CN104317981A - Propeller hub center non-linear dynamic characteristic modeling method - Google Patents

Abstract

The invention discloses a propeller hub center non-linear dynamic characteristic modeling method, which belongs to helicopter theoretical modeling technology. The propeller hub center non-linear dynamic characteristic modeling method is characterized by comprising the following steps: establishing an engine body coordinate system, and describing the motion of an engine body and undercarriages; carrying out the balance computation of single undercarriage, and establishing force and position relationship between airplane wheels and a buffer; carrying out the balance computation of the engine body on the undercarriage; and determining the non-linear constraint force of an undercarriage system to the motion of the engine body in a time domain, and inertial load acted to the engine body, establishing an engine body motion equation on a fixed coordinate system by adopting a d'alembert's principle, and simultaneously establishing the balance equation of each undercarriage and the motion equations of the engine body on the undercarriage to obtain a propeller hub center non-linear dynamic characteristic equation of the engine body on the undercarriage. The invention can be applied to helicopter propeller hub center non-linear dynamic characteristic analysis and ground resonance modeling and analysis and can improve the accuracy of the propeller hub center non-linear dynamic characteristic analysis and the ground resonance stability analysis.

Description

A kind of propeller hub center Nonlinear Dynamic Characteristic modeling method

Technical field

The invention belongs to helicopter theoretical modeling technology, relate to a kind of propeller hub center Nonlinear Dynamic Characteristic modeling method for helicopter body propeller hub center Dynamic Characteristics and ground resonance modeling and analysis on undercarriage.

Background technology

According to code requirement, when can new model or Landing Gear System carry out, before the helicopter ground resonance running experience of large change, must carrying out propeller hub center dynamic response test and analysis, carrying out ground resonance analysis with this, provide the conclusion driven.In the Dynamic Characteristics of helicopter hub center, engineering practice adopts usually the linear processing methods based on equilibrium position microvariations, suppose that the kinematic behavior of undercarriage buffer and wheel is linear, consider in a little amplitude range like this, microcosmic is seen, be correct when actual amplitude does not exceed the result that this scope draws, but just can not draw correct conclusion to the situation exceeding this amplitude range.In fact there is nonlinearity characteristic in the rigidity of undercarriage buffer and wheel, damping, and it is more responsive to environmental change, especially landing at sea or sliding under the situation helicopter such as coarse, the fitful wind in road surface exists large motion amplitude when running, linearization process will bring very big error to propeller hub center Dynamic Characteristics and ground resonance analysis.

Summary of the invention

The technical problem to be solved in the present invention: propose a kind of propeller hub center Nonlinear Dynamic Characteristic modeling method, for helicopter body propeller hub center Dynamic Characteristics and ground resonance modeling and analysis on undercarriage, the accuracy of propeller hub center Dynamic Characteristics and ground resonance stability analysis can be improved, the comparatively big error avoiding linearization process to bring.

Technical scheme of the present invention: adopt general body axis system system, describe the motion of body, undercarriage; Equilibrium state calculates carries out in two steps: the first step, carries out the EQUILIBRIUM CALCULATION FOR PROCESS of single undercarriage, sets up the power between wheel and impact damper and position relationship; Second step, carries out the EQUILIBRIUM CALCULATION FOR PROCESS of body on undercarriage, determines that in time domain, Landing Gear System is to the non-linear constrain power of body movement, and acts on the inertial load of body, adopts D'Alembert's principle to be based upon the body movement equation of fixed coordinate system; The each undercarriage balance equation of simultaneous and body equation of motion on undercarriage, obtain body propeller hub center Nonlinear Dynamic Characteristic equation on undercarriage.

The first step of EQUILIBRIUM CALCULATION FOR PROCESS, in single undercarriage EQUILIBRIUM CALCULATION FOR PROCESS, the load model of impact damper and wheel have employed non-linear form.When setting up impact damper nonlinear model, the axial force of impact damper is expressed as air spring force, internal friction and fluid damping force sum, carry out air spring force modeling, determine the air spring force of undercarriage buffer low pressure chamber and the air spring force of high pressure chest, set up impact damper internal friction and fluid damping force models, utilize least square method to try to achieve undetermined coefficient in model and, with the variation relation of decrement, finally set up impact damper non-linear rigidity damper model; When setting up wheel nonlinear model, according to the structural parameters (charge pressure, diameter, width) of wheel, carry out wheel vertical stiffness, lateral rigidity, course rigidity and torsional rigidity modeling, carry out that wheel is vertical, side direction, course and torsion Damping Modeling, according to wheel Static compression properties, dynamic rate damping test data, utilize least square method, solve undetermined coefficient in model, finally set up wheel non-linear rigidity damper model.

A kind of propeller hub center Nonlinear Dynamic Characteristic modeling method, is characterized in that:

(1) set up the coordinate system describing body and move on undercarriage, adopt bikini, column undercarriage layout, other configuration similarly can be reduced to this pattern.Definition body axis system initial point is at body center of gravity place; X-axis is course, is just backward; Y-axis is side direction, is just to the right; Z axis is vertical, is just upwards.Body has the motion of six-freedom degree at center of gravity place: course, side direction and vertical displacement, and roll, pitching and yawing rotation.(X _g, Y _g, Z _g) be full machine displacement of center of gravity; (φ _x, φ _y, φ _z) for Quan Ji center is around the corner of X, Y, Z axis, the motion of body on undercarriage is described, define the coordinate of each undercarriage, left main coordinate (Xm ,-Ym, Zm), starboard main landing gear coordinate (Xm, Ym, Zm), tail undercarriage coordinate (Xn, 0, Zn), determine each undercarriage touchdown point place displacement.

(2) the EQUILIBRIUM CALCULATION FOR PROCESS first step; carry out single undercarriage EQUILIBRIUM CALCULATION FOR PROCESS; the load p that stopped status undercarriage is subject to is relevant with lift T with whole machine weight G with wheel touchdown point; impact damper axial force Fzh; the vertical force that impact damper is subject to is Fzh+P, wheel vertical load Fzt, and wheel is Fzt+P by landing load; P is static load, is caused by body gravity.Namely led P=Xn (G-T)/(Xn+Xm)/2, tail plays P=Xm (G-T)/(Xn+Xm).According to the nonlinear model of impact damper and wheel, and the series relationship of wheel and impact damper, set up the dynamic balance relation of single undercarriage buffer and wheel.

(3) EQUILIBRIUM CALCULATION FOR PROCESS second step, carries out the EQUILIBRIUM CALCULATION FOR PROCESS of body on undercarriage, the kinetic landing-gear load of computer body, and set up the non-linear load that each undercarriage acts on body, this load is expressed as the relation of compression displacement, movement velocity; During body movement, force and moment suffered by body comprises: gravity G, inertial force, moment of inertia, undercarriage acts on elastic load and the damping force of body, according to D'Alembert's principle, the force and moment acted on body must be corresponding with it inertial force and equalising torque, set up the equation of motion of corresponding body six degrees of freedom of motion.

(4) set up propeller hub center nonlinear model, each undercarriage balance equation of simultaneous and body equation of motion on undercarriage, obtain body propeller hub center dynamic characteristic equation on undercarriage, matrix form: $\left[M\right]\left\{\stackrel{\·\·}{X}\right\}+\left[C\right]\left\{\stackrel{\·}{X}\right\}+\left[K\right]\left\{X\right\}=\left\{F\right\},$ In formula, $\left\{X\right\}=\{X_G,Y_G,Z_G,{\mathrm{\φ}}_x,$ ${{\mathrm{\φ}}_y,{\mathrm{\φ}}_z,Z_T^L,Z_T^R,Z_T^T\}}^T$ Be the vector of 9 elements, wherein be vertical deviation that is main, tail undercarriage wheel, [M], [K], [C], { F} is quality, rigidity, damping, the outer non-linear matrix carried.

Key point of the present invention is:

Set up a kind of propeller hub center Nonlinear Dynamic Characteristic model, utilize this model can carry out propeller hub center Dynamic Characteristics, ground resonance modeling and analysis, the accuracy of propeller hub center Dynamic Characteristics and ground resonance stability analysis can be improved, the comparatively big error avoiding linearization process to bring.

Described foundation describes the coordinate system that body moves on undercarriage.

The described EQUILIBRIUM CALCULATION FOR PROCESS first step, carries out single undercarriage EQUILIBRIUM CALCULATION FOR PROCESS, sets up the dynamic balance relation of single undercarriage.

Described EQUILIBRIUM CALCULATION FOR PROCESS second step, carries out the EQUILIBRIUM CALCULATION FOR PROCESS of body on undercarriage, sets up the non-linear load that each undercarriage acts on body; Load born by engine body is analyzed, and according to D'Alembert's principle, sets up body six-freedom motion equation.

Described propeller hub center of setting up nonlinear model, each undercarriage balance equation of simultaneous and body equation of motion on undercarriage, set up body propeller hub center dynamic characteristic equation on undercarriage.

Beneficial effect of the present invention: propeller hub center of the present invention Nonlinear Dynamic Characteristic modeling method, utilize this propeller hub center Nonlinear Dynamic Characteristic model can carry out propeller hub center Dynamic Characteristics, ground resonance modeling analysis, the accuracy of helicopter hub center Dynamic Characteristics and ground resonance stability analysis can be improved, the comparatively big error avoiding linearization process to bring.

Accompanying drawing explanation

Fig. 1 is the coordinate system of body on undercarriage that the present invention relates to;

Fig. 2 is the force diagram of single undercarriage buffer and the wheel that the present invention relates to;

Fig. 3 is the body movement model that the present invention relates to.

Embodiment

Below in conjunction with accompanying drawing, propeller hub center Nonlinear Dynamic Characteristic modeling method involved in the present invention is described in further details.

The first step: set up the coordinate system describing body and move on undercarriage, adopt bikini, column undercarriage layout, other configuration similarly can be reduced to this pattern, sees Fig. 1.Definition body axis system initial point is at body center of gravity place; X-axis is course, is just backward; Y-axis is side direction, is just to the right; Z axis is vertical, is just upwards.Body has the motion of six-freedom degree at center of gravity place: course, side direction and vertical displacement, and roll, pitching and yawing rotation.(X _g, Y _g, Z _g) be full machine displacement of center of gravity; (φ _x, φ _y, φ _z) for Quan Ji center is around the corner of X, Y, Z axis, namely use { X _g, Y _g, Z _g, φ _x, φ _y, φ _zdegree of freedom variable describes the motion of body on undercarriage, define the coordinate of each undercarriage, determine the displacement of each undercarriage at touchdown point.

Second step: the EQUILIBRIUM CALCULATION FOR PROCESS first step; carry out single undercarriage EQUILIBRIUM CALCULATION FOR PROCESS; the load p that stopped status undercarriage is subject to is relevant with lift T with whole machine weight G with wheel touchdown point; the axial force that impact damper is subject to is P+Fzh; wheel is P+Fzt by landing load; P is static load, is caused by body gravity.Namely led P=Xn (G-T)/(Xn+Xm)/2, tail plays P=Xm (G-T)/(Xn+Xm).The force analysis of single undercarriage buffer and wheel is shown in Fig. 2.If the compression displacement of impact damper is S, the compression displacement of wheel is Z _t, the vertical compression total displacement of single undercarriage is Z=S+Z _t.According to the nonlinear model of impact damper and wheel, main slow, the axial load that tail impact damper axial load can be expressed as corresponding compression displacement, movement velocity in left and right: left and right main wheel, tail wheel axial load are also expressed as the axial load of corresponding compression displacement, movement velocity: again according to wheel and impact damper series relationship, and do not consider the inertial load of impact damper and wheel, set up the dynamic balance relation of single undercarriage buffer and wheel: $\begin{array}{c}{F}_S^L(Z^L,{\stackrel{\·}{Z}}^L,Z_T^L,{\stackrel{\·}{Z}}_T^L)=F_Z^L(Z_T^L,{\stackrel{\·}{Z}}_T^L)\\ F_S^R=(Z^R,{\stackrel{\·}{Z}}^R,Z_T^R,{\stackrel{\·}{Z}}_T^R)=F_Z^R(Z_T^R,{\stackrel{\·}{Z}}_T^R)\\ F_S^T=(Z^T,{\stackrel{\·}{Z}}^T,Z_T^T,{\stackrel{\·}{Z}}_T^T)=F_Z^T(Z_T^T,{\stackrel{\·}{Z}}_T^T)\end{array}..$

3rd step: EQUILIBRIUM CALCULATION FOR PROCESS second step, carry out the EQUILIBRIUM CALCULATION FOR PROCESS of body on undercarriage, first the kinetic landing-gear load of computer body, the course of undercarriage, sideway movement are only subject to elasticity and the damping force load restraint of wheel, impact damper only provides vertical load to undercarriage, and this load is equal with wheel vertical load.Set up the non-linear load that each undercarriage acts on body, this load is expressed as the relation of compression displacement, movement velocity.

The load that left main acts on body is:;

$F_x^L=F_X^L(Z_T^L,{\stackrel{\·}{Z}}_T^L,X_T^L)$

$F_y^L=F_Y^L(Z_T^L,{\stackrel{\·}{Z}}_T^L,Y_T^L)$

$F_z^L=F_Z^L(Z_T^L,{\stackrel{\·}{Z}}_T^L)$

The load that starboard main landing gear acts on body is:;

$F_x^R=F_X^R(Z_T^R,{\stackrel{\·}{Z}}_T^R,X_T^R)$

$F_y^R=F_Y^R(Z_T^R,{\stackrel{\·}{Z}}_T^R,Y_T^R)$

$F_z^R=F_Z^R(Z_T^R,{\stackrel{\·}{Z}}_T^R)$

The load that tail undercarriage acts on body is:.

$F_x^T=F_X^T(Z_T^T,{\stackrel{\·}{Z}}_T^T,X_T^T)$

$F_y^T=F_Y^T(Z_T^T,{\stackrel{\·}{Z}}_T^T,Y_T^T)$

$F_z^T=F_Z^T(Z_T^T,{\stackrel{\·}{Z}}_T^T)$

During body movement, force and moment suffered by body comprises: gravity G, inertial force, moment of inertia, undercarriage acts on elastic load and the damping force of body, see Fig. 3, according to D'Alembert's principle, the force and moment acted on body must be corresponding with it inertial force and equalising torque, the equation of motion of corresponding body six degrees of freedom of motion can be listed thus, for three equilibrium equations of body center of gravity place X, Y, Z-direction and body center of gravity place are around three torque equilibrium equations of X, Y, Z axis.

4th step: set up propeller hub center nonlinear model, each undercarriage balance equation (second step) of simultaneous and body equation of motion (the 3rd step) on undercarriage, set up body propeller hub center dynamic characteristic equation on undercarriage, matrix form is: $\left[M\right]\left\{\stackrel{\·\·}{X}\right\}+\left[C\right]\left\{\stackrel{\·}{X}\right\}+\left[K\right]\left\{X\right\}=\left\{F\right\},$ In formula, $\left\{X\right\}={\{X_G,Y_G,Z_G,{\mathrm{\φ}}_x,{\mathrm{\φ}}_y,{\mathrm{\φ}}_z,Z_T^L,Z_T^R,Z_T^T\}}^T$ Be the vector of 9 elements, wherein be vertical deviation that is main, tail undercarriage wheel, [M], [K], [C], { F} is quality, rigidity, damping, the outer non-linear matrix carried.

Claims (5)

1. a propeller hub center Nonlinear Dynamic Characteristic modeling method, is characterized in that:

(1) coordinate system that body moves on undercarriage is set up;

(2) the EQUILIBRIUM CALCULATION FOR PROCESS first step, carries out single undercarriage EQUILIBRIUM CALCULATION FOR PROCESS, and undercarriage buffer, wheel force analysis set up the dynamic balance relation of single undercarriage;

(3) EQUILIBRIUM CALCULATION FOR PROCESS second step, carries out the EQUILIBRIUM CALCULATION FOR PROCESS of body on undercarriage, sets up the non-linear load that each undercarriage acts on body; Analyze the whole force and moments suffered by body, according to D'Alembert's principle, list the equation of motion of corresponding body six degrees of freedom of motion;

(4) each undercarriage balance equation of simultaneous and body equation of motion on undercarriage, obtains body propeller hub center Nonlinear Dynamic Characteristic equation on undercarriage.

2. propeller hub center according to claim 1 Nonlinear Dynamic Characteristic modeling method, is characterized in that: the described coordinate system set up description body and move on undercarriage, and definition body axis system initial point is at body center of gravity place; X-axis is course, is just backward; Y-axis is side direction, is just to the right; Z axis is vertical, is just upwards; Body has the motion of six-freedom degree at center of gravity place: course, side direction and vertical displacement, and roll, pitching and yawing rotation.

3. propeller hub center according to claim 1 Nonlinear Dynamic Characteristic modeling method; it is characterized in that: the described EQUILIBRIUM CALCULATION FOR PROCESS first step; carry out single undercarriage EQUILIBRIUM CALCULATION FOR PROCESS; the load p that stopped status undercarriage is subject to is relevant with lift T with whole machine weight G with wheel touchdown point; the axial force that impact damper is subject to is P+Fzh; wheel is P+Fzt by landing load; P=Xn (G-T)/(Xn+Xm)/2 are led; tail plays P=Xm (G-T)/(Xn+Xm); according to wheel and impact damper series relationship, set up the dynamic balance relation of single undercarriage.

4. propeller hub center according to claim 1 Nonlinear Dynamic Characteristic modeling method, it is characterized in that: described EQUILIBRIUM CALCULATION FOR PROCESS second step, carry out the EQUILIBRIUM CALCULATION FOR PROCESS of body on undercarriage, first the kinetic landing-gear load of computer body, set up the non-linear load that each undercarriage acts on body; Secondly, during body movement, the force and moment suffered by body comprises: gravity G, inertial force, moment of inertia, and undercarriage acts on elastic load and the damping force of body, according to D'Alembert's principle, lists the equation of motion of corresponding body six degrees of freedom of motion.

5. propeller hub center according to claim 1 Nonlinear Dynamic Characteristic modeling method, it is characterized in that: describedly set up propeller hub center nonlinear model, the each undercarriage balance equation of simultaneous and body equation of motion on undercarriage, obtain body propeller hub center dynamic characteristic equation on undercarriage.