CN113609574B - Equal-damage-line-based method for representing damage resistance of multi-axis special vehicle tire system - Google Patents

Equal-damage-line-based method for representing damage resistance of multi-axis special vehicle tire system Download PDF

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CN113609574B
CN113609574B CN202110773628.5A CN202110773628A CN113609574B CN 113609574 B CN113609574 B CN 113609574B CN 202110773628 A CN202110773628 A CN 202110773628A CN 113609574 B CN113609574 B CN 113609574B
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高钦和
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Abstract

The invention relates to a method for representing the damage resistance of a multi-axis special vehicle tire system based on an equal damage line, which aims at the functional influence of the whole vehicle system in a tire damage state, quantitatively represents the bearing capacity, the driving capability and the steering capacity of the tire system based on a vehicle dynamics theory, and establishes a calculation model of the multi-axis special vehicle tire system functional damage; quantitative characterization and bullet intersection analysis are carried out on the shock wave overpressure field by adopting an explosion damage theory, and a calculation model of physical damage of a tire system is established; according to the relation between the explosive centers of the attacking warheads and the relative positions of the vehicles, adopting a calculation characteristic line facing the whole area of the vehicles to establish a line-of-damage calculation model of a tire system and the like; and finally, taking a certain type of five-axis special vehicle as an example, verifying the characterization method and performing example analysis. The characterization method can be applied to the characterization of the damage resistance of the multi-axis special vehicle tire system under the battlefield attack threat, and lays a model foundation for the subsequent optimization of the maneuvering evasion and protection capability promotion of the multi-axis special vehicle battlefield.

Description

Equal-damage-line-based method for representing damage resistance of multi-axis special vehicle tire system
Technical Field
The invention belongs to the field of tire damage assessment method research, and particularly relates to a method for representing the damage resistance of a multi-axis special vehicle tire system based on equal damage lines.
Background
The good maneuverability is an important guarantee for the strong survival of the multi-axis special vehicle in a battlefield environment, the tire system is used as a core component for implementing the maneuverability of the multi-axis special vehicle, and due to the characteristics of large quantity, large exposed area and weak protection capability, the tire system is constantly subjected to various types of attack and damage of enemies in the battlefield environment, so that the maneuverability of the whole vehicle is influenced, and the survival capability of the vehicle is greatly threatened. Therefore, the damage resistance of the multi-axis special vehicle tire system is evaluated in advance, the maneuvering ability of the vehicle in a battlefield environment can be mastered in advance, and reference is provided for battlefield planning and decision-making of a commander.
The multi-axle special vehicle tire system is used as the only contact component of the vehicle and the ground, is an important guarantee that the multi-axle special vehicle can complete the bearing, transportation and launching tasks of a large weapon system and realize high maneuverability and operability under complex road working conditions and severe operating environments. Compared with the common vehicle, the tire system of the multi-axle special vehicle has the characteristics of large structural size, large quantity and weak protective capability, and is extremely easy to be attacked and damaged by various types of enemies in a battlefield environment, so that the completion of the maneuvering combat task is influenced.
If the damage resistance of the multi-axis special vehicle tire system can be reasonably represented, the survival probability of the operational force can be given in advance before the multi-axis special vehicle tire system enters a battlefield environment, and reference is provided for a commander to make a decision. However, at present, related researchers at home and abroad mainly carry out intensive research on the aspect of target damage assessment, focus on the damage degree of weaponry, and relatively few researches in the field of damage resistance assessment and characterization of weaponry.
Disclosure of Invention
The technical problem solved by the invention is as follows: aiming at the problem that the traditional evaluation method depends on subjective judgment of expert scoring and artificial empowerment, and the evaluation result reliability is low due to the insufficient consideration of the structure and the arrangement of equipment to be evaluated, the multi-axis special vehicle tire system damage resistance evaluation calculation method which avoids the artificial empowerment, considers the influence of the overall arrangement of the tire system and can perform system power activation is provided, the problem can be effectively solved, and the evaluation reliability is improved.
The technical scheme of the invention is as follows: the method for representing the damage resistance of the multi-axis special vehicle tire system based on the equal damage line comprises the following steps:
step 1: generating a calculation characteristic line matrix according to the vehicle related parameters and the tire structure function parameters;
step 2: calculating the law of the damage probability on each characteristic line along with the change of the position, and comprising the following substeps;
step 2.1: establishing a tire system damage-resistant model, wherein the input parameters of the model are as follows: tire system parameters, damage field parameters and judgment index parameters;
step 2.2: obtaining the coordinates of each tire of the tire system according to the model input parameters in the step 1, thereby obtaining the overall arrangement of the whole tire system;
step 2.3: sequentially generating tire position coordinates to be deleted, calculating the position of the center of mass of the vehicle with the tires at a certain position removed, and calculating the number of the limit missing tires;
the method comprises the following substeps:
step 2.3.1: calculating and judging the vehicle bearing capacity under the working conditions of different tires missing;
step 2.3.2: calculating and judging the driving capability of the vehicle lacking different tire working conditions;
step 2.3.3: calculating and judging the steering capacity of the vehicle under different tire missing working conditions;
the maximum number of the missing tires can be found by deleting the tires at different positions and carrying out cyclic calculation, and the missing tires need to simultaneously meet the three judgment conditions;
step 2.4: simulating the position of the explosive core of the attacking warhead, calculating the distribution of a fragmentation field and a shock wave field, intersecting the overall arrangement of a tire system with the fragmentation field and the shock wave field, comparing the fragment specific kinetic energy and the shock wave overpressure with the equivalent aluminum thickness resistance and the overpressure resistance of the tire, and calculating the damage probability of the tire at each position;
step 2.5: arranging the obtained tire damage probabilities from large to small, namely: p is 1 ，P 2 ，P 3 ，P 4 \8230; the damage degree of the tire system is divided into different grades, and the damage probability and the damage resistance probability under the corresponding different grades are calculated according to the number of the tires lost in each grade.
And step 3: connecting the burst center positions with the same damage probability of the tire system on the different characteristic lines obtained in the step (2) to form a closed curve, namely the equal damage lines under the damage probability;
and 4, step 4: the damage resistance of the tire system can be calculated by calculating the dimensionless ratio of the area surrounded by the closed curve formed by the equal damage lines of the damage probabilities to the area formed by the outer boundary of the multi-axis special vehicle tire system and combining the corresponding damage probability distribution:
Figure BDA0003154859670000031
wherein, the area of the polygon is calculated according to a coordinate method:
Figure BDA0003154859670000032
in the formula x i ,y i Respectively as the x and y coordinates of each tire location;
Figure BDA0003154859670000033
in the formula x k ,y k Respectively an x coordinate and a y coordinate of the explosive core position of the damage line closed curve forming each damage probability and the like.
The further technical scheme of the invention is as follows: in the step 1, the step of processing the raw material, according to the position of each tire of the vehicle, namely, the starting point ST = [ (x) of the characteristic line q1 ,y q1 ,z q1 )…(x qi ,y qi ,z qi )]The slope J = [ J ] of the characteristic line at each tire set q1 ,J q2 …J qi ]Generating a characteristic line matrix, expressing the principle of the straight line according to one point on the known straight line and the slope of the straight line, and calculating the coordinate P of any point on the characteristic line i (x, y, z) = f (J, ST), that is, the assumed position of the center of burst, the relative relationship between the assumed position of the center of burst on each characteristic line and each tire position point
Figure BDA0003154859670000034
Wherein the matrix expression is:
Figure BDA0003154859670000035
in the formula, the positional relationship between the assumed explosion point on the characteristic line corresponding to the characteristic point A and each tire is defined, and B, C and D-Q have the same meaning. The matrix R is a variable that varies with the location of the assumed explosion point, and expresses the relative distance of the assumed core location from each tire location.
The further technical scheme of the invention is as follows: the tire system parameters specifically include vehicle centroid coordinates(xm, ym, zm), each tire position coordinate (xqi, yqi, zqi), sprung mass m, friction force F, tire radius R, roll center to center of mass distance e, roll center height h, wheel axle distance B, tire three-dimensional force (Fxi, fyi, fzi) wherein vehicle center of mass coordinate (xm, ym, zm), each tire position coordinate (xqi, yqi, zqi), sprung mass m, friction force F, tire radius R, roll center to center of mass distance e, center of mass height h, wheel axle distance B is an initial known parameter, tire force (Fxi, fyi), load bearing capacity Fzi is an unknown parameter, tire force specific calculation formula F xi ＝f(α,λ,F zi )；
Figure BDA0003154859670000041
The parameters of the damage field specifically comprise initial aiming coordinates (x 0, y0, z 0) of an attacking warhead, an empirical coefficient xi and an air resistance coefficient C related to the attacking warhead d The method comprises the following steps of determining the initial aiming coordinates (x 0, y0 and z 0) of an attacking warhead, the empirical coefficient xi and the aerodynamic drag coefficient C of the attacking warhead, the fragment specific kinetic energy E, the shell wall thickness t, the shell coefficients a and b, the loading quantity C, the related radius d of the fragment, the shell mass M, the opening angle alpha between the fragment and a blasting point, the atmospheric density rho, the fragment shape coefficient k, the equivalent aluminum thickness H, the included angle phi between the external normal line of the fragment and the axis of the warhead, the polytropic index gamma and the blasting center position (x, y and z), wherein the initial aiming coordinates (x 0, y0 and z 0) of the attacking warhead, the empirical coefficient xi and the aerodynamic drag coefficient C of the attacking warhead d The method comprises the following steps of calculating the blasting center position by adopting a formula, wherein the formula comprises the following unknown parameters, the formula comprises the specific kinetic energy E of a burst piece, the wall thickness t of a shell, the coefficients a and b of the shell, the loading amount c, the related radius d of the burst piece, the mass M of the shell, the opening angle alpha between the burst piece and a blasting point, the atmospheric density rho, the shape coefficient k of the burst piece, the equivalent aluminum thickness H, the included angle phi between the outer normal line of the burst piece and the axis of a warhead, and the polytropic index gamma which is an initial known parameter and is the blasting center position (x, y and z), and the formula for calculating the unknown parameters respectively adopts the formula for calculating the blasting center position
Figure BDA0003154859670000051
The evaluation index parameters specifically comprise the standard maximum bearing capacity F of the tire zmax Vehicle operationMinimum maneuver velocity v required for war xmin Rollover evaluation index LTR, target specific kinetic energy Eb0, tire shock wave resistance Pt, wherein the standard maximum bearing capacity F of the tire zmax Minimum vehicle speed v required for vehicle operation xmin The rollover evaluation index LTR, the target specific kinetic energy Eb0 and the tire shock wave resistance Pt are initial known parameters.
The further technical scheme of the invention is as follows: in step 2, when the coordinates xi (xqi, yqi, zqi) of each tire are input in step 1, the coordinate matrix of the entire tire system is ST = [ x1, x2 \8230, xi ].
The further technical scheme of the invention is as follows: the tire system bearing capacity calculation model is as follows:
Figure BDA0003154859670000052
wherein m is the sprung mass, F zi Is a tire vertical force, F yi Lateral friction of the tire, F xi Is the longitudinal friction force of the tire, and n is the number of the tires; definition if F zi ＞F zmax Judging that the tire system fails at the moment; f zmax Is the standard maximum load capacity of the tire.
The further technical scheme of the invention is as follows: in the step 2.3.2, if the vehicle running speed provided by the sum of the longitudinal forces of the tires in the tire system is less than the minimum maneuvering speed required by the vehicle battle, the tire system is disabled, that is:
v＜v xmin
in the formula, v xmin For the minimum maneuvering speed required for the vehicle to fight, v is solved by the following formula:
Figure BDA0003154859670000061
wherein m is the sprung mass, F xi For each tire longitudinal force: f xi ＝f(α,λ,F zi ) α is a tire slip angle, λ is a tire slip ratio; f. of Fx For longitudinal friction, non-driving, of tyresThe sum of the friction of the traction wheels and the wind resistance of the vehicle.
The further technical scheme of the invention is as follows: in the step 2.3.3, LTR is adopted as the rollover evaluation index,
Figure BDA0003154859670000062
wherein the content of the first and second substances,
Figure BDA0003154859670000063
to a side inclination angle, a y The lateral acceleration is obtained, e is the distance from the side-tipping center to the center of mass, g is the gravity acceleration, and B is the wheel wheelbase;
if the LTR value in the tire system is greater than the vehicle rollover critical LTR value, the tire system fails, that is:
Figure BDA0003154859670000064
the further technical scheme of the invention is as follows: in the step 2.4, the following substeps are included:
(1): establishing a shot random model:
Figure BDA0003154859670000065
wherein (x, y, z) is the coordinates of the center of pop of the attacking warhead, (x) 0 ,y 0 ,h 0 ) Initial aiming coordinates of the attacking warhead, xi is an empirical coefficient related to the attacking warhead, CEP is a circular probability deviation, xi 1 ，ξ 2 Are mutually independent random variables;
(2): the distribution of the obtained fragment fields is:
Figure BDA0003154859670000066
in the formula, mu is the average mass of fragments, omega is the charge correlation coefficient, and t is the bombThe thickness of the shell wall, d is the inner diameter of the shell, m p Grading the quality of the fragments;
(3): the distribution of the impact field was obtained as:
Figure BDA0003154859670000071
in the formula, r is the distance between the center of burst and the target;
(5): intersecting the overall arrangement of the tire system with the fragmentation field and the shock wave field;
(6) Calculating the probability:
the damage probability of the fragment to the target is as follows:
Figure BDA0003154859670000072
wherein E b For the specific kinetic energy when the fragment hits the target, the calculation formula is as follows:
Figure BDA0003154859670000073
h is the equivalent aluminum thickness of the target protection;
the probability of damage to the target by the shock wave is:
Figure BDA0003154859670000074
wherein p is t Is the targeted resistance.
The further technical scheme of the invention is as follows: in the step 2.5, the damage degree of the tire system is divided into three grades of meeting combat requirements, meeting driving requirements and failure, damage probability and damage resistance probability under different grades are calculated according to the number of the tires lost in each grade, and the number of the tires lost in each grade is defined as n 1 ，n 2 ，n 3 And then:
the damage probability meeting the combat requirement is P 1 *P 2 *…P n1 With a damage resistance probability of 1-P 1 *P 2 *…P n1 ；
The damage probability meeting the driving requirement is P 1 *P 2 *…P n2 The damage resistance probability is 1-P 1 *P 2 *…P n2 ；
The failure probability satisfying the failure requirement is P 1 *P 2 *…P n3 With a damage resistance probability of 1-P 1 *P 2 *…P n3 。
Effects of the invention
The invention has the technical effects that: the method is based on the vehicle dynamics theory, quantitative characterization modeling is carried out on the bearing capacity, the driving capacity and the steering capacity of a tire system, a calculation model of the number of limit missing tires of the multi-axle special vehicle is established according to combat requirements and driving requirements, the number of the limit missing tires is used for dividing the function loss level of the vehicle, and the problem that the reliability of an evaluation result is reduced due to artificial empowerment is solved.
Drawings
FIG. 1 is a process for examining the damage line of a tire system
FIG. 2 is a schematic representation of the line of constant damage
FIG. 3 is a calculated feature line
FIG. 4 is a calculation flow of the anti-damage capability characterization method
FIG. 5 is a vehicle coordinate system
FIG. 6 is a graph showing the damage rate of the characteristic line calculated in the front and rear regions of the vehicle
FIG. 7 is a graph showing the calculated damage rate of the characteristic line in the right side region of the vehicle
FIG. 8 is a schematic view of the damage lines
FIG. 9 is a schematic diagram showing the characterization of the damage resistance
Detailed Description
In the description of the present invention, it is to be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", and the like, indicate orientations and positional relationships based on those shown in the drawings, and are used only for convenience of description and simplicity of description, and do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, should not be considered as limiting the present invention.
Referring to fig. 1-9, the isodestruct line characterization method is a closed curve connecting the locations of the explosive centers around the vehicle where the damage probability of the tire system is equal, and the damage probability that the vehicle may suffer can be estimated according to the relative location relationship between the vehicle and the explosive centers of the attacking warheads based on the isodestruct line anti-damage capability characterization method. The method is based on the explosion shock wave overpressure damage criterion, introduces the functional damage degree based on the tire-vehicle function influence relation, establishes the tire system damage judgment criterion, and further adopts the equal damage lines to represent the damage resistance of the tire system. The specific technical scheme is as follows:
criterion for damage judgment of tire system
1.1 quantification of degree of functional damage to tire System
(1) Bearing capacity
The tire system of a certain multi-axle special vehicle has n tires, and the coordinate of the grounding position of each tire is Q i (x qi ,y qi ,z qi ) The coordinate of the mass center M of the vehicle is M (x) m ,y m ,z m ) And then the distance vector from each tire grounding position to the mass center of the vehicle is as follows:
Figure BDA0003154859670000091
because the additional dynamic load is generated in the motion state and is larger than the tire force in the static state, the tire in the static state can be used for calculation. Setting the acting force of each tire force in a static state as the longitudinal friction force f of each tire xi Lateral frictional force f yi And a vertical force F zi Then the vector forces of each tire are:
Figure BDA0003154859670000092
namely, the moment of each tire force to the vehicle mass center is as follows:
Figure BDA0003154859670000093
then, establishing a tire system bearing capacity calculation model as follows:
Figure BDA0003154859670000101
wherein m is the sprung mass.
If the vertical force of each tire in the tire system is larger than the standard maximum bearing capacity of the tire, the tire is burst, and the tire system fails. Namely:
F zi ＞F zmax (5)
in the formula, F zmax Is the standard maximum load capacity of the tire.
(2) Driving capability
Setting the tire longitudinal force of each driving shaft in a motion state to be F xi The sum of the longitudinal friction of each driving wheel, the friction of the non-driving wheel, and the resistance of the vehicle, such as wind resistance, is f Fx Namely, the following steps are provided:
Figure BDA0003154859670000102
where v is the vehicle running speed
Wherein, each tire longitudinal force can be solved by MF tire magic formula [15] ：
F xi ＝f(α,λ,F zi ) (7)
In the formula, α is a tire slip angle, and λ is a tire slip ratio.
If the vehicle running speed provided by the sum of the longitudinal forces of the tires in the tire system is less than the minimum maneuvering speed required by the vehicle for fighting, the tire system fails. Namely:
v＜v xmin (8)
in the formula, v xmin Minimum motor speed required for vehicle combat
(3) Steering ability
The method aims at the turning and rollover phenomena of a multi-axle special vehicle in a tire system damage state, generally because the wheels on one side of the vehicle are simultaneously unstable off the ground, and the rollover analysis can be carried out by adopting the transverse load transfer rate of the vehicle.
At present, rollover evaluation indexes mainly used in related researches are evaluation indexes such as vehicle LTR, SSF and RPM, and the LTR is selected as the rollover evaluation index:
Figure BDA0003154859670000111
in the formula, F l Is the sum of the vertical forces of the left tire, F r Is the sum of vertical forces of right-side tires, V LTR Is LTR value with the range of [ -1,1 []. In an ideal steady state, the tire vertical forces on both sides are equal, and the LTR value is 0.
In the moving and steering state, the influence of the dynamic roll acting force is also considered, and G is the mass center of the vehicle, C is the roll center of the vehicle, h is the height from the roll center to the ground,
Figure BDA0003154859670000112
to a side inclination angle, a y The lateral acceleration is, e is the distance from the roll center to the center of mass, and B is the wheel base. Namely, the following steps are included:
Figure BDA0003154859670000113
due to the smaller roll angle, there may be:
Figure BDA0003154859670000114
Figure BDA0003154859670000115
the lateral acceleration can be solved by the lateral force, the lateral force of each tire can be solved by an MF tire magic formula, and the tire lateral force of each driving shaft in a motion state is set to be F yi Then, there are:
Figure BDA0003154859670000116
F yi ＝f(α,λ,F zi ) (14)
the binding formulae (10) to (12) give:
Figure BDA0003154859670000121
if the LTR value in the tire system is greater than the vehicle rollover threshold LTR value, the tire system fails. Namely:
Figure BDA0003154859670000122
in the formula (I), the compound is shown in the specification,
Figure BDA0003154859670000123
critical LTR value for vehicle rollover
1.2 tire System physical Damage quantification
(1) Location of core of explosion
The damage degree of the multi-axle special vehicle is greatly influenced by the explosive core of the attacking warhead, and the Monte-Carlo method (Monte-Carlo) is generally adopted to simulate the randomness of the explosive core of the attack threat. The calculation model is as follows:
Figure BDA0003154859670000124
wherein (x, y, z) is the coordinates of the center of pop of the attacking warhead, (x) 0 ,y 0 ,h 0 ) For the initial aiming coordinate of the attacking part of the warhead, xi is an empirical coefficient related to the attacking part of the warhead, the core strike is 1, the conventional strike is (0, 1), CEP is the deviation of the probability of the circle, xi 1 ，ξ 2 Are random variables independent of each other.
(2) Model for damage by shock wave
Compared with static explosion, the peak overpressure of dynamic explosive shock waves generated by the high-speed motion of an oncoming warhead is larger, and meanwhile, considering the influence of the outer shell of the warhead on the explosive shock waves, the existing research mostly adopts a theoretical formula to make the moving cased explosive equivalent to TNT bare explosive:
Figure BDA0003154859670000125
χ＝c/(c+M) (19)
wherein a and b are the form factor of the cartridge case, d 0 Is the initial radius of the cartridge case, d m Is the radius of cartridge case fracture and gamma is the polytropic index.
Calculating the overpressure of the explosion shock wave according to a Heenrych formula as follows:
Figure BDA0003154859670000131
wherein r is the distance between the center of the explosion and the target.
Calculating the damage probability of the shock wave to the target according to the overpressure as follows:
Figure BDA0003154859670000141
in the formula, p t Is the targeted resistance.
2 relative position relationship of damage site
2.1 creation of computational feature lines
Because the shot positions of the attacking warheads have strong randomness and wide distribution range, accurate quantitative damage lines and the like are difficult to obtain if the shot positions are not restrained. In order to comprehensively reflect the relative position relationship of the damage field, the structural characteristics of the multi-axis special vehicle tire system and the whole vehicle system are considered, and a multi-axis special vehicle tire system damage field calculation characteristic line model shown in fig. 3 is established by taking a five-axis vehicle as an example.
As shown in fig. 3, the damage site calculation characteristic line of the multi-axis special vehicle tire system is divided into four regions, namely a front region, a rear region, a left region and a right region, and the four regions are composed of two types:
in the left and right areas of the vehicle, a left and right area calculation characteristic line is established by extending the central line of each shaft of the vehicle;
in the front and rear areas of the vehicle, a front and rear area calculation characteristic line is established by extending the longitudinal center line of the vehicle and extending the longitudinal center lines of the tires at two sides by 45 degrees;
position conversion
The relative position of the damage site mainly comprises a vehicle position and a center of burst position, wherein the vehicle position is provided by vehicle-mounted positioning equipment, and the center of burst position is provided by an early warning radar. Therefore, the relative position of the vehicle and the center of percussion needs to be converted into the relative position of the starting point (a, B, c.. Q) of the calculation characteristic line and the center of percussion.
As shown in FIG. 4, a vehicle position point provided by a certain type of five-axis characteristic vehicle-mounted positioning device is assumed to be G (x) g ,y g ,z g ) Then, according to the vehicle structure information, the relative relationship between the starting point of each calculation characteristic line and the vehicle position point can be obtained:
Figure BDA0003154859670000151
in the formula, w i The feature line start point position coordinates are calculated for each.
Then the relative position of the starting point of each calculated characteristic line and the center of the explosion is as follows:
Figure BDA0003154859670000152
in the formula (I), the compound is shown in the specification,
Figure BDA0003154859670000153
the relative relationship between the center of explosion and the vehicle position point.
A calculation characteristic line matrix representing the relative position relationship of the damage field can be established:
Figure BDA0003154859670000154
3 anti-damage capability characterization method based on equal damage line
3.1 method description and assumptions
The method for representing the damage resistance based on the equal damage lines comprises the steps of calculating the change rule of the damage probability of a specific domain (calculating characteristic lines) along with the distance of a burst (the distance between the center of a burst and the starting point of the calculating characteristic lines), connecting the positions of the center of a burst with the same damage probability of a tire system in the specific domain to form a closed curve, estimating the damage probability possibly suffered by a vehicle according to the relative position relation of the vehicle and the center of a burst of an attacking warhead, and representing the damage resistance of the tire system.
The area enclosed by a closed curve formed by the equal damage lines of all the damage probabilities is S i The area formed by the outer boundary of the multi-axle special vehicle tire system is S 0 The damage resistance of the tire system can be S i And S 0 Is characterized by the following dimensionless ratio:
Figure BDA0003154859670000155
obviously, for the tire systems of different vehicles, in the same probability damage line, the larger the Z value is, the weaker the damage resistance is. In addition, the calculation of the change rule of the damage probability along with the burst distance is based on an overpressure physical damage criterion, and the judgment of the functional damage degree of the multi-axis special vehicle tire system is introduced, so that a tire system damage judgment criterion is established. To facilitate the study, the following 3-point assumptions were made:
assuming that 1, the tire system exists independently, and the damage influence of other components of the vehicle on the tire system is ignored;
2, assuming that the specifications of tires in a tire system are consistent, neglecting the influence of damage on the interchange installation among the tires;
suppose 3 that the destructive effects of the different tires are independent.
3.2 method calculation procedure
According to the description of the method in section 3.1 and related assumptions, the calculation flow of the method for establishing the multi-axis special vehicle tire system anti-damage capability characterization is shown in fig. 4, and the main calculation steps are as follows:
step 1, generating a complete tire system coordinate matrix ST and a calculation characteristic line matrix R according to vehicle related parameters and tire structure functional parameters, and performing digital characterization on a tire system;
step 2 influence on the overall vehicle system function based on the loss of the tire system, from the load capacity F Z The driving capability v and the steering capability LTR carry out quantitative calculation on the function damage degree of the tire system;
step 3, carrying out quantitative calculation on the physical damage degree delta of the tire system according to relevant parameters of an attacking warhead and the overpressure-impulse protection performance of the tire system;
and 4, generating an equal damage line of the tire system based on the established calculation characteristic line matrix and the comprehensive damage probability of the functions/physics of the tire system, and calculating the dimensionless representation of the damage resistance Z of the tire system.
Example analysis
Inputting parameters
In order to make the model of the method for characterizing the anti-damage capability of the multi-axis special vehicle tire system usable, a five-axis special vehicle is taken as an example for calculation and analysis. According to the following principle that a central line of a vehicle shaft is a y-axis, a longitudinal central axis of the vehicle is an x-axis, and a coordinate system is established for a z-axis in the direction vertical to a plane of a tire system, as shown in fig. 5, each relevant input parameter is as follows:
(3) Special vehicle parameters: n =10,Q 1 (0,1.2,0)，Q 2 (2.2,1.2,0)，Q 3 (6.4,1.2,0)，Q 4 (8.6,1.2,0)，Q 5 (10.8,1.2,0)，Q 6 (0,-1.2,0)，Q 7 (2.2,-1.2,0)，Q 8 (6.4,-1.2,0)，Q 9 (8.6,-1.2,0)，Q 10 (10.8,-1.2,0)，
(4)m＝50t，M(6.3,0,1.6)，R＝0.53，B＝2.4，h＝1.09，e＝0.57，F zmax ＝6500kg，
Figure BDA0003154859670000171
(5) Parameters of the attacking warhead: non-prefabricated natural fragment blast-killing warhead with damage radius of 80m, M =100kg, c =154kg c ＝8000m/s，d 0 ＝320mm，d m ＝400mm，γ＝1，α＝40°，L＝1.8m，d＝300mm，t＝20mm，φ＝60°。
Analysis of results
Due to the symmetry of the vehicle on the left and right, in order to reduce the calculation data, only the front, rear and right domains are calculated, i.e., the damage rates on the calculation characteristic lines of B, C, D, E, F, H, I, J and K are calculated, and the damage probability on each calculation characteristic line obtained by calculation is shown in FIG. 6, FIG. 7 and Table 1.
The results of fig. 6 and 7 show that:
(a) Under the striking action of the attacking warhead, the damage probability of the tire system is 1 within the range of 25m away from the vehicle position, namely the tire system is destroyed; compared with the damage rate of the front side of the vehicle, the range with the damage probability of 1 at the rear side and two sides of the vehicle is expanded to be within 27 m;
(b) When the damage probability of the tire system is 10%, the distance range between the front side and the rear side of the vehicle is within 46 m; the range of both sides of the vehicle is within 60 m. Obviously, the damage rate of the front side and the rear side of the vehicle is lower than that of the two sides of the vehicle when the explosion distance is the same;
(c) When the damage probability is out of the maximum range corresponding to 1, the damage probability of the tire system is rapidly reduced along with the increase of the explosion range; under the striking action of the attacking warhead, the damage probability of the five-axis special vehicle can be reduced to 10% within the range of 46-60 m.
The distribution of the isobar lines of the tire system is shown in table 1 and fig. 8.
TABLE 1 Damage probability distribution on each calculated feature line
Tab.1 damage probability distribution of characteristic lines
Figure BDA0003154859670000181
According to the data in table 1, the ratio of the damage probability distribution area of the five-axis vehicle under the attack of the attacking warhead is calculated, and is shown in fig. 9.
The results of fig. 8 and 9 show that the distribution range of the relative positions of the blast centers of the attacking warhead and the vehicle is mainly concentrated in the region with the damage probability of 1 and the damage probabilities of 0.2 and 0.1, which also corresponds to the phenomenon that the damage probability of the tire system is rapidly reduced along with the increase of the explosion range shown in fig. 7 and 8, and the distribution range of the relative positions of the blast centers with the moderate damage probability is smaller. Meanwhile, the anti-damage capability of the tire system of the five-axis special vehicle under the attack of the attacking warhead is calculated to be 153.524. According to the calculation flow, the anti-damage capability of the multi-axis special vehicle tire systems of different models is calculated, and the anti-damage capability of the tire systems of vehicles of different models can be compared and graded.
4 conclusion
The article takes the damage of a large equivalent explosive shock wave as an action background according to the actual battlefield threat environment faced by a multi-axle special vehicle, and introduces the functional damage degree based on the functional influence of the structural damage of a tire system on the whole vehicle system and on the basis of the overpressure damage criterion of the explosive shock wave, and establishes a tire system shock wave damage probability model; according to the trajectory tracking and the explosive center position estimation of the vehicle-mounted positioning equipment and the coming warhead, the damage resistance characterization method based on the isodamage line is provided. By taking a certain five-axis special vehicle as an example, verification and example analysis of a characterization method are carried out, and the result shows that the method can be applied to characterization of the damage resistance of a multi-axis special vehicle tire system under the battlefield attack threat, and lays a model foundation for subsequent maneuvering evasion and protection capability improvement optimization of the multi-axis special vehicle battlefield.

Claims (9)

1. The method for representing the damage resistance of the multi-axis special vehicle tire system based on the equal damage lines is characterized by comprising the following steps of:
step 1: generating a calculation characteristic line matrix according to the vehicle related parameters and the tire structure function parameters;
step 2: calculating the change rule of the damage probability on each characteristic line along with the position, and comprising the following substeps;
step 2.1: establishing a tire system damage-resistant model, wherein the input parameters of the model are as follows: tire system parameters, damage site parameters and judgment index parameters;
step 2.2: obtaining the coordinates of each tire of the tire system according to the model input parameters in the step 1, thereby obtaining the overall arrangement of the whole tire system;
step 2.3: sequentially generating tire position coordinates to be deleted, calculating the position of the center of mass of the vehicle with the tires at a certain position removed, and calculating the number of the limit missing tires;
the method comprises the following substeps:
step 2.3.1: calculating and judging the vehicle bearing capacity under the working conditions of different tires missing;
step 2.3.2: calculating and judging the driving capability of the vehicle lacking different tire working conditions;
step 2.3.3: calculating and judging the steering capacity of the vehicle under different tire missing working conditions;
the maximum number of the missing tires can be found by deleting tires at different positions and carrying out cyclic calculation, and the missing tires need to simultaneously meet the three judgment conditions;
step 2.4: simulating the position of the explosive core of the attacking warhead, calculating the distribution of a fragmentation field and a shock wave field, intersecting the overall arrangement of a tire system with the fragmentation field and the shock wave field, comparing the fragment specific kinetic energy and the shock wave overpressure with the equivalent aluminum thickness resistance and the overpressure resistance of the tire, and calculating the damage probability of the tire at each position;
step 2.5: arranging the obtained tire damage probabilities from large to small, namely: p 1 ，P 2 ，P 3 ，P 4 \8230; dividing the damage degree of the tire system intoAnd calculating damage probability and damage resistance probability corresponding to different grades according to the number of the tires lost in each grade.
And 3, step 3: connecting the burst center positions with the same damage probability of the tire system on the different characteristic lines obtained in the step (2) to form a closed curve, namely the equal damage lines under the damage probability;
and 4, step 4: the damage resistance of the tire system can be calculated by calculating the dimensionless ratio of the area surrounded by the closed curve formed by the equal damage lines of the damage probabilities to the area formed by the outer boundary of the multi-axis special vehicle tire system and combining the corresponding damage probability distribution:
Figure FDA0003154859660000021
wherein, the area of the polygon is calculated according to a coordinate method:
Figure FDA0003154859660000022
in the formula x i ,y i X and y coordinates of each tire position respectively;
Figure FDA0003154859660000023
in the formula x k ,y k The x coordinate and the y coordinate of the position of the explosive core forming the damage line closed curves with the damage probability and the like are respectively shown.
2. The method for characterizing damage resistance of a multi-axis special vehicle tire system based on the same damage line as claimed in claim 1, wherein in step 1, the starting point ST = [ (x) according to the position of each tire of the vehicle, i.e. the characteristic line q1 ,y q1 ,z q1 )…(x qi ,y qi ,z qi )]The slope J = [ J ] of the characteristic line at each tire q1 ,J q2 …J qi ]Generating characteristic line matrix, expressing the principle of the straight line according to one point on the known straight line and the slope of the straight line, and calculating the coordinate P of any point on the characteristic line i (x, y, z) = f (J, ST), that is, the assumed position of the center of burst, the relative relationship between the assumed position of the center of burst on each characteristic line and each tire position point
Figure FDA0003154859660000024
Wherein the matrix expression is:
Figure FDA0003154859660000025
in the formula, the positional relationship between the assumed explosion point on the characteristic line corresponding to the characteristic point A and each tire is defined, and B, C and D-Q have the same meaning. The matrix R is a variable that varies with the location of the assumed explosion point, and expresses the relative distance of the assumed core location from each tire location.
3. The method for evaluating the damage resistance of a multi-axle special vehicle tire system considering operational requirements as claimed in claim 1, wherein the tire system parameters specifically include vehicle center-of-mass coordinates (xm, ym, zm), each tire position coordinate (xqi, yqi, zqi), sprung mass m, friction force F, tire radius R, distance e from roll center to center of mass, height h of roll center, wheel axle distance B, tire three-directional force (Fxi, fyi, fzi), wherein the vehicle center-of-mass coordinates (xm, ym, zm), each tire position coordinate (xqi, yqi, zqi), sprung mass m, friction force F, tire radius R, distance e from roll center to center of mass, height h of wheel center, distance B of wheel axle, initial known parameters, tire force (Fxi, fyi), bearing capacity Fzi as unknown parameters, tire force-specific calculation formula F xi ＝f(α,λ,F zi ) (ii) a The bearing capacity is calculated by the formula
Figure FDA0003154859660000031
The parameters of the damage field specifically comprise initial aiming coordinates (x 0, y0, z 0) of an attacking warhead, experience coefficients xi related to the attacking warhead, and nullCoefficient of air resistance C d The method comprises the following steps of determining the initial aiming coordinates (x 0, y0 and z 0) of an attacking warhead, the empirical coefficient xi and the aerodynamic drag coefficient C of the attacking warhead, the fragment specific kinetic energy E, the shell wall thickness t, the shell coefficients a and b, the loading quantity C, the related radius d of the fragment, the shell mass M, the opening angle alpha between the fragment and a blasting point, the atmospheric density rho, the fragment shape coefficient k, the equivalent aluminum thickness H, the included angle phi between the external normal line of the fragment and the axis of the warhead, the polytropic index gamma and the blasting center position (x, y and z), wherein the initial aiming coordinates (x 0, y0 and z 0) of the attacking warhead, the empirical coefficient xi and the aerodynamic drag coefficient C of the attacking warhead d The method comprises the following steps of calculating the position of a core of a bullet by using a formula, wherein the formula comprises the following unknown parameters, the formula comprises the specific kinetic energy E of the core, the wall thickness t of the shell, the coefficients a and b of the shell, the charge c, the related radius d of the core, the mass M of the shell, the opening angle alpha between the core and the initiation point, the atmospheric density rho, the shape coefficient k of the core, the equivalent aluminum thickness H, the included angle phi between the outer normal line of the core and the axis of a warhead, and the polytropic index gamma which is an initial known parameter and is the core position (x, y and z), and the formula for calculating the unknown parameters adopts the formula for calculating the core position
Figure FDA0003154859660000032
The evaluation index parameters specifically comprise the standard maximum bearing capacity F of the tire zmax Minimum vehicle speed v required for vehicle operation xmin Rollover evaluation index LTR, target specific kinetic energy Eb0, tire shock wave resistance Pt, wherein the standard maximum bearing capacity F of the tire zmax Minimum vehicle speed v required for vehicle operation xmin The rollover evaluation index LTR, the target specific kinetic energy Eb0 and the tire shock wave resistance Pt are initial known parameters.
4. The method for evaluating the damage resistance of the multi-axis special vehicle tire system considering the combat requirement as claimed in claim 1, wherein in the step 2, the coordinates xi (xqi, yqi, zqi) of each tire are input in the step 1, and the coordinate matrix of the whole tire system is ST = [ x1, x2 \8230; xi ].
5. The method for evaluating the damage resistance of the multi-axle special vehicle tire system in consideration of the combat requirement as claimed in claim 1, wherein the tire system bearing capacity calculation model is as follows:
Figure FDA0003154859660000041
wherein m is the sprung mass, F zi Vertical force of the tire, F yi Lateral friction of the tire, F xi Is the longitudinal friction force of the tire, and n is the number of the tires; definition if F zi ＞F zmax Judging that the tire system fails at the moment; f zmax Is the standard maximum load capacity of the tire.
6. The method for evaluating the damage resistance of a multi-axle special vehicle tire system considering the battle requirements as claimed in claim 1, wherein in step 2.3.2, if the vehicle running speed provided by the sum of the longitudinal forces of the tires in the tire system is less than the minimum maneuvering speed required by the vehicle battle, the tire system fails:
v＜v xmin
in the formula, v xmin For the minimum maneuvering speed required for the vehicle to fight, v is solved by the following formula:
Figure FDA0003154859660000042
wherein m is the sprung mass, F xi For each tire longitudinal force: f xi ＝f(α,λ,F zi ) α is a tire slip angle, λ is a tire slip ratio; f. of Fx Is the sum of the longitudinal friction of the tire, the friction of the non-driving wheels and the wind resistance of the vehicle.
7. The method for evaluating the damage resistance of the multi-axle special vehicle tire system considering the battle requirements as claimed in claim 1, wherein in the step 2.3.3, LTR is adopted as the rollover evaluation index,
Figure FDA0003154859660000051
wherein the content of the first and second substances,
Figure FDA0003154859660000052
to a roll angle, a y The lateral acceleration is, e is the distance from the roll center to the center of mass, g is the gravitational acceleration, and B is the wheel wheelbase;
if the LTR value in the tire system is greater than the vehicle rollover critical LTR value, the tire system fails, that is:
Figure FDA0003154859660000053
8. the method for evaluating the damage resistance of the multi-axle special vehicle tire system in consideration of the combat requirement as claimed in claim 1, wherein the step 2.4 comprises the following substeps:
(1): establishing a random model of the explosive core:
Figure FDA0003154859660000054
wherein (x, y, z) is the coordinates of the explosive center of the attacking warhead, (x) 0 ,y 0 ,h 0 ) Initial aiming coordinates of the attacking warhead, xi is an empirical coefficient related to the attacking warhead, CEP is a circular probability deviation, xi 1 ，ξ 2 Are mutually independent random variables;
(2): the distribution of the obtained fragment fields is:
Figure FDA0003154859660000055
in the formula, mu is the average mass of fragments, omega is the related coefficient of charge, t is the shell wall thickness, d is the shell inner diameter, m p Grading the quality of the fragments;
(3): the distribution of the impact field was obtained as:
Figure FDA0003154859660000061
in the formula, r is the distance between the center of burst and the target;
(5): intersecting the overall arrangement of the tire system with the breaker field and the shock wave field;
(6) Calculating the probability:
the damage probability of the fragment to the target is as follows:
Figure FDA0003154859660000062
wherein E b For the specific kinetic energy when the fragment hits the target, the calculation formula is as follows:
Figure FDA0003154859660000063
h is the equivalent aluminum thickness of the target protection;
the probability of damage to the target by the shock wave is:
Figure FDA0003154859660000064
wherein p is t Is the targeted resistance.
9. The method for evaluating the damage resistance of the multi-axle special vehicle tire system considering the combat requirement as claimed in claim 1, wherein in the step 2.5, the damage degree of the tire system is divided into three grades of meeting the combat requirement, meeting the driving requirement and failing, the damage probability and the damage resistance probability under different grades are calculated according to the number of the tires lost in each grade, and the number of the tires lost in each grade is defined as n 1 ，n 2 ，n 3 Then:
the damage probability meeting the battle requirements is P 1 *P 2 *.....P n1 The damage resistance probability is 1-P 1 *P 2 *.....P n1 ；
The damage probability meeting the driving requirement is P 1 *P 2 *.....P n2 With a damage resistance probability of 1-P 1 *P 2 *.....P n2 ；
The failure probability of satisfying the failure requirement is P 1 *P 2 *.....P n3 The damage resistance probability is 1-P 1 *P 2 *.....P n3 。
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地地导弹突击机场对停放飞机的毁伤效果评估;秦宇飞等;《计算机仿真》;20090215(第02期);全文 *
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Inventor after: Gao Qinhe

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