Calculation method for reversing turning process of aircraft electric taxiing system

Abstract

The invention discloses a method for calculating the reversing turning process of an aircraft electric taxiing system, and belongs to the field of aircraft electric taxiing systems. The method comprises the following steps: constructing a simplified model for reversing and turning of the aircraft electric taxiing system; presetting turning center coordinates of the aircraft; calculating the vertical load of each tire of the aircraft; the turning radius and turning angular velocity of the aircraft are calculated; calculating the sideslip angle of each tire of the aircraft; calculating lateral friction force and longitudinal friction force borne by each tire of the aircraft; the turning resultant moment, the tangential resultant force and the centripetal resultant force borne by the aircraft are calculated; judging whether differences between the turning resultant moment, the tangential resultant force and the centripetal resultant force and the centrifugal force meet a residual convergence standard or not; and the required motor driving power is calculated according to the active friction force. According to the method, the problem that the turning radius and the motor driving power cannot be accurately calculated by an existing common aircraft ground turning calculation method is solved.

Description

Technical Field

[0001] The invention belongs to the field of aircraft electric taxiing systems, and in particular relates to a calculation method for a reverse turning process of an aircraft electric taxiing system. Background Art

[0002] As a new taxiing method, the aircraft electric taxiing system uses the aircraft's own auxiliary power system (APU) to drive the electric motor installed on the landing gear wheels, allowing the aircraft to taxi autonomously without the need for a trailer. The aircraft electric taxiing system has many advantages, such as reducing fuel consumption and emissions, reducing aircraft runway occupancy time, and improving controllability and safety. With the continuous development and improvement of more-electric aircraft and all-electric aircraft, the electric taxiing system is expected to be more widely used and promoted in the future.

[0003] An important function of the aircraft electric taxiing system is to enable the aircraft to reverse and turn, which can greatly improve the aircraft's ground maneuverability and adaptability to simple runways. Compared with traditional aircraft that use engines to provide thrust, the aircraft electric taxiing system uses electric motors to generate active forward or backward friction to make the aircraft move forward or backward. In order to design the driving power of the electric motor, it is inevitable to calculate its reverse turning process to obtain the turning radius and motor driving force of the aircraft under different front wheel turning conditions. However, this process involves the balance of force and torque between the electric driving force, lateral and longitudinal friction of the wheels, and centrifugal force that the aircraft is subjected to during the turning process, and the usual algorithms in the aircraft design manual cannot be applied.

[0004] The prior art proposes a method of using differential braking to control the aircraft's extreme turning. The method first determines the maximum allowable friction coefficient under the aircraft's current taxiing conditions, establishes the aircraft's motion and dynamics equations, and then calculates the aircraft's turning radius; however, this technology is only applicable to conventional powered aircraft, not to aircraft using electric taxiing systems. The prior art proposes a comprehensive control method and system for an aircraft electric drive system, which integrates the wheel brake system and the front wheel turning system. When a turning command is detected, the damping of the aircraft during turning is reduced by controlling the left wheel speed, the right wheel speed, and the front wheel turning angle; however, this method is mainly designed for the control logic of the aircraft electric drive system, and does not provide a specific calculation method for the electric drive power required during the turning process.

[0005] Therefore, there is an urgent need for a calculation method for the reverse turning process of an aircraft electric taxiing system to solve the above problems. Summary of the invention

[0006] Technical issues to be solved:

[0007] In order to avoid the shortcomings of the prior art, the present invention provides a calculation method for the reverse turning process of an aircraft electric taxiing system, which can be used to solve the problem that the existing common aircraft ground turning calculation method cannot accurately calculate the turning radius and motor driving power.

[0008] The technical solution of the present invention is: a calculation method for the reverse turning process of an aircraft electric taxiing system, the specific steps are as follows:

[0009] Construct a simplified model of the aircraft electric taxiing system's reverse turning and record the number of iterative calculations;

[0010] According to the front wheel steering angle, preset the turning center coordinates of the aircraft;

[0011] Calculate the vertical load on each tire of the aircraft based on the aircraft's center of gravity, landing gear distribution, and friction on the tires;

[0012] Calculate the turning radius and turning angular speed of the aircraft;

[0013] Calculate the sideslip angle of each tire of the aircraft;

[0014] Calculate the lateral friction and longitudinal friction on each tire of the aircraft;

[0015] Calculate the turning moment, tangential force and centripetal force acting on the aircraft;

[0016] Determine whether the difference between the turning moment, tangential force, centripetal force and centrifugal force meets the residual convergence standard. If yes, proceed to the next step; if not, update the turning center coordinates of the aircraft and recalculate;

[0017] Determine whether the number of iterations k is greater than or equal to the set maximum number of iterations kmax. If so, proceed to the next step. Otherwise, set k=k+1 and reset the turning center coordinates for calculation.

[0018] The required motor drive power is calculated from the active friction force.

[0019] A further technical solution of the present invention is: the simplified model of the reverse turning of the aircraft electric taxiing system includes the center of gravity of the aircraft, the front wheels and multiple rows of main wheels, and a coordinate system is established with the center of gravity of the aircraft as the circle point; the coordinate of the turning center of the aircraft is preset as (-y N cotγ N , 0), where γ N is the steering angle of the front wheels.

[0020] A further technical solution of the present invention is: the vertical load calculation formula of each tire of the aircraft is as follows:

[0021]

[0022] Among them, k N is the vertical stiffness of the front landing gear, k M is the vertical stiffness of the main engine wheel frame, a M The main track width, y N is the longitudinal distance from the front landing gear to the center of gravity of the aircraft, γ N is the steering angle of the front wheels, y M,i is the longitudinal distance from the i-th row of main landing gear to the center of gravity of the aircraft, Z N is the vertical load on the front landing gear tire, Z ML,i is the vertical load on the left side i-th row main landing gear tire, Z MR,i is the vertical load on the right side i-th row main landing gear tire, d G is the sinking height of the aircraft's center of gravity, α is the pitch angle of the aircraft, and β is the roll angle of the aircraft; Substitute the above formula into the following formula, that is, solve d through the aircraft's force balance and moment balance equations G , α and β:

[0023]

[0024] Where W is the mass of the aircraft, h is the height of the aircraft's center of gravity, S N is the lateral friction force on the front landing gear tire, T N is the longitudinal friction force on the front landing gear tire, S ML,i is the lateral friction force on the left side i-th row main landing gear tire, S MR,i is the lateral friction force on the right side i-th row main landing gear tire, T ML,i is the longitudinal friction force on the left side i-th row main landing gear tire, T MR,i is the longitudinal friction force on the right side i-th row main landing gear tire; in the first iterative calculation, that is, k = 1, the lateral and longitudinal friction forces on the tire are both set to 0, and the lateral force result obtained in the previous iterative calculation is used in subsequent calculations.

[0025] A further technical solution of the present invention is: the calculation formula of the turning radius and turning angular velocity of the aircraft is as follows:

[0026]

[0027] Among them, r A is the turning radius of the aircraft, ω A is the turning angular velocity of the aircraft, V A is the speed of the aircraft, (x C ,y C ) is the turning center coordinate of the aircraft.

[0028] A further technical solution of the present invention is: the calculation formula of the sideslip angle of each tire of the aircraft is as follows:

[0029]

[0030] Among them, η N is the sideslip angle of the front wheel, η ML,i is the sideslip angle of the i-th row of main landing gear tires on the left side, η MR,i is the sideslip angle of the i-th row of main landing gear tires on the right side.

[0031] A further technical solution of the present invention is: the lateral friction force on each tire of the aircraft is calculated as follows:

[0032]

[0033] Among them, S N is the lateral friction of the front wheel, S ML,i is the lateral friction of the left i-th row main landing gear tire, S MR,i is the lateral friction of the right i-th row main landing gear tire, C p and μ max is the tire parameter obtained according to the tire test, and sgn is the sign function.

[0034] A further technical solution of the present invention is that the longitudinal friction forces on each tire of the aircraft are respectively:

[0035] The longitudinal friction force on the front tire of the aircraft is the motor driving force. In the first iterative calculation, k = 1, the longitudinal friction force on the front tire is set to 0, and the calculation results of the previous iterative calculation are used in the subsequent calculations.

[0036] The calculation formula of the longitudinal friction force on the aircraft main wheel tire is as follows:

[0037] T ML,i =μ g Z ML,i ,T MR,i =μ g Z MR,i

[0038] Among them, μ g is the wheel rolling friction coefficient, ranging from 0.005 to 0.02.

[0039] A further technical solution of the present invention is that the calculation formulas for the turning moment, tangential force and centripetal force on the aircraft are as follows:

[0040]

[0041] Among them, M t is the total turning moment on the aircraft, F t is the centripetal force on the aircraft, F his the tangential force on the aircraft, and the calculation formula of ζ is as follows:

[0042]

[0043] A further technical solution of the present invention is: the residual convergence standard is taken as 0.001, and when the convergence standard is not met, the Newton iteration method or the gradient descent method is used to update the turning center coordinates.

[0044] A further technical solution of the present invention is: the required motor drive power calculation formula is as follows:

[0045]

[0046] Beneficial Effects

[0047] The beneficial effect of the present invention is that the calculation method of the reverse turning process of the aircraft electric taxiing system provided by the present invention calculates the turning torque, centripetal force and tangential force of the aircraft in the steady-state turning process by constructing a simplified aircraft ground turning model, and obtains the turning radius of the aircraft and the required motor drive power at different front wheel turning angles through iterative calculation. The calculation process of the present invention takes into account the force and torque balance relationship of the aircraft in the steady-state turning process, and takes into account the vertical load change of the tire caused by the lateral force, and can calculate a relatively accurate turning radius and motor drive power, which can be applied to the design of the aircraft electric taxiing system. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is a flow chart of a calculation method of a reverse turning process of an aircraft electric taxiing system according to the present invention;

[0049] Figure 2 This is a schematic diagram of the landing gear layout of a typical large aircraft;

[0050] Figure 3 This is a schematic diagram of the relationship between the aircraft's front wheel turning angle, turning radius, and motor power. DETAILED DESCRIPTION

[0051] The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, but should not be construed as limiting the present invention.

[0052] Based on the problem that the conventional aircraft ground turning calculation method cannot accurately calculate the turning radius and the motor driving power, the present invention provides a calculation method for the reverse turning process of an aircraft electric taxiing system, which comprises the following specific steps:

[0053] S100: Construct a simplified model of the aircraft electric taxiing system reverse turning and record the number of iterative calculations;

[0054] S101: preset the turning center coordinates of the aircraft;

[0055] S102: Calculate the vertical load of each tire of the aircraft based on the center of gravity of the aircraft, the distribution of the landing gear, and the friction force on the tires;

[0056] S103: Calculate the turning radius and turning angular velocity of the aircraft;

[0057] S104: Calculate the sideslip angle of each tire of the aircraft;

[0058] S105: Calculate the lateral friction and longitudinal friction of each tire of the aircraft;

[0059] S106: Calculate the turning moment, tangential force and centripetal force acting on the aircraft;

[0060] S107: Determine whether the difference between the turning torque, the tangential force, the centripetal force and the centrifugal force meets the residual convergence standard. If so, proceed to step S108. If not, update the turning center coordinates of the aircraft and re-enter step S103.

[0061] S108: Determine whether the number of iterative calculations k is greater than or equal to the set maximum number of iterations kmax. If so, proceed to step S109; otherwise, set k=k+1 and re-enter step S101.

[0062] S109: Calculate the required motor driving power based on the active friction force.

[0063] The above technical solution is further described below with reference to the accompanying drawings and examples:

[0064] Reference Figure 1 As shown, this embodiment provides a calculation method for the reverse turning process of the electric taxiing system of a typical large aircraft, including the following steps:

[0065] Step S100: construct a simplified model of reverse turning of the aircraft electric taxiing system, and record the number of iterative calculations k=1.

[0066] In step S100, a simplified analysis model of an aircraft turning includes the center of gravity of the aircraft, a front wheel and multiple rows of main wheels, and a coordinate system is established with the center of gravity of the aircraft as a circle. Figure 2 A typical large aircraft landing gear layout is given, including a front landing gear and three rows of main landing gears, each landing gear is a parallel double wheel type, and since the two tires are close to each other, they are simplified to one tire for analysis. In this embodiment, the drive motor is installed on the front landing gear, so active friction is generated on the front wheel.

[0067] Step S101: estimate the turning center coordinates (x C ,y C );

[0068] In step S101, the coordinates of the turning center of the aircraft can be estimated to be (-y N cotγ N , 0), where γ N is the steering angle of the front wheels.

[0069] Step S102, calculating the vertical load of each tire of the aircraft according to the center of gravity of the aircraft, the distribution of the landing gear, and the friction force on the tires;

[0070] In step S102, the vertical load on each tire of the aircraft is:

[0071]

[0072] Among them, k N is the vertical stiffness of the front landing gear, k M is the vertical stiffness of the main engine wheel frame, a M Main track, y N is the longitudinal distance from the front landing gear to the center of gravity of the aircraft, γ N is the steering angle of the front wheels, y M,i is the longitudinal distance from the i-th row of main landing gear to the center of gravity of the aircraft, Z N is the vertical load on the front landing gear tire, Z ML,i is the vertical load on the left side i-th row main landing gear tire, Z MR,i is the vertical load on the right side i-th row main landing gear tire, d G is the sinking height of the aircraft's center of gravity, α is the aircraft's pitch angle, β is the aircraft's roll angle, and d G , α and β are solved by the force balance and moment balance equations of the aircraft:

[0073]

[0074] Where W is the mass of the aircraft, h is the height of the aircraft's center of gravity, S N is the lateral friction force on the front landing gear tire, T N is the longitudinal friction force on the front landing gear tire, S ML,i is the lateral friction force on the left side i-th row main landing gear tire, S MR,i is the lateral friction force on the right side i-th row main landing gear tire, T ML,i is the longitudinal friction force on the left side i-th row main landing gear tire, T MR,i is the longitudinal friction force on the right side i-th row main landing gear tire. In the first iterative calculation (k=1), the lateral and longitudinal friction forces of the tire can be set to 0, and the lateral force result obtained in the previous iterative calculation is used in subsequent calculations.

[0075] Step S103, calculating the turning radius and turning angular velocity of the aircraft;

[0076] In step S103, the turning radius and turning angular velocity of the aircraft are calculated by the following formula:

[0077]

[0078] Among them, r A is the turning radius of the aircraft, ω A is the turning radius of the aircraft, V A is the speed of the aircraft.

[0079] Step S104, calculating the sideslip angle of each tire of the aircraft;

[0080] In step S104, the sideslip angle of each tire of the aircraft is calculated by the following formula:

[0081]

[0082] Among them, η N is the sideslip angle of the front wheel, η ML,i is the sideslip angle of the i-th row of main landing gear tires on the left side, η MR,i is the sideslip angle of the i-th row of main landing gear tires on the right side.

[0083] Step S105, calculating the lateral friction and longitudinal friction of each tire of the aircraft;

[0084] In step S105, the lateral friction force of each tire of the aircraft can be calculated by the following empirical formula:

[0085]

[0086] Among them, S N is the lateral friction of the front wheel, S ML,i is the lateral friction of the left i-th row main landing gear tire, S MR,i is the lateral friction of the right i-th row main landing gear tire, C p and μ max is the tire parameter, which can be obtained according to the tire test, and sgn is the sign function.

[0087] In step S105, the longitudinal friction force on the front tire of the aircraft is the motor driving force. In the first iteration calculation (k=1), it can be set to 0, and the result obtained in the previous iteration calculation is used in subsequent calculations. The longitudinal friction force of the main wheel tire is calculated by the following formula:

[0088] T ML,i =μ g Z ML,i ,T MR,i =μ g Z MR,i

[0089] Among them, μ g It is the wheel rolling friction coefficient, which is related to the tire and runway conditions and is generally taken as 0.005~0.02.

[0090] Step S106, calculating the turning moment, tangential force and centripetal force acting on the aircraft;

[0091] In step S106, in this example, the turning moment, the centripetal force and the tangential force acting on the aircraft can be calculated by the following formula:

[0092]

[0093] Among them, M t is the total turning moment on the aircraft, F t is the centripetal force on the aircraft, F h is the tangential force on the aircraft, ζ can be calculated by the following formula:

[0094]

[0095] Step S107, judging whether the difference between the turning torque, the tangential force, the centripetal force and the centrifugal force meets the residual convergence standard, if so, proceeding to step S108, if not, updating the turning center coordinates of the aircraft, and re-entering step S103;

[0096] In step S107, the centrifugal force calculation formula is:

[0097]

[0098] In step S107, the residual convergence standard can be selected according to the actual calculation accuracy, and can generally be taken as 0.001. When the convergence standard is not met, the Newton iteration method or the gradient descent method can be used to update the turning center coordinates.

[0099] Step S108: Determine whether k is greater than or equal to k max If yes, the calculation ends; otherwise, let k=k+1 and re-enter step S101.

[0100] In step S108, the maximum number of iterations k max It can be set according to the actual calculation situation.

[0101] Step S109: Calculate the required motor driving power based on the active friction force.

[0102] In step S109, the motor drive power calculation formula is:

[0103]

[0104] The turning radius calculation method provided in this embodiment is applicable to the ground turning system of an aircraft, and is applicable to the turning radius calculation in various scenarios such as main wheel coordinated turning.

[0105] The turning radius calculation method provided in this embodiment is used to obtain the following in actual calculation:

[0106] Assume that the aircraft has the following parameters: aircraft mass W = 100t, front landing gear vertical stiffness k N =1.5×10 6 N / m, vertical stiffness of main engine wheel frame k M =2.5×10 6 N / m, main wheelbase a M = 8m, aircraft center of gravity height h = 4m, longitudinal distance from front wheel to aircraft center of gravity y N =10m, the longitudinal distances from the main wheel to the center of gravity of the aircraft are y M,1 =0.5m,y M,2 =-0.5m,y M,3 =-1.5m. Let the aircraft speed be 5km / h, and the front wheel steering angle γ N is 40 degrees, μ g Take it as 0.01.

[0107] In order to consider the change of vertical load on the tire caused by tire friction, an iterative solution is required. The number of iterations k is max is 5, and the calculation results are shown in Table 1. It can be seen that after four cycles, the results have not changed, indicating that the iteration has converged.

[0108] When considering the change in the vertical load on the tire caused by the lateral force, an iterative solution is also required. The number of iterations kmax is taken as 5. The calculation results are shown in Table 1. It can be seen that after four cycles, the results have not changed, indicating that the iteration has converged.

[0109] Reference Figure 3 As shown in the figure, the results under different front wheel turning angles are given. It can be seen that as the front wheel turning angle increases, the turning radius decreases, and the required motor drive power also gradually increases.

[0110] Table 1 Iterative calculation results

[0111]

[0112]

[0113] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and intent of the present invention.

Claims

1. A calculation method for the reverse turning process of an aircraft electric taxiing system, Features The specific steps are as follows: Construct a simplified model of the aircraft electric taxiing system's reverse turning and record the number of iterative calculations; According to the front wheel steering angle, preset the turning center coordinates of the aircraft; Calculate the vertical load on each tire of the aircraft based on the aircraft's center of gravity, landing gear distribution, and friction on the tires; Calculate the turning radius and turning angular speed of the aircraft; Calculate the sideslip angle of each tire of the aircraft; Calculate the lateral friction and longitudinal friction on each tire of the aircraft; Calculate the turning moment, tangential force and centripetal force acting on the aircraft; Determine whether the differences between the turning torque, tangential force, centripetal force and centrifugal force meet the residual convergence standard. If so, proceed to the next step. If not, update the aircraft's turning center coordinates and recalculate; Determine whether the number of iterations k is greater than or equal to the set maximum number of iterations kmax. If so, proceed to the next step. Otherwise, set k=k+1 and reset the turning center coordinates for calculation. The required motor drive power is calculated from the active friction force.

2. A calculation method for a reverse turning process of an aircraft electric taxiing system according to claim 1, Features: The simplified model of the reverse turning of the aircraft electric taxiing system includes the center of gravity of the aircraft, the front wheels and multiple rows of main wheels, and a coordinate system is established with the center of gravity of the aircraft as the circle point; the coordinate of the turning center of the aircraft is preset as (-y N cotγ N , 0), where γ N is the steering angle of the front wheels.

3. According to claim 2, a calculation method for the reverse turning process of an aircraft electric taxiing system, Features: The vertical load calculation formula for each tire of the aircraft is as follows: Among them, k N is the vertical stiffness of the front landing gear, k M is the vertical stiffness of the main engine wheel frame, a M The main track width, y N is the longitudinal distance from the front landing gear to the center of gravity of the aircraft, γ N is the steering angle of the front wheels, y M,i is the longitudinal distance from the i-th row of main landing gear to the center of gravity of the aircraft, Z N is the vertical load on the front landing gear tire, Z ML,i is the vertical load on the left side i-th row main landing gear tire, Z MR,i is the vertical load on the right side i-th row main landing gear tire, d G is the sinking height of the aircraft's center of gravity, α is the pitch angle of the aircraft, and β is the roll angle of the aircraft; Substitute equation (1) into equation (2), that is, solve d through the aircraft's force balance and moment balance equations G , α and β: Where W is the mass of the aircraft, h is the height of the aircraft's center of gravity, S N is the lateral friction force on the front landing gear tire, T N is the longitudinal friction force on the front landing gear tire, S ML,i is the lateral friction force on the left side i-th row main landing gear tire, S MR,i is the lateral friction force on the right side i-th row main landing gear tire, T ML,i is the longitudinal friction force on the left side i-th row main landing gear tire, T MR,i is the longitudinal friction force on the right side i-th row main landing gear tire; in the first iterative calculation, that is, k = 1, the lateral and longitudinal friction forces on the tire are both set to 0, and the lateral force result obtained in the previous iterative calculation is used in subsequent calculations.

4. A calculation method for a reverse turning process of an aircraft electric taxiing system according to claim 3, Features: The calculation formulas for the turning radius and turning angular velocity of the aircraft are as follows: Among them, r A is the turning radius of the aircraft, ω A is the turning angular velocity of the aircraft, V A is the speed of the aircraft, (x C ,y C ) is the turning center coordinate of the aircraft.

5. A method for calculating the reverse turning process of an aircraft electric taxiing system according to claim 4, Features: The calculation formula of the sideslip angle of each tire of the aircraft is as follows: Among them, η N is the sideslip angle of the front wheel, η ML,i is the sideslip angle of the i-th row of main landing gear tires on the left side, η MR,i is the sideslip angle of the i-th row of main landing gear tires on the right side.

6. A method for calculating the reverse turning process of an aircraft electric taxiing system according to claim 5, Features: The calculation formula of the lateral friction force on each tire of the aircraft is as follows: Among them, S N is the lateral friction of the front wheel, S ML,i is the lateral friction of the left i-th row main landing gear tire, S MR,i is the lateral friction of the right i-th row main landing gear tire, C p and μ max is the tire parameter obtained according to the tire test, and sgn is the sign function.

7. A method for calculating a reverse turning process of an aircraft electric taxiing system according to claim 6, Features: The longitudinal friction forces on each tire of the aircraft are: The longitudinal friction force on the front tire of the aircraft is the motor driving force. In the first iterative calculation, k = 1, the longitudinal friction force on the front tire is set to 0, and the calculation results of the previous iterative calculation are used in the subsequent calculations. The calculation formula of the longitudinal friction force on the aircraft main wheel tire is as follows: T ML,i =μ g Z ML,i ,T MR,i =μ g Z MR,i (6) Among them, μ g is the wheel rolling friction coefficient, ranging from 0.005 to 0.

02.

8. A method for calculating a reverse turning process of an aircraft electric taxiing system according to claim 7, Features: The calculation formulas for the turning moment, tangential force and centripetal force on the aircraft are as follows: Among them, M t is the total turning moment on the aircraft, F t is the centripetal force on the aircraft, F h is the tangential force on the aircraft, and the calculation formula of ζ is as follows:

9. A method for calculating a reverse turning process of an aircraft electric taxiing system according to claim 8, Features: The residual convergence standard is set to 0.

001. When the convergence standard is not met, the Newton iteration method or the gradient descent method is used to update the turning center coordinates.

10. A method for calculating a reverse turning process of an aircraft electric taxiing system according to claim 9, Features: The required motor drive power calculation formula is as follows:

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