CN103400041A - Method for determining value range of elasticity modulus of butt joint rod of rod-cone type butt joint mechanism - Google Patents

Abstract

The invention provides a method for determining the value range of the elasticity modulus of a butt joint rod of a rod-cone type butt joint mechanism. The determining method comprises the following steps that S10, a dynamics equation of the rod-cone type butt joint mechanism is determined; S20, a first relationship equation between the normal contact force and the normal amount of compression in a contact region of the rod-cone type butt joint mechanism is determined; S30, a group of driven-end parameters and a plurality of groups of driving-end parameters are acquired; S40, iterative computations are carried out to obtain the maximum value of the normal contact force; S50, the maximum value of a plurality of contact stresses is obtained; S60, the value range of the elasticity modulus of the butt joint rod is determined. The method effectively solves the problem that collision contact may damage the inner conical surface of a butt joint cone in the butt joint process in the prior art.

Description

Elastic Modulus Values to the extension bar method of determining range of bar bevel-type docking mechanism

Technical field

The present invention relates to middle-size and small-size satellites coupling impacting technology field, in particular to a kind of method of determining range of Elastic Modulus Values to extension bar and bar bevel-type docking mechanism of bar bevel-type docking mechanism.

Background technology

Following middle-size and small-size satellites coupling process, do not need to carry out the transportation of personnel and goods, and bar bevel-type docking concept has feasibility.Bar bevel-type docking mechanism of the prior art in design process, has been placed on main focus in the design of butt-joint cushion device, and the method for designing of extension bar is rarely had and mentions.Yet the most complicated structure of bar bevel-type docking mechanism with snubber assembly, be not suitable for the application on middle-size and small-size satellite.

At present, document " Xiang Z; Yiyong H; et al.Research of flexible beam impact dynamics based on space probe-cone docking mechanism[J] .Advances in Space Research.2012; 49:1053-1061. " a kind of scheme of soft-dock based on the rods technology proposed, this scheme is utilized the achieve a butt joint buffering of collision impact effect of the deformation characteristic of rods, thereby simplify the labyrinth of docking mechanism, for the application of middle-size and small-size satellites coupling process provides theoretical direction.

In addition, document " Xiang Z; Yiyong H; et al.Design of docking probe based on dynamics model of flexible beam impact[J] .Applied Mechanics and Materials.2012,120:371-374. " node configuration to extension bar design has been carried out some inquiry work.

Yet, in the docking collision process, to extension bar with dock cone each other issuable collision injure temporary transient unmanned consideration, that following docking mechanism is reused design sense is great but the consideration contact-impact is injured.Ground simulating by bar bevel-type docking mechanism docking operation finds, the aluminum that the docking mechanism tradition adopts to extension bar with dock cone, bumping while contacting, the surperficial and inner conical surface of bulb all will be subjected to injuring to a certain extent.

Summary of the invention

The present invention aims to provide a kind of method of determining range of Elastic Modulus Values to extension bar and bar bevel-type docking mechanism of bar bevel-type docking mechanism, to solve the problem of the damage that in prior art, in docking operation, the collision contact may cause the inner conical surface of docking cone.

To achieve these goals, according to an aspect of the present invention, provide a kind of method of determining range of Elastic Modulus Values to extension bar of bar bevel-type docking mechanism, comprised the following steps: step S10: the kinetics equation of determining bar bevel-type docking mechanism; Step S20: determine normal direction contact force in the contact area of bar bevel-type docking mechanism and the first relation equation formula between the normal direction decrement, wherein, the normal direction decrement be the normal direction decrement sum that the normal direction decrement of extension bar and docking are bored; Step S30: obtain one group of Partner parameter and many group drive end parameters; Step S40: with one group of Partner parameter, organize more drive end parameter and the first relation equation formula respectively the substitution kinetics equation carry out iterative computation obtain with every group of drive end parameter one to one a plurality of bar bevel-type docking mechanisms to extension bar and dock the maximal value of the normal direction contact force of cone in contact area; Step S50: determine contact stress in contact area and the second relation equation formula between the normal direction contact force, with the maximal value substitution of a plurality of normal direction contact forces the second relation equation formula, to obtain the maximal value of a plurality of contact stress; Step S60: determine the maximal value of a plurality of contact stress and a plurality of to the relation curve between the elastic modulus of extension bar according to the maximal value of a plurality of elastic modulus to extension bar and a plurality of contact stress in many groups drive end parameter, according to relation curve, determine span to the elastic modulus of extension bar.

Further, kinetics equation is as follows:

$\underset{(n+6)\×(n+6)}{M}\underset{(n+6)\×1}{\overset{\·\·}{q}}+{\stackrel{\·}{\mathrm{\θ}}}_1\underset{(n+6)\×1}{D_1}+{\stackrel{\·}{\mathrm{\θ}}}_1^2\underset{(n+6)\×1}{D_2}+\underset{(n+6)\×1}{D_3}=\underset{(n+6)\×1}{N}{F}_N+\underset{(n+6)\×1}{\mathrm{\τ}}{F}_{\mathrm{\τ}},$ Wherein, n is the rank number of mode that adopts in mode superposition method,

For (n+6) * (n+6) rank mass matrix of bar bevel-type docking mechanism, For the second derivative of the generalized displacement vector of docking system integral body, θ ₁Axially depart from horizontal direction angle, F for docking rod end satellite _NFor normal direction contact force, F _τFor tangential contact force,

With

Be the matrix of coefficients of kinetics equation.

Further, step S40 is further comprising the steps: with one group of Partner parameter, organize more drive end parameter and the first relation equation formula respectively the substitution kinetics equation carry out iterative computation and obtain the time history curve of a plurality of normal direction contact forces, determine the maximal value of a plurality of normal direction contact forces according to the time history curve of each normal direction contact force.

Further, the first relation equation formula is as follows:

$F_N=\frac{{4E}^{*}\sqrt{R_e}}{3F_2^{\frac{3}{2}}\left(e\right)}{\mathrm{\&delta;}}_{\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HDA00003629392500032.png,HDA00003629392500041.png"\; state="\{\{state\}\}">N</figure-callout>}}^{\frac{3}{2}},$

Wherein, F _NFor normal direction contact force, δ _NFor the normal direction decrement; Wherein, E ^*Solve according to first following third side's formula:

$\frac{1}{E^{*}}=\frac{1-{\mathrm{\&mu;}}_1^2}{{\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="HDA00003629392500021.png,HDA00003629392500032.png"\; state="\{\{state\}\}">E</figure-callout>}}_1}+\frac{1-{\mathrm{\&mu;}}_2^2}{E_2},$

Wherein, E ₁For the elastic modulus to extension bar, E ₂For the elastic modulus of docking cone, μ ₁For the Poisson ratio to extension bar, μ ₂Be respectively the Poisson ratio of docking cone; Wherein, R _eFor equivalent redius, R _eSolve according to second following third side's formula:

$R_e={\left(R^{\&prime;}{R}^{\&prime;\&prime;}\right)}^{\frac{1}{2}},$

Wherein, R ' and R ' ' are first and second relative principal curvature radius of docking surface of contact;

F ₂(e) solve according to the 3rd following third side's formula:

$F_2\left(e\right)=\frac{2}{\mathrm{\&pi;}}{\left(\frac{b}{a}\right)}^{\frac{1}{2}}{\left\{F_1\left(e\right)\right\}}^{-\frac{1}{3}}K\left(e\right),$

$F_1\left(e\right)=\frac{4}{{\mathrm{\&pi;e}}^2}{\left(\frac{b}{a}\right)}^{\frac{3}{2}}{\left\{\right[{\left(\frac{a}{b}\right)}^{2}E\left(e\right)-K\left(e\right)\left]\right[K\left(e\right)-E\left(e\right)\left]\right\}}^{\frac{1}{2}},$

$e={(1-\frac{b^2}{a^2})}^{\frac{1}{2}},$

Wherein, a is the semi-major axis of Contact Ellipse, and b is the minor semi-axis of Contact Ellipse, F ₁(e) be second third side's formula, e is the excentricity of Contact Ellipse, and K (e) is the elliptic integral of the first kind of Contact Ellipse, and E (e) is the elliptic integral of the second kind of Contact Ellipse.

Further, semi-major axis a, minor semi-axis b and normal direction contact force F _NBetween have a following relation:

$\sqrt{\mathrm{ab}}={\left[\frac{{3F}_N{R}_e{F}_1\left(e\right)}{{4E}^{*}}\right]}^{\frac{1}{3}},$

$\frac{b}{a}={\left(\frac{A}{B}\right)}^{\frac{1}{2}}={\left(\frac{R^{\&prime;\&prime;}}{R^{\&prime;}}\right)}^{\frac{1}{2}},$

Wherein, intermediate parameters A and B meet following relational expression:

$A+B=\frac{1}{2}(\frac{1}{R^{\&prime;}}+\frac{1}{R^{\&prime;\&prime;}})=\frac{1}{2}(\frac{1}{R_1^{\&prime;}}+\frac{1}{R_1^{\&prime;\&prime;}}+\frac{1}{R_2^{\&prime;}}+\frac{1}{R_2^{\&prime;\&prime;}}),$

$B-A=\frac{1}{2}{\{{(\frac{1}{{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HDA00003629392500021.png,HDA00003629392500032.png"\; state="\{\{state\}\}">R</figure-callout>}}_1^{\&prime;}}-\frac{1}{{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HDA00003629392500021.png,HDA00003629392500032.png"\; state="\{\{state\}\}">R</figure-callout>}}_1^{\&prime;\&prime;}})}^2+{(\frac{1}{R_2^{\&prime;}}-\frac{1}{R_2^{\&prime;\&prime;}})}^2+2(\frac{1}{R_1^{\&prime;}}-\frac{1}{R_1^{\&prime;\&prime;}})(\frac{1}{R_2^{\&prime;}}-\frac{1}{R_2^{\&prime;\&prime;}})\cos \left(2\mathrm{\&alpha;}\right)\}}^{\frac{1}{2}},$

Wherein, a is the semi-major axis of Contact Ellipse, and b is the minor semi-axis of Contact Ellipse, F _NFor normal direction contact force, R _eFor equivalent redius.

Further, the second relation equation formula is as follows:

${\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="HDA00003629392500032.png,HDA00003629392500041.png"\; state="\{\{state\}\}">P</figure-callout>}}_0=\frac{{3F}_N}{2\mathrm{\&pi;ab}}={\left(\frac{{6F}_N{E}^{*2}}{{\mathrm{\&pi;}}^3{R_e}^2}\right)}^{\frac{1}{3}}{\left\{F_1\left(e\right)\right\}}^{-\frac{2}{3}},$

Wherein, P ₀For the maximal value of contact stress, F _NFor the normal direction contact force, a is the semi-major axis of Contact Ellipse, and b is the minor semi-axis of Contact Ellipse, R _eFor equivalent redius.

According to a further aspect in the invention, provide a kind of bar bevel-type docking mechanism, comprised that the elastic modulus of docking cone is determined according to above-mentioned definite method to extension bar and docking cone.

Apply technical scheme of the present invention, technical scheme of the present invention is applicable to the docking operation of middle-size and small-size satellite, selection requirement for the soft-dock of bar bevel-type docking mechanism, by the degree of impairment of considering that collision contact in docking operation may cause inner conical surface, obtain the system of selection of docking bar material, for the reusable design of docking mechanism in middle-size and small-size satellites coupling process provides guidance.Therefore, design with respect to traditional rod bevel-type docking mechanism, the present invention is directed to the expanded application of bar bevel-type docking mechanism, the docking bar material system of selection that provides is meticulousr, can directly apply in the development process of following repeatedly reusable middle-size and small-size satellites coupling mechanism.

Description of drawings

The Figure of description that forms the application's a part is used to provide a further understanding of the present invention, and illustrative examples of the present invention and explanation thereof are used for explaining the present invention, do not form improper restriction of the present invention.In the accompanying drawings:

Fig. 1 shows the schematic flow sheet according to the embodiment of the method for determining range of the Elastic Modulus Values to extension bar of bar bevel-type docking mechanism of the present invention;

Fig. 2 shows the mated condition schematic diagram to extension bar and docking cone of bar bevel-type docking mechanism;

Fig. 3 shows the analysis schematic diagram to extension bar;

Fig. 4 shows the contact process schematic diagram to extension bar and docking cone;

Fig. 5 shows extension bar and docking cone contact area shape at a time and large logotype;

Fig. 6 shows extension bar and docking is bored at the contact area distribution of contact schematic diagram with Fig. 5 synchronization; And

Fig. 7 shows the maximal value of a plurality of contact stress and a plurality of to the relation curve schematic diagram between the elastic modulus of extension bar.

Embodiment

Need to prove, in the situation that do not conflict, embodiment and the feature in embodiment in the application can make up mutually.Describe below with reference to the accompanying drawings and in conjunction with the embodiments the present invention in detail.

The application's technical scheme is applicable to middle-size and small-size satellite, and according to quality classification, middle-size and small-size satellite mainly refers to the satellite of quality less than 1000Kg.。In the docking operation of middle-size and small-size satellite, as shown in Figure 2, docking cone end satellite is target satellite, and docking rod end satellite is the service satellite.In this application, the material decision (such as aluminium alloy used in the prior art) of docking cone end satellite, determine span to the elastic modulus of extension bar according to the maximal value of contact stress with the variation relation of the elastic modulus to extension bar.

As shown in Figure 1, the method for determining range of the Elastic Modulus Values to extension bar of the bar bevel-type docking mechanism of the present embodiment comprises the following steps:

Step S10: the kinetics equation of determining bar bevel-type docking mechanism.This kinetics equation following (definite method of kinetics equation will be elaborated in subsequent content):

$\underset{(n+6)\&times;(n+6)}{M}\underset{(n+6)\&times;1}{\overset{\&CenterDot;\&CenterDot;}{q}}+{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_1\underset{(n+6)\&times;1}{D_1}+{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_1^2\underset{(n+6)\&times;1}{D_2}+\underset{(n+6)\&times;1}{D_3}=\underset{(n+6)\&times;1}{N}{F}_N+\underset{(n+6)\&times;1}{\mathrm{\&tau;}}{F}_{\mathrm{\&tau;}},$

Wherein, n is the rank number of mode that adopts in mode superposition method, For (n+6) * (n+6) rank mass matrix of bar bevel-type docking mechanism,

For the second derivative of generalized displacement vector, θ ₁Axially depart from horizontal direction angle, F for propulsion plant _NFor normal direction contact force, F _τFor tangential contact force,

With

Be matrix of coefficients.

Step S20: determine normal direction contact force in the contact area of bar bevel-type docking mechanism and the first relation equation formula between the normal direction decrement, wherein, the normal direction decrement be the normal direction decrement sum that the normal direction decrement of extension bar and docking are bored.

As shown in Figure 4, S ₁With S ₂Be respectively two curved surfaces that come in contact, S ₁For the bulb surface of contact lever, S ₂Interior poppet surface for the contact cone.What in Fig. 4, solid line represented is the juxtaposition metamorphose situation of two Surface formings of reality.Being the shape that two curved surfaces do not deform under situation and should present if dotted line represents, is a kind of situation of hypothesis.z ₁With z ₂Expression is the height of any point Distance surface minimum point when compression deformation does not occur hypothesis on two curved surfaces respectively. With Represent respectively when on two curved surfaces, any point is collided compression the extrusion deformation degree that occurs on normal direction.δ _NFor intrusion amount size total in collision process, namely the normal direction decrement, be the normal direction decrement of extension bar and the normal direction decrement sum of docking cone.Pass between them is:

On surface of contact, every bit all meets the above-mentioned relation formula, and the normal direction decrement reaches maximal value in centre.

The first relation equation formula between normal direction decrement in normal direction contact force and contact area is as follows:

Wherein, F _NFor normal direction contact force, δ _NFor the normal direction decrement.

Wherein, E ^*Solve according to first following third side's formula:

Wherein, E ₁For the elastic modulus to extension bar, E ₂For the elastic modulus of docking cone, μ ₁For the Poisson ratio to extension bar, μ ₂Be respectively the Poisson ratio of docking cone.

Wherein, R _eFor equivalent redius, R _eSolve according to second following third side's formula:

Wherein, R ' is the radius-of-curvature to extension bar, and R ' ' is the radius-of-curvature of docking cone.

F ₂(e) solve according to the 3rd following third side's formula:

$F_2\left(e\right)=\frac{2}{\mathrm{\&pi;}}{\left(\frac{b}{a}\right)}^{\frac{1}{2}}{\left\{F_1\left(e\right)\right\}}^{-\frac{1}{3}}K\left(e\right),$

$F_1\left(e\right)=\frac{4}{{\mathrm{\&pi;e}}^2}{\left(\frac{b}{a}\right)}^{\frac{3}{2}}{\left\{\right[{\left(\frac{a}{b}\right)}^{2}E\left(e\right)-K\left(e\right)\left]\right[K\left(e\right)-E\left(e\right)\left]\right\}}^{\frac{1}{2}},$ $e={(1-\frac{b^2}{a^2})}^{\frac{1}{2}},$

Wherein, a is the semi-major axis of Contact Ellipse, and b is the minor semi-axis of Contact Ellipse, F ₁(e) be second third side's formula, e is the excentricity of Contact Ellipse, and K (e) is the elliptic integral of the first kind of Contact Ellipse, and E (e) is the elliptic integral of the Equations of The Second Kind of Contact Ellipse.

Step S30: obtain one group of Partner parameter and many group drive end parameters.Wherein, docking cone is Partner, and is identical in the parameter of docking cone and prior art, to extension bar, is drive end, and the elastic modulus of drive end need be got many class values herein, and other parameters all remain unchanged.Concrete desired parameters is as follows:

Table 1 parameter list

Step S40: with one group of Partner parameter, organize more drive end parameter and the first relation equation formula respectively the substitution kinetics equation carry out iterative computation obtain with every group of drive end parameter one to one a plurality of bar bevel-type docking mechanisms to extension bar and dock the maximal value of the normal direction contact force of cone in contact area.Each parameter in table 1 is mainly used in the iterative of the kinetics equation of above-mentioned bar bevel-type docking mechanism,, because said method can be realized by means of the prior art, does not repeat them here.

Preferably, step S40 is further comprising the steps:

With one group of Partner parameter, organize more drive end parameter and the first relation equation formula respectively the substitution kinetics equation carry out iterative computation and obtain the time history curve of a plurality of normal direction contact forces, determine the maximal value of a plurality of normal direction contact forces according to the time history curve of each normal direction contact force.

Semi-major axis a, minor semi-axis b and normal direction contact force F _NBetween have a following relation:

$\sqrt{\mathrm{ab}}={\left[\frac{{3F}_N{R}_e{F}_1\left(e\right)}{{4E}^{*}}\right]}^{\frac{1}{3}},$

$\frac{b}{a}={\left(\frac{A}{B}\right)}^{\frac{1}{2}}={\left(\frac{R^{\&prime;\&prime;}}{R^{\&prime;}}\right)}^{\frac{1}{2}},$

Wherein, intermediate parameters A and B meet following relational expression:

$A+B=\frac{1}{2}(\frac{1}{R^{\&prime;}}+\frac{1}{R^{\&prime;\&prime;}})=\frac{1}{2}(\frac{1}{{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HDA00003629392500021.png,HDA00003629392500032.png"\; state="\{\{state\}\}">R</figure-callout>}}_1^{\&prime;}}+\frac{1}{{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HDA00003629392500021.png,HDA00003629392500032.png"\; state="\{\{state\}\}">R</figure-callout>}}_1^{\&prime;\&prime;}}+\frac{1}{R_2^{\&prime;}}+\frac{1}{R_2^{\&prime;\&prime;}}),$

$B-A=\frac{1}{2}{\{{(\frac{1}{{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HDA00003629392500021.png,HDA00003629392500032.png"\; state="\{\{state\}\}">R</figure-callout>}}_1^{\&prime;}}-\frac{1}{{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HDA00003629392500021.png,HDA00003629392500032.png"\; state="\{\{state\}\}">R</figure-callout>}}_1^{\&prime;\&prime;}})}^2+{(\frac{1}{R_2^{\&prime;}}-\frac{1}{R_2^{\&prime;\&prime;}})}^2+2(\frac{1}{{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HDA00003629392500021.png,HDA00003629392500032.png"\; state="\{\{state\}\}">R</figure-callout>}}_1^{\&prime;}}-\frac{1}{{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HDA00003629392500021.png,HDA00003629392500032.png"\; state="\{\{state\}\}">R</figure-callout>}}_1^{\&prime;\&prime;}})(\frac{1}{R_2^{\&prime;}}-\frac{1}{R_2^{\&prime;\&prime;}})\cos \left(2\mathrm{\&alpha;}\right)\}}^{\frac{1}{2}},$

Wherein, a is the semi-major axis of Contact Ellipse, and b is the minor semi-axis of Contact Ellipse, F _NFor normal direction contact force, R _eFor equivalent redius.

, in conjunction with the aforementioned semi-major axis of having determined and the ratio relation between minor semi-axis, can determine each not size of Contact Ellipse in the same time.Particularly, at first pass through

Can determine the ratio relation between semi-major axis and minor semi-axis, then in the situation that try to achieve each constantly normal direction contact force, according to Can try to achieve

, so these two kinds of relations of simultaneous, can try to achieve a and b, can determine each size of Contact Ellipse constantly.

Step S50: determine contact stress in contact area and the second relation equation formula between the normal direction contact force, with the maximal value substitution of a plurality of normal direction contact forces the second relation equation formula, to obtain the maximal value of a plurality of contact stress.After obtaining the stress value in Elliptical Contacts zone, the elliposoidal regularity of distribution according to stress in elliptic region, then consider the impact that the tangential friction force counter stress distributes, and can determine its stress distribution law.

Maximal value contact stress and the second relation equation formula between the normal direction contact force in contact area are as follows:

${\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="HDA00003629392500032.png,HDA00003629392500041.png"\; state="\{\{state\}\}">P</figure-callout>}}_0=\frac{{3F}_N}{2\mathrm{\&pi;ab}}={\left(\frac{{6F}_N{E}^{*2}}{{\mathrm{\&pi;}}^3{R_e}^2}\right)}^{\frac{1}{3}}{\left\{F_1\left(e\right)\right\}}^{-\frac{2}{3}},$

Wherein, P ₀For the maximal value of contact stress, F _NFor the normal direction contact force, in the second relation equation formula, F _NValue be normal direction contact force maximal value, a is the semi-major axis of Contact Ellipse, b is the minor semi-axis of Contact Ellipse, R _eFor equivalent redius.

Step S60: according to the maximal value of a plurality of elastic modulus to extension bar and a plurality of contact stress in many groups drive end parameter, determine the maximal value of a plurality of contact stress and a plurality of to the relation curve between the elastic modulus of extension bar, relation curve as shown in Figure 7, is determined span to the elastic modulus of extension bar according to relation curve.After obtaining relation curve,, in conjunction with docking cone inner conical surface elastic limit of materials and strength degree, determine the span of corresponding docking bar material elastic modulus, thereby instruct the selection of docking bar material.

Definite method of the kinetics equation in step S10 is specific as follows:

(1), by how much and force analysis, obtain the displacement vector of each point.

As shown in Figure 2, the dynamics of satellite counterweight and docking cone is approximately rigid model, and main analog satellite quality and principal moments of inertia, adopt elastomer model to extension bar.Analyze separately the anamorphic effect of flexible docking bar, might as well will be reduced to the central shaft curve to extension bar, as shown in Figure 3.

The length of rods (to extension bar) part is l ₁, it is θ that docking rod end satellite axially departs from the horizontal direction angle ₁, the distance of rods (to extension bar) end and whole star barycenter is a _cThe elastic deformation of supposing rods still meets the small deformation hypothesis, and be that on the beam axis at x place, 1 Q arrives Q ' point after distortion apart from the rods end when not being out of shape, its axial displacement and transversely deforming are respectively u (x, t), v (x, t), in inertial coordinates system, the displacement vector of Q ' can be expressed as:

$\stackrel{\&RightArrow;}{r}(x,t)=\{{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00003629392500021.png,HDA00003629392500032.png"\; state="\{\{state\}\}">u</figure-callout>}}_1+[a+x+u(x,t)]\cos \left({\mathrm{\&theta;}}_1\right)-v(x,t)\sin \left({\mathrm{\&theta;}}_1\right)\}\stackrel{\&RightArrow;}{i}$ ，

$+\{{\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="HDA00003629392500021.png,HDA00003629392500032.png"\; state="\{\{state\}\}">v</figure-callout>}}_1+[a+x+u(x,t)]\sin \left({\mathrm{\&theta;}}_1\right)+v(x,t)\cos \left({\mathrm{\&theta;}}_1\right)\}\stackrel{\&RightArrow;}{j}$

In docking system, the displacement vector of docking rod end centroid of satellite in inertial coordinate is expressed as:

u ₁With v ₁The displacement that represents respectively two coordinate directions,

The displacement vector of docking cone end centroid of satellite in inertial coordinates system is expressed as:

u ₂With v ₂The displacement that represents respectively two coordinate directions,

(2) kinetic energy of docking system and potential energy expression formula.

The kinetic energy T of docking collision system is:

$T=\frac{1}{2}{m}_1{\stackrel{\&CenterDot;}{\stackrel{\&RightArrow;}{r}}}_1{\stackrel{\&CenterDot;}{\stackrel{\&RightArrow;}{r}}}_1+\frac{1}{2}{I}_1{{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_1}^2+\frac{1}{2}{m}_2{\stackrel{\&CenterDot;}{\stackrel{\&RightArrow;}{r}}}_2{\stackrel{\&CenterDot;}{\stackrel{\&RightArrow;}{r}}}_2+\frac{1}{2}{I}_2{{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_2}^2+\frac{1}{2}\mathrm{\&rho;A}\underset{0}{\overset{l_1}{\&Integral;}}\stackrel{\&CenterDot;}{\stackrel{\&RightArrow;}{r}}\stackrel{\&CenterDot;}{\stackrel{\&RightArrow;}{r}}\mathrm{dx}+\frac{1}{2}{M}_p{\stackrel{\&CenterDot;}{\stackrel{\&RightArrow;}{r}}}_{\left(l_1\right)}{\stackrel{\&CenterDot;}{\stackrel{\&RightArrow;}{r}}}_{\left(l_1\right)},$

Wherein, m ₁For the quality of docking rod end counterweight, I ₁For the whole star principal moments of inertia of docking rod end, m ₂For docking cone end gross mass, I ₂For the whole star principal moments of inertia of docking cone end, ρ is the density of material to extension bar, and A is to extension bar cross-sectional area, M _pFor to extension bar bulb lumped mass,

For docking boom end velocity.

The potential energy V of docking collision system is:

$V=\frac{1}{2}{E}_{1}A\underset{0}{\overset{l_1}{\&Integral;}}{\left(\frac{\&PartialD;u}{\&PartialD;x}\right)}^2\mathrm{dx}+\frac{1}{2}{E}_{1}J\underset{0}{\overset{l_1}{\&Integral;}}{\left(\frac{{\&PartialD;}^{2}v}{{\&PartialD;x}^2}\right)}^2\mathrm{dx},$

Wherein, E ₁For the elastic modulus of docking bar material, J is to the extension bar cross sectional moment of inertia.

(3) introducing mode superposition method is described rods transversely deforming and axial displacement

To axial not extending Euler-Bernoulli beam model, negligible axial distortion, following relational expression is arranged between the axial displacement u (x, t) that is caused by transversely deforming and v (x, t):

$u(x,t)=-\frac{1}{2}\underset{0}{\overset{x}{\&Integral;}}{\left(\frac{\&PartialD;v(\mathrm{\&sigma;},t)}{\&PartialD;\mathrm{\&sigma;}}\right)}^2\mathrm{d\&sigma;},$

Adopt the hypothesis modal method to describe the dynamics of flexible docking bar part:

$v(x,t)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&phi;}}_i\left(x\right)q_i\left(t\right),$

Wherein, φ _i(x) be the model function of vibration of rods, q _i(t) be its modal coordinate, n is rank number of mode.

(4) utilize the Lagrange analytical mechanics theoretical, obtain the rods docking kinetics equation based on bar bevel-type docking mechanism.

The application also provides a kind of bar bevel-type docking mechanism, comprises that the elastic modulus of docking cone is determined according to above-mentioned definite method to extension bar and docking cone.

As can be seen from the above description, the above embodiments of the present invention have realized following technique effect:

Technical scheme of the present invention is applicable to the docking operation of middle-size and small-size satellite, selection requirement for the soft-dock of bar bevel-type docking mechanism, by the degree of impairment of considering that collision contact in docking operation may cause inner conical surface, obtain the system of selection of docking bar material, for the reusable design of docking mechanism in middle-size and small-size satellites coupling process provides guidance.Therefore, design with respect to traditional rod bevel-type docking mechanism, the present invention is directed to the expanded application of bar bevel-type docking mechanism, the docking bar material system of selection that provides is meticulousr, can directly apply in the development process of following repeatedly reusable middle-size and small-size satellites coupling mechanism.

The foregoing is only the preferred embodiments of the present invention, be not limited to the present invention, for a person skilled in the art, the present invention can have various modifications and variations.Within the spirit and principles in the present invention all, any modification of doing, be equal to replacement, improvement etc., within all should being included in protection scope of the present invention.

Claims (7)

1. the method for determining range of the Elastic Modulus Values to extension bar of a bar bevel-type docking mechanism, is characterized in that, comprises the following steps:

Step S10: the kinetics equation of determining bar bevel-type docking mechanism;

Step S20: determine normal direction contact force in the contact area of described bar bevel-type docking mechanism and the first relation equation formula between the normal direction decrement, wherein, described normal direction decrement is the normal direction decrement sum of the described decrement of normal direction to extension bar and described docking cone;

Step S30: obtain one group of Partner parameter and many group drive end parameters;

Step S40: with one group of described Partner parameter, organize more described drive end parameter and described the first relation equation formula respectively the described kinetics equation of substitution carry out iterative computation obtain with every group of described drive end parameter one to one a plurality of described bar bevel-type docking mechanisms to extension bar and dock the maximal value of the normal direction contact force of cone in described contact area;

Step S50: determine contact stress in described contact area and the second relation equation formula between described normal direction contact force, with described the second relation equation formula of the maximal value substitution of a plurality of described normal direction contact forces, to obtain the maximal value of a plurality of described contact stress;

Step S60: determine the maximal value of a plurality of described contact stress and a plurality of described to the relation curve between the elastic modulus of extension bar according to the maximal value of a plurality of described elastic modulus to extension bar and a plurality of described contact stress in many groups of described drive end parameters, determine the span of described elastic modulus to extension bar according to described relation curve.

2. definite method according to claim 1, is characterized in that, described kinetics equation is as follows:

$\underset{(n+6)\&times;(n+6)}{M}\underset{(n+6)\&times;1}{\overset{\&CenterDot;\&CenterDot;}{q}}+{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_1\underset{(n+6)\&times;1}{D_1}+{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_1^2\underset{(n+6)\&times;1}{D_2}+\underset{(n+6)\&times;1}{D_3}=\underset{(n+6)\&times;1}{N}{F}_N+\underset{(n+6)\&times;1}{\mathrm{\&tau;}}{F}_{\mathrm{\&tau;}},$

Wherein, described n is the rank number of mode that adopts in mode superposition method, and is described

For (n+6) * (n+6) rank mass matrix of described bar bevel-type docking mechanism, described For the second derivative of the generalized displacement vector of described docking system integral body, described θ ₁Axially depart from horizontal direction angle, described F for docking rod end satellite _NFor described normal direction contact force, described F _τFor tangential contact force,

With

Be the matrix of coefficients of described kinetics equation.

3. definite method according to claim 1, is characterized in that, described step S40 is further comprising the steps:

With one group of described Partner parameter, organize more described drive end parameter and described the first relation equation formula respectively the described kinetics equation of substitution carry out iterative computation and obtain the time history curve of a plurality of described normal direction contact forces, the time history curve of normal direction contact force according to each is determined the maximal value of a plurality of described normal direction contact forces.

4. definite method according to claim 1, is characterized in that, described the first relation equation formula is as follows:

$F_N=\frac{{4E}^{*}\sqrt{R_e}}{3F_2^{\frac{3}{2}}\left(e\right)}{\mathrm{\&delta;}}_N^{\frac{3}{2}},$

Wherein, described F _NFor described normal direction contact force, described δ _NFor described normal direction decrement;

Wherein, described E ^*Solve according to first following third side's formula:

$\frac{1}{E^{*}}=\frac{1-{\mathrm{\&mu;}}_1^2}{E_1}+\frac{1-{\mathrm{\&mu;}}_2^2}{E_2},$

Wherein, described E ₁For described elastic modulus to extension bar, described E ₂For the elastic modulus of described docking cone, described μ ₁For described Poisson ratio to extension bar, described μ ₂Be respectively the Poisson ratio of described docking cone;

Wherein, described R _eFor equivalent redius, described R _eSolve according to second following third side's formula:

$R_e={\left(R^{\&prime;}{R}^{\&prime;\&prime;}\right)}^{\frac{1}{2}},$

Wherein, described R ' and R ' ' are first and second relative principal curvature radius of docking surface of contact;

Described F ₂(e) solve according to the 3rd following third side's formula:

$F_2\left(e\right)=\frac{2}{\mathrm{\&pi;}}{\left(\frac{b}{a}\right)}^{\frac{1}{2}}{\left\{F_1\left(e\right)\right\}}^{-\frac{1}{3}}K\left(e\right),$

$F_1\left(e\right)=\frac{4}{{\mathrm{\&pi;e}}^2}{\left(\frac{b}{a}\right)}^{\frac{3}{2}}{\left\{\right[{\left(\frac{a}{b}\right)}^{2}E\left(e\right)-K\left(e\right)\left]\right[K\left(e\right)-E\left(e\right)\left]\right\}}^{\frac{1}{2}},$

$e={(1-\frac{b^2}{a^2})}^{\frac{1}{2}},$

Wherein, described a is the semi-major axis of Contact Ellipse, and described b is the minor semi-axis of described Contact Ellipse, described F ₁(e) be second third side's formula, described e is the excentricity of Contact Ellipse, and described K (e) is the elliptic integral of the first kind of described Contact Ellipse, and described E (e) is the elliptic integral of the second kind of described Contact Ellipse.

5. definite method according to claim 4, is characterized in that, described semi-major axis a, described minor semi-axis b and described normal direction contact force F _NBetween have a following relation:

$\sqrt{\mathrm{ab}}={\left[\frac{{3F}_N{R}_e{F}_1\left(e\right)}{{4E}^{*}}\right]}^{\frac{1}{3}},$

$\frac{b}{a}={\left(\frac{A}{B}\right)}^{\frac{1}{2}}={\left(\frac{R^{\&prime;\&prime;}}{R^{\&prime;}}\right)}^{\frac{1}{2}},$

Wherein, the described A of intermediate parameters and described B meet following relational expression:

$A+B=\frac{1}{2}(\frac{1}{R^{\&prime;}}+\frac{1}{R^{\&prime;\&prime;}})=\frac{1}{2}(\frac{1}{R_1^{\&prime;}}+\frac{1}{R_1^{\&prime;\&prime;}}+\frac{1}{R_2^{\&prime;}}+\frac{1}{R_2^{\&prime;\&prime;}}),$

$B-A=\frac{1}{2}{\{{(\frac{1}{R_1^{\&prime;}}-\frac{1}{R_1^{\&prime;\&prime;}})}^2+{(\frac{1}{R_2^{\&prime;}}-\frac{1}{R_2^{\&prime;\&prime;}})}^2+2(\frac{1}{R_1^{\&prime;}}-\frac{1}{R_1^{\&prime;\&prime;}})(\frac{1}{R_2^{\&prime;}}-\frac{1}{R_2^{\&prime;\&prime;}})\cos \left(2\mathrm{\&alpha;}\right)\}}^{\frac{1}{2}},$

Wherein, described a is the semi-major axis of Contact Ellipse, and described b is the minor semi-axis of described Contact Ellipse, described F _NFor described normal direction contact force, described R _eFor described equivalent redius.

6. definite method according to claim 5, is characterized in that, described the second relation equation formula is as follows:

$P_0=\frac{{3F}_N}{2\mathrm{\&pi;ab}}={\left(\frac{{6F}_N{E}^{*2}}{{\mathrm{\&pi;}}^3{R_e}^2}\right)}^{\frac{1}{3}}{\left\{F_1\left(e\right)\right\}}^{-\frac{2}{3}},$

Wherein, P ₀For the maximal value of described contact stress, described F _NFor described normal direction contact force, described a is the semi-major axis of Contact Ellipse, and described b is the minor semi-axis of described Contact Ellipse, R _eFor described equivalent redius.

7. bar bevel-type docking mechanism, comprise extension bar and docking cone, it is characterized in that, the elastic modulus of described docking cone according to claim 1 to 6 the described definite method of any one determine.

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