Cable vibration response solving method based on coupled dynamics model and cable climbing robot

Abstract

The application provides a cable vibration response solving method based on a coupling dynamics model and a cable climbing robot, and the method comprises the following steps: step 1, a simplified model is established based on a tilt-rotor flight cable climbing robot and a cable, and four coordinate systems are introduced based on the simplified model; step 2, a simplified rotation matrix of a rolling angle of the body is solved; step 3, a resultant force in the direction of the cable acting on the flight robot in the cable coordinate system {C} is solved F X ; step 4, a flight robot-cable coupling dynamics model in the body coordinate system is established; step 5, a wind-cable-robot coupling dynamics model in the direction of the cable acting on the cable is established; and step 6, the amplitude of the cable in the direction is inversely solved. The climbing speed of the application is fast, and the application provides a theoretical reference for enhancing the adaptability of the cable climbing robot in the cable vibration environment caused by different natural winds.

Description

Technical Field

[0001] This invention belongs to the field of cable robot technology, and particularly relates to a cable vibration response solution method based on a coupled dynamics model and a cable climbing robot. Background Technology

[0002] Cable-stayed bridges and suspension bridges are new bridge types that have emerged in recent decades. Due to their excellent seismic performance and economic efficiency, they have been widely used worldwide. With the rapid development of transportation construction in my country, long-span bridges are increasingly appearing on rivers and lakes, and cable-stayed bridges and suspension bridges, as extra-large economic bridges, are commonly used. The cables, as the main components of these bridges, are almost entirely made of high-strength steel wire or strand, and can be considered the lifeline of the bridge; their safety is of paramount importance. However, the cables are exposed to the air for a long time, and the surface PE protective layer hardens and is damaged to varying degrees due to wind and rain. Subsequently, the internal steel wire bundles are corroded, and in severe cases, even wire breaks occur. In addition, the towers of modern cable-stayed bridges are over 300 meters high, and the cable length is over 650 meters. Due to wind vibration, rain vibration and other factors, the cable vibration is more intense. Many scholars at home and abroad have conducted field measurements on the dynamic response of bridge cables. The amplitude of some cables reaches 0.5m, while the amplitude of some bridge cables can reach 0.7m when the average wind speed is 6-10m / s. Especially in long-span cable-stayed bridges, these highly flexible and low-mass cables are more susceptible to the influence of random winds at high altitudes, resulting in large-amplitude vibrations. Such intense vibrations can also damage the cables.

[0003] Wind is the main cause of cable vibration. Most of the dynamic models in the existing technology are based on the structure and force characteristics of the robot and lack analysis of environmental interference factors. Specifically, the impact of cable vibration on the robot is not considered. Summary of the Invention

[0004] The purpose of this invention is to provide a cable vibration response solution method based on a coupled dynamics model and a cable-climbing robot, which offers fast climbing speed and provides a theoretical reference for enhancing the adaptability of cable-climbing robots to cable vibration environments caused by different natural winds. To achieve the above objective, the following solution is adopted:

[0005] A tilt-rotor flying cable-climbing robot, comprising:

[0006] The fuselage is fitted around the outer perimeter of the cable and can fly and hover along the outer wall of the cable at a set cable height.

[0007] The independent suspension mechanism is symmetrically arranged about the cable, with one set of independent suspension mechanisms hinged to the upper section of the body and the other set of independent suspension mechanisms hinged to the lower section of the body;

[0008] Each independent suspension mechanism includes two parallel steering brackets, the apex of which is hinged to the body. A support wheel is rotatably mounted between one end of the two steering brackets, and a first force transmission shaft is rotatably mounted between the other ends. A tension spring is mounted between the first and second force transmission shafts. The second force transmission shaft is rotatably mounted on the body.

[0009] The support wheel is used to drive the corresponding independent suspension mechanism to rotate. The support wheel has a V-shaped surface, and the V-shaped groove is used to clamp the cable.

[0010] The system includes a quadcopter drive mechanism that provides lift to drive the fuselage along the cable axis and achieves rotation and tilting. The four quadcopter drive mechanisms are symmetrically distributed along the circumference of the cable. Each quadcopter drive mechanism includes a servo motor fixed to the fuselage. The rotating end of the servo motor is connected to the housing of the duct fan. The motor of the duct fan is mounted on the housing, and its output end is connected to the duct fan. The line connecting the centers of the four duct fans forms a square. The two motors on the diagonal rotate in the same direction. The two adjacent motors rotate in opposite directions.

[0011] Preferably, the support wheel includes:

[0012] Two half-wheels, the two half-wheels form a V-shaped wheel;

[0013] The connecting rod passes through the V-shaped wheel and fixes the V-shaped wheel in the middle position of the connecting rod;

[0014] The end of the ram's horn frame connected to the V-shaped wheel is fixed with a bearing. The connecting rod is inserted into the bearings on both sides to enable the rotation of the support wheel.

[0015] Preferably, it further includes a self-locking mechanism, which comprises:

[0016] The clamp is fitted around the outer periphery of the cable below the machine body, and its top end is hinged to the T-shaped plate; one end of the T-shaped plate is rotatably mounted on the machine body;

[0017] The telescopic rod retracts to drive the clamp to grip the cable; its upper end connects to the machine body, and its lower end connects to the other end of the T-shaped plate.

[0018] A method for solving cable vibration response based on a coupled dynamics model of wind-cable-flying robot includes the following steps:

[0019] Step 1: Based on the tilt-rotor flying cable-climbing robot and the cable, establish a simplified model and introduce four coordinate systems based on the simplified model;

[0020] In the simplified model, the fuselage is simplified to a frame, the quadcopter drive mechanism is simplified to a motor, and the servo motor is simplified to a hinge point connecting the fuselage and the motor.

[0021] The four coordinate systems include: inertial coordinate system Cable coordinate system Body coordinate system Motor coordinate system ;

[0022] The origins of the inertial coordinate system {E} and the cable coordinate system {C} coincide.

[0023] The direction is the projection of the cable onto the horizontal plane, and the vector axis is in the same direction as gravity. With the vector axis pointing downwards along the cable axis The included angle between them is , It is the angle formed between the cable and the ground. Supplementary angle;

[0024] The body coordinate system {B} is attached to the body and moves with the flight robot. Its origin is the robot's center of mass. Perpendicular to , Pointing directly below the machine. and and This constitutes a right-handed coordinate system;

[0025] There are four motor coordinate systems {W}, with the origin located at the centroid of each of the four motors. Initially... , , The direction is the same as the direction of the body coordinate system {B};

[0026] Step 2: Based on the rotation matrix used for coordinate system transformation, which includes Euler angles (roll angle, pitch angle, and yaw angle), solve for the roll angle alignment of the airframe. The simplified rotation matrix;

[0027] The rotation matrix includes the rotation matrix from the body coordinate system {B} to the inertial coordinate system {E}. Transformation matrix from inertial coordinate system {E} to cable coordinate system {C} Rotation matrix from body coordinate system {B} to cable coordinate system {C} Rotation matrix from motor coordinate system {W} to body coordinate system {B} ;

[0028] Wherein, the rotation matrix before simplification :

[0029]

[0030] Simplified rotation matrix :

[0031] ;

[0032] Rotation matrix :

[0033]

[0034] Rotation matrix =Simplified rotation matrix Rotation matrix :

[0035] ;

[0036] Assume the motor tilts at an angle relative to its initial position. Therefore, the rotation matrix from the motor coordinate system {W} to the body coordinate system {B} is... for:

[0037] ;

[0038] in, for , for , The roll angle in the inertial coordinate system. The pitch angle in the inertial coordinate system. The yaw angle in the inertial coordinate system;

[0039] Step 3: Based on the simplified rotation matrix Rotation matrix Rotation matrix Solve for the along-axis forces acting on the flying robot in the cable coordinate system {C}. The resultant force F in the direction X ;

[0040] Among them, the resultant force acting on the flying robot in the cable coordinate system {C} This includes the flying robot's own gravity in the cable coordinate system. Support force acting on the support wheel Friction between the support wheel and the cable The lift generated by the four duct fans and air resistance ;

[0041] Specifically, the following steps are included:

[0042] Step 3A: Solve for the gravity expression in the cable coordinate system {C}. The sum of the lift generated by the four duct fans Specifically, it includes the following steps:

[0043] Solving the expression for gravity :

[0044] ;

[0045] ;

[0046] in, Let {E} be the gravitational acceleration in the inertial coordinate system {E}.

[0047] Solve for the sum of lift generated by the four duct fans. :

[0048]

[0049] W3-Z w The unit vector in the direction, C T -Lift coefficient;

[0050] Among them, T W - The sum of lifting forces along the z-axis in the motor coordinate system {W}: - The angular velocity of the motor;

[0051] Step 3B: Based on the Newton-Euler equations, solve for the equations along... The resultant force F in the direction X :

[0052]

[0053] ;

[0054] ;

[0055] ;

[0056] ;

[0057] ;

[0058] Therefore, F X =0;

[0059] Step 4: Establish a dynamic model of the flying robot-cable coupling in the body coordinate system. :

[0060]

[0061] Step 5: Based on the wind-cable coupling dynamics model and the flying robot-cable coupling dynamics model Establishing an effect along the cable Directional wind-cable-robot coupled dynamics model:

[0062] Among them, the wind-cable coupled dynamics model is as follows:

[0063] ;

[0064] quality is Flying robots at speed When climbing on the cable Wind-cable-robot coupled dynamics model in direction:

[0065] ;

[0066] -Inertial force; - Damping force; -Resilience;

[0067] Step 6: Obtain the pitch angle at the initial state using sensors. Real-time pitch angle during operation ;

[0068] Based on the solution The output value of the wind-cable-robot coupled dynamics model is obtained. The wind speed is then input into the wind-cable-robot coupled dynamics model to inversely calculate the cable speed along the [unclear - possibly a path or direction]. Amplitude in direction .

[0069] Preferably, step 6 further includes the following steps:

[0070] The servo motor control uses PID control;

[0071] If the difference between the initial pitch angle and the real-time pitch angle If positive, the servo rotates in the negative direction of the pitch angle. Degree; if If the value is negative, the servo will rotate in the positive direction of the pitch angle. Spend.

[0072] Preferably, step 3 further includes solving for the net external torque acting on the flying robot in the body coordinate system {B}. Steps;

[0073] Among them, the net external torque acting on the flying robot in the body coordinate system {B} Including the sum of lift torque Supporting force and torque Frictional torque ;

[0074] Due to the symmetry of the flying robot, air resistance does not generate torque; therefore, 4 The resultant torque is 0;

[0075] Treating the robot as a point mass, we can ignore its internal deformation; assuming that each support wheel is equidistant from the center of mass and experiences the same supporting force on each wheel, therefore, the four... The resultant torque is 0;

[0076] Therefore, it is only necessary to find the solution. , The specific solution process includes:

[0077] Step 31: In the motor coordinate system {W}, solve for the angular velocity of the machine body when the rolling angle is 0°. :

[0078]

[0079] ;

[0080] Step 32: In the motor coordinate system {W}, solve for the system input U:

[0081] ;

[0082] ;

[0083] in, - The angular velocity of the motor;

[0084] The sum of the total torque of the four motors, the component of the sum of the total torque along the X direction, the component of the sum of the total torque along the Y direction, and the resistance torque along the Z direction are arranged in sequence to form the following matrix U;

[0085] Step 33, based on U and Solve :

[0086] .

[0087] Compared with the prior art, the advantages of the present invention are:

[0088] 1. The flying cable inspection robot uses a non-powered wheeled support module. All climbing power comes from four ducted fans in the quadcopter drive mechanism, significantly improving climbing speed and preventing the wheeled support module from scratching the cable surface when clamping force increases. In contrast, existing cable inspection robots rely on the friction between the wheels and the cable to climb, which is prone to slippage and results in very slow climbing speed.

[0089] 2. Taking a flying cable-climbing robot powered by a quadcopter mechanism consisting of four pipe fans as the research object, a coupled dynamic model of the flying robot and the cable is established. Finally, based on the principle that the climbing of the flying robot will induce forced vibration of the cable, and the vibration of the cable will also affect the climbing stability of the robot, a coupled dynamic model of wind-cable-robot is established.

[0090] By monitoring the pitch angle, the lifting force is always parallel to the cable axis. The purpose of this is: the lifting force will not act on the cable, meaning the robot moves forward against the cable; the tension of the spring will not be affected by the lifting force. If the spring experiences a sudden increase in force under the lifting force, it may break.

[0091] The characteristics of cable vibration under different wind speeds and the impact of cable vibration on the climbing stability of the flying robot were analyzed through simulation.

[0092] 3. The quadcopter drive mechanism and the T-plate have multiple fixing holes, which can continuously adjust the relative positions of the internal structures of the robot according to the diameter of the cable to be tested, so as to adapt to the operation of different cable diameters.

[0093] 4. The spring is fixed to the tension transmission shaft on the quadcopter drive mechanism and the tension transmission shaft at one end of the ram's horn frame, and the ram's horn frame can rotate to provide clamping force to the wheels to clamp the cable, so that the wheels always clamp the cable, enabling the robot to overcome obstacles, while ensuring that the flying cable robot can climb along the cable direction and will not deviate from the predetermined direction.

[0094] 5. The self-locking mechanism not only ensures that the flying cable robot stays on the cable surface, but also transforms the flying cable inspection robot into a fixed anchor point for a heavy-duty robot carrying heavy inspection equipment when heavy inspection equipment such as magnetic flux leakage detectors are needed. The two are connected by a traction rope, and the heavy-duty robot climbs upward by retracting the winch, greatly improving the robot's load capacity. Attached Figure Description

[0095] Figure 1 A 3D view of a tiltrotor flying cable-climbing robot;

[0096] Figure 2 Force analysis diagram for independent suspension mechanism;

[0097] Figure 3 This is a schematic diagram of an independent suspension mechanism.

[0098] Figure 4 This is a side view of the self-locking mechanism structure;

[0099] Figure 5 This is a three-dimensional diagram of the self-locking mechanism.

[0100] Figure 6 Establishment of coordinate system and force analysis diagram;

[0101] Figure 7 This is a diagram of the wind-cable coupling dynamics model.

[0102] Figure 8 The response changes at the midpoint of the cable;

[0103] Figure 9 The response changes of the wind-cable-flying robot coupled dynamics model;

[0104] Figure 10 The spring stretching changes under different wind speeds;

[0105] Figure 11 The changes in spring tension under the same wind speed;

[0106] Figure 12 This is a PID control graph;

[0107] Figure 13 The principle for solving the middle two rows of matrix U;

[0108] Figure 14 A side view of a tiltrotor flying cable-climbing robot;

[0109] Figure 15 This is a schematic diagram illustrating the principle of solving rotation matrices in existing technologies.

[0110] Among them, 1-support wheel, 2-tension spring, 3-horn frame, 4-hinge, 5-telescopic rod, 6-T-shaped plate, 7-duct fan; 8-gripper, 9-electronic box, 10-second tension transmission shaft, 11-first tension transmission shaft, 12-servo motor. Detailed Implementation

[0111] The cable vibration response solution method based on a coupled dynamics model and the cable-climbing robot of the present invention will be described in more detail below with reference to the schematic diagrams, which illustrate preferred embodiments of the present invention. It should be understood that those skilled in the art can modify the present invention described herein while still achieving the advantageous effects of the present invention. Therefore, the following description should be understood as being of general knowledge to those skilled in the art and is not intended to limit the present invention.

[0112] like Figures 1-7 A tilt-rotor flying cable-climbing robot, comprising:

[0113] The fuselage is fitted around the outer perimeter of the cable and can hover along the outer wall of the cable at a set cable height.

[0114] The body can be connected by hinges and latches (there are two hinges on one side and two latches on the other side, such as...). Figure 14 (As shown) The quadcopter opens and closes in half, with independent suspension mechanisms and self-locking mechanisms connected to both sides of the fuselage. The fuselage has mounting holes, and the electronics boxes are located below the quadcopter drive mechanism on both sides, without covers. The electronics boxes house the flight control board, a lidar for measuring the aircraft's altitude, two lithium battery packs (powering the ducted fans) placed separately on the two electronics boxes for even weight distribution, and various electronic devices. The fuselage has 12mm diameter mounting holes (connecting to cylinders extending to both sides from one end of the T-shaped plate). Appropriate mounting holes can be selected based on the cable diameter to adjust the position of the independent suspension mechanisms and self-locking mechanisms relative to the quadcopter drive mechanism.

[0115] The independent suspension system is symmetrically arranged about the cables, with one set of independent suspension mechanisms hinged to the upper section of the chassis and the other set of independent suspension mechanisms hinged to the lower section of the chassis.

[0116] Each independent suspension mechanism includes two parallel saddles, and the four saddles move synchronously.

[0117] The apex of the ram's horn frame is hinged to the machine body. A support wheel is rotatably mounted between one end of the two ram's horn frames, and a first tension transmission shaft is rotatably mounted between the other ends. A tension spring is mounted between the first and second tension transmission shafts. The tension spring provides the support wheel with the clamping force of the cable. The second tension transmission shaft is rotatably mounted on the machine body.

[0118] The support wheel is used to drive the corresponding independent suspension mechanism to rotate. The support wheel has a V-shaped surface and the V-shaped groove is used to clamp the cable, making the robot's climbing on the cable more stable, less prone to slipping, and less prone to deviation.

[0119] The support wheels include:

[0120] Two half-wheels, the two half-wheels form a V-shaped wheel;

[0121] The connecting rod passes through the V-shaped wheel and fixes the V-shaped wheel in the middle position of the connecting rod;

[0122] The end of the ram's horn frame connected to the V-shaped wheel is fixed with a bearing. The connecting rod is inserted into the bearings on both sides to enable the rotation of the support wheel.

[0123] During its ascent, the flying cable inspection robot encounters obstacles caused by cable damage, with boss-type obstacles being the most difficult to overcome. The robot's spurs can rotate relative to each other at the joints. When encountering a boss obstacle, the cable's surface diameter changes, causing the support wheels to rotate, extending the tension springs, increasing the clamping force, and allowing for better adhesion to the cable surface, thus enabling the robot to overcome the obstacle. During obstacle crossing, the duct fan provides sufficient driving force to allow the wheels to smoothly climb over the boss.

[0124] The independent suspension mechanism allows each wheel to respond individually and overcome obstacles independently with minimal mutual interference, thus improving the robot's stability during cable-stayed ascent and providing excellent climbing performance.

[0125] The quadcopter drive mechanism provides lift to drive the robot body along the cable axis and achieves rotation and tilting. The quadcopter drive mechanisms are symmetrically distributed circumferentially along the cable. Each quadcopter drive mechanism includes a servo motor fixed to the robot body. The rotating end of the servo motor is connected to the housing of the duct fan. The motor of the duct fan is mounted on the housing, and its output end is connected to the duct fan. The line connecting the centers of the four duct fans forms a square. The two motors on the diagonals rotate in the same direction; adjacent motors rotate in opposite directions. The thrust of a single duct fan 7 is 4.8 kg, and the four duct fans can support a robot weight of 19.2 kg. Each duct fan 7 can rotate under the drive of the servo motor, ensuring that the lift direction is always parallel to the cable axis, i.e., ensuring that the airflow is always parallel to the cable.

[0126] Driven by a ducted fan, the robot no longer relies on the friction between the wheels and the cable to climb. Therefore, an independent suspension mechanism without power (existing robots use motors to drive the wheels, and the motors and wheels are connected by a conveyor belt; in this embodiment, the power is provided by the ducted fan, and the wheels are only used to ensure that the robot climbs along the cable direction) is used to keep the robot moving along the cable axis.

[0127] The self-locking mechanism consists of two identical parts, symmetrically distributed along the cable. It includes four telescopic rods, two T-plates, and two grippers. When the telescopic rods retract, the grippers open. When the robot needs to be secured to the cable, the telescopic rods extend, clamping the cable and completing the self-locking process. Specifically, it includes:

[0128] The clamp is fitted around the cable at the bottom of the machine body, and its top end is hinged to a T-shaped plate; one end of the T-shaped plate is rotatably mounted on the machine body. That is, the other end of the T-shaped plate extends to both sides and inserts into the fixing holes located on the machine body, ensuring that the T-shaped plate can rotate.

[0129] The telescopic boom, which retracts to drive the gripper to tighten the cable, connects at its upper end to the fuselage and at its lower end to the other end of a T-plate. The T-plate is inserted into the fixing hole of the quadcopter drive mechanism.

[0130] When the telescopic rod retracts, the gripper opens. When the robot needs to be secured to the cable, the telescopic rod 5 extends to clamp the cable, completing the self-locking process. The T-shaped plate is T-shaped with fixing holes on its surface, allowing it to change shape. One end is connected to two telescopic rods, the other end is connected to the gripper, and the other end extends outwards on both sides and inserts into the fixing holes of the quadcopter drive mechanism.

[0131] The self-locking mechanism not only ensures that the flying cable robot stays on the cable surface, but also transforms the flying cable inspection robot into a fixed anchor point for a heavy-duty robot carrying heavy inspection equipment when heavy inspection equipment such as magnetic flux leakage detectors are needed. The two are connected by a traction rope, and the heavy-duty robot climbs upward by retracting a winch, lifting the robot carrying a load of more than 40 kg.

[0132] The cable vibration response solution method based on the coupled dynamics model of wind-cable-flying robot includes the following steps:

[0133] Step 1: Based on the tilt-rotor flying cable-climbing robot and the cable, establish a simplified model and introduce four coordinate systems based on the simplified model.

[0134] In the simplified model, the fuselage is simplified to a frame, the quadcopter drive mechanism is simplified to a motor, and the servo is simplified to a hinge point connecting the fuselage and the motor. Figure 3 In the middle, the spring tension .

[0135] The four coordinate systems include: inertial coordinate system Cable coordinate system Body coordinate system Motor coordinate system ;

[0136] The origins of the inertial coordinate system {E} and the cable coordinate system {C} coincide.

[0137] The direction is the projection of the cable onto the horizontal plane, and the vector axis is in the same direction as gravity. With the vector axis pointing downwards along the cable direction The included angle between them is , It is the angle formed between the cable and the ground. Supplementary angle;

[0138] The body coordinate system {B} is attached to the body and moves with the flight robot. Its origin is the robot's center of mass. Perpendicular to , Pointing directly below the machine. and and This constitutes a right-handed coordinate system;

[0139] There are four motor coordinate systems {W}, with the origin located at the centroid of each of the four motors. Initially... , , The direction is the same as the direction of the body coordinate system {B}.

[0140] Step 2: Based on the rotation matrix used for coordinate system transformation, which includes Euler angles (roll angle, pitch angle, and yaw angle), solve for the roll angle alignment of the airframe. The simplified rotation matrix;

[0141] The rotation matrix includes the rotation matrix from the body coordinate system {B} to the inertial coordinate system {E}. Transformation matrix from inertial coordinate system {E} to cable coordinate system {C} Rotation matrix from body coordinate system {B} to cable coordinate system {C} Rotation matrix from motor coordinate system {W} to body coordinate system {B} ;

[0142] Wherein, the rotation matrix before simplification :

[0143] ;

[0144] Because the support wheels have a "V"-shaped structure, they can make contact with the cable over a larger area and prevent the robot from easily getting tangled when moving along the cable. The axis rotates, meaning that during the upward climbing process of the flying robot, the roll angle of the body approaches 0°.

[0145] Simplified rotation matrix :

[0146] ;

[0147] Rotation matrix :

[0148] .

[0149] like Figure 15 As shown, its solution process belongs to existing technology. Length is :

[0150]

[0151] Rotation matrix =Simplified rotation matrix Rotation matrix :

[0152] ;

[0153] Assume the motor tilts at an angle relative to its initial position. Therefore, the rotation matrix from the motor coordinate system {W} to the body coordinate system {B} (the w coordinate system rotates counterclockwise around the yw axis) Get b) for:

[0154] ;

[0155] in, for , for , The roll angle in the inertial coordinate system. The pitch angle in the inertial coordinate system. This is the yaw angle in the inertial coordinate system.

[0156] The solution process is the same as the rotation matrix mentioned above. The solution process is the same.

[0157] Step 3: Based on the simplified rotation matrix Rotation matrix Rotation matrix Solve for the along-axis forces acting on the flying robot in the cable coordinate system {C}. The resultant force F in the direction X ;

[0158] Among them, the resultant force acting on the flying robot in the cable coordinate system {C} This includes the flying robot's own gravity in the cable coordinate system. Support force acting on the support wheel Friction between the support wheel and the cable The lift generated by the four duct fans and air resistance . , All along direction.

[0159] Specifically, the following steps are included:

[0160] Step 3A: Solve for the gravity expression in the cable coordinate system {C}. The sum of the lift generated by the four duct fans Specifically, it includes the following steps:

[0161] Solving the expression for gravity :

[0162] ;

[0163] ;

[0164] in, Let {E} be the gravitational acceleration in the inertial coordinate system {E}.

[0165] Solve for the sum of lift generated by the four duct fans. :

[0166] ;

[0167] W3-Z w The unit vector in the direction, C T - Lift coefficient.

[0168] The thrust generated by the motor is always parallel to the cable, meaning that Zw is always parallel to Zc, i.e., w and c are in the same coordinate system.

[0169] Among them, T W - The sum of lifting forces along the z-axis in the motor coordinate system {W}: - The angular velocity of the motor;

[0170] Step 3B: Solve for F based on the Newton-Euler equations. X :

[0171] ;

[0172] ;

[0173] ;

[0174] ;

[0175] ;

[0176] ;

[0177] Therefore, F X =0;

[0178] From the above, we can see that: the two in the upper section sum , exist The directional components of the force cancel each other out.

[0179] The sum of the support forces in the cable coordinate system (only the two support wheels in the upper section are subject to support forces). , , They are respectively:

[0180] ; for Unit vector in the direction;

[0181] ; refers to the two frictional forces in the upper section. sum;

[0182] - Unit vector in the direction; - The coefficient of friction of the cable surface;

[0183]

[0184] Is the velocity v in Z c Components in direction;

[0185] Among them, flying robots are characterized by speed Climbing upwards, and thanks to the presence of "V"-shaped support wheels, the flying robot only... , It performs translational motion in the direction, and Translational motion in the direction is relatively small. The air friction resistance in the direction can be ignored.

[0186] b3 is Unit vector in the direction; This is the wind resistance coefficient.

[0187] Step 4: Establish a dynamic model of the flying robot-cable coupling in the body coordinate system. :

[0188] ;

[0189] From the above, we can see that the weight of the machine is in The component force on the axis is canceled out by the total support force; therefore, the cable along... The external forces acting in the direction include the weight of itself along the direction. Component of the force in direction, along the edge acting on the flying robot The resultant force F in the direction X .

[0190] According to existing technology, as a rigid body, the forces and torques acting on the flying robot are controlled by the Newton-Euler equations:

[0191]

[0192] in, For the quality of the flying robot, Let be the linear velocity of the flying robot in the cable coordinate system. Let {C} be the resultant force acting on the flying robot in the cable coordinate system {C}. The inertia matrix of the flying robot. Let be the angular velocity of the flying robot in the body coordinate system. This is the net external torque acting on the flying robot in the body coordinate system.

[0193] Step 5: Based on the wind-cable coupling dynamics model and the flying robot-cable coupling dynamics model Establishing an effect along the cable Directional wind-cable-robot coupled dynamics model:

[0194] Among them, the wind-cable coupled dynamics model (existing technology):

[0195] .

[0196] The mass per unit length of the cable is , diameter is stiffness is Damping is .

[0197] Specifically, for The component of the force on the plane orthogonal to the plane of motion, with an angle of attack of θ. . and It can be represented in the following form:

[0198]

[0199] Assume the vertical vibration velocity of the cable is The relative wind speed can be obtained. and relative wind angle of attack :

[0200]

[0201] Therefore, the vertical aerodynamic force (existing technology) is obtained:

[0202]

[0203] in air density, For gravity, , These are the lift coefficient and drag coefficient, respectively. , The value can be: , , , , , , , .

[0204] According to d'Alembert's principle, the equation for the vertical vibration of a cable is:

[0205] .

[0206] quality is Flying robots at speed When climbing on the cable Wind-cable-robot coupled dynamics model in direction:

[0207] ;

[0208] in, - During the vibration process, the cable is subjected to aerodynamic forces;

[0209] -Inertial force; - Damping force; -Resilience.

[0210] Step 6: Obtain the pitch angle at the initial state using sensors. Real-time pitch angle during operation ;

[0211] Depend on and The output value of the wind-cable-robot coupled dynamics model is obtained. The wind speed is then input into the wind-cable-robot coupled dynamics model to inversely calculate the cable speed along the [unclear - possibly a path or direction]. Amplitude in direction .

[0212] The servo control uses PID control.

[0213] like Figure 12 If the difference between the initial pitch angle and the real-time pitch angle is... If positive, the servo rotates in the negative direction of the pitch angle. Degree; if If the value is negative, the servo will rotate in the positive direction of the pitch angle. Spend.

[0214] Furthermore, step 3 also includes solving for the net external torque acting on the flying robot in the body coordinate system {B}. Steps;

[0215] Among them, the net external torque acting on the flying robot in the body coordinate system {B} Including the sum of lift torque Supporting force and torque Frictional torque ;

[0216] Due to the symmetry of the flying robot, air resistance does not generate torque, and the inertial matrix... It is a diagonal matrix, therefore, 4 The resultant torque is 0;

[0217] Treating the robot as a point mass, we can ignore its internal deformation; assuming that each support wheel is equidistant from the center of mass and experiences the same supporting force on each wheel, therefore, the four... The resultant torque is 0;

[0218] Therefore, it is only necessary to find the solution. , The specific solution process includes:

[0219] Step 31: In the motor coordinate system {W}, solve for the angular velocity of the machine body when the rolling angle is 0°. :

[0220]

[0221] ;

[0222] Step 32: In the motor coordinate system {W}, solve for the system input U, such as... Figure 13 :

[0223] ;

[0224] ;

[0225] in, - The angular velocity of the motor;

[0226] The sum of the total torque of the four motors, the component of the sum of the total torque along the X direction, the component of the sum of the total torque along the Y direction, and the resistance torque along the Z direction are arranged in sequence to form the following matrix U;

[0227] Step 33, based on U and Solve :

[0228] .

[0229] The last row of the matrix represents the resistance torque in the z-direction. If the fan blades rotate counterclockwise, the resistance will be opposite, as shown in the diagram above. According to the right-hand rule, if the thumb points in the z-axis direction, the rotation direction is negative if it is the same as the direction the four fingers are bent, and positive if it is opposite.

[0230] Finally, Euler's formula is used to determine the relationship between torque and rotation.

[0231] Based on the above, the complete robot dynamics model obtained in step 3 is as follows:

[0232]

[0233] Inertia matrix It is a diagonal matrix.

[0234] The last two formulas are used during fuselage control.

[0235] Force analysis of independent suspension mechanism:

[0236] Force analysis of independent suspension mechanism as follows Figure 2 As shown, the mechanism contains a cable supporting the support wheel with a force N and a tension spring exerting a tensile force F on the ram's horn. According to the design, , , , The length of the stretched spring in the initial state .

[0237] Assume the height of the obstacle to be climbed is The stretching of the spring can be obtained. for:

[0238] The spring tension can be obtained from the above formula. Furthermore, the supporting force can be obtained from the principle of torque balance and trigonometric functions. With spring tension The relationship between them can be represented as:

[0239] ;

[0240] The supporting force on the support wheel can be obtained by combining the formula. With spring tension The relationship between them is approximately as follows:

[0241] .

[0242] Simulation Analysis: To investigate the impact of different wind speeds on the wind-cable-flying robot coupling system and the performance of the independent suspension mechanism in maintaining fuselage attitude and climb stability under cable vibration conditions, wind speeds of Beaufort scale 3 (4.3 m / s) and 6 (12.2 m / s) were selected as the research objects. The relevant parameters of the selected cable and flying robot are shown in Table 1.

[0243] Table 1 Cable Parameters

[0244]

[0245] The effect of different wind speeds on cable vibration:

[0246] Because the vibration characteristics of the cable differ significantly at different locations, the middle section, where the vibration response is most pronounced, is selected as the research object. The AR linear filtering method is used to simulate the pattern of fluctuating wind, and the fourth-order Runge-Kutta method is used to obtain the cable's response at different wind speeds. Figure 8 As shown.

[0247] The results show that the vibration frequency of the cable under a force 3 wind is approximately The amplitude is approximately The frequency under the influence of a Force 6 wind is The amplitude is approximately Its variation curve approximates a sine function.

[0248] When the robot The speed increases during the ascent in the middle section of the cable, i.e., when the flying robot is added to the aforementioned wind-cable coupling system. The response of the cable carrying the flying robot at different wind speeds is obtained, such as... Figure 9 As shown.

[0249] The results show that when the robot is climbing the cable, the vibration frequency under a level 3 wind is approximately The amplitude is approximately The frequency under the influence of a Force 6 wind is The amplitude is approximately Its variation curve approximates a sine function.

[0250] Stability analysis of robot climbing under cable vibration:

[0251] Cable vibration can affect the climbing stability of a robot. During vibration, the cable's own weight and vibrational acceleration exert a force on the support wheel. The magnitude of the force transmitted through the ram's horn to the tension spring can be obtained, thus determining the tension spring's extension. The tension spring's extension condition effectively reflects the robot's current posture; that is, the smaller the tension spring's extension under the cable's vibration force, the better the robot's climbing stability.

[0252] like Figure 10 As shown in the figure, the stiffness is... The tension of the tension spring under cable vibration caused by different wind speeds.

[0253] The results show that the maximum tensile force of the tension spring under a force 3 wind is Under the influence of a force 6 wind, the maximum stretch is .

[0254] like Figure 11 As shown in the figure, this diagram illustrates two springs with different stiffnesses. , The tension of the cable under the same wind speed (level 3 wind) caused by vibration.

[0255] The results show that stiffness The maximum stretch of the tension spring under a force 3 wind is Significantly smaller than tension spring The maximum amount of stretching.

[0256] Simulations of the coupled dynamics model using MATLAB yielded two conclusions: First, wind induces cable vibration, and the impact of wind on cable vibration increases as the robot climbs the cable. Second, in a cable vibration environment, selecting springs with higher stiffness is beneficial to the robot's climbing stability.

[0257] The above are merely preferred embodiments of the present invention and do not constitute any limitation on the present invention. Any equivalent substitutions or modifications made by those skilled in the art to the technical solutions and content disclosed in the present invention without departing from the scope of the present invention shall be deemed to have remained within the protection scope of the present invention.

Claims

1. A cable vibration response solution method based on the coupling dynamics model of the wind-cable-flight robot, characterized in that, Includes the following steps: Step 1: Based on the tilt-rotor flying cable-climbing robot and the cable, establish a simplified model and introduce four coordinate systems based on the simplified model; In the simplified model, the fuselage is simplified to a frame, the quadcopter drive mechanism is simplified to a motor, and the servo motor is simplified to a hinge point connecting the fuselage and the motor. The four coordinate systems include: an inertial coordinate system , a cable coordinate system , a body coordinate system , and a motor coordinate system ; The origins of the inertial coordinate system {E} and the cable coordinate system {C} coincide. The direction is the projection of the cable onto the horizontal plane, and the vector axis is in the same direction as gravity. With the vector axis pointing downwards along the cable axis The included angle between them is , It is the angle formed between the cable and the ground. Supplementary angle; The body coordinate system {B} is attached to the body and moves with the motion of the flying robot, with the origin being the robot's center of mass, perpendicular to , pointing straight down, with and forming a right-handed coordinate system; There are four motor coordinate systems {W}, whose origins are located at the mass center of the four motors, and their initial states are the same as the direction of the body coordinate system {B}. , , the direction of the body coordinate system {B}. Step 2, solve the roll angle of the body based on the simplified rotation matrix including the Euler angles of roll, pitch, and yaw angles for coordinate system transformation; The rotation matrix includes the rotation matrix from the body coordinate system {B} to the inertial coordinate system {E}. The transformation matrix from the inertial coordinate system {E} to the cable coordinate system {C} Rotation matrix from body coordinate system {B} to cable coordinate system {C} Rotation matrix from motor coordinate system {W} to body coordinate system {B} ; wherein the rotation matrix before simplification : ; simplified rotation matrix : ； Rotation matrix : ; Rotation matrix =Simplified rotation matrix Rotation matrix : ； Let the angle of the motor tilt from the initial position be The rotation matrix of the motor coordinate system {W} to the body coordinate system {B} is therefore ​ ； wherein is , is , is a roll angle in an inertial coordinate system, is a pitch angle in an inertial coordinate system, is a yaw angle in an inertial coordinate system; Step 3, based on the simplified rotation matrix , rotation matrix , rotation matrix , solving the resultant force F in the direction of the cable coordinate system {C} acting on the flying robot body X ;​ Among them, the resultant force acting on the flying robot in the cable coordinate system {C} This includes the flying robot's own gravity in the cable coordinate system. Support force acting on the support wheel Friction between the support wheel and the cable The lift generated by the four duct fans and air resistance ; Specifically, the following steps are included: Step 3A, solving the gravity expression in cable coordinate system {C} the sum of the lift forces generated by the four duct fans and specifically comprising the steps of: Solving the gravitational expression : ; ; wherein g is the gravitational acceleration in the inertial frame {E}; solving for the sum of the lift generated by the four ducted fans : ； W3-Z w unit vector in the direction of C T - lift coefficient; where T W - the sum of the lift forces in the z-axis of the motor coordinate system {W}: - the angular velocity of the motor; Step 3B, based on Newton-Euler equations, solve for the resultant force F in the direction of the velocity vector v X : ; ； ； ； ； ； So, F X =0; Step 4, Establish the flight robot-cable coupling dynamics model under the body coordinate system : ； Step 5, based on the wind-cable coupling dynamics model and the flying robot-cable coupling dynamics model , the wind-cable-robot coupling dynamics model in the direction of the action on the cable is established ​ Among them, the wind-cable coupled dynamics model is as follows: ； mass is flying robots to move at speeds wind-cable-robot coupling dynamics model in direction while climbing on a cable: ； - inertial forces; - damping forces; - restoring forces; Step 6, pitch angle at initial state acquisition by sensor real-time pitch angle during operation ; Based on the solution The output value of the wind-cable-robot coupled dynamics model is obtained. The wind speed is then input into the wind-cable-robot coupled dynamics model to inversely calculate the cable speed along the [unclear - possibly a path or direction]. Amplitude in direction .

2. The cable vibration response solution method based on the wind-cable-flight robot coupling dynamics model according to claim 1, characterized in that, Step 6 also includes the following steps: The servo motor control uses PID control; If the difference between the pitch angle at the initial state and the real-time pitch angle is positive , the steering gear rotates toward the negative direction of the pitch angle by a certain degree; if , the steering gear rotates toward the positive direction of the pitch angle by a certain degree.

3. The cable vibration response solution method based on the wind-cable-flying robot coupled dynamics model according to claim 1, characterized in that, The step of solving the resultant external moment acting on the flying robot in the body coordinate system {B} is also included in step 3 ; Wherein, the resultant external moment acting on the flying robot in the body coordinate system {B} Including the sum of lift moments , support force moments , friction force moments ; Due to the symmetry of the flying robot, the air resistance does not generate a moment, thus, the 4 resultant moments are 0; Treating the robot as a point mass, we can ignore its internal deformation; assuming that each support wheel is equidistant from the center of mass and experiences the same supporting force on each wheel, therefore, the four... The resultant torque is 0; Thus, only the solution of , The specific solution process of the above equation includes: Step 31, in the motor coordinate system {W}, solve the body angular velocity when the roll angle is 0° : ; ； Step 32: In the motor coordinate system {W}, solve for the system input U: ； ； wherein, - an angular velocity of the electric machine; The sum of the total torque of the four motors, the component of the sum of the total torque along the X direction, the component of the sum of the total torque along the Y direction, and the resistance torque along the Z direction are arranged in sequence to form the following matrix U; Step 33, based on U and , solve for : 。 4. A tilt-rotor cable-climbing robot based on the cable vibration response solution method based on the wind-cable-flight robot coupling dynamics model according to any one of claims 1-3, characterized in that, include: The fuselage is fitted around the outer perimeter of the cable and can fly and hover along the outer wall of the cable at a set cable height. The independent suspension mechanism is symmetrically arranged about the cable, with one set of independent suspension mechanisms hinged to the upper section of the body and the other set of independent suspension mechanisms hinged to the lower section of the body; Each independent suspension mechanism includes two parallel steering brackets, the apex of which is hinged to the body. A support wheel is rotatably mounted between one end of the two steering brackets, and a first force transmission shaft is rotatably mounted between the other ends. A tension spring is mounted between the first and second force transmission shafts. The second force transmission shaft is rotatably mounted on the body. The support wheel is used to drive the corresponding independent suspension mechanism to rotate. The support wheel has a V-shaped surface, and the V-shaped groove is used to clamp the cable. The quadcopter drive mechanism provides lift to drive the fuselage to move along the cable axis and achieve rotation and tilting. The quadcopter drive mechanisms are symmetrically distributed along the circumference of the cable. Each quadcopter drive mechanism includes a servo motor fixed to the fuselage. The rotating end of the servo motor is connected to the housing of the duct fan. The motor of the duct fan is mounted on the housing, and its output end is connected to the duct fan. The line connecting the centers of the four duct fans forms a square. The two motors on the diagonal rotate in the same direction. The two adjacent motors rotate in opposite directions.

5. The yaw-rotor cable-climbing robot of claim 4, wherein, The support wheel includes: Two half-wheels, the two half-wheels form a V-shaped wheel; The connecting rod passes through the V-shaped wheel and fixes the V-shaped wheel in the middle position of the connecting rod; The end of the ram's horn frame connected to the V-shaped wheel is fixed with a bearing. The connecting rod is inserted into the bearings on both sides to enable the rotation of the support wheel.

6. The yaw-rotor cable-climbing robot of claim 4, wherein, It also includes a self-locking mechanism, which includes: The clamp is fitted around the outer periphery of the cable below the machine body, and its top end is hinged to the T-shaped plate; one end of the T-shaped plate is rotatably mounted on the machine body; The telescopic rod retracts to drive the clamp to grip the cable; its upper end connects to the machine body, and its lower end connects to the other end of the T-shaped plate.

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