Weapon System Received 20000407, the author is the researcher of the three-in-one research institute of China Aerospace Electromechanical Corporation, the research on the aerodynamic servo elasticity of foreign aircraft. Chen Wenjun structural natural vibration and unsteady aerodynamic calculation method pneumatic servo elastic modeling and model simplified pneumatic servo elastic analysis method Integrated design with computer program structure/control Pneumatic heating adversely affects the application of pneumatic servo elastic analysis and design techniques.
Key words pneumatic servo elastic mechanics aerodynamic servo thermoelastic structure / control integrated design overview Pneumatic servo elastic mechanics is mainly to study the various kinds of aircraft caused by elastic force, inertial force, aerodynamics and control force (even thermal) A comprehensive discipline of mechanical phenomena. In a nutshell, pneumatic servo elasticity is the cross-science of structural dynamics, unsteady aerodynamics, and automatic control system dynamics (see Figure 1).
Pneumatic servo elastic mechanics are very broad and can be basically attributed to two types of problems, namely stability problems (such as flutter and divergence) and response problems (such as chattering and gust response). They affect aircraft fatigue life, ride quality and payload, especially instability that reduces maneuverability, limits flight envelopes, and can even lead to catastrophic accidents.
With the increase of flight speed and the development of intelligent materials, pneumatic servo elastic mechanics is bound to face more severe challenges. Pneumatic servo elastic mechanics has become a hot research topic in the world.
Pneumatic servo elasticity research has evolved with the development of human aerospace activities and aircraft. In the aspect of structural analysis, the simple finite element analysis of aerodynamic theory evolved from simple beam theory to quasi-stationary theory to complete unsteady lift surface theory control system analysis also by univariate input/univariate output system. The frequency domain is judged to extend the state space robustness estimation to the multivariate input/multivariable output system. The smart material is being combined with the composite material. The structure/control integration design will replace the traditional structure and control design. practice.
1 Structural analysis and unsteady aerodynamic calculations 1. The modal parameters (natural frequency, natural mode, generalized stiffness, generalized mass and damping coefficient) of the structural natural vibration analysis structure are the raw data of aerodynamic servo elasticity analysis.
For the slender body (bomb) body and the large aspect ratio lifting surface, the beam can be used to simulate its natural vibration characteristics. For small aspect ratio complex structure lifting surface, finite element modeling is usually used, and subspace iteration method is used. , Lanzos method, Givenshaus Hod method solve matrix eigenvalue problem.
The advantage of subspace iteration method is that the algorithm is stable, easy to use computer external memory, the program is easy to standardize, and it can solve the problem of real symmetric matrix eigenvalue with considerable bandwidth. The disadvantage is that the convergence speed is slow. The outstanding advantage of the Lanzos method is that it converges quickly, usually 5 to 10 times faster than the subspace iteration method, but is not as good as the subspace iteration method in terms of the degree of automation of using external memory and algorithms. The Givens Hausehed method is one of the most effective methods for solving some or all of the features of the standard eigenvalue problem of dense real symmetric matrices. It is stable, fast, flexible, and has a wide range of applications.
There are many mature methods available for solving matrix eigenvalue problems. For the study of pneumatic servo elasticity, it can be said that there is no such problem.
In terms of finite element modeling, the finite element model of normal temperature and conventional material structure appeared in the 1980s as early as the 1960s. In this model, the thermal effect (reaction in the stiffness matrix) was successfully included. However, the finite element model of the intelligent material structure is the result of research in recent years, and it is still being developed and improved. The unsteady aerodynamic calculation method is divided by the Mach number Ma range, which is used in the pneumatic servo elasticity analysis. The main unsteady aerodynamic calculation method is as follows: using the incompressible flow theory ≤ 0. 95), using the kernel function configuration method and the dipole grid method ≤ 1. 05), using the small disturbance potential theory 4) the low supersonic range (1 05 Ma ≤ 3), using Mach box method or harmonic gradient theory and impact theory 6) Hypersonic range (Ma 10), using quasi-stationary theory.
The above method is applicable regardless of the aspect ratio of the airfoil. However, for large aspect ratio airfoils, there are simple, flexible and accurate calculation methods, namely strip theory and modified strip theory, which are suitable for the subsonic to hypersonic range.
The above unsteady aerodynamic theory is limited to the small angle of attack range. In the pneumatic servo elasticity analysis, only the small angle of attack range is usually involved. However, it is sometimes necessary to study the problem of aerodynamic servo elasticity at high angles of attack.
In recent years, although the research on unsteady aerodynamics of large angle of attack has made some progress, the unsteady aerodynamic calculation method for large angle of attack that can be used for engineering analysis is not yet mature, and research in this area is still a hot topic. The large angle of attack aerodynamic servo elasticity study in [3] is still based on the unsteady aerodynamic force of small angle of attack.
The study of aerodynamic servo elasticity of transonic and high angle of attack aircraft requires a nonlinear aerodynamic calculation method. In recent years, although considerable achievements have been made in the study of nonlinear aerodynamic theory, it is expensive to calculate for engineering calculations.
Although the linear lift surface theory is cheap, it cannot be used for transonic or high angle airfoil. In order to extend the linearized lift surface theory to such an airfoil, corrections have long been corrected to correct the correction factor method.
2 Pneumatic Servo Elasticity Analysis 2. 1 Pneumatic Servo Elastic Equation of Motion 2. 1. 1 Frequency domain equation with a finite set of low-frequency rigid body and elastic vibration mode, control surface mode and gust velocity mode as generalized coordinates The generalized mass, generalized stiffness and generalized damping of the servo-elastic system are calculated by the simple harmonic oscillatory unsteady aerodynamic method described above. The generalized aerodynamics in the frequency domain are calculated. Using the Lagrangian equation, the equation of motion in the frequency domain can be obtained.
2. 1. 2 time domain (state space) equations The application of various modern control design techniques, simulation and optimization methods, and the efficient implementation of linear system algorithms require that the aerodynamic servo elastic equations be transformed from a frequency domain to a linear time. Changed state space form.
The main difficulty in establishing a state space equation is the determination of an unsteady aerodynamic expression. Since in the flexible aircraft motion, the unsteady aerodynamic term is described by the transcendental function in the Laplace domain and is not easily converted directly. Therefore, it is necessary to seek to describe unsteady aerodynamic forces using a rational function approximation of the Lagrangian variable. Such rational function approximation can achieve the purpose of the equation of motion of the pneumatic servo elastic system into a linear time-invariant state space equation. There are mainly three aerodynamic rational function approximations and minimum state (MS) methods.
In the literature, based on the general formula of aerodynamic rational function approximation, the state space motion equation is derived from the frequency domain equation. In the latter equation, an augmented aerodynamic state vector that is not present in the frequency domain equation appears. This vector is related not only to the structural mode, the control surface mode, and the gust velocity mode, but also to the aerodynamic rational function approximation method and the approximate root number. Therefore, approximating the aerodynamic rational function may greatly increase the degree of the state vector.
Some literatures (such as [5]) deduced the state space motion equations of aerodynamic servo-elastic systems for typical wing profiles, composite airfoil, full-aircraft and general conditions and discussed the problem of aerodynamic servo elastic modeling.
2. 1. 3 Spiral Servo Elastic Model Simplification Method The order of the above state space model (motion equation) is the number of modes (structural mode, control plane mode and gust velocity mode), the approximate root number of aerodynamic function and The function of the approximation method The order of this equation must be very high, and it is difficult to solve without proper simplification. The simplified model should start from the following aspects: 1) Select the aerodynamic rational function approximation method 2) Select the structural natural vibration mode 3) Differentiate the important mode and the secondary mode 4) Apply the approximation constraint 5) Use the physical weighting 6) Implement the structure The state remains.
2. 2 Pneumatic Servo Elasticity Analysis Method When the motion equation does not include external disturbances such as gusts, the aerodynamic servo elastic analysis is the stability analysis, and when the motion equation includes external disturbances, it is the response analysis.
2. 2. 1 Pneumatic Servo Elastic Stability Analysis Method The single-input/single-output system stability analysis method is basically a traditional method, namely the Nai's diagram method, the root locus method and the method. These methods are comprehensively introduced in the "Handbook of Aeroelasticity of Aircraft" in China.
The robustness of the feedback system under model perturbation is an important topic in the field of pneumatic servo elasticity. A reasonable closed-loop system must have good stability, resistance to model perturbations and external interference. In a single-variable system, these properties can be reliably estimated from the Naith plots plotted by the open-loop transfer function by gain and phase. In multivariable systems, the stability of a closed-loop system can be determined using the stability criteria of the perturbation system.
In recent years, a multi-variable system robustness analysis method based on singular value theory is popular in the world. The stability, sensitivity and anti-interference ability of the system are studied by the singular value of the system's hysteresis matrix. The stability of the closed loop system can be determined using the stability criteria of the perturbation system. This method can consider both control loops and the coupling between them. This method is based on the equation of state space motion.
2. 2. 2 Pneumatic Servo Elastic Response Analysis Method The pneumatic servo elastic response problem varies with external disturbances, and the analysis method of the problem is also diverse. Common methods are power spectral density method and matched filter theory.
2. 2. 2. 1 Power Spectral Density Method The Federal Aviation Administration's charter states that the power spectral density method must be used to determine the aircraft's dynamic response to atmospheric turbulence unless a more rational approach is used.
The basic quantity of the power spectral density method is the power spectral density function, ie the power spectrum. The power spectrum contains statistics describing the stochastic process, including the root mean square value. Among the issues discussed now, the stochastic process is the aircraft response of atmospheric disturbances. Assuming the input is Gaussian, the output is also Gaussian (because the system is linear). For more information, please see the reference [6].
2. 2. 2. 2 Matched Filters The theory of matched filter theory is used to design such a critical gust mode (time lapse of vertical gust velocity): it produces a response with a selected load (worst case) and Time-dependent response to other loads. The implementation steps of this theory are described in reference [6].
2. 3 Pneumatic Servo Elasticity Analysis Program Many computer programs for pneumatic servo elasticity analysis have been developed abroad. For example, ISAC was developed in the early 1970s by the Center for Pneumatic Servo Elastic Modeling. This program was enhanced and improved in the 1980s. Among them, the aerodynamic theory is the dipole grid method, the aerodynamic rational function approximation method is the least squares method and the MS (minimum state) method is equipped with modal truncation and structural residue schemes, which are programmed into main modules such as preprocessor modules. DLAT is a program module for calculating unsteady aerodynamics by using the dipole grid method. The reference to the DLIN module SPLFIT is to determine the aerodynamic rational function approximation and optimize the data generated by the program module DLAT of the denominator pole to form a model and perform The large-scale and extensive engineering application of dynamic analysis program modules proves to be an effective tool for today's pneumatic servo elastic modeling and analysis. The article [7] gave a special introduction to ISAC. Other procedures are not introduced one by one.
3 Pneumatic servo elastic design 3.1 Structural/control integrated design material is the basis of pneumatic servo elastic design. New materials will inevitably lead to new structures and new design methods. For example, the emergence of composite materials has led to composite structures and new methods of designing such structures - aeroelastic tailoring. Today, smart materials are being combined with composite materials to form smart structures. This structure tightly integrates certain components (drivers and sensors) of the control system with the body structure. It is both a structure and a control system, and has the dual functions of a structure and a control system. Therefore, for the intelligent structure design, the traditional method can no longer be used, that is, the pneumatic servo elastic design is artificially decomposed into the aeroelastic cutting and active control design, and the main structure and the control system should be regarded as one in the optimal way by the system engineering viewpoint. Design at the same time.
In recent years, the necessity of integrated design of structure/control has become a consensus. In [8], the multi-disciplinary airfoil integration design problem is proposed, and an integrated framework document for the design of active controlled fiber composite airfoil [9] is proposed for the laminated composite lifting surface structure/control integration design. Mathematical formulas and confirmed the validity of these formulas [10] summarized the problem of intelligent structure pneumatic servo elastic design, that is, the use of intelligent material drives to control the structural deformation of aeroelastic systems. Many foreign literatures have studied the design and pressure of piezoelectric strain actuators. The active control of the electric coupling system and the design method of the two control laws (listed in the literature [2]). The structure/control integration of the aerodynamic servo thermoelastic design problem of the shape memory alloy piezoelectric material composite integrated intelligent structure The design method is based on hierarchical multi-level problem decomposition and optimization (see Figure 3). The hierarchical decomposition method facilitates the natural adjustment of design goals to system-level and subsystem-level goals. This adjustment creates a structure that coordinates subsystem performance within a design law to improve system performance. Utilizing existing design methods and tools, the subsystem design is independently obtained under a set of fixed design integrated parameters.
Using subsystem optimization method and optimal solution sensitivity concept to obtain subsystem design sensitivity information can provide a reasonable method to coordinate subsystem performance. Subsystem design sensitivity information is used at the system level design to make decisions that affect subsystem design toward improving overall system performance.
In the composite structure/control integration design, the objective function is usually: 1) maximize the aeroelastic critical speed of the airfoil (system-level objective function) 2) minimize the control performance index (control-level objective function).
The design variables are: 1) layup direction 2) layup thickness 3) layup sequence 4) control system design speed 5) drive position and number 6) closed loop pole 7) control gain.
Constraints are generally: 1) structural natural frequency limits 2) control performance constraints 3) design variable limits.
The whole optimization design problem can be briefly described as: In the design space formed by the constraints, a set of design variables satisfying the requirements of the objective function is sought. The optimized design briefing procedure is shown in Figure 4.
3. 2 Optimized Design Procedures [9] introduced two optimized design computer programs, namely IDESIGN is based on the combination of performance index limits and recursive quadratic algorithms, while NEWSUM TA is based on the use of the Newton method. The sequence of approximate derivatives is unconstrained to minimize the algorithm.
4 Influence of heat on pneumatic servo elasticity With the advent of supersonic aircraft, the influence of aerodynamic heating on structural mechanical properties has attracted people's attention.
Heating can weaken the structural stiffness from two aspects, one is to reduce the elastic modulus of the material, and the other is that the internal stress generated by the temperature gradient causes a change in stiffness. Attenuation of stiffness typically results in a decrease in the natural frequency of the structure and a change in frequency, thereby reducing aeroelastic and pneumatic servo elastic properties. Therefore, the structural analysis must take into account the effect of temperature on stiffness. In [11], a method for introducing thermal effects into finite element analysis is introduced.
The steps affected by the stiffness matrix.
Structural modal analysis is performed using the stiffness matrix taking into account the thermal effect, and the obtained modal analysis results are used for aeroelastic analysis and aeroelastic analysis. These three analyses are thermal vibration analysis, aeroelastic analysis and pneumatic servo heat. Elastic analysis.
A block diagram of the analysis method. Using the above thermal effect analysis method, many calculation results were obtained. They show that heat has an adverse effect on the aerodynamic servo-elastic properties, and this effect is even alarming.
5 Structural/Control Integration Analysis and Design Technology Application The above-mentioned structural/control integration analysis and design methods are increasingly used for aircraft pneumatic servo elastic analysis and design.
They evaluated the aerodynamic servo-elastic properties of the design and improved the quality and design efficiency of the pneumatic servo-elastic design.
Some application examples are provided below.
1) The structural/control integration analysis method has been used for the evaluation and analysis of the flight control system design of the X29 aircraft, so that the flight control system design can be corrected in time to avoid the instability problem. 2) The aforementioned ISAC program has been used to support many projects and Scientific research projects, such as and 2 (aerodynamic and structural test aeroelastic research 1 and 2 wings) b) general X wing feasibility study c) elastic oblique wing analysis active flexible wing wind tunnel test plan e ) High-speed civil transport aircraft wind tunnel flutter model hypersonic vehicle (including guide h) benchmark active control test plan.
In the program, examples of the application of aerodynamic servo elasticity analysis of aeronautical missiles are listed, including examples of aeroelastic thermoelastic applications.
4) According to the pneumatic servo thermoelastic analysis method, the active control technology not only avoids the thermal effect on the shuttle flutter speed, but also improves the flutter speed and improves the ride quality. 5) According to the literature [6], pneumatic Servo thermoelastic theory has been used in the design of flutter active suppression systems (FSS) and ride quality (RQ) improvement systems. The flutter active suppression system can recover the chattering vibration loss caused by the thermal effect, and the ride quality improvement system designed in this way can reduce the acceleration peak of the short period mode and the elastic mode, and can also reduce the random gust. The small acceleration response has a root mean square value of 30.
6) In the literature [9], the structural design of a rectangular laminated composite was optimized using the structural/control integrated design method. If the airfoil does not use a control system, the aeroelastic response at any airflow speed of 45 m / s is unstable regardless of the design. An active aeroelastic suppression system was designed using the structural/control integrated design method to make the airfoil stable at this airflow speed.
7) The literature [6] also uses the structural/control integrated design method to integrate the above-mentioned rectangular composite airfoil control system. The aeroelastic critical speed and control performance of the design results are increased by 102 and reduced by 75 (the lower the control performance index, the better) than the non-integrated design.
8) Literature [2] has a structural/control integrated design of the piezoelectric composite airfoil. Under the conditions of the same structural quality and control requirements, the flutter speed is increased by 48, and the control efficiency is increased from 6.5 to 2 Qiu Tao. Active Suppression of Airfoil Flutter with Winged Tip Tanks Using Strain Drives [Thesis]. Graduate School of Beijing University of Aeronautics and Astronautics,
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