Multi-objective optimization balancing method for dynamic and static unbalance of large-inertia special-shaped rotating load satellite

Abstract

The invention discloses a dynamic and static unbalance multi-objective optimization balancing method for a large-inertia special-shaped rotating load satellite, and belongs to the field of dynamic balance balancing. The objective of the invention is to solve the problems of insufficient balancing reliability and many artificial iterations in the existing ground dynamic balancing test. According to the method, a multi-objective function is constructed by taking minimization of static unbalance, even unbalance and additional torque as objectives and taking the number of counterweight points and single-point maximum counterweight mass as constraints, a Pareto optimal solution set of the counterweight mass and the position is obtained through global search, the optimal solution set is loaded to a special-shaped rotating load satellite, then test solution is carried out, and the optimal solution set of the counterweight mass and the position is obtained. And the dynamic balancing of the special-shaped rotating load satellite is realized. The method is used for realizing dynamic balancing of the special-shaped rotating load satellite.

Description

Technical Field

[0001] The invention relates to the field of dynamic balancing. Background Art

[0002] In the field of satellite attitude control and high-precision remote sensing observation, large, irregularly shaped rotating payload satellites (such as microwave radiometers, scatterometers, and slewing antennas) often experience uneven mass distribution due to manufacturing and assembly errors, bearing wobble, and complex orbital environmental disturbances. This results in incomplete alignment of the principal axis of inertia and the axis of rotation, leading to dynamic and static imbalance. These imbalances generate additional inertial forces and moments during rotation, which can induce structural deformation, force frequent attitude corrections on the satellite, and consume precious propellant and electrical energy. They can also reduce image registration and geolocation accuracy, and even affect the conformality of the payload surface and the accuracy of communication pointing. Therefore, conducting efficient and accurate dynamic balancing tests on irregularly shaped rotating payload satellites is a key step in improving the overall performance and lifespan of the satellite.

[0003] Existing ground-based dynamic balancing tests typically rely on a dual-plane vertical balancing machine (VDBM) and the "two-plane balancing method" to decompose unbalanced forces. This type of equipment is large and heavy, placing stringent requirements on the installation foundation and operating environment (vacuum level, temperature control, vibration isolation, etc.). Furthermore, its vibration measurement system must simultaneously capture centrifugal force and torque signals. Under low speed and high mass load conditions, these two signals are severely coupled, limiting the accuracy of translational-oscillation decoupling, resulting in large measurement errors and insufficient trimming reliability. The two-plane method originated in the field of high-speed rotors such as steam turbines and generators. When applied to low-speed, high-inertia satellite payloads, it often faces challenges such as low trimming efficiency, high randomness, and reliance on empirical iterations. The imbalance is also affected by multiple uncertainties such as flexible deformation, windage, and shaft deviation, further exacerbating the uncertainty of the balancing solution.

[0004] To reduce aerodynamic disturbances, some experiments are conducted in vacuum tanks. However, vacuum balancing machines are expensive and have limited chamber size. When experiments are conducted at atmospheric pressure or in a semi-vacuum environment, airflow disturbances can alter the measured imbalance. Repeated calibration and balancing of the same payload at different pressures often require additional testing cycles and costs. Furthermore, as payload size increases and the number of balance points and loading space become limited, the traditional serial process of manually selecting points, adding blocks, measuring, and adding more blocks is difficult to achieve within an acceptable number of times to achieve a high-precision balance state. This has become a bottleneck affecting the progress of satellite development. Summary of the Invention

[0005] The purpose of the invention is to solve the problems of insufficient balancing reliability and high number of manual iterations in existing ground dynamic balancing tests, and a multi-objective optimization balancing method for dynamic and static imbalance of satellites with large inertia and special-shaped rotating payloads is proposed.

[0006] A multi-objective optimization balancing method for dynamic and static imbalance of a satellite with large inertia and special-shaped rotating payloads, the method comprising the following contents:

[0007] Step 1: preset the total number and positions of counterweights on the special-shaped rotating payload satellite, and perform the i-th round of counterweighting on each counterweight position, and when i=1, no counterweight mass is loaded on each counterweight position;

[0008] Step 2: Load the i-th round of counterweights to each counterweight position on the special-shaped rotating payload satellite;

[0009] Step 3: Place the special-shaped rotating payload satellite in a dynamic balancing machine, and start the dynamic balancing machine by the control system. The process of starting the dynamic balancing machine is as follows: evacuate the dynamic balancing machine (1) to simulate the low-pressure environment on orbit, and control the dynamic balancing machine to drive the special-shaped rotating payload satellite (2) to rotate, and obtain the j-th output data of the control system, where the initial value of j is 1; and the control system output data includes: static unbalance, even unbalance and additional torque;

[0010] Step 4: With the goal of minimizing static unbalance, couple unbalance, and additional torque, and with the number of counterweight points and the maximum counterweight mass at a single point as constraints, a multi-objective function is constructed;

[0011] Step 5: Solve the multi-objective function to obtain the counterweight point position and the counterweight mass at the corresponding position as the counterweight solution for the i-th round;

[0012] Step 6: Determine whether i is greater than or equal to a preset value. If not, go to step 7; if yes, go to step 8.

[0013] Step 7: Multiply the mass of each counterweight at each counterweight point in the i-th round counterweight scheme by the same preset coefficient to obtain the mass of each counterweight at each counterweight point in the optimized i-th round counterweight scheme. Load the optimized i-th round counterweight scheme onto the special-shaped rotating payload satellite and execute step 9.

[0014] Step 8: Load the i-th round of counterweight solution onto the special-shaped rotating payload satellite and execute step 9;

[0015] Step 9: Detect whether the static unbalance, couple unbalance, and additional torque outputted for the jth time are all less than respective preset thresholds; if not, set j=j+1, i=i+1, and execute step 3; if yes, execute step 10;

[0016] Step 10, execute steps 3 to 4, solve the multi-objective function, obtain the counterweight point position to be reduced and the weight reduction mass at the corresponding position as the weight reduction plan, reduce the weight of the special-shaped rotating payload satellite according to the weight reduction plan, start the dynamic balancing machine after weight reduction, control the system to output the static imbalance, couple imbalance and additional torque, and detect whether the static imbalance, couple imbalance and additional torque output at this time are all less than their respective preset thresholds. If so, the special-shaped rotating payload satellite has completed balancing after weight reduction. If not, the last round of counterweight plan before weight reduction is the balancing plan for the special-shaped rotating payload satellite.

[0017] Preferably, the multi-objective function:

[0018] ;

[0019] Where, is a multi-objective function, is the static unbalance, is the even unbalance quantity, is the additional torque, is the total number of counterweights installed on the six main surfaces of the special-shaped rotating payload satellite, For the The mass of the counterweight applied at each counterweight point, For the The maximum counterweight mass allowed for each counterweight point, , , , is the mass of the special-shaped rotating payload satellite, is the y-axis coordinate of the center of mass of the special-shaped rotating payload satellite, is the z-axis coordinate of the center of mass of the special-shaped rotating payload satellite, is the x-axis coordinate of the center of mass of the special-shaped rotating payload satellite, For the The y-axis coordinate of the counterpoint, For the The z-axis coordinate of the counterpoint, For the The x-axis coordinate of a counterpoint.

[0020] Preferably, the preset coefficient is a value in the range of 70%–90%.

[0021] Preferably, in step 4, the preset value is 3.

[0022] Preferably, the dynamic balancing machine includes a vacuum tank, a vacuum pump, a turntable and a six-component force-torque sensor;

[0023] The special-shaped rotating payload satellite is arranged on a turntable, the turntable and the special-shaped rotating payload satellite are covered by a vacuum tank, and a six-component force-torque sensor is arranged on the turntable for measuring six-component force-torque signals;

[0024] The control system controls the vacuum pump to evacuate the vacuum tank to simulate the low-pressure environment in orbit, and controls the turntable to drive the special-shaped rotating payload satellite to rotate.

[0025] Preferably, the vacuum tank includes an observation window, a hatch, a first compartment, a second compartment, a third compartment and a limiting column;

[0026] Limiting columns are provided on the first compartment, the second compartment and the third compartment. The first compartment, the second compartment and the third compartment are connected in sequence from top to bottom to form a closed vacuum tank, and the three limiting columns on the first compartment, the second compartment and the third compartment are aligned in a straight line; the first compartment door is provided on the first compartment, and the observation window is provided on the second compartment.

[0027] Preferably, the static unbalance, the couple unbalance and the additional torque are obtained by:

[0028] Start the dynamic balancing machine, control the system output device operation data, combine with the pre-input basic data of the special-shaped rotating load satellite, and based on the principle of double-sided vertical balancing machine, obtain the static unbalance, couple unbalance and additional torque.

[0029] Preferably, the displayed output data includes rotational speed, axial displacement and six-component force-torque signals;

[0030] The basic data include the radius R2 of the upper calibration block, the radius R1 of the lower calibration block, the axial distance B between the upper and lower calibration blocks, the axial distance A between the lower calibration block and the turntable, the initial phase of the rotation axis and the coordinates of the satellite center of mass position.

[0031] The beneficial effects of the present invention are:

[0032] This invention aims to address existing issues in satellite dynamic balancing experiments involving irregular rotating payloads, such as bulky equipment, difficult measurement decoupling, tedious manual iteration, poor environmental adaptability, and high costs. By providing a "satellite dynamic balancing test based on a multi-objective optimization method," this experiment constructs a multi-objective model of static imbalance, couple imbalance, and additional torque. This model rapidly outputs an optimal weight balance solution during a closed-loop ground-based measurement and loading process, shortening the test cycle and reducing residual imbalance. This allows for precise, efficient, and economical balancing of low-speed rotating payloads in both atmospheric and vacuum environments.

[0033] It features a compact test bench and an integrated measurement-balancing device. Through a closed-loop "measurement-decision-loading" process driven by a multi-objective approach, it can rapidly perform dynamic balancing for satellites with various sizes and masses, even with rotating payloads of varying shapes, within the confines of a limited ground test space. The system utilizes a high-resolution six-component force-torque sensor and a low-speed, high-stability drive shaft system to accurately capture subtle changes in unbalance forces and additional torques, significantly improving the accuracy of residual unbalance measurement and assessment. Multi-objective optimization allows for a comprehensive balancing solution that simultaneously addresses multiple metrics, including static unbalance, coupler unbalance, and additional torque, significantly reducing iterations and overall test cycle time. A modular quick-release balancing fixture and environmental coupling compensation design enable rapid switching between various environments, such as atmospheric pressure and semi-vacuum, eliminating the need for recalibration and enabling immediate testing. An integrated software-hardware interface provides real-time visualization of measurement data, convergence curves, and optimization suggestions, streamlining the operational process, reducing reliance on manual experience, and ensuring repeatable and reliable results. Compared with traditional large-scale balancing machines, the present invention significantly reduces the equipment size and operation and maintenance costs, improves the flexibility of on-site deployment, and provides a support means with economic value and engineering practicality for improving the accuracy and life of satellite attitude control.

[0034] The present invention constructs a multi-objective optimization model with static unbalance, couple unbalance and additional torque as targets, which can give a unified trade-off of balancing indicators at the beginning of the experiment, avoiding multiple single-indicator trial and error, and covering all balancing targets at one time, greatly saving experimental time.

[0035] The invention adopts a closed-loop iterative process of "measurement → multi-objective optimization → loading → re-measurement". Each round of measurement data is immediately fed back to the optimization model, the iterative path converges automatically, and manual judgment and experience intervention are minimized, thereby improving balancing accuracy and consistency.

[0036] The dynamic threshold self-stop strategy of the present invention automatically terminates the experiment when all imbalance indicators are synchronously lower than the preset threshold, avoiding overloading or invalid iterations, and reducing the number of experimental rounds and the amount of counterweight used on average;

[0037] The modular quick-release counterweight fixture of the present invention is combined with a streamlined loading procedure to complete fixture installation, counterweight replacement, and retesting at the same station. The counterweight can be adjusted without removing the load, and the switch between normal pressure and vacuum environments is rapid, with strong on-site adaptability.

[0038] The environmental coupling compensation process of the present invention: the measurement link automatically reads pressure and temperature and corrects the experimental data, ensuring the consistency of the unbalanced values ​​measured under normal pressure, semi-vacuum and high vacuum, and reducing repeated calibration;

[0039] The present invention records data throughout the entire process and provides a visual decision-making interface. In the experimental process, the indicator decline curve and suggested solutions are displayed in real time, allowing the operator to intuitively grasp the convergence trend, reduce operational risks, and facilitate quality traceability. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 Schematic diagram of the external structure of the dynamic balancing machine;

[0041] Figure 2 This is a transmission diagram of the dynamic balancing machine;

[0042] Figure 3 (a) is the rectangular coordinate system relationship diagram of the dynamic balancing machine and the special-shaped rotating payload satellite. is the radius of the lower calibration block, is the radius of the upper calibration block, B is the axial distance between the two calibration blocks, and A is the distance between the lower calibration block and the table. is the satellite center of mass position coordinate, is the payload compartment coordinate system, is the coordinate system of the balancing machine;

[0043] Figure 3 (b) shows the relationship between the cylindrical coordinate system of the dynamic balancing machine and the special-shaped rotating payload satellite;

[0044] Figure 4 It is the measurement output software interface based on the dynamic balancing machine;

[0045] Figure 5 It is the software interface for satellite trimming of special-shaped rotating payloads based on multi-objective optimization algorithm. DETAILED DESCRIPTION

[0046] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0047] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments of the present invention can be combined with each other. The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but they are not intended to limit the present invention.

[0048] Example:

[0049] This embodiment, based on a multi-objective optimization algorithm, simultaneously considers multiple performance indicators, including static imbalance, couple imbalance, and torque. Through a global search, it obtains the Pareto optimal solution set for counterweight mass and position. Experiments demonstrate higher convergence efficiency and lower residual imbalance than traditional empirical methods. This enables rapid and precise trimming of large, low-speed rotating loads, laying the technical foundation for subsequent on-orbit dynamic balance and attitude stability control.

[0050] A multi-objective optimization balancing method for dynamic and static imbalance of a satellite with large inertia and special-shaped rotating payloads is characterized in that the method includes the following contents:

[0051] Step 1: preset the total number and positions of counterweights on the special-shaped rotating payload satellite 2, and perform the i-th round of counterweighting on each counterweight position, and when i=1, no counterweight mass is loaded on each counterweight position;

[0052] Step 2: Load the i-th round of counterweights to each counterweight position on the special-shaped rotating payload satellite 2;

[0053] Step 3: Place the special-shaped rotating payload satellite 2 in the dynamic balancing machine 1, and start the dynamic balancing machine 1 by the control system. The process of starting the dynamic balancing machine 1 is as follows: evacuate the dynamic balancing machine 1 to simulate the low-pressure environment in orbit, and control the dynamic balancing machine 1 to drive the special-shaped rotating payload satellite 2 to rotate, and obtain the j-th output data of the control system, where the initial value of j is 1; and the control system output data includes: static unbalance, couple unbalance, and additional torque;

[0054] Step 4: With the goal of minimizing static unbalance, couple unbalance, and additional torque, and with the number of counterweight points and the maximum counterweight mass at a single point as constraints, a multi-objective function is constructed;

[0055] Step 5: Solve the multi-objective function to obtain the counterweight point position and the counterweight mass at the corresponding position as the counterweight solution for the i-th round;

[0056] Step 6: Determine whether i is greater than or equal to a preset value. If not, go to step 7; if yes, go to step 8.

[0057] Step 7: Multiply the mass of each counterweight at each counterweight point in the i-th round counterweight scheme by the same preset coefficient to obtain the mass of each counterweight at each counterweight point in the optimized i-th round counterweight scheme. Load the optimized i-th round counterweight scheme onto the special-shaped rotating payload satellite 2, and execute step 9.

[0058] Step 8: Load the i-th round of counterweight solution to the special-shaped rotating payload satellite 2 and execute step 9;

[0059] Step 9: Detect whether the static unbalance, couple unbalance, and additional torque outputted for the jth time are all less than respective preset thresholds; if not, set j=j+1, i=i+1, and execute step 3; if yes, execute step 10;

[0060] Step 10, execute steps 3 to 4, solve the multi-objective function, obtain the counterweight point position to be reduced and the weight reduction mass at the corresponding position as the weight reduction plan, reduce the weight of the special-shaped rotating payload satellite 2 according to the weight reduction plan, and after weight reduction, start the dynamic balancing machine 1, control the system to output the static imbalance, the even imbalance and the additional torque, and detect whether the static imbalance, the even imbalance and the additional torque output at this time are all less than their respective preset thresholds. If so, the special-shaped rotating payload satellite 2 has completed balancing after weight reduction. If not, the last round of counterweight plan before weight reduction is the balancing plan for the special-shaped rotating payload satellite 2.

[0061] Combine Figure 1 , further defined, the structure of the dynamic balancing machine 1: the dynamic balancing machine 1 includes a vacuum tank, a vacuum pump 1-7, a turntable 1-8 and a six-component force-torque sensor;

[0062] The special-shaped rotating payload satellite 2 is arranged on the turntable 1-8. The vacuum tank covers the turntable 1-8 and the special-shaped rotating payload satellite 2 inside. The six-component force-torque sensor is arranged on the turntable 1-8 for measuring the six-component force-torque signal.

[0063] The control system controls the vacuum pump 1-7 to evacuate the vacuum tank to simulate the low-pressure environment on orbit, and controls the turntable 1-8 to drive the special-shaped rotating payload satellite 2 to rotate.

[0064] The vacuum tank includes an observation window 1-5, a hatch 1-4, a first compartment 1-1, a second compartment 1-2, a third compartment 1-3 and a limiting column 1-6;

[0065] Limiting columns 1-6 are provided on the first compartment 1-1, the second compartment 1-2 and the third compartment 1-3. The first compartment 1-1, the second compartment 1-2 and the third compartment 1-3 are sequentially connected from top to bottom to form a closed vacuum tank, and the three limiting columns on the first compartment 1-1, the second compartment 1-2 and the third compartment 1-3 are aligned in a straight line; a cabin door 1-4 is provided on the first compartment 1-1, and an observation window 1-5 is provided on the second compartment 1-2.

[0066] Further defined, the method of obtaining the static unbalance, the couple unbalance and the additional torque is specifically as follows:

[0067] Start the dynamic balancing machine 1, control the device output operation data, combine the pre-input basic data of the special-shaped rotating load satellite 2, and obtain the static unbalance, couple unbalance and additional torque based on the principle of the double-sided vertical balancing machine.

[0068] It is further defined that the display output data includes rotational speed, axial displacement and six-component force-torque signals;

[0069] The basic data include the radius R2 of the upper calibration block, the radius R1 of the lower calibration block, the axial distance B between the upper and lower calibration blocks, the axial distance A between the lower calibration block and the turntable, the initial phase of the rotation axis and the coordinates of the satellite center of mass position.

[0070] It is further defined that the preset coefficient is a value in the range of 70%–90%.

[0071] Further limiting, the default value is 3.

[0072] Specifically, the dynamic balancing machine can operate in three environments: open at normal pressure, closed at normal pressure, and closed at vacuum. This embodiment can automatically generate a counterweight solution in a closed-loop process through a multi-objective optimization method, thereby achieving fast and high-precision dynamic balancing.

[0073] The following describes the functions that the dynamic balancing machine can achieve when working in three environments: open at normal pressure, closed at normal pressure, and closed at vacuum:

[0074] 1. Assembly and normal pressure opening pre-commissioning:

[0075] S1. Place the third compartment 1-3 on a level platform calibrated with a spirit level and secure it with three-point support, ensuring that the verticality deviation between its axis and the ground is ≤0.05 mm / m.

[0076] S2. Install and debug turntables 1-8: First, connect the signal cables of the six-component force-torque sensors, then check the zero drift and sensitivity on the host computer.

[0077] S3, vertically install the limit column 1-6 on the third compartment 1-3, and its coaxiality deviation 0.03mm, which can provide a reference for the subsequent coaxial assembly of the first compartment 1-1 and the second compartment 1-2;

[0078] S4. Use the transition flange to fix the special-shaped rotating payload satellite 2 to the turntable 1-8; now you can carry out the first round of dynamic balancing pre-test under normal pressure open conditions to verify the sensor measurement accuracy and the basic effectiveness of the multi-objective optimization process, and make preliminary corrections to the concentricity of the rotating axis.

[0079] 2. Normal pressure sealing test:

[0080] S5. After ensuring that the third compartment 1-3 is centered, the first compartment 1-1 and the second compartment 1-2 are installed in sequence to form a three-dimensional enclosed turntable. Compared to the open environment at normal pressure, the closed experiment at normal pressure effectively shields the random disturbances caused by external wind resistance and temperature gradients, and its measurement results are closer to the actual operating conditions on orbit.

[0081] S6. Experimenters check the turntable operation and satellite rotation attitude in real time through observation windows 1-5, and can tighten or adjust internal components through hatches 1-4 when necessary.

[0082] 3. Vacuum sealing test:

[0083] S7, start vacuum pumps 1-7 and pump air step by step. When the pressure in the tank is After 100Pa, the gate valve is locked and the vacuum sealing test phase begins. At this point, the ambient aerodynamic resistance has been reduced to a negligible level, which can minimize the impact of the low-pressure environment on the imbalance.

[0084] S8. Enter the test parameters in the software interface and start the turntable. The system displays the speed, axial displacement, and six-component force-torque signals in real time and automatically completes sensor zero calibration.

[0085] S9. Based on the principle of a double-plane vertical balancing machine, enter the following parameters during initial calibration: the radius of the upper calibration block, R2, and the radius of the lower calibration block, R1; the axial spacing between the two calibration blocks, B and A; the initial phase of the rotary axis and the coordinates of the satellite's center of mass. These data are used as geometric and constraint conditions in subsequent multi-objective optimization calculations.

[0086] In this embodiment, steps 1 through 9 form a closed-loop test-optimization-load process. In step 1, no counterweighting is performed during the initial solution of the multi-objective function. In step 3, while the dynamic balancing machine 1 is rotating and sampling, the software (control system) outputs in real time: upper unbalance / phase, lower unbalance / phase, static unbalance / phase, even unbalance / phase, and additional torque / phase. Convergence is considered achieved when each indicator curve reaches a plateau and maintains a rate of change of less than 1% over three speed cycles. This means that the data output in step 3 is stable.

[0087] In steps 4 and 5, after rotation stops, the software automatically invokes a solver based on a multi-objective optimization method. With the goal of minimizing static unbalance, couple unbalance, and additional torque, and subject to the number of counterweight points and the maximum counterweight mass per point as constraints, it outputs a second-round counterweight solution (no counterweighting in the first round). In this embodiment, multiple counterweight point locations are pre-set on the special-shaped rotating payload satellite 2. Step 7 requires that the counterweight solutions for the first three rounds undergo the optimization process of step 5. Due to measurement noise and inherent errors in double-sided vertical balancing machines, if 100% of the calculated value is applied at once, retest results often show over- or under-compensation, requiring reverse weight addition, which in turn increases the number of iterations. For this reason, 70%–90% of the calculated mass is taken when loading the weight scheme for the first three rounds, and the rest is left for the next round of iterative correction. For example, the weight scheme obtained in the first round is that the mass required for point E1 is 50g, and the mass required for point E2 is 30g. Then, 50×70%=35g, 30g×70%=21g, and a mass of 35g is applied to point E1 and a mass of 21g is applied to point E2. Then, if the weight scheme obtained in the second round is that the mass required for point E5 is 40g, and the mass required for point E1 is 21g, then the mass required for point E5 is 40g. The required mass is 10g, then 40×70%=28g, 10×70%=7g, 28g of mass is applied to point E5, and 28g of mass is applied to point E1 on the basis of the 35g already in the first round. In addition, although the present application has selected the position of the counterweight for adding mass on the special-shaped rotating payload satellite 2 in advance, not all preset points need to be applied with counterweights in the end. The method of this embodiment is used to achieve load balance with the minimum application point and minimum mass as the goal.

[0088] Step 8 is the iterative and reverse weight reduction process. In steps 7 and 8, loading the optimized i-th round weight balance plan onto the special-shaped rotating payload satellite 2 or loading the i-th round weight balance plan onto the special-shaped rotating payload satellite 2 requires releasing the vacuum, opening the hatch, and manually loading according to the optimized i-th round weight balance plan or the i-th round weight balance plan; re-closing the hatch, evacuating the vacuum, and repeating steps 3-9 until all three types of imbalance indicators are below the threshold.

[0089] Step 10 is to introduce the reverse weight reduction procedure after the first convergence is completed: the sensitivity of all loaded counterweights is reversed, the redundant mass is identified and the minimum reduction amount is calculated. Under the premise of ensuring that the balancing index does not rebound, the excess counterweight is removed piece by piece to achieve the secondary optimization goal of "achieving the target balancing with the minimum total mass". The mass of the weight reduction is also solved using the objective function. After the secondary optimization, a quick retest is performed again to confirm that all imbalances still meet the threshold requirements, and the test can be terminated. In addition, the sensitivity reverse deduction method used in step 10 can be used to determine how much weight should be reduced for each counterweight point. This technology is an existing technology.

[0090] This embodiment defines five key coordinate systems (as shown in Figures 3(a) and 3(b)) to describe the motion characteristics of the satellite payload module: The rectangular coordinate system of the satellite payload module body: The rectangular coordinate system of the satellite payload module body takes the origin O of the payload module bottom plate -X plane as the coordinate origin, the X axis is perpendicular to the bottom plate and upward, the Z axis is parallel to the long side of the bottom plate and points from the high-resolution camera to the multi-function camera, the Y axis forms a right-handed system with the X and Z axes and is negative normal to the orbital plane under normal operation; the rectangular coordinate system of the satellite payload module center of mass: The origin Oc is the center of mass position of the payload module, and its Xc, Yc, and Zc axes are parallel to the X, Y, and Z axes of the satellite payload module body rectangular coordinate system respectively; the rectangular coordinate system of the balancing machine: The origin Ob coincides with the origin of the body coordinate system, and its Xb, Yb, and Zb axes are parallel to the X, Y, and Z axes of the satellite payload module body rectangular coordinate system respectively; the cylindrical coordinate system of the satellite payload module body: The origin Oc coincides with the origin of the satellite payload module body rectangular coordinate system. axis is parallel to the Y axis, The axis is parallel to the Z axis, and the zc axis is parallel to the X axis; the balancing machine column coordinate system: the origin Ob is the intersection of the balancing machine rotation axis and the installation table, The axis is perpendicular to the axis of rotation and points to the calibration point, Axis perpendicular to The axis points to the zero-point rotation tangent direction, and the zb axis is parallel to the rotation axis and points to the sky. 、 The axes form a right-hand system.

[0091] The cylindrical coordinate system is established because the satellite mounting interface cannot be fully aligned with the dynamic balancing machine, resulting in a phase difference between the two. Therefore, the cylindrical coordinate system is used. The phase difference is mainly used to compensate for this phase difference during conversion. The rectangular coordinate system is established because the mass block must be installed according to the rectangular coordinate system. Therefore, measurements are taken according to the dynamic balancing machine. When performing inverse calculations, the coordinate system of the satellite payload compartment should be used.

[0092] Further limit, multi-objective function:

[0093] ;

[0094] Where, is a multi-objective function, is the static unbalance, is the even unbalance quantity, is the additional torque, is the total number of counterweights installed on the six main surfaces of the special-shaped rotating payload satellite, For the The mass of the counterweight applied at each counterweight point, For the The maximum counterweight mass allowed for each counterweight point, , , , is the mass of the special-shaped rotating payload satellite, is the y-axis coordinate of the center of mass of the special-shaped rotating payload satellite, is the z-axis coordinate of the center of mass of the special-shaped rotating payload satellite, is the x-axis coordinate of the center of mass of the special-shaped rotating payload satellite, For the The y-axis coordinate of the counterpoint, For the The z-axis coordinate of the counterpoint, For the The x-axis coordinate of a counterpoint.

[0095] Specifically, the establishment of a multi-objective function and the use of this function to solve the weight balancing and weight reduction process are introduced below:

[0096] 1. Define design variables and design space:

[0097] To achieve dynamic balance during the rotation of the payload compartment, the mass loaded at each counterweight is considered a key design variable. If the load structure is a hexahedron, counterweights are pre-set on the six principal surfaces of the payload compartment (+X, -X, +Y, -Y, +Z, -Z) to accommodate mass blocks. The total number is N. The spatial position of each counterweight is represented using two coordinate systems: Cartesian coordinates within the payload compartment's rectangular coordinate system, and polar coordinates within the payload compartment's cylindrical coordinate system, which facilitates the calculation of radial unbalance moments.

[0098] Order The mass loaded by each counterweight is , then the design variable vector of all balancing points is:

[0099]

[0100] in, For the The maximum counterweight mass allowed at each counterweight point is determined by the structural installation space and the load-bearing capacity of the load compartment.

[0101] During the experiment, if some counterweights have been installed and cannot be increased, these counterweights will be deleted from the set of available counterweights. The set of available counterweights is recorded as:

[0102]

[0103] At this time, the design variable vector becomes:

[0104]

[0105] 2. Constructing multi-objective functions:

[0106] The optimization process aims to eliminate the static and dynamic imbalance of the payload cabin caused by manufacturing errors, assembly deviations and external disturbances (such as wind resistance) during the rotation of the payload cabin by rationally configuring the mass distribution of the counterweight. The optimization objective function is set to generate the following equation: 、 、 minimize.

[0107]

[0108] in, 、 、 Respectively expressed as:

[0109]

[0110]

[0111]

[0112] in, 、 、 、 is the mass and center of mass position of the payload cabin.

[0113] Therefore, the overall multi-objective optimization problem can be described as:

[0114]

[0115] 3. Set engineering constraints:

[0116] To ensure that the optimization results meet the requirements of engineering applications, this study set the following constraints during the optimization process: (1) The mass load of each counterweight must meet the preset upper and lower limit constraints; (2) The number of counterweights required must be minimized while ensuring the optimization goal. Through this dual-constraint optimization strategy, the optimal configuration of the counterweight system can be achieved while ensuring dynamic and static balance performance (i.e., achieving balance requirements with the minimum number of counterweights and the minimum additional mass). It should be noted that the specific counterweight number limit and mass constraint range can be adjusted according to actual engineering needs.

[0117] 4. Multi-objective optimization problem:

[0118] The multi-objective optimization problem can be expressed as follows:

[0119]

[0120] In order to improve optimization efficiency and avoid slow convergence due to an overly large search space, it is usually necessary to first perform a sensitivity analysis on each design variable to limit its reasonable value range.

[0121] 5. Obtain initial values: Based on the experimental measurement results of the dynamic balancing machine, input them into the optimization program to find the optimal counterweight position and counterweight mass.

[0122] 6. Multi-target global search:

[0123] A multi-objective optimization algorithm is run on the prediction model to obtain a set of non-dominated (Pareto) solutions; the algorithm automatically balances the three indicators, avoiding manual trial and error in weighting.

[0124] 7. Dynamic model update:

[0125] If the prediction error is found to increase or the diversity of the solution set is reduced during the search process, representative points are automatically selected from the current solution set for actual measurement, samples are supplemented and the prediction model is rebuilt to maintain global accuracy.

[0126] 8. Convergence judgment and candidate screening:

[0127] When the rate of change of the non-dominated frontier is lower than the threshold or reaches the set maximum number of generations within K consecutive iterations, it is considered to have converged;

[0128] 9. Experiment loading and iteration:

[0129] Load candidate solutions at a ratio of 70%-90% and retest 、 、 If any indicator exceeds the limit, the measured value will be sent back to S4 to re-enter the "measurement-optimization-load" closed loop until the three indicators are synchronously lower than the threshold.

[0130] 10. Reverse weight loss and final confirmation:

[0131] When the balancing indicators meet the requirements, a sensitivity analysis is performed on the loaded counterweights, redundant mass is eliminated, and the test is repeated; if the indicators are still qualified, the counterweights are locked with the minimum counterweight mass and the optimization ends.

[0132] Through the above steps 1-10, under the premise of ensuring the quality, quantity and processing feasibility of the counterweight, the static unbalance, the couple unbalance and the additional torque can be quickly converged to the target threshold, thus achieving efficient and low-cost dynamic balancing of the satellite payload.

[0133] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely illustrative of the principles and applications of the invention. It should be understood that many modifications may be made to the illustrative embodiments, and that other arrangements may be devised, without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in ways other than those described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be employed in conjunction with other described embodiments.

Claims

1. A multi-objective optimization balancing method for dynamic and static imbalance of satellites with large inertia and special-shaped rotating payloads, characterized by: The method includes the following: Step 1: preset the total number and positions of counterweights on the special-shaped rotating payload satellite (2), and perform the i-th round of counterweighting on each counterweight position, and when i=1, no counterweight mass is loaded on each counterweight position; Step 2, loading the i-th round of counterweights onto each counterweight position on the special-shaped rotating payload satellite (2); Step 3: Place the special-shaped rotating payload satellite (2) in the dynamic balancing machine (1), and start the dynamic balancing machine (1) by the control system. The process of starting the dynamic balancing machine (1) is as follows: evacuate the dynamic balancing machine (1) to simulate the low-pressure environment on orbit, and control the dynamic balancing machine (1) to drive the special-shaped rotating payload satellite (2) to rotate, and obtain the j-th output data of the control system, where the initial value of j is 1; and the control system output data includes: static unbalance, even unbalance and additional torque; Step 4: With the goal of minimizing static unbalance, couple unbalance, and additional torque, and with the number of counterweight points and the maximum counterweight mass at a single point as constraints, a multi-objective function is constructed; Step 5: Solve the multi-objective function to obtain the counterweight point position and the counterweight mass at the corresponding position as the counterweight solution for the i-th round; Step 6: Determine whether i is greater than or equal to a preset value. If not, go to step 7; if yes, go to step 8. Step 7: multiply the mass of each counterweight at each counterweight point in the i-th round counterweight scheme by the same preset coefficient to obtain the mass of each counterweight at each counterweight point in the optimized i-th round counterweight scheme, load the optimized i-th round counterweight scheme into the special-shaped rotating payload satellite (2), and execute step 9; Step 8, load the i-th round counterweight solution to the special-shaped rotating payload satellite (2), and execute step 9; Step 9: Detect whether the static unbalance, couple unbalance, and additional torque outputted for the jth time are all less than respective preset thresholds; if not, set j=j+1, i=i+1, and execute step 3; if yes, execute step 10; Step 10, executing steps 3 to 4, solving the multi-objective function, obtaining the counterweight position to be reduced and the weight reduction mass at the corresponding position as a weight reduction plan, reducing the weight of the special-shaped rotating payload satellite (2) according to the weight reduction plan, starting the dynamic balancing machine (1) after weight reduction, controlling the system to output the static unbalance amount, the even unbalance amount and the additional torque, detecting whether the static unbalance amount, the even unbalance amount and the additional torque output at this time are all less than their respective preset thresholds, if yes, the special-shaped rotating payload satellite (2) after weight reduction has completed balancing, if not, the last round of counterbalance plan before weight reduction is the balancing plan for the special-shaped rotating payload satellite (2).

2. The multi-objective optimization balancing method for dynamic and static imbalance of a large inertia special-shaped rotating payload satellite according to claim 1 is characterized in that: Multi-objective function: Formula 1, Where, is a multi-objective function, is the static unbalance, is the even unbalance quantity, is the additional torque, is the total number of counterweights installed on the six main surfaces of the special-shaped rotating payload satellite, For the The mass of the counterweight applied at each counterweight point, For the The maximum counterweight mass allowed for each counterweight point, ， ， , is the mass of the special-shaped rotating payload satellite, is the y-axis coordinate of the center of mass of the special-shaped rotating payload satellite, is the z-axis coordinate of the center of mass of the special-shaped rotating payload satellite, is the x-axis coordinate of the center of mass of the special-shaped rotating payload satellite, For the The y-axis coordinate of the counterpoint, For the The z-axis coordinate of the counterpoint, For the The x-axis coordinate of a counterpoint.

3. The multi-objective optimization balancing method for dynamic and static imbalance of a large inertia special-shaped rotating payload satellite according to claim 1 or 2, characterized in that: The preset coefficients are values ​​in the range of 70%–90%.

4. The multi-objective optimization balancing method for dynamic and static imbalance of a large inertia special-shaped rotating payload satellite according to claim 3 is characterized in that: In step 4, the default value is 3.

5. The multi-objective optimization balancing method for dynamic and static imbalance of a large inertia special-shaped rotating payload satellite according to claim 2 or 4, characterized in that: The dynamic balancing machine (1) includes a vacuum tank, a vacuum pump (1-7), a turntable (1-8) and a six-component force-torque sensor; The special-shaped rotating payload satellite (2) is arranged on the turntable (1-8), the turntable (1-8) and the special-shaped rotating payload satellite (2) are covered by a vacuum tank, and a six-component force-torque sensor is arranged on the turntable (1-8) for measuring six-component force-torque signals; The control system controls the vacuum pump (1-7) to evacuate the vacuum tank to simulate the low-pressure environment on orbit, and controls the turntable (1-8) to drive the special-shaped rotating payload satellite (2) to rotate.

6. The multi-objective optimization balancing method for dynamic and static imbalance of a large inertia special-shaped rotating payload satellite according to claim 5 is characterized in that: The vacuum tank includes an observation window (1-5), a hatch (1-4), a first cabin section (1-1), a second cabin section (1-2), a third cabin section (1-3) and a limiting column (1-6); Limiting columns (1-6) are provided on the first compartment (1-1), the second compartment (1-2) and the third compartment (1-3); the first compartment (1-1), the second compartment (1-2) and the third compartment (1-3) are sequentially connected from top to bottom to form a closed vacuum tank, and the three limiting columns on the first compartment (1-1), the second compartment (1-2) and the third compartment (1-3) are aligned in a straight line; a cabin door (1-4) is provided on the first compartment (1-1), and an observation window (1-5) is provided on the second compartment (1-2).

7. The multi-objective optimization balancing method for dynamic and static imbalance of a satellite with large inertia and special-shaped rotating payload according to claim 6 is characterized in that: The method of obtaining static unbalance, couple unbalance and additional torque is as follows: The dynamic balancing machine (1) is started, and the operating data of the control system output device is combined with the pre-input basic data of the special-shaped rotating load satellite (2), and based on the principle of the double-sided vertical balancing machine, the static unbalance amount, the couple unbalance amount and the additional torque are obtained.

8. The multi-objective optimization balancing method for dynamic and static imbalance of a satellite with large inertia and special-shaped rotating payload according to claim 7 is characterized in that: Display output data includes rotational speed, axial displacement and six-component force-torque signals; The basic data include the radius R2 of the upper calibration block, the radius R1 of the lower calibration block, the axial distance B between the upper and lower calibration blocks, the axial distance A between the lower calibration block and the turntable, the initial phase of the rotation axis and the coordinates of the satellite center of mass position.

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