CN118090045A - Aircraft gravity center measuring method based on moment balance principle - Google Patents
Aircraft gravity center measuring method based on moment balance principle Download PDFInfo
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Abstract
An aircraft gravity center measuring method based on a moment balance principle comprises the following steps: according to the moment balance of the gravity born by the aircraft and the central line moment of the supporting force born by the front wheels relative to the rear wheel axle, the longitudinal position of the gravity center of the aircraft is calculated, and according to the moment balance of the ground supporting forces born by the front wheels and the rear wheels on two sides of the aircraft relative to the gravity center projection point, the transverse position of the gravity center of the aircraft is calculated, wherein the gravity center projection point is the projection point of the gravity center of the aircraft on the horizontal plane; lifting the front wheel and determining the height of the center of gravity of the aircraft by the tangent value of the lifting angle and the load change of the rear wheel axis. The method is simple to operate, does not need complex measuring equipment, and is low in cost and high in measuring precision.
Description
Technical Field
The invention belongs to the technical field of aerospace, and particularly relates to an aircraft gravity center measuring method.
Background
Various rotations of the aircraft in flight are performed around the center of gravity. The resultant force of weight of each part of the aircraft, fuel oil, mission load, passengers and the like is called the center of gravity of the aircraft. The position of the aircraft's center of gravity directly affects the stability of flight, maneuverability, and stability of ground jogging. The center of gravity of the aircraft is ensured to be within a reasonable design range, and the method is one of key factors for ensuring the flight safety and the service life of the aircraft. The measurement of the center of gravity of the aircraft is an important ground test of various types of aircraft before first flying, so that the accurate measurement of the position of the center of gravity of the aircraft plays an important role in the design of the whole aircraft, the weight arrangement of the aircraft and the safety.
In the existing aircraft gravity center measuring method, special measuring equipment is needed, and the measuring method is complex, high in cost, low in efficiency, long in time consumption, low in measuring accuracy and seriously affects the production efficiency of the aircraft.
Disclosure of Invention
In view of the above, there is a need for a simple, low cost and accurate aircraft center of gravity measurement method.
An aircraft center of gravity measurement method, comprising:
and calculating the longitudinal position of the center of gravity of the airplane according to the moment balance of the gravity of the airplane and the supporting force of the front wheel relative to the axis of the rear wheel.
According to the moment balance of the ground supporting forces borne by the front wheels and the rear wheels of the aircraft relative to the gravity center projection points, the transverse position of the gravity center of the aircraft is calculated, wherein the gravity center projection points are the projection points of the gravity center of the aircraft on a horizontal plane;
Lifting the front wheel and determining the height of the center of gravity of the aircraft by the tangent value of the lifting angle and the load change of the rear wheel axis.
Further, in the above aircraft center of gravity measurement method, the step of lifting the front wheel and determining the aircraft center of gravity height through a tangent value of a lifting angle and an axle load change of an axis of the rear wheel of the aircraft includes:
gradually lifting the front wheel of the airplane within a certain angle range, recording the tangent value of the lifting angle of the front wheel of the airplane and the axle load of the rear wheel axle of the airplane under each angle, and carrying out linear fitting on the recorded tangent value and the axle load to obtain an axle load linear equation: y=a·x+b, where a and B are constants in the axle load linear equation, y is the rear axle load, and x is the lift angle tangent;
and determining an axle load relation between the height of the center of gravity of the airplane and the axis of the rear wheel of the airplane according to the moment balance of the gravity of the airplane passing through the center of gravity of the airplane relative to the supporting point of the front wheel of the airplane, and calculating the height of the center of gravity of the airplane according to the relation and the axle load linear equation.
Further, in the above aircraft center of gravity measuring method, the axle load relation between the height of the aircraft center of gravity and the axis of the rear wheel of the aircraft is:
wherein Z cg is the height of the center of gravity of the aircraft, l is the distance between the front wheel and the rear wheel axis, m l is the axle load of the rear wheel axis when the front wheel of the aircraft is lifted, m' l is the axle load of the rear wheel axis when the front wheel of the aircraft is horizontally placed, mass is the total mass of the aircraft, and r is the net load radius of the rear wheel of the aircraft.
Further, the aircraft center of gravity measuring method, wherein the step of calculating the aircraft center of gravity according to the relation and the axle load linear equation includes:
according to the relation and the axle load linear equation, determining a calculation formula of the gravity center height of the airplane as follows:
Wherein A and B are constants in the axis load linear equation;
according to the uniqueness of the aircraft gravity center height value, the aircraft gravity center height calculation formula is processed, and a processed aircraft gravity center height calculation formula is obtained:
Where k is the slope of the processed axis load linear equation.
Further, in the above aircraft gravity center measuring method, a calculation formula of a longitudinal position of the aircraft gravity center is:
Where X cg is the longitudinal position of the centre of gravity, m' l is the load on the axis of the rear wheel when the aircraft is placed horizontally, mass is the total mass of the aircraft, and l is the distance between the axes of the front and rear wheels.
Further, in the above aircraft gravity center measuring method, a calculation formula of a lateral position of the aircraft gravity center is:
Wherein b is the wheel tread of the rear wheel, m 3 and m 2 are the wheel loads of the two wheels of the rear wheel respectively, and mass is the total mass of the aircraft.
Further, in the aircraft center of gravity measurement method, the angle range is 5-10 °.
Further, in the aircraft center of gravity measurement method, when the aircraft front wheel is lifted, a lifting plane of the lifting platform is kept horizontal.
In the embodiment of the invention, the longitudinal and transverse positions of the gravity center of the airplane are obtained through a moment balance principle when the airplane is horizontally stationary, and the gravity center height value of the airplane is calculated through measuring the tangent value of the lifting angle of the front wheel of the airplane and the corresponding change condition of the axial load of the axis of the rear wheel. The method is simple to operate, low in cost and high in measurement accuracy, and does not need complex measurement equipment.
Drawings
FIG. 1 is a schematic view of the front and rear wheels of an aircraft
FIG. 2 is a schematic diagram of a force analysis of the transverse position of the center of gravity of an aircraft
FIG. 3 is a schematic view of an aircraft in a horizontal position
FIG. 4 is a schematic view of the front wheel of the aircraft lifting gamma
FIG. 5 is a block diagram of the method for measuring the center of gravity of an aircraft according to the present invention
Detailed Description
In order to facilitate understanding of the present invention, the following further describes the technical solution of the present invention.
Referring to fig. 1, a schematic view of the positions of front and rear wheels of an aircraft according to the present invention is illustrated with a three-point landing gear aircraft, where the front wheel is located before the center of gravity of the aircraft, the rear wheel is located behind the center of gravity of the aircraft, and the aircraft is configured as a rigid body, and the center of gravity position does not change with the transfer of the axle load of the aircraft.
And S1, calculating the longitudinal position of the gravity center of the airplane according to the balance of the gravity born by the airplane and the supporting force born by the front wheel relative to the moment of the axis of the rear wheel.
When the aircraft is stationary, the stress balance is carried out everywhere, and the longitudinal position and the transverse position of the gravity center of the aircraft can be obtained according to the moment balance principle. For example, in this embodiment, when the aircraft is placed horizontally, the gravity force applied to the aircraft and the supporting force applied to the rear wheel axis are balanced with respect to the moment of the front wheel of the aircraft, and according to the moment balancing principle, it is known that:
Where X cg is the longitudinal position of the centre of gravity, m l is the load on the axis of the rear wheel when the aircraft is placed horizontally, mass is the total mass of the aircraft, and l is the distance between the axes of the front and rear wheels.
And S2, calculating the transverse position of the gravity center of the airplane according to the moment balance of the ground supporting force on two sides of the rear wheel of the airplane relative to the gravity center projection point, wherein the gravity center projection point is the projection point of the gravity center of the airplane on the horizontal plane.
Specifically, as shown in fig. 2, assuming that the horizontal projection of the center of gravity of the aircraft is G, the distance from G to the longitudinal center plane of the aircraft is Ycg, when the aircraft is stationary, the ground supporting forces on the left rear wheel, the right rear wheel and the front wheel are balanced with respect to the moment of G, so that it can be known that:
Wherein b is the wheel distance of the rear wheels, and m 1、m2、m3 is the wheel load of the front wheels, the right rear wheels and the left rear wheels respectively. The calculation formula of the transverse position of the center of gravity of the airplane is further obtained by deduction:
Wherein b is the wheel tread of the rear wheel, m 3 and m 2 are the wheel loads of the two wheels of the rear wheel respectively, and mass is the total mass of the aircraft.
Specifically, the wheel load, the total mass and the wheel track of the airplane can be obtained from the existing basic specification parameters, and can also be obtained by measurement according to national army standards.
And S3, lifting the front wheel of the airplane, and determining the height of the center of gravity of the airplane through the tangent value of the lifting angle and the change of the axle load of the rear axle.
The following is a specific description of lifting the front wheels of an aircraft. As shown in fig. 3, when the aircraft is in a horizontal rest state, the aircraft center of gravity height Z cg is the sum of the distance Z from the aircraft center of gravity G to the plane corresponding to the wheel axis center line and the rear wheel dead load radius r. Wherein the static load radius of the rear wheel is the vertical distance between the center of gravity of the wheel axle and the supporting plane under the vertical load of the tire when the rear wheel is in a static state, namely, Z cg =Z+r
In a specific measurement, r may be the average of the static load radii of the two rear wheels.
As shown in fig. 4, when the front wheel is lifted to the angle γ, the gravity (mass·g) passing through the center of gravity G of the aircraft is moment-balanced with respect to the front wheel support point. Thus, according to the moment balance principle, it is possible to obtain:
[(Z·tanγ+L1)·sinγ]·mass·g＝l·sinγ·ml·g
Wherein m l is the axle load of the rear wheel axis when the front wheel of the aircraft is lifted, and L 1 is the projection distance between the center of the front wheel and the center of gravity G of the aircraft on the horizontal plane, namely the longitudinal position of the center of gravity of the aircraft.
Therefore, when the front wheel of the airplane lifts, the relation between the height of the gravity center of the airplane and the axis of the rear wheel is as follows:
Where l is the distance between the front wheel and the rear wheel axis, m l is the axle load of the rear wheel axis when the front wheel of the aircraft is lifted, m' l is the axle load of the rear wheel axis when the aircraft is placed horizontally, and mass is the total mass of the aircraft.
In the measuring process, the axle load of the rear axle line can be measured through an axle load meter, and the minimum lifting angle gamma of the airplane is determined according to the accuracy of the axle load meter.
In the embodiment, when the height of the center of gravity of the airplane is measured, the front wheel is lifted gradually within a certain angle range, the tangent value of the lifting angle of the front wheel and the axle load of the rear wheel axle under each angle are recorded, and the recorded tangent value and the axle load are subjected to linear fitting to obtain an axle load linear equation;
and then calculating the height of the center of gravity of the airplane according to an axle load relation equation of the height of the center of gravity of the airplane and the axis of the rear wheel and an axle load linear equation.
For example, in actual measurement, the front wheel is lifted by 2 °,4 °,6 °,8 °,10 ° in sequence, and the axle load of the rear wheel axis at each lifting angle and the tangent value of the lifting angle γ are recorded, respectively. And fitting a graph according to the recorded axle load and the lift angle tangent value, and obtaining a curve equation. The linear relation between the rear axle load and the lifting angle tangent value is obtained through data processing, namely, the axle load linear equation is:
y＝A·x+B
Wherein y is the load of the rear axle, A and B are constants, and x is the lift tangent value.
The aircraft gravity center height calculation formula can be obtained by substituting the formula into the formula, and is as follows:
where k is the slope of the processed axis load linear equation, and it can be known from the equation that the altitude of the center of gravity of the aircraft is unique.
In the embodiment, the longitudinal and transverse positions of the center of gravity of the aircraft are obtained by applying a moment balance principle, and the height value of the center of gravity of the aircraft is calculated by measuring the tangent value of the lifting angle and the corresponding change condition of the axle load. The method is simple to operate, does not need complex measuring equipment, and is low in cost and high in measuring accuracy.
Please refer to fig. 5, which illustrates steps of an aircraft center of gravity measurement method according to an embodiment of the present invention.
And S1, calculating the longitudinal position of the gravity center of the airplane according to the balance of the gravity born by the airplane and the supporting force born by the front wheel relative to the moment of the axis of the rear wheel.
And S2, calculating the transverse position of the gravity center of the airplane according to the moment balance of the ground supporting force borne by the rear wheels at two sides relative to the gravity center projection points, wherein the gravity center projection points are the projection points of the gravity center of the airplane on the horizontal plane.
Step S3, gradually lifting the front wheels of the aircraft within a certain angle range, recording the tangent value of the lifting angle of the front wheels and the axle load of the rear axle under each angle, and performing linear fitting on the recorded tangent value and the axle load to obtain an axle load linear equation.
Wherein, the relation between the rear wheel axle load y and the tangent value x of the front wheel lifting angle is as follows: y=a·x+b.
And S4, obtaining an axle load relation between the height of the center of gravity of the airplane and the axis of the rear wheel of the airplane according to the moment balance of the gravity of the airplane passing through the center of gravity of the airplane relative to the supporting point of the front wheel of the airplane.
And S5, obtaining an aircraft gravity center height calculation formula according to the relation and the axle load linear equation.
In the above steps, the relation between the height of the center of gravity of the aircraft and the axle load of the rear axle is:
wherein l is the distance between the front wheel and the rear wheel axis, m l is the axle load of the rear wheel axis when the front wheel of the aircraft is lifted, m' l is the axle load of the rear wheel axis when the aircraft is placed horizontally, mass is the total mass of the aircraft, and r is the net load radius of the rear wheel of the aircraft.
And (3) taking y into the relation between the gravity center height of the airplane and the load of the rear wheel shaft to obtain a calculation formula of the gravity center height of the airplane:
and S6, processing an aircraft gravity center height calculation formula according to the uniqueness of the aircraft gravity center height value, and calculating the aircraft gravity center height according to the processed aircraft gravity center height calculation formula and an axle load linear equation.
Claims (8)
1. An aircraft gravity center measuring method based on a moment balance principle is characterized by comprising the following steps of:
calculating the longitudinal position of the gravity center of the airplane according to the moment balance of the gravity born by the airplane and the supporting force born by the front wheel relative to the axis of the rear wheel;
According to the moment balance of the ground supporting forces borne by the front wheels and the rear wheels of the aircraft relative to the gravity center projection points, the transverse position of the gravity center of the aircraft is calculated, wherein the gravity center projection points are the projection points of the gravity center of the aircraft on the horizontal plane;
the front wheel is lifted and the height of the center of gravity of the aircraft is determined by the tangent value of the lifting angle and the load change of the rear wheel axis.
2. A method of measuring the centre of gravity of an aircraft based on the principle of moment balance according to claim 1, wherein the step of lifting the front wheels and determining the height of the centre of gravity of the aircraft from the tangent value of the lifting angle and the load variation of the rear wheel axis comprises:
Gradually lifting the front wheel within a certain angle range, recording the tangent value of the lifting angle of the front wheel and the load of the axis of the rear wheel under each angle, and performing linear fitting on the recorded tangent value and load to obtain an axis load linear equation:
y=a·x+b, where a and B are constants in the axle load linear equation, y is the rear axle load, and x is the lift angle tangent;
And determining a relation between the height of the center of gravity of the airplane and the axle load of the rear wheel axle according to the moment balance of the gravity of the airplane passing through the center of gravity of the airplane relative to the supporting point of the front wheel, and calculating the height of the center of gravity of the airplane according to the relation and the axle load linear equation.
3. The method for measuring the center of gravity of an aircraft based on the moment balance principle according to claim 2, wherein the relation between the height of the center of gravity of the aircraft and the axle load of the rear wheel axle is:
Wherein Z cg is the height of the center of gravity of the aircraft, l is the distance between the front wheel and the rear wheel axis, m l is the axle load of the rear wheel axis when the front wheel of the aircraft is lifted, m ′ l is the axle load of the rear wheel axis when the front wheel of the aircraft is horizontally placed, mass is the total mass of the aircraft, and r is the net load radius of the rear wheel of the aircraft.
4. A method of measuring the center of gravity of an aircraft based on the principle of moment balance as claimed in claim 3 wherein the step of calculating the altitude of the center of gravity of the aircraft based on the relationship and the axis load linear equation comprises:
According to the relation and the axle load straight line equation, the aircraft gravity center height calculation formula is determined as follows:
wherein A and B are constants in the axis load linear equation;
according to the uniqueness of the aircraft gravity center height value, processing an aircraft gravity center height calculation formula to obtain a processed aircraft gravity center height calculation formula:
Where k is the slope of the processed axis load linear equation.
5. The method for measuring the center of gravity of an aircraft based on the principle of moment balance according to claim 1, wherein the calculation formula of the longitudinal position of the center of gravity of the aircraft is:
Where X cg is the longitudinal position of the centre of gravity, m ′ l is the load on the axis of the rear wheel when the aircraft is placed horizontally, mass is the total mass of the aircraft, and l is the distance between the axis of the front wheel and the axis of the rear wheel.
6. The method for measuring the center of gravity of an aircraft based on the principle of moment balance according to claim 1, wherein the calculation formula of the lateral position of the center of gravity of the aircraft is:
Wherein b is the wheel tread of the rear wheel, m 3 and m 2 are the wheel loads of the two wheels of the rear wheel respectively, and mass is the total mass of the aircraft.
7. An aircraft gravity center measuring method based on a moment balance principle according to claim 2, wherein the angle range of lifting the front wheels is 5-10 °.
8. A method for measuring the centre of gravity of an aircraft based on the principle of moment balance as claimed in claim 2, wherein the lifting plane of the lifting platform is kept horizontal when the front wheel of the aircraft is lifted.
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| CN202311652667.5A CN118090045A (en) | 2023-12-04 | 2023-12-04 | Aircraft gravity center measuring method based on moment balance principle |
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