CN105631234A - Momentum wheel disturbance response assessment method - Google Patents

Abstract

The invention discloses a momentum wheel disturbance response assessment method. A phase difference between a force and a force moment is taken as a random variable, a designated transfer function is established to realize convolution with white noise, the phase difference between the force and the force moment includes all possible conditions in an acquired force vector time sequence, and a response time sequence acquired by taking the force vector as excitation includes all possible amplitudes. Response extremes can be obtained by one-time response analysis according to the method, which is greatly significant to reduce technical risks of momentum wheel disturbance response assessment.

Description

A kind of momenttum wheel disturbance response appraisal procedure

Technical field

The present invention relates to momenttum wheel technical field, particularly relate to a kind of momenttum wheel disturbance response appraisal procedure.

Background technology

Static unbalance and dynamic imbalance are the major causes causing momenttum wheel disturbance. Uneven coefficient quiet, dynamic only can determine the amplitude of disturbing force, moment, can not determine the phase differential between disturbing force, moment, if ignoring this phase differential to carry out perturbation analysis, the result of calculating must not be guarded.

In order to can be conservative analyze momenttum wheel disturbance produce impact, the method adopted at present repeatedly calculates, when calculating every time, between disturbing force and disturbing moment, different phase differential is set, by the maximum value of the momenttum wheel disturbing influence the most of the maximum value in calculation result. This kind of method calculated amount is big, and is easily subject to the interference of human factor and can not obtain affecting the maximum value of result, brings certain risk to the analysis and evaluation of response.

Summary of the invention

In view of this, the present invention provides a kind of momenttum wheel disturbance response appraisal procedure, it is possible to reduce the technical risk of momenttum wheel disturbance response assessment.

A kind of momenttum wheel disturbance response appraisal procedure, comprises the steps:

Step one: stochastic generation white Gaussian noise time series N respectively₁(t) and N₂(t);

Step 2, the parameter quiet, dynamic uneven of momenttum wheel is utilized to generate pulse response function time series respectively:

If C_staFor momenttum wheel static unbalance parameter, C_dynFor momentum moves in turn uneven parameter, �� is momenttum wheel rotating speed, and the time series of pulse response function utilizes following formula fitting:

$G\left(t\right)=\left[\begin{array}{cccc}{g}_{s1}\left(t\right)& & & \\ & g_{s2}\left(t\right)& & \\ & & g_{d1}\left(t\right)& \\ & & & g_{d2}\left(t\right)\end{array}\right]$

Wherein:

Wherein,

Wherein,

Wherein,

Wherein,

��_s=��_d=0.01

The white Gaussian noise that the time series of step 3, pulse response function step 2 obtained and step one obtain carries out convolution, finally obtains the noisy data of momenttum wheel:

$\left\{\begin{array}{c}{F}_{sx}\left(t\right)\\ F_{sy}\left(t\right)\\ M_{ds}\left(t\right)\\ M_{dy}\left(t\right)\end{array}\right\}={\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}\left[\begin{array}{cccc}{g}_{s1}(t-\mathrm{\τ})& & & \\ & g_{s2}(t-\mathrm{\τ})& & \\ & & g_{d1}(t-\mathrm{\τ})& \\ & & & g_{b2}(t-\mathrm{\τ})\end{array}\right]\left\{\begin{array}{c}{N}_1\left(t\right)\\ N_1\left(t\right)\\ N_2\left(t\right)\\ N_2\left(t\right)\end{array}\right\}d\mathrm{\τ}$

Wherein F_sx(t)��F_syT disturbing force that () is momenttum wheel, M_dx(t)��M_dyT disturbing moment that () is momenttum wheel; �� is integration variable;

Step 4, by force vector $\left\{\begin{array}{c}{F}_{sx}\left(t\right)\\ F_{sy}\left(t\right)\\ M_{dx}\left(t\right)\\ M_{dy}\left(t\right)\end{array}\right\}$ As the input of time domain disturbance response, being applied on momenttum wheel, the response obtaining momenttum wheel exports, and momenttum wheel is quiet, the dynamic uneven disturbance response of the maximum value utilizing response to export is assessed.

Wherein said response export in displacement time domain response obtain according to Du Hamei integral formula:

$\left\{\begin{array}{c}{x}_1\left(t\right)\\ .\\ .\\ .\\ x_i\left(t\right)\\ .\\ .\\ .\\ x_n\left(t\right)\end{array}\right\}={\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}\left[\begin{array}{cccc}{h}_{11}(t-\mathrm{\τ})& h_{12}(t-\mathrm{\τ})& h_{13}(t-\mathrm{\τ})& h_{14}(t-\mathrm{\τ})\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ h_{i1}(t-\mathrm{\τ})& h_{i2}(t-\mathrm{\τ})& h_{i3}(t-\mathrm{\τ})& h_{i4}(t-\mathrm{\τ})\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ h_{11}(t-\mathrm{\τ})& h_{12}(t-\mathrm{\τ})& h_{13}(t-\mathrm{\τ})& h_{14}(t-\mathrm{\τ})\end{array}\right]\left\{\begin{array}{c}{F}_{sx}\left(t\right)\\ F_{sy}\left(t\right)\\ M_{dx}\left(t\right)\\ M_{dy}\left(t\right)\end{array}\right\}d\mathrm{\τ}$

Wherein, $X\left(t\right)=\left\{\begin{array}{c}{x}_1\left(t\right)\\ .\\ .\\ .\\ x_i\left(t\right)\\ .\\ .\\ .\\ x_n\left(t\right)\end{array}\right\}$ For the time domain response sequence exported, $H\left(t\right)=\left[\begin{array}{cccc}{h}_{11}\left(t\right)& h_{12}\left(t\right)& h_{13}\left(t\right)& h_{14}\left(t\right)\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ h_{i1}\left(t\right)& h_{i2}\left(t\right)& h_{i3}\left(t\right)& h_{i4}\left(t\right)\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ h_{11}\left(t\right)& h_{12}\left(t\right)& h_{13}\left(t\right)& h_{14}\left(t\right)\end{array}\right]$ For the pulse response function matrix of momenttum wheel, n is the dimension of matrix H (t).

The present invention has following useful effect:

Phase differential between wind tunnel is considered as stochastic variable by the present invention, carries out convolution by constructing the transport function specified and white Gaussian noise, and in the force vector time series of acquisition, the phase differential of wind tunnel contains situation about likely occurring. Using this force vector as excitation, the time of response sequence of acquisition contains the amplitude likely occurred. By a response analysis, the method just can obtain the extreme value of response, and the technical risk of reduction momenttum wheel disturbance response assessment is significantly by this.

Accompanying drawing explanation

Fig. 1 is the momenttum wheel disturbance response appraisal procedure schema of the present invention.

Fig. 2 is the momenttum wheel system of coordinates schematic diagram of the present invention.

Embodiment

Develop simultaneously embodiment below in conjunction with accompanying drawing, describe the present invention.

A kind of momenttum wheel disturbance response appraisal procedure of the present invention, as shown in Figure 1, specifically comprises the steps:

(1) white Gaussian noise time series is generated;

The generation method of white Gaussian noise has multiple, does not specifically list here.

(2) the uneven parameter quiet, dynamic of momenttum wheel is utilized to generate pulse response function time series respectively;

If C_staFor momenttum wheel static unbalance parameter, C_dynFor momentum moves in turn uneven parameter, �� is momenttum wheel rotating speed, and the time series of pulse response function utilizes following formula fitting.

$G\left(t\right)=\left[\begin{array}{cccc}{g}_{s1}\left(t\right)& & & \\ & g_{s2}\left(t\right)& & \\ & & g_{d1}\left(t\right)& \\ & & & g_{d2}\left(t\right)\end{array}\right]$

Wherein

Wherein,

Wherein,

Wherein,

Wherein,

��_s=��_d=0.01.

(3) time series of pulse response function and white Gaussian noise carry out convolution, finally obtain the noisy data of momenttum wheel.

$\left\{\begin{array}{c}{F}_{sx}\left(t\right)\\ F_{sy}\left(t\right)\\ M_{ds}\left(t\right)\\ M_{dy}\left(t\right)\end{array}\right\}={\∫}_{-\mathrm{\∞}}^{\mathrm{\∞}}\left[\begin{array}{cccc}{g}_{s1}(t-\mathrm{\τ})& & & \\ & g_{s2}(t-\mathrm{\τ})& & \\ & & g_{d1}(t-\mathrm{\τ})& \\ & & & g_{d2}(t-\mathrm{\τ})\end{array}\right]\left\{\begin{array}{c}{N}_1\left(t\right)\\ N_1\left(t\right)\\ N_2\left(t\right)\\ N_2\left(t\right)\end{array}\right\}d\mathrm{\τ}$

Wherein, �� is integration variable; F_sx(t)��F_syT disturbing force that () is momenttum wheel, the two direction and momenttum wheel system of coordinates X, Y-axis are parallel; M_dx(t)��M_dyT disturbing moment that () is momenttum wheel, the two direction and momenttum wheel system of coordinates X, Y-axis are parallel; N₁(t)��N₂(t) white Gaussian noise for independently producing.

(4) force vector $\left\{\begin{array}{c}{F}_{sx}\left(t\right)\\ F_{sy}\left(t\right)\\ M_{dx}\left(t\right)\\ M_{dy}\left(t\right)\end{array}\right\}$ Directly as the input of time domain disturbance response, the upper limit of the uneven disturbance response quiet as momenttum wheel, dynamic of the maximum value in analytical results can be got. During displacement, domain response can calculate according to Du Hamei integral formula:

$\left\{\begin{array}{c}{x}_1\left(t\right)\\ .\\ .\\ .\\ x_i\left(t\right)\\ .\\ .\\ .\\ x_n\left(t\right)\end{array}\right\}={\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}\left[\begin{array}{ccc}{h}_{11}(t-\mathrm{\τ})& \mathrm{...}& h_{1n}(t-\mathrm{\τ})\\ .& & \\ .& & \\ .& & \\ h_{i1}(t-\mathrm{\τ})& \mathrm{...}{h}_{ij}(t-\mathrm{\τ})\mathrm{...}& h_{in}(t-\mathrm{\τ})\\ .& & \\ .& & \\ .& & \\ h_{n1}(t-\mathrm{\τ})& \mathrm{...}& h_{nn}(t-\mathrm{\τ})\end{array}\right]\left\{\begin{array}{c}{f}_1\left(t\right)\\ .\\ .\\ .\\ f_j\left(t\right)\\ .\\ .\\ .\\ f_n\left(t\right)\end{array}\right\}d\mathrm{\τ}$

$\left\{\begin{array}{c}{x}_1\left(t\right)\\ .\\ .\\ .\\ x_i\left(t\right)\\ .\\ .\\ .\\ x_n\left(t\right)\end{array}\right\}={\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}\left[\begin{array}{cccc}{h}_{11}(t-\mathrm{\τ})& h_{12}(t-\mathrm{\τ})& h_{13}(t-\mathrm{\τ})& h_{14}(t-\mathrm{\τ})\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ h_{i1}(t-\mathrm{\τ})& h_{i2}(t-\mathrm{\τ})& h_{i3}(t-\mathrm{\τ})& h_{i4}(t-\mathrm{\τ})\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ h_{11}(t-\mathrm{\τ})& h_{12}(t-\mathrm{\τ})& h_{13}(t-\mathrm{\τ})& h_{14}(t-\mathrm{\τ})\end{array}\right]\left\{\begin{array}{c}{F}_{sx}\left(t\right)\\ F_{sy}\left(t\right)\\ M_{dx}\left(t\right)\\ M_{dy}\left(t\right)\end{array}\right\}d\mathrm{\τ}$

Wherein, $X\left(t\right)=\left\{\begin{array}{c}{x}_1\left(t\right)\\ .\\ .\\ .\\ x_i\left(t\right)\\ .\\ .\\ .\\ x_n\left(t\right)\end{array}\right\}$ For time domain response sequence, $H\left(t\right)=\left[\begin{array}{cccc}{h}_{11}\left(t\right)& h_{12}\left(t\right)& h_{13}\left(t\right)& h_{14}\left(t\right)\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ h_{i1}\left(t\right)& h_{i2}\left(t\right)& h_{i3}\left(t\right)& h_{i4}\left(t\right)\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ h_{11}\left(t\right)& h_{12}\left(t\right)& h_{13}\left(t\right)& h_{14}\left(t\right)\end{array}\right]$ For the pulse response function matrix of structure, n is the dimension of matrix H (t), $F\left(t\right)=\left\{\begin{array}{c}{F}_{sx}\left(t\right)\\ F_{sy}\left(t\right)\\ M_{dx}\left(t\right)\\ M_{dy}\left(t\right)\end{array}\right\}$ For vector. The upper limit of disturbance response is time domain response sequence maximum value max (abs (X (t))), assesses for momenttum wheel is quiet, dynamic uneven disturbance response.

In sum, these are only the better embodiment of the present invention, it is not intended to limit protection scope of the present invention. Within the spirit and principles in the present invention all, any amendment of doing, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (2)

1. a momenttum wheel disturbance response appraisal procedure, it is characterised in that, comprise the steps:

Step one: stochastic generation white Gaussian noise time series N respectively₁(t) and N₂(t);

Step 2, the parameter quiet, dynamic uneven of momenttum wheel is utilized to generate pulse response function time series respectively:

If C_staFor momenttum wheel static unbalance parameter, C_dynFor momentum moves in turn uneven parameter, �� is momenttum wheel rotating speed, and the time series of pulse response function utilizes following formula fitting:

$G\left(t\right)=\left[\begin{array}{cccc}{g}_{s1}\left(t\right)& & & \\ & g_{s2}\left(t\right)& & \\ & & g_{d1}\left(t\right)& \\ & & & g_{d2}\left(t\right)\end{array}\right]$

Wherein:

Wherein,

Wherein,

Wherein,

Wherein,

��_s=��_d=0.01

The white Gaussian noise that the time series of step 3, pulse response function step 2 obtained and step one obtain carries out convolution, finally obtains the noisy data of momenttum wheel:

$\left\{\begin{array}{c}{F}_{sx}\left(t\right)\\ F_{sy}\left(t\right)\\ M_{ds}\left(t\right)\\ M_{dy}\left(t\right)\end{array}\right\}={\∫}_{-\mathrm{\∞}}^{\mathrm{\∞}}\left[\begin{array}{cccc}{g}_{s1}(t-\mathrm{\τ})& & & \\ & g_{s2}(t-\mathrm{\τ})& & \\ & & g_{d1}(t-\mathrm{\τ})& \\ & & & g_{d2}(t-\mathrm{\τ})\end{array}\right]\left\{\begin{array}{c}{N}_1\left(t\right)\\ N_1\left(t\right)\\ N_2\left(t\right)\\ N_2\left(t\right)\end{array}\right\}d\mathrm{\τ}$

Wherein F_sx(t)��F_syT disturbing force that () is momenttum wheel, M_dx(t)��M_dyT disturbing moment that () is momenttum wheel; �� is integration variable;

Step 4, by force vector $\left\{\begin{array}{c}{F}_{sx}\left(t\right)\\ F_{sy}\left(t\right)\\ M_{dy}\left(t\right)\\ M_{dy}\left(t\right)\end{array}\right\}$ As the input of time domain disturbance response, being applied on momenttum wheel, the response obtaining momenttum wheel exports, and momenttum wheel is quiet, the dynamic uneven disturbance response of the maximum value utilizing response to export is assessed.

2. momenttum wheel disturbance response appraisal procedure as claimed in claim 1 a kind of, it is characterised in that, wherein said response export in displacement time domain response obtain according to Du Hamei integral formula:

$\left\{\begin{array}{c}{x}_1\left(t\right)\\ .\\ .\\ .\\ x_i\left(t\right)\\ .\\ .\\ .\\ x_n\left(t\right)\end{array}\right\}={\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}\left[\begin{array}{cccc}{h}_{11}(t-\mathrm{\τ})& h_{12}(t-\mathrm{\τ})& h_{13}(t-\mathrm{\τ})& h_{14}(t-\mathrm{\τ})\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ h_{i1}(t-\mathrm{\τ})& h_{i2}(t-\mathrm{\τ})& h_{i3}(t-\mathrm{\τ})& h_{i4}(t-\mathrm{\τ})\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ h_{11}(t-\mathrm{\τ})& h_{12}(t-\mathrm{\τ})& h_{13}(t-\mathrm{\τ})& h_{14}(t-\mathrm{\τ})\end{array}\right]\left\{\begin{array}{c}{F}_{sx}\left(t\right)\\ F_{sy}\left(t\right)\\ M_{dx}\left(t\right)\\ M_{dy}\left(t\right)\end{array}\right\}d\mathrm{\τ}$

Wherein, $X\left(t\right)=\left\{\begin{array}{c}{x}_1\left(t\right)\\ .\\ .\\ .\\ x_i\left(t\right)\\ .\\ .\\ .\\ x_n\left(t\right)\end{array}\right\}$ For the time domain response sequence exported, $H\left(t\right)=\left[\begin{array}{cccc}{h}_{11}\left(t\right)& h_{12}\left(t\right)& h_{13}\left(t\right)& h_{14}\left(t\right)\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ h_{i1}\left(t\right)& h_{i2}\left(t\right)& h_{i3}\left(t\right)& h_{i4}\left(t\right)\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ h_{11}\left(t\right)& h_{12}\left(t\right)& h_{13}\left(t\right)& h_{14}\left(t\right)\end{array}\right]$ For the pulse response function matrix of momenttum wheel, n is the dimension of matrix H (t).