CN113513557A - Magnetorheological damper and loading force control method under wind load vibration - Google Patents

Magnetorheological damper and loading force control method under wind load vibration Download PDF

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CN113513557A
CN113513557A CN202110618809.0A CN202110618809A CN113513557A CN 113513557 A CN113513557 A CN 113513557A CN 202110618809 A CN202110618809 A CN 202110618809A CN 113513557 A CN113513557 A CN 113513557A
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cable
damper
robot
magnetorheological
piston rod
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徐丰羽
常天水
林金星
吕凡
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Nanjing University of Posts and Telecommunications
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Nanjing University of Posts and Telecommunications
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F13/00—Units comprising springs of the non-fluid type as well as vibration-dampers, shock-absorbers, or fluid springs
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F9/00—Springs, vibration-dampers, shock-absorbers, or similarly-constructed movement-dampers using a fluid or the equivalent as damping medium
    • F16F9/32—Details
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F9/00—Springs, vibration-dampers, shock-absorbers, or similarly-constructed movement-dampers using a fluid or the equivalent as damping medium
    • F16F9/32—Details
    • F16F9/3207—Constructional features
    • F16F9/3235—Constructional features of cylinders
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F9/00—Springs, vibration-dampers, shock-absorbers, or similarly-constructed movement-dampers using a fluid or the equivalent as damping medium
    • F16F9/32—Details
    • F16F9/50—Special means providing automatic damping adjustment, i.e. self-adjustment of damping by particular sliding movements of a valve element, other than flexions or displacement of valve discs; Special means providing self-adjustment of spring characteristics
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F9/00—Springs, vibration-dampers, shock-absorbers, or similarly-constructed movement-dampers using a fluid or the equivalent as damping medium
    • F16F9/32—Details
    • F16F9/53—Means for adjusting damping characteristics by varying fluid viscosity, e.g. electromagnetically
    • F16F9/535—Magnetorheological [MR] fluid dampers
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F2222/00—Special physical effects, e.g. nature of damping effects
    • F16F2222/12—Fluid damping

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  • Engineering & Computer Science (AREA)
  • General Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Physics & Mathematics (AREA)
  • Electromagnetism (AREA)
  • Bridges Or Land Bridges (AREA)

Abstract

The invention discloses a magnetorheological damper and a loading force control method under wind load vibration, which comprises the following steps of 1, installing the magnetorheological damper; step 2, establishing a coordinate system; step 3, establishing a wind vibration model; step 4, establishing an adjusting model; step 5, measuring the speed; and 6, adjusting the loading force of the magnetorheological damper. According to the method, the magnetic induction intensity of the corresponding magneto-rheological damper is calculated by establishing a cable-robot coupling dynamic model in a vibration environment according to the wind speed and the climbing speed and combining the established wind vibration model and the established regulation model; then, the magnetic induction intensity is adjusted, and the loading force of the magnetorheological damper is further adjusted, so that the roller is pressed on the surface of the inhaul cable, and the slipping phenomenon is avoided.

Description

Magnetorheological damper and loading force control method under wind load vibration
Technical Field
The invention relates to the technical field of cable-stayed bridge cable detection, in particular to a magnetorheological damper and a loading force control method under wind load vibration.
Background
Scholars at home and abroad do a great deal of work on the aspects of design, dynamics research and the like of the guy cable detection robot, climbing mechanisms of the guy cable detection robot can be divided into three types, namely a roller type, a creeping type and a bionic type, and the clamping modes of most mechanisms are loaded by springs. The roller type robot has the advantages of light structure, low energy consumption, high climbing speed and the like, so that the roller type robot is concerned by more and more research workers, and a few bridge detection mechanisms are used for detecting the surface of a bridge cable at present. Although researchers have conducted a great deal of research on roller robots, there are still some problems that require further research.
Firstly, the cable detection robot studied at present usually uses a spring to clamp on the surface of a cable, and the clamping force of the robot is changed under the influence of vibration, so that the climbing stability of the robot is influenced, and the problems of unclear shaking of the detected image and the like are caused. Therefore, the vibration damping mechanism is designed to solve the problem that the robot causes self vibration under the condition of stay cable vibration, and the important problem of the current stay cable detection robot is solved.
Secondly, although many researches related to kinematics and dynamics of the guy cable detection robot are available, the researches mainly focus on the mechanism driving performance and the obstacle crossing performance, the influence caused by guy cable vibration is less considered, and the problem of climbing stability of the robot is not solved. Especially, modern stayed-cable bridge structures are developing towards the direction of large span, light structure and low damping, are more sensitive to random disturbance of high-altitude wind load, bridge deck vehicles and the like, and can generate various types of vibration under the excitation of the high-altitude wind load and the vibration of cable towers. Some students consider the influence of line vibration on robot movement in robot research similar to a high-voltage line inspection robot, but the robot and a guy cable detection robot are different in force loading mode, so that the influence of the line on the robot and the designed solution are different. Therefore, considering the action of the guy cable on the robot is an important content for researching the dynamics of the robot.
The stay cable of the large-span cable-stayed bridge is a flexible long straight stress member and is easy to generate different forms of vibration under the influence of high-altitude wind load. Most of force loading mechanisms of currently researched stay cable detection robots generate clamping force through springs and are adhered to the surfaces of stay cables to climb. Indoor experiments on the robot clamped by the spring show that the robot with the mechanism easily generates the change of clamping force under the inhaul cable vibration environment, so that the robot slips due to insufficient clamping force in the climbing process.
Disclosure of Invention
The invention aims to solve the technical problems of the prior art and provides a magnetorheological damper and a loading force control method under wind load vibration. In addition, the coupled vibration characteristics of the robot and the inhaul cable are analyzed, and a vibration damping mechanism is researched and designed to ensure that the robot climbs stably and safely.
In order to solve the technical problems, the invention adopts the technical scheme that:
a loading force control method of a magnetorheological damper under wind load vibration is applied to a cable-stayed bridge climbing robot and specifically comprises the following steps.
Step 1, installing a magnetorheological damper: the cable-stayed bridge climbing robot is a three-wheeled robot and comprises three rollers, an upper rack and a lower rack; three rollers are respectively Oa、ObAnd Oc(ii) a The top of the upper frame is provided with a roller OaThe bottom of the upper frame is hinged with the middle part of the lower frame, and the hinged point is E; one end of the lower frame is provided with a roller ObThe other end of the lower frame is provided with a roller Oc(ii) a The magneto-rheological damper is arranged along the length of the cable, and two ends of the magneto-rheological damper are respectively connected with the rollers OaAnd Ob(ii) a The included angle between the magneto-rheological damper and the upper frame is theta1The angle between the magneto-rheological damper and the lower frame is theta2(ii) a Roller OaDistance L from hinge point E2Idler wheel OcDistance L from hinge point E3(ii) a In addition, the magneto-rheological damper is opposite to the cable-stayed bridge at the current time tThe axial loading force of the climbing robot is recorded as Ft。
Step 2, establishing a coordinate system: the coordinate system comprises a guy cable coordinate system and a robot coordinate system; the inhaul cable coordinate system takes a ground installation point of an inhaul cable as an original point O, the horizontal direction is an x axis, and the vertical direction is a y axis; the included angle between the inhaul cable and the horizontal direction is alpha; the robot coordinate system uses the center of the cable-stayed bridge climbing robot as an original point O, the length direction of the cable under the tensioning and balance state is the x direction, and the length direction of the cable under the tensioning and balance state is the y direction.
Step 3, establishing Ft、vkAnd a wind vibration model of y (x, t), specifically.
Figure BDA0003098856230000021
Wherein: N-Na+Nb+Nc
Figure BDA0003098856230000022
In the formula, vkThe moving speed of the robot at the current time t,
Figure BDA0003098856230000023
the moving acceleration of the robot at the current time t is obtained; y (x, t) is the offset displacement of the stay cable in the y direction at the current time t and under the robot coordinate system;
Figure BDA0003098856230000024
solving the y-direction offset acceleration of the stay cable at the current time t and under the robot coordinate system by adopting a Galerkin method as a function related to the wind speed; m is the mass of the cable-stayed bridge climbing robot; n is a radical ofa、NbAnd NcAre respectively a roller Oa、ObAnd OcClamping force on the surface of the cable; n is the total clamping force of the three rollers on the surface of the inhaul cable; ffa、FfbAnd FfcClimbing with three rollers respectivelyA driving force; f is the rolling friction resistance of the roller; k is a radical offIs the wind resistance coefficient.
Step 4, establishing FtAnd B, specifically.
Figure BDA0003098856230000031
Wherein the content of the first and second substances,
τ＝p4B4+p3B3+p2B2+p1B+p0 (7)
in the formula, k is the elastic coefficient of a spring in the magnetorheological damper; x is the initial deformation of the spring in the magneto-rheological damper; x' is the deformation quantity generated by the compression spring in the climbing process of the robot;
Figure BDA0003098856230000032
the deformation acceleration generated by compressing the spring in the climbing process of the robot is obtained; d is the diameter of a piston rod in the magnetorheological damper; l is the length of a magnetorheological fluid channel in the magnetorheological damper; tau is the shear yield strength of the magnetorheological fluid in the magnetorheological damper; b is the magnetic induction intensity of the magneto-rheological damper; p is a radical of0、p1、p2、p3And p4Respectively, are a plurality of fitting coefficients.
Step 5, speed measurement: the cable-stayed bridge climbing robot detects the wind speed and climbing speed in climbing in real time in the climbing process along a cable.
Step 6, adjusting Ft: according to the wind speed and the climbing speed in the step 5, and by combining the wind vibration model established in the step 3 and the adjusting model established in the step 4, calculating to obtain the magnetic induction intensity B of the corresponding magneto-rheological damper; then, the loading force F is adjusted by adjusting the magnetic induction intensity BtThe roller is pressed on the surface of the inhaul cable, and the phenomenon of slipping is avoided.
In step 3, solving by adopting a Galerkin method
Figure BDA0003098856230000033
The method of (4), comprising the following steps.
And step 31, solving F (x, t), wherein a specific solving formula is as follows.
Figure BDA0003098856230000034
In the formula, F (x, t) is the wind load borne by the stay cable at the position x and at the current time t; g is the acceleration of gravity; ρ is the air flow density; u. ofsInstantaneous wind speed in the horizontal direction; u shapesThe average wind speed in the horizontal direction; dcThe cross section area of the stay cable is shown; c. CdIs the drag coefficient of the stay cable; c. ClThe lift coefficient of the inhaul cable; delta is the declination angle of the horizontal average wind speed relative to the guy cable.
Step 32, solving q (t): the bottom end of the inhaul cable is connected with the ground through an inhaul cable damper, and the concrete solving formula of q (t) is as follows:
Figure BDA0003098856230000035
wherein A is a known mass matrix of the inhaul cable damper, C is a known damping matrix of the inhaul cable damper, K is a known rigidity matrix of the inhaul cable damper, phidThe damping force of the stay rope damper to the stay rope is obtained; q (t) is the generalized displacement of the stay cable in the y direction at the current time t and under the robot coordinate system;
Figure BDA0003098856230000041
the generalized speed of the stay cable in the y direction at the current time t and under the robot coordinate system is obtained;
Figure BDA0003098856230000042
the generalized acceleration of the stay cable in the y direction at the current time t and under the robot coordinate system is obtained;
step 33, establishing a relationship model between y (x, t) and q (t), specifically:
Figure BDA0003098856230000043
in the formula (I), the compound is shown in the specification,
Figure BDA0003098856230000044
for the first order vibration mode function of the cable, take
Figure BDA0003098856230000045
Step 34, solving
Figure BDA0003098856230000046
According to the steps 31 to 33, solving to obtain y (x, t), and then carrying out second-order derivation on y (x, t) to obtain
Figure BDA0003098856230000047
In the step 5, in the process that the cable-stayed bridge climbing robot climbs along the cable, the obstacle crossing capability of the cable-stayed bridge climbing robot is improved by reducing the initial damping of the magnetorheological damper.
In step 6, the variation range of the magnetic induction B is 0T to 0.6T.
A magneto-rheological damper comprises a piston rod, a cylinder, a positioning disc, a magnetic conductive disc, a wire winding disc, an excitation coil and a spring.
The cylinder barrel is coaxially sleeved on the periphery of the middle part of the piston rod, and the front end and the rear end of the cylinder barrel are in sealing sliding connection with the piston rod through a flange plate.
The magnetic conductive discs and the winding discs are closely and alternately arranged on the piston rod in the cylinder barrel along the axial direction, a magnetorheological fluid channel is formed between the inner circumferential surfaces of the magnetic conductive discs and the winding discs and the piston rod, and magnetorheological fluid is filled in the magnetorheological cavity.
And each wire spool is wound with an excitation coil, and the excitation coils on all the wire spools are connected in series.
The positioning disc is coaxially sleeved on the piston rod positioned on the outer side of the front end flange disc.
The spring housing is established in the cylinder periphery, and spring one end is installed on the positioning disk, and the spring other end is installed on the ring flange that is located the rear end.
One end of the positioning disk is connected with a roller OaOr ObPiston rod connecting roller O on one side departing from positioning platebOr Oa。
The quantity of magnetic conduction dish is four, and the quantity of wire reel is three, and the magnetic conduction dish sets up between two adjacent wire reels and between wire reel and the ring flange.
By varying the number of turns N of the windings in the field coil1And exciting current I, and further adjusting the magnetic induction intensity B in the magnetorheological fluid channel, wherein the specific adjustment formula is as follows.
N1I＝BSRm (8)
Wherein S is the magnetic flux area of the magnetorheological fluid channel, RmIs the total reluctance of the magnetic circuit.
Magnetic circuit total reluctance RmThe calculation formula of (2) is as follows.
Rm＝R1+2R2+2R3+R4 (9)
Wherein.
Figure BDA0003098856230000051
Figure BDA0003098856230000052
Figure BDA0003098856230000053
Figure BDA0003098856230000054
In the formula, R1Is the piston rod reluctance; r2Is the magnetic resistance of the magnetic conductive disc; r3Is the magnetic resistance in the magnetorheological fluid channel; r4Is the magnetic resistance in the cylinder barrel shell; mu.s0The magnetic permeability of the piston rod; mu.s1Is the magnetic permeability of the magnetorheological fluid; l istIs the axial length of the magnetically conductive disc、L1Is the axial length of the spool; r is1The outer diameter of the cylinder barrel; r is2Is the inner diameter of the cylinder barrel; and d is the radial thickness of the magnetorheological fluid channel.
The piston rod diameter D satisfies the following calculation formula.
Figure BDA0003098856230000055
In the formula, F is the axial force born by the piston rod, and [ sigma ] is the allowable stress of the piston rod material.
The model of the magnetorheological fluid is MRF-132 DG.
The invention has the following beneficial effects:
1. the magnetorheological damper is added in the clamping mechanism of the robot to inhibit the vibration of the robot in the climbing process, so that the influence of the vibration of the existing stay cable on the climbing stability of the robot is avoided, and the phenomenon of slipping is prevented. In addition, the coupled vibration characteristics of the robot and the inhaul cable are analyzed, and a vibration damping mechanism is researched and designed to ensure that the robot climbs stably and safely.
2. The magneto-rheological damper generates damping force under the condition of large influence of inhaul cable vibration so as to reduce the influence on the climbing performance of the robot and ensure that the mechanism stably climbs.
3. Establishing a guy cable-robot coupling dynamic model in a vibration environment, and calculating to obtain the magnetic induction intensity B of the corresponding magneto-rheological damper according to the wind speed and the climbing speed by combining the established wind vibration model and the established regulation model; then, the loading force F is adjusted by adjusting the magnetic induction intensity BtThe roller is pressed on the surface of the inhaul cable, and the phenomenon of slipping is avoided.
4. By reducing the initial damping of the magnetorheological damper, the obstacle crossing capability of the cable-stayed bridge climbing robot is improved, and the cable-stayed bridge climbing robot can climb higher obstacles such as thread type obstacles.
Drawings
Fig. 1 shows a schematic structural diagram of a cable-stayed bridge climbing robot using a magnetorheological damper of the invention.
FIG. 2 is a schematic perspective view of a magnetorheological damper of the present invention.
FIG. 3 is a schematic cross-sectional view of a magnetorheological damper of the present invention.
Fig. 4 shows a schematic diagram of the installation position and size identification of the magnetorheological damper and the cable-stayed bridge climbing robot in the invention.
Fig. 5 shows a schematic view of a cable coordinate system and a robot coordinate system.
FIG. 6 shows the damping force F at zero magnetic fieldtGraph against piston rod displacement.
FIG. 7 shows the damping force FtGraph with current.
Among them are:
1. a magnetorheological damper;
10. a piston rod; 20. a cylinder barrel; 21. a flange plate; 30. a field coil; 31. a wire spool; 40. a magnetically conductive disc; 50. positioning a plate; 60. a magnetorheological fluid channel; 70. a spring;
2. roller Oa(ii) a 2-1, driving a motor; 2-2, a speed limiting mechanism; 3. roller Ob(ii) a 4. Roller Oc(ii) a 5. A hinge point E; 6. an upper frame; 7. a lower frame; 8. a synchronous pulley.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific preferred embodiments.
In the description of the present invention, it is to be understood that the terms "left side", "right side", "upper part", "lower part", etc., indicate orientations or positional relationships based on those shown in the drawings, and are only for convenience of describing the present invention and simplifying the description, but do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and that "first", "second", etc., do not represent an important degree of the component parts, and thus are not to be construed as limiting the present invention. The specific dimensions used in the present example are only for illustrating the technical solution and do not limit the scope of protection of the present invention.
As shown in fig. 1, a cable-stayed bridge climbing robot is a three-wheel robot and comprises three rollers, an upper frame 6 and a lower frame 7.
Three rollers are roller O respectivelya2. Roller O b3 and roller O c4; wherein, the roller O a2. Preferably a driving wheel, is driven by a driving motor 2-1, and is speed-limited by a speed limiting mechanism 2-2. The three rollers are preferably driven by a synchronous belt wheel 8 to synchronously rotate. Alternatively, the three rollers can be driving wheels, and at the moment, the cable-stayed bridge climbing robot is a three-wheel full-drive robot.
The top of the upper frame is provided with a roller OaThe bottom of the upper frame is hinged with the middle part of the lower frame, and the hinged point is E5; one end of the lower frame is provided with a roller ObThe other end of the lower frame is provided with a roller Oc. The magnetorheological damper 1 is arranged along the length of the cable, and two ends of the magnetorheological damper are respectively connected with the rollers OaAnd Ob。
As shown in fig. 2 and 3, a magnetorheological damper comprises a piston rod 10, a cylinder 20, a positioning disc 50, a magnetic conductive disc 40, a wire winding disc 31, an excitation coil 30 and a spring 70.
The cylinder barrel is coaxially sleeved on the periphery of the middle part of the piston rod, and the front end and the rear end of the cylinder barrel are in sealing sliding connection with the piston rod through a flange plate 21.
The magnetic conductive disc and the winding disc are closely and alternately arranged on the piston rod in the cylinder barrel along the axial direction. In this embodiment, the number of the magnetic conductive disks is preferably four, the number of the wire spools is preferably three, and the magnetic conductive disks are disposed between two adjacent wire spools and between the wire spools and the flange.
A magnetorheological fluid channel 60 is formed between the inner circumferential surfaces of the magnetic conductive disc and the wire winding disc and the piston rod, and magnetorheological fluid is filled in the magnetorheological cavity.
The type of the magnetorheological fluid is preferably MRF-132DG, the magnetorheological fluid reacts quickly under the action of a magnetic field, and the shear stress reaching 70kPa can be provided to meet the damping force output by the damper; exhibits a low yield strength at zero field and allows a controlled range of field strengths from 0T to 0.6T.
And each wire spool is wound with an excitation coil, and the excitation coils on all the wire spools are connected in series.
The positioning disc is coaxially sleeved on the piston rod positioned on the outer side of the front end flange disc.
The spring housing is established in the cylinder periphery, and spring one end is installed on the positioning disk, and the spring other end is installed on the ring flange that is located the rear end. The pre-tightening force of the spring is adjusted by rotating the rear end flange plate, so that the clamping force of the robot on the surface of the inhaul cable is changed.
One end of the positioning disk is connected with a roller OaOr ObPiston rod connecting roller O on one side departing from positioning platebOr Oa。
In this embodiment, the size parameters of the magnetorheological damper are preferably set as follows:
parameter(s) Value/mm
Diameter of piston rod 16
Width of magnetic rheological liquid channel 1
Thickness of single magnetic conductive disc 12
Thickness of single winding coil 10
Inner diameter of cylinder barrel 2 x r1 32
Cylinder barrel external diameter 2 x r2 36
A loading force control method of a magnetorheological damper under wind load vibration comprises the following steps.
Step 1, installing the magneto-rheological damper.
As shown in FIG. 4, the two ends of the magnetorheological damper 1 are respectively connected with the rollers OaAnd Ob. At the moment, the included angle between the magnetorheological damper and the upper frame is theta1The angle between the magneto-rheological damper and the lower frame is theta2(ii) a Roller OaDistance L from hinge point E2Idler wheel OcDistance L from hinge point E3(ii) a In addition, the axial loading force of the magnetorheological damper on the climbing robot of the cable-stayed bridge at the current time t is recorded as Ft。
And 2, establishing a coordinate system.
As shown in FIGS. 5 and 4, the coordinate system includes a cable coordinate system { O }lAnd robot coordinate system { O }k}; wherein, the cable coordinate system takes the ground mounting point of the cable as the original point O, and the horizontal direction is the x axis (also called x)lAxis) and the vertical direction is the y-axis (also called y)lA shaft); stay cable and horizontal direction xlThe included angle of the axes is alpha.
The robot coordinate system takes the center of the cable-stayed bridge climbing robot as an original point O, and the stay cable is tensioned and in a balanced state, and the x direction (also called as x) is arranged along the length direction of the stay cablekShaft), the guy cable is tensioned and is vertical to the length direction of the guy cable in a balanced state in the y direction (also called as y)kA shaft).
Step 3, establishing Ft、vkAnd a wind vibration model of y (x, t), specifically:
Figure BDA0003098856230000081
wherein: N-Na+Nb+Nc
Figure BDA0003098856230000082
In the formula, vkThe moving speed of the robot at the current time t,
Figure BDA0003098856230000083
the moving acceleration of the robot at the current time t is obtained; y (x, t) is the offset displacement of the stay cable in the y direction at the current time t and under the robot coordinate system;
Figure BDA0003098856230000084
solving the y-direction offset acceleration of the stay cable at the current time t and under the robot coordinate system by adopting a Galerkin method as a function related to the wind speed; m is the mass of the cable-stayed bridge climbing robot; n is a radical ofa、NbAnd NcAre respectively a roller Oa、ObAnd OcClamping force on the surface of the cable; n is the total clamping force of the three rollers on the surface of the inhaul cable; ffa、FfbAnd FfcThe climbing driving force of the three rollers is respectively; f is the rolling friction resistance of the roller; k is a radical offIs the wind resistance coefficient.
In step 3, solving by adopting a Galerkin method
Figure BDA0003098856230000085
The method of (4), comprising the following steps.
And step 31, solving F (x, t), wherein a specific solving formula is as follows.
Figure BDA0003098856230000091
In the formula, F (x, t) is the wind load borne by the stay cable at the position x and at the current time t; g is the acceleration of gravity; ρ is the air flow density; u. ofsInstantaneous wind speed in the horizontal direction; u shapesThe average wind speed in the horizontal direction (typically the average wind speed within 10 minutes of observation); dcThe cross section area of the stay cable is shown; c. CdIs the drag coefficient of the stay cable; c. ClThe lift coefficient of the inhaul cable; stay cable with delta being horizontal average wind speedThe declination angle of (c).
Step 32, solving q (t): the bottom end of the inhaul cable is connected with the ground through an inhaul cable damper, and the concrete solving formula of q (t) is as follows:
Figure BDA0003098856230000092
wherein A is a known mass matrix of the inhaul cable damper, C is a known damping matrix of the inhaul cable damper, K is a known rigidity matrix of the inhaul cable damper, phidThe damping force of the stay rope damper to the stay rope is obtained; q (t) is the generalized displacement of the stay cable in the y direction at the current time t and under the robot coordinate system;
Figure BDA0003098856230000093
the generalized speed of the stay cable in the y direction at the current time t and under the robot coordinate system is obtained;
Figure BDA0003098856230000094
the generalized acceleration of the guy cable in the y direction at the current time t and under the robot coordinate system is shown.
Step 33, establishing a relationship model between y (x, t) and q (t), specifically:
Figure BDA0003098856230000095
in the formula (I), the compound is shown in the specification,
Figure BDA0003098856230000096
for the first order vibration mode function of the cable, take
Figure BDA0003098856230000097
Step 34, solving
Figure BDA0003098856230000098
According to the steps 31 to 33, solving to obtain y (x, t), and then carrying out second-order derivation on y (x, t) to obtain
Figure BDA0003098856230000099
Step 4, establishing FtAnd B, specifically:
Figure BDA00030988562300000910
wherein the content of the first and second substances,
τ＝p4B4+p3B3+p2B2+p1B+p0 (7)
in the formula, k is the elastic coefficient of a spring in the magnetorheological damper; x is the initial deformation of the spring in the magneto-rheological damper; x' is the deformation quantity generated by the compression spring in the climbing process of the robot;
Figure BDA00030988562300000911
the deformation acceleration generated by compressing the spring in the climbing process of the robot is obtained; d is the diameter of a piston rod in the magnetorheological damper; l is the length of a magnetorheological fluid channel in the magnetorheological damper; tau is the shear yield strength of the magnetorheological fluid in the magnetorheological damper; b is the magnetic induction intensity of the magneto-rheological damper; p is a radical of0、p1、p2、p3And p4Respectively, a plurality of fitting coefficients, preferably: p is a radical of4＝-304kPa/T4，p3＝-756kPa/T3，p2＝793.9kPa/T2，p1＝-41.31kPa/T，p0＝1.073kPa。
Step 5, speed measurement: the cable-stayed bridge climbing robot detects the wind speed and climbing speed in climbing in real time in the climbing process along a cable.
The climbing robot for the cable-stayed bridge has the advantages that the initial damping of the magneto-rheological damper is reduced in the climbing process along the cable, so that the obstacle crossing capability of the climbing robot for the cable-stayed bridge is improved.
In the magnetic circuit in the magneto-rheological damper, the magnetic flow area of the piston rod and the cylinder barrel is small, and the magnetic conduction disc cannot be too thick in order to avoid that the output damping force of the damper cannot reach the required maximum damping force due to premature saturation of the magnetic induction intensity of the part. Through internal magnetic field finite element analysis under the single-stage coil and the two-stage coil structure, the magnetic inductor intensity at the two sides of the magnetic conductive disc is lower, and the magnetic induction intensity close to the coil part is higher and exceeds the saturation magnetic induction intensity. The internal structure is designed into a three-level coil structure by combining the size requirement of the damper and the finite element analysis result of the internal magnetic field, and the design requirement of the magnetic field intensity can be met through the finite element analysis.
When the robot crosses an obstacle, the compression spring in the figure needs to be further deformed and compressed, and if the damping force of the damper is too large, the compression spring cannot be deformed to cause the robot to be stuck at the obstacle position. In the shearing mode, the output damping force of the magnetorheological damper under the condition of zero magnetic field is shown in fig. 6, and the output damping force of the damper is small at the moment, so that the magnetorheological damper is suitable for a robot to cross an obstacle in the obstacle crossing process.
In the obstacle crossing process of the robot, the compression spring is easier to deform by reducing the input current of the magnetorheological damper. The higher the height of the obstacle is, the smaller the input current of the magnetorheological damper is, and the current of the output coil of the magnetorheological damper can be controlled by the relation between the damping force and the current in the figure 7.
Climbing and obstacle crossing experiment: when the large-span cable-stayed bridge cable is exposed to the air for a long time, the outer PE protective material of the large-span cable-stayed bridge cable is aged and cracked to form pits and bulges on the surface of the cable. In order to suppress the influence of wind vibration and rain vibration on the stay cable, spiral ribs, circular or elliptical recesses, or protrusions are generally provided on the surface of the stay cable. These factors will all constitute obstacles in the climbing process of the guy cable detection robot. Therefore, the stay cable detection robot needs to have certain obstacle crossing capability in the detection operation process.
The diameter through the cable experiment platform of putting up in the laboratory is the barrier that highly is 7mm on 90 mm's the hard PVC pipe, and shaking table vibration frequency sets up to 5Hz, and the amplitude is 2mm, and the three gyro wheel of experiment test robot all can climb smoothly through the barrier. When the robot just contacts with an obstacle in the obstacle crossing process, the speed is obviously reduced, but the reduction amplitude is not more than 0.01m/s, so that the robot can still stably pass through the obstacle with a certain height under the vibration condition.
Step 6, adjusting Ft: according to the wind speed and the climbing speed in the step 5, and by combining the wind vibration model established in the step 3 and the adjusting model established in the step 4, calculating to obtain the magnetic induction intensity B of the corresponding magneto-rheological damper; then, the loading force F is adjusted by adjusting the magnetic induction intensity BtThe roller is pressed on the surface of the inhaul cable, and the phenomenon of slipping is avoided.
The variation range of the magnetic induction B is preferably 0T to 0.6T; by varying the number of turns N of the windings in the field coil1And exciting current I, and further adjusting the magnetic induction intensity B in the magnetorheological fluid channel, wherein the specific adjustment formula is as follows.
N1I＝BSRm (8)
Wherein S is the magnetic flux area of the magnetorheological fluid channel, RmIs the total reluctance of the magnetic circuit.
Magnetic circuit total reluctance RmThe calculation formula of (2) is as follows.
Rm＝R1+2R2+2R3+R4 (9)
Wherein.
Figure BDA0003098856230000111
Figure BDA0003098856230000112
Figure BDA0003098856230000113
Figure BDA0003098856230000114
In the formula, R1Is the piston rod reluctance; r2Is the magnetic resistance of the magnetic conductive disc; r3Is the magnetic resistance in the magnetorheological fluid channel; r4Is the magnetic resistance in the cylinder barrel shell; mu.s0The magnetic permeability of the piston rod; mu.s1Is the magnetic permeability of the magnetorheological fluid; l istIs the axial length, L, of the magnetically conductive disc1Is the axial length of the spool; r is1The outer diameter of the cylinder barrel; r is2Is the inner diameter of the cylinder barrel; and d is the radial thickness of the magnetorheological fluid channel.
The above-described piston rod diameter D satisfies the following calculation formula.
Figure BDA0003098856230000115
In the formula, F is the axial force born by the piston rod, and [ sigma ] is the allowable stress of the piston rod material.
The invention can know through simulation analysis that:
1. when the force loading mechanism only compresses the spring, the inertia force generated by the random vibration of the inhaul cable acts on the mechanism to generate the forced vibration of the mechanism, and the rigidity of the spring determines the displacement of the mechanism. Compared with the vibration response calculation results of the spring loading mechanism and the spring-magnetorheological damping coupling loading mechanism, the vibration of the inhaul cable can cause the obvious vibration of the force loading mechanism, the maximum amplitude of the spring loading mechanism is 76.1356mm, the input current of the magnet exciting coil of the damper is set to be 0.2A by using the improved spring-magnetorheological damping coupling loading mechanism, and the maximum amplitude is 13.9419mm which is 0.18 times of the maximum amplitude generated by using the spring loading mechanism. Therefore, the force loading mechanism employing the damper can effectively suppress vibration.
2. With the increase of the wind speed, the acceleration of the stay cable vibration is obviously increased, so that the inertia force acting on the robot is increased.
Although the preferred embodiments of the present invention have been described in detail, the present invention is not limited to the details of the embodiments, and various equivalent modifications can be made within the technical spirit of the present invention, and the scope of the present invention is also within the scope of the present invention.

Claims (10)

1. A loading force control method of a magnetorheological damper under wind load vibration is applied to a cable-stayed bridge climbing robot and is characterized in that: the method specifically comprises the following steps:
step 1, installing a magnetorheological damper: the cable-stayed bridge climbing robot is a three-wheeled robot and comprises three rollers, an upper rack and a lower rack; three rollers are respectively Oa、ObAnd Oc(ii) a The top of the upper frame is provided with a roller OaThe bottom of the upper frame is hinged with the middle part of the lower frame, and the hinged point is E; one end of the lower frame is provided with a roller ObThe other end of the lower frame is provided with a roller Oc(ii) a The magneto-rheological damper is arranged along the length of the cable, and two ends of the magneto-rheological damper are respectively connected with the rollers OaAnd Ob(ii) a The included angle between the magneto-rheological damper and the upper frame is theta1The angle between the magneto-rheological damper and the lower frame is theta2(ii) a Roller OaDistance L from hinge point E2Idler wheel OcDistance L from hinge point E3(ii) a In addition, the axial loading force of the magnetorheological damper on the climbing robot of the cable-stayed bridge at the current time t is recorded as Ft；
Step 2, establishing a coordinate system: the coordinate system comprises a guy cable coordinate system and a robot coordinate system; the inhaul cable coordinate system takes a ground installation point of an inhaul cable as an original point O, the horizontal direction is an x axis, and the vertical direction is a y axis; the included angle between the inhaul cable and the horizontal direction is alpha; the robot coordinate system takes the center of the cable-stayed bridge climbing robot as an original point O, the cable is tensioned and in a balanced state, the x direction is along the length direction of the cable, and the y direction is perpendicular to the length direction of the cable in a balanced state;
step 3, establishing Ft、vkAnd a wind vibration model of y (x, t), specifically:
Figure RE-FDA0003258854870000011
wherein: N-Na+Nb+Nc
Figure RE-FDA0003258854870000012
In the formula, vkThe moving speed of the robot at the current time t,
Figure RE-FDA0003258854870000013
the moving acceleration of the robot at the current time t is obtained; y (x, t) is the offset displacement of the stay cable in the y direction at the current time t and under the robot coordinate system;
Figure RE-FDA0003258854870000014
solving the y-direction offset acceleration of the stay cable at the current time t and under the robot coordinate system by adopting a Galerkin method as a function related to the wind speed; m is the mass of the cable-stayed bridge climbing robot; n is a radical ofa、NbAnd NcAre respectively a roller Oa、ObAnd OcClamping force on the surface of the cable; n is the total clamping force of the three rollers on the surface of the inhaul cable; ffa、FfbAnd FfcThe climbing driving force of the three rollers is respectively; f is the rolling friction resistance of the roller; k is a radical offIs the wind resistance coefficient;
step 4, establishing FtAnd B, specifically:
Figure RE-FDA0003258854870000025
wherein the content of the first and second substances,
τ＝p4B4+p3B3+p2B2+p1B+p0 (7)
in the formula, k is the elastic coefficient of a spring in the magnetorheological damper; x is the initial deformation of the spring in the magneto-rheological damper; x' is the deformation quantity generated by the compression spring in the climbing process of the robot;
Figure RE-FDA0003258854870000021
the deformation acceleration generated by compressing the spring in the climbing process of the robot is obtained; d is the diameter of a piston rod in the magnetorheological damper; l is the length of a magnetorheological fluid channel in the magnetorheological damper; tau is the shear yield strength of the magnetorheological fluid in the magnetorheological damper; b is the magnetic induction intensity of the magneto-rheological damper; p is a radical of0、p1、p2、p3And p4Respectively, a plurality of fitting coefficients;
step 5, speed measurement: the method comprises the following steps that in the process of climbing along a cable, a cable-stayed bridge climbing robot detects the wind speed and climbing speed in climbing in real time;
step 6, adjusting Ft: according to the wind speed and the climbing speed in the step 5, and by combining the wind vibration model established in the step 3 and the adjusting model established in the step 4, calculating to obtain the magnetic induction intensity B of the corresponding magneto-rheological damper; then, the loading force F is adjusted by adjusting the magnetic induction intensity BtThe roller is pressed on the surface of the inhaul cable, and the phenomenon of slipping is avoided.
2. The loading force control method of the magnetorheological damper under wind-load vibration according to claim 1, characterized in that: in step 3, solving by adopting a Galerkin method
Figure RE-FDA0003258854870000022
The method comprises the following steps:
step 31, solving F (x, t), wherein a concrete solving formula is as follows:
Figure RE-FDA0003258854870000023
in the formula, F (x, t) is the wind load borne by the stay cable at the position x and at the current time t; g is the acceleration of gravity; ρ is the air flow density; u. ofsInstantaneous wind speed in the horizontal direction; u shapesThe average wind speed in the horizontal direction; dcThe cross section area of the stay cable is shown; c. CdIs the drag coefficient of the stay cable; c. ClThe lift coefficient of the inhaul cable; delta is deviation of horizontal average wind speed relative to stay cableAn angle;
step 32, solving q (t): the bottom end of the inhaul cable is connected with the ground through an inhaul cable damper, and the concrete solving formula of q (t) is as follows:
Figure RE-FDA0003258854870000024
wherein A is a known mass matrix of the inhaul cable damper, C is a known damping matrix of the inhaul cable damper, K is a known rigidity matrix of the inhaul cable damper, phidThe damping force of the stay rope damper to the stay rope is obtained; q (t) is the generalized displacement of the stay cable in the y direction at the current time t and under the robot coordinate system;
Figure RE-FDA0003258854870000031
the generalized speed of the stay cable in the y direction at the current time t and under the robot coordinate system is obtained;
Figure RE-FDA0003258854870000032
the generalized acceleration of the stay cable in the y direction at the current time t and under the robot coordinate system is obtained;
step 33, establishing a relationship model between y (x, t) and q (t), specifically:
Figure RE-FDA0003258854870000033
in the formula (I), the compound is shown in the specification,
Figure RE-FDA0003258854870000034
for the first order vibration mode function of the cable, take
Figure RE-FDA0003258854870000035
Step 34, solving
Figure RE-FDA0003258854870000036
According to the steps 31 to 33, y (x, t) is obtained by solving, and then y (x, t) is obtained) Performing second-order derivation to obtain
Figure RE-FDA0003258854870000037
3. The loading force control method of the magnetorheological damper under wind-load vibration according to claim 1, characterized in that: in the step 5, in the process that the cable-stayed bridge climbing robot climbs along the cable, the obstacle crossing capability of the cable-stayed bridge climbing robot is improved by reducing the initial damping of the magnetorheological damper.
4. The loading force control method of the magnetorheological damper under wind-load vibration according to claim 1, characterized in that: in step 6, the variation range of the magnetic induction B is 0T to 0.6T.
5. A magnetorheological damper, comprising: the device comprises a piston rod, a cylinder barrel, a positioning disc, a magnetic conductive disc, a wire winding disc, an excitation coil and a spring;
the cylinder barrel is coaxially sleeved on the periphery of the middle part of the piston rod, and the front end and the rear end of the cylinder barrel are in sealing sliding connection with the piston rod through a flange plate;
the magnetic conductive discs and the winding discs are closely and alternately arranged on the piston rod in the cylinder barrel along the axial direction, a magnetorheological fluid channel is formed between the inner circumferential surfaces of the magnetic conductive discs and the winding discs and the piston rod, and magnetorheological fluid is filled in the magnetorheological cavity;
each wire spool is wound with an excitation coil, and the excitation coils on all the wire spools are connected in series;
the positioning disc is coaxially sleeved on the piston rod positioned on the outer side of the front end flange disc;
the spring is sleeved on the periphery of the cylinder barrel, one end of the spring is arranged on the positioning disc, and the other end of the spring is arranged on the flange plate positioned at the rear end; one end of the positioning disk is connected with a roller OaOr ObPiston rod connecting roller O on one side departing from positioning platebOr Oa。
6. The magnetorheological damper of claim 5, wherein: the quantity of magnetic conduction dish is four, and the quantity of wire reel is three, and the magnetic conduction dish sets up between two adjacent wire reels and between wire reel and the ring flange.
7. The magnetorheological damper of claim 5, wherein: by varying the number of turns N of the windings in the field coil1And exciting current I, and further adjusting the magnetic induction intensity B in the magnetorheological fluid channel, wherein the specific adjustment formula is as follows:
N1I＝BSRm (8)
wherein S is the magnetic flux area of the magnetorheological fluid channel, RmIs the total reluctance of the magnetic circuit.
8. The magnetorheological damper of claim 7, wherein: magnetic circuit total reluctance RmThe calculation formula of (2) is as follows:
Rm＝R1+2R2+2R3+R4 (9)
wherein:
Figure RE-FDA0003258854870000041
Figure RE-FDA0003258854870000042
Figure RE-FDA0003258854870000043
Figure RE-FDA0003258854870000044
in the formula, R1Is the piston rod reluctance; r2Is the magnetic resistance of the magnetic conductive disc; r3Is the magnetic resistance in the magnetorheological fluid channel; r4Is the magnetic resistance in the cylinder barrel shell; mu.s0The magnetic permeability of the piston rod; mu.s1Is the magnetic permeability of the magnetorheological fluid; l istIs the axial length, L, of the magnetically conductive disc1Is the axial length of the spool; r is1The outer diameter of the cylinder barrel; r is2Is the inner diameter of the cylinder barrel; and d is the radial thickness of the magnetorheological fluid channel.
9. The magnetorheological damper of claim 8, wherein: the diameter D of the piston rod satisfies the following calculation formula:
Figure RE-FDA0003258854870000045
in the formula, F is the axial force born by the piston rod, and [ sigma ] is the allowable stress of the piston rod material.
10. The magnetorheological damper of claim 5, wherein: the model of the magnetorheological fluid is MRF-132 DG.
CN202110618809.0A 2021-06-03 2021-06-03 Magnetorheological damper and loading force control method under wind load vibration Pending CN113513557A (en)

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