Load-balanced large-scale structure attitude adjustment driving force distribution method

Abstract

The invention provides a load-balanced large-scale structure attitude adjustment driving force distribution method, which specifically comprises the following steps: firstly, constructing an attitude adjustment mechanism accurate power model considering the friction force of a locator and the motion inertia so as to establish a constraint model between the attitude adjustment track and the attitude adjustment driving force of a large-scale structure; thirdly, constructing a positioner driving force optimization model by defining a driving shaft load coefficient, and performing assembly driving force optimization by adopting a penalty function method; and finally, fitting the discrete driving force of the driving shaft by adopting quintic polynomial fitting so as to obtain the real-time driving force of the attitude adjusting mechanism. The problem that part of driving shafts are overloaded in the posture adjusting and positioning process of a large structure is solved, the loads of all the driving shafts are balanced by reasonably distributing driving force output by different driving shafts, and the situation that part of drivers are overloaded is improved.

Description

Technical Field

[0001] This invention relates to the field of large structure attitude adjustment driving force distribution, and more particularly to a load-balanced method for large structure attitude adjustment driving force distribution. Background Technology

[0002] The large-structure attitude adjustment mechanism used in large-structure assembly consists of three positioners. Because the number of drive shafts in the adjustment mechanism exceeds the degrees of freedom of the large structure, the distribution of drive force among the positioners is uncertain under the same adjustment trajectory. An unreasonable drive force distribution method may cause some drive shafts to bear a much higher load than others. On the one hand, prolonged excessive load on the drive shafts will cause additional stress on the mechanical structure, accelerating the wear of its components. The motor windings may also overheat due to prolonged overload, significantly shortening the equipment's lifespan. On the other hand, excessive load will lead to unstable drive shaft speeds, preventing the positioners from operating at the preset speed and accuracy, severely affecting the stability and accuracy of large-structure attitude adjustment. Therefore, this invention proposes a load-balanced drive force optimization method for large-structure assembly. By rationally distributing the drive force output by different drive shafts, the load on some drive shafts is reduced, thereby improving the accuracy of large-structure attitude adjustment and extending the equipment's lifespan. Summary of the Invention

[0003] The purpose of this invention is to provide a load-balanced method for distributing the attitude adjustment driving force of large structures, thereby solving the problems mentioned in the background art. A specific implementation includes: firstly, constructing a dynamic model of the attitude adjustment mechanism considering the friction and inertial forces of the positioner itself, thus establishing a precise constraint relationship between the attitude adjustment trajectory and the attitude adjustment driving force of the large structure; nextly, constructing an optimization model of the positioner driving force by defining the drive shaft load coefficient, and optimizing the attitude adjustment driving force using the penalty function method; finally, fitting the discrete attitude adjustment driving force using a fifth-order polynomial to obtain the real-time driving force of the attitude adjustment mechanism.

[0004] To achieve the above objectives, the present invention provides the following technical solution: a load-balanced method for distributing the attitude adjustment driving force of a large structure, the specific steps of which are as follows:

[0005] Step 1: Perform dynamic modeling on the large structure and the CNC positioner respectively, and establish a constraint model between the large structure's attitude adjustment trajectory and attitude adjustment driving force;

[0006] Step 2: Establish an attitude adjustment driving force optimization model by defining the drive shaft load coefficient, and use the penalty function method to optimize the assembly driving force;

[0007] Step 3: Use a polynomial to fit the discrete driving force to obtain the real-time driving force of the attitude adjustment mechanism.

[0008] As an improvement, step one, establishing a precise constraint model between the attitude adjustment trajectory and the attitude adjustment driving force of the large structure, specifically includes:

[0009] (1.1) Constructing the base coordinate system and local coordinate system of large structures The specific global coordinate system This is the reference coordinate system of the attitude adjustment mechanism, with its z-axis perpendicular to the horizontal plane, and the movement directions of each axis of the positioner consistent with the global coordinate system; the local coordinate system... It is a coordinate system fixed to the large structure itself, which moves with the movement of the large structure and represents the position and orientation of the large structure.

[0010] (1.2) The locator and the large structure are connected by a ball joint. Let the coordinates of the center of the i-th ball joint in the local coordinate system of the large structure be... The coordinates of the i-th ball joint center in the global coordinate system are: The position vector of the large structure relative to the base coordinate system is The attitude angle vector is , This refers to the spatial trajectory of a large structure; based on the principle of coordinate system transformation, the following formula is obtained.

[0011] (1),

[0012] in

[0013] (2),

[0014] (3),

[0015] (1.3) According to Newton's laws, the kinematic equations of a large structure consisting of three positioners in the base coordinate system are expressed as follows:

[0016] (4),

[0017] in, Let be the force exerted by positioner i on the large structure during the attitude adjustment process, and m be the mass of the large structure. For the gravity matrix of large components, Given the acceleration of the large structure, according to Euler's equations, the kinematic equations of the large structure in the local coordinate system are:

[0018] (5),

[0019] In the formula, I is the rotational inertia matrix of the large component. For large structures, the angular velocity is equivalent to that of a local coordinate system. For large structures, angular acceleration.

[0020] (6),

[0021] (1.4) In addition to driving the movement of large components, the driving force of the positioner is also used to overcome its own friction and inertial forces. The kinematic equation of the positioner is established according to Newton's second law as follows:

[0022] (7),

[0023] In the formula, The driving force for positioner i, Let be the friction coefficient matrix, inertia coefficient matrix, and acceleration matrix of positioner i, respectively, with the following specific expressions:

[0024] (8),

[0025] in, The coefficient of friction of the sliding pairs on each axis of the positioner i; These are the masses of the X-axis translation stage, Y-axis translation stage, and Z-axis translation stage of positioner i, respectively. The acceleration output by positioner i along each axis is expressed as follows:

[0026] (10),

[0027] The load pressure on each axis of the positioner i mainly comes from the reaction force of the large structure on the positioner and the inertial force from the translation stage of each axis. It can be represented as

[0028] (11),

[0029] in, Representing vectors The 2-norm.

[0030] (1.5) Substituting formula (7) into formulas (4) and (5) yields the attitude adjustment driving force F and the attitude adjustment trajectory. Constraint Model

[0031] (12),

[0032] Write formula (12) in the form of matrix multiplication.

[0033] (13),

[0034] In the formula

[0035] (14),

[0036] in, It is a third-order identity matrix. yes anti-slant symmetric matrix, The driving force of the j-th axis of the attitude adjustment mechanism is represented by equation (13), which contains 6 equations and 9 unknowns. Therefore, under the same attitude adjustment trajectory, the distribution of the driving force of the attitude adjustment mechanism is uncertain.

[0037] As an improvement, the process of optimizing the attitude adjustment driving force in step two includes:

[0038] (2.1) Let the rated driving force of the j-th axis of the attitude adjustment mechanism be... ,definition is the load factor for the j-th axis.

[0039] (15),

[0040] When the driving force of the positioner shaft When approaching the rated driving force, the larger the load factor, the worse the stability of the attitude adjustment mechanism. Therefore, when distributing the driving force during assembly, the load factor should be reduced as much as possible. Therefore, the optimization model for the attitude adjustment driving force of large components can be expressed as follows:

[0041] (16),

[0042] (2.2) The above attitude adjustment driving force optimization model is a nonlinear optimization problem with equality constraints. The penalty function method is used to transform the constrained optimization problem into an unconstrained optimization problem. The penalty function is defined as follows:

[0043] (17),

[0044] in, This is a penalty factor.

[0045] As an improvement, the algorithm flow for optimizing the attitude adjustment driving force using the penalty function method in step two is as follows:

[0046] ① Select the initial value of the attitude adjustment driving force based on experience. Initial penalty factor Amplification factor c (c > 1), termination criterion ε, let k = 0;

[0047] ② Calculate the gradient vector of the penalty function. ;

[0048] ③If ,but That is the optimal driving force value; otherwise... Proceed to step ②.

[0049] As an improvement, step three includes the following process for fitting the real-time attitude adjustment driving force:

[0050] (3.1) Fit the discrete optimal driving force, which is the optimal driving force obtained in step two based on the attitude adjustment trajectory at a certain moment; let the attitude adjustment time be... If the time interval for optimizing the attitude adjustment driving force is T, then the optimal driving force sequence obtained through optimization can be expressed as follows: , , ,in represent The integer part;

[0051] (3.2) Considering the accuracy of the fitting and the complexity of the calculation, a fifth-order polynomial is used to fit the driving force. The resulting set of driving force fitting equations is as follows:

[0052] (18),

[0053] Formula (18) can be written in the form of matrix multiplication.

[0054] (19),

[0055] in

[0056] (20),

[0057] (3.3) The coefficients are calculated by minimizing the square of the driving force fitting residuals using the least squares method. The least squares solution is

[0058] (twenty one),

[0059] Finally, the real-time solution of the attitude adjustment driving force is obtained as

[0060] (twenty two).

[0061] Beneficial Effects: The attitude adjustment driving force distribution method proposed in this invention can solve the problem of excessive load on some drive bearings during the attitude adjustment process of large structures. Balanced distribution of the load on each axis of the positioner can significantly improve the working reliability and stability of the attitude adjustment mechanism, reduce equipment failures and maintenance costs, and extend the service life of the equipment. Simultaneously, balanced load distribution control of each axis helps improve the assembly accuracy of large equipment, thereby enhancing the overall quality and safety of the equipment. Attached Figure Description

[0062] Figure 1This is a flowchart illustrating a load-balanced method for distributing the attitude adjustment driving force of a large structure, as proposed in this invention.

[0063] Figure 2 It is a large-scale structural attitude adjustment mechanism.

[0064] Figure 3 This is a schematic diagram of the positioner structure.

[0065] Figure 4 This is the software interface of the attitude adjustment control system in Embodiment 1 of the present invention.

[0066] Figure 5 This is the load factor of the drive shaft in Embodiment 1 of the present invention.

[0067] Figure 6 This refers to the final pose deviation of the wing simulation component in Embodiment 1 of the present invention.

[0068] In the diagram: 1 Large structure, 2 Positioner 1, 3 Positioner 2, 4 Positioner 3, 5 Ball joint, 6 Z-axis translation stage, 7 Y-axis translation stage, 8 X-axis translation stage, 9 Base. Detailed Implementation

[0069] The technical solutions in the embodiments of the present invention will be clearly and completely described below, so that those skilled in the art can better understand the advantages and features of the present invention, thereby making a clearer definition of the scope of protection of the present invention. The embodiments described in this invention are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0070] See Figure 1 The flowchart shown is a flowchart of the present invention, specifically proposing a load-balanced method for distributing the attitude adjustment driving force of a large structure. The specific steps are as follows:

[0071] Step 1: Perform dynamic modeling on the large structure and the CNC positioner respectively, and establish a constraint model between the large structure's attitude adjustment trajectory and attitude adjustment driving force;

[0072] Step 2: Establish an attitude adjustment driving force optimization model by defining the drive shaft load coefficient, and use the penalty function method to optimize the assembly driving force;

[0073] Step 3: Use a polynomial to fit the discrete driving force to obtain the real-time driving force of the attitude adjustment mechanism.

[0074] See Figures 2-3The diagram shows a large structure constructed in this invention, which includes three positioners: positioner 1 (2), positioner 2 (3), and positioner 3 (4). Each positioner is connected to the large structure 1 via a ball joint (5). A track (9) is installed at the bottom of the positioner, and a Z-axis translation stage (6), a Y-axis translation stage (7), and an X-axis translation stage (8) are installed on the base (9) to adjust the Z-axis, Y-axis, and X-axis directions of the positioner.

[0075] The specific steps of the method described above in this invention will be explained and illustrated below through a specific embodiment 1.

[0076] Example 1

[0077] To further evaluate the feasibility of the load-balanced large-structure attitude adjustment driving force distribution method proposed in this invention for reducing the maximum load coefficient of the positioner drive shaft, an attitude adjustment experiment was conducted using an aircraft wing simulator attitude adjustment system built in the laboratory. The masses of the X-axis, Y-axis, and Z-axis translation stages of the positioner are known to be 9.5 kg, 8.3 kg, and 7.2 kg, respectively; the friction coefficient of each sliding pair of the positioner is 0.15; and the rated driving forces of the X-axis, Y-axis, and Z-axis of the positioner are 150 N, 150 N, and 300 N, respectively. The coordinates of the ball joint center in the local coordinate system of the wing simulator are as follows: mm mm and The wing simulator has a mass m of 18.1 kg and a moment of inertia I of diag(5.219, 6.193, 1.857) × 10 mm. 4 kg.mm². A total of 6 attitude adjustment experiments were conducted. The initial and target poses of the wing simulator are shown in Table 1. The software interface of the attitude adjustment control system is shown in... Figure 4 As shown.

[0078] Table 1 Initial and target poses of the wing simulator

[0079] Taking the first group of attitude adjustment experiments as an example, the process of optimizing the driving force using the load-balanced large structure attitude adjustment driving force distribution method proposed in this invention is as follows:

[0080] First, the attitude adjustment trajectory is planned based on the initial and target poses of the wing simulation component. The attitude adjustment time is shown in Table 2. The time interval for discretizing the attitude adjustment trajectory is T = 2s.

[0081] Table 2 Attitude Adjustment Time of Wing Simulator

[0082]

[0083] Next, based on the mass characteristics, structural parameters, and spatial trajectories of the discrete wing simulation components of the attitude adjustment mechanism, the driving force sequence of the attitude adjustment mechanism is calculated using the methods in steps one and two, as shown in Table 3.

[0084] Table 3. Driving force sequence of the attitude adjustment mechanism

[0085]

[0086] Then, based on the driving force sequence of the attitude adjustment mechanism, a fifth-order polynomial is used to fit the real-time attitude adjustment driving force, and the coefficients of the fitted polynomial are... As shown in Table 4.

[0087] Table 4 Polynomial coefficients

[0088] Finally, based on the real-time attitude adjustment driving force obtained by fitting, an attitude adjustment experiment of the wing simulator was carried out. During the attitude adjustment process, the load coefficient of the drive shaft was collected every 0.1s. After the attitude adjustment was completed, the actual spatial pose of the wing simulator was measured using a laser tracker and compared with the theoretical target pose of the wing simulator to obtain the spatial pose deviation of the wing simulator.

[0089] In contrast, the conventional least-norm 2 method was used for drive force distribution, and the initial and target poses of the wing simulator are also shown in Table 1. The maximum load factor of the drive shaft under both drive distribution methods is as follows: Figure 5 As shown, the final pose deviation of the wing simulator is as follows: Figure 6 As shown, it can be seen that the load-balanced drive force distribution method proposed in this invention can significantly reduce the load coefficient of the drive shaft and improve the final positioning accuracy of large structures.

[0090] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the appended claims.

Claims

1. A load-balanced method for distributing the attitude adjustment driving force of a large structure, characterized in that, The specific steps are as follows: Step 1: Perform dynamic modeling on the large structure and the CNC positioner respectively, and establish a constraint model between the large structure's attitude adjustment trajectory and attitude adjustment driving force; Step 2: Establish an attitude adjustment driving force optimization model by defining the drive shaft load coefficient, and use the penalty function method to optimize the assembly driving force; Step 3: Use a polynomial to fit the discrete driving force to obtain the real-time driving force of the attitude adjustment mechanism.

2. The load-balanced large-structure attitude adjustment driving force distribution method according to claim 1, characterized in that, Step one, establishing a precise constraint model between the attitude adjustment trajectory and the attitude adjustment driving force of a large structure, specifically includes: (1.1) Constructing the base coordinate system and local coordinate system of large structures : Global coordinate system This is the reference coordinate system of the attitude adjustment mechanism, with its z-axis perpendicular to the horizontal plane, and the movement directions of each axis of the positioner consistent with the global coordinate system; the local coordinate system... It is a coordinate system fixed to the large structure itself, which moves with the movement of the large structure and represents the position and orientation of the large structure. (1.2) The locator and the large structure are connected by a ball joint. Let the coordinates of the center of the i-th ball joint in the local coordinate system of the large structure be... The coordinates of the i-th ball joint center in the global coordinate system are: The position vector of the large structure relative to the base coordinate system is The attitude angle vector is , This refers to the spatial trajectory of a large structure, which, based on the principle of coordinate system transformation, yields the following formula. (1)， in (2)， (3)， (1.3) According to Newton's laws, the kinematic equations of a large structure consisting of three positioners in the base coordinate system are expressed as follows: (4)， in, Let be the force exerted by positioner i on the large structure during the attitude adjustment process, and m be the mass of the large structure. For the gravity matrix of large components, Given the acceleration of the large structure, according to Euler's equations, the kinematic equations of the large structure in the local coordinate system are: (5)， In the formula, I is the rotational inertia matrix of the large component. For large structures, the angular velocity is equivalent to that of a local coordinate system. For large structures, angular acceleration; (6)， The kinematic equations of the positioner, based on Newton's second law, are as follows: (7)， In the formula, The driving force for positioner i, Let be the friction coefficient matrix, inertia coefficient matrix, and acceleration matrix of positioner i, respectively, with the following specific expressions: (8)， In the formula, The coefficient of friction of the sliding pairs on each axis of the positioner i; These are the masses of the X-axis translation stage, Y-axis translation stage, and Z-axis translation stage of positioner i, respectively. The acceleration output by positioner i along each axis is expressed as follows: (10)， (11)， in, Representing vectors The 2-norm, The load pressure on each axis of positioner i; (1.4) Substituting formula (7) into formula (4) and formula (5) yields the attitude adjustment driving force F and the attitude adjustment trajectory. Constraint Model (12)， Write formula (12) in the form of matrix multiplication. (13)， In the formula (14)， in, It is a third-order identity matrix. yes anti-slant symmetric matrix, The driving force of the j-th axis of the attitude adjustment mechanism is represented by equation (13), which contains 6 equations and 9 unknowns. Therefore, under the same attitude adjustment trajectory, the distribution of the driving force of the attitude adjustment mechanism is uncertain.

3. The load-balanced large-structure attitude adjustment driving force distribution method according to claim 1, characterized in that, Step two, the process of optimizing the attitude adjustment driving force, includes: (2.1) Let the rated driving force of the j-th axis of the attitude adjustment mechanism be... ,definition The load factor of the j-th axis (15)， When the driving force of the positioner shaft Approximately close to the rated driving force, the larger the load factor, the worse the stability of the attitude adjustment mechanism. Therefore, when distributing the driving force during assembly, the load factor should be reduced. The optimization model for the attitude adjustment driving force of large components is expressed as follows: (16)， (2.2) The above attitude adjustment driving force optimization model is a nonlinear optimization problem with equality constraints. The penalty function method is used to transform the constrained optimization problem into an unconstrained optimization problem. The penalty function is defined as follows: (17)， in, This is a penalty factor.

4. The load-balanced large-structure attitude adjustment driving force distribution method according to claim 1 or 2, characterized in that, In step two, the algorithm flow for optimizing the attitude adjustment driving force using the penalty function method is as follows: ① Select the initial value of the attitude adjustment driving force based on experience. Initial penalty factor Amplification factor c (c > 1), termination criterion ε, let k = 0; ② Calculate the gradient vector of the penalty function. ; ③If ,but That is the optimal driving force value; otherwise... Proceed to step ②.

5. The load-balanced large-structure attitude adjustment driving force distribution method according to claim 1, characterized in that, Step three, the real-time attitude adjustment driving force fitting process includes: (3.1) Fit the discrete optimal driving force, where the optimal driving force is obtained in step two based on the attitude adjustment trajectory at a certain moment, and is the optimal driving force at that moment; let the attitude adjustment time be... If the time interval for optimizing the attitude adjustment driving force is T, then the optimal driving force sequence obtained by optimization is expressed as follows: , , ,in represent The integer part; (3.2) A fifth-order polynomial is used to fit the driving force, and the resulting set of driving force fitting equations is as follows: (18)， Formula (18) can be written in the form of matrix multiplication. (19)， in (20)， (3.3) The coefficients are calculated by minimizing the square of the driving force fitting residuals using the least squares method. The least squares solution is (21)， The real-time solution for attitude adjustment driving force is obtained as (22)。

Images