CN111651923A - Multi-degree-of-freedom passive vibration isolation system optimization design method - Google Patents
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Abstract
A multi-degree-of-freedom passive vibration isolation system optimization design method comprises the steps of carrying out vibration characteristic analysis on vibration isolation objects, calculating the coordinate ranges of upper and lower hinge points of each vibration isolator according to the set number of the vibration isolators, setting multi-aspect constraint, randomly generating a group of initial design variable values through a program, and calculating to obtain six-degree-of-freedom inherent frequency and variance of a vibration isolation system; if the variance does not meet the termination condition, generating a group of new design variable values through selection, intersection and variation programs for iteration and judging again, repeating the iteration process until the termination condition is met and outputting the optimal design variable; after the optimization iteration is completed, generating a geometric simplified model of the vibration isolation system, and performing three-dimensional modeling and multi-body dynamics simulation on the vibration isolation system; and judging whether the parameters obtained by simulation meet all technical indexes, and further optimizing until all the technical indexes are met. The invention can complete the optimized design of the multi-degree-of-freedom vibration isolation system in a short time, avoids the complexity of manual iteration and is suitable for different vibration isolation performance requirements.
Description
Technical Field
The invention belongs to the field of design of multi-degree-of-freedom vibration isolation systems, and particularly relates to an optimal design method of a multi-degree-of-freedom passive vibration isolation system.
Background
In the fields of aerospace and other industries, the vibration isolation technology is an important technical means for ensuring the stable operation of a system in a vibration environment. Through the vibration isolation technology, the normal work of sensitive equipment on the moving carrier can be ensured, and other equipment on the same carrier can also be ensured not to be influenced by a vibration source. The passive vibration isolation system is widely applied to the industrial field due to the advantages of high reliability, no need of external energy supply and the like. In designing a vibration isolation system, many factors such as the layout and configuration of the vibration isolation system, the number of vibration isolation components, and the modal characteristics of the vibration isolation system and the components are generally considered. Considering the complexity of repeated iteration, the complexity of design variables, and the diversity and difficulty of design objects and technical indexes of the traditional manual design method, a designer is difficult to complete an optimal design scheme meeting the technical indexes in a short period. Therefore, a method for quickly and optimally designing the multi-degree-of-freedom vibration isolation system with strong adaptability, engineering significance and guidance value is needed.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the optimization design method of the multi-degree-of-freedom vibration isolation system is used for the rapid configuration optimization design of the multi-degree-of-freedom passive vibration isolator system, and avoids the complexity of manual optimization design.
The technical scheme adopted by the invention for solving the technical problems is as follows: a multi-degree-of-freedom passive vibration isolation system optimization design method comprises the following steps:
step 1: carrying out vibration characteristic analysis on the vibration isolation object;
step 2: inputting vibration characteristics of a vibration isolation object and vibration isolation object mass, inertia and mass center coordinates;
and step 3: setting the number of the vibration isolators, and calculating the coordinate range of the upper and lower hinged points of each vibration isolator in the vibration isolation system in a cylindrical coordinate system;
and 4, step 4: inputting constraint parameters or establishing a constraint function, wherein the constraint parameters comprise configuration constraint, rigidity constraint, frequency constraint and interference constraint;
and 5: randomly generating a group of initial design variable values in the range of the upper and lower limits of the constraint or referring to the existing design parameter values, namely the initial upper and lower hinge point coordinates and the axial radial stiffness coefficient;
step 6: calculating to obtain a mass matrix of the vibration isolation object according to the characteristics of the vibration isolation object input in the step 2 and the initial design variable value generated in the step 5, writing a matrix form dynamic equation to the columns of the vibration isolation system, and further calculating to obtain six-degree-of-freedom inherent frequency and variance of the vibration isolation system;
and 7: judging whether the six-degree-of-freedom inherent frequency variance of the vibration isolation system meets a termination condition; if the termination condition is met, performing a step 8, if the termination condition is not met, generating a new set of design variable values through selection, intersection and variation, and returning to the step 6;
and 8: outputting the optimal upper and lower hinge point coordinates and the axial radial stiffness coefficient of the vibration isolation system;
and step 9: generating a geometric simplified model of the vibration isolation system according to the coordinates of the upper hinged point and the lower hinged point obtained by optimization;
step 10: performing three-dimensional modeling and multi-body dynamics simulation on the vibration isolation system according to the coordinates of the upper and lower hinged points and the axial and radial stiffness coefficients obtained by optimization;
step 11: judging whether the structural and modal parameters of the vibration isolation system obtained by simulation meet various technical indexes, if so, finishing the optimization design, and if not, returning to the step 4, adjusting constraint conditions, and carrying out iteration optimization design again until all technical indexes are met;
step 12: and storing the design parameters of the vibration isolation systems and the vibration isolators meeting all technical indexes, and selecting whether to design by referring to the stored design parameters by a designer when designing the next time.
Further, the vibration characteristic in step 1 is a first-order vibration frequency or a first-order frequency doubling of the rotation speed of the vibration isolation object, and is obtained through a vibration experiment or finite element analysis.
Further, the configuration constraint in step 4 comprises: the height range of a mechanical interface surface of the vibration isolation object and the two-dimensional coordinate upper and lower limits of the upper and lower hinge points of the vibration isolation system are defined; the stiffness constraints include: vibration isolator axial and radial stiffness ranges; the frequency constraints include: calculating the six-degree-of-freedom natural frequency range of the vibration isolation system or according to the vibration frequency of the vibration isolation object obtained in the step 1; the interference constraint comprises a spatial distance minimum constraint of the vibration isolator and a vibration isolation object and a spatial distance minimum constraint of an adjacent vibration isolator.
Further, the stiffness of each degree of freedom of the vibration isolation system in the step 6 is the vector sum of components of all the radial stiffness of the vibration isolator in a certain degree of freedom direction of the system; the six-degree-of-freedom natural frequency of the vibration isolation system is calculated through a system rigidity matrix and a mass matrix of a vibration isolation object.
Preferably, the vibration isolation object inertia in the step 2 is a three-axis moment of inertia passing through a center of mass rotating shaft; the origin of a coordinate system where the centroid coordinate is located is the centroid of the vibration isolation object, and the coordinate axis is consistent with the three-axis direction of the vibration isolation object.
Preferably, the initial design variable value in step 5 is randomly generated by a Matlab program.
Preferably, the step 7 is performed by a genetic algorithm program of a Matlab platform, the termination condition is set according to the iteration precision of the optimization process, and the parameters of selection, intersection and variation are set according to the optimization requirement.
Preferably, said step 9 is shown by Matlab three-dimensional mapping.
Preferably, each technical index in step 11 includes a position of a resonance peak of the high-frequency structure, a structure quality, a six-degree-of-freedom natural frequency interval, and an attenuation rate at a specific frequency point.
The invention has the advantages that:
(1) the invention has less limitation on vibration isolation objects and can be widely applied to the design of multi-freedom passive vibration isolation systems with different vibration isolation performance requirements;
(2) the invention can complete the optimized design of the multi-degree-of-freedom vibration isolation system in a short time, and avoid the complexity of manual iteration;
(3) the design result of the invention has strong visibility, which is helpful for designers in the field to quickly judge the design result;
(4) the method comprises a simulation verification link for optimization design, the engineering practice of the design result is good, and the method has guiding significance for the configuration design of the multi-degree-of-freedom vibration isolation system in various fields;
(5) the invention provides two design modes, and a designer can choose whether to design by referring to the existing vibration isolation system parameters when designing a new vibration isolation system, so that the design results before and after the design are inherited and continued.
Drawings
FIG. 1 is a flow chart of the method for optimally designing a multi-degree-of-freedom vibration isolation system.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, rather than all embodiments, and all other embodiments obtained by a person skilled in the art based on the embodiments of the present invention belong to the protection scope of the present invention without creative efforts.
As shown in fig. 1, a flow chart of the method for optimally designing a multiple degree of freedom vibration isolation system is shown, and taking a four-vibration isolator multiple degree of freedom vibration isolation system for controlling a moment gyro on a spacecraft as an example, the method specifically comprises the following design steps:
step 1: carrying out vibration experiment or finite element simulation on the control moment gyroscope to obtain a first rotating speed frequency multiplication;
step 2: input control moment gyro mass m, three-axis moment of inertia I through mass center rotating shaftxx、Iyy、IzzAnd establishing a coordinate system at the geometric center of the control moment gyroscope, wherein the coordinates of the mass center are (Mx, My and Mz).
And step 3: according to the number of the vibration isolators, the coordinate ranges of hinge points on four vibration isolators in the vibration isolation system in a coordinate system are (0, pi/2, h), (pi/2, pi, h), (pi, 3 pi/2, h), (3 pi/2, 2 pi, h) in sequence, the coordinate ranges of lower hinge points in the coordinate system are (0, pi/2, 0), (pi/2, pi, 0), (pi, 3 pi/2, 0), (3 pi/2, 2 pi, 0) in sequence, wherein h is the height difference of the planes of the upper hinge point and the lower hinge point;
and 4, step 4: inputting constraint parameters, configuring constraints: setting the height constraint of the vibration isolation system and the upper and lower limits of the coordinates of the upper and lower hinged points according to the overall dimension of the control moment gyroscope, the height of the mechanical interface plane and the range of the mechanical interface of the spacecraft platform; and (3) rigidity constraint: setting the axial stiffness range and the radial stiffness range of the vibration isolators, wherein the axial stiffness and the radial stiffness of the four vibration isolators are the same; and (3) frequency constraint: setting a six-degree-of-freedom inherent frequency range of the vibration isolation system according to the first frequency multiplication of the rotating speed of the control moment gyroscope; interference constraint: constraining the minimum spatial distance between the vibration isolator and the control moment gyro and the minimum spatial distance between the adjacent vibration isolators;
and 5: a program randomly generates a group of initial design variable values, namely initial upper and lower hinge point coordinates and axial radial stiffness coefficients, in a constraint upper and lower limit range;
step 6: calculating to obtain a mass matrix M of the vibration isolation object according to the characteristics of the control moment gyro input in the step 2 and the initial design variable value generated in the step 5, writing a matrix form dynamic equation to the column of the vibration isolation system, and further calculating to obtain a stiffness matrix K of the vibration isolation system, thereby calculating to obtain the six-degree-of-freedom inherent frequency f and the variance D of the vibration isolation system:
let M-1K＝A，λ＝ω2And { theta } is a vector function for describing the planar motion of the upper hinge point, namely (A-lambda I) { theta } is 0, and the equation is solved to obtain a characteristic value
Six-degree-of-freedom natural frequency of vibration isolation system
Variance (variance)
And 7: setting the termination condition to reach the iteration precision 10-6Judging whether the six-degree-of-freedom inherent frequency variance D iterative process of the vibration isolation system meets a termination condition; if the termination condition is met, performing step 8, if the termination condition is not met, selecting, crossing and mutating the current set of design variables through a function in the Matlab platform to generate a new set of design variable values, and returning to step 6; wherein, the method adopts Stochastic uniform function, adopts Scattered function alternately, randomly generates genetic binary vector to cross according to 0-1, and adopts Adaptive feasible function for variationCounting;
and 8: outputting the optimal upper and lower hinge point coordinates and the axial radial stiffness coefficient of the vibration isolation system;
and step 9: calling a Matlab program to draw a geometric simplified model of the vibration isolation system according to the coordinates of the upper hinge point and the lower hinge point obtained by optimization;
step 10: performing three-dimensional modeling and multi-body dynamics simulation on the vibration isolation system according to the coordinates of the upper and lower hinged points and the axial and radial stiffness coefficients obtained by optimization;
step 11: and judging whether the parameters of the structure and the mode of the vibration isolation system obtained by simulation meet various technical indexes, such as the position of a resonance peak of a high-frequency structure, the structure quality, the natural frequency interval of six degrees of freedom, the attenuation rate at a rotating speed-frequency doubling position and the like, if so, finishing the optimal design, otherwise, returning to the step 4, adjusting constraint conditions, and carrying out iterative optimal design again until all the technical indexes are met.
Step 12: and storing the design parameters of the vibration isolation system and the vibration isolator which meet all technical indexes for the designer to refer when designing the next time.
The above examples are intended to assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that, for those skilled in the art, without departing from the concept of the present invention, several changes and modifications can be made, such as coordinate system definition changes, constraint types and variable changes, adjustment before and after the optimization procedure steps, optimization process convergence judgment condition changes, etc., which all belong to the protection scope of the present invention.
Claims (9)
1. A multi-degree-of-freedom passive vibration isolation system optimization design method is characterized by comprising the following steps:
step 1: carrying out vibration characteristic analysis on the vibration isolation object;
step 2: inputting vibration characteristics of a vibration isolation object and vibration isolation object mass, inertia and mass center coordinates;
and step 3: setting the number of the vibration isolators, and calculating the coordinate range of the upper and lower hinged points of each vibration isolator in the vibration isolation system in a cylindrical coordinate system;
and 4, step 4: inputting constraint parameters or establishing a constraint function, wherein the constraint parameters comprise configuration constraint, rigidity constraint, frequency constraint and interference constraint;
and 5: randomly generating a group of initial design variable values in the range of the upper and lower limits of the constraint or referring to the existing design parameter values, namely the initial upper and lower hinge point coordinates and the axial radial stiffness coefficient;
step 6: calculating to obtain a mass matrix of the vibration isolation object according to the characteristics of the vibration isolation object input in the step 2 and the initial design variable value generated in the step 5, writing a matrix form dynamic equation to the column of the vibration isolation system, and further calculating to obtain a rigidity matrix of the vibration isolation system, thereby calculating to obtain the inherent frequency and the variance of the six degrees of freedom of the vibration isolation system;
and 7: judging whether the six-degree-of-freedom inherent frequency variance of the vibration isolation system meets a termination condition; if the termination condition is met, performing a step 8, if the termination condition is not met, generating a new set of design variable values through selection, intersection and variation, and returning to the step 6;
and 8: outputting the optimal upper and lower hinge point coordinates and the axial radial stiffness coefficient of the vibration isolation system;
and step 9: generating a geometric simplified model of the vibration isolation system according to the coordinates of the upper hinged point and the lower hinged point obtained by optimization;
step 10: performing three-dimensional modeling and multi-body dynamics simulation on the vibration isolation system according to the coordinates of the upper and lower hinged points and the axial and radial stiffness coefficients obtained by optimization;
step 11: judging whether the structural and modal parameters of the vibration isolation system obtained by simulation meet various technical indexes, if so, finishing the optimization design, and if not, returning to the step 4, adjusting constraint conditions, and carrying out iteration optimization design again until all technical indexes are met;
step 12: and storing the design parameters of the vibration isolation systems and the vibration isolators meeting all technical indexes, and selecting whether to design by referring to the stored design parameters by a designer when designing the next time.
2. The optimized design method of the multi-degree-of-freedom passive vibration isolation system according to claim 1, characterized in that:
the vibration characteristic in the step 1 is first-order vibration frequency or first-order frequency multiplication of rotating speed of the vibration isolation object, and is obtained through vibration experiments or finite element analysis.
3. The optimized design method of the multi-degree-of-freedom passive vibration isolation system according to claim 1, characterized in that: the inertia of the vibration isolation object in the step 2 is the three-axis moment of inertia passing through the mass center rotating shaft; the origin of a coordinate system where the centroid coordinate is located is the geometric center of the vibration isolation object, and the coordinate axis is consistent with the three-axis direction of the vibration isolation object.
4. The optimized design method of the multi-degree-of-freedom passive vibration isolation system according to claim 1, characterized in that: in the step 4:
configuration constraints include: the height range of a mechanical interface surface of the vibration isolation object and the two-dimensional coordinate upper and lower limits of the upper and lower hinge points of the vibration isolation system are defined;
the stiffness constraints include: vibration isolator axial and radial stiffness ranges;
the frequency constraints include: calculating the six-degree-of-freedom natural frequency range of the vibration isolation system or according to the vibration frequency of the vibration isolation object obtained in the step 1;
the interference constraint comprises a spatial distance minimum constraint of the vibration isolator and a vibration isolation object and a spatial distance minimum constraint of an adjacent vibration isolator.
5. The optimized design method of the multi-degree-of-freedom passive vibration isolation system according to claim 1, characterized in that:
and the initial design variable value in the step 5 is randomly generated by a Matlab program.
6. The optimized design method of the multi-degree-of-freedom passive vibration isolation system according to claim 1, characterized in that:
the stiffness of each degree of freedom of the vibration isolation system in the step 6 is the vector sum of components of the radial stiffness of all vibration isolator shafts in a certain degree of freedom direction of the system; the six-degree-of-freedom natural frequency of the vibration isolation system is calculated through a system rigidity matrix and a mass matrix of a vibration isolation object.
7. The optimized design method of the multi-degree-of-freedom passive vibration isolation system according to claim 1, characterized in that:
and 7, the step is carried out through a genetic algorithm program of a Matlab platform, the termination condition is set according to the iteration precision of the optimization process, and the parameters of selection, intersection and variation are set according to the optimization requirement.
8. The optimized design method of the multi-degree-of-freedom passive vibration isolation system according to claim 1, characterized in that: said step 9 is shown by a Matlab three-dimensional plot.
9. The optimized design method of the multi-degree-of-freedom passive vibration isolation system according to claim 1, characterized in that:
in the step 11, each technical index comprises a high-frequency structure resonance peak position, structure quality, a six-degree-of-freedom inherent frequency interval and an attenuation rate at a specific frequency point.
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