Equipment three-dimensional centroid eccentric balancing method considering structural constraint

Abstract

The invention discloses an equipment three-dimensional centroid eccentricity balancing method considering structural constraints, which comprises the following steps of: firstly, establishing a centroid eccentricity vector module and a balancing weight total mass weighted balancing objective function, then determining the position and size constraints of a balancing weight according to the structural size constraints of complex equipment, and optimizing the balancing objective function by adopting a particle swarm optimization method, so as to obtain the three-dimensional centroid eccentricity balancing method. And an optimal balancing scheme is obtained. According to the balancing optimization method, the balancing weights can be optimally selected in the equipment design stage, then balancing of actual equipment is guided, the tedious trial and error process of manual balancing is avoided, and digitalization of the balancing process is achieved.

Description

Technical Field

[0001] The invention belongs to the technical field of flight control, and in particular relates to a three-dimensional center-of-mass eccentric balancing method for equipment considering structural constraints. Background Art

[0002] During the design process of complex equipment such as aerospace vehicles, aircraft, and optoelectronic pods, it is often difficult to achieve the coincidence of the equipment's rotation center and the equipment's center of mass due to the installation of various complex equipment inside. This causes the center of mass to be eccentric, and then gravity causes an eccentric torque on the center of mass, which increases the difficulty of equipment system control and affects the equipment's control accuracy.

[0003] Rotary equipment is widely used in the industrial field, such as aircraft, spacecraft, optoelectronic pods, rotary shaft systems, etc. Rotary motion plays an indispensable role in the above equipment. In order to solve the problem of difficult balance of center of mass eccentricity of rotary equipment, technicians have developed many methods for achieving center of mass eccentricity balance. According to the literature, the center of mass eccentricity of the equipment can cause the center of mass eccentricity torque under the action of the equipment gravity.

[0004] In the prior art, Chinese patent application No. 2012102406504 discloses a particle swarm optimization method for aircraft trimming, which establishes a nonlinear dynamic model of the aircraft and uses a particle swarm optimization method for trimming optimization. However, this method does not consider the installation position and size constraints of the counterweight.

[0005] The Chinese patent application with application number 2021101562078 discloses a method and system for adjusting the center of mass balance of a three-axis air-floating platform. The three-axis air-floating platform is studied and three orthogonal counterweights are used to achieve the three-axis balance of the air-floating platform. However, this method is difficult to use for balancing in a closed space with complex constraint equipment, and the ball screw structure adds extra weight to the system and increases the difficulty of system control.

[0006] After searching the existing literature, no method was found for three-dimensional center-of-mass eccentric balancing that takes into account the structural constraints of rotating equipment. Summary of the invention

[0007] In view of the strict space constraint problem of center of mass eccentricity and counterweight of complex rotating equipment such as aerospace vehicles, aircraft, optoelectronic pods, etc., the present invention discloses a three-dimensional center of mass eccentricity optimization balancing method for rotating equipment considering structural constraints.

[0008] The technical solution adopted by the present invention to solve the technical problem is: a three-dimensional center of mass eccentric balancing method of equipment considering structural constraints, comprising the following steps:

[0009] S1. For the mass eccentric device to be balanced, establish the rotation coordinate system {r} of the mass eccentric device to be balanced, use 3D modeling software to analyze the mass m and mass eccentricity of the device, or use mass center measurement equipment to measure the mass m and mass eccentricity of the device, and obtain the 3D mass eccentricity vector p of the mass eccentric device to be balanced in the rotation coordinate system {r}. g =(x g ,y g ,z g );

[0010] S2, according to the spatial structure size of the eccentric center of mass equipment to be leveled, determine the installation bottom center position p of each cylindrical counterweight block i , bottom dimension constraint vector d i,max and the height constraint vector h i,max ;

[0011] S3, the mass m and mass eccentricity vector p of the equipment to be balanced g , the feasible installation position of each cylindrical counterweight block is the center position of the installation bottom surface p i , bottom dimension constraint vector d i,max , height constraint vector h i,max , the density ρ of the counterweight block is input into the Matlab program and the program is run. The Matlab program calculates the mass m of the eccentric center of mass device to be balanced and the eccentric center of mass vector p according to the input g The feasible installation positions of each cylindrical counterweight and the density ρ of the counterweight are used to optimize the selection of the counterweight, and the objective function of the weighted vector modulus of the center of mass eccentricity and the total mass of the counterweight is established:

[0012]

[0013] where |p n | for p n The modulus of γ is the equilibrium|p n |With m z The weight factor, d i is the bottom diameter of the counterweight, h i is the height of the counterweight block; the particle swarm optimization method is used to calculate the mass of each counterweight block and the eccentricity vector of the center of mass after adding the counterweight block to optimize the objective function, and the structural size d i With h i Perform iterative optimization to obtain the optimal structural dimensions of the counterweight block, i.e., bottom diameter and height;

[0014] S4, in the three-dimensional modeling software, drawing the corresponding three-dimensional model of the counterweight block according to the optimal structural dimensions of each counterweight block, and setting its material and density properties;

[0015] S5. In the 3D modeling software, create an equipment assembly drawing, import the mass eccentricity equipment to be balanced, import the counterweight blocks in sequence, install each counterweight block at the corresponding designed position, and analyze and verify the mass and mass eccentricity of the equipment after counterweighting.

[0016] Furthermore, in step S2, the number of feasible installation positions is set to I, and the three-dimensional coordinates of the installation bottom center position of each cylindrical counterweight block relative to the center of the rotation coordinate system of the eccentric center of mass device to be leveled are determined, and the three-dimensional coordinates of the bottom center of the i-th cylindrical counterweight block are recorded as p i =(x i ,y i ,z i ), the maximum radius of the cylinder base is d i,max , the maximum height of the cylinder is h i,max .

[0017] Furthermore, in step S3, the density ρ of the counterweight block is specified according to the material of the counterweight block, and the mass of the i-th counterweight block is m i =ρ·π·d i 2 ·h i / 4, the center of mass position of the ith counterweight is p i ′ can be obtained by p i With h i The total mass of the counterweight is calculated to be

[0018] Furthermore, after adding the counterweight in step S3, the center of mass position of the device can be expressed as:

[0019]

[0020] The beneficial effects of the present invention are:

[0021] The present invention studies the mass center eccentricity of equipment gravity in three-dimensional space, analyzes the position selection and size constraints of counterweight blocks under structural constraints, establishes a weighted objective function of the mass center eccentricity vector modulus and the total mass of the counterweight blocks after balancing, and uses a particle swarm optimization method to optimize the objective function to obtain the optimal counterweight block balancing solution.

[0022] The optimized balancing method of the present invention fully considers the structural constraints of the equipment, optimizes the selection of the counterweight block under the size constraints of the equipment, and avoids interference and collision between the counterweight block and the equipment itself.

[0023] The optimization balancing method of the present invention establishes a balancing objective function by weighting the eccentric vector modulus of the center of mass after balancing and the total mass of the counterweight block, which can ensure that the weighted eccentric vector modulus of the center of mass after balancing and the total mass of the counterweight block are minimized.

[0024] The optimized balancing method of the present invention can optimize the selection of counterweights during the equipment design stage, thereby guiding the balancing of actual equipment, avoiding the tedious trial and error process of manual balancing, and realizing the digitization of the balancing process. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 is a flow chart of the balancing method of the present invention;

[0026] Figure 2 It is the flow chart of Matlab program;

[0027] Figure 3 The body of the mass center eccentric device to be balanced;

[0028] Figure 4 The counterweights obtained for optimization;

[0029] Figure 5 This is a diagram of the equipment after balancing according to the method of this patent. DETAILED DESCRIPTION

[0030] In order to make the principles, operation steps and advantages of the present invention more clearly understood, the present invention is further described in detail below in combination with theoretical derivation, drawings and examples. It should be noted that the specific embodiments described herein are only for explaining the present invention and are not intended to limit the present invention.

[0031] The center of mass eccentric device is the object of three-dimensional balancing, and its center of rotation does not coincide with the center of mass. The counterweight is used to be fixed at the specified position of the center of mass eccentric device to offset the center of mass eccentricity of the center of mass eccentric device itself and achieve the coincidence of the center of rotation and the center of mass. The present invention studies the optimal balancing of three-dimensional center of mass eccentricity under spatial constraints, derives the center of mass eccentricity balance equation in three-dimensional space, establishes the weighted balancing objective function of the center of mass eccentricity vector modulus and the total mass of the counterweight, determines the position and size constraints of the counterweight according to the structural size constraints of complex equipment, and uses the particle swarm optimization method to optimize the balancing objective function to obtain the optimal balancing solution.

[0032] Reference Figure 1 As shown, the present invention discloses a method for 3D center of mass eccentric balancing of equipment considering structural constraints, and the steps are as follows.

[0033] Step 1: For the mass eccentric device to be balanced, establish the rotation coordinate system {r} of the mass eccentric device to be balanced, use 3D modeling software to analyze the mass m and mass eccentricity of the device, or use mass center measurement equipment to measure the mass m and mass eccentricity of the device, and obtain the 3D mass eccentricity vector p of the mass eccentric device to be balanced in the rotation coordinate system {r}. g =(x g ,y g ,z g ).

[0034] Step 2: According to the spatial structural dimensions of the eccentric mass center equipment to be leveled, i.e., the structural constraints, determine the installation bottom center position p of each cylindrical counterweight block. i , bottom size constraint vector d i,max (maximum base radius) and height constraint vector h i,max (maximum height) is the possible installation position.

[0035] In this step, it is necessary to determine the feasible installation positions of the cylindrical counterweights according to the spatial structural dimensions of the eccentric mass center device to be balanced, set the number of feasible installation positions as I, and determine the three-dimensional coordinates of the installation bottom center position of each cylindrical counterweight relative to the center of the rotation coordinate system of the eccentric mass center device to be balanced. The three-dimensional coordinates of the bottom center of the i-th counterweight are recorded as p i =(x i ,y i ,z i ), the maximum radius of the cylinder base is d i,max 、The maximum height of the cylinder is h i,max .

[0036] Reference Figure 2 As shown in the figure, the size parameters of the counterweight block are optimized by using the Matlab calculation program: the calculation program input is the mass of the center of mass eccentric device, the three-dimensional center of mass eccentric coordinates of the center of mass, the feasible installation position coordinates and size constraints of the counterweight block, and the particle swarm optimization algorithm is used to iteratively optimize the objective function to obtain the optimal counterweight block installation position coordinates and size.

[0037] Step 3: Substitute the mass m and mass eccentricity vector p of the equipment to be balanced. g , the feasible installation position of each cylindrical counterweight block is the center position of the installation bottom surface p i , bottom dimension constraint vector d i,max , height constraint vector h i,max The density ρ of the counterweight is input into the Matlab program and the program is run.

[0038] The Matlab program calculates the mass m of the eccentric center of mass equipment to be balanced and the eccentric center of mass vector p according to the input g The optimal selection of the counterweights is performed based on the feasible installation positions of the cylindrical counterweights and the density ρ of the counterweights, and the objective function consisting of the moment balance equation of the mass center eccentricity balancing and the weighted mass of the counterweights is obtained, that is, the mass center eccentricity balancing optimization objective function e of the mass center eccentricity equipment to be balanced:

[0039]

[0040] where |p n | for p n The modulus of γ is the weight factor used to balance |pn |With m z , d i is the bottom diameter of the counterweight, h i is the height of the counterweight. The objective function e is to minimize the weighted sum of the modulus of the center of mass eccentricity vector after balancing and the total mass of the counterweight.

[0041] The Matlab program uses particle swarm optimization method to calculate the mass of each counterweight block and the eccentricity vector of the center of mass after adding the counterweight block for the objective function e, and optimizes the structural size d in the objective function. i With h i After iterative optimization is performed and the optimal balancing solution is obtained, the optimal structural dimensions of the counterweight blocks at each position are output, thereby guiding the balancing of the equipment with eccentric center of mass to be balanced.

[0042] In this step, the density of the counterweight block is specified according to the material of the counterweight block. The density of the counterweight block is ρ, and the mass of the i-th counterweight block is m. i =ρ·π·d i 2 ·h i / 4, the center of mass position of the ith counterweight is p i ′ can be obtained by p i With h i The total mass of the counterweight is calculated to be

[0043] After adding the counterweight in this step, the center of mass position of the equipment can be expressed as

[0044] Step 4: In the 3D modeling software, draw the corresponding counterweight according to the structural dimensions of each counterweight, and set its material and density properties. This step draws the 3D model of the counterweight based on the optimal structural dimensions of the counterweight obtained in step 3, obtains the mass and the 3D center of mass eccentric coordinates and the center of mass eccentric balance equation of the mass center relative to the center of the rotating coordinate system based on the 3D model, and determines the feasible installation position coordinates and size constraints of the counterweight according to its structural dimensions and space constraints, the mass of the center of mass eccentric device, the 3D center of mass eccentric coordinates of the center of mass, and the feasible installation position coordinates and size constraints of the counterweight.

[0045] Step 5. In the 3D modeling software, create an equipment assembly drawing, import the eccentric center of mass equipment to be balanced, import the counterweight blocks in sequence, install each counterweight block at the corresponding designed position, and analyze and verify the mass and eccentric center of mass of the equipment after counterbalancing.

[0046] The center of mass eccentric device to be balanced is as follows Figure 3 As shown, the optimized counterweight block is as follows Figure 4 As shown, the equipment after balancing according to the patent method is as shown Figure 5 shown.

[0047] Based on the center of mass eccentricity balance equation of the equipment, the present invention develops a balancing optimization method that takes into account the structural constraints of the equipment, aiming to obtain the optimal balancing solution, that is, the installation position and shape and size of the counterweight block, and realize the digital balancing of the center of mass eccentricity equipment through this method. The weighted balancing objective function of the center of mass eccentricity vector modulus and the total mass of the counterweight block is established, and the position and size constraints of the counterweight block are determined according to the structural size constraints of the complex equipment, and the particle swarm optimization method is used to optimize the balancing objective function to obtain the optimal balancing solution.

[0048] The above embodiments are only illustrative of the principles and effects of the present invention, as well as some of the embodiments of its application. For ordinary technicians in this field, several modifications and improvements can be made without departing from the creative concept of the present invention, which all belong to the protection scope of the present invention. The above embodiments are only illustrative of the principles and effects of the present invention, as well as some of the embodiments of its application. For ordinary technicians in this field, several modifications and improvements can be made without departing from the creative concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A three-dimensional center of mass eccentric balancing method for equipment considering structural constraints, characterized in that: The following steps are included S1, establish the rotation coordinate system {r} of the mass center eccentric device to be balanced, use 3D modeling software to analyze the mass m and mass center eccentricity of the device, or use mass center measurement equipment to measure the mass m and mass center eccentricity of the device, and obtain the 3D mass center eccentricity vector p of the mass center eccentric device to be balanced in the rotation coordinate system {r} g =(x g ,y g ,z g ); S2, according to the spatial structure size of the eccentric center of mass equipment to be leveled, determine the installation bottom center position p of the cylindrical counterweight block i , bottom dimension constraint vector d i,max and the height constraint vector h i,max ; S3, m, p g 、p i d i,max 、h i,max The density ρ of the counterweight block is input into the Matlab program, which optimizes the selection of the counterweight block and establishes the objective function of the weighted vector modulus of the center of mass eccentricity and the total mass of the counterweight block: where |p n | for p n The modulus of γ is the equilibrium|p n |With m z The weight factor, d i is the bottom diameter of the counterweight, h i is the height of the counterweight block; the particle swarm optimization method is used to calculate the mass of each counterweight block and the eccentricity vector of the center of mass after adding the counterweight block to optimize the objective function. i With h i Perform iterative optimization to obtain the optimal counterweight structure size; S4, in the three-dimensional modeling software, drawing a corresponding three-dimensional model of the counterweight block according to the optimal structural dimensions of the counterweight block, and setting its material properties; S5, establish the equipment assembly drawing, import the mass center eccentric equipment to be balanced, import the counterweight blocks in sequence, install each counterweight block in the corresponding position, and verify the mass and mass center eccentricity of the equipment after counterbalancing.

2. A method for balancing the equipment in three-dimensional mass center with eccentricity considering structural constraints according to claim 1, characterized in that: In step S2, the number of feasible installation positions is set to I, and the three-dimensional coordinates of the installation bottom center position of each cylindrical counterweight block relative to the center of the rotation coordinate system of the eccentric center of mass device to be leveled are determined. The three-dimensional coordinates of the bottom center of the i-th cylindrical counterweight block are recorded as p i =(x i ,y i ,z i ), the maximum radius of the cylinder base is d i,max , the maximum height of the cylinder is h i,max .

3. A method for balancing the equipment in three-dimensional mass center with eccentricity considering structural constraints according to claim 2, characterized in that: In step S3, the density ρ of the counterweight block is specified according to the material of the counterweight block, and the mass of the i-th counterweight block is m i =ρ·π·d i 2 ·h i / 4, the center of mass position of the ith counterweight is p i ′ by p i With h i The total mass of the counterweight is calculated to be 4. A method for balancing the equipment in three-dimensional mass center with eccentricity considering structural constraints according to claim 3, characterized in that: The center of mass position of the device after adding the counterweight in step S3 is expressed as

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