Inertial parameter error-oriented optimal trim quality gradient prediction method

Abstract

The invention relates to an inertial parameter error-oriented optimal balancing mass gradient prediction method, which comprises the following steps of: based on balancing mass minimization, establishing and solving a constraint optimization problem of optimal balancing of dynamic and static imbalance of a satellite, and obtaining optimal balancing mass and position meeting an existing counterweight mounting position set of the satellite; analyzing a gradient matrix of the optimal balancing quality relative to the dynamic and static unbalance of the satellite; establishing a transformation matrix from the local coordinate system of each part of the satellite to the overall coordinate system of the satellite, and further calculating the gradient value of the dynamic and static unbalance of the satellite relative to the inertial parameters of each equipment or part; and in combination with the balancing quality optimal solution, the gradient matrix, the transformation matrix and the gradient value, analyzing the influence of the inertial parameter error of each device or part on the optimal balancing quality.

Description

TECHNICAL FIELD

[0001] The present application relates to an optimal trimming mass gradient prediction method for inertia parameter error, and belongs to the field of satellite spacecraft application overall design. BACKGROUND

[0002] With the rapid development of space technology and application demand, the application of rotating loads in satellite spacecraft is becoming more and more widespread, and the integration of rotating load systems is becoming more and more complex. The satellite rotating body gradually develops from a simple device or component to a subsystem level, a whole cabin level or even a whole satellite level, and the control accuracy of the rotating body is also required to be higher based on the load application demand. In view of the complex rotating body, in order to reduce the difficulty of satellite control and improve the rotating control accuracy and stability of the rotating load, high-precision mass trimming is required on the ground to achieve the minimum residual of dynamic and static unbalance.

[0003] In the traditional ground trimming test, a double-face trimming method is generally used, mainly relying on a dynamic balancing machine to measure the static and dynamic unbalance of the rotating test piece, and gradually eliminating the minimum residual of the dynamic and static unbalance by adding or reducing weight on the virtual two trimming planes. In actual engineering application, the installation position of the satellite counterweight is usually arranged according to experience, and cannot well support the installation of the target position of the virtual trimming plane used in the trimming test. In addition, the ground dynamic balancing machine test is an effective means to obtain the dynamic and static unbalance of the satellite or component, which can only be carried out at the later stage of the satellite prototype development. Due to the uncertainty of the inertia parameter estimation error, installation error and assembly implementation of each integrated device or component, the accurate dynamic and static unbalance of the rotating body cannot be obtained during the design of the whole satellite scheme, so the trimming point position cannot be effectively considered, and the efficient trimming of the subsequent development test cannot be realized. The satellite design uses CAE software to support the integration of system inertia parameters after the input of the determined inertia parameters of each component, and cannot quickly and effectively evaluate the influence of the inertia parameter error of each component on the inertia parameters of the integrated system and trimming. SUMMARY

[0004] The technical problem solved by the present application is that, in view of the evaluation difficulty and trimming problem existing in the prior art, an optimal trimming mass gradient prediction method for inertia parameter error is proposed.

[0005] The present application solves the above technical problem by the following technical scheme: An optimal trimming mass gradient prediction method for inertia parameter error, comprising: establishing a satellite dynamic and static unbalance optimal trimming constraint optimization model for selecting a satellite dynamic and static unbalance optimal trimming strategy; obtaining a gradient matrix of the optimal trimming weight relative to the inertia parameters of each installed device or component of the satellite according to the satellite dynamic and static unbalance optimal trimming strategy; Gradient analysis of the influence of the optimal trim weight on the gradient of the dynamic and static imbalance of the satellite rotating body, and gradient analysis of the influence of the residual dynamic and static imbalance of the satellite rotating body on the gradient of the mass of the trim weight; Establish the transformation matrix of the local coordinate system of each component of the satellite to the overall coordinate system of the satellite, and calculate the gradient value of the dynamic and static imbalance of the satellite relative to the inertia parameters of each device or component; Determine the influence of the inertia parameter error of each device or component on the optimal trim weight using the optimal trim weight, the gradient matrix, the transformation matrix, and the gradient value, and adjust the optimal trim weight according to the influence.

[0006] The optimal trim constraint optimization condition for the dynamic and static imbalance of the satellite is: selecting the best trim point position from the subset of the satellite installable trim weight positions U D xyz , the inertia product of the satellite rotating body I xy and I xz , the lateral center of mass position y c and z c are numerically negligible and satisfy the total mass of the trim weight used for trimming M a .

[0007] According to the optimal trim constraint optimization condition for the dynamic and static imbalance of the satellite, an optimal trim constraint optimization model for the dynamic and static imbalance of the satellite is constructed, which is:

[0008]

[0009]

[0010]

[0011]

[0012] In the formula, x is the rotation axis of the satellite rotating body, is the mass of the trim weight installed at the i th trim point, N is the number of trim points, is the target value of the satellite trimming, is the subset of the trim point positions of the satellite installable trim weight, and are the upper and lower limits of the installable trim weight mass at a single trim point position, respectively.

[0013] ​Based on the solution values ​​of the optimal trim constraint optimization model for satellite dynamic and static imbalance, the method for selecting the optimal trim strategy for satellite dynamic and static imbalance is to uniformly select initial values ​​at multiple points within the upper and lower limits of the optimal trim constraint optimization conditions. Calculate the balancing results corresponding to each initial value, select the balancing constraint parameter information corresponding to the result with the smallest total mass, and record it as the optimal balancing strategy for satellite dynamic and static imbalance.

[0014] The method for establishing the gradient matrix of the optimal trim weight relative to the inertial parameters of each installed equipment or component of the satellite is as follows: To obtain the function of the dynamic and static imbalance of the total trim mass relative to the satellite's rotating body under the optimal trim weight, i.e., the total trim mass. M a Relative satellite rotational body dynamic and static imbalance I xy , I xz , y c , z c The gradient matrix function is: .

[0015] The method for gradient analysis of the gradient effect of the optimal trim weight relative to the dynamic and static imbalance of the satellite rotating body is as follows:

[0016] The method for gradient analysis of the effect of the residual dynamic and static imbalance of the satellite's rotating body on the mass of the counterweight is as follows:

[0017] In the formula, The gradient operator represents the dynamic and static imbalance of the satellite's rotating body. This represents the error or change in the dynamic and static imbalance of the satellite's rotating body. , These represent the errors in the two lateral inertial product parameters of the satellite, Δ. y c Δ z c These represent the errors in the two lateral centroid positions of the satellite; The error amount of the dynamic and static imbalance is calculated based on the relationship between the residual dynamic and static imbalance of the satellite rotating body and the inertial parameter error of each device or component. The calculation method is as follows:

[0018]

[0019]

[0020]

[0021] wherein, M is the total mass of the satellite, n is the total number of devices or components, is the position of the mass center of the i-th device or component in the satellite global coordinate system, i and is the value of the product of inertia of the i-th device or component relative to its mass center in the payload coordinate system, i i represents the mass of the i-th device or component. m The satellite dynamic-static unbalance quantity relative to the inertia parameters of each device or component includes the inertia parameters of the i-th device or component relative to the product of inertia of the mass center in the local coordinate system, and the inertia parameters of the i-th device or component relative to the mass center in the local coordinate system of the i-th device or component;

[0022] i After the transformation matrix of the local coordinate system of each component of the satellite to the global coordinate system of the satellite is established, the gradient value of the product of inertia of the i-th device or component relative to the mass center in the payload coordinate system is confirmed according to the transformation matrix, and is converted into the inertia parameters in the local coordinate system, specifically: i i

[0023]

[0024] wherein, R [ r 1; r 2; r 3] are the rotation transformation matrices of the satellite global coordinate system to the local coordinate system of the device or component, (A ) represents the element point product of the matrix, I 1 is the inertia parameter error matrix of the device or component relative to the local coordinate system of the device or component; The calculation method of the inertia parameters of the mass center of the i-th device or component relative to the local coordinate system of the i-th device or component is as follows: i

[0025]

[0026] wherein, P 0=[ T is the position of the mass center of the device or component in the payload coordinate system, i ​​​​​​​The mass center parameter error matrix of the device or component relative to its local coordinate system; After the relationship between the dynamic and static imbalance of the satellite and the inertia parameters and mass center inertia parameters of each device or component is determined, the gradient value of the optimal trimming mass relative to the dynamic and static imbalance of the satellite is solved by a numerical method.

[0027] The method for calculating the influence of the inertia parameter error of each device or component on the optimal trimming mass is:

[0028] In the formula, the total mass of the counterweight block M a is I xy , I xz , y c , z c a nonlinear function.

[0029] The gradient operator of the optimal trimming total mass relative to the dynamic and static imbalance of the satellite is The numerical method of finite difference is used for calculation, and the calculation method is:

[0030] In the formula, i =2,3,…, N -1, N the number of numerical sampling points, respectively, the dynamic and static imbalance of the satellite , is the analysis step; The gradient values of the boundary points are calculated by using the forward difference and backward difference methods respectively, and the calculation method is:

[0031] In the formula, j=1,2,3,4, X1-X4 respectively represent I xy , I xz , y c , z c .

[0032] Compared with the prior art, the present application has the advantages of: (1) The optimal trimming mass gradient prediction method for inertial parameter error provided by the application firstly proposes the constraint optimization solution based on the optimal trimming problem and gradient analysis of the trimming total mass relative to the inertial parameters such as the dynamic and static imbalance of the satellite, establishes the mathematical relationship between the inertial parameter error of each component and the residual error of the dynamic and static imbalance of the satellite rotating body after system integration and the trimming mass, can efficiently analyze the comprehensive influence of the inertial parameter error such as the center of mass and moment of inertia of all integrated devices or components of the satellite on the optimal trimming mass of the satellite rotating body, quickly predict the trimming mass of the satellite, and guide the satellite trimming design in the satellite design stage such as scheme or initial sample. The constraint optimization solution based on the optimal trimming problem and the multiple trimming mass comprehensive optimization strategy proposed at the same time can guide the trimming implementation in the satellite trimming test, and realize the minimum trimming mass meeting the minimum dynamic and static imbalance residual error requirement; (2) The application proposes the constraint optimization solution based on the optimal trimming problem and the gradient analysis method of the trimming weight relative to the inertial parameters of each installed device or component of the satellite, which can efficiently analyze the comprehensive influence of the inertial parameter error such as the center of mass and moment of inertia of all integrated devices or components of the satellite on the optimal trimming mass of the satellite rotating body. In the satellite design stage such as scheme or initial sample, the trimming mass of the satellite can be quickly predicted, and strong support is provided for the satellite system scheme design; (3) The satellite optimal trimming strategy proposed by the application is a beneficial supplement to the traditional ground trimming test double-face trimming method, can select an optimal position subset from the existing trimming weight installation positions of the satellite, realize the minimum trimming mass meeting the minimum dynamic and static imbalance residual error requirement, and can also effectively guide the trimming point position design in the satellite design stage, and solve the problem of blindness in traditional experience design; (4) The application proposes a multi-dimensional trimming mass comprehensive optimization strategy, which can realize the local optimization of single trimming of the trimming point position and the trimming total mass, and also can realize the global optimization after multiple trimmings, and effectively make up for the low trimming efficiency caused by the large measurement error of the dynamic balancing machine and the poor unbalance reduction rate. BRIEF DESCRIPTION OF DRAWINGS

[0033] Figure 1 The satellite trimming mass gradient prediction method for inertial parameter error provided by the application is provided with a flow chart; Figure 2 The trimming point distribution schematic diagram obtained by the single optimal trimming strategy provided by the application is provided; Figure 3 The trimming point distribution schematic diagram obtained by the global optimal trimming strategy provided by the application is provided; Figure 4 The influence result schematic diagram of the inertial product parameter error on the trimming total mass provided by the application is provided; Figure 5 The influence result schematic diagram of the center of mass parameter error on the trimming total mass provided by the application is provided; Figure 6 A schematic diagram of gradient analysis of the minimum balancing mass relative to the unbalance of the couple provided by the present invention; Figure 7 A schematic diagram of gradient analysis of the minimum balancing mass relative to static unbalance provided by the present invention; Figure 8 This is a schematic diagram illustrating the impact of inertia parameter error on satellite dynamic imbalance provided by the present invention. Figure 9 A schematic diagram illustrating the impact of the inertial parameter error of device 1 on the minimum balancing mass provided by the present invention; Figure 10 A schematic diagram showing the effect of the inertial parameter error of device 2 on the minimum balancing mass provided by the present invention. Detailed Implementation

[0034] An optimal trim quality gradient prediction method for inertial parameter errors is proposed. Based on minimizing the trim quality, a constrained optimization problem of optimal trimming of satellite dynamic and static imbalance is established and solved. The gradient matrix of the optimal trim quality relative to the satellite dynamic and static imbalance is analyzed. The transformation matrix from the local coordinate system of each satellite component to the global coordinate system of the satellite is established, and the gradient value of the satellite dynamic and static imbalance relative to the inertial parameters of each device or component is further calculated. Combining the optimal trim quality solution, gradient matrix, transformation matrix and gradient value, the influence of the inertial parameter errors of each device or component on the optimal trim quality is analyzed.

[0035] The optimal balancing quality gradient prediction method includes the following steps: An optimal trim constraint optimization model for satellite dynamic and static imbalance is established to select the optimal trim strategy for satellite dynamic and static imbalance. According to the optimal trim strategy for satellite dynamic and static imbalance, obtain the gradient matrix of the optimal trim weight relative to the inertial parameters of each installed equipment or component of the satellite; Gradient analysis was performed to investigate the gradient effect of the optimal balancing weight relative to the dynamic and static imbalance of the satellite rotating body, and to investigate the gradient effect of the residual dynamic and static imbalance of the satellite rotating body on the mass of the counterweight. Establish the transformation matrix from the local coordinate system of each satellite component to the global coordinate system of the satellite, and calculate the gradient value of the satellite's dynamic and static imbalance relative to the inertial parameters of each device or component; Using the optimal balancing weight, gradient matrix, transformation matrix, and gradient value, determine the influence of the inertial parameter error of each device or component on the optimal balancing quality, and adjust the optimal balancing quality according to the influence.

[0036] The optimal balancing constraint for satellite dynamic and static imbalance is: within a subset of locations where counterweights can be installed on the satellite. U Select the optimal balancing point location D xyzSatellite rotating body inertia product I xy And I xz Lateral centroid position y c And z c Numerical neglect and meet the total mass of counterweight for trim M a Minimize.

[0037] According to the satellite dynamic and static imbalance optimal trim constraint optimization condition to build satellite dynamic and static imbalance optimal trim constraint optimization model, for:

[0038]

[0039]

[0040]

[0041]

[0042] In the formula, x The axis is the satellite rotating body rotation axis, The first i The weight of the mass block installed at the N The number of trim points, The target value of satellite trim, The subset of the trim point position of the satellite installable counterweight, And The upper and lower limits of the installable mass block quality of a single counterweight position, respectively.

[0043] According to the satellite dynamic and static imbalance optimal trim constraint optimization model, the method for selecting the satellite dynamic and static imbalance optimal trim strategy is to select the initial value In the upper and lower limit interval of the optimal trim constraint optimization condition, the initial value The trim results of each initial value are calculated, and the trim constraint parameter information corresponding to the result with the smallest total mass is selected, and the total is recorded as the satellite dynamic and static imbalance optimal trim strategy.

[0044] The gradient matrix of the optimal trim weight relative to the inertia parameters of each installed equipment or component of the satellite is established as follows: Under the optimal trim weight, the function of the trim total mass relative to the dynamic and static imbalance of the satellite rotating body, that is, the trim total mass M a The dynamic and static imbalance of the satellite rotating body I xy ,I xz , y c , z c The gradient matrix function is: .

[0045] The method for gradient analysis of the gradient effect of the optimal trim weight relative to the dynamic and static imbalance of the satellite rotating body is as follows:

[0046] The method for gradient analysis of the effect of the residual dynamic and static imbalance of the satellite's rotating body on the mass of the counterweight is as follows:

[0047] In the formula, The gradient operator represents the dynamic and static imbalance of the satellite's rotating body. This represents the error or change in the dynamic and static imbalance of the satellite's rotating body. , These represent the errors in the two lateral inertial product parameters of the satellite, Δ. y c Δ z c These represent the errors in the two lateral centroid positions of the satellite.

[0048] The error amount of dynamic and static imbalance is calculated based on the relationship between the residual dynamic and static imbalance of the satellite's rotating body and the inertial parameter errors of each device or component. The calculation method is as follows:

[0049]

[0050]

[0051]

[0052] In the formula, M The total mass of the satellite's rotating body. n The total number of equipment or components. For the first i The position of the center of mass of a device or component in the global coordinate system of the satellite. and For the first i The value of the product of inertia of a device or component relative to its center of mass in the load cabin coordinate system.

[0053] The satellite's dynamic and static imbalance relative to the inertial parameters of each device or component, including the first... iThe inertial parameters of a device or component relative to its center of mass in the local coordinate system, and the product of inertia of the first device or component with respect to its center of mass. i The centroid inertial parameters of a device or component relative to its local coordinate system; After establishing the transformation matrices from the local coordinate systems of each satellite component to the global coordinate system, the first... i The gradient value of the product of inertia of each device or component relative to its center of mass in the load chamber coordinate system is converted into inertial parameters in the local coordinate system, specifically:

[0054]

[0055] In the formula, R =[ r 1; r 2; r 3] is the rotation transformation matrix from the satellite's body coordinate system to the local coordinate system of the equipment or component. ) represents the element-wise dot product of matrices. I 1 represents the inertia parameter error matrix of the equipment or component relative to its local coordinate system; No. i The method for calculating the centroid inertial parameters of a device or component relative to its local coordinate system is as follows:

[0056]

[0057] In the formula, P 0=[ T For equipment or components i The position of the center of mass in the load compartment coordinate system This is the centroid parameter error matrix of the equipment or component relative to its local coordinate system; After determining the relationship between the satellite's dynamic and static imbalance and the inertial parameters of each device or component, and the inertial parameters of the center of mass, the gradient value of the optimal balancing weight relative to the dynamic and static imbalance of the satellite's rotating body is solved numerically.

[0058] The method for calculating the influence of the inertial parameter errors of each device or component on the optimal balancing quality is as follows:

[0059] In the formula, the total mass of the counterweight is... M a for I xy , I xz , y c ,z c a non-linear function.

[0060] Gradient operator of optimal trim mass relative to dynamic and static imbalance of satellite rotating body The numerical method is calculated by finite difference method, and the calculation method is:

[0061] In the formula, i =2,3,…, N -1, N The number of numerical sampling points, respectively, the dynamic and static imbalance of the satellite rotating body , is the analysis step; The gradient values of the boundary points are calculated by forward difference and backward difference method respectively, and the calculation method is:

[0062] In the formula, j =1,2,3,4.

[0063] The following will be further described in combination with the drawings of the specification and the preferred embodiments: In the current embodiment, as shown in Figure 1 , a flow chart of a satellite optimal trim mass gradient prediction method for inertial parameter error is given. First, based on the constraint optimization solution S2 of the optimal trim problem and the gradient analysis S80 of the trim total weight relative to the satellite dynamic and static imbalance of the satellite, the mathematical relationship S83 between the inertial parameter error S81 of each component and the residual error of the dynamic and static imbalance of the satellite rotating body and the trim mass after system integration is established, the comprehensive influence S100 of the inertial parameter error such as the center of mass and the moment of inertia of all integrated devices or components of the satellite on the optimal trim mass of the satellite rotating body is analyzed efficiently, the trim mass S50 of the satellite is quickly predicted, and the satellite trim design is guided in the satellite design stage such as scheme or prototype. Based on the constraint optimization solution of the optimal trim problem and the multiple trim mass comprehensive optimization strategy S84, the trim implementation can be guided during the satellite trim test, the optimal position subset is selected from the existing trim weight installation position of the satellite, and the minimum trim mass cost S50 that meets the minimum dynamic and static imbalance residual error requirement is realized. The specific implementation includes the following steps.

[0064] Steps S10, S11 and S12 analyze the input conditions of optimal trim, including collecting the trim point position set U, evaluating the initial inertial parameters of the satellite rotating body (which can be obtained by analyzing the value or measuring by the dynamic balancing machine), and determining the target dynamic and static imbalance upper limit value .

[0065] Step S2 establishes and solves the constrained optimization problem for optimal balancing, equating the satellite's optimal balancing strategy to the subset of locations where counterweights can be installed on the satellite. U Select the optimal balancing point location D xyz This causes the inertial product of the satellite's rotating body to... I xy and I xz Lateral centroid position y c and z c The value is close to zero and satisfies the total mass of the counterweights used for balancing. M a Minimize S40, i.e.

[0066]

[0067]

[0068]

[0069]

[0070] In the formula, x The axis is the rotation axis of the satellite's rotating body. For the first i The weight of the installation mass block at each balancing point. N The number of balancing points, The target value for satellite balancing, This is a subset of the balancing points where counterweights can be installed on the satellite. and These represent the upper and lower limits of the mass of counterweights that can be installed at a single counterweight location.

[0071] Step S30, solving the constrained optimization problem for optimal balancing, can be implemented using various algorithms, including the interior point method, trust region reflection method, and active set method. The active set method is recommended. Simultaneously, the more robust algorithmic strategy employed in step S20 is used, with initial values... Multiple points are selected uniformly within the upper and lower limits of the balancing quality constraint, and the balancing results of each point are calculated. The result with the smallest total mass is selected as the optimal balancing strategy S50.

[0072] Step S60 employs the finite difference method to perform gradient analysis of the optimal trim weight relative to the inertial parameters of each installed device or component on the satellite. First, the total trim mass is established. M aDynamic and static imbalance of satellite rotating body I xy 、 I xz 、 y c 、 z c function of the dynamic and static imbalance of the satellite rotating body calculated by steps S10-S50.

[0073] Further, the gradient matrix of the optimal trimming mass relative to the dynamic and static imbalance of the satellite is obtained based on the gradient operator, i.e.

[0074] wherein denotes the gradient operator.

[0075] Further, the gradient operator of the optimal trimming total mass relative to the dynamic and static imbalance of the satellite rotating body is calculated by using the finite difference numerical method, i.e.

[0076] wherein i =2,3,…, N -1, N the number of numerical sampling points, respectively denote the dynamic and static imbalance of the satellite rotating body , is the analysis step length.

[0077] The gradient values of the boundary points are calculated by using the forward difference and backward difference methods, respectively, i.e. j =1,2,3,4 Step 80 uses the gradient to analyze the influence of the dynamic and static imbalance residual of the satellite rotating body on the mass of the counterweight, i.e.

[0078] wherein denotes the error or change of the corresponding variable.

[0079] wherein, according to the relationship between the dynamic and static imbalance residual of the satellite rotating body and the error of the inertia parameters of each device or component, the error of the dynamic and static imbalance can be directly calculated, i.e.

[0080]

[0081]

[0082]

[0083] In the formula, M The total mass of the satellite's rotating body. n The total number of equipment or components. For the first i The position of the center of mass of a device or component in the global coordinate system of the satellite. and For the first i The value of the product of inertia of a device or component relative to its center of mass in the load cabin coordinate system.

[0084] Steps S81, S82, and S83 further consider the transformation of the inertial parameter reference coordinate system of the equipment or component, converting each physical parameter vector to a unified reference coordinate system. Based on the transformation matrix from the local coordinate system of each satellite component to the overall satellite coordinate system, the... i The value of the product of inertia of a device or component relative to its center of mass in the load chamber coordinate system can be converted into inertial parameters in its local coordinate system, i.e.

[0085]

[0086] In the formula, R =[ r 1; r 2; r 3] is the rotation transformation matrix from the satellite's body coordinate system to the local coordinate system of the equipment or component. () represents the element-wise dot product of matrices. I 1 represents the inertia parameter error matrix of the device or component relative to its local coordinate system.

[0087] Correspondingly, the first i The centroid inertial parameters of a device or component relative to its local coordinate system can be expressed as:

[0088]

[0089] In the formula, P 0=[ T For equipment or components i The position of the center of mass in the load compartment coordinate system This is the centroid parameter error matrix of the device or component relative to its local coordinate system.

[0090] Step S90 involves analyzing the optimal solution for overall balancing quality, the gradient matrix, the transformation matrix, and the inertial parameter error matrix. The following formula is used to analyze the impact of the inertial parameter errors of each device or component on the optimal balancing quality:

[0091] Meanwhile, in actual satellite trimming implementation, the dynamic balancing machine system has a certain measurement error, and the imbalance reduction rate in a single operation is generally below 90%, requiring multiple trimming operations to achieve the final goal. Step S84 provides an implementation method for a multi-dimensional comprehensive optimization strategy for trimming quality. First, based on the local optimization results of multiple trimming operations obtained in steps S2 and S50, the trimming quality is based on the obtained multiple sets of optimal trimming strategies. M i and position coordinates D xyzi Further, the coordinate transformation in step S82 and the inertial parameter analysis in step S83 are used, and the inverse of the analysis result is used as the initial input for the inertial parameters for the final optimal balancing. The formula for calculating the initial inertial parameters is:

[0092]

[0093]

[0094]

[0095] in, R =[ r 1; r 2; r [3] represents the rotation transformation matrix from the satellite body coordinate system to the local coordinate system of the balancing mass block. M s The total mass of the satellite's rotating body. m This represents the total number of balancing mass blocks. To balance the mass block i The position of the centroid in its local coordinate system =[ x r ; y r ; z r Balancing mass block i The position of the local coordinate system origin in the satellite body coordinate system. To balance the mass block i The inertia matrix relative to its local coordinate system.

[0096] In actual implementation, if the volume of the balancing mass block is small, then and All can be approximated as 0, and the above formula can be further simplified. Through steps S84, S12, and S2, and simultaneously the input conditions of steps S10 and S11, the optimal balancing strategy result of step S50 is obtained, achieving global optimal balancing.

[0097] Further illustrated below are the accompanying drawings and preferred embodiments of the present application: Embodiment One A satellite optimal trimming mass gradient prediction method for inertia parameter error, solving the optimal trimming strategy S50, first establishes the constraint optimization problem of optimal trimming S2, including collecting the set of trimming point positions S10, determining the target dynamic and static imbalance upper limit value of trimming S11, determining the initial inertia parameter error of the satellite rotating body S12 through analysis or dynamic balancing machine measurement, based on the estimated series of trimming mass initial values S20, using the constraint optimization problem solving algorithm effective set method S30 to iteratively calculate the optimal trimming point position and the minimum trimming total mass S11, and obtaining the optimal trimming strategy S50.

[0098] In this embodiment, as shown in Figure 2 , a total of 126 (see Figure 2 blue points) trimming point positions are collected, and the target dynamic and static imbalance of trimming is less than 10 kgmm and 0.01 kgm 2 , respectively. According to the balancing machine test data (double-face trimming): the upper trimming plane imbalance is 1410.8 g / 125°; the lower trimming plane imbalance is 1059.3 g / 315.9°. The initial trimming mass is evenly distributed in the range of 0.01 kg~5 kg, and 30 values are obtained. According to the constraint optimization solving of optimal trimming, 5 target points (see Figure 2 red circle marked positions) are obtained in the set of 126 positions, and the optimal trimming result is shown in the following table:

[0099] Embodiment Two A satellite optimal trimming mass gradient prediction method for inertia parameter error, obtaining the global optimal trimming solution S84, according to the one-step procedure of the foregoing embodiment, after multiple trimmings, collecting all the trimming point mass block positions and inertia parameters, converting the inertia parameters of each mass block from their respective local coordinate systems to the satellite overall coordinate system S82, analyzing the inertia parameters of the satellite rotating body S83, obtaining the initial inertia parameters S12 for global trimming optimization, repeating the one-step procedure of the embodiment, and obtaining the optimal trimming strategy S50.

[0100] In this embodiment, according to the balancing machine test data, the distribution of the trimming points after multiple trimmings is as shown in Table 17 positions, as shown in Figure 3 (red circle marked positions), and the total trimming mass is 19.854 kg. According to the satellite rotating body inertia parameters calculated from the initial inertia parameters by S82 and S83, and further S84, S12 and S2, the globally optimal trimming point distribution is as shown in Table 7 positions, as shown in Figure 3(Black triangle mark position), the total mass of 13.34 kg. Global optimization can save weight about 6.5 kg, the residual change of satellite rotating body dynamic and static imbalance before and after global optimization is 0.06 kgm 2 And 0.13 mm, the residual amount is small, which can be balanced by subsequent fine balance with less than 1 kg of balance weight to achieve the balance target.

[0101]

[0102] Example three: A satellite optimal trim mass gradient prediction method for inertial parameter error, analyzes the influence of each device or component inertial parameter error on the optimal trim mass, first collects the inertial parameter error of each device or component and its position in the satellite coordinate system S81, converts the inertial parameters of each device or component from their local coordinate system to the satellite global coordinate system S82, analyzes the satellite rotating body inertial parameter error S83; Combined with the steps of example one, calculate S60 using finite difference method, get the gradient matrix of optimal trim mass relative to satellite dynamic and static imbalance S80; Comprehensive analysis of optimal solution of trim mass, gradient matrix, transformation matrix and inertial parameter error matrix, analyze the influence of each device or component inertial parameter error on the optimal trim mass S100.

[0103] Take two key load devices of satellite as an example, device 1 is installed vertically (local coordinate axis is parallel to global coordinate axis), device 2 is installed obliquely (local coordinate axis has angle with global coordinate axis), two devices account for 60% of the total mass of satellite rotating body, so their inertial parameter error has great influence on the total dynamic and static imbalance and trim mass.

[0104] As shown in Figure 4 , Figure 6 , the influence distribution of initial inertia product parameters of rotating body (corresponding to dynamic imbalance) and center of mass position parameters (corresponding to static imbalance) on the optimal trim mass, the maximum trim mass is close to 30 kg. As shown in Figure 5 , Figure 7 , calculated by steps S60 and S80, corresponding to the gradient matrix value. As shown in Figure 8 , the device inertial parameter error analysis result of the whole inertial parameter error calculated according to steps S81, S82 and S83. As shown in Figure 9 , Figure 10As shown, the influence of the inertial parameter error (4mm of center of mass deviation and 10% of inertia parameter deviation) of device 1 and device 2 on the minimum balancing mass is shown, and the analysis of the optimal solution of the balancing mass, the gradient matrix, the transformation matrix and the inertial parameter error matrix is integrated, the influence of the center of mass deviation and the inertia parameter deviation of the device on the optimal balancing mass is obtained, and the balancing mass caused by the multi-source error is 38.7kg, wherein the center of mass deviation of device 1 has the greatest influence, close to 7kg; and the inertia parameter error of device 2 has the greatest influence, about 11kg or so.

[0105] The embodiment is aimed at the demand of high-precision balancing of a satellite, and proposes a constraint optimization solution based on the optimal balancing problem and a gradient analysis method of the total balancing mass relative to the inertial parameters such as the dynamic and static imbalance of the satellite, which can efficiently analyze the comprehensive influence of the inertial parameter errors such as the center of mass and the inertia of all integrated devices or components of the satellite on the optimal balancing mass of the satellite rotating body, and can quickly predict the balancing mass of the satellite in the satellite design stage such as a scheme or a prototype, thereby providing strong support for the satellite system scheme design; the optimal balancing strategy of the satellite is a beneficial supplement to the traditional ground balancing test double-face balancing method, can select an optimal position subset from the existing balancing weight installation positions of the satellite, and realizes the minimum balancing mass meeting the minimum dynamic and static imbalance residual requirement. Meanwhile, the satellite design stage can also effectively guide the balancing point position design, and solves the problem of blindness in the traditional experience design; the proposed multi-dimensional balancing mass comprehensive optimization strategy can realize single balancing local optimization of the balancing point position and the total balancing mass, and can also realize global optimization after multiple balancings, thereby effectively making up for the low balancing efficiency caused by the large measurement error of the dynamic balancing machine and the poor imbalance reduction rate.

[0106] Although the present application has been disclosed with reference to the preferred embodiments above, it is not intended to limit the present application, and any person skilled in the art can make possible changes and modifications to the technical solutions of the present application by using the disclosed methods and technical contents without departing from the spirit and scope of the present application, therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present application, which does not depart from the content of the technical solutions of the present application, belongs to the protection scope of the technical solutions of the present application.

[0107] The contents not described in detail in the specification of the present application belong to the known technology of the person skilled in the art.

Claims

1. A method for predicting the optimal balancing mass gradient based on inertial parameter errors, characterized in that... include: An optimal trim constraint optimization model for satellite dynamic and static imbalance is established to select the optimal trim strategy for satellite dynamic and static imbalance. According to the optimal trim strategy for satellite dynamic and static imbalance, obtain the gradient matrix of the optimal trim weight relative to the inertial parameters of each installed equipment or component of the satellite; Gradient analysis was performed to investigate the gradient effect of the optimal balancing weight relative to the dynamic and static imbalance of the satellite rotating body, and to investigate the gradient effect of the residual dynamic and static imbalance of the satellite rotating body on the mass of the counterweight. Establish the transformation matrix from the local coordinate system of each satellite component to the global coordinate system of the satellite, and calculate the gradient value of the satellite's dynamic and static imbalance relative to the inertial parameters of each device or component; Using the optimal balancing weight, gradient matrix, transformation matrix, and gradient value, determine the influence of the inertial parameter error of each device or component on the optimal balancing quality, and adjust the optimal balancing quality according to the influence.

2. The optimal balancing mass gradient prediction method for inertial parameter errors according to claim 1, characterized in that: The optimal balance constraint for satellite dynamic and static imbalance is: within a subset of locations where counterweights can be installed on the satellite. U Select the optimal balancing point location D xyz This causes the inertial product of the satellite's rotating body to... I xy and I xz Lateral centroid position y c and z c The numerical values ​​are negligible and the total mass of the counterweights used for balancing is satisfied. M a minimize.

3. The optimal balancing mass gradient prediction method for inertial parameter errors according to claim 2, characterized in that: Based on the optimal trim constraint optimization conditions for satellite dynamic and static imbalance, the optimal trim constraint optimization model for satellite dynamic and static imbalance is constructed as follows: In the formula, x The axis is the rotation axis of the satellite's rotating body. For the first i The weight of the installation mass block at each balancing point. N The number of balancing points, The target value for satellite balancing, This is a subset of the balancing points where counterweights can be installed on the satellite. and These represent the upper and lower limits of the mass of counterweights that can be installed at a single counterweight location.

4. The optimal balancing mass gradient prediction method for inertial parameter errors according to claim 3, characterized in that: Based on the solution values ​​of the optimal trim constraint optimization model for satellite dynamic and static imbalance, the method for selecting the optimal trim strategy for satellite dynamic and static imbalance is to uniformly select initial values ​​at multiple points within the upper and lower limits of the optimal trim constraint optimization conditions. Calculate the balancing results corresponding to each initial value, select the balancing constraint parameter information corresponding to the result with the smallest total mass, and record it as the optimal balancing strategy for satellite dynamic and static imbalance.

5. The optimal balancing mass gradient prediction method for inertial parameter errors according to claim 4, characterized in that: The method for establishing the gradient matrix of the optimal trim weight relative to the inertial parameters of each installed equipment or component of the satellite is as follows: To obtain the function of the dynamic and static imbalance of the total trim mass relative to the satellite's rotating body under the optimal trim weight, i.e., the total trim mass. M a Relative satellite rotational body dynamic and static imbalance I xy , I xz , y c , z c The gradient matrix function is: 。 6. The optimal balancing mass gradient prediction method for inertial parameter errors according to claim 5, characterized in that: The method for gradient analysis of the gradient effect of the optimal trim weight relative to the dynamic and static imbalance of the satellite rotating body is as follows: The method for gradient analysis of the effect of the residual dynamic and static imbalance of the satellite's rotating body on the mass of the counterweight is as follows: In the formula, The gradient operator represents the dynamic and static imbalance of the satellite's rotating body. This represents the error or change in the dynamic and static imbalance of the satellite's rotating body. , These represent the errors in the two lateral inertial product parameters of the satellite, Δ. y c Δ z c These represent the errors in the two lateral centroid positions of the satellite.

7. The optimal balancing mass gradient prediction method for inertial parameter errors according to claim 6, characterized in that: The error amount of the dynamic and static imbalance is calculated based on the relationship between the residual dynamic and static imbalance of the satellite rotating body and the inertial parameter error of each device or component. The calculation method is as follows: In the formula, M The total mass of the satellite's rotating body. n The total number of equipment or components. For the first i The position of the center of mass of a device or component in the global coordinate system of the satellite. and For the first i The value of the product of inertia of a device or component relative to its center of mass in the load cabin coordinate system. m i This represents the mass of the i-th device or component.

8. The optimal balancing mass gradient prediction method for inertial parameter errors according to claim 7, characterized in that: The satellite's dynamic and static imbalance relative to the inertial parameters of each device or component, including the first... i The inertial parameters of a device or component relative to its center of mass in the local coordinate system, and the product of inertia of the first device or component with respect to its center of mass. i The centroid inertial parameters of a device or component relative to its local coordinate system; After establishing the transformation matrices from the local coordinate systems of each satellite component to the global coordinate system, the first... i The gradient value of the product of inertia of each device or component relative to its center of mass in the load chamber coordinate system is converted into inertial parameters in the local coordinate system, specifically: In the formula, R =[ r 1; r 2; r 3] is the rotation transformation matrix from the satellite's body coordinate system to the local coordinate system of the equipment or component. ) represents the element-wise dot product of matrices. I 1 represents the inertia parameter error matrix of the equipment or component relative to its local coordinate system; No. i The method for calculating the centroid inertial parameters of a device or component relative to its local coordinate system is as follows: In the formula, P 0=[ T For equipment or components i The position of the center of mass in the load compartment coordinate system This is the centroid parameter error matrix of the equipment or component relative to its local coordinate system; After determining the relationship between the satellite's dynamic and static imbalance and the inertial parameters of each device or component, and the inertial parameters of the center of mass, the gradient value of the optimal balancing weight relative to the dynamic and static imbalance of the satellite's rotating body is solved numerically.

9. The optimal balancing mass gradient prediction method for inertial parameter errors according to claim 8, characterized in that: The method for calculating the influence of the inertial parameter errors of each device or component on the optimal balancing quality is as follows: In the formula, the total mass of the counterweight is... M a for I xy , I xz , y c , z c Nonlinear functions.

10. The optimal balancing mass gradient prediction method for inertial parameter errors according to claim 8, characterized in that: The gradient operator of the optimal balanced total mass relative to the dynamic and static imbalance of the satellite rotating body The calculation is performed using the finite difference numerical method, as follows: In the formula, i =2,3,…, N -1, N Number of numerical sampling points These are the dynamic and static imbalances of the satellite's rotating body. , For analysis step size; The gradient values ​​at the boundary points are calculated using both forward and backward differencing methods, as follows: In the formula, j=1,2,3,4, and X1~X4 represent respectively I xy , I xz , y c , z c .

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