CN112149232A - Heavy helicopter flight dynamics rigid-elastic coupling modeling method - Google Patents

Abstract

The invention provides a rigid-bomb coupling modeling method for the flight dynamics of a heavy-duty helicopter. First, the motion equation of the helicopter body and the motion equation of the blade are defined, and then the relationship between the motion state quantity of the rotor and the motion state quantity of the body is analyzed, and the acceleration of the body is combined. The relationship between the amount and the acceleration of the hub, the motion state of the blade is brought into the blade motion equation and sorted out, the motion equation is divided into two parts, and both parts are expressed as an explicit matrix form; then the rotor force is expressed as the same The two parts of , convert the rotor force into the generalized external force of the body, and bring it into the body motion equation; finally get the whole machine coupled motion equation explicitly. Based on the impedance matching method, the present invention deduces an explicit helicopter flight dynamics rigid-elastic coupling dynamic model, which has the advantage of simultaneously reflecting the rigid body motion and aeroelasticity of the helicopter, can adapt to the low structural rigidity of the heavy-duty helicopter, and can be used for Study the coupling problem of driver and airframe structure.

Description

A rigid-bomb coupling modeling method for the flight dynamics of heavy helicopters

technical field

The invention relates to the field of flight dynamics, in particular to a rigid-bomb coupling modeling method for the flight dynamics of a heavy helicopter.

Background technique

The interaction between the helicopter pilot and the airframe structure mode may lead to obvious oscillation of the airframe structure mode, especially with the large size and low structural rigidity of the heavy-duty helicopter, the frequency of the airframe structure is reduced, and the driver and the airframe structure are not connected. The coupled oscillation phenomenon becomes impossible to ignore. Walden reviews the past 40 years of cases and solutions related to coupled oscillations of the pilot and airframe structural modes, noting that these solutions need to be analyzed and validated solidly based on flight tests, but rethought after incidents of coupled oscillations occur. The solution is lagging and has already caused considerable losses. If the accident can be analyzed and predicted through a large number of flight simulations before the accident occurs, the accident can be avoided as much as possible and the loss can be avoided. In order to accurately reflect the coupling problem between the driver and the body structure that may occur during flight, it is first necessary to establish a helicopter flight dynamics simulation model with rigid-bomb coupling, which can not only reflect the low-frequency rigid body motion in the actual flight process, such as trajectory motion and attitude change And so on, it should also be able to reflect the aerodynamic and inertial coupling relationship between the body structure and each sub-component, such as rotor/fuselage coupling, in addition, the interaction relationship between rigid body motion and elastic deformation should also be reflected.

At present, the helicopter flight dynamics simulation model often regards the body as a six-degree-of-freedom rigid body to study the stability, maneuverability and flight quality during flight. In the field of helicopter structural dynamics research, the actual motion of the helicopter is often ignored, and high-precision elastic modeling of the body and blade structure is carried out based on the ideal flight situation, and the aeroelastic coupling between the rotor and the body is studied.

During the development of the CH-53K helicopter, Sahasrabudhe used the linear method based on the AB array and the loose coupling method to consider the influence of the elastic deformation of the airframe on the flight quality. There are precedents in the research fields of fixed-wing aircraft, hypersonic vehicles, and space vehicles that consider elastic deformation of airframes in flight dynamics analysis. These studies use modeling methods including average shafting method, quasi-coordinate system method, and transient coordinate method. system. On the helicopter, Cribbs established a tightly coupled helicopter rigid-bomb coupling model using the average shafting method, and studied the vibration reduction of the helicopter body based on active structural response control, but Meirovitch questioned that Cribbs' model could not truly reflect the deformation of the flexible body However, the amount of symbolic operations involved in this method is too large and cannot be simplified, so it is difficult to use in practice.

In the prior art, the flight dynamics and structural dynamics of helicopters are often regarded as independent disciplines. Both disciplines have very mature analytical models, but the research on the combination of the two is very rare. In the current helicopter flight dynamics research, even if the body structure elasticity is considered, most of them adopt the loose coupling method to separate the rigid body motion and elastic deformation of the body. The load is then applied to the body elasticity model. Even if the tightly coupled method is adopted, the rigid-bomb coupled modeling method of helicopter flight dynamics is still controversial. There is no unified modeling method and the calculation efficiency is low, which is difficult to meet the needs of a large number of flight simulations.

SUMMARY OF THE INVENTION

In order to solve the problems in the prior art, the present invention provides a rigid-bomb coupling modeling method for the flight dynamics of heavy helicopters. Reflecting the advantages of helicopter rigid body motion and aeroelasticity, it can adapt to the low structural rigidity of heavy helicopters, and can be used to study the coupling between the driver and the body structure.

The invention provides a rigid-bomb coupling modeling method for the flight dynamics of a heavy-duty helicopter, which expands the explicit impedance matching method in the coupled aero-elastic analysis method of the rotor and the fuselage, so that it is suitable for the situation of elastic blades and elastic body , including the following process:

1) Define the equation of motion of the helicopter body and the equation of motion of the blades;

2) Analyze the relationship between the motion state quantity of the rotor and the body motion state quantity;

3) Combining the relationship between the acceleration of the body and the acceleration of the hub, the motion state of the blade is brought into the blade motion equation and sorted, and the motion equation is divided into two parts. The first part is only related to the internal motion state of the rotor, and the other part It is related to the motion state quantity of the body, and both parts are expressed in an explicit matrix form;

4) Express the rotor force as the same two parts, convert the rotor force into the generalized external force of the body, bring it into the body motion equation, and divide it into two parts related to the internal motion state quantity of the rotor and the body motion state quantity and have nothing to do with both. part;

5) To sum up, the full-machine coupled motion equation is obtained explicitly.

The specific process of expanding the explicit impedance matching method in the rotor and fuselage coupled aeroelastic analysis method is as follows:

机体的加速度量为

表式如下：1) Write down the acceleration of the rotor in the helicopter system as

The acceleration of the body is

The formula is as follows:

和

分别是各片桨叶的挥舞角加速度、摆振角加速度和桨叶变形广义坐标的加速度；

和

分别是机体在体轴系下的平移加速度、转动加速度和机身变形广义坐标的加速度；in:

and

are the flapping angular acceleration, the swaying angular acceleration and the acceleration of the generalized coordinates of the blade deformation of each blade, respectively;

and

are the translational acceleration, rotational acceleration and the acceleration of the generalized coordinates of the body deformation under the body axis system;

The equation of motion of the helicopter body can be expressed as:

表示角速度的叉乘矩阵，波浪符号代表叉乘矩阵,右下标F表示机体的量，右上标F表示机体轴系下的量；A _F0表示从静止轴系到体轴系的坐标转换矩阵，0代表静止轴系，F代表机体轴系；g ⁰表示静止轴系下的重力加速度，右上标⁰代表静止坐标系下的量；机体的速度二次项Q _v,F、广义外力Q _e,F和结构内力Q _i,F拆分成了平移V、转动ω和弹性变形p三部分；where: M _jk (j,k=V,ω,p) is the coupled mass matrix of acceleration k to acceleration j;

The cross product matrix representing the angular velocity, the tilde symbol represents the cross product matrix, the subscript F on the right represents the quantity of the body, and the superscript F on the right represents the quantity under the body axis; A _F0 represents the coordinate transformation matrix from the stationary axis system to the body axis system, 0 represents the stationary axis system, F represents the body axis system; g ⁰ represents the gravitational acceleration under the stationary axis system, and the upper right ⁰ represents the quantity under the stationary coordinate system; the quadratic term of the speed of the body Q _v,F , the generalized external force Q _{e, F} and structural internal force Q _i,F are divided into three parts: translation V, rotation ω and elastic deformation p;

The equation of motion of the blade can be expressed as:

表示在桨叶坐标系下挥舞和摆振铰对桨叶作用的未知集中力，N_β和N_ζ表示挥舞铰和摆振铰的已知铰链弹簧阻尼力矩，是挥舞和摆振角度和角速度的函数，

表示桨叶弹性变形在挥舞/摆振铰处的转角位移量形函数；Where: Q _c,B represents the binding force on the blade;

Represents the unknown concentrated force acting on the blade by the flapping and swaying hinges in the blade coordinate system, N _β and N _ζ represent the known hinge spring damping moments of the flapping and swaying hinges, which are a function of the flapping and swaying angles and angular velocities function,

Represents the angular displacement shape function of the blade elastic deformation at the flapping/swing hinge;

2) The motion coupling between the rotor and the body is reflected in the generalized external force Q _{e, F} on the body and the motion state quantity of the rotor, because the force of the rotor on the body is related to the current motion state of each blade on the rotor, while the The motion state of the blade is related to the motion state of the body, and the relationship between the motion state quantity of the rotor and the body motion state quantity is as follows:

和

分别表示对象k在坐标系j下的速度和角速度，

和

表示相应的加速度；A _jk表示从坐标系k到坐标系j的坐标转换矩阵；Ω＝[0 0 Ω]^T表示旋翼转速，

是其叉乘矩阵；

表示桨毂不旋转轴系S下从桨毂中心到挥舞/摆振铰的位置矢量；

表示由挥舞和摆振角速度引起的桨叶坐标系的角速度，

是欧拉角速度矩阵，

是欧拉角速度列向量，β表示桨叶挥舞角，上挥为正，ζ表示桨叶摆振角，前摆为正，相应的，

表示欧拉角加速度列向量；skew(*)和波浪符号

的意义相同，都代表某三维列向量的叉乘矩阵；

表示欧拉角速度矩阵的导数；Among them: the subscript 0 represents the static coordinate system, and the meanings of the other subscripts are: the propeller hub S, the flapping/swing hinge H and the elastic blade B, and the corresponding coordinate systems are the non-rotating shaft system S of the propeller hub, and the propeller hub. The rotating shaft system H and the blade coordinate system B; the subscripts acc and velo respectively represent the part related to acceleration and the part not related to acceleration;

and

respectively represent the velocity and angular velocity of the object k in the coordinate system j,

and

represents the corresponding acceleration; A _jk represents the coordinate transformation matrix from the coordinate system k to the coordinate system j; Ω = [0 0 Ω] ^T represents the rotor speed,

is its cross product matrix;

Represents the position vector from the center of the propeller hub to the swing/swing hinge when the propeller hub does not rotate the shaft system S;

represents the angular velocity of the blade coordinate system caused by the flapping and swaying angular velocity,

is the Euler angular velocity matrix,

is the Euler angular velocity column vector, β represents the blade swing angle, the upward swing is positive, ζ represents the blade swing angle, and the forward swing is positive, correspondingly,

represents the Euler angular acceleration column vector; skew(*) and tilde

The meanings are the same, they all represent the cross-product matrix of a three-dimensional column vector;

represents the derivative of the Euler angular velocity matrix;

和桨毂加速度

和

的关系：3) Combined with the acceleration of the body

and hub acceleration

and

Relationship:

By bringing the motion state of the blade into the blade motion equation and sorting it, the motion equation can be divided into two parts. The first part is only related to the internal motion state quantity of the rotor, and the other part is related to the body motion state quantity. The matrix form of the formula is:

是从旋翼状态未知量之间的耦合阻抗矩阵；

是从桨毂运动加速度到旋翼状态未知量的阻抗矩阵；

和

分别表示各片桨叶的挥舞、摆振和弹性变形方程中与加速度无关的量列矩阵；in:

is the coupling impedance matrix between the unknowns from the rotor state;

is the impedance matrix from the motion acceleration of the propeller hub to the unknown quantity of the rotor state;

and

respectively represent the acceleration-independent matrix in the flapping, swaying and elastic deformation equations of each blade;

和

表示为同样的两部分：4) Rotor force

and

Represented as the same two parts:

和

分别是与加速度项无关的桨毂载荷；in:

and

are the hub loads independent of the acceleration term, respectively;

The conversion relationship from the rotor force to the generalized external force of the body is:

The body motion equation can also be divided into two parts related to the rotor's internal motion state quantity and the body motion state quantity, and a part that has nothing to do with both;

5) To sum up, the equation of motion coupled with the whole machine is explicitly expressed as:

where: H represents the impedance matrix from right subscript to right superscript; f represents the right-hand term of the equation that does not include acceleration; I is the identity matrix.

The beneficial effect of the invention is that: based on the impedance matching method, an explicit helicopter flight dynamics rigid-bomb coupling dynamic model is derived, which has the advantage of simultaneously reflecting the rigid body motion and aeroelasticity of the helicopter, and can adapt to the low structural rigidity of the heavy-duty helicopter. , which can be used to study the coupling between the driver and the body structure.

Description of drawings

Figure 1 is a schematic diagram of the rigid-bomb coupling model of helicopter flight dynamics;

Figure 2 is the verification diagram of the UH-60A front flight trim curve;

Figure 3 shows Bousman's rotor/body coupling experimental model;

Figure 4 is a graph showing the variation of each modal frequency of the system with the rotor speed in Bousman's rotor/body coupling experiment configuration 1;

Figure 5 is a graph of the real part of each modal eigenvalue of the system in Bousman's rotor/airframe coupling experiment configuration 1 as a function of rotor speed.

Detailed ways

The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

In multi-body dynamics, the aircraft is classified as a rootless system, that is, a system that is not connected to a stationary coordinate system. The component with the largest mass in the system is often used as the basis, and other components are connected to this foundation through constraints. For heavy helicopters, The body with the highest mass is used as the foundation, and the rotor, tail rotor and flat/vertical tail are used as components connected to this foundation. Yu Zhihao once established a dynamic analysis model of the rotor system based on multi-body dynamics and studied the aeroelastic stability of the rotor. The advantage is that the equations are unified and the coupling relationship between the rotor and the body can be implicitly handled. Due to its high complexity, it is difficult to be used in flight dynamics analysis.

Different from multi-body dynamics, in the traditional helicopter flight dynamics modeling method, the inertial force of each blade on the hub is first calculated and then accumulated on the body. Since it is a rigid blade, it can be explicitly derived. Impedance matrix from hub acceleration to hub load. The six-degree-of-freedom rigid body motion of the body will be reflected in the motion of the propeller hub, and it is also easy to obtain the impedance matrix from the acceleration of the body motion to the acceleration of the propeller hub, so that the rotor/body coupling relationship can be handled by the explicit impedance matching method. When considering the elastic deformation of the blade, the impedance matrix of the rotor becomes more complicated. Li Pan used a numerical method to obtain the impedance matrix of the rotor in each calculation step, which solved the coupling problem of the elastic deformation of the blade and the motion of the body.

机体的加速度量为

则全机的动力学方程可以表示为：The invention expands the explicit impedance matching method in the traditional method, so that it is suitable for the situation of the elastic blade and the elastic body. The acceleration of the rotor in the system is recorded as

The acceleration of the body is

Then the dynamic equation of the whole machine can be expressed as:

where: H represents the impedance matrix from right subscript to right superscript; f represents the right-hand term of the equation that does not include acceleration; I is the identity matrix.

1 Elastic body dynamics model

According to the content of multi-body dynamics, the motion equation of a free flexible body in space in a floating coordinate system (quasi-coordinate system) can be written as:

表示广义加速度；Q _v表示速度二次项；Q _e表示广义外力；Q _i表示结构内力。where: M represents the mass matrix;

represents the generalized acceleration; Q _v represents the quadratic term of velocity; Q _e represents the generalized external force; Q _i represents the internal force of the structure.

Equation (2) can be used as the motion equation of the helicopter body, the floating coordinate system corresponds to the body axis system, and the generalized acceleration can be expressed as:

是体轴系空间位置坐标的绝对加速度；

是体轴系空间转角坐标的绝对加速度；

是机体弹性广义坐标的加速度。in:

is the absolute acceleration of the spatial position coordinates of the body axis system;

is the absolute acceleration of the body axis space corner coordinates;

is the acceleration of the generalized coordinate of body elasticity.

In the traditional helicopter flight dynamics modeling, the velocity and angular velocity under the body axis system are usually regarded as the state quantities of rigid body motion, so the generalized acceleration corresponding to equation (3) is changed as follows:

是体轴系下的平移加速度；

是体轴系的转动加速度in:

is the translational acceleration under the body axis;

is the rotational acceleration of the body axis

Correspondingly, the dynamic equation corresponding to equation (2) has also been changed accordingly, and the influence of gravity is considered and the angle scale is added to obtain:

表示角速度的叉乘矩阵，波浪符号代表叉乘矩阵,右下标F表示机体的量，右上标F表示机体轴系下的量；A _F0表示从静止轴系到体轴系的坐标转换矩阵，0代表静止轴系，F代表机体轴系；g⁰表示静止轴系下的重力加速度，右上标⁰代表静止坐标系下的量；机体的速度二次项Q _v,F、广义外力Q _e,F和结构内力Q _i,F拆分成了平移V、转动ω和弹性变形p三部分。where: M _jk (j,k=V,ω,p) is the coupled mass matrix of acceleration k to acceleration j;

The cross product matrix representing the angular velocity, the tilde symbol represents the cross product matrix, the subscript F on the right represents the quantity of the body, and the superscript F on the right represents the quantity under the body axis; A _F0 represents the coordinate transformation matrix from the stationary axis system to the body axis system, 0 represents the stationary axis system, F represents the body axis system; g ⁰ represents the gravitational acceleration under the stationary axis system, and the upper right ⁰ represents the quantity under the stationary coordinate system; the quadratic term of the speed of the body Q _v,F , the generalized external force Q _{e, F} and structural internal force Q _i,F are divided into three parts: translation V, rotation ω and elastic deformation p.

In formula (5), the component M _jk of the mass matrix will change with the change of the deformation of the body, but because the deformation of the helicopter body is small, the part related to the deformation in M _jk can be ignored, so that the elastic body moves. The mass matrix of the equation is a constant matrix. The generalized external force Q _e,F comes from various components on the body, and is composed of the aerodynamic and inertial forces acting on the body. For heavy helicopters with conventional configurations, these components include rotors, tail rotors, horizontal tails and vertical tails. This model mainly considers the rotor/airframe coupling, and the mass of the latter three is relatively small. It can be assumed that the mass of the tail rotor, horizontal tail and vertical tail is zero, and only aerodynamic force is applied to the airframe. The generalized external force can be expressed as follows:

表示部件i在机身体轴系下位置的叉乘矩阵；

表示机体变形在部件i处的平移变形量形函数矩阵；

表示机体变形在部件i处的转动变形量形函数矩阵；

和

分别表示局部坐标系下部件i对机身的作用力和力矩。Among them: the angle mark i represents other components (rotor, tail rotor, horizontal and vertical tail, suspension system and fuselage aerodynamic force); A _jk represents the coordinate transformation matrix from coordinate system k to coordinate system j;

The cross-product matrix representing the position of component i under the axis of the fuselage;

represents the translational deformation shape function matrix of the body deformation at part i;

Represents the rotational deformation shape function matrix of the body deformation at component i;

and

respectively represent the force and moment of component i on the fuselage in the local coordinate system.

2 Dynamic model of elastic blade rotor

Based on the assumption that the flapping/swinging hinges are in the same position, the rotor model consists of the propeller hub S, the flapping/swinging hinges H, and the elastic blades B. The corresponding coordinate systems are the non-rotating shaft system S of the propeller hub and the rotating shaft of the propeller hub, respectively. system H and blade coordinate system B. Similar to the recursive method in multi-body dynamics, the motion state of the blade can be obtained based on the current motion state of the body and the relative motion between adjacent coordinate systems, and the state quantity is expressed in the absolute coordinate system to avoid implicated acceleration , the final motion state of the blade is:

和

分别表示对象k在坐标系j下的速度和角速度，

和

表示相应的加速度；A _jk表示从坐标系k到坐标系j的坐标转换矩阵；Ω＝[0 0 Ω]^T表示旋翼转速，

是其叉乘矩阵；

表示桨毂不旋转轴系S下从桨毂中心到挥舞/摆振铰的位置矢量；Among them: 0 represents the static coordinate system; the subscripts acc and velo represent the part related to acceleration and the part not related to acceleration respectively;

and

respectively represent the velocity and angular velocity of the object k in the coordinate system j,

and

represents the corresponding acceleration; A _jk represents the coordinate transformation matrix from the coordinate system k to the coordinate system j; Ω = [0 0 Ω] ^T represents the rotor speed,

is its cross product matrix;

Represents the position vector from the center of the propeller hub to the swing/swing hinge when the propeller hub does not rotate the shaft system S;

是欧拉角速度矩阵，

是欧拉角速度列向量，β表示桨叶挥舞角(上挥为正)，ζ表示桨叶摆振角(前摆为正)，相应的，

表示欧拉角加速度列向量；skew(*)和波浪符号

的意义相同，都代表某三维列向量的叉乘矩阵；

表示欧拉角速度矩阵的导数。represents the angular velocity of the blade coordinate system caused by the flapping and swaying angular velocity,

is the Euler angular velocity matrix,

is the Euler angular velocity column vector, β represents the blade swing angle (upward swing is positive), ζ represents the blade swing angle (forward swing is positive), correspondingly,

represents the Euler angular acceleration column vector; skew(*) and tilde

The meanings are the same, they all represent the cross-product matrix of a three-dimensional column vector;

Represents the derivative of the Euler angular velocity matrix.

Compared with the motion equation of the body in equation (5), since the blade is constrained by the flapping/swing hinge, the motion equation of the blade should also include the constraint force, which is represented by Q _c , so the motion equation of the blade should be written as:

Among them: the binding force can be expressed as

表示在桨叶坐标系下挥舞和摆振铰对桨叶作用的未知集中力，N_β和N_ζ表示挥舞铰和摆振铰的已知铰链弹簧阻尼力矩，是挥舞和摆振角度和角速度的函数，

表示桨叶弹性变形在挥舞/摆振铰处的转角位移量形函数。

Represents the unknown concentrated force acting on the blade by the flapping and swaying hinges in the blade coordinate system, N _β and N _ζ represent the known hinge spring damping moments of the flapping and swaying hinges, which are a function of the flapping and swaying angles and angular velocities function,

Represents the angular displacement magnitude function of the blade elastic deformation at the flapping/swinging hinge.

仅体现在平移方程中，而转动和变形方程中全部是已知的量，从而可以带入桨叶运动方程(10)并将其拆分开，得到桨叶平移、转动和弹性变形对应的方程如下(记N _hg＝[N_β 0 N_ζ]^T是铰链弹簧阻尼力矩列向量)：Observing equation (11), it can be found that the unknown concentration force in the binding force

It is only reflected in the translation equation, and the rotation and deformation equations are all known quantities, so it can be brought into the blade motion equation (10) and split, and the equations corresponding to the blade translation, rotation and elastic deformation can be obtained As follows (note N _hg = [N _β 0 N _ζ ] ^T is the hinge spring damping moment column vector):

Taking equation (8) into equations (12)-(14) and sorting them according to known and unknown variables, the constraint force equation, the swing motion equation and the blade elastic deformation equation can be obtained.

1) Constraining force equation and propeller hub load

Equation (12) can be organized as:

表示桨毂旋转轴系H下铰对桨叶的约束力；

表示不同的加速度项对铰约束力的惯性质量，下标dv、dw、dΘ和dp分别表示桨毂平移加速度、桨毂转动加速度、挥舞摆振角加速度和桨叶弹性变形的惯性质量；

和

分别表示铰约束力中的外力部分和速度二次项部分。in:

Represents the binding force on the blade by the lower hinge of the hub rotating shaft system H;

Represents the inertial mass of different acceleration terms on the hinge binding force, and the subscripts dv, dw, dΘ and dp represent the inertial mass of the hub translational acceleration, the rotational acceleration of the hub, the flapping angular acceleration and the elastic deformation of the blade, respectively;

and

respectively represent the external force part and the quadratic part of the velocity in the hinge constraint force.

和力矩

可表示为：The rotor hub load can be obtained by accumulating the restraint reaction force and the hinge stiffness damping moment of each blade to the hub, denoting the number of blades as N _B , the i-th (i=1,...,N _B ) blade related The quantity is represented by the left superscript i, and the formula (15) is brought into the accumulated result and expanded, then the propeller hub load force

and torque

can be expressed as:

2) Swing vibration equation of motion

Equation (13) can be organized as:

Where: M _ωω represents the moment of inertia of the blade under the blade shafting, and only the moment of inertia of the blade relative to the flapping/swing hinge (denoted as I _b ) is considered in the flight dynamics modeling, then:

Therefore, the equation in the second row of equation (18) is: 0≡0. Extracting the equations in the first and third rows can obtain the motion equations of waving and swaying:

和

分别来自于桨叶受到的外力以及速度二次项引起的惯性力和铰约束力的和。Among them: the right superscript [i] represents the i-th row of the matrix; M _{Θ, *} represents the contribution of different acceleration terms to the swaying angular acceleration, and the meaning represented by * is the same as in equation (15);

and

It comes from the external force on the blade and the sum of the inertial force and hinge constraint force caused by the quadratic term of the velocity, respectively.

3) The blade elastic deformation equation

Equation (14) can be organized as:

和

分别来自于桨叶受到的外力以及速度二次项引起的惯性力、结构内力和铰约束力的和。Among them: M _{p, *} represents the contribution of different acceleration terms to the blade elastic deformation acceleration, and the meaning represented by * is the same as in equation (15) and equations (20) and (21);

and

They come from the external force on the blade and the sum of inertial force, structural internal force and hinge constraint force caused by the quadratic term of velocity.

3 Rotor/Airframe Coupling Equations of Motion

机体的加速度量为

表示如下：In Parts 1 and 2, the motion equation of the elastic body and the motion equation of the elastic blade rotor are deduced, and the specific expressions are obtained. In order to clarify the coupling relationship between the two, this section derives the impedance matrix and the right-hand side item. According to the derivation in Sections 2.1 and 2.2, the acceleration of the rotor in equation (1) can be expressed as

The acceleration of the body is

It is expressed as follows:

和

分别是各片桨叶的挥舞角加速度、摆振角加速度和桨叶变形广义坐标的加速度；

和

分别是机体在体轴系下的平移加速度、转动加速度和机身变形广义坐标的加速度。in:

and

are the flapping angular acceleration, the swaying angular acceleration and the acceleration of the generalized coordinates of the blade deformation of each blade, respectively;

and

They are the translational acceleration, the rotational acceleration and the acceleration of the generalized coordinates of the body deformation under the body axis system, respectively.

以及从旋翼状态量导数到桨毂载荷的中间阻抗矩阵

从而可以将式(16)和式(17)的桨毂载荷表达成如下矩阵形式：The impedance matrix in Eq. (1) can be expressed as the product of multiple matrices. First, these intermediate matrices are expressed based on the derivation results in Sections 2.1 and 2.2. According to the rotor load equations of equations (16) and (17), the intermediate impedance matrix from the translational and rotational acceleration of the hub to the hub load can be obtained

and the intermediate impedance matrix from the rotor state quantity derivative to the hub load

Therefore, the hub loads of equations (16) and (17) can be expressed in the following matrix form:

和

分别是与加速度项无关的桨毂载荷。in:

and

are the hub loads independent of the acceleration term, respectively.

以及从桨毂运动加速度到旋翼状态未知量的阻抗矩阵

从而可以将旋翼的运动方程组合并整理为：Then, according to equations (20), (21) and (22), the coupling impedance matrix between the unknowns from the rotor state is obtained

and the impedance matrix from the hub motion acceleration to the rotor state unknown

Thus, the equations of motion of the rotor can be combined and organized as:

和

分别表示各片桨叶的挥舞、摆振和弹性变形方程中与加速度无关的量列矩阵。in:

and

respectively represent the acceleration-independent matrix in the flapping, swaying and elastic deformation equations of each blade.

和桨毂加速度的关系：Then build up the acceleration of the body

Relationship with propeller hub acceleration:

和

分别表示桨毂位置处的平移和转动位移量的模态形函数矩阵。in:

and

The modal shape function matrices representing the translational and rotational displacements at the hub location, respectively.

By substituting equation (27) into equation (26), the impedance matrix and the right-hand side term in the rotor part motion equation in the total rotor/airframe coupled motion equation (1) can be obtained. Substitute equation (27) into the propeller hub load equation (25) in matrix form, and then substitute equation (25) into the generalized external force term (6) of the body motion equation, and combine with the body motion equation (5), the total Impedance matrix and right-hand term in the equation of motion of the airframe part in the rotor/airframe coupled motion equation (1).

So far, the rotor/airframe coupling dynamics equation has been deduced, and all terms in the formula have explicit expressions, which do not need to be solved by numerical methods, and can clearly reflect the influence of the airframe and blade elasticity on the system.

4. Verification of low-frequency rigid body motion characteristics of helicopters

In the absence of verification data for heavy helicopters, in order to verify the correctness of the established model, this paper adopts the method of separate verification of high and low frequencies. First, the low-frequency rigid body motion characteristics of the model are verified based on the flight test data of the UH-60A helicopter, and then the high-frequency rotor/airframe coupling characteristics of the model are verified based on Bousman's rotor/body coupling experimental data, so that the rationality of the model can be determined. and accuracy.

The low-frequency rigid body motion characteristics of the model are verified based on the test flight data of the UH-60A helicopter.

Figure 2 compares the model calculated value and the test flight test value of the UH-60A forward flight trim curve, and the two are in good agreement. Among them, δ _col , δ _lat , δ _lon and δ _ped represent the collective pitch, lateral joystick, longitudinal joystick and pedal displacement of the helicopter, respectively, and φ and θ represent the roll angle and pitch angle of the helicopter, respectively.

The rotor/airframe coupling model is verified based on Bousman's experimental data. In this experiment, the fuselage is simulated by rotating hinges and support rods on the ground, and the rolling and pitching motion stiffness of the airframe is adjusted by setting the stiffness of the rods. The experiment is established by a method similar to the previous one. The model of the system, the specific experimental verification model is shown in Figure 3.

表示，Y轴代表俯仰运动，俯仰角用θ_E表示；坐标系(O-XYZ)_S表示旋翼桨毂轴系，X,Y,Z轴与地面铰坐标系平行。In Figure 3, the actual model is represented in a schematic way and the coordinate system is established. The coordinate system (O-XYZ) _E represents the ground hinge coordinate system, the origin is at the rotating hinge on the ground, the X axis represents the rolling motion, and the rolling angle use

The Y axis represents the pitch motion, and the pitch angle is represented by θ _E ; the coordinate system (O-XYZ) _S represents the rotor hub shaft system, and the X, Y, and Z axes are parallel to the ground hinge coordinate system.

则桨毂状态量为：Note that the ground hinge state quantity is:

Then the state quantity of the propeller hub is:

where: h _S is the distance from the ground hinge to the center of the hub; T ₁ and T ₂ are constant matrices.

The propeller hub state quantity derivative is:

The state equation of the ground articulated system can be expressed as:

和I_θ分别是滚转和俯仰转动惯量；

和m_θ分别是计算滚转和俯仰运动时的质量；

和h_θcg分别是计算滚转和俯仰时的质心距离地面较的高度；

和如前文建模中定义，为桨毂载荷。in:

and I _θ are the roll and pitch moments of inertia, respectively;

and m _θ are the masses when calculating roll and pitch motions, respectively;

and h _θcg are the heights of the center of mass from the ground when calculating roll and pitch, respectively;

and As defined in the previous modeling, it is the hub load.

Equations (30) and (31) represent the interaction between the rotor and the body in the Bousman experimental configuration. Combined with the previous modeling of the rotor, and using the impedance matching method to deal with the rotor/body coupling relationship, the experimental verification model can be obtained. The rotor-support impedance matching model of:

是地面铰状态量导数。in:

is the ground hinge state quantity derivative.

The system parameters corresponding to configuration 1 in the Bousman experiment are brought into the model, and then based on the multi-blade coordinate transformation method, the frequency and the real part of the eigenvalues of each system mode when the rotational speed is from 0 to 1000 rpm are calculated, and the calculated value and the experimental value are The comparison results are shown in Figure 4 and Figure 5. The meanings of the marks in the figure are: Pitch (body pitch); Roll (body roll); vi (uniform rotor inflow); FP, FC and FR represent the rotor swing forward type, set type and backward type respectively; LP, LC and LR stands for rotor swing forward type, collective type and backward type, respectively.

Observing the curve of 700-800 rpm in Fig. 4, it can be found that in this speed range, the frequency of the shimmy receding type is similar to the rolling motion frequency, which leads to the characteristics of the swaying receding type in the same rotational speed range in Fig. 5 The real part of the value has changed significantly, making it a positive value, which means that the sway back type has a divergence phenomenon, and the rolling motion of the body has also changed significantly, but it may not be reflected in the experimental results due to limited testing methods. But it is clearly reflected in the change curve of the real part of the eigenvalue of the rolling motion. Therefore, the results shown in Figures 4 and 5 show that the model established in this paper can more completely reflect the rotor/body coupling characteristics, and can more accurately reflect the rigid-bomb coupling dynamic characteristics of the helicopter, which is sufficient for applications involving flight dynamics and The study of structural dynamics.

There are many specific application ways of the present invention, and the above are only the preferred embodiments of the present invention. It should be pointed out that for those skilled in the art, without departing from the principles of the present invention, several improvements can be made. These Improvements should also be considered within the scope of protection of the present invention.

Claims (2)

1. a rigid-bomb coupling modeling method for heavy helicopter flight dynamics, is characterized in that: expand the explicit impedance matching method in the coupled aero-elastic analysis method of rotor and fuselage, so that it is suitable for elastic blade and elastic body , including the following processes: 1) Define the equation of motion of the helicopter body and the equation of motion of the blades; 2) Analyze the relationship between the motion state quantity of the rotor and the body motion state quantity; 3) Combining the relationship between the acceleration of the body and the acceleration of the hub, the motion state of the blade is brought into the blade motion equation and sorted, and the motion equation is divided into two parts. The first part is only related to the internal motion state of the rotor, and the other part It is related to the motion state quantity of the body, and both parts are expressed in an explicit matrix form; 4) Express the rotor force as the same two parts, convert the rotor force into the generalized external force of the body, bring it into the body motion equation, and divide it into two parts related to the internal motion state quantity of the rotor and the body motion state quantity and have nothing to do with both. part; 5) To sum up, the full-machine coupled motion equation is obtained explicitly. 2. the rigid-bomb coupling modeling method of heavy helicopter flight dynamics according to claim 1, is characterized in that: the concrete process that the explicit impedance matching method in the described rotor and fuselage coupling aero-elastic analysis method is expanded as follows: 1) Write down the acceleration of the rotor in the helicopter system as

The acceleration of the body is

The formula is as follows:

in:

and

are the flapping angular acceleration, the swaying angular acceleration and the acceleration of the generalized coordinates of the blade deformation of each blade, respectively;

and

are the translational acceleration, rotational acceleration and the acceleration of the generalized coordinates of the body deformation under the body axis system; The equation of motion of the helicopter body can be expressed as:

where: M _jk (j,k=V,ω,p) is the coupled mass matrix of acceleration k to acceleration j;

The cross product matrix representing the angular velocity, the tilde symbol represents the cross product matrix, the subscript F on the right represents the quantity of the body, and the superscript F on the right represents the quantity under the body axis; A _F0 represents the coordinate transformation matrix from the stationary axis system to the body axis system, 0 represents the stationary axis system, F represents the body axis system; g ⁰ represents the gravitational acceleration under the stationary axis system, and the upper right ⁰ represents the quantity under the stationary coordinate system; the quadratic term of the speed of the body Q _v,F , the generalized external force Q _{e, F} and structural internal force Q _i,F are divided into three parts: translation V, rotation ω and elastic deformation p; The equation of motion of the blade can be expressed as:

Where: Q _c,B represents the binding force on the blade;

Represents the unknown concentrated force acting on the blade by the flapping and swaying hinges in the blade coordinate system, N _β and N _ζ represent the known hinge spring damping moments of the flapping and swaying hinges, which are a function of the flapping and swaying angles and angular velocities function,

Represents the angular displacement shape function of the blade elastic deformation at the flapping/swing hinge; 2) The motion coupling between the rotor and the body is reflected in the generalized external force Q _{e, F} on the body and the motion state quantity of the rotor, because the force of the rotor on the body is related to the current motion state of each blade on the rotor, while the The motion state of the blade is related to the motion state of the body, and the relationship between the motion state quantity of the rotor and the body motion state quantity is as follows:

Among them: the subscript 0 represents the static coordinate system, and the meanings of the other subscripts are: the propeller hub S, the flapping/swing hinge H and the elastic blade B, and the corresponding coordinate systems are the non-rotating shaft system S of the propeller hub, and the propeller hub. The rotating shaft system H and the blade coordinate system B; the subscripts acc and velo respectively represent the part related to acceleration and the part not related to acceleration;

and

respectively represent the velocity and angular velocity of the object k in the coordinate system j,

and

represents the corresponding acceleration; A _jk represents the coordinate transformation matrix from the coordinate system k to the coordinate system j; Ω = [0 0 Ω] ^T represents the rotor speed,

is its cross product matrix;

Represents the position vector from the center of the propeller hub to the swing/swing hinge when the propeller hub does not rotate the shaft system S;

represents the angular velocity of the blade coordinate system caused by the flapping and swaying angular velocity,

is the Euler angular velocity matrix,

is the Euler angular velocity column vector, β represents the blade swing angle, the upward swing is positive, ζ represents the blade swing angle, and the forward swing is positive, correspondingly,

represents the Euler angular acceleration column vector; skew(*) and tilde

The meanings are the same, they all represent the cross-product matrix of a three-dimensional column vector;

represents the derivative of the Euler angular velocity matrix; 3) Combined with the acceleration of the body

and hub acceleration

and

Relationship:

By bringing the motion state of the blade into the blade motion equation and sorting it, the motion equation can be divided into two parts. The first part is only related to the internal motion state quantity of the rotor, and the other part is related to the body motion state quantity. The matrix form of the formula is:

in:

is the coupling impedance matrix between the unknowns from the rotor state;

is the impedance matrix from the motion acceleration of the propeller hub to the unknown quantity of the rotor state;

and

respectively represent the acceleration-independent matrix in the flapping, swaying and elastic deformation equations of each blade; 4) Rotor force

and

Represented as the same two parts:

in:

and

are the hub loads independent of the acceleration term, respectively; The conversion relationship from the rotor force to the generalized external force of the body is:

The body motion equation can also be divided into two parts related to the rotor's internal motion state quantity and the body motion state quantity, and a part that has nothing to do with both; 5) To sum up, the equation of motion coupled with the whole machine is explicitly expressed as:

where: H represents the impedance matrix from right subscript to right superscript; f represents the right-hand term of the equation that does not include acceleration; I is the identity matrix.

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