CN101726426B - Method for evaluating micro-gravity dual-axis gyrator - Google Patents

Abstract

The invention relates to a method for evaluating a micro-gravity dual-axis gyrator, the dual-axis gyrator consists of an inner ring and an outer ring, and the method for evaluating the micro-gravity dual-axis gyrator comprises the following steps: 11) carrying out physical modeling for the dual-axis gyrator; 12) establishing three coordinate systems of a base coordinate system, an inner ring coordinate system and an outer ring coordinate system, as shown in Figure 2, wherein the base coordinate system is a fixed coordinate system; 13) utilizing the rotating vector properties of the coordinate systems for finally deriving an apparent gravity acceleration formula of an object, wherein apparent gravity acceleration is the projection of gravitational acceleration under the inner ring coordinate system, and the value is the vector sum of the acceleration and the gravitational acceleration produced by the rotation of the inner ring and the outer ring, and 14) utilizing the apparent gravity acceleration formula and a simulation platform for evaluating the effect of simulating micro-gravity of parameter settings according to parameters set by the micro-gravity dual-axis gyrator, if the obtained apparent gravity acceleration can achieve all rotating positions, the parameter settings can simulate the micro-gravity effect.

Description

A kind of method that is used for evaluating micro-gravity dual-axis gyrator

Technical field

The present invention relates to simulate the dual-axis gyrator of biological microgravity effect, particularly a kind of method that is used for evaluating micro-gravity dual-axis gyrator.

Background technology

Along with the development of aerospace industry, the microgravity effect in the space has caused scientific research personnel's attention gradually.Materials such as biology, material can show more not available unique properties in gravity environment under microgravity environment, thereby have driven the development in science and technology of association area, and wherein biological microgravity effect is one of the focus of microgravity research especially.But because space environment is complicated, costly, make many experiments carry out, therefore, utilize the ground experiment device to carry out the first-selection that the microgravity effect analog becomes many experiments.

In the middle of the simulation of biology weightlessness effect, microgravity gyrator (Clinostat) is a kind of analogy method preferably.Compare with other analogy method, gyrator has characteristics such as simulated time is long, running expense is low, environment is single, has therefore received researchers' extensive welcome.

Gyrator is to have utilized experiment product in some biological experiment that the variation of gravity is had lag-effect (like some biological cell; The root of plant, stem etc.); The suffered gravity direction of experiment product is continuously changed, just can be in the biological process under the microgravity environment that simulates of equivalence on this experiment product.The setting of gyrator parameter plays crucial effects for the simulation of microgravity effect.But because adjustable kinematic parameter is more, the motion of trial target in gyrator is complicated with stressing conditions, and therefore, to the influence of trial target motion conditions how different parameter settings always is a problem that perplexs the researchist.

Summary of the invention

To the influence of trial target motion conditions how the object of the invention is, for overcoming different parameter settings, proposed a kind of method that is used for evaluating micro-gravity dual-axis gyrator, and by the Matlab platform different parameter settings has been simulated.

For realizing the foregoing invention purpose; The present invention proposes a kind of method that is used for evaluating micro-gravity dual-axis gyrator; This dual-axis gyrator is made up of inner and outer rings, and the axle that inner and outer rings independently centers on respectively separately carries out 360 degree rotations, encircles in object is fixed on and goes up with interior ring rotation; It is characterized in that the described method that is used for evaluating micro-gravity dual-axis gyrator comprises following steps:

11) dual-axis gyrator is carried out physical modeling;

12) set up base coordinate system, interior cyclic coordinate system and three coordinate systems of outer shroud coordinate system, wherein, base coordinate system is a fixed coordinate system;

13) utilize the vectorial property of coordinate system rotation; Finally derive the apparent gravity Acceleration Formula of object; This apparent gravity acceleration is an acceleration of gravity in the projection down of interior cyclic coordinate system, its value for the vector of the acceleration of inner and outer rings rotation generation and acceleration of gravity and;

14) parameter that is provided with according to micro-gravity dual-axis gyrator; Utilize above-mentioned this parameter of apparent gravity Acceleration Formula evaluation that the effect of simulated microgravity is set; This parameter is provided with ability simulated microgravity effect if the apparent gravity acceleration that obtains can reach all position of rotation; Micro-gravity dual-axis gyrator can simulated microgravity, otherwise that parameter is provided with is improper, and micro-gravity dual-axis gyrator can not simulated microgravity.

The described method that is used for evaluating micro-gravity dual-axis gyrator is characterized in that described outer shroud is fixed on the pedestal, and interior ring is fixed on the outer shroud.

The described method of deciding that is used for evaluating micro-gravity dual-axis gyrator is characterized in that direction cosine between described outer shroud-pedestal such as following table:

Direction cosine such as following table in described between the ring-outer shroud:

Thus, direction cosine such as the following table between the described interior ring-pedestal:

The described method that is used for evaluating micro-gravity dual-axis gyrator is characterized in that step 13) further comprises:

13-1) obtain between outer shroud and the pedestal and the direction cosine between interior ring and the outer shroud, and derive the direction cosine between interior ring and the pedestal according to the conversion principle under the rotating coordinate system; The position formula of object in coordinate system does;

r=xi+yj+zk

Object in described being fixed on the ring has fixing interior cyclic coordinate (X under interior cyclic coordinate is _i, Y _i, Z _i); The relevant position of described object under basic coordinate system is:

$\left\{\begin{array}{ccc}{X}_b=& X_i\cos {\mathrm{\θ}}_i& +Z_i\sin {\mathrm{\θ}}_i\\ Y_b=& X_i\sin {\mathrm{\θ}}_i\sin {\mathrm{\θ}}_o+Y_i\cos {\mathrm{\θ}}_o& -Z_i\cos {\mathrm{\θ}}_i\sin {\mathrm{\θ}}_o\\ Z_b=& -X_i\sin {\mathrm{\θ}}_i\cos {\mathrm{\θ}}_o+Y_i\sin {\mathrm{\θ}}_o& +Z_i\cos {\mathrm{\θ}}_i\cos {\mathrm{\θ}}_o\end{array}\right.$

Object absolute angle speed under base coordinate system is respectively along the component of x, y and z coordinate axis:

$\left\{\begin{array}{c}{\mathrm{\ω}}_x={\mathrm{\ω}}_o\cos {\mathrm{\θ}}_i\\ {\mathrm{\ω}}_y={\mathrm{\ω}}_i\\ {\mathrm{\ω}}_z={\mathrm{\ω}}_o\sin {\mathrm{\θ}}_i\end{array}\right.$

13-2) acceleration of gravity is to be the acceleration of g perpendicular to the ground size under the base coordinate system, and formula is: g=-gk _b

According to the coordinate cosine table between interior ring and the pedestal:

Z _bk _b＝-sinθ _icosθ _oX _ii _i+sinθ _oY _ij _i+cosθ _icosθ _oZ _ik _i

The component of gravity acceleration g on interior cyclic coordinate axle represented then with

:

$g=g_{x_i}{i}_i+g_{y_i}{j}_i+g_{z_i}{k}_i$

Obtain acceleration of gravity by above three formula:

$\left\{\begin{array}{cc}{g}_{x_i}& =g\cos {\mathrm{\θ}}_o\sin {\mathrm{\θ}}_i\\ g_{y_i}& =-g\sin {\mathrm{\θ}}_o\\ g_{z_i}& =-g\cos {\mathrm{\θ}}_o\cos {\mathrm{\θ}}_i\end{array}\right.$

13-4) coordinate system is rotated with angular velocity omega, and then the derivative of vector G finally is expressed as:

$\frac{\mathrm{dG}}{\mathrm{dt}}=\frac{d{G}_x}{\mathrm{dt}}i+G_x\frac{\mathrm{di}}{\mathrm{dt}}+\frac{d{G}_y}{\mathrm{dt}}j+G_y\frac{\mathrm{dj}}{\mathrm{dt}}+\frac{d{G}_z}{\mathrm{dt}}k+G_z\frac{\mathrm{dk}}{\mathrm{dt}}$

$=(\frac{{\mathrm{dG}}_x}{\mathrm{dt}}i+\frac{d{G}_y}{\mathrm{dt}}j+\frac{d{G}_z}{\mathrm{dt}}k)+(G_x\frac{\mathrm{di}}{\mathrm{dt}}+G_y\frac{\mathrm{dj}}{\mathrm{dt}}+G_z\frac{\mathrm{dk}}{\mathrm{dt}})$

Finally be expressed as according to dynamics and space rotating coordinate system character following formula:

$\frac{\mathrm{dG}}{\mathrm{dt}}=\frac{\tilde{d}G}{\mathrm{dt}}+\mathrm{\ω}\×G$

13-5) bring the speed v of rotating object into following formula:

$v=\frac{\mathrm{dr}}{\mathrm{dt}}=\frac{\tilde{d}r}{\mathrm{dt}}+\mathrm{\ω}\×r$

Object is owing to the component of absolute acceleration under interior cyclic coordinate is that coordinate system rotation produces is:

$\left\{\begin{array}{ccc}{W}_{X_i}=& W_X\cos {\mathrm{\θ}}_i+W_Y\sin {\mathrm{\θ}}_i\sin {\mathrm{\θ}}_o& -W_Z\sin {\mathrm{\θ}}_i\cos {\mathrm{\θ}}_o\\ W_{Y_i}=& +W_Y\cos {\mathrm{\θ}}_o& +W_Z\sin {\mathrm{\θ}}_o\\ W_{Z_i}=& W_X\sin {\mathrm{\θ}}_i-W_Y\cos {\mathrm{\θ}}_i\sin {\mathrm{\θ}}_o& +W_Z\cos {\mathrm{\θ}}_i\cos {\mathrm{\θ}}_i\end{array}\right.$

The projection sum of the acceleration W that is produced by gravity acceleration g and coordinate system rotation according to the apparent acceleration A of object under interior cyclic coordinate system, formula is: A=g+W

It is that the component of each is down along interior cyclic coordinate:

$\left\{\begin{array}{ccc}{A}_x=& g\cos {\mathrm{\θ}}_o\sin {\mathrm{\θ}}_i& +W_{X_i}\\ A_y=& -g\sin {\mathrm{\θ}}_o& +W_{Y_i}\\ A_z=& -g\cos {\mathrm{\θ}}_o\cos {\mathrm{\θ}}_i& +W_{Z_i}\end{array}\right..$

Described micro-gravity dual-axis gyrator parameter setting method is characterized in that, the acceleration in the object of which movement process comprises acceleration and the acceleration of gravity that the inner and outer ring rotation produces.

Described micro-gravity dual-axis gyrator parameter setting method is characterized in that, the described outer shroud of step 12) is fixed on the pedestal, and interior ring is fixed on the outer shroud; In ring, and outer shroud carries out independence 360 degree around separately axle and rotates.

In the gyrator experiment, cyclic coordinate was down in object was fixed in, and moved with the inner and outer ring rotation.The acceleration that this moment, object was experienced is called " apparent acceleration ", is the projection of absolute acceleration under interior cyclic coordinate is with respect to earth axes of object.

The acceleration of object in motion process mainly is made up of 2 parts: because acceleration and acceleration of gravity that the inner and outer ring rotation produces.Therefore, the apparent acceleration of calculating object is acceleration and the projection of acceleration of gravity under interior cyclic coordinate is that rotation produces.

Parameter-definition:

If the parameter of interior ring and outer shroud is represented with subscript o and i respectively, subscript 0 expression initial value.Like this, parameter-definition is promptly shown in the table 1:

Dual-axis gyrator is through after rotating, and the angle theta of inner and outer ring and initial position is:

$\mathrm{\θ}={\mathrm{\θ}}^0+{\mathrm{\ω}}^{0}t+\frac{1}{2}\mathrm{\ξ}{t}^2---\left(1\right)$

And angular velocity omega is:

$\mathrm{\ω}=\frac{\mathrm{d\θ}}{\mathrm{dt}}={\mathrm{\ω}}^0+\mathrm{\ξt}---\left(2\right)$

The derivative of angular velocity is angular acceleration ξ:

$\frac{\mathrm{d\ω}}{\mathrm{dy}}=\mathrm{\ξ}---\left(3\right)$

In addition; In the analysis of this paper; The angular acceleration of supposing inner and outer ring is a constant, i.e.

The invention has the advantages that; Propose some and helped to judge the parameter index of micro-gravity dual-axis gyrator simulated microgravity effect; Can assist the scientific research personnel who uses gyrator to carry out biology microgravity effect study to carry out the design of gyrator parameter, hold different parameters more accurately the effect to the microgravity simulation is set.

Description of drawings

Fig. 1 is the dual-axis gyrator that inner and outer ring constitutes;

Fig. 2 sets up basic coordinate system, interior cyclic coordinate system and outer shroud coordinate system;

Fig. 3 is a unit vector in the space;

Fig. 4 is the Matlab emulation platform;

Fig. 5 works as X _i=Y _i=Z _i=0.1 (m), ω _i=ω _oRuuning situation figure during=0.1 (rad/s);

Fig. 6 works as X _i=Y _i=Z _i=0.1 (m), ω _i=ω _oRuuning situation figure during=1 (rad/s);

Fig. 7 works as X _i=Z _i=0.1 (m) Y _i=0 (m), ω _i=0.1 (rad/s) ω _oRuuning situation figure during=1 (rad/s);

Fig. 8 works as X _i=Y _i=Z _i=0.1 (m), ω _iω _oRuuning situation figure in the time of at random;

Fig. 9 is X _i=Z _i=0.1 (m) Y _i=0 (m), ω _iω _oRuuning situation figure in the time of at random;

Figure 10 works as X _i=Z _i=0.01 (m) Y _i=0 (m), ω _iω _oRuuning situation figure in the time of at random;

Figure 11 works as X _i=Z _i=0.01 (m) Y _i=0.1 (m), ω _iω _oRuuning situation figure in the time of at random;

Figure 12 works as X _i=0.12 (m), Y _i=0.08 (m), Z _i=0.19 (m), ω _i=0.2 (rpm) ω _oRuuning situation figure during the rotation of=0.2 (rpm) constant speed;

Figure 13 works as X _i=0.12 (m), Y _i=0.08 (m), Z _i=0.19 (m), ω _i=0.5 (rpm) ω _oRuuning situation figure during the rotation of=0.5 (rpm) constant speed;

Figure 14 works as X _i=0.12 (m), Y _i=0.08 (m), Z _i=0.19 (m), ω _i=2 (rpm) ω _oRuuning situation figure during the rotation of=2 (rpm) constant speed;

Figure 15 works as X _i=0.12 (m), Y _i=0.08 (m), Z _i=0.19 (m), ω _iω _oRuuning situation figure when rotating at random.

Embodiment

Below in conjunction with accompanying drawing and specific embodiment the present invention is carried out detailed explanation.

1) sets up the coordinate system row-coordinate conversion of going forward side by side

Set up basic coordinate system, outer shroud coordinate system and interior cyclic coordinate system are shown in accompanying drawing 2;

If pedestal, outer shroud and interior ring are represented with subscript b, o and i respectively, according to the conversion principle under the rotating coordinate system, listed direction cosine between outer shroud-pedestal like following table 2;

Like the direction cosine between the ring-outer shroud in the following table 3;

Table 2 and table 3 can tables 4 thus, promptly in direction cosine between the ring-pedestal, as follows:

2) calculation of parameter

2.1.1 position

Shown in accompanying drawing 7, the position of object in coordinate system can be defined as:

r=xi+yj+zk (4)

In the actual moving process, therefore object has fixing interior cyclic coordinate (Xi owing under the cyclic coordinate system in being fixed on; Yi; Zi).According to table 4, the relevant position of object under absolute coordinate system (base coordinate system) is:

$\left\{\begin{array}{ccc}{X}_b=& X_i\cos {\mathrm{\θ}}_i& +Z_i\sin {\mathrm{\θ}}_i\\ Y_b=& X_i\sin {\mathrm{\θ}}_i\sin {\mathrm{\θ}}_o+Y_i\cos {\mathrm{\θ}}_o& -Z_i\cos {\mathrm{\θ}}_i\sin {\mathrm{\θ}}_o\\ Z_b=& -X_i\sin {\mathrm{\θ}}_i\cos {\mathrm{\θ}}_o+Y_i\sin {\mathrm{\θ}}_o& +Z_i\cos {\mathrm{\θ}}_i\cos {\mathrm{\θ}}_o\end{array}\right.---\left(5\right)$

2.1.2 angular velocity and angular acceleration

Owing to object is fixed on interior cyclic coordinate is down, and the kinematic parameter of therefore interior cyclic coordinate is the kinematic parameter of object.Therefore, according to table 2 and table 3, object absolute angle speed under base coordinate system is respectively along the component of x, y and z coordinate axis:

$\left\{\begin{array}{c}{\mathrm{\ω}}_x={\mathrm{\ω}}_o\cos {\mathrm{\θ}}_i\\ {\mathrm{\ω}}_y={\mathrm{\ω}}_i\\ {\mathrm{\ω}}_z={\mathrm{\ω}}_o\sin {\mathrm{\θ}}_i\end{array}\right.---\left(6\right)$

Its derivative is:

$\left\{\begin{array}{c}\frac{d{\mathrm{\ω}}_x}{\mathrm{dt}}={\mathrm{\ξ}}_o\cos {\mathrm{\θ}}_i-{\mathrm{\ω}}_o\sin {\mathrm{\θ}}_i({\mathrm{\ω}}_i^0+{\mathrm{\ξ}}_{i}t)\\ \frac{d{\mathrm{\ω}}_y}{\mathrm{dt}}={\mathrm{\ξ}}_i\\ \frac{{\mathrm{d\ω}}_z}{\mathrm{dt}}={\mathrm{\ξ}}_o\sin {\mathrm{\θ}}_i+{\mathrm{\ω}}_o\cos {\mathrm{\θ}}_i({\mathrm{\ω}}_i^0+{\mathrm{\ξ}}_{i}t)\end{array}\right.---\left(7\right)$

2.1.3 apparent gravity acceleration

The apparent gravity acceleration is the projection of acceleration of gravity under interior cyclic coordinate is.Acceleration of gravity is to be the acceleration of g perpendicular to the ground size under the base coordinate system, that is:

g＝-gk _b (8)

Can know by accompanying drawing 6:

Z _bk _b＝-sinθ _icosθ _oX _ii _i+sinθ _oY _ij _i+cosθ _icosθ _oZ _ik _i

With the expression of the component of gravity acceleration g on interior cyclic coordinate axle, then with

:

$g=g_{x_i}{i}_i+g_{y_i}{j}_i+g_{z_i}{k}_i---\left(10\right)$

Contrast formula (8), (9) and formula (10) get final product:

$\left\{\begin{array}{cc}{g}_{x_i}& =g\cos {\mathrm{\θ}}_o\sin {\mathrm{\θ}}_i\\ g_{y_i}& =-g\sin {\mathrm{\θ}}_o\\ g_{z_i}& =-g\cos {\mathrm{\θ}}_o\cos {\mathrm{\θ}}_i\end{array}\right.---\left(11\right)$

2.1.4 the vector derivative under the rotating coordinate system

If certain vector G is arranged in certain coordinate system, it can be expressed as:

G＝G _xi+G _yj+G _zk (12)

If this coordinate system is rotated with angular velocity omega, then the derivative dG/dt of this vector G is:

$\frac{\mathrm{dG}}{\mathrm{dt}}=\frac{d{G}_x}{\mathrm{dt}}i+G_x\frac{\mathrm{di}}{\mathrm{dt}}+\frac{d{G}_y}{\mathrm{dt}}j+G_y\frac{\mathrm{dj}}{\mathrm{dt}}+\frac{d{G}_z}{\mathrm{dt}}k+G_z\frac{\mathrm{dk}}{\mathrm{dt}}$

$=(\frac{{\mathrm{dG}}_x}{\mathrm{dt}}i+\frac{d{G}_y}{\mathrm{dt}}j+\frac{d{G}_z}{\mathrm{dt}}k)+(G_x\frac{\mathrm{di}}{\mathrm{dt}}+G_y\frac{\mathrm{dj}}{\mathrm{dt}}+G_z\frac{\mathrm{dk}}{\mathrm{dt}})---\left(13\right)$

First relative difference quotient of expression in the formula.

According to kinematics, under the rotating coordinate system of space, have:

$\left\{\begin{array}{c}\frac{\mathrm{di}}{\mathrm{dt}}=\mathrm{\&omega;}\&times;i=\left|\begin{array}{ccc}i& j& k\\ {\mathrm{\&omega;}}_x& {\mathrm{\&omega;}}_y& {\mathrm{\&omega;}}_z\\ 1& 0& 0\end{array}\right|={\mathrm{\&omega;}}_{x}j-{\mathrm{\&omega;}}_{y}k\\ \frac{\mathrm{dj}}{\mathrm{dt}}=\mathrm{\&omega;}\&times;j=\left|\begin{array}{ccc}i& j& k\\ {\mathrm{\&omega;}}_x& {\mathrm{\&omega;}}_y& {\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="0"\; label="z"\; filenames="H2009102422670E00022.png"\; state="\{\{state\}\}">z</figure-callout>}}\\ 0& 1& 0\end{array}\right|=-{\mathrm{\&omega;}}_{z}i+{\mathrm{\&omega;}}_{z}k\\ \frac{\mathrm{dk}}{\mathrm{dt}}=\mathrm{\&omega;}\&times;k=\left|\begin{array}{ccc}i& j& k\\ {\mathrm{\&omega;}}_x& {\mathrm{\&omega;}}_y& {\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="0"\; label="z"\; filenames="H2009102422670E00022.png"\; state="\{\{state\}\}">z</figure-callout>}}\\ 0& 0& 1\end{array}\right|={\mathrm{\&omega;}}_{y}i-{\mathrm{\&omega;}}_{x}j\end{array}\right.---\left(14\right)$

Therefore second in formula (13) is:

$G_x\frac{\mathrm{di}}{\mathrm{dt}}+G_y\frac{\mathrm{dj}}{\mathrm{dt}}+G_z\frac{\mathrm{dk}}{\mathrm{dt}}=G_z({\mathrm{\&omega;}}_{z}j-{\mathrm{\&omega;}}_{y}k)+G_y(-{\mathrm{\&omega;}}_{z}i+{\mathrm{\&omega;}}_{x}k)+G_z({\mathrm{\&omega;}}_{y}i-{\mathrm{\&omega;}}_{x}j)$

$=({\mathrm{\&omega;}}_y{G}_z-{\mathrm{\&omega;}}_z{G}_y)i+({\mathrm{\&omega;}}_z{G}_x-{\mathrm{\&omega;}}_x{G}_z)j+({\mathrm{\&omega;}}_x{G}_y-{\mathrm{\&omega;}}_y{G}_x)k---\left(15\right)$

And because:

$\mathrm{\&omega;}\&times;G=\left|\begin{array}{ccc}i& k& j\\ {\mathrm{\&omega;}}_x& {\mathrm{\&omega;}}_y& {\mathrm{\&omega;}}_z\\ G_x& G_y& G_z\end{array}\right|---\left(16\right)$

$=({\mathrm{\&omega;}}_y{G}_z-{\mathrm{\&omega;}}_z{G}_y)i+({\mathrm{\&omega;}}_z{G}_x-{\mathrm{\&omega;}}_x{G}_z)j+({\mathrm{\&omega;}}_x{G}_y-{\mathrm{\&omega;}}_y{G}_x)k$

Therefore formula (13) finally can be written as:

$\frac{\mathrm{dG}}{\mathrm{dt}}=\frac{\tilde{d}G}{\mathrm{dt}}+\mathrm{\&omega;}\&times;G---\left(17\right)$

2.1.5 rotation apparent acceleration

For asking the speed v of rotating object, with formula (4) substitution (17):

$v=\frac{\mathrm{dr}}{\mathrm{dt}}=\frac{\tilde{d}r}{\mathrm{dt}}+\mathrm{\&omega;}\&times;r---\left(18\right)$

For asking the acceleration a=dv/dt of object,, can get v=G substitution formula (17):

$a=\frac{\mathrm{dv}}{\mathrm{dt}}=\frac{d}{\mathrm{dt}}(\frac{\tilde{d}r}{\mathrm{dt}}+\mathrm{\&omega;}\&times;r)$

$=\frac{d}{\mathrm{dt}}\left(\frac{\tilde{d}r}{\mathrm{dt}}\right)+\frac{d(\mathrm{\&omega;}\&times;r)}{\mathrm{dt}}---\left(19\right)$

$=\frac{{\tilde{d}}^{2}r}{\mathrm{dt}}+\mathrm{\&omega;}\&times;\frac{\tilde{d}r}{\mathrm{dt}}+(\frac{\tilde{d}\mathrm{\&omega;}}{\mathrm{dt}}+\mathrm{\&omega;}\&times;\mathrm{\&omega;})\&times;r+\mathrm{\&omega;}\&times;(\frac{\tilde{d}r}{\mathrm{dt}}+\mathrm{\&omega;}\&times;r)$

$=\frac{{\tilde{d}}^{2}r}{\mathrm{dt}}+2\mathrm{\&omega;}\&times;\frac{\tilde{d}r}{\mathrm{dt}}+\frac{\tilde{d}\mathrm{\&omega;}}{\mathrm{dt}}\&times;r+\mathrm{\&omega;}\&times;(\mathrm{\&omega;}\&times;r)$

Because in the cyclic coordinate system, its relative velocity and relative acceleration all were 0, that is: in object was fixed in

$\left\{\begin{array}{c}\frac{\tilde{d}r}{\mathrm{dt}}=0\\ \frac{{\tilde{d}}^{2}r}{\mathrm{dt}}=0\end{array}\right.---\left(20\right)$

If the absolute acceleration that object produces owing to coordinate system rotation is W:

$W=\frac{d^{2}r}{d{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="H2009102422670E00081.png"\; state="\{\{state\}\}">t</figure-callout>}}^2}=\frac{\tilde{d}\mathrm{\&omega;}}{\mathrm{dt}}\&times;r+\mathrm{\&omega;}\&times;(\mathrm{\&omega;}\&times;r)---\left(21\right)$

Each component is in the base coordinate system lower edge for it:

$\left\{\begin{array}{c}{W}_X=(Z\frac{d{\mathrm{\&omega;}}_y}{\mathrm{dt}}-Y\frac{d{\mathrm{\&omega;}}_z}{\mathrm{dt}})+[{\mathrm{\&omega;}}_x(Y{\mathrm{\&omega;}}_y+Z{\mathrm{\&omega;}}_z)-X({\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="H2009102422670E00081.png"\; state="\{\{state\}\}">y</figure-callout>}}^2+{\mathrm{\&omega;}}_z^2)]\\ W_Y=(X\frac{d{\mathrm{\&omega;}}_z}{\mathrm{dt}}-Z\frac{d{\mathrm{\&omega;}}_x}{\mathrm{dt}})+[{\mathrm{\&omega;}}_y(X{\mathrm{\&omega;}}_x+Z{\mathrm{\&omega;}}_z)-Y({\mathrm{\&omega;}}_x^2+{\mathrm{\&omega;}}_z^2)]\\ W_Z=(Y\frac{d{\mathrm{\&omega;}}_x}{\mathrm{dt}}-X\frac{d{\mathrm{\&omega;}}_y}{\mathrm{dt}})+[{\mathrm{\&omega;}}_z(X{\mathrm{\&omega;}}_x+Y{\mathrm{\&omega;}}_y)-Z({\mathrm{\&omega;}}_x^2+{\mathrm{\&omega;}}_y^2)]\end{array}\right.---\left(22\right)$

Then object is owing to the component of absolute acceleration under interior cyclic coordinate is that coordinate system rotation produces is:

$\left\{\begin{array}{ccc}{W}_{X_i}=& W_X\cos {\mathrm{\&theta;}}_i+W_Y\sin {\mathrm{\&theta;}}_i\sin {\mathrm{\&theta;}}_o& -W_Z\sin {\mathrm{\&theta;}}_i\cos {\mathrm{\&theta;}}_o\\ W_{Y_i}=& +W_Y\cos {\mathrm{\&theta;}}_o& +W_Z\sin {\mathrm{\&theta;}}_o\\ W_{Z_i}=& W_X\sin {\mathrm{\&theta;}}_i-W_Y\cos {\mathrm{\&theta;}}_i\sin {\mathrm{\&theta;}}_o& +W_Z\cos {\mathrm{\&theta;}}_i\cos {\mathrm{\&theta;}}_i\end{array}\right.---\left(23\right)$

According to table 4, the apparent acceleration A of object by gravity acceleration g and coordinate system rotation produce acceleration W projection sum under interior cyclic coordinate system form, that is:

A＝g+W

It is that the component of each is down along interior cyclic coordinate:

$\left\{\begin{array}{ccc}{A}_x=& g\cos {\mathrm{\&theta;}}_o\sin {\mathrm{\&theta;}}_i& +W_{X_i}\\ A_y=& -g\sin {\mathrm{\&theta;}}_o& +W_{Y_i}\\ A_z=& -g\cos {\mathrm{\&theta;}}_o\cos {\mathrm{\&theta;}}_i& +W_{Z_i}\end{array}\right.---\left(25\right)$

3) emulation

3.1 simulation parameter and each parameter-definition

Through location parameter and inner and outer rings angular velocity of rotation being set and by the Matlab emulation platform apparent gravity acceleration that obtains being simulated, and then judge that parameter is provided with the effect to the microgravity simulation, wherein the emulation interface is shown in accompanying drawing 4.

User's parameter importation and numerical result output mainly comprise following components from left to right at the top at interface:

Position: the coordinate figure of position under interior cyclic coordinate is that need to refer to emulation;

Angular velocity: comprise definite value and two kinds of patterns at random.When selecting deterministic model, inner and outer ring can select a fixing angular velocity to carry out emulation; When selecting random pattern, after having set the highest angular velocity and angular acceleration, simulated program will be selected the rotating speed of inner and outer ring at random;

Time: the length overall, simulation step-length and the analysis window that comprise simulated time respectively are long;

The result: when the user clicks " calculating " button, analogue system will be moved.Comprise peak acceleration, minimum acceleration, 1*10 ^-3Acceleration number percent peace slip velocity is spent the cycle in the scope.

The lower part of software interface is figure output result, mainly comprises following components:

The apparent acceleration absolute value: comprise the absolute value of apparent acceleration under absolute coordinate system, and along the absolute value of the component of x, y and z coordinate axis;

Average apparent acceleration: be meant in analysis window is long apparent acceleration vector and absolute value;

Space motion track: refer to analyze run location under absolute coordinate system according to step-length;

The apparent acceleration space view;

Acceleration profile;

3.2 canonical parameter simulation result

Accompanying drawing 5 has shown the ruuning situation when the inner and outer ring rotating speed is even, can see that by locus figure its running orbit is shown as the space ring-type, and apparent acceleration biases toward downwards towards integral body.Accompanying drawing 6 has shown 6 times of the outer shroud rotating speeds situation when interior ring rotating speed, and its running orbit is the wire track on segment surface, and the apparent acceleration direction disperses to all directions.Contrasting two analog results in addition can find out, at gravity 1*10 ^-3On the number percent of acceleration, accompanying drawing 5 is 100% in the scope, and accompanying drawing 10 is about 24.5%.

Contrast accompanying drawing 5 can find out with accompanying drawing 7, and when setup parameter Yi=0 (m), the space motion track is become the fixation locus of whole sphere by the fixation locus on the segment.Accompanying drawing 8 is set at random pattern with the angular velocity of inner and outer ring, because the relation of coordinate position, the space motion position is the whole surface of segment.

When in the accompanying drawing 9 being parameter Yi=0 (m), the simulation result of angular velocity random value, can see that run location in publishing picture can reach the surface of whole ball.Location parameter in the accompanying drawing 10 is 1/10 in the accompanying drawing 9, can see at gravity 1*10 ^-3On the number percent of acceleration, accompanying drawing 10 is about 99.3% in the scope, and accompanying drawing 9 is about 48.4%.

3.3 interpretation of result:

Accompanying drawing 12 is depicted as laboratory sample and the simulation result on the gyrator that is installed in Space Sci. & Application Research Center, Chinese Academy of Sciences's development.Simulation result and experimental result when the constant speed rotation that is respectively different rotating speeds shown in accompanying drawing 12, accompanying drawing 13 and the accompanying drawing 14.Can find out according to simulation result, be the constant speed rotation owing to what carry out, and apparent acceleration can not reach all position of rotation, so the microgravity effect does not appear in laboratory sample yet.And accompanying drawing 15 is depicted as simulation result and experimental result when rotating at random.Apparent acceleration can rotate to all positions of pointing space, and the microgravity effect has also appearred in laboratory sample.

It should be noted last that above embodiment is only unrestricted in order to technical scheme of the present invention to be described.Although the present invention is specified with reference to embodiment; Those of ordinary skill in the art is to be understood that; Technical scheme of the present invention is made amendment or is equal to replacement, do not break away from the spirit and the scope of technical scheme of the present invention, it all should be encompassed in the middle of the claim scope of the present invention.

Claims (2)

1. method that is used for evaluating micro-gravity dual-axis gyrator; This dual-axis gyrator is made up of inner and outer rings; The axle that inner and outer rings independently centers on respectively separately carries out 360 degree rotations; Ring was gone up with interior ring rotation in object was fixed on, and it is characterized in that the described method that is used for evaluating micro-gravity dual-axis gyrator comprises following steps:

11) dual-axis gyrator is carried out physical modeling;

12) set up base coordinate system, interior cyclic coordinate system and three coordinate systems of outer shroud coordinate system, wherein, base coordinate system is a fixed coordinate system;

13) utilize the vectorial property of coordinate system rotation; Finally derive the apparent gravity Acceleration Formula of object; This apparent gravity acceleration is an acceleration of gravity in the projection down of interior cyclic coordinate system, its value for the vector of the acceleration of inner and outer rings rotation generation and acceleration of gravity and;

14) parameter that is provided with according to micro-gravity dual-axis gyrator; Utilize above-mentioned this parameter of apparent gravity Acceleration Formula evaluation that the effect of simulated microgravity is set; This parameter is provided with ability simulated microgravity effect if the apparent gravity acceleration that obtains can reach all position of rotation; Micro-gravity dual-axis gyrator can simulated microgravity, otherwise that parameter is provided with is improper, and micro-gravity dual-axis gyrator can not simulated microgravity;

Direction cosine between outer shroud-pedestal such as following table:

Direction cosine such as following table between the interior ring-outer shroud:

Thus, direction cosine between interior ring-pedestal such as following table:

Step 13) further comprises:

13-1) obtain between outer shroud and the pedestal and the direction cosine between interior ring and the outer shroud, and derive the direction cosine between interior ring and the pedestal according to the conversion principle under the rotating coordinate system;

The position formula of object in coordinate system does;

r=xi+yj+zk

Object in described being fixed on the ring has fixing interior cyclic coordinate (X under interior cyclic coordinate is _i, Y _i, Z _i);

The relevant position of described object under basic coordinate system is:

$\left\{\begin{array}{ccc}{X}_b=& X_i\cos {\mathrm{\&theta;}}_i& +Z_i\sin {\mathrm{\&theta;}}_i\\ Y_b=& X_i\sin {\mathrm{\&theta;}}_i\sin {\mathrm{\&theta;}}_o+Y_i\cos {\mathrm{\&theta;}}_o& -Z_i\cos {\mathrm{\&theta;}}_i\sin {\mathrm{\&theta;}}_o\\ Z_b=& -X_i\sin {\mathrm{\&theta;}}_i\cos {\mathrm{\&theta;}}_o+Y_i\sin {\mathrm{\&theta;}}_o& +Z_i\cos {\mathrm{\&theta;}}_i\cos {\mathrm{\&theta;}}_o\end{array}\right.$

Object absolute angle speed under base coordinate system is respectively along the component of x, y and z coordinate axis:

$\left\{\begin{array}{c}{\mathrm{\&omega;}}_x={\mathrm{\&omega;}}_o\cos {\mathrm{\&theta;}}_i\\ {\mathrm{\&omega;}}_y={\mathrm{\&omega;}}_i\\ {\mathrm{\&omega;}}_z={\mathrm{\&omega;}}_o\sin {\mathrm{\&theta;}}_i\end{array}\right.$

13-2) acceleration of gravity is to be the acceleration of g perpendicular to the ground size under the base coordinate system, and formula is: g=-gk _b

According to the coordinate cosine table between interior ring and the pedestal:

Z _bk _b＝-sinθ _icosθ _oX _ii _i+sinθ _oY _ij _i+cosθ _icosθ _oZ _ik _i

The gravitational acceleration g in the inner ring axis component with

indicates then:

$g=g_{x_i}{i}_i+g_{y_i}{j}_i+g_{z_i}{k}_i$

Obtain acceleration of gravity by above three formula:

$\left\{\begin{array}{c}{g}_{x_i}=g\cos {\mathrm{\&theta;}}_o\sin {\mathrm{\&theta;}}_i\\ g_{y_i}=-g\sin {\mathrm{\&theta;}}_o\\ g_{z_i}=-g\cos {\mathrm{\&theta;}}_o\cos {\mathrm{\&theta;}}_i\end{array}\right.$

13-4) coordinate system is rotated with angular velocity omega, and then the derivative of vector G finally is expressed as:

$\frac{\mathrm{dG}}{\mathrm{dt}}=\frac{{\mathrm{dG}}_x}{\mathrm{dt}}i+G_x\frac{\mathrm{di}}{\mathrm{dt}}+\frac{{\mathrm{dG}}_y}{\mathrm{dt}}j+G_y\frac{\mathrm{dj}}{\mathrm{dt}}+\frac{{\mathrm{dG}}_z}{\mathrm{dt}}k+G_z\frac{\mathrm{dk}}{\mathrm{dt}}$

$=(\frac{{\mathrm{dG}}_x}{\mathrm{dt}}i+\frac{{\mathrm{dG}}_y}{\mathrm{dt}}j+\frac{{\mathrm{dG}}_z}{\mathrm{dt}}k)+(G_x\frac{\mathrm{di}}{\mathrm{dt}}+G_y\frac{\mathrm{dj}}{\mathrm{dt}}+G_z\frac{\mathrm{dk}}{\mathrm{dt}})$

Finally be expressed as according to dynamics and space rotating coordinate system character following formula:

$\frac{\mathrm{dG}}{\mathrm{dt}}=\frac{\tilde{d}G}{\mathrm{dt}}+\mathrm{\&omega;}\&times;G$

13-5) bring the speed v of rotating object into following formula:

$v=\frac{\mathrm{dr}}{\mathrm{dt}}=\frac{\tilde{d}r}{\mathrm{dt}}+\mathrm{\&omega;}\&times;r$

Object is owing to the component of absolute acceleration under interior cyclic coordinate is that coordinate system rotation produces is:

$\left\{\begin{array}{ccc}{W}_{X_i}=& W_X\cos {\mathrm{\&theta;}}_i+W_Y\sin {\mathrm{\&theta;}}_i\sin {\mathrm{\&theta;}}_o& -W_Z\sin {\mathrm{\&theta;}}_i\cos {\mathrm{\&theta;}}_o\\ W_{Y_i}=& +W_Y\cos {\mathrm{\&theta;}}_o& +W_Z\sin {\mathrm{\&theta;}}_o\\ W_{Z_i}=& W_X\sin {\mathrm{\&theta;}}_i-W_Y\cos {\mathrm{\&theta;}}_i\sin {\mathrm{\&theta;}}_o& +W_Z\cos {\mathrm{\&theta;}}_i\cos {\mathrm{\&theta;}}_o\end{array}\right.$

The projection sum of the acceleration W that is produced by gravity acceleration g and coordinate system rotation according to the apparent acceleration A of object under interior cyclic coordinate system, formula is: A=g+W

It is that the component of each is down along interior cyclic coordinate:

$\left\{\begin{array}{ccc}{A}_x=& g\cos {\mathrm{\&theta;}}_o\sin {\mathrm{\&theta;}}_i& +W_{X_i}\\ A_y=& -g\sin {\mathrm{\&theta;}}_o& +W_{Y_i}\\ A_z=& -g\cos {\mathrm{\&theta;}}_o\cos {\mathrm{\&theta;}}_i& +W_{Z_i}\end{array}\right..$

2. the method that is used for evaluating micro-gravity dual-axis gyrator according to claim 1 is characterized in that described outer shroud is fixed on the pedestal, and interior ring is fixed on the outer shroud.

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