An aircraft weighing method to eliminate the influence of landing gear deformation

Abstract

The present invention belongs to the field of aircraft weighing technology, and specifically relates to an aircraft weighing method that eliminates the effects of landing gear deformation. This method uses a laser tracker to measure standard points on the aircraft at the weighing site to establish an aircraft weighing coordinate system. The main wheel center is no longer used as a weighing reference point, thus avoiding the effects of landing gear deformation. The center of gravity coordinates are obtained by solving a system of linear equations involving the center of gravity coordinates Xw and Zw.

Description

Technical Field

[0001] The invention belongs to the technical field of aircraft weighing, and in particular relates to an aircraft weighing method for eliminating the influence of landing gear deformation. Background Art

[0002] Aircraft weighing is an important technical means to determine the actual weight and center of gravity position of the aircraft, to test the conformity between the theoretical value and the actual value of the aircraft weight and center of gravity, and to configure the required aircraft center of gravity according to specific flight requirements. For small aircraft, the commonly used weighing methods currently include wheel weighing method, jack weighing method, etc.

[0003] The wheel weighing method involves placing the aircraft's nose and main wheels directly on a scale or on pads attached to the scale surface. Based on the weights and measured geometric dimensions, the aircraft's weight and center of gravity can be calculated using either graphical or analytical methods. This method offers the advantages of simple equipment and procedures, and a wide range of methods for calculating weight and center of gravity. However, the significant deformation of the aircraft's landing gear, caused by the weight of the aircraft, can often lead to significant errors in the calculation of the aircraft's center of gravity.

[0004] The jack weighing method uses a jack instead of wheels to support the aircraft for weighing. Based on the measured weight and geometric dimensions, the aircraft weight and center of gravity are calculated analytically. This method has the advantage over the wheel weighing method in that the jack's deformation is minimal, thus eliminating the influence of landing gear deformation that is common in wheel weighing. However, this method requires the jack's installation position to be pre-determined during structural design and manufacturing, which presents significant challenges for weighing many already-produced aircraft. Furthermore, the jacks required for weighing differ from aircraft model to model, and when not being weighed, they sit idle, resulting in wasted resources and increased costs. Finally, since the jacks are not secured to the aircraft using fasteners, using them to adjust the aircraft's nose-up and nose-down positions during jack weighing presents significant risks. Summary of the Invention

[0005] Purpose of the invention: To provide an aircraft weighing method that eliminates the influence of landing gear deformation, avoids the center of gravity measurement error caused by the deformation of the landing gear due to gravity during the aircraft weighing process, and completes the effective measurement of the center of gravity of the aircraft weight.

[0006] Technical solution:

[0007] An aircraft weighing method for eliminating the influence of landing gear deformation, comprising:

[0008] At the weighing site, a laser tracker is used to measure the standard points on the aircraft, and the aircraft weighing coordinate system O-XYZ is established, with the coordinate origin as the weighing reference point;

[0009] Set up a vertical pole on the open space on one side of the aircraft, and set two standard holes A and B on the pole;

[0010] Place the front wheel, left main wheel, and right main wheel on three scales respectively, and adjust the aircraft pitch angle to obtain at least two pitch states;

[0011] Select two pitch states, respectively according to the front scale reading W forward , Left scale reading W left , right scale reading W right , and the separately measured addition W z and missing item W q Read the reading to determine the empty weight G of the aircraft;

[0012] In the two selected pitch states, the laser tracker is used to measure the front wheel center coordinates (X 前i ,Y 前i ,Z 前i ), the coordinates of the midpoint of the line connecting the left main wheel and the right main wheel (X 主i ,Y 主I , Z 主i )、Point A coordinates (X Ai ,Y Ai ,Z Ai )、Point B coordinates (X Bi ,Y Bi ,Z Bi )、Point C coordinates (X Ci ,Y Ci ,Z Ci )、D point coordinates (X Di ,Y Di ,Z Di ), and determine the gravity and support force vectors, the force arm vectors of the gravity and support forces, the pitch angle of the aircraft, and the moment M of the support force on the front wheel center about the coordinate origin. 前i , the moment M of the support force exerted on the midpoint of the main wheel center line to the origin of the body coordinate 主i , the moment M of gravity at the center of gravity of the aircraft on the origin of the body coordinate wi， The value of i corresponds to a certain pitch state, i = 1 or 2;

[0013] According to the moment balance M in the first pitch state w1 =M 前1 +M 主1 And the moment balance M in the first pitch state w2 =M 前2 +M 主2Determine the coordinates of the aircraft's center of gravity (Xw, 0, Zw).

[0014] Furthermore, a laser tracker is used to establish an aircraft weighing coordinate system at the weighing site, specifically including:

[0015] The aircraft weighing coordinate system is corrected and fitted using the standard points on the aircraft, so that the fitted aircraft weighing coordinate system coincides with the aircraft body coordinate system in the three-dimensional digital model.

[0016] Furthermore, the standard points on the aircraft include standard holes reserved as required during the production and processing process for use in level measurement.

[0017] Furthermore, in each pitch state, according to the front scale reading W forward , Left scale reading W left And the right scale reading W right , and the separately measured addition W z and missing item W q The readings are used to determine the empty weight of the aircraft, G, including:

[0018] Determine the empty weight G1 and G2 of each pitch state respectively. When the difference between G1 and G2 is less than the predetermined error, the average value of G1 and G2 is taken as the empty weight G of the aircraft. i =N 前i +N 主i -W zi +W qi =W forwardi +W lefti +W righti -W zi +W qi .

[0019] Furthermore, the gravity and support force vectors are: Among them, the unit direction vector for:

[0020] in, is the support force vector of the front wheel, N 前i is the support force on the front wheel, is the support force vector at the midpoint of the line connecting the left and right main wheel centers, N 主i is the support force on the midpoint of the line connecting the left and right main wheel centers, is the gravity vector of the aircraft, W i is the gross weight of the aircraft,

[0021] Furthermore, the gravity vector and the arm vector of the support force are: in, is the moment arm vector of the front wheel center, is the moment arm vector of the midpoint of the line connecting the left and right main wheel centers, is the gravity arm of the aircraft.

[0022] Furthermore, the pitch angle a of the aircraft i for:

[0023] Furthermore, the moment M of the support force on the front wheel center about the coordinate origin is 前i , the moment M of the support force exerted on the midpoint of the main wheel center line to the origin of the body coordinate 主i , the moment M of gravity at the center of gravity of the aircraft on the origin of the body coordinate wi They are:

[0024]

[0025]

[0026]

[0027] Beneficial effects:

[0028] This method adopts the method of establishing the body coordinate system and no longer uses the main wheel center as the weighing reference point, thereby avoiding the influence of landing gear deformation. The center of gravity coordinates are obtained by solving a set of two-variable linear equations including the center of gravity coordinates Xw and Zw. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 Schematic diagram of the principle of calculating the vector angle by vector dot product;

[0030] Figure 2 Schematic diagram of the body coordinate system established by the laser tracker at the weighing site. DETAILED DESCRIPTION

[0031] The present invention adopts an aircraft weighing method that eliminates the influence of landing gear deformation. The method uses a laser tracker to establish an aircraft weighing coordinate system at the weighing site, such as Figure 2After correction and fitting of standard points on the aircraft (standard measurement points reserved as required during the production process, such as standard holes for horizontal measurement), this coordinate system coincides with the aircraft's body coordinate system in the three-dimensional digital model. During the weighing process, the total weight of the aircraft can be calculated by reading the readings of each scale and the actual additions and omissions. The coordinates of the front wheel and main wheel centers are measured using a laser tracker, and the coordinates of the support force vector at the wheel center and the distance of the wheel center relative to the coordinate origin can be determined. The angle between the support force at the wheel center and the line connecting the wheel and the weighing reference point is calculated using spatial vector dot multiplication. The torque of the support force at the wheel center (the midpoint of the line connecting the front wheel and the two main wheel centers) relative to the weighing reference point is calculated. Based on the moment balance formula relative to the coordinate origin, a linear equation of two variables is established regarding the aircraft's center of gravity coordinates Xw and Zw. By adjusting the aircraft's pitch angle, a system of linear equations of two variables regarding the aircraft's center of gravity coordinates Xw and Zw can be obtained. Solving these equations yields the aircraft's center of gravity coordinates (Xw, Zw).

[0032] The details are as follows:

[0033] Taking the weighing of a light sport aircraft as an example, the origin of the aircraft coordinate system is located in front of the nose. The principle of calculating the vector angle by vector dot product is shown in Figure 1 :

[0034] For a force F acting on point A, its moment M relative to point O can be expressed as the product of the projection of the force perpendicular to line segment AO and the length L between AO, that is:

[0035]

[0036] The angle a can be obtained by taking the arc cosine of the dot product of the vector and its modulus:

[0037]

[0038] So ultimately:

[0039]

[0040] From this we can see that the torque can be calculated as long as the spatial coordinates of the force vector and the lever arm vector are determined.

[0041] 1. Establish the coordinate system for weighing

[0042] At the weighing site, a laser tracker is used to measure standard points on the aircraft (such as reserved horizontal measurement points). By comparing the measured values ​​and their coordinate values ​​in the three-dimensional digital model, a spatial coordinate system O-XYZ is re-established in the laser tracker. This coordinate system coincides with the body coordinate system in the three-dimensional digital model of the aircraft.

[0043] 2. Measurement

[0044] When weighing an aircraft at different pitch angles, different weighing conditions are used. Points C and D are two standard holes on the fuselage that are on the same horizontal line when the aircraft is placed horizontally. They are used to calculate the aircraft's pitch angle. When weighing, a vertical pole is erected on the ground on one side of the aircraft. The pole remains stationary during the measurement process. Two standard holes, A and B, are set on the pole. The coordinates of A and B are measured under different weighing conditions to serve as the direction vectors of gravity and support force. The measurement items are as follows:

[0045] Table 1 Weight measurement record

[0046]

[0047]

[0048] Table 2 Coordinate measurement record table

[0049]

[0050]

[0051] 3. Calculation of aircraft weight and center of gravity

[0052] Select the data of two states (state 1 and state 2 are selected for illustration) for processing. The two states with the empty weight difference within the error range are selected. Use i (i is 1, 2, 3) to represent the weighing state, then the front wheel coordinate is (X 前i ,Y 前i ,Z 前i ), the front wheel supported force is N 前 , the distance from the front wheel center to the coordinate origin is L 前i ; Midpoint of the line connecting the left and right main wheel centers (X 主i ,Y 主i ,Z 主i ), the supported force is N 主i (The resultant force on the left and right main wheels is equivalent to the force on the midpoint of the line connecting the wheel centers). The distance from the midpoint of the line connecting the left and right main wheels to the coordinate origin is L. 主i Assume that the distance between the center of gravity of the aircraft and the origin of the body coordinate system is L w , the gross weight of the aircraft is W i , the empty weight of the aircraft is G i Since the coordinates of the center of gravity do not change with the change of weighing state, it is assumed that the coordinates of the center of gravity are (X w ,0,Z w ).

[0053] For weighing status 1:

[0054] N 前1 =W forward1

[0055] N 主1 =W left1 +W right1

[0056] W1=N 前1 +N 主1 =W forward1 +W left1 +W right1

[0057] G1=N 前1 +N 主1 -W z1 +W q1 =W forward1 +W left1 +W right1 -W z1 +W q1

[0058] Unit direction vectors of gravity and support forces for:

[0059]

[0060] The gravity vector and support force vector are:

[0061]

[0062]

[0063]

[0064] The gravity vector and the arm vector of the support force are:

[0065]

[0066]

[0067]

[0068] The vector from point D to point C is:

[0069]

[0070] The aircraft pitch angle is:

[0071]

[0072] Calculation of the moment of the support force on the front wheel center to the body coordinate origin:

[0073]

[0074] Calculation of the moment of the support force exerted on the midpoint of the main wheel center line to the origin of the aircraft coordinate system:

[0075]

[0076] Calculation of the moment of gravity at the center of gravity of the aircraft on the origin of the aircraft coordinate system:

[0077]

[0078] According to the moment balance about the coordinate origin, we get the equation:

[0079] M w1 =M 前1 +M 主1 (1)

[0080] Similarly, for weighing state 2:

[0081] N 前2 =W forward2

[0082] N 主2 =W left2 +W right2

[0083] W2=N 前2 +N 主2 =W forward2 +W left2 +W right2

[0084] G2=N 前2 +N 主2 -W z2 +W q2 =W forward2 +W left2 +W right2 -W z2 +W q2

[0085] Unit direction vectors of gravity and support forces for:

[0086]

[0087] The gravity vector and support force vector are:

[0088]

[0089]

[0090]

[0091] The gravity vector and the arm vector of the support force are:

[0092]

[0093]

[0094]

[0095] The vector from point D to point C is:

[0096]

[0097] The aircraft pitch angle is:

[0098]

[0099] Calculation of the moment of the support force on the front wheel center to the body coordinate origin:

[0100]

[0101] Calculation of the moment of the support force exerted on the midpoint of the main wheel center line to the origin of the aircraft coordinate system:

[0102]

[0103] Calculation of the moment of gravity at the center of gravity of the aircraft on the origin of the aircraft coordinate system:

[0104]

[0105] According to the moment balance about the coordinate origin, we get the equation:

[0106] M w2 =M 前2 +M 主2 (2)

[0107] Substituting the weighing data (scale reading (kg)) and the measurement data (coordinates) into the equilibrium equations (1) and (2) under the two states, we can obtain a set of linear equations containing the coordinates of the center of gravity Xw and Zw:

[0108]

[0109] Solving the above equations can obtain the coordinates of the center of gravity of the aircraft (Xw, 0, Zw). Since the equations are relatively complex, MATLAB software can be used to solve them.

Claims

1. A method for weighing an aircraft to eliminate the influence of landing gear deformation, characterized in that: include: At the weighing site, a laser tracker is used to measure the standard points on the aircraft, and the aircraft weighing coordinate system O-XYZ is established, with the coordinate origin as the weighing reference point; Set up a vertical pole on the open space on one side of the aircraft, and set two standard holes A and B on the pole; Place the front wheel, left main wheel, and right main wheel on three scales respectively, and adjust the aircraft pitch angle to obtain at least two pitch states; Select two pitch states, respectively according to the front scale reading W forward , Left scale reading W left , right scale reading W right , and the separately measured addition W z and missing item W q Read the reading to determine the empty weight G of the aircraft; In the two selected pitch states, the laser tracker is used to measure the front wheel center coordinates (X 前i ,Y 前i ,Z 前i ), coordinates of the midpoint of the line connecting the left main wheel and the right main wheel (X 主i ,Y 主I , Z 主i )、Point A coordinates (X Ai ,Y Ai ,Z Ai )、Point B coordinates (X Bi ,Y Bi ,Z Bi )、Point C coordinates (X Ci ,Y Ci ,Z Ci )、D point coordinates (X Di ,Y Di ,Z Di ), and determine the gravity and support force vectors, the force arm vectors of the gravity and support forces, the pitch angle of the aircraft, and the moment M of the support force on the front wheel center about the coordinate origin 前i , the moment M of the support force exerted on the midpoint of the main wheel center line to the origin of the body coordinate 主i , the moment M of gravity at the center of gravity of the aircraft on the origin of the body coordinate wi， Among them, the value of i corresponds to a certain pitch state, i=1 or 2; According to the moment balance in the first pitch state And the moment balance in the second pitch state Determine the coordinates of the aircraft's center of gravity (Xw, 0, Zw).

2. The aircraft weighing method for eliminating the influence of landing gear deformation according to claim 1, characterized in that: The aircraft weighing coordinate system is established at the weighing site using a laser tracker, specifically including: The aircraft weighing coordinate system is corrected and fitted using the standard points on the aircraft, so that the fitted aircraft weighing coordinate system coincides with the aircraft body coordinate system in the three-dimensional digital model.

3. The aircraft weighing method for eliminating the influence of landing gear deformation according to claim 2, characterized in that: The standard points on the aircraft include standard holes reserved for horizontal measurement as required during the production and processing process.

4. The aircraft weighing method for eliminating the influence of landing gear deformation according to claim 1, characterized in that: In each pitch state, according to the front scale reading W forward , Left scale reading W left And the right scale reading W right , and the separately measured addition W z and missing item W q The readings are used to determine the empty weight of the aircraft, G, including: Determine the empty weight G1 and G2 for each pitch state respectively. When the difference between G1 and G2 is less than a predetermined error, take the average of G1 and G2 as the empty weight G of the aircraft. 。 5. The aircraft weighing method for eliminating the influence of landing gear deformation according to claim 1, characterized in that: The gravity and support force vectors are: , , , where the unit direction vector for: ,in, is the support force vector of the front wheel, is the support force on the front wheel, is the support force vector at the midpoint of the line connecting the left and right main wheel centers, is the support force on the midpoint of the line connecting the left and right main wheel centers, is the gravity vector of the aircraft, is the gross weight of the aircraft.

6. The aircraft weighing method for eliminating the influence of landing gear deformation according to claim 5, characterized in that: The gravity vector and the support force arm vector are: , , ,in, is the moment arm vector of the front wheel center, is the moment arm vector of the midpoint of the line connecting the left and right main wheel centers, is the gravity arm of the aircraft.

7. The aircraft weighing method for eliminating the influence of landing gear deformation according to claim 6, characterized in that: The pitch angle of the aircraft for: .

8. The aircraft weighing method for eliminating the influence of landing gear deformation according to claim 6, characterized in that: The moment M of the support force on the front wheel center about the coordinate origin 前i , the moment M of the support force exerted on the midpoint of the main wheel center line to the origin of the body coordinate 主i , the moment M of gravity at the center of gravity of the aircraft on the origin of the body coordinate wi They are: ； ； 。

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