Method for calculating length variation of constant-height air-retaining mooring rope of ship-borne captive balloon under wind disturbance

Abstract

The invention discloses a method for calculating the length variation of a constant-height air-retaining mooring rope of a ship-borne captive balloon under wind disturbance. The method comprises the following three steps of 1, real-time wind field model establishment, 2, balloon-mooring rope system mechanical modeling and 3, mooring rope length calculation. The method has the beneficial effects that the real-time wind field model is established to obtain the wind speed time-domain function representing captive balloon operation, so that the wind speed data is more universal; the method comprises the steps of infinitesimal mooring rope equivalent to a'spring-damping 'unit, tethered balloon establishment, mechanical modeling of the tethered rope, iterative calculation of the length of the infinitesimal mooring rope and summation to obtain the length variation of the mooring rope, has the advantages of reasonable analysis and simple and reliable modeling calculation, provides data support for active compensation control of the tethered balloon under wind interference, and has a wide application prospect. And long-time continuous stable-height air-leaving operation of the captive balloon is realized.

Description

Technical Field

[0001] The invention belongs to a method for calculating the length variation of a cable of a shipborne tethered balloon, and in particular relates to a method for calculating the length variation of a constant-altitude airborne cable of a shipborne tethered balloon under wind disturbance. Background Art

[0002] The ship-borne tethered balloon is a small or medium-sized tethered balloon system loaded on ships. It consists of a sphere, mission payload, tethering cable, mooring winch, control system and other main parts. It usually carries radar, communication, jamming, reconnaissance and other electronic equipment under the sphere. Due to its long airborne time, large coverage area, and continuous and uninterrupted operation, it is widely used in maritime security, territorial waters and border monitoring, and naval military field monitoring. In comparison, the performance of tethered balloons is slightly better than other equipment, and has high military application value and significance.

[0003] The tethered cable is a key component for controlling the launch, recovery, residence, and attitude adjustment of the tethered balloon. It also provides energy for the balloon and sometimes provides an information transmission channel between the balloon and the ship system. Since the ship-borne tethered balloon needs to stay in the air for a long time during daily work, in the harsh ocean environment, the tethered balloon is often affected by the time-varying strong sea breeze, causing the tethered cable to be stretched under the time-varying tension, and even fatigue fracture of the cable that is thousands of meters long, which affects the stability and safety of the tethered object, causing great damage and loss to the production operation. In addition, it may also cause the tethered balloon to deviate from the original stable position. Since the balloon needs to be stable at a certain height for a long time, when the wind speed changes greatly without control, the tethered balloon will lose its ability to stay in the air. Usually, active compensation control of wind disturbance is performed through the mooring and retracting winch to improve the stability of the tethered balloon in the air and the safety and utilization of the onboard equipment. The elongation of the tethered cable under wind disturbance is the key control quantity of active compensation control. Therefore, by establishing a balloon-cable dynamic model, analyzing the movement trend of the balloon-cable system under wind disturbance, and calculating the change in cable length, data support is provided for active wind disturbance compensation control, which is of great significance to enable the tethered balloon to remain in the air for a long time at a stable altitude under wind disturbance. Summary of the invention

[0004] The present invention relates to a method for calculating the length variation of a constant-altitude airborne cable of a ship-borne tethered balloon under wind disturbance, which is characterized by obtaining a wind speed time domain function characterizing the operation of the tethered balloon by establishing a real-time wind field model, micro-elementing the tethered cable and making it equivalent to a "spring-damping" unit, establishing mechanical modeling of the tethered balloon and the tethered cable, iteratively calculating the micro-element cable length, and summing up to obtain the cable length variation, and performing the following three steps: step one, establishing a real-time wind field model, step two, mechanical modeling of the balloon-cable system, and step three, calculating the cable length.

[0005] Step 1: Establishing real-time wind field model The real-time wind field model during tethered balloon operation includes the average wind speed model, gust wind speed model, and turbulent wind speed model. The specific model is established as follows: (1) The average wind speed model expression is: V P = c (1) In the formula, c is a constant; (2) The gust wind speed model expression is: (2) Where: V Gmax is the maximum peak gust wind speed; (3) The turbulent wind speed model expression is: V T =V Tmax ran (-1,1)sin(2 πt + ω n ) (3) In the formula, V Tmax is the peak value of turbulent wind speed, ran (-1,1) is a random number between -1 and 1. ω n The initial phase angle of the turbulent wind ranges from 0 to 2 π Random angles between From equations (1) to (3), the real-time wind field model that characterizes the time domain function of the tethered balloon operation wind speed can be obtained: V 风 = V P + V G + V T (4) Step 2: Mechanical modeling of the balloon-cable system The balloon-cable system includes a balloon and a cable. First, the balloon-cable system is simplified, and then the balloon and the microelement cable are mechanically modeled to analyze the force and geometric relationship under the stable state, as follows: (1) Cable “spring-damper” microelementization Keep the tethered balloon at a high altitude h Divide into n Equal parts, each part has a height of △ h, and then divide the cable into equal parts according to the height n segment, and the differentiated cable unit is equivalent to a "spring-damper" unit; (2) Balloon mechanical modeling At time t Under the real-time wind field, the balloon mechanical model is established as follows: The vertical force balance equation is: F 升 =sin a 1. T 1+ G (5) In the formula, F 升 is the lift of the balloon, T 1 is the cable tension between the cable and the balloon, α 1 Cable tension and x The angle of the axis, G is the weight of the balloon and mission payload; and F 升 It is generated by the buoyancy and aerodynamic lift of the balloon, so it is also expressed as (6) In the formula, F 浮 is the buoyancy of the balloon, F 气 is the aerodynamic lift of the balloon, V is the volume of the balloon, ρ a is the air density at the current altitude of the balloon, ρ h The density of the helium in the balloon, v t for t Real-time wind speed at the moment, s b is the characteristic area of ​​the balloon, C L is the balloon aerodynamic lift coefficient, m is the mass of the balloon and the load, g is the acceleration due to gravity; The horizontal force balance equation is: F 风 =cos α 1. T 1 (7) In the formula, F 风 is the horizontal thrust of the balloon; and F 风is the horizontal resistance of the balloon due to the wind, so it can also be expressed as (8) In the formula, C D is the balloon aerodynamic drag coefficient; (3) Cable mechanical modeling Select i The microelement cable is subjected to stress analysis and the mechanical model of the mooring cable is established as follows: by X i The node is the object of analysis and its force balance equation is: T i cos α i = T i+1 cos α i+1 (9) T i sin α i = T i+1 sin α i+1 + ρ 绳 l i (10) In the formula, T i , T i+1 Respectively i , i +1 microelement of cable tension, α i , α i+1 Respectively i , i +1 microelement cable horizontal angle, ρ 绳 is the linear density of the cable, l i For the i The original length of the microelement cable; Combining equation (9) and equation (10), we can get (11) According to the characteristics of the "spring-damper" unit, we can get (12) In the formula, A is the cross-sectional area of ​​the cable,E is the elastic modulus of the cable, η is the cable damping coefficient, ε i is the rate of change of characteristic element elongation; ε i The expression is (13) In the formula, l i ' For the i The length of the microelement cable after extension; Due to the flexible nature of the cable, the cable is pulled but not compressed. (14) In the i In the infinitesimal cable, according to the geometric relationship, we can get △ h = l i ' sin α i (15) Combining equations (13) and (15), we can get the expression of the original length of the cable: (16) Step 3: Calculate the cable length Initialize the basic parameters of the wind field, balloon, cable and the air height, and transform the cable into microelement according to the equal height principle. n , t Time to lower the cable and balloon connection point X The state of 0 is the boundary condition, calculated by equation (5)-(8) t The connection point at the moment X 0 boundary condition parameters T 1. a 1. From i =1, and then loop through equations (9), (11), and (16) to calculate l i , T i+1 , a i+1 ,Will T i+1 , a i+1 Substitute into the next loop until i = n , and then calculate according to formula (17) t The change in cable length at time is (17) In the formula, L (t) Windlass for anchoring t The actual length of the cable that has been released at that moment.

[0006] The beneficial effects of the present invention are as follows: the present invention relates to a method for calculating the length change of a constant-altitude airborne cable of a ship-borne tethered balloon under wind disturbance, establishes a real-time wind field model to obtain a wind speed time-domain function that characterizes the operation of the tethered balloon, and makes wind speed data more universal; the tethered cable is micro-elemented and equivalent to a "spring-damping" unit, a mechanical modeling of the tethered balloon and the tethered cable is established, the micro-element cable length is iteratively calculated, and the cable length change is obtained by summing, which has the advantages of reasonable analysis, simple and reliable modeling and calculation; and provides data support for the active compensation control of the tethered balloon under wind disturbance, so as to realize the tethered balloon's continuous and stable altitude air operation for a long time. BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 This is a flow chart of a method for calculating the length variation of a constant-altitude airborne cable of a ship-borne tethered balloon under wind disturbance of the present invention; Figure 2 It is a time domain diagram of the wind field under the fourth wind speed of the present invention; Figure 3 This is a structural diagram of the balloon-cable system of the present invention; Figure 4 This is a force analysis diagram of the shipborne tethered balloon of the present invention; Figure 5 This is the force analysis diagram of the "spring-damper" unit of the present invention; Figure 6 This is a flow chart of calculating the cable length of the present invention; Figure 7 This is a diagram of the cable length under wind interference when the height of the present invention is 500m; Figure 8 This is a diagram of the cable length under wind interference when the height is 1000m; Fig. 9 This is a diagram of cable length variation under wind interference when the height is 500m and 1000m according to the present invention. DETAILED DESCRIPTION

[0007] The present invention will be further described below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0008] See attached figure, Figure 1 The present invention is a flow chart of a method for calculating the length change of a constant-altitude airborne cable of a ship-borne tethered balloon under wind disturbance, which includes the following three steps: (1) establishing a real-time wind field model, (2) mechanical modeling of the balloon-cable system, and (3) calculating the cable length.

[0009] Step 1: Establishing real-time wind field model Select level 4 wind speed for real-time wind field modeling. Under level 4 wind speed, the average wind speed is 5.5m / s and the peak gust speed is V Gmax 2m / s, peak turbulent wind speed V Tmax is 4m / s, t 0=10s, t 1=30s, t 2=50s, ω n 6 / π , substituting into equation (1)-(4) to obtain the real-time wind field model, setting the simulation time to 1-50s, the simulation results are as follows Figure 2 The time domain diagram of the wind field under level 4 wind speed is shown.

[0010] Step 2: Dynamics modeling of the balloon-cable system See attached figure, Figure 3 This is a structural diagram of the balloon-cable system of the present invention. The tethered balloon system includes a balloon and a cable. The balloon is selected as a certain ship-borne tethered balloon, and the cable is selected as a photoelectric composite cable specially used for the tethered balloon. The basic parameters of the tethered balloon are as follows: Helium density ρ h =0.17kg / m 3 , main airbag volume V =4504.1m 3 , the maximum cross-sectional area of ​​the airship s b =183.8m 2 , the mass of the balloon and the mass of the payload are 163.7kg and 500kg respectively, so the total mass of the balloon and the payload is m =663.7kg, acceleration due to gravity g =9.8m / s 2 , the balloon aerodynamic lift coefficient C L =0.1, balloon aerodynamic drag coefficient C D =0.53; the basic parameters of the cable are as follows: cable density ρ 绳 =134g / m, cable damping coefficient η =1.2, cable elastic modulus E =172GPa, the cable diameter is D =15mm, so the cross-sectional area of ​​the cable A =0.001414m 2 The basic parameters of the tethered balloon's airborne environment are as follows: the air density at an altitude of 500 meters is 1.19 kg / m 3 , the ambient air density at an altitude of 1000 meters is 1.11kg / m 3 .

[0011] (1) Cable "spring-damper" micro-elementization, Balloon altitude h Choose between 500m and 1000m, the balloon will stay empty h =500 meters is divided into n =50000 equal parts, each part has a height of △ h 0.01 m, and then divide the cable into 50,000 segments according to the height, and equate the differential cable unit to a "spring-damper" unit; the balloon is left empty at a height of h =1000 meters is divided into n =100000 equal parts, each part has a height of △h The cable is then divided into 100,000 segments according to the height, and the differential cable unit is equivalent to a "spring-damper" unit.

[0012] (2) Balloon mechanical modeling See attached figure, Figure 4 This is the force analysis diagram of the shipborne tethered balloon of the present invention. t The real-time wind speed, balloon basic parameters and environmental basic parameters at the moment are substituted into equations (5) to (8) to obtain the balloon mechanical model.

[0013] (3) Cable mechanical modeling See attached figure, Figure 5 It is the force analysis diagram of the "spring-damper" unit of the present invention. Substituting the basic parameters of the cable into equations (9) to (16), the cable mechanical model is obtained.

[0014] Step 3: Calculate the cable length See attached figure, Figure 6 is a flow chart of cable length calculation of the present invention, t At this moment, the cable is connected to the balloon. X 0 is the boundary condition, calculated by equation (5)-(8) t The connection point at the moment X 0 boundary condition parameters T 1. a 1. From i =1, and then loop through equations (9), (11), and (16) to calculate l i , T i+1 , a i+1 ,Will T i+1 , a i+1 Substitute into the next loop until i = n, and then calculate according to formula (17) t The change of cable length at time h When the cable lengths are 500m and 1000m respectively, the cable lengths under wind interference are Figure 7 , Figure 8 As shown, the cable length changes as Fig. 9 shown.

Claims

1. A method for calculating the length variation of the constant altitude airborne cable of a ship-borne tethered balloon under wind disturbance, characterized in that: The wind speed time domain function that characterizes the tethered balloon operation is obtained by establishing a real-time wind field model, the tethered cable is micro-elemented and equivalent to a "spring-damper" unit, the mechanical modeling of the tethered balloon and the tethered cable is established, the micro-element cable length is iteratively calculated, and the cable length change is obtained by summing up. The following three steps are followed: Step 1, establishment of real-time wind field model, Step 2, mechanical modeling of balloon-cable system, Step 3, cable length calculation; Step 1: Establishing real-time wind field model The real-time wind field model during tethered balloon operation includes the average wind speed model, gust wind speed model, and turbulent wind speed model. The specific model is established as follows: (1) The average wind speed model expression is: V P = c （1） In the formula, c is a constant; (2) The gust wind speed model expression is: （2） Where: V Gmax is the maximum peak gust wind speed; (3) The turbulent wind speed model expression is: V T =V Tmax ran (-1,1)sin(2 πt + ω n ) (3) In the formula, V Tmax is the peak value of turbulent wind speed, ran (-1,1) is a random number between -1 and 1. ω n The initial phase angle of the turbulent wind ranges from 0 to 2 π Random angles between From equations (1) to (3), the real-time wind field model that characterizes the time domain function of the tethered balloon operation wind speed can be obtained: V 风 = V P + V G + V T （4） Step 2: Mechanical modeling of the balloon-cable system The balloon-cable system includes a balloon and a cable. First, the balloon-cable system is simplified, and then the balloon and the microelement cable are mechanically modeled to analyze the force and geometric relationship under the stable state, as follows: (1) Cable "spring-damper" micro-elementization Keep the tethered balloon at a high altitude h Divide into n Equal parts, each part has a height of △ h , and then divide the cable into equal parts according to the height n segment, and the differentiated cable unit is equivalent to a "spring-damper" unit; (2) Balloon mechanical modeling At time t Under the real-time wind field, the balloon mechanical model is established as follows: The vertical force balance equation is: F 升 =sin a 1· T 1+ G (5) In the formula, F 升 is the lift of the balloon, T 1 is the cable tension between the cable and the balloon, α 1 Cable tension and x The angle of the axis, G is the weight of the balloon and mission payload; and F 升 It is generated by the buoyancy and aerodynamic lift of the balloon, so it is also expressed as （6） In the formula, F 浮 is the buoyancy of the balloon, F 气 is the aerodynamic lift of the balloon, V is the volume of the balloon, ρ a is the air density at the current altitude of the balloon, ρ h The density of the helium in the balloon, v t for t Real-time wind speed at the moment, s b is the characteristic area of ​​the balloon, C L is the balloon aerodynamic lift coefficient, m is the mass of the balloon and the load, g is the acceleration due to gravity; The horizontal force balance equation is: F 风 =cos α 1· T 1 (7) In the formula, F 风 is the horizontal thrust of the balloon; and F 风 is the horizontal resistance of the balloon due to the wind, so it can also be expressed as （8） In the formula, C D is the balloon aerodynamic drag coefficient; (3) Cable mechanical modeling Select i The microelement cable is subjected to stress analysis and the mechanical model of the mooring cable is established as follows: by X i The node is the object of analysis and its force balance equation is: T i cos α i = T i+1 cos α i+1 (9) T i its α i = T i+1 its α i+1 + ρ 绳 l i (10) In the formula, T i , T i+1 Respectively i , i +1 microelement of cable tension, α i , α i+1 Respectively i , i +1 microelement cable horizontal angle, ρ 绳 is the linear density of the cable, l i For the i The original length of the microelement cable; Combining equation (9) and equation (10), we can get （11） According to the characteristics of the "spring-damper" unit, we can get （12） In the formula, A is the cross-sectional area of ​​the cable, E is the elastic modulus of the cable, η is the cable damping coefficient, ε i is the rate of change of characteristic element elongation; ε i The expression is （13） In the formula, l i ' For the i The length of the microelement cable after extension; Due to the flexible nature of the cable, the cable is pulled but not compressed. （14） In the i In the infinitesimal cable, according to the geometric relationship, we can get △ h = l i ' sin α i (15) Combining equations (13) and (15), we can get the expression of the original length of the cable: （16） Step 3: Calculate the cable length Initialize the basic parameters of the wind field, balloon, cable and the air height, and transform the cable into microelement according to the equal height principle. n , t Time to lower the cable and balloon connection point X The state of 0 is the boundary condition, calculated by equation (5)-(8) t The connection point at the moment X 0 boundary condition parameters T 1. a 1. From i =1, and then loop through equations (9), (11), and (16) to calculate l i , T i+1 , a i+1 ,Will T i+1 , a i+1 Substitute into the next loop until i = n , and then calculate according to formula (17) t The change in cable length at time is （17） In the formula, L (t) Windlass for anchoring t The actual length of the cable that has been released at that moment.

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