CN107577843A - Collision waveform and the evaluation method of constrained system characteristic coupled relation - Google Patents
Collision waveform and the evaluation method of constrained system characteristic coupled relation Download PDFInfo
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Abstract
The invention discloses the evaluation method of collision waveform and constrained system characteristic coupled relation, the problem of overcoming CAE emulation technologies amount of calculation be huge and time-consuming when studying body construction and occupant restraint system performance coupled relation, step：1. the foundation of occupant's response surface based on one degree of freedom modeling：1) parameters for shape characteristic of double-trapezoidal wave and Trilinear constraint stiffness curve is defined:2) one degree of freedom modeling solves occupant's response surface；3) to response surface XY to being averaging respectively；2. occupant responds and collision waveform relation analysis of parameter：1) collision waveform parameter definition is supplemented；2) collision waveform basic parameter and A are extracted from occupant's response surfacevCorresponding relation, carry out linear regression analysis；3. collision waveform and the evaluation of constrained system characteristic coupled relation：1) collision waveform comprehensive evaluation index α foundation；2) constrained system comprehensive evaluation index β foundation；3) collision waveform and a of constrained system characteristic comprehensive evaluation indexoFoundation.
Description
Technical field
The present invention relates to the evaluation method of a kind of automotive body structure and constrained system coupling effect, more specifically
Say, the present invention relates to a kind of collision waveform and the evaluation method of constrained system characteristic coupled relation.
Background technology
Vehicle safety is together decided on by the minibus and the aspect of occupant restraint system two of body construction.Vehicle safety at present
Property development process be mainly complete vehicle structure minibus design after carry out constrained system matching again.With the two area researches
Go deep into, enterprise successively in all its bearings carry out minibus mechanical development and constrained system device exploitation.Car body minibus designs
Due to the preliminary stage in security development process, still direct relation can not be established with occupant injury, so mainly with larger
Energy absorption characteristics and good front-end architecture rigidity etc. are used as design considerations.Later stage rank of the constrained system design in security exploitation
Section, it sometimes appear that the phenomenon that matching constraint systematic parameter occupant injury always remains high in any case.There is this phenomenon
The main reason for be that shortcoming is considered to body construction and occupant restraint system performance coupled relation in conceptual phase, cause car
Body minibus designs to disconnect between constrained system design.If go out at safety Design initial stage from coupled relation angle
Hair, propose the minibus and occupant restraint requirement of system design of body construction, it is possible to matching effect is carried out from macroscopically whole
Body control.
Because body construction and occupant restraint system performance coupled relation affecting parameters are numerous, and parameters are mutually dry
Disturb, if all parameter levels are put into simulation model, amount of calculation will be very huge, so being unfavorable for carrying out by emulation mode
Coupled relation is studied.Domestic and foreign scholars expand coupled relation research from collision dynamics theoretic, have obtained a series of important
Conclusion, but there has been no clear and definite evaluation index.Further strengthen contacting for coupled relation theoretical research and engineering practice, for referring to
Lead the design of body construction minibus and constrained system matched design is significant.
The content of the invention
The technical problems to be solved by the invention are to overcome CAE emulation technologies in research body construction and occupant restraint system
Unite characteristic coupled relation when amount of calculation is huge and time-consuming problem, there is provided a kind of collision waveform and constrained system characteristic coupling
The evaluation method of conjunction relation.
In order to solve the above technical problems, the present invention adopts the following technical scheme that realization：Described collision waveform with about
The step of evaluation method of beam system characteristic coupled relation, is as follows：
1) foundation of occupant's response surface based on one degree of freedom modeling：
(1) parameters for shape characteristic of double-trapezoidal wave and Trilinear constraint stiffness curve is defined:
(2) one degree of freedom modeling solves occupant's response surface；
(3) to response surface XY to being averaging respectively：
Occupant's response is averaging towards X-coordinate direction, obtains the flat of all occupant's responses corresponding to each collision waveform
Average, with symbol AvRepresent；
Occupant's response is averaging towards Y-coordinate direction, you can obtain all occupants corresponding to each constrained system rigidity
The average value of response, with symbol ArRepresent；
2) occupant's response and collision waveform relation analysis of parameter：
(1) the definition supplement of collision waveform parameter；
(2) collision waveform basic parameter and A are extracted from occupant's response surfacevCorresponding relation, linear regression analysis is carried out,
And relative coefficient is collected；
3) collision waveform and the evaluation of constrained system characteristic coupled relation：
(1) collision waveform comprehensive evaluation index α foundation；
(2) constrained system comprehensive evaluation index β foundation；
(3) collision waveform and a of constrained system characteristic comprehensive evaluation indexoFoundation.
The parameters for shape characteristic of definition double-trapezoidal wave and Trilinear constraint stiffness curve described in technical scheme refers to:
G1For the first rank acceleration magnitude, i.e. acceleration magnitude corresponding to BC sections；The duration of first rank acceleration is tBC,
Unit is g；
G2For second-order acceleration magnitude, i.e., acceleration magnitude corresponding to DE sections, the duration of second-order acceleration is tDE, it is single
Position is g；
s1、s2、s3Respectively straight line AB, CD and resilience section EF slope；
C1For the conquassation amount of motor head, unit m；
CmaxFor the maximum dynamic conquassation amount of car body front-end architecture, unit m；
k1It is safety belt specific stiffness for OP slope over 10, OP sections correspond to the safety belt linear extension stage；
GLFor limiter acceleration；
k2It is air bag rigidity for QR slope over 10；
D1When reaching limiter value for belt force occupant relative to car body moving displacement；
D2For air bag start effect when occupant relative to car body moving displacement.
The definition supplement of collision waveform parameter described in technical scheme refers to：
1) ladder compares i：Define two rank height G of equivalent double-trapezoidal wave2With G1The ratio between be ladder ratio；
2) width compares w：Width is than the conquassation amount C for motor head1With maximum dynamic conquassation amount CmaxThe ratio between；
3) mean rigidity KAE：Mean rigidity is the second-order height G of equivalent double-trapezoidal wave2With maximum dynamic conquassation amount Cmax
The ratio between；
4) energy density compares a：Energy density is than the ratio for motor head energy absorption and the total energy absorption of car body front-end architecture；
In formula:v0For impact velocity, unit m/s；G1For the height of first step, unit g；tCWhen being collided for engine
Carve, unit s；s1For the slope of straight line AB sections, unit g/s.
5) the waveform centre of form (to, Go)：The waveform centre of form refers to the geometry that acceleration-time graph surrounds with time shaft
The centre of form, the abscissa of the centre of form are referred to as centre of form moment to, centre of form ordinate is referred to as centre of form acceleration Go；
In formula:T is the time, unit s；For car body acceleration, unit g.
One degree of freedom modeling described in technical scheme solves occupant's response surface and referred to：
(1) vehicle and occupant are reduced to lumped mass block M and m, car by the one degree of freedom modeling for solving the response surface respectively
The Collapse of Concrete of body structure in an impact is reduced to spring rate K compression process, and is approximately equivalent double-trapezoidal wave；Constraint system
The deformation process of system in an impact is reduced to the compression process of rigidity k, and is approximately Trilinear constraint rigidity；Occupant is two
Retarded motion forward is done under the common effect of vibration of individual spring vibration system, therefore the size of occupant's response is by two spring vibrations
The coupled relation of dynamic system determines；
(2) according to the form parameter scope and step-length set, 1 is shown in Table, can obtain 3204 different double trapezoid waveforms
With 3136 Trilinear constraint rigidity；The double trapezoid waveform of acquisition and constrained system rigidity are subjected to one-to-one combination, using
Some one degree of freedom modeling iterative algorithms quickly carry out occupant to each combination and respond solution, obtain about 10,000,000 differences altogether
The matching result of double trapezoid waveform and different constrained system rigidity, such as table 2, a in table0For occupant's acceleration peak value；
The scope and step-length of the form parameter of table 1
The different collision waveform parameters of table 2 and the matching result of constrained system stiffness parameters
(3) numbered using different double trapezoid waveforms from 1 to 3204 as X-coordinate, with different constrained system rigidity from 1 to 3136
Numbering is used as Y-coordinate, using occupant's acceleration peak value as Z coordinate, can be plotted in different collision waveforms and different constrained systems are firm
The occupant's acceleration peak value response surface spent under combined situation, referred to as occupant's response surface.
The foundation of collision waveform comprehensive evaluation index α described in technical scheme refers to：
This step mainly establishes wave-average filtering response AvDirect quantitative relationship between collision waveform parameter, determines function
P, realizes the preliminary independent evaluation of collision waveform, and the technical program uses the method approximation A of multiple regressionvWith collision waveform
The functional relation P of parameter；
G among collision waveform parametero、tE、KAE、G2It is higher but basic in view of collision waveform with the correlation of occupant's response
The importance of parameter, so the technical program chooses G1、G2、tC、tE、Go、KAEThis six collision waveform parameters carry out multiple regression
Analysis；Complexity and mutual relation in view of waveform parameter, the technical program construct polynary quadratic regression mould
Type, this six parameters are used into x respectively for convenience of description1、x2……x6Six variables represent that corresponding dependent variable is Av, it is polynary secondary
Regression model expression formula is as follows：
Wherein a0For constant term, a1、a2……a6For Monomial coefficient, a(1,1),a(1,2)……a(6,6)For secondary term coefficient.
Being rejected by regression analysis influences less project, wherein tCItem is rejected completely, remaining 7 to be had a great influence to regression result
Project, each project and corresponding coefficient are as shown in table 4.
The collision waveform parameter quadratic regression of table 4 corresponds to project and coefficient
The analysis result of the even experiment design is as shown in table 5, where it is determined that coefficient be close to 1, F statistics compared with
Greatly, the P values of inspection are 0, illustrate that regression result is preferable；
The analysis result of the collision waveform parameter quadratic regression model of table 5
AvThe average level of collision waveform is represented, by the A for contrasting different collision waveformsvSize can realize collision ripple
The superior and inferior evaluating of shape, in order that AvNondimensionalization and and ArBetween same chemotactic, the technical program uses min-max standardization sides
Method, to AvMake standardization, obtain nondimensional collision waveform evaluation index, be defined as that " collision waveform overall merit refers to
Mark ", is represented, collision waveform comprehensive evaluation index α computational methods are with symbol α：
A is determined according to occupant's response surfacevMaximum is 79.28g, minimum value 36.70g, according to formula (7) and (8), is obtained
It is to α calculation formula：
α is distributed between 0 to 1, is considered from occupant's acceleration angle, and the smaller corresponding collision waveform of the value is better.But
Occur that α is more than 1 or the situation less than 0 when the usual range that collision waveform parameter determines beyond the technical program.
The foundation of constrained system comprehensive evaluation index β described in technical scheme refers to：
This step mainly establishes ArDirect quantitative relationship between constrained system stiffness parameters, function Q is determined, realized about
The preliminary independent evaluation of beam system characteristic；This step equally uses the method approximation A of multiple regressionrWith constrained system rigidity
The functional relation Q of parameter；
Because constrained system stiffness parameters are less, the technical program chooses all constrained system stiffness parameters k1、k2、GL、D2
Even experiment design is built, this four parameters are used into y respectively for convenience of description1、y2、y3、y4Four variables represent, corresponding
Dependent variable is Ar, even experiment design expression formula is as follows：
Wherein b0For constant term, b1、b2、b3、b4For Monomial coefficient, b(1,1)、b(1,2)……b(4,4)For secondary term coefficient；
Being rejected by regression analysis influences less project, wherein parameter D2Rejected completely, be left 7 to be had a great influence to regression model
Individual project, each project and corresponding coefficient are as shown in table 6；
The constrained system stiffness parameters quadratic regression of table 6 corresponds to project and coefficient
The analysis result of the even experiment design is as shown in table 7, where it is determined that coefficient is larger close to 1, F statistics,
The P values of inspection are 0, illustrate that regression result is preferable；
The analysis result of the constrained system stiffness parameters quadratic regression model of table 7
ArThe average level of constrained system rigidity is represented, by the A for contrasting different constrained system rigidityrSize can be real
The superior and inferior evaluating of existing constrained system rigidity, in order that ArNondimensionalization and and AvBetween same chemotactic, marked herein using min-max
Quasi-ization method, to ArMake standardization, obtain the evaluation index of dimensionless constrained system characteristic, be defined as that " constrained system is comprehensive
Close evaluation index ", represented with symbol beta, its computational methods is：
A is determined according to occupant's response surfacerMaximum is 69.12g, minimum value 44.60g.According to formula (10) and (11),
β is obtained to be calculated as：
β is distributed between 0 to 1, is considered from occupant's acceleration angle, and the smaller corresponding constrained system rigidity of the value is better；
But when the usual range that constrained system stiffness parameters determine beyond the technical program it is possible that β is more than 1 or less than 0
Situation.
Collision waveform and a of constrained system characteristic comprehensive evaluation index described in technical schemeoFoundation refer to：
This step mainly establishes occupant's acceleration responsive aoCommented with collision waveform comprehensive evaluation index α and constrained system synthesis
Valency index β direct quantitative relationship, so as to be realized according to the preliminary independent evaluation result of collision waveform and constrained system characteristic
Overall coupled relation evaluation, because α and β is respectively by AvAnd ArStandardization obtains, so aoAnd AvWith ArBetween incremental letter
Number R can be equivalent to aoIncreasing function relation R between α and β；Corresponding relation that can be by occupant's response surface according to α and β, draw
Go out alpha-beta-aoResponse surface, for the ease of observation, response surface is replaced with grid, whole curved surface shows preferable increasing trend；
The technical program uses the method approximation a of surface fittingoIncreasing function relation R between α and β, with α with
β is independent variable, to alpha-beta-aoResponse surface carries out Quadratic Surface Fitting, shown in surface fitting such as formula (13), wherein c0、c1、c2、
c3、c4、c5For each term coefficient, it is as shown in table 8 that every coefficient value is obtained by least square method；
ao=c0+c1α+c2β+c3α2+c4αβ+c5β2 (13)
Alpha-beta-a of table 8oResponse surface Quadratic Surface Fitting result
Because α and β square term coefficient is close to 0, so surface fitting formula can be reduced to：
aoThe α β (14) of+161.8 β of=280.5+335.1 α+168
The coefficient of determination R of the fitting result2Reach 0.986, fitting precision is higher.
Compared with prior art the beneficial effects of the invention are as follows：
1. a kind of collision waveform of the present invention and the evaluation method of constrained system characteristic coupled relation can be by touching
Hitting waveform synthesis evaluation index α and constrained system comprehensive evaluation index β can realize that collision waveform and the coupling of constrained system characteristic are closed
System's evaluation, and intuitively find the link to be gone wrong among collision waveform and constrained system parameter designing process.
2. a kind of collision waveform of the present invention and the evaluation method of constrained system characteristic coupled relation establish alpha-beta-ao
Response surface fitting surface, it can estimate that occupant adds by collision waveform comprehensive evaluation index α and constrained system comprehensive evaluation index β
Velocity peak values, control errors that are simple, conveniently and with one degree of freedom modeling calculating are 10%.
Brief description of the drawings
The present invention is further illustrated below in conjunction with the accompanying drawings：
Fig. 1 is the flow chart of collision waveform of the present invention and the evaluation method of constrained system characteristic coupled relation；
Fig. 2-a are collision waveform of the present invention and car body in the evaluation method of constrained system characteristic coupled relation-multiply
Member's single-degree-of-freedom solving model schematic diagram；
Fig. 2-b are collision waveform of the present invention and car body in the evaluation method of constrained system characteristic coupled relation-multiply
The double-trapezoidal wave schematic diagram that member's single-degree-of-freedom solving model uses；
Fig. 2-c are collision waveform of the present invention and car body in the evaluation method of constrained system characteristic coupled relation-multiply
The three linear rigidity curve synoptic diagrams that member's single-degree-of-freedom solving model uses；
Fig. 3-a are collision waveform of the present invention and time-domain etc. in the evaluation method of constrained system characteristic coupled relation
Imitate double-trapezoidal wave shape parameter schematic diagram；
Fig. 3-b are collision waveform of the present invention and displacement fields etc. in the evaluation method of constrained system characteristic coupled relation
Imitate double-trapezoidal wave shape parameter schematic diagram；
Fig. 4 is collision waveform of the present invention and Trilinear constraint in the evaluation method of constrained system characteristic coupled relation
Rigidity characteristic parameter schematic diagram；
Fig. 5 is the schematic diagram of collision waveform of the present invention and the evaluation method of constrained system characteristic coupled relation；
Fig. 6 is the alpha-beta-a of collision waveform of the present invention and the evaluation method of constrained system characteristic coupled relationoResponse
Face figure；
Fig. 7 is that collision waveform of the present invention and extraction in the evaluation method of constrained system characteristic coupled relation six are double
Trapezoidal waveform；
Fig. 8 is that collision waveform of the present invention and collision waveform in the evaluation method of constrained system characteristic coupled relation are comprehensive
Close evaluation index α and occupant's chest acceleration peak value corresponding relation；
Fig. 9 is that collision waveform of the present invention and constrained system in the evaluation method of constrained system characteristic coupled relation are comprehensive
Close evaluation index β and occupant's chest acceleration peak value corresponding relation；
Figure 10 is collision waveform of the present invention and occupant's chest in the evaluation method of constrained system characteristic coupled relation
Acceleration peak value relativity figure.
Embodiment
The present invention is explained in detail below in conjunction with the accompanying drawings：
Refering to Fig. 1, the step of the evaluation method of collision waveform of the present invention and constrained system characteristic coupled relation such as
Under:
1. the foundation of occupant's response surface based on one degree of freedom modeling
1) parameters for shape characteristic of double-trapezoidal wave and Trilinear constraint stiffness curve is defined
Refering to Fig. 3-a to Fig. 3-b, collision waveform of the present invention and the evaluation method of constrained system characteristic coupled relation
The middle collision waveform that uses is equivalent double-trapezoidal wave, and A, B, C, D, E, F are the characteristic point of equivalent double-trapezoidal wave in Fig. 3-a；Its
In：A is that point occurs for collision, is 0 at the time of it is corresponding；B is the point that front longitudinal encounters obstacle；C is engine and obstacle contact point,
It is t at the time of correspondingC；D is the point that roof side rail encounters obstacle；E is that car body displacement reaches maximum dynamic conquassation amount point, and it is corresponding
At the time of be tE, tEWith maximum dynamic conquassation moment tmaxIt is equal；F is collision end point；
G1For the first rank acceleration magnitude, i.e. acceleration magnitude corresponding to BC sections；The duration of first rank acceleration is tBC,
Unit is g；
G2For second-order acceleration magnitude, i.e., acceleration magnitude corresponding to DE sections, the duration of second-order acceleration is tDE, it is single
Position is g；
s1、s2、s3Respectively straight line AB, CD and resilience section EF slope；
C1For the conquassation amount of motor head, unit m；
CmaxFor the maximum dynamic conquassation amount of car body front-end architecture, unit m.
Refering to Fig. 4, used in the evaluation method of collision waveform of the present invention and constrained system characteristic coupled relation
Constrained system stiffness curve is Trilinear constraint stiffness curve.O, P, Q, R in Fig. 4 are the features of " Trilinear constraint rigidity "
For collision point occurs for point, wherein O；P points are safety belt force limiting device application point；Q points are that air bag acts on starting point；R points are
Maximum relative displacement point.
k1It is safety belt specific stiffness for OP slope over 10, OP sections correspond to the safety belt linear extension stage；
GLFor limiter acceleration；
k2It is air bag rigidity for QR slope over 10；
D1When reaching limiter value for belt force occupant relative to car body moving displacement；
D2For air bag start effect when occupant relative to car body moving displacement.
2) one degree of freedom modeling solves occupant's response surface
Collision waveform of the present invention and the evaluation method of constrained system characteristic coupled relation are using occupant's response surface as data
Basis.The response surface is to carry out occupant's acceleration responsive using one degree of freedom modeling iterative algorithm fast and accurately to solve, and is obtained
Different collision waveform parameters and constrained system stiffness parameters matching result.
(1) Fig. 2-a to Fig. 2-c are referred to, vehicle is reduced to by the one degree of freedom modeling for solving the response surface respectively with occupant
Lumped mass block M and m, the Collapse of Concrete of body construction in an impact is reduced to spring rate K compression process, and is approximately
Imitate double-trapezoidal wave；The deformation process of constrained system in an impact is reduced to the compression process of rigidity k, and is approximately three linear
Constrain rigidity；Occupant does retarded motion forward under the common effect of vibration of two spring vibration systems, therefore occupant responds
Size determined by the coupled relation of two spring vibration systems.
(2) according to the form parameter scope and step-length set, 1 is shown in Table, can obtain 3204 different double trapezoid waveforms
With 3136 Trilinear constraint rigidity.The double trapezoid waveform of acquisition and constrained system rigidity are subjected to one-to-one combination, using
Some one degree of freedom modeling iterative algorithms quickly carry out occupant to each combination and respond solution, obtain about 10,000,000 differences altogether
The matching result of double trapezoid waveform and different constrained system rigidity, such as table 2, a in table0For occupant's acceleration peak value.
The scope and step-length of the form parameter of table 1
The different collision waveform parameters of table 2 and the matching result of constrained system stiffness parameters
(3) numbered using different double trapezoid waveforms from 1 to 3204 as X-coordinate, with different constrained system rigidity from 1 to 3136
Numbering is used as Y-coordinate, using occupant's acceleration peak value as Z coordinate, can be plotted in different collision waveforms and different constrained systems are firm
The occupant's acceleration peak value response surface spent under combined situation, referred to as occupant's response surface.
3) to response surface XY to being averaging respectively
Occupant's response is averaging towards X-coordinate direction, obtains the flat of all occupant's responses corresponding to each collision waveform
Average, with symbol AvRepresent；Occupant's response is averaging towards Y-coordinate direction, you can it is corresponding to obtain each constrained system rigidity
All occupants response average value, with symbol ArRepresent.
2. occupant responds and collision waveform relation analysis of parameter
1) the definition supplement of collision waveform parameter is as follows：
(1) ladder compares i：Define two rank height G of equivalent double-trapezoidal wave2With G1The ratio between be ladder ratio；
(2) width compares w：Width is than the conquassation amount C for motor head1With maximum dynamic conquassation amount CmaxThe ratio between；
(3) mean rigidity KAE：Mean rigidity is the second-order height G of equivalent double-trapezoidal wave2With maximum dynamic conquassation amount Cmax
The ratio between；
(4) energy density compares a：Energy density is than for motor head energy absorption and the total energy absorption of car body front-end architecture
Than；
In formula:v0For impact velocity, unit m/s；G1For the height of first step, unit g；tCWhen being collided for engine
Carve, unit s；s1For the slope of straight line AB sections, unit g/s.
(5) the waveform centre of form (to, Go)：The waveform centre of form refers to the geometry that acceleration-time graph surrounds with time shaft
The centre of form, the abscissa of the centre of form are referred to as centre of form moment to, centre of form ordinate is referred to as centre of form acceleration Go；
In formula:T is the time, unit s；For car body acceleration, unit g.
2) collision waveform basic parameter and A are extracted from occupant's response surfacevCorresponding relation, utilize Origin mapping softwares
Linear regression analysis is carried out, and relative coefficient is collected, as shown in table 3；
The collision waveform parameter of table 3 and AvCorrelation
As shown in Table 3, Go、tE、KAE、G2It is higher with the correlation of occupant's response.
3. collision waveform and the evaluation of constrained system characteristic coupled relation
On the basis of collision waveform and constrained system stiffness parameters correlation analysis, research collision waveform, constraint system
Characteristic of uniting and the between the two method for quantitatively evaluating of coupled relation.AvAlthough can the approximate quality for characterizing collision waveform,
Its calculating process stills need the intervention of constrained system parameter.Establish AvDirect quantitative relationship between collision waveform parameter, such as
Form shown in the function P of formula 1, constrained system parameter can be departed from and realize that collision waveform is preliminary only according to collision waveform parameter
Independent quantitatively evaluating；Establish ArWith the quantitative relationship between constrained system stiffness parameters, the form as shown in the function Q of formula 2 can be with
Depart from collision waveform and realize the preliminary independent quantitatively evaluating of constrained system characteristic according only to constrained system stiffness parameters；
Av=P (G1,G2,tE,tC,...) (4)
Ar=Q (k1,k2,GL,D1,...) (5)
According to occupant's response surface, work as AvAnd ArWhen value determines, there is unique occupant's acceleration responsive aoIt is corresponding.Due to row
Being incremented by for rule is integrally presented in occupant's response surface after sequence, it is believed that occupant responds aoWith AvAnd ArBetween exist it is a kind of be incremented by letter
Number relation, the form as shown in the function R of formula 3, can thus set up collision waveform and individually quantify with constrained system characteristic
Evaluate the relation between overall couple；
ao=R (Av,Ar) (6)
Refering to Fig. 5, determine that above functional relation can establish whole coupled relation evaluation method, evaluation method step master
Including：
(1) function P is determined using the method for multiple regression, so as to realize that collision waveform is preliminary according to collision waveform parameter
Individually evaluation；
(2) function Q is determined using the method for multiple regression, so as to realize constrained system spy according to constrained system stiffness parameters
Property preliminary independent evaluation；
(3) by the surface fitting function of MATLAB softwares, function R is determined, so as to be according to collision waveform and constraint
The preliminary independent evaluation result of system characteristic realizes overall coupled relation evaluation.
1) collision waveform comprehensive evaluation index α foundation
This step mainly establishes wave-average filtering response AvDirect quantitative relationship between collision waveform parameter, determines function
P, realize the preliminary independent evaluation of collision waveform.The technical program uses the method approximation A of multiple regressionvWith collision waveform
The functional relation P of parameter.
G among collision waveform parametero、tE、KAE、G2It is higher but basic in view of collision waveform with the correlation of occupant's response
The importance of parameter, so the technical program chooses G1、G2、tC、tE、Go、KAEThis six collision waveform parameters carry out multiple regression
Analysis.Complexity and mutual relation in view of waveform parameter, the technical program construct polynary quadratic regression mould
Type.This six parameters are used into x respectively for convenience of description1、x2……x6Six variables represent that corresponding dependent variable is Av, it is polynary secondary
Regression model expression formula is as follows：
Wherein a0For constant term, a1、a2……a6For Monomial coefficient, a(1,1),a(1,2)……a(6,6)For secondary term coefficient.
Being rejected by regression analysis influences less project, wherein tCItem is rejected completely, remaining 7 to be had a great influence to regression result
Project, each project and corresponding coefficient are as shown in table 4.
The collision waveform parameter quadratic regression of table 4 corresponds to project and coefficient
The analysis result of the even experiment design is as shown in table 5.Where it is determined that coefficient be close to 1, F statistics compared with
Greatly, the P values of inspection are 0, illustrate that regression result is preferable.
The analysis result of the collision waveform parameter quadratic regression model of table 5
AvThe average level of collision waveform is represented, by the A for contrasting different collision waveformsvSize can realize collision ripple
The superior and inferior evaluating of shape.In order that AvNondimensionalization and and ArBetween same chemotactic, the technical program uses min-max standardization sides
Method, to AvMake standardization, obtain nondimensional collision waveform evaluation index, be defined as that " collision waveform overall merit refers to
Mark ", is represented with symbol α.Collision waveform comprehensive evaluation index α computational methods are：
A is determined according to occupant's response surfacevMaximum is 79.28g, minimum value 36.70g.According to formula (7) and (8), obtain
It is to α calculation formula：
α is distributed between 0 to 1, is only considered from occupant's acceleration angle, and the smaller corresponding collision waveform of the value is better.So
And when the usual range that collision waveform parameter determines beyond the technical program it is possible that α is more than 1 or the feelings less than 0
Condition.
2) constrained system comprehensive evaluation index β foundation
This step mainly establishes ArDirect quantitative relationship between constrained system stiffness parameters, function Q is determined, realized about
The preliminary independent evaluation of beam system characteristic；This step equally uses the method approximation A of multiple regressionrWith constrained system rigidity
The functional relation Q of parameter.
Because constrained system stiffness parameters are less, the technical program chooses all constrained system stiffness parameters k1、k2、GL、D2
Build even experiment design.This four parameters are used into y respectively for convenience of description1、y2、y3、y4Four variables represent, corresponding
Dependent variable is Ar.Even experiment design expression formula is as follows：
Wherein b0For constant term, b1、b2、b3、b4For Monomial coefficient, b(1,1)、b(1,2)……b(4,4)For secondary term coefficient.
Being rejected by regression analysis influences less project, wherein parameter D2Rejected completely, be left 7 to be had a great influence to regression model
Individual project, each project and corresponding coefficient are as shown in table 6.
The constrained system stiffness parameters quadratic regression of table 6 corresponds to project and coefficient
The analysis result of the even experiment design is as shown in table 7.Where it is determined that coefficient is larger close to 1, F statistics,
The P values of inspection are 0, illustrate that regression result is preferable.
The analysis result of the constrained system stiffness parameters quadratic regression model of table 7
ArThe average level of constrained system rigidity is represented, by the A for contrasting different constrained system rigidityrSize can be real
The superior and inferior evaluating of existing constrained system rigidity.In order that ArNondimensionalization and and AvBetween same chemotactic, marked herein using min-max
Quasi-ization method, to ArMake standardization, obtain the evaluation index of dimensionless constrained system characteristic, be defined as that " constrained system is comprehensive
Close evaluation index ", represented with symbol beta, its computational methods is：
A is determined according to occupant's response surfacerMaximum is 69.12g, minimum value 44.60g.According to formula (10) and (11),
β is obtained to be calculated as：
β is distributed between 0 to 1, is only considered from occupant's acceleration angle, and the smaller corresponding constrained system rigidity of the value is got over
It is good.But when the usual range that constrained system stiffness parameters determine beyond the technical program it is possible that β is more than 1 or small
In 0 situation.
3) collision waveform and a of constrained system characteristic comprehensive evaluation indexoFoundation
Can be respectively to collision waveform by collision waveform comprehensive evaluation index α and constrained system comprehensive evaluation index β
And constrained system characteristic makes preliminary independent evaluation.But the final protecting effect of occupant is by collision waveform and constraint
Both system performances together decide on.Even if collision waveform design is fine, if corresponding poor constrained system characteristic, it is likely that total
Body does not reach preferable passenger protection effect, and it is before ensureing one of constrained system compatible matching that can only say good collision waveform
Put forward condition.Same good constrained system characteristic is also a precondition of collision waveform compatible matching.
This step mainly establishes occupant's acceleration responsive aoCommented with collision waveform comprehensive evaluation index α and constrained system synthesis
Valency index β direct quantitative relationship, so as to be realized according to the preliminary independent evaluation result of collision waveform and constrained system characteristic
Overall coupled relation evaluation.Because α and β are respectively by AvAnd ArStandardization obtains, so aoWith AvAnd ArBetween incremental letter
Number R can be equivalent to aoIncreasing function relation R between α and β.Corresponding relation that can be by occupant's response surface according to α and β, draw
Go out alpha-beta-aoResponse surface, for the ease of observation, response surface is replaced with grid, as shown in fig. 6, whole curved surface shows and preferably passed
Increasing trend.
The technical program uses the method approximation a of surface fittingoIncreasing function relation R between α and β.With α and
β is independent variable, to alpha-beta-aoResponse surface carries out Quadratic Surface Fitting, shown in surface fitting such as formula (13).Wherein c0、c1、c2、
c3、c4、c5For each term coefficient.It is as shown in table 8 that every coefficient value is obtained by least square method.
ao=c0+c1α+c2β+c3α2+c4αβ+c5β2 (13)
Alpha-beta-a of table 8oResponse surface Quadratic Surface Fitting result
Because α and β square term coefficient is close to 0, so surface fitting formula can be reduced to：
aoThe α β (14) of+161.8 β of=280.5+335.1 α+168
The coefficient of determination R of the fitting result2Reach 0.986, fitting precision is higher.
Embodiment 1
M6 vehicles collision waveform and the evaluation of constrained system characteristic coupled relation
The present embodiment according to collision waveform and constrained system characteristic coupled relation evaluation method to the collision waveforms of M6 vehicles,
Constrained system characteristic and both coupled relations make evaluation.The collision waveform parameter and constrained system stiffness parameters of M6 vehicles
It is shown in Table 9.Evaluation method step is as follows：
Table 9M6 vehicles collision waveform and constrained system stiffness parameters
1. establish occupant's response surface based on one degree of freedom modeling
According to the equivalent double-trapezoidal wave set in table 1 and the span and step of the form parameter of three linear rigidity curves
It is long, it can obtain 3204 different double trapezoid waveforms and 3136 Trilinear constraint rigidity.By the double trapezoid waveform of acquisition and about
Beam system rigidity carries out one-to-one combination, and quickly occupant is carried out to each combination using existing one degree of freedom modeling iterative algorithm
Response solves, and obtains the matching result of about 10,000,000 different double trapezoid waveforms and different constrained system rigidity altogether, such as table 2,
A in table0For occupant's acceleration peak value.
Numbered from 1 to 3204 as X-coordinate using different double trapezoid waveforms, compiled with different constrained system rigidity from 1 to 3136
Number Y-coordinate is used as, using occupant's acceleration peak value as Z coordinate, different collision waveforms and different constrained system rigidity can be plotted in
Occupant's acceleration peak value response surface under combined situation, referred to as occupant's response surface
Occupant's response is averaging towards X-coordinate direction, obtains the flat of all occupant's responses corresponding to each collision waveform
Average, with symbol AvRepresent.The response surface is averaging to Y-coordinate direction, you can obtain corresponding to each constrained system rigidity
The average value of all responses, with symbol ArRepresent.
2. occupant responds and collision waveform relation analysis of parameter
Collision waveform basic parameter (G is extracted from occupant's response surface1、G2、C1、Cmax、tC、tE、i、w、KAE、a、Go、to)
With AvCorresponding relation, linear regression analysis is carried out, and relative coefficient is collected, as shown in table 3.As shown in Table 3, Go、tE、KAE、
G2It is higher with the correlation of occupant's response.
3. collision waveform and the evaluation of constrained system characteristic coupled relation
1) A is builtvWith collision waveform parameter (G1、G2、tE、GO、KAE) functional relation P (even experiment design), point
Analyse result such as table 5：
The analysis result of the collision waveform parameter quadratic regression model of table 5
Using min-max standardized methods, using formula (5) to AvMake standardization, obtain nondimensional collision ripple
Shape comprehensive evaluation index α.A is determined according to occupant's response surfacevMaximum is 79.28g, minimum value 36.70g.According to formula (7)
(8) it is formula (9), to obtain α calculating formulas；
The collision waveform comprehensive evaluation index α of M6 vehicles can be calculated using formula (9) according to parameter in table 9：
2) A is equally builtrWith constrained system stiffness parameters (k1、k2、GL) functional relation Q (even experiment design),
Analysis result such as table 6：
The constrained system stiffness parameters quadratic regression of table 6 corresponds to project and coefficient
Using min-max standardized methods, according to formula (7), to ArMake standardization, obtain nondimensional constraint system
Unite comprehensive evaluation index β.A is determined according to occupant's response surfacerMaximum is 69.12g, minimum value 44.60g.According to formula
(10) and (11), it is formula (12) to obtain β calculating formulas：
The constrained system comprehensive evaluation index of M6 vehicles can be calculated using formula (12) also according to parameter in table 9
β：
3) method approximation occupant's acceleration responsive a of surface fitting is usedoWith collision waveform comprehensive evaluation index α and
Increasing function relation R between constrained system comprehensive evaluation index β.Using α and β as independent variable, to alpha-beta-aoResponse surface carries out two
Secondary surface fitting, surface fitting formula is such as shown in (13), wherein c0、c1、c2、c3、c4、c5For each term coefficient.Pass through least square
It is as shown in table 8 that method obtains every coefficient value；
Alpha-beta-a of table 8oResponse surface Quadratic Surface Fitting result
α and β quadratic term are given up, surface fitting formula is：
aoThe α β (14) of+161.8 β of=280.5+335.1 α+168
Utilize alpha-beta-aoSurface fitting formula (14), occupant's acceleration responsive a of M6 vehicles can be calculatedo：
aoThe α β of+161.8 β of=280.5+335.1 α+168
=280.5+335.1 × 0.56+161.8 × 0.44+168 × 0.56 × 0.44
=580.74m/s2
The α and β calculating formula tried to achieve, and alpha-beta-ao surface fitting formula may be directly applied to any vehicle
Evaluation；
Evaluated from the collision waveform of M6 vehicles and the coupled relation of constrained system characteristic, occupant's acceleration peak value is
580.74m/s2More than 50g, show to match between the collision waveform of the vehicle and constrained system characteristic bad.β is smaller than α, phase
Collision waveform is more weaker for, can subsequently optimize collision waveform to reduce occupant's acceleration peak value.
Embodiment 2
The present embodiment uses M6 occupant restraint system simulation models herein, to of the present invention three in Madymo softwares
Individual standard diagrams do further checking.
Six double trapezoid waveforms that α is respectively 0,0.2,0.4,0.6,0.8,1 are have chosen from 3204 collision waveforms, such as
Shown in Fig. 8.It has chosen herein from 3136 constrained system rigidity corresponding six when β is respectively 0,0.2,0.4,0.6,0.8,1
Individual constrained system rigidity, its constrained system parameter, as shown in table 9.
The constrained system stiffness parameters of table 9 are converted into constrained system parameter
Using choose six waveforms successively as the acceleration field of M6 occupant restraint system simulation models, constrained system is not
Become, corresponding occupant's chest acceleration responsive curve is obtained by simulation calculation.Closed according to α and occupant's chest acceleration peak value
System, as shown in figure 8, both have higher uniformity.
The constrained system parameter of M6 occupant restraint system simulation models is sequentially adjusted in as six groups of constrained system parameters in table 9
Value, collision waveform is constant, and corresponding occupant's chest acceleration responsive curve is obtained by simulation calculation.According to β and occupant's chest
Acceleration peak value relation, as shown in figure 9, both have higher uniformity.
6 collision waveforms are brought into M6 occupant successively with 6 groups of constrained system parameter combined crosswises into 36 coupling conditions
Constrained system simulation model, 36 groups of occupant's chest accelerating curves are obtained by simulation calculation.Each occupant's chest is extracted to accelerate
Peak of curve is spent, is depicted as response surface, as shown in Figure 10, the response surface overall trend obtained with fitting formula is basically identical, multiplies
Member's chest acceleration peak value control errors are 10%.
Claims (7)
1. a kind of collision waveform and the evaluation method of constrained system characteristic coupled relation, it is characterised in that described collision waveform
The step of with the evaluation method of constrained system characteristic coupled relation, is as follows：
1) foundation of occupant's response surface based on one degree of freedom modeling：
(1) parameters for shape characteristic of double-trapezoidal wave and Trilinear constraint stiffness curve is defined:
(2) one degree of freedom modeling solves occupant's response surface；
(3) to response surface XY to being averaging respectively：
Occupant's response is averaging towards X-coordinate direction, obtains the average value of all occupant's responses corresponding to each collision waveform,
With symbol AvRepresent；
Occupant's response is averaging towards Y-coordinate direction, you can obtain all occupant's responses corresponding to each constrained system rigidity
Average value, with symbol ArRepresent；
2) occupant's response and collision waveform relation analysis of parameter：
(1) the definition supplement of collision waveform parameter；
(2) collision waveform basic parameter and A are extracted from occupant's response surfacevCorresponding relation, linear regression analysis is carried out, and will
Relative coefficient collects；
3) collision waveform and the evaluation of constrained system characteristic coupled relation：
(1) collision waveform comprehensive evaluation index α foundation；
(2) constrained system comprehensive evaluation index β foundation；
(3) collision waveform and a of constrained system characteristic comprehensive evaluation indexoFoundation.
2. according to the collision waveform described in claim 1 and the evaluation method of constrained system characteristic coupled relation, it is characterised in that
Described definition double-trapezoidal wave and the parameters for shape characteristic of Trilinear constraint stiffness curve refer to:
G1For the first rank acceleration magnitude, i.e. acceleration magnitude corresponding to BC sections；The duration of first rank acceleration is tBC, unit
For g；
G2For second-order acceleration magnitude, i.e., acceleration magnitude corresponding to DE sections, the duration of second-order acceleration is tDE, unit is
g；
s1、s2、s3Respectively straight line AB, CD and resilience section EF slope；
C1For the conquassation amount of motor head, unit m；
CmaxFor the maximum dynamic conquassation amount of car body front-end architecture, unit m；
k1It is safety belt specific stiffness for OP slope over 10, OP sections correspond to the safety belt linear extension stage；
GLFor limiter acceleration；
k2It is air bag rigidity for QR slope over 10；
D1When reaching limiter value for belt force occupant relative to car body moving displacement；
D2For air bag start effect when occupant relative to car body moving displacement.
3. according to the collision waveform described in claim 1 and the evaluation method of constrained system characteristic coupled relation, it is characterised in that
The definition supplement of described collision waveform parameter refers to：
1) ladder compares i：Define two rank height G of equivalent double-trapezoidal wave2With G1The ratio between be ladder ratio；
2) width compares w：Width is than the conquassation amount C for motor head1With maximum dynamic conquassation amount CmaxThe ratio between；
3) mean rigidity KAE：Mean rigidity is the second-order height G of equivalent double-trapezoidal wave2With maximum dynamic conquassation amount CmaxThe ratio between；
4) energy density compares a：Energy density is than the ratio for motor head energy absorption and the total energy absorption of car body front-end architecture；
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The abscissa of the centre of form is referred to as centre of form moment to, centre of form ordinate is referred to as centre of form acceleration Go；
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In formula:T is the time, unit s；For car body acceleration, unit g.
4. according to the collision waveform described in claim 1 and the evaluation method of constrained system characteristic coupled relation, it is characterised in that
Described one degree of freedom modeling solves occupant's response surface and referred to：
(1) vehicle and occupant are reduced to lumped mass block M and m, car body knot by the one degree of freedom modeling for solving the response surface respectively
The Collapse of Concrete of structure in an impact is reduced to spring rate K compression process, and is approximately equivalent double-trapezoidal wave；Constrained system exists
Deformation process in collision is reduced to the compression process of rigidity k, and is approximately Trilinear constraint rigidity；Occupant is in two bullets
Retarded motion forward is done under the common effect of vibration of spring vibrational system, therefore the size of occupant's response is by two spring vibration systems
The coupled relation of system determines；
(2) according to the form parameter scope and step-length that set, be shown in Table 1, can obtain 3204 different double trapezoid waveforms with
3136 Trilinear constraint rigidity；The double trapezoid waveform of acquisition and constrained system rigidity are subjected to one-to-one combination, using
One degree of freedom modeling iterative algorithm quickly carry out occupant to each combination and respond to solve, it is double to obtain about 10,000,000 differences altogether
The matching result of trapezoidal waveform and different constrained system rigidity, such as table 2, a in table0For occupant's acceleration peak value；
The scope and step-length of the form parameter of table 1
The different collision waveform parameters of table 2 and the matching result of constrained system stiffness parameters
(3) numbered from 1 to 3204 as X-coordinate using different double trapezoid waveforms, numbered with different constrained system rigidity from 1 to 3136
As Y-coordinate, using occupant's acceleration peak value as Z coordinate, different collision waveforms and different constrained system rigidity groups can be plotted in
Occupant's acceleration peak value response surface in the case of conjunction, referred to as occupant's response surface.
5. according to the collision waveform described in claim 1 and the evaluation method of constrained system characteristic coupled relation, it is characterised in that
Described collision waveform comprehensive evaluation index α foundation refers to：
This step mainly establishes wave-average filtering response AvDirect quantitative relationship between collision waveform parameter, function P is determined, it is real
The preliminary independent evaluation of existing collision waveform, the technical program use the method approximation A of multiple regressionvWith collision waveform parameter
Functional relation P；
G among collision waveform parametero、tE、KAE、G2It is higher with the correlation of occupant's response, but consider collision waveform basic parameter
Importance, so the technical program choose G1、G2、tC、tE、Go、KAEThis six collision waveform parameters carry out multiple regression point
Analysis；Complexity and mutual relation, the technical program in view of waveform parameter construct even experiment design,
This six parameters are used into x respectively for convenience of description1、x2……x6Six variables represent that corresponding dependent variable is Av, polynary secondary returning
Return model expression as follows：
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Regression analysis, which is rejected, influences less project, wherein tCItem is rejected completely, remaining 7 items being had a great influence to regression result
Mesh, each project and corresponding coefficient are as shown in table 4.
The collision waveform parameter quadratic regression of table 4 corresponds to project and coefficient
The analysis result of the even experiment design is as shown in table 5, where it is determined that coefficient is larger close to 1, F statistics, inspection
The P values tested are 0, illustrate that regression result is preferable；
The analysis result of the collision waveform parameter quadratic regression model of table 5
AvThe average level of collision waveform is represented, by the A for contrasting different collision waveformsvSize can realize collision waveform
Superior and inferior evaluating, in order that AvNondimensionalization and and ArBetween same chemotactic, the technical program uses min-max standardized methods, right
AvMake standardization, obtain nondimensional collision waveform evaluation index, " collision waveform comprehensive evaluation index " is defined as, with symbol
Number α represents that collision waveform comprehensive evaluation index α computational methods are：
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Calculating formula is：
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α is distributed between 0 to 1, is considered from occupant's acceleration angle, and the smaller corresponding collision waveform of the value is better.But work as and touch
Occur that α is more than 1 or the situation less than 0 when hitting the usual range that waveform parameter determines beyond the technical program.
6. according to the collision waveform described in claim 1 and the evaluation method of constrained system characteristic coupled relation, it is characterised in that
Described constrained system comprehensive evaluation index β foundation refers to：
This step mainly establishes ArDirect quantitative relationship between constrained system stiffness parameters, function Q is determined, realize constraint system
The preliminary independent evaluation of characteristic of uniting；This step equally uses the method approximation A of multiple regressionrWith constrained system stiffness parameters
Functional relation Q；
Because constrained system stiffness parameters are less, the technical program chooses all constrained system stiffness parameters k1、k2、GL、D2Structure
Even experiment design, this four parameters are used into y respectively for convenience of description1、y2、y3、y4Four variables represent, corresponding because becoming
Measure as Ar, even experiment design expression formula is as follows：
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Regression analysis, which is rejected, influences less project, wherein parameter D2Rejected completely, remaining 7 items being had a great influence to regression model
Mesh, each project and corresponding coefficient are as shown in table 6；
The constrained system stiffness parameters quadratic regression of table 6 corresponds to project and coefficient
The analysis result of the even experiment design is as shown in table 7, where it is determined that coefficient is larger close to 1, F statistics, examines
P values be 0, illustrate that regression result is preferable；
The analysis result of the constrained system stiffness parameters quadratic regression model of table 7
ArThe average level of constrained system rigidity is represented, by the A for contrasting different constrained system rigidityrSize can be realized about
The superior and inferior evaluating of beam system rigidity, in order that ArNondimensionalization and and AvBetween same chemotactic, standardized herein using min-max
Method, to ArMake standardization, obtain the evaluation index of dimensionless constrained system characteristic, be defined as " constrained system synthesis comment
Valency index ", is represented with symbol beta, and its computational methods is：
<mrow>
<mi>&beta;</mi>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>A</mi>
<mi>r</mi>
</msub>
<mo>-</mo>
<mi>min</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>A</mi>
<mi>r</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>A</mi>
<mi>r</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>min</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>A</mi>
<mi>r</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>11</mn>
<mo>)</mo>
</mrow>
</mrow>
A is determined according to occupant's response surfacerMaximum is 69.12g, minimum value 44.60g.According to formula (10) and (11), β is obtained
It is calculated as：
<mrow>
<mi>&beta;</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2452</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mn>1295</mn>
<mo>+</mo>
<mn>21</mn>
<msub>
<mi>k</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<mn>0.006</mn>
<msup>
<msub>
<mi>k</mi>
<mn>1</mn>
</msub>
<mn>2</mn>
</msup>
<mo>-</mo>
<mn>0.01</mn>
<msup>
<msub>
<mi>k</mi>
<mn>2</mn>
</msub>
<mn>2</mn>
</msup>
<mo>-</mo>
<mn>0.005</mn>
<msub>
<mi>k</mi>
<mn>1</mn>
</msub>
<msub>
<mi>k</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<mn>0.3</mn>
<msub>
<mi>k</mi>
<mn>1</mn>
</msub>
<msub>
<mi>G</mi>
<mi>L</mi>
</msub>
<mo>-</mo>
<mn>0.2</mn>
<msub>
<mi>k</mi>
<mn>2</mn>
</msub>
<msub>
<mi>G</mi>
<mi>L</mi>
</msub>
<mo>+</mo>
<mn>2</mn>
<msup>
<msub>
<mi>G</mi>
<mi>L</mi>
</msub>
<mn>2</mn>
</msup>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
</mrow>
β is distributed between 0 to 1, is considered from occupant's acceleration angle, and the smaller corresponding constrained system rigidity of the value is better；But
When the usual range that constrained system stiffness parameters determine beyond the technical program it is possible that β is more than 1 or the feelings less than 0
Condition.
7. according to the collision waveform described in claim 1 and the evaluation method of constrained system characteristic coupled relation, it is characterised in that
Described collision waveform and a of constrained system characteristic comprehensive evaluation indexoFoundation refer to：
This step mainly establishes occupant's acceleration responsive aoRefer to collision waveform comprehensive evaluation index α and constrained system overall merit
β direct quantitative relationship is marked, it is overall so as to be realized according to the preliminary independent evaluation result of collision waveform and constrained system characteristic
Coupled relation is evaluated, because α and β is respectively by AvAnd ArStandardization obtains, so aoAnd AvWith ArBetween increasing function R can
It is equivalent to aoIncreasing function relation R between α and β；Corresponding relation that can be by occupant's response surface according to α and β, draw out alpha-beta-
aoResponse surface, for the ease of observation, response surface is replaced with grid, whole curved surface shows preferable increasing trend；
The technical program uses the method approximation a of surface fittingoIncreasing function relation R between α and β, using α and β as certainly
Variable, to alpha-beta-aoResponse surface carries out Quadratic Surface Fitting, shown in surface fitting such as formula (13), wherein c0、c1、c2、c3、c4、
c5For each term coefficient, it is as shown in table 8 that every coefficient value is obtained by least square method；
ao=c0+c1α+c2β+c3α2+c4αβ+c5β2 (13)
Alpha-beta-a of table 8oResponse surface Quadratic Surface Fitting result
Because α and β square term coefficient is close to 0, so surface fitting formula can be reduced to：
aoThe α β (14) of+161.8 β of=280.5+335.1 α+168
The coefficient of determination R of the fitting result2Reach 0.986, fitting precision is higher.
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