so that the two bodies can only move along the separating direction until the heat shield is separated from the restraining mechanism, and the two bodies are completely separated and move independently. For the two-stage separation process, lagrange mechanics or ADAMS software is generally adopted to predict the separation state of the heat shield, and besides, a cfe (constraint Force equalization) method is also adopted to calculate the separation process of the interstage of the aircraft. However, these methods need to consider various translational and rotational constraints, and the calculation process is relatively complex and has low accuracy.
Disclosure of Invention
The purpose of the invention is: aiming at the problem of low safety analysis accuracy rate in the two-stage separation process in the prior art, a method for forecasting the interstage separation state of the heat shield and analyzing the safety is provided.
The technical scheme adopted by the invention to solve the technical problems is as follows:
a method for forecasting an interstage separation state of a heat shield and analyzing safety comprises the following steps:
the method comprises the following steps: acquiring a visual acceleration difference between an access cabin and a heat shield;
step two: acquiring separation actuating force and aerodynamic force data of the heat shield and specific force data of an accelerometer entering the cabin, and acquiring acceleration difference of the heat shield and the accelerometer entering the cabin in a separation direction according to the separation actuating force and the aerodynamic force data of the heat shield and the specific force data of the accelerometer entering the cabin;
step three: obtaining a separation state equation according to the difference of the apparent acceleration of the access cabin and the heat shield and the difference of the acceleration of the heat shield and the access cabin in the separation direction, and obtaining the movement between the heat shield and the access cabin along the separation direction according to the separation state equation;
step four: acquiring the motion state of the access cabin, and performing state prediction on the motion state of the heat shield under the constraint of the separation mechanism according to the motion between the heat shield and the access cabin along the separation direction and the motion state of the access cabin;
step five: the speed of the heat shield when the heat shield leaves the separating mechanism is obtained according to the state forecast, and the motion state of the heat shield after separation is forecasted according to the speed of the heat shield when the heat shield leaves the separating mechanism;
step six: according to the motion state of the separated heat shield and the motion state of the heat shield entering the cabin, the apparent motion of the heat shield under a cabin entering body coordinate system is obtained;
step seven: firstly, simplifying the lower outline of an access cabin into a conical shape, simplifying the shape of a heat shield into a regular pyramid, then obtaining a ray distance according to the visual motion of the heat shield under an access cabin body coordinate system and by adopting a ray tracing method, and selecting the shortest distance between the access cabin and the heat shield according to the ray distance so as to obtain a shortest distance curve;
step eight: and judging the collision safety of the heat shield and the entering cabin according to the shortest distance curve.
Further, the apparent acceleration difference is expressed as:
arel＝(ah-av)x-(ahc-avc)x-(ahe-ave)x-(ahr-avr)x
(ahc-avc)x＝0
(ahe-ave)x＝0
Figure RE-GDA0003426184920000021
wherein x isrelIndicating the separation distance, a, between the access compartment and the heat shieldhRepresents the absolute acceleration of the heat shield, ahcIndicating the Criotris acceleration of the heat shield, aheRepresenting linear acceleration due to angular acceleration to which the heat shield is subjected, ahrDenotes the centrifugal acceleration of the heat shield, avRepresenting the absolute acceleration of the entering cabin, avcIndicating the Kresolis acceleration into the cabin, aveRepresenting linear acceleration due to angular acceleration to which the access compartment is subjected, avrRepresents the centrifugal acceleration of the entry into the chamber, ()xRepresenting the x-axis component, ωyIndicating yaw rate, ω, of entering the cabinzRepresenting the pitch rate of the entry into the cabin, arelIndicating the difference in the apparent acceleration of the access compartment and the heat shield.
Further, the acceleration difference is expressed as:
Figure RE-GDA0003426184920000022
wherein A ishIndicating the direction of separation of the heat shield, FsRepresents separation power, mhRepresenting the mass of the heat shield and f the specific force data into the cabin accelerometer.
Further, the separation equation of state is expressed as:
Figure RE-GDA0003426184920000023
Figure RE-GDA0003426184920000031
Figure RE-GDA0003426184920000032
wherein v isrelIndicating the speed of separation of the access compartment and the heat shield, t0The initial moment of separation of the access cabin from the heat shield is shown, t is the current moment, tau is an integral variable, e is an exponential function, and D (tau) and W (t-tau) are respectively shown as two functions.
Further, the motion state of the heat shield under the constraint of the separation mechanism is represented as follows:
Figure RE-GDA0003426184920000033
wherein, VhbRepresenting apparent velocity, v, of the heat shield in a body coordinate systemeRepresenting the linear velocity, omega, resulting from rotation of the body coordinate systemxRepresenting the roll rate, r, of the entering cabinhzRepresenting the projection of the position of the heat shield on the Z-axis of the body coordinate system, rhyRepresenting the projection of the position of the heat shield on the Y-axis of the body coordinate system, rhxRepresenting the projection of the position of the heat shield on the X-axis of the body coordinate system, VhThe absolute velocity of the heat shield is indicated.
Further, the motion of the heat shield after separation is obtained according to rigid body kinetic equations which comprise a mass center translation kinetic equation, a mass center translation kinematic equation, a rotation kinetic equation around the mass center and a rotation kinematic equation around the mass center;
the centroid translational kinetic equation is expressed as:
Figure RE-GDA0003426184920000034
wherein (C)bRepresenting the projection in a body coordinate system, ω representing the angular velocity of the access compartment, ωmRepresenting the angular velocity of rotation of the Mars coordinate system relative to the Mars inertial system, V representing the velocity vector of the lander relative to the Mars, r tableThe position vector of the landing gear is shown, m represents the mass of the landing gear, P represents the vector sum of the thrust force and other external forces applied to the landing gear, R represents the aerodynamic force applied to the landing gear, g represents the gravitational acceleration vector,
Figure RE-GDA0003426184920000035
a derivative representing the projection of the velocity vector V in the body coordinate system;
the centroid translational kinematic equation is expressed as:
Figure RE-GDA0003426184920000041
Figure RE-GDA0003426184920000042
Figure RE-GDA0003426184920000043
wherein, Vu、VE、VNRespectively representing the velocity components of the sky, east and north, r representing the fire center distance, phi representing the fire center latitude,
Figure RE-GDA0003426184920000044
the derivative of the distance between the two fire centers is represented,
Figure RE-GDA0003426184920000045
the derivative of the longitude of the fire center is represented,
Figure RE-GDA0003426184920000046
a derivative representing the latitude of the fire center;
the equation of the dynamics of rotation around the center of mass is expressed as:
Figure RE-GDA0003426184920000047
wherein，(I)bThe moment of the lander is expressed by M which is an inertia tensor under a body coordinate system;
the rotational kinematics equation around the center of mass is expressed as:
Figure RE-GDA0003426184920000048
Figure RE-GDA0003426184920000049
Figure RE-GDA00034261849200000410
wherein, ω isbux、ωbuy、ωbuzRepresenting the three-axis components of relative angular velocity, psi is the yaw angle, gamma is the roll angle,
Figure RE-GDA00034261849200000411
the derivative of the pitch angle is represented,
Figure RE-GDA00034261849200000412
the derivative of the yaw angle is represented,
Figure RE-GDA00034261849200000413
the derivative of the roll angle is represented.
Further, the apparent motion of the heat shield in the cabin body coordinate system is represented as follows:
Figure RE-GDA00034261849200000414
Figure RE-GDA00034261849200000415
Figure RE-GDA00034261849200000416
wherein, CamA transformation matrix (R) representing the cabin coordinate system relative to the local coordinate systemh)m、(Ra)mRespectively showing the position of the heat shield and the access cabin in the local coordinate system, phihIndicating the fire center latitude, λ, of the shieldhThe longitude of the fire center, r, of the heat shieldhIndicating the core distance of the heat shieldaIndicating the latitude of the fire, λ, entering the cabinaIndicating the fire center longitude, r, of the entry into the cabinaIndicating the distance of the fire centers entering the cabin.
Further, the ray tracing method comprises the following specific steps:
dense rays are emitted from the center of mass of the entering cabin, one part of rays are not intersected with the heat shield, the other part of rays are intersected with the heat shield, the length of the rays intersected with the heat shield is calculated, the shortest distance between the entering cabin and the heat shield is obtained, namely the ray tracing is performed once, and then the ray tracing at equal time intervals is performed to obtain the shortest distance curve between the entering cabin and the heat shield.
The invention has the beneficial effects that:
the method can judge the relative distance between the heat shield and the compartment, and further can analyze the safety problem of heat shield separation, and the difference between the separation speed of the heat shield and the actual state of the compartment when the heat shield is separated from the restraint mechanism is not more than 0.1 m/s. The method and the device can improve the accuracy of safety analysis in the two-stage separation process.
Drawings
FIG. 1 is a schematic diagram illustrating a ray tracing method for determining relative distance;
FIG. 2 is a schematic view of the heat shield in relation to the access compartment in two different situations 1;
FIG. 3 is a schematic view of the relative distance of the heat shield from the access compartment in two different situations 2;
FIG. 4 is a block diagram of the present application as a whole;
FIG. 5 is a schematic view of the separation distance;
FIG. 6 is a schematic illustration of the separation speed;
FIG. 7 is a schematic view of the angular velocity of the heat shield;
FIG. 8 is a schematic view of the position of the heat shield;
FIG. 9 is a shape profile view of a heat shield;
fig. 10 is a schematic diagram of relative distances.
Detailed Description
It should be noted that, in the present invention, the embodiments disclosed in the present application may be combined with each other without conflict.
The first embodiment is as follows: specifically describing the present embodiment with reference to fig. 1 and 4, the method for forecasting the interstage separation state of the heat shield and analyzing the safety of the heat shield according to the present embodiment includes the following steps:
the method comprises the following steps: acquiring a visual acceleration difference between an access cabin and a heat shield;
step two: acquiring separation actuating force and aerodynamic force data of the heat shield and specific force data of an accelerometer entering the cabin, and acquiring acceleration difference of the heat shield and the accelerometer entering the cabin in a separation direction according to the separation actuating force and the aerodynamic force data of the heat shield and the specific force data of the accelerometer entering the cabin;
step three: obtaining a separation state equation according to the difference of the apparent acceleration of the access cabin and the heat shield and the difference of the acceleration of the heat shield and the access cabin in the separation direction, and obtaining the movement between the heat shield and the access cabin along the separation direction according to the separation state equation;
step four: acquiring the motion state of the access cabin, and performing state prediction on the motion state of the heat shield under the constraint of the separation mechanism according to the motion between the heat shield and the access cabin along the separation direction and the motion state of the access cabin;
step five: the speed of the heat shield when the heat shield leaves the separating mechanism is obtained according to the state forecast, and the motion state of the heat shield after separation is forecasted according to the speed of the heat shield when the heat shield leaves the separating mechanism;
step six: according to the motion state of the separated heat shield and the motion state of the heat shield entering the cabin, the apparent motion of the heat shield under a cabin entering body coordinate system is obtained;
step seven: firstly, simplifying the lower outline of an access cabin into a conical shape, simplifying the shape of a heat shield into a regular pyramid, then obtaining a ray distance according to the visual motion of the heat shield under an access cabin body coordinate system and by adopting a ray tracing method, and selecting the shortest distance between the access cabin and the heat shield according to the ray distance so as to obtain a shortest distance curve;
step eight: and judging the collision safety of the heat shield and the entering cabin according to the shortest distance curve.
The separation safety of the heat shield and the entering cabin can be judged according to the shortest distance curve, if the shortest distance curve changes monotonically and increases along with time, the separation process of the heat shield and the entering cabin is safe enough, if the shortest distance between the heat shield and the entering cabin becomes a negative value, the heat shield collides with the entering cabin, the separation process is unsafe, and even if the shortest distance does not become a negative value, if the curve has a descending trend and the wave trough is smaller than a threshold value, the separation process of the heat shield and the entering cabin is unsafe.
The second embodiment is as follows: this embodiment is a further description of the first embodiment, and the difference between this embodiment and the first embodiment is that the apparent acceleration difference is expressed as:
arel＝(ah-av)x-(ahc-avc)x-(ahe-ave)x-(ahr-avr)x
(ahc-avc)x＝0
(ahe-ave)x＝0
Figure RE-GDA0003426184920000061
wherein x isrelIndicating the separation distance, a, between the access compartment and the heat shieldhRepresents the absolute acceleration of the heat shield, ahcIndicates the Coriolis acceleration of the heat shield, aheRepresenting linear acceleration due to angular acceleration to which the heat shield is subjected, ahrDenotes the centrifugal acceleration of the heat shield, avIndicating entryAbsolute acceleration of the cabin, avcDenotes the Coriolis (Coriolis) acceleration of the entry into the cabin, aveRepresenting linear acceleration due to angular acceleration to which the access compartment is subjected, avrRepresents the centrifugal acceleration of the entry into the chamber, ()xRepresenting the x-axis component, ωyIndicating yaw rate, ω, of entering the cabinzRepresenting the pitch rate of the entry into the cabin, arelIndicating the difference in the apparent acceleration of the access compartment and the heat shield.
The third concrete implementation mode: this embodiment is a further description of the second embodiment, and is different from the second embodiment in that the acceleration difference is expressed as:
Figure RE-GDA0003426184920000071
wherein A ishIndicating the direction of separation of the heat shield, FsRepresents separation power, mhRepresenting the mass of the heat shield and f the specific force data into the cabin accelerometer.
The fourth concrete implementation mode: the present embodiment is a further description of a third specific embodiment, and the difference between the present embodiment and the third specific embodiment is that the separation state equation is expressed as:
Figure RE-GDA0003426184920000072
Figure RE-GDA0003426184920000073
Figure RE-GDA0003426184920000074
wherein v isrelIndicating the speed of separation of the access compartment and the heat shield, t0Denotes the initial moment of separation of the access compartment from the heat shield, t denotes the current moment, τ denotes the integral variable, e denotes the indexThe functions D (τ) and W (t- τ) represent two functions, respectively.
The fifth concrete implementation mode: the present embodiment is further described with respect to a fourth embodiment, and the difference between the present embodiment and the fourth embodiment is that the movement state of the heat shield under the constraint of the separation mechanism is represented as follows:
Figure RE-GDA0003426184920000075
wherein, VhbRepresenting apparent velocity, v, of the heat shield in a body coordinate systemeRepresenting the linear velocity, omega, resulting from rotation of the body coordinate systemxRepresenting the roll rate, r, of the entering cabinhzRepresenting the projection of the position of the heat shield on the Z-axis of the body coordinate system, rhyRepresenting the projection of the position of the heat shield on the Y-axis of the body coordinate system, rhxRepresenting the projection of the position of the heat shield on the X-axis of the body coordinate system, VhThe absolute velocity of the heat shield is indicated.
The sixth specific implementation mode: the fifth embodiment is a further description of the fifth embodiment, and the difference between the fifth embodiment and the fifth embodiment is that the motion of the heat shield after separation is obtained according to rigid body kinetic equations, wherein the rigid body kinetic equations comprise a centroid translational kinetic equation, a centroid translational kinematic equation, a centroid rotational kinetic equation and a centroid rotational kinematic equation;
the centroid translational kinetic equation is expressed as:
Figure RE-GDA0003426184920000081
wherein (C)bRepresenting the projection in a body coordinate system, ω representing the angular velocity of the access compartment, ωmRepresenting the angular velocity of rotation of the Mars coordinate system relative to the Mars inertial system, V representing the velocity vector of the lander relative to the Mars, R representing the position vector of the lander, m representing the mass of the landing rover, P representing the vector sum of the thrust force and other external forces to which the landing rover is subjected, R representing the gas to which the landing rover is subjectedPower, g represents the gravitational acceleration vector,
Figure RE-GDA0003426184920000082
a derivative representing the projection of the velocity vector V in the body coordinate system;
the centroid translational kinematic equation is expressed as:
Figure RE-GDA0003426184920000083
Figure RE-GDA0003426184920000084
Figure RE-GDA0003426184920000085
wherein Vu、VE、VNRespectively representing the velocity components of the sky, east and north, r representing the fire center distance, phi representing the fire center latitude,
Figure RE-GDA0003426184920000086
the derivative of the distance between the two fire centers is represented,
Figure RE-GDA0003426184920000087
the derivative of the longitude of the fire center is represented,
Figure RE-GDA0003426184920000088
a derivative representing the latitude of the fire center;
the equation of the dynamics of rotation around the center of mass is expressed as:
Figure RE-GDA0003426184920000089
wherein (I)bThe moment of the lander is expressed by M which is an inertia tensor under a body coordinate system;
the rotational kinematics equation around the center of mass is expressed as:
Figure RE-GDA0003426184920000091
Figure RE-GDA0003426184920000092
Figure RE-GDA0003426184920000093
wherein ω isbux、ωbuy、ωbuzRepresenting the three-axis components of relative angular velocity, psi is the yaw angle, gamma is the roll angle,
Figure RE-GDA0003426184920000094
the derivative of the pitch angle is represented,
Figure RE-GDA0003426184920000095
the derivative of the yaw angle is represented,
Figure RE-GDA0003426184920000096
the derivative of the roll angle is represented.
The seventh embodiment: the present embodiment is further described with respect to a sixth embodiment, and the difference between the present embodiment and the sixth embodiment is that the apparent motion of the heat shield in the cabin entry coordinate system is represented as:
Figure RE-GDA0003426184920000097
Figure RE-GDA0003426184920000098
Figure RE-GDA0003426184920000099
wherein C isamA transformation matrix (R) representing the cabin coordinate system relative to the local coordinate systemh)m、(Ra)mRespectively showing the position of the heat shield and the access cabin in the local coordinate system, phihIndicating the fire center latitude, λ, of the shieldhThe longitude of the fire center, r, of the heat shieldhIndicating the core distance of the heat shieldaIndicating the latitude of the fire, λ, entering the cabinaIndicating the fire center longitude, r, of the entry into the cabinaIndicating the distance of the fire centers entering the cabin.
The specific implementation mode is eight: the present embodiment is further described with reference to the seventh embodiment, and the difference between the present embodiment and the seventh embodiment is that the ray tracing method specifically includes the steps of:
dense rays are emitted from the center of mass of the entering cabin, one part of rays are not intersected with the heat shield, the other part of rays are intersected with the heat shield, the length of the rays intersected with the heat shield is calculated, the shortest distance between the entering cabin and the heat shield is obtained, namely the ray tracing is performed once, and then the ray tracing at equal time intervals is performed to obtain the shortest distance curve between the entering cabin and the heat shield.
The specific thought of the application is as follows:
1. the difference in the apparent acceleration of the two bodies is calculated, taking into account that the separation of the heat shield and the access compartment is carried out under the constraint of the separating mechanism. The heat shields and access compartments being constrained to move only in the separation direction during separation, i.e.
rrel＝rhb-rvb＝[xrel 0 0]T
In the formula rrelIs the separation displacement of the heat shield and the access cabin under a body coordinate system; r ishbIs the apparent motion of the heat shield in a body coordinate system, rvbThe visual motion of the entering cabin under a body coordinate system; x is the number ofrelIs the two-body separation distance.
The derivative of time is solved for both sides of the equation, and the apparent velocity difference of two bodies in a body coordinate system can be obtained.
Figure RE-GDA0003426184920000101
Apparent velocity in a moving coordinate system (system) according to the theory of rotation of the coordinate system
Figure RE-GDA0003426184920000102
Equal to the difference between the absolute velocity in the absolute coordinate system (ground coordinate system) and the linear velocity caused by the rotation of the moving coordinate system, i.e.
Figure RE-GDA0003426184920000103
In the formula (I), the compound is shown in the specification,
Figure RE-GDA0003426184920000104
absolute velocity of heat shield, veIs the linear velocity of the drag line caused by rotation, such that [ omega ]x ωy ωz]TFor the heat shield and angular velocity of the access hatch (the same for both bodies due to the constraint of the separation mechanism), [ rhx rhy rhz]TFor the projection of the position of the heat shield in the body coordinate system, there are
Figure RE-GDA0003426184920000105
Similarly, take [ rhx rhy rhz]TFor the projection of the position of the entry cabin in the body coordinate system, the apparent speed of the entry cabin is
Figure RE-GDA0003426184920000106
The apparent acceleration of the heat shield in the body coordinate system also needs to consider the influence caused by the rotation of the moving coordinate system
Figure RE-GDA0003426184920000107
In the formula, ahIs the absolute acceleration of the heat shield, ahcIs the Coriolis (Coriolis) acceleration, aheIs linear acceleration due to angular acceleration, ahrIs the centrifugal acceleration, the terms are respectively
Figure RE-GDA0003426184920000108
Figure RE-GDA0003426184920000109
Figure RE-GDA0003426184920000111
The expression of the absolute speed of the entering cabin is similar to the above expression
Figure RE-GDA0003426184920000112
In the formula, avIs the absolute acceleration of the entering cabin, avcIs the Coriolis (Coriolis) acceleration, aveIs linear acceleration due to angular acceleration, avrIs the centrifugal acceleration, the terms are respectively
Figure RE-GDA0003426184920000113
Figure RE-GDA0003426184920000114
Figure RE-GDA0003426184920000115
Then, according to the expression of the apparent velocities of the two bodies, the expression of the apparent acceleration difference of the two bodies can be obtained
Figure RE-GDA0003426184920000116
The difference in apparent acceleration in the separating direction is the difference in the x-axis component of each acceleration
arel＝(ah-av)x-(ahc-avc)x-(ahe-ave)x-(ahr-avr)x
Wherein each item is
(ahc-avc)x＝0
(ahe-ave)x＝0
Figure RE-GDA0003426184920000117
2. According to the specific force data of the accelerometer entering the cabin, calculating the acceleration difference of the heat shield and the acceleration difference of the heat shield entering the cabin in the separation direction, and obtaining the specific force data f through the accelerometer entering the cabin, wherein the acceleration entering the cabin is
av＝f+G
Wherein G is gravitational acceleration.
The heat shield has a separation direction acceleration of
Figure RE-GDA0003426184920000121
In the formula, AhFor protection against separating-direction aerodynamic forces to which the heat shield is subjected, FsFor separating power (G)xThe gravitational acceleration of the entry capsule and the thermal shield may be considered equal due to the proximity of the entry capsule and the thermal shield. Then there is
Figure RE-GDA0003426184920000122
3. According to the difference of the apparent acceleration of the two bodies, the movement of the heat shield and the entering cabin along the separation direction is calculated
The state space expression for the movement between the heat shield and the access compartment in the separation direction can be written as
Figure RE-GDA0003426184920000123
In fact, the process of separating the heat shield under the constraint of the constraint mechanism is short, the length of the constraint mechanism is usually short, the separation actuating force is large, the separation process is usually finished only within 0.1s, and the state of the heat shield entering the cabin in the process can be regarded as unchanged, so that the heat shield separation state equation can be solved.
This linear steady state system can be written as
Figure RE-GDA0003426184920000124
Wherein each item is respectively
Figure RE-GDA0003426184920000125
Figure RE-GDA0003426184920000126
The solution of this equation of state is
Figure RE-GDA0003426184920000127
At the start of the separation, the separation distance and the separation speed between the heat shield and the access compartment are both 0, so that the initial state is
Figure RE-GDA0003426184920000128
Due to the zero initial state of the equation of state, the solution to the equation is
Figure RE-GDA0003426184920000129
4. According to the motion state of the entrance cabin, the motion of the heat shield is rapidly forecasted
In addition, the motion state of the heat shield can be predicted according to the equation, and the state of the entry cabin in the navigation information is required
Figure RE-GDA0003426184920000131
Figure RE-GDA0003426184920000132
Can be substituted to obtain
Figure RE-GDA0003426184920000133
Knowing the pneumatic load and the separation actuating force of the heat shield, the separation state under the restraint of the heat shield can be accurately predicted, and attention needs to be paid to VhbxThe apparent speed of the heat shield in the body coordinate system, and if the absolute speed of the heat shield is obtained, the linear speed caused by the rotation of the body coordinate system needs to be considered
Figure RE-GDA0003426184920000134
Wherein Vhb＝[Vhbx Vhby Vhbz]TAnd the apparent speed V of the heat shield in two directions of the Y-axis and Z-axis of the systemhby、VhbzApparent speed V of entering cabin in Y-axis and Z-axis directionsvby、VvbzRespectively equal.
5. Forecasting the movement of the shield after separation based on the speed at which the shield leaves the restraint mechanism
So far, the motion process of the heat shield along the separating mechanism can be predicted quickly, and after the heat shield is separated from the separating mechanism, the heat shield and the entering cabin become two rigid bodies moving independently, and the motion processes of the heat shield and the entering cabin can be solved by rigid body kinetic equations respectively.
The rigid body dynamic equations comprise a centroid translation dynamic equation, a centroid translation kinematic equation, a centroid rotation dynamic equation and a centroid rotation kinematic equation.
Equation of motion of mass center translation
Figure RE-GDA0003426184920000135
Wherein: omegamRepresenting the angular velocity of rotation of the Mars coordinate system relative to the Mars inertial system. V represents the velocity vector of the lander relative to the mars. r represents the position vector of the lander. m represents the quality of the landing rover; p represents the vector sum of the thrust received by the landing patrol instrument and other external forces (such as parachute line force, initiating explosive device acting force and the like); r represents the aerodynamic force to which the landing patrol machine is subjected; g represents the gravitational acceleration vector
A centroid translation kinematics equation. For convenience of describing the movement of the lander, the position of the lander is described by the center distance r, the center longitude λ and the center latitude φ
Figure RE-GDA0003426184920000141
Figure RE-GDA0003426184920000142
Figure RE-GDA0003426184920000143
Wherein Vu、VE、VNRepresenting the velocity components in the sky, east and north directions, respectively.
Equation of dynamics of rotation around centroid
Figure RE-GDA0003426184920000144
Wherein (I)bIs tensor of inertia (omega)bIs angular velocity
The kinematic equation is rotated around the center of mass. When the relative angular velocity (i.e. the angular velocity of the land object coordinate system relative to the local coordinate system) ω is knownbuThen, the euler angles in z-y-x order of rotation relative to the local coordinate system can be found: pitch angle theta, yaw angle psi, roll angle gamma.
Figure RE-GDA0003426184920000145
Figure RE-GDA0003426184920000146
Figure RE-GDA0003426184920000147
Wherein ω isbux、ωbuy、ωbuzThe three-axis component representing the relative angular velocity,
the above ordinary differential equation is numerically integrated to obtain the three-axis velocity (V) of the systembThe six-degree-of-freedom motion state of the access cabin and the heat shield can be obtained according to the fire center distance r, the fire center longitude lambda, the fire center latitude phi and the attitude angle (the pitch angle theta, the yaw angle psi and the roll angle gamma).
6. According to the motion states of the heat shield and the access cabin, calculating the apparent motion of the heat shield under the coordinate system of the access cabin body
In order to ensure the safety of the separation of the heat shield, the shortest distance between the heat shield and the lander is forecasted after the heat shield leaves the separation mechanism, and the apparent motion of the heat shield under a coordinate system of an access cabin body needs to be calculated firstly
Position of heat shield under coordinate system of cabin entering body
Figure RE-GDA0003426184920000148
Wherein C isamIs a conversion matrix of the cabin entering body coordinate system relative to the local coordinate system; (R)h)m、(Ra)mThe positions of the heat shield and the entering cabin under a local coordinate system can be respectively calculated by the respective fire center distance r, the fire center longitude lambda and the fire center latitude phi of the heat shield and the entering cabin
Figure RE-GDA0003426184920000151
Figure RE-GDA0003426184920000152
And the posture of the heat shield relative to the access cabin can be given by a relative posture conversion matrix
Figure RE-GDA0003426184920000153
In the formula Cam、ChmRespectively as transformation matrix from local coordinate system to coordinate system of access cabin body and coordinate system of heat-proof cover body
After the apparent motion and the relative posture of the heat shield in the cabin body coordinate system are obtained through calculation, the shortest distance between the heat shield and the cabin is calculated through the method described below.
7. Simplifying the shapes of the lander and the heat shield, judging the separation safety by adopting a ray tracing method, calculating the ray distance and obtaining the shortest distance
The relative distance between the outsole and the lander needs to be seen not only by the relative distance between the outsole and the center of mass of the lander, but also by the posture of the outsole relative to the lander, and whether collision occurs or not can not be well judged by considering the outsole and the lander as mass points without considering the shapes of the mass points and the lander. A ray tracing method for calculating the shortest distance between the outsole and the lander is presented. The method is illustrated in fig. 1, a plurality of rays are emitted from the centroid of the access cabin, a part of rays do not intersect with the heat shield, a part of rays intersect with the heat shield, if enough rays are emitted from the centroid of the access cabin, rays with enough density intersect with the heat shield, and the relative distance between the access cabin and the heat shield can be judged through the intersected rays.
The lower contour of the entrance capsule is reduced to a cone, while for the sake of calculation the shape of the outsole is reduced to a regular pyramid, sufficiently many facets to make the polygonal pyramid approximate a cone. And performing ray radiation at intervals, and selecting the line with the shortest distance from rays intersecting with the heat shield as the shortest distance between the heat shield and the access cabin at the current time.
8. Judging the collision safety of the heat shield and the entering cabin by the shortest distance curve
The shortest distance mentioned here is not the line of the shape of the heat shield and the shape of the access opening that is the shortest in analytical sense, but only the shortest of the rays we have used, but such a distance is sufficient to judge the safety of the heat shield separation in the case where sufficiently dense rays are chosen and sufficiently accurate approximation of the shape of the outsole.
A relative distance graph may be plotted based on the selected ray shortest distance at each time instant. The trend of the relative distance profile is different according to different movement patterns of the heat shield and the access compartment. The present application presents graphs for both cases. As the heat shield leaves the restraint mechanism, the movement of the heat shield is no longer directly affected by the access compartment and parachute, tending to move away from the access compartment, as shown in fig. 2, but may even collide due to the pneumatic coupling between the heat shield and the access compartment, and the violent rotation of the heat shield. Generally, due to the effect of the restraining and disengagement forces of the restraining mechanism, the relative distance increases gradually as the shield begins to disengage the restraining mechanism, after which the relative distance begins to decrease and even becomes negative, meaning that the shield collides with the access compartment, as shown in fig. 3.
In conclusion, the relative distance between the heat shield and the access cabin can be judged through a ray tracing method, the safety problem of heat shield separation can be further analyzed,
a simulation example is performed for the method for forecasting the separation state of the heat shield, and compared with the actual separation process of the heat shield, the simulation result is shown in fig. 5 and 6, fig. 5 shows the separation distance between the heat shield and the entering cabin in the separation direction, and fig. 6 shows the separation speed between the heat shield and the entering cabin in the separation direction. In the figure, the dotted line represents an actual separation state, the solid line represents a forecast state, and it can be seen that compared with the actual state, the state forecast by the analysis method is basically accurate, and the difference between the separation speed of the heat shield, which is calculated by the forecast method, when the heat shield is separated from the constraint mechanism and enters the cabin and the actual state is not more than 0.1 m/s.
And further forecasting the flying state of the heat shield after the heat shield is separated according to the forecasting result of the state of the heat shield when the heat shield is separated from the constraint mechanism, wherein the position of the heat shield is shown in fig. 7 and fig. 8.
After the motion state of the heat shield is obtained, the apparent motion of the heat shield under the cabin entering body coordinate system is calculated, the relative motion of the heat shield and the cabin entering body is judged through a ray tracing method, as shown in fig. 9, rays emitted from the center of mass of the cabin entering body intersect with the appearance of the heat shield to form a contour dot matrix of the heat shield, the dot matrix at the leftmost end in the figure is a lower contour of the cabin entering body, points with gradually changing colors rightward are heat shield contours at different times, the heat shield gradually keeps away from the heat shield along with the time, and the red color in the figure is lighter and lighter. Extracting and plotting figure 10 the shortest distance from the projected ray into the centre of mass of the capsule at each moment, it can be seen that in this simulation example the heat shields are progressively further away from the access capsule, without risk of collision.
It should be noted that the detailed description is only for explaining and explaining the technical solution of the present invention, and the scope of protection of the claims is not limited thereby. It is intended that all such modifications and variations be included within the scope of the invention as defined in the following claims and the description.

Claims (8)

1. A method for forecasting an interstage separation state of a heat shield and analyzing safety is characterized by comprising the following steps:
the method comprises the following steps: acquiring a visual acceleration difference between an access cabin and a heat shield;
step two: acquiring separation actuating force and aerodynamic force data of the heat shield and specific force data of an accelerometer entering the cabin, and acquiring acceleration difference of the heat shield and the accelerometer entering the cabin in a separation direction according to the separation actuating force and the aerodynamic force data of the heat shield and the specific force data of the accelerometer entering the cabin;
step three: obtaining a separation state equation according to the difference of the apparent acceleration of the access cabin and the heat shield and the difference of the acceleration of the heat shield and the access cabin in the separation direction, and obtaining the movement between the heat shield and the access cabin along the separation direction according to the separation state equation;
step four: acquiring the motion state of the access cabin, and performing state prediction on the motion state of the heat shield under the constraint of the separation mechanism according to the motion between the heat shield and the access cabin along the separation direction and the motion state of the access cabin;
step five: the speed of the heat shield when the heat shield leaves the separating mechanism is obtained according to the state forecast, and the motion state of the heat shield after separation is forecasted according to the speed of the heat shield when the heat shield leaves the separating mechanism;
step six: according to the motion state of the separated heat shield and the motion state of the heat shield entering the cabin, the apparent motion of the heat shield under a cabin entering body coordinate system is obtained;
step seven: firstly, simplifying the lower outline of an access cabin into a conical shape, simplifying the shape of a heat shield into a regular pyramid, then obtaining a ray distance according to the visual motion of the heat shield under an access cabin body coordinate system and by adopting a ray tracing method, and selecting the shortest distance between the access cabin and the heat shield according to the ray distance so as to obtain a shortest distance curve;
step eight: and judging the collision safety of the heat shield and the entering cabin according to the shortest distance curve.
2. The method for forecasting the status of interstage separation of heat shields and analyzing safety as claimed in claim 1, wherein the difference of apparent acceleration is expressed as:
arel＝(ah-av)x-(ahc-avc)x-(ahe-ave)x-(ahr-avr)x
(ahc-avc)x＝0
(ahe-ave)x＝0
Figure FDA0003206765460000011
wherein x isrelIndicating the separation distance, a, between the access compartment and the heat shieldhRepresents the absolute acceleration of the heat shield, ahcIndicating the Criotris acceleration of the heat shield, aheRepresenting linear acceleration due to angular acceleration to which the heat shield is subjected, ahrDenotes the centrifugal acceleration of the heat shield, avRepresenting the absolute acceleration of the entering cabin, avcIndicating the Kresolis acceleration into the cabin, aveRepresenting linear acceleration due to angular acceleration to which the access compartment is subjected, avrRepresents the centrifugal acceleration of the entry into the chamber, ()xRepresenting the x-axis component, ωyIndicating yaw rate, ω, of entering the cabinzRepresenting the pitch rate of the entry into the cabin, arelIndicating the difference in the apparent acceleration of the access compartment and the heat shield.
3. The method for forecasting the status of interstage separation of heat shields and analyzing safety as claimed in claim 2, wherein the acceleration difference is expressed as:
Figure FDA0003206765460000021
wherein A ishPneumatic device for indicating separation direction of heat shieldForce, FsRepresents separation power, mhRepresenting the mass of the heat shield and f the specific force data into the cabin accelerometer.
4. The method for forecasting the interstage separation state of the heat shield and analyzing the safety as claimed in claim 3, wherein the separation state equation is expressed as:
Figure FDA0003206765460000022
Figure FDA0003206765460000023
Figure FDA0003206765460000024
wherein v isrelIndicating the speed of separation of the access compartment and the heat shield, t0The initial moment of separation of the access cabin from the heat shield is shown, t is the current moment, tau is an integral variable, e is an exponential function, and D (tau) and W (t-tau) are respectively shown as two functions.
5. The method for forecasting the interstage separation state and analyzing the safety of the heat shield according to claim 4, wherein the motion state of the heat shield under the constraint of a separation mechanism is represented as follows:
Figure FDA0003206765460000025
wherein, VhbRepresenting apparent velocity, v, of the heat shield in a body coordinate systemeRepresenting the linear velocity, omega, resulting from rotation of the body coordinate systemxRepresenting the roll rate, r, of the entering cabinhzRepresenting the projection of the position of the heat shield on the Z-axis of the body coordinate system, rhyRepresenting an in-vivo coordinate system of a heat shieldPosition projection of the Y axis, rhxRepresenting the projection of the position of the heat shield on the X-axis of the body coordinate system, VhThe absolute velocity of the heat shield is indicated.
6. The method for forecasting the interstage separation state and analyzing the safety of the heat shield according to claim 5, wherein the motion of the heat shield after separation is obtained according to rigid body kinetic equations, wherein the rigid body kinetic equations comprise a centroid translation kinetic equation, a centroid translation kinematic equation, a centroid rotation kinetic equation and a centroid rotation kinematic equation;
the centroid translational kinetic equation is expressed as:
Figure FDA0003206765460000031
wherein (C)bRepresenting the projection in a body coordinate system, ω representing the angular velocity of the access compartment, ωmRepresenting the angular velocity of rotation of the Mars coordinate system relative to the Mars inertial system, V representing the velocity vector of the lander relative to the Mars, R representing the position vector of the lander, m representing the mass of the landing rover, P representing the vector sum of the thrust force received by the landing rover and other external forces, R representing the aerodynamic force received by the landing rover, g representing the gravitational acceleration vector,
Figure FDA0003206765460000032
a derivative representing the projection of the velocity vector V in the body coordinate system;
the centroid translational kinematic equation is expressed as:
Figure FDA0003206765460000033
Figure FDA0003206765460000034
Figure FDA0003206765460000035
wherein, Vu、VE、VNRespectively representing the velocity components of the sky, east and north, r representing the fire center distance, phi representing the fire center latitude,
Figure FDA0003206765460000036
the derivative of the distance between the two fire centers is represented,
Figure FDA0003206765460000037
the derivative of the longitude of the fire center is represented,
Figure FDA0003206765460000038
a derivative representing the latitude of the fire center;
the equation of the dynamics of rotation around the center of mass is expressed as:
Figure FDA0003206765460000039
wherein (I)bThe moment of the lander is expressed by M which is an inertia tensor under a body coordinate system;
the rotational kinematics equation around the center of mass is expressed as:
Figure FDA0003206765460000041
Figure FDA0003206765460000042
Figure FDA0003206765460000043
wherein, ω isbux、ωbuy、ωbuzRepresenting the three-axis components of relative angular velocity, psi is the yaw angle, gamma is the roll angle,
Figure FDA0003206765460000044
the derivative of the pitch angle is represented,
Figure FDA0003206765460000045
the derivative of the yaw angle is represented,
Figure FDA0003206765460000046
the derivative of the roll angle is represented.
7. The method for forecasting the interstage separation state and analyzing the safety of the heat shield according to claim 6, wherein the apparent motion of the heat shield under a coordinate system of an access cabin is represented as follows:
Figure FDA0003206765460000047
Figure FDA0003206765460000048
Figure FDA0003206765460000049
wherein, CamA transformation matrix (R) representing the cabin coordinate system relative to the local coordinate systemh)m、(Ra)mRespectively showing the position of the heat shield and the access cabin in the local coordinate system, phihIndicating the fire center latitude, λ, of the shieldhThe longitude of the fire center, r, of the heat shieldhIndicating the core distance of the heat shieldaIndicating the latitude of the fire, λ, entering the cabinaIndicating the fire center longitude, r, of the entry into the cabinaIndicating the distance of the fire centers entering the cabin.
8. The method for forecasting the interstage separation state of the heat shield and analyzing the safety as claimed in claim 7, wherein the ray tracing method comprises the following specific steps:
dense rays are emitted from the center of mass of the entering cabin, one part of rays are not intersected with the heat shield, the other part of rays are intersected with the heat shield, the length of the rays intersected with the heat shield is calculated, the shortest distance between the entering cabin and the heat shield is obtained, namely the ray tracing is performed once, and then the ray tracing at equal time intervals is performed to obtain the shortest distance curve between the entering cabin and the heat shield.
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