CN115108486A - Tower crane group tower anti-collision method based on movement trend - Google Patents

Tower crane group tower anti-collision method based on movement trend Download PDF

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CN115108486A
CN115108486A CN202210854805.7A CN202210854805A CN115108486A CN 115108486 A CN115108486 A CN 115108486A CN 202210854805 A CN202210854805 A CN 202210854805A CN 115108486 A CN115108486 A CN 115108486A
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杨晓娇
何跃川
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Sichuan Institute of Building Research
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B66—HOISTING; LIFTING; HAULING
    • B66C—CRANES; LOAD-ENGAGING ELEMENTS OR DEVICES FOR CRANES, CAPSTANS, WINCHES, OR TACKLES
    • B66C23/00—Cranes comprising essentially a beam, boom, or triangular structure acting as a cantilever and mounted for translatory of swinging movements in vertical or horizontal planes or a combination of such movements, e.g. jib-cranes, derricks, tower cranes
    • B66C23/88—Safety gear
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B66—HOISTING; LIFTING; HAULING
    • B66C—CRANES; LOAD-ENGAGING ELEMENTS OR DEVICES FOR CRANES, CAPSTANS, WINCHES, OR TACKLES
    • B66C13/00—Other constructional features or details
    • B66C13/18—Control systems or devices
    • B66C13/48—Automatic control of crane drives for producing a single or repeated working cycle; Programme control
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    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B66—HOISTING; LIFTING; HAULING
    • B66C—CRANES; LOAD-ENGAGING ELEMENTS OR DEVICES FOR CRANES, CAPSTANS, WINCHES, OR TACKLES
    • B66C2700/00—Cranes
    • B66C2700/03—Cranes with arms or jibs; Multiple cranes

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Abstract

The invention discloses a tower crane group anti-collision method based on a movement trend, which comprises the steps of obtaining coordinates of two adjacent tower cranes and calculating the distance between the two tower cranes; acquiring the lengths of the crane arms of two adjacent tower cranes, and entering a tower crane group collision algorithm if the sum of the lengths of the crane arms of the two tower cranes is greater than or equal to the distance between the two tower cranes: receiving real-time information of the tower crane and inquiring a collision mode; and judging the minimum distance between the current moment and the safety storage moment according to a collision mode, if the minimum distance at the current moment is less than or equal to the minimum safety alarm limit value of the group tower, further judging whether the minimum distance at the current moment is less than the minimum safety alarm limit value of the group tower, otherwise, calculating the minimum distance after the safety storage moment, and if the minimum distance at the current moment is less than or equal to the minimum safety alarm limit value of the group tower, alarming and braking. According to the invention, the current working state of the local tower crane is judged according to the movement trend of the local tower crane and the surrounding tower cranes, and then whether the local tower crane is in a dangerous state is judged, so that the safety of the whole tower crane system is ensured.

Description

Tower crane group anti-collision method based on motion trend
Technical Field
The invention relates to the technical field of operation safety management of tower cranes in construction sites, in particular to a tower crane group anti-collision method based on a motion trend.
Background
The safety operation of the tower crane (tower crane for short) is an important factor influencing the construction management effect, and for a single tower crane, a certain safety protection effect can be achieved through the safety monitoring system and the limiter. However, due to the limitation of efficiency requirements and places, a plurality of tower cranes are often operated in the same area on site, and the potential danger of mutual collision of adjacent tower cranes in the operation process may occur, so that serious engineering accidents are caused. The existing group tower anti-collision calculation method mostly takes an interference area of adjacent tower cranes as an early warning area, and the precision degree is insufficient by judging whether a hanging object is taken as an alarm condition in the early warning area at the same time, so that the actual requirement is difficult to meet. The anti-collision evaluation accuracy of the tower cluster tower is improved, the operation safety of the tower cluster is improved, the unsafe behaviors of people and the unsafe states of objects are reduced, and the possibility of safety accidents is reduced.
Therefore, how to provide a tower crane group tower anti-collision method based on a motion trend is an urgent problem to be solved by those skilled in the art.
Disclosure of Invention
In view of the above, the invention provides a tower crane group anti-collision method based on a motion trend, and the anti-collision evaluation accuracy of the tower crane group is improved.
In order to achieve the purpose, the invention adopts the following technical scheme:
a tower crane group tower anti-collision method based on motion trend comprises the following steps:
acquiring coordinates of two adjacent tower cranes, and calculating the distance between the two tower cranes;
acquiring the lengths of the cargo booms of two adjacent tower cranes, and entering a collision algorithm between the tower cranes if the sum of the lengths of the cargo booms of the two tower cranes is greater than or equal to the distance between the two tower cranes:
receiving real-time information of the tower crane and inquiring a collision mode;
and judging the minimum distance between the current moment and the safety storage moment according to the collision mode, and performing early warning deceleration or warning braking according to the relation between the minimum distance, the minimum safety early warning limit of the tower group and the minimum safety warning limit value of the group tower.
Preferably, the receiving of the real-time information of the tower crane and the query of the collision mode specifically comprise:
obtaining real-time information of two tower cranes in real time, comprisingHeight H of tower cap of tower crane A 3a (tower crane top to bottom of cargo boom), tower cap height H of tower crane B 3b And the sagging bottom height H of the balance weight of the tower crane A pa And the height H of the drooping bottom of the balance weight of the tower crane B pb And the bottom height H of the cargo boom of the tower crane A qa Bottom height H of cargo boom of tower crane B qb The height of a cargo boom (the length between the upper edge and the lower edge of the cargo boom) h of the tower crane A qa Height h of lifting arm of tower crane B qb ；
If H is qa -H pa If the value is larger than the preset value, the safety reserve is considered to be enlarged, and the order can be changed to the original h qa Increase in value (H) qa -H pa ) Consider that h is qa ＝h qa +(H qa -H pa )。
If H is qb -H pb If the value is larger than the preset value, the safety reserve is considered to be enlarged, and the order can be changed to the original h qb Increase in value (H) qb -H pb ) Consider that h is qb ＝h qb +(H qb -H pb )。
When H is present qa ≥H qb When, if H qa -H qb ≤h qb Or when H qa ＜H qb When is at H qb -H qa ≤h qa When the current time reaches the A00 mode;
when H is present qa ≥H qb When is at H qa -H qb ＞h qb Entering an A10 mode;
when H is present qa ＜H qb When, if H qb -H qa ＞h qa Entering an A01 mode;
when H is present qa ≥H qb When, if H qb +H 3b -H qa ≤h qa Entering an A20 mode;
when H is present qa ＜H qb When is at H qa +H 3a -H qb ≤h qb And enters the a02 mode.
Preferably, the principle of early warning deceleration or warning braking judgment is as follows:
judging whether the minimum distance at the current moment is less than or equal to the group tower minimum safety early warning limit value or not, if so, further judging whether the minimum distance at the current moment is less than the group tower minimum safety early warning limit value or not, if not, calculating the minimum distance after the safety storage moment, judging whether the minimum distance after the safety storage moment is less than or equal to the group tower minimum safety early warning limit value or not, if so, early warning and decelerating, otherwise, the minimum distance is in a safety state;
and judging whether the minimum distance at the current moment is less than or equal to the group tower minimum safety alarm limit value, if so, alarming and braking, and if not, early warning and deceleration are not met.
Preferably, the judging the minimum distance according to the collision mode specifically includes:
in the a00 mode, the current time t is calculated at the current time 1 Front and rear arm line segment coordinates of tower crane A and current time t 1 Calculating the minimum distance at the current moment according to the line segment coordinates of the front arm and the rear arm of the tower crane B; when calculating the minimum distance after the safe reserve moment, respectively calculating t 1 Coordinates of line segment of front arm and rear arm of tower crane A at moment of +/-delta t and t 1 Calculating the minimum distance after the safe storage moment according to the coordinates of the front arm and the rear arm of the tower crane B at the moment of +/-deltat;
in the a10 mode, the current time t is calculated at the current time 1 Coordinates of center point of lifting rope A of tower crane and current moment t 1 Calculating the minimum distance at the current moment according to the line segment coordinates of the front arm and the rear arm of the tower crane B; when calculating the minimum distance after the safe reserve moment, respectively calculating t 1 Coordinate of center point of lifting rope A of tower crane at moment +/-Delta t and t 1 Calculating the minimum distance after the safe storage moment according to the coordinates of the front arm and the rear arm of the tower crane B at the moment of +/-deltat;
in the a01 mode, the current time t is calculated at the current time 1 The line segment coordinates of the front arm and the rear arm of the tower crane A and the current moment t 1 The coordinate of the central point of the lifting rope of the tower crane B is used for calculating the minimum distance at the current moment; when calculating the minimum distance after the safe reserve moment, respectively calculating t 1 Coordinates of line segment of front arm and rear arm of tower crane A at moment of +/-delta t and t 1 Calculating the coordinate of the center point of the lifting rope of the tower crane B at the moment of +/-deltat, and further calculating the minimum distance after the safe storage moment;
in the a20 mode, the current time t is calculated at the current time 1 The line segment coordinates of the front arm and the rear arm of the tower crane B and the current moment t 1 The plane coordinates of the tower crane A are calculated, and then the minimum distance at the current moment is calculated; when calculating the minimum distance after the safe reserve moment, respectively calculating t 1 + delta t tower crane plane A coordinate and t 1 Calculating the minimum distance after the safe storage moment according to the coordinates of the front arm and the rear arm of the tower crane B at the + delta t moment;
in the a02 mode, the current time t is calculated at the current time 1 The line segment coordinates of the front arm and the rear arm of the tower crane A and the current moment t 1 The plane coordinates of the tower crane B are calculated, and then the minimum distance at the current moment is calculated; when calculating the minimum distance after the safe reserve moment, respectively calculating t 1 + delta t time tower crane A front and rear arm line segment coordinate and t 1 And calculating the minimum distance after the safe storage moment according to the plane coordinate of the tower crane B at the + delta t moment.
Preferably, the current time t 1 And t 1 The concrete calculation method of the front and rear arm line segments of the tower crane A and the front and rear arm line segments of the tower crane B at the moment of + delta t is as follows:
respectively calculating the current time t 1 The plane coordinates of the front end of the lifting arm and the back end of the counterweight arm of the tower crane A and the tower crane B pass through the current time t 1 Calculating the current time t by the plane coordinates of the front end of the lifting arm and the plane coordinates of the rear end of the counterweight arm of the tower crane A 1 The front and rear arm line segments of the tower crane A pass through the current time t 1 Calculating current time t by using plane coordinates of front end of lifting arm and plane coordinates of rear end of counterweight arm of tower crane B 1 Front and rear arm line segments of a tower crane B;
separately calculate t 1 The planar coordinates of the front ends of the lifting arms and the planar coordinates of the rear ends of the counterweight arms of the tower cranes A and B at the moment of + delta t are passed through t 1 Calculating t according to plane coordinates of front end of lifting arm and plane coordinates of rear end of counterweight arm of tower crane A at moment + delta t 1 The segment of the front and rear arms of the tower crane A at the moment of + delta t passes through t 1 Calculating t according to plane coordinates of front end of lifting arm and rear end of counterweight arm of tower crane B at + delta t moment 1 And the line segments of the front arm and the rear arm of the tower crane B at the moment of + delta t.
Preferably, the current time t 1 Crane arm front end plane coordinate P of tower crane A qa1 (X qa1 ，Y qa1 ) And the plane coordinate P of the rear end of the counterweight arm pa1 (X pa1 ，Y pa1 ) The specific calculation formula is as follows:
X qa1 ＝X a +R qa sinθ a1
Y qa1 ＝Y a +R qa cosθ a1
X pa1 ＝X a +R pa sin(θ a1 +180°)
Y pa1 ＝Y a +R pa cos(θ a1 +180°)
wherein, X a ，Y a Respectively represent the horizontal and vertical coordinates, R, of the plane A of the tower crane qa Representing radius of boom A, R of tower crane pa Representing the length, theta, of the balance arm A of the tower crane a1 Indicates the current time t 1 A boom of a tower crane A rotates by an angle;
t 1 + delta t moment tower crane A crane boom front end plane coordinate P qat (X qat ，Y qat ) And the plane coordinate P of the rear end of the counterweight arm pat (X pat ，Y pat ) The specific calculation formula is as follows:
X qat ＝X a +R qa sinθ at
Y qat ＝Y a +R qa cosθ at
X pat ＝X a +R pa sin(θ at +180°)
Y pat ＝Y a +R pa cos(θ at +180°)
wherein, theta at Represents t 1 The tower crane A boom rotation angle at + delta t moment has the calculation formula as follows:
Figure BDA0003751062580000051
Figure BDA0003751062580000052
Figure BDA0003751062580000053
wherein, theta a0 Represents t 0 Moment tower crane A boom rotation angle, omega qa1 ，ω qa0 Respectively representing the current time t 1 And t 0 Angular velocity of tower crane A boom at time, a qa1 Indicates the current time t 1 Angular acceleration of the jib of tower crane a.
Preferably, the current time t ， Coordinate P of central point of lifting rope of tower crane A da1 (X da1 ，Y da1 ) The specific calculation formula is as follows:
X da1 ＝X a +R fa1 sinθ a1
Y da1 ＝Y a +R fa1 cosθ a1
wherein, X a ，Y a Respectively represent the horizontal and vertical coordinates theta of the plane A of the tower crane a1 Indicates the current time t 1 Slewing angle of tower crane A boom, R fa1 Indicates the current time t 1 A trolley amplitude value of a tower crane A;
t 1 + delta t tower crane A lifting rope central point coordinate P dat (X dat ，Y dat ) The specific calculation formula is as follows:
X dat ＝X a +R fat sinθ at
Y dat ＝Y a +R fat cosθ at
wherein, theta at Represents t 1 + delta t moment tower crane A boom rotation angle, R fat Denotes t 1 The amplitude value of the tower crane A trolley at the moment of + delta t is calculated by the following specific formula:
Figure BDA0003751062580000061
Figure BDA0003751062580000062
Figure BDA0003751062580000063
wherein R is fa0 、R fa1 Represents t 0 Time and current time t 1 Amplitude value of tower crane A car, v fa0 And v fa1 Respectively represent t 0 Time and current time t 1 Speed of movement of tower crane A car, a fa1 Respectively representing the current time t 1 And (5) accelerating the movement of the trolley of the tower crane A.
Preferably, the current time t 1 Crane arm front end plane coordinate P of tower crane B qb1 (X qb1 ，Y qb1 ) And the plane coordinate P of the rear end of the counterweight arm pb1 (X pb1 ，Y pb1 ) The specific calculation formula is as follows:
X qb1 ＝X b +R qb sinθ b1
Y qb1 ＝Y b +R qb sinθ b1
X pb1 ＝X b +R pb sin(θ b1 +180°)
Y pb1 ＝Y b +R pb sin(θ b1 +180°)
wherein, X b ，Y b Respectively represent the horizontal and vertical coordinates, R, of the plane B of the tower crane qb Representing radius of boom of tower crane B, R pb Representing the length, theta, of the balance arm of the tower crane B b1 Indicates the current time t 1 A boom rotation angle of a tower crane B;
t 1 + delta t moment tower crane B crane boom front end plane coordinate P qbt (X qbt ，Y qbt ) And the plane coordinate P of the rear end of the counterweight arm pbt (X pbt ，Y pbt ) The specific calculation formula is as follows:
X qbt ＝X b +R qb sinθ bt
Y qbt ＝Y b +R qb sinθ bt
X pbt ＝X b +R pb sin(θ bt +180°)
Y pbt ＝Y b +R pb sin(θ bt +180°)
wherein, theta bt Represents t 1 The slewing angle of the cargo boom of the tower crane B at the moment of + delta t is calculated by the following formula:
Figure BDA0003751062580000071
Figure BDA0003751062580000072
Figure BDA0003751062580000073
wherein, theta b0 Represents t 0 Moment tower crane B boom rotation angle, omega qb1 ，ω qb0 Indicates the current time t 1 And t 0 Angular velocity of the jib of the tower crane B at that moment, a qb1 Indicates the current time t 1 Angular acceleration of the jib of tower crane B.
Preferably, the current time t 1 Coordinate P of central point of lifting rope of tower crane B db1 (X db1 ，Y db1 ) The specific calculation formula is as follows:
X db1 ＝X b +R fb1 sinθ b1
Y db1 ＝Y b +R fb1 sinθ b1
wherein, X b ，Y b Respectively representing the horizontal and vertical coordinates theta of the plane B of the tower crane b1 Indicates the current time t 1 Slewing angle of jib of tower crane B, R fb1 Indicates the current time t 1 The trolley amplitude value of the tower crane B;
t 1 + delta t tower crane B lifting rope central point coordinate P dbt (X dbt ，Y dbt ) The specific calculation formula is as follows:
X dbt ＝X b +R fbt sinθ bt
Y dbt ＝Y b +R fbt cosθ bt
wherein, theta bt Represents t 1 B boom rotation angle, R, of tower crane at moment of +/-delta t fbt Denotes t 1 The tower crane B trolley amplitude value at the moment of +/-deltat has the specific calculation formula as follows:
Figure BDA0003751062580000081
Figure BDA0003751062580000082
Figure BDA0003751062580000083
wherein R is fb0 ,R fb1 Represents t 0 Time and current time t 1 Amplitude value of tower crane B fb0 And v fb1 Respectively represent t 0 Time and current time t 1 Speed of movement of tower crane B carriage, a fb1 Respectively represent the current time t 1 And (5) accelerating the movement of the trolley of the tower crane B.
According to the technical scheme, compared with the prior art, the anti-collision method for the tower crane group based on the motion trend is provided, the safe time reserve delta t required by a driver from receiving a pre-alarm to finishing the anti-collision operation is considered, the motion trend of the tower crane and surrounding tower cranes is used for estimating the running position relation in the current time and the braking time, the current working state of the tower crane is judged, and whether the tower crane is in a dangerous state or not is further judged, so that the safety of the whole tower crane system is ensured.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the embodiments or the prior art descriptions will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
Fig. 1 is a flow chart of a tower crane group anti-collision method based on motion trend provided by the invention.
Fig. 2 is a plan view of the distance between the tower crane A and the tower crane B.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment of the invention discloses a tower crane group anti-collision method based on a movement trend, which comprises the following steps as shown in figure 1:
s1: obtaining coordinates of two adjacent tower cranes, and calculating a distance LL between the two tower cranes, as shown in FIG. 2:
Figure BDA0003751062580000091
wherein X a ,Y a Respectively represents the horizontal and vertical coordinates, X, of the plane A of the tower crane b ,Y b Respectively representing the horizontal and vertical coordinates of the plane B of the tower crane;
s2: acquiring the lengths of the crane arms of two adjacent tower cranes, if the sum of the lengths of the crane arms of the two tower cranes is greater than or equal to the distance between the two tower cranes, considering A, B anti-collision between the tower cranes, entering a collision algorithm between the tower cranes, and otherwise, not considering collision between the tower cranes;
s3: when the anti-collision between the tower cranes needs to be considered, inquiring a collision mode based on the acquired real-time data:
when H is present qa ≥H qb When, if H qa -H qb ≤H qb Or when H qa ＜H qb When, if H qb -H qa ≤h qa Then, enter a00 mode:
in the a00 mode, the current time t is calculated respectively 1 The plane coordinates of the front end of the lifting arm and the back end of the counterweight arm of the tower crane A and the tower crane B pass through the current time t 1 Calculating the current time t by the plane coordinates of the front end of the lifting arm and the plane coordinates of the rear end of the counterweight arm of the tower crane A 1 The coordinates of the front and rear arm line segments of the tower crane A pass through the current time t 1 Calculating the current time t by the plane coordinates of the front end of the lifting arm and the plane coordinates of the rear end of the counterweight arm of the tower crane B 1 Coordinates of line segments of front and rear arms of a tower crane B;
calculating t 1 Planar coordinates of front ends of lifting arms and rear ends of counterweight arms of tower cranes A and B at moment of +/-delta t, passing through t 1 Calculating t by using plane coordinates of front end of lifting arm and plane coordinates of rear end of counterweight arm of tower crane A at moment of +/-delta t 1 Coordinates of front and rear arm line segments of tower crane A at moment of +/-delta t, passing through t 1 Calculating t from plane coordinates of front end of lifting arm and plane coordinates of rear end of counterweight arm of tower crane B at moment of +/-delta t 1 Coordinates of front and rear arm line segments of the tower crane B at the moment of +/-deltat;
when calculating the minimum distance at the time, the current time t is passed 1 Line segment coordinates of front arm and rear arm of tower crane A and current time t 1 The coordinates of the front and rear arm line segments of the tower crane B are obtained, and when the minimum distance after the safe storage moment is calculated, the t is passed 1 Coordinates of line segments of front arm and rear arm of tower crane A at moment of +/-delta t and t 1 And (5) obtaining the coordinates of the front and rear arm line sections of the tower crane B at the moment of +/-delta t.
The A00 mode is used for dealing with the situations that a crane boom A of a tower crane is forbidden to be close to a crane boom B of the tower crane, the crane boom A of the tower crane is forbidden to be close to a counterweight arm B of the tower crane, the crane boom B of the tower crane is forbidden to be close to a counterweight arm A of the tower crane and the like.
When H is present qa ≥H qb When is at H qa -H qb ＞h qb Entering a10 mode:
respectively calculating the current time t 1 The plane coordinates of the front end of the lifting arm and the back end of the counterweight arm of the tower crane B pass through the current moment t 1 Calculating current time t by using plane coordinates of front end of lifting arm and plane coordinates of rear end of counterweight arm of tower crane B 1 Line segment coordinates of front arm and rear arm of tower crane BCalculating the current time t 1 Coordinates of the central point of a lifting rope of the tower crane A;
calculating t 1 The plane coordinates of the front end of the lifting arm and the rear end of the counterweight arm of the tower crane B at the moment of +/-delta t pass through t 1 Calculating t by using plane coordinates of front end of lifting arm and plane coordinates of rear end of counterweight arm of tower crane B at moment of +/-delta t 1 Coordinates of front and rear arm line segments of tower crane B at +/-delta t moment and t calculation 1 Coordinates of the center point of a lifting rope of the tower crane A at the moment of +/-deltat;
when calculating the minimum distance at the time, the current time t is passed 1 Line segment coordinates of front arm and rear arm of tower crane B and current moment t 1 The coordinate of the central point of the lifting rope of the tower crane A is obtained, and when the minimum distance after the safe storage moment is calculated, the t is passed 1 Coordinates of line segments of front arm and rear arm of tower crane B at moment of +/-delta t and t 1 And obtaining coordinates of the center point of the lifting rope A of the tower crane at the moment of +/-delta t.
The A10 mode deals with the risk that a lifting rope of the tower crane A collides with a lifting arm or a counterweight arm of a tower crane B; and the lifting rope of the tower crane A is forbidden to lean on the lifting arm or the counterweight arm of the tower crane B.
When H is present qa ＜H qb When, if H qb -H qa ＞H qa Entering a01 mode:
respectively calculating the current time t 1 The plane coordinates of the front end of the lifting arm and the back end of the counterweight arm of the tower crane A pass through the current moment t 1 Calculating the current time t by the plane coordinates of the front end of the lifting arm and the plane coordinates of the rear end of the counterweight arm of the tower crane A 1 Calculating the coordinates of the front and rear arm line segments of the tower crane A at the current moment t 1 Coordinates of the central point of a lifting rope of the tower crane B;
calculating t 1 The plane coordinates of the front end of the lifting arm and the rear end of the counterweight arm of the tower crane A at the moment of +/-delta t are passed through t 1 Calculating t by using plane coordinates of front end of lifting arm and plane coordinates of rear end of counterweight arm of tower crane A at moment of +/-delta t 1 Coordinates of front arm and rear arm line of tower crane A at moment of +/-delta t and calculating t 1 Coordinates of the center point of a lifting rope of a tower crane B at the moment of +/-deltat;
when calculating the minimum distance at the time, the current time t is passed 1 Line segment coordinates of front arm and rear arm of tower crane A and current time t 1 Coordinate calculation of center point of B lifting rope of tower craneWhen the minimum distance after calculating the safe reserve time is calculated, pass t 1 Coordinates of line segments of front arm and rear arm of tower crane A at moment of +/-delta t and t 1 And obtaining coordinates of the center point of the lifting rope of the tower crane B at the moment of +/-delta t.
The A01 mode deals with the risk that the lifting arm of the tower crane A collides with the lifting rope of the tower crane B; and the crane arm of the tower crane A is forbidden to lean on the lifting rope of the tower crane B.
When H is present qa ≥H qb When, if H qb +H 3b -H qa ≤h qa Entering a20 mode:
respectively calculating the current time t 1 The plane coordinates of the front end of the lifting arm and the back end of the counterweight arm of the tower crane B pass through the current moment t 1 Calculating current time t by using plane coordinates of front end of lifting arm and plane coordinates of rear end of counterweight arm of tower crane B 1 Coordinates of line segments of front and rear arms of a tower crane B; and calculating the current time t 1 The plane coordinates of the tower crane A;
calculating t 1 The plane coordinates of the front end of the lifting arm and the rear end of the counterweight arm of the tower crane B at the moment of +/-delta t are t 1 Calculating t by using plane coordinates of front end of lifting arm and plane coordinates of rear end of counterweight arm of tower crane B at moment of +/-delta t 1 Coordinates of front and rear arm line segments of the tower crane B at the moment of +/-deltat; and calculating t 1 A tower crane A plane coordinate at the moment of +/-delta t;
when calculating the minimum distance at the time, the current time t is passed 1 Line segment coordinates of front arm and rear arm of tower crane B and current time t 1 The plane coordinate of the tower crane A is calculated, and when the minimum distance after the safe storage moment is calculated, the minimum distance is obtained through t 1 Coordinates of line segments of front arm and rear arm of tower crane B at moment of +/-delta t and t 1 And obtaining the plane coordinates of the tower crane A at the moment of +/-delta t.
The A20 mode is used for dealing with the condition that a crane arm of a tower crane B is forbidden to lean on a tower body of the tower crane A.
When H is present qa ＜H qb When, if H qa +H 3a -H qb ≤h qb Entering a02 mode:
respectively calculating the current time t 1 The plane coordinates of the front end of the lifting arm and the back end of the counterweight arm of the tower crane A pass through the current moment t 1 Plane coordinates of front end of lifting arm and plane seat of rear end of counterweight arm of tower crane ACalculating the current time t 1 Coordinates of front and rear arm line segments of a tower crane A; and calculating the current time t 1 The plane coordinates of the tower crane B;
calculating t 1 The plane coordinates of the front end of the lifting arm and the rear end of the counterweight arm of the tower crane A at the moment of +/-delta t are passed through t 1 Calculating t by using plane coordinates of front end of lifting arm and plane coordinates of rear end of counterweight arm of tower crane A at moment of +/-delta t 1 Coordinates of the front arm and the rear arm of the tower crane A at the moment of + delta t; and calculating t 1 And (4) plane coordinates of the tower crane B at the moment of +/-delta t.
When calculating the minimum distance at the time, the current time t is passed 1 Line segment coordinates of front arm and rear arm of tower crane A and current time t 1 The B plane coordinate of the tower crane is obtained, and when the minimum distance after the safe storage moment is calculated, the t is passed 1 Coordinates of line segments of front arm and rear arm of tower crane A at moment of +/-delta t and t 1 And obtaining the plane coordinate of the tower crane B at the moment of +/-delta t.
The A02 mode is used for dealing with the condition that a crane arm of a tower crane A forbids a tower body of a tower crane B.
Wherein, the current time t 1 Crane arm front end plane coordinate P of tower crane A qa1 (X qa1 ，Y qa1 ) And the plane coordinate P of the rear end of the counterweight arm pa1 (X pal ，Y pa1 ) The specific calculation formula is as follows:
X qa1 ＝X a +R qa sinθ a1
Y qa1 ＝Y a +R qa cosθ a1
X pa1 ＝X a +R pa sin(θ a1 +180°)
Y pa1 ＝Y a +R pa cos(θ a1 +180°)
wherein X a ，Y a Respectively represent the horizontal and vertical coordinates, R, of the plane A of the tower crane qa Representing radius of boom A, R of tower crane pa Representing the length, theta, of the balance arm A of the tower crane a1 Representing the current time t 1 A boom of the tower crane A rotates by an angle;
t 1 + delta t moment tower crane A crane boom front end plane coordinate P qat (X qat ，Y qat ) And a counterweight armRear end plane coordinate P pat (X pat ，Y pat ) The specific calculation formula is as follows:
X qat ＝X a +R qa sinθ at
Y qat ＝Y a +R qa cosθ at
X pat ＝X a +R pa sin(θ at +180°)
Y pat ＝Y a +R pa cos(θ at +180°)
wherein, theta at Represents t 1 The slewing angle of the jib A of the tower crane at the moment of + delta t is calculated by the following formula:
Figure BDA0003751062580000131
Figure BDA0003751062580000132
Figure BDA0003751062580000133
wherein, theta a0 Represents t 0 Moment tower crane A boom rotation angle, omega qa1 ，ω qa0 Respectively representing the current time t 1 And t 0 Angular velocity of tower crane A boom at time, a qa1 Indicates the current time t 1 Angular acceleration of the jib of tower crane a.
Current time t 1 Coordinate P of central point of lifting rope of tower crane A da1 (X dal ，Y da1 ) The specific calculation formula is as follows:
X da1 ＝X a +R fa1 sinθ a1
Y da1 ＝Y a +R fa1 cosθ a1
wherein, X a ，Y a Respectively representing the horizontal and vertical coordinates theta of the plane A of the tower crane a1 Indicating the current timeMoment t 1 Slewing angle of tower crane A boom, R fa1 Indicates the current time t 1 A trolley amplitude value of the tower crane A;
t 1 + delta t tower crane A lifting rope central point coordinate P dat (X dat ，Y dat ) The specific calculation formula is as follows:
X dat ＝X a +R fat sinθ at
Y dat ＝Y a +R fat cosθ at
wherein, theta at Represents t 1 + delta t moment tower crane A boom rotation angle, R fat Represents t 1 The amplitude value of the tower crane A trolley at the moment of + delta t is calculated by the following specific formula:
Figure BDA0003751062580000141
Figure BDA0003751062580000142
Figure BDA0003751062580000143
wherein R is fa0 、R fa1 Represents t 0 Time and current time t 1 Amplitude value of tower crane A car, v fa0 And v fa1 Respectively represent t 0 Time and current time t 1 Speed of travel of Tower A Cart, a fa1 Respectively representing the current time t 1 And (5) accelerating the movement of the trolley of the tower crane A.
Current time t 1 Crane arm front end plane coordinate P of tower crane B qb1 (X qb1 ，Y qb1 ) And the plane coordinate P of the rear end of the counterweight arm pb1 (X pb1 ，Y pb1 ) The specific calculation formula is as follows:
X qb1 ＝X b +R qb sinθ b1
Y qb1 ＝Y b +R qb sinθ b1
X pb1 ＝X b +R pb sin(θ b1 +180°)
Y pb1 ＝Y b +R pb sin(θ b1 +180°)
wherein, X b ，Y b Respectively represent the horizontal and vertical coordinates, R, of the plane B of the tower crane qb Representing radius of boom of tower crane B, R pb Representing the length, theta, of the balance arm of the tower crane B b1 Indicates the current time t 1 A boom rotation angle of a tower crane B;
t 1 + delta t moment tower crane B crane boom front end plane coordinate P qbt (X qbt ，Y qbt ) And the plane coordinate P of the rear end of the counterweight arm pbt (X pbt ，Y pbt ) The specific calculation formula is as follows:
X qbt ＝X b +R qb sinθ bt
Y qbt ＝Y b +R qb sinθ bt
X pbt ＝X b +R pb sin(θ bt +180°)
Y pbt ＝Y b +R pb sin(θ bt +180°)
wherein, theta bt Represents t 1 The rotating angle of a cargo boom of the tower crane B at the moment of + delta t has the calculation formula as follows:
Figure BDA0003751062580000151
Figure BDA0003751062580000152
Figure BDA0003751062580000153
wherein, theta b0 Represents t 0 Moment tower crane B boom rotation angle, omega qb1 ，ω qb0 Indicates the current time t 1 And t 0 Angular velocity of the jib of the tower crane B at that moment, a qb1 Indicates the current time t 1 Angular acceleration of the jib of tower crane B.
Current time t 1 Coordinate P of central point of lifting rope of tower crane B db1 (X db1 ，Y db1 ) The specific calculation formula is as follows:
X db1 ＝X b +R fb1 sinθ b1
Y db1 ＝Y b +R fb1 sinθ b1
wherein, X b ，Y b Respectively representing the horizontal and vertical coordinates theta of the plane B of the tower crane b1 Indicates the current time t 1 Slewing angle of jib of tower crane B, R fb1 Indicates the current time t 1 The trolley amplitude value of the tower crane B;
t 1 + delta t tower crane B lifting rope central point coordinate P dbt (X dbt ，Y dbt ) The specific calculation formula is as follows:
X dbt ＝X b +R fbt sinθ bt
Y dbt ＝Y b +R fbt cosθ bt
wherein, theta bt Represents t 1 + delta t moment tower crane B boom rotation angle, R fbt Represents t 1 The tower crane B trolley amplitude value at the moment of + delta t has the specific calculation formula as follows:
Figure BDA0003751062580000154
Figure BDA0003751062580000161
Figure BDA0003751062580000162
wherein R is fb0 ,R fb1 Represents t 0 Time and current time t 1 Amplitude value of tower crane B fb0 And v fb1 Respectively represent t 0 Time and current time t 1 Speed of movement of tower crane B carriage, a fb1 Respectively representing the current time t 1 And (5) accelerating the movement of the trolley of the tower crane B.
S4: according to group tower minimum safety precaution limit value (LL) min1 ) Group tower minimum safety alarm limit (LL) min2 ) And calculating whether to perform pre-alarming. First at the current moment according to the current moment minimum distance (LL) min ) Judging and judging LL min ≤LL min1 If yes, determining LL if yes min ≤LL min2 Whether the result is true or not; if not, the minimum distance LL at the current moment min >LL min1 If the time after delta t is entered, the minimum distance LL after the safe reserve time is calculated mint If LL is mint ≤LL min1 Early warning and decelerating; if LL mint >LL min1 The operation is safe;
in judging LL min ≤LL min2 And if the brake is established, alarming and braking are performed, and early warning and deceleration are not established.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. The device disclosed by the embodiment corresponds to the method disclosed by the embodiment, so that the description is simple, and the relevant points can be referred to the method part for description.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (9)

1. A tower crane group anti-collision method based on motion trend is characterized by comprising the following steps:
acquiring coordinates of two adjacent tower cranes, and calculating the distance between the two tower cranes;
acquiring the lengths of the cargo booms of two adjacent tower cranes, and entering a collision algorithm between the tower cranes if the sum of the lengths of the cargo booms of the two tower cranes is greater than or equal to the distance between the two tower cranes:
receiving real-time information of the tower crane and inquiring a collision mode;
and judging the minimum distance between the current moment and the safety storage moment according to the collision mode, and performing early warning deceleration or warning braking according to the relation between the minimum distance, the minimum safety early warning limit of the tower group and the minimum safety warning limit value of the group tower.
2. The tower crane group tower anti-collision method based on the motion trend as claimed in claim 1, wherein the receiving of the real-time information of the tower cranes and the query of the collision mode specifically comprises:
acquiring real-time information of two tower cranes in real time, wherein the real-time information comprises the height H of a tower cap of a tower crane A 3a Tower cap height H of tower crane B 3b And the sagging bottom height H of the balance weight of the tower crane A pa And the height H of the drooping bottom of the balance weight of the tower crane B pb And the bottom height H of the cargo boom of the tower crane A qa And the bottom height H of the cargo boom of the tower crane B qb And the height h of the cargo boom of the tower crane A qa Height h of cargo boom of tower crane B qb ；
If H qa -H pa If the value is greater than the preset value, the safety reserve is enlarged, h qa ＝h qa +(H qa -H pa )；
If H is qb -H pb If the value is greater than the preset value, the safety reserve is enlarged, h qb ＝h qb +(H qb -H pb )；
When H is present qa ≥H qb When, if H qa -H qb ≤h qb Or when H qa ＜H qb When, if H qb -H qa ≤h qa When the current time reaches the A00 mode;
when H is present qa ≥H qb When the temperature of the water is higher than the set temperature,if H is qa -H qb ＞h qb Entering an A10 mode;
when H is present qa ＜H qb When, if H qb -H qa ＞h qa Entering an A01 mode;
when H is present qa ≥H qb When, if H qb +H 3b -H qa ≤h qa Entering an A20 mode;
when H is present qa ＜H qb When, if H qa +H 3a -H qb ≤h qb And enters the a02 mode.
3. The tower crane group tower anti-collision method based on the motion trend as claimed in claim 2, wherein the early warning deceleration or warning braking judgment principle is as follows:
judging whether the minimum distance at the current moment is less than or equal to the minimum safety early warning limit value of the group tower or not, if so, further judging whether the minimum distance at the current moment is less than the minimum safety early warning limit value of the group tower or not, if not, calculating the minimum distance after the safety storage moment, judging whether the minimum distance after the safety storage moment is less than or equal to the minimum safety early warning limit value of the group tower or not, if so, early warning and decelerating, otherwise, the minimum distance is in a safety state;
and judging whether the minimum distance at the current moment is less than or equal to the group tower minimum safety alarm limit value, if so, alarming and braking, and if not, early warning and deceleration are not met.
4. The tower crane group tower anti-collision method based on the motion trend as claimed in claim 3, wherein the minimum distance judgment according to the collision mode specifically comprises:
in the a00 mode, the current time t is calculated at the current time 1 Front and rear arm line segment coordinates of tower crane A and current time t 1 Calculating the minimum distance at the current moment according to the line segment coordinates of the front arm and the rear arm of the tower crane B; when calculating the minimum distance after the safe reserve moment, respectively calculating t 1 Coordinates of line segment of front arm and rear arm of tower crane A at moment of +/-delta t and t 1 Coordinates of front and rear arm line segments of tower crane B at +/-delta t moment so as to calculate minimum value after safe storage momentA distance;
in the a10 mode, the current time t is calculated at the current time 1 Coordinates of center point of lifting rope A of tower crane and current moment t 1 Calculating the minimum distance at the current moment according to the line segment coordinates of the front arm and the rear arm of the tower crane B; when calculating the minimum distance after the safe reserve moment, respectively calculating t 1 Coordinate of center point of lifting rope A of tower crane at moment +/-Delta t and t 1 Calculating the minimum distance after the safe storage moment according to the coordinates of the front arm and the rear arm of the tower crane B at the moment of +/-deltat;
in the a01 mode, the current time t is calculated at the current time 1 The line segment coordinates of the front arm and the rear arm of the tower crane A and the current moment t 1 The coordinate of the central point of the lifting rope of the tower crane B is used for calculating the minimum distance at the current moment; when calculating the minimum distance after the safe reserve moment, respectively calculating t 1 Coordinates of line segment of front arm and rear arm of tower crane A at moment of +/-delta t and t 1 Calculating the coordinate of the center point of the lifting rope of the tower crane B at the moment of +/-deltat, and further calculating the minimum distance after the safe storage moment;
in the a20 mode, the current time t is calculated at the current time 1 The line segment coordinates of the front arm and the rear arm of the tower crane B and the current moment t 1 The plane coordinates of the tower crane A are calculated, and then the minimum distance at the current moment is calculated; when calculating the minimum distance after the safe reserve moment, respectively calculating t 1 Tower crane plane A coordinate and t at moment of +/-delta t 1 Calculating the minimum distance after the safe storage moment according to the coordinates of the front arm and the rear arm of the tower crane B at the moment of +/-deltat;
in the a02 mode, the current time t is calculated at the current time 1 The line segment coordinates of the front arm and the rear arm of the tower crane A and the current moment t 1 The plane coordinates of the tower crane B are calculated, and then the minimum distance at the current moment is calculated; when calculating the minimum distance after the safe reserve moment, respectively calculating t 1 Coordinates of line segment of front arm and rear arm of tower crane A at moment of +/-delta t and t 1 And calculating the minimum distance after the safe storage time according to the plane coordinate of the tower crane B at the moment of +/-delta t.
5. The tower crane group tower anti-collision method based on motion trend as claimed in claim 4, wherein the current time is the current timeMoment t 1 And t 1 The concrete calculation method of the front and rear arm line segments of the tower crane A and the front and rear arm line segments of the tower crane B at the moment of +/-delta t is as follows:
respectively calculating the current time t 1 The plane coordinates of the front end of the lifting arm and the back end of the counterweight arm of the tower crane A and the tower crane B pass through the current time t 1 Calculating the current moment t1 of the front and rear arm line segments of the tower crane A according to the plane coordinates of the front end of the lifting arm and the rear end of the counterweight arm of the tower crane A, and calculating the current moment t1 of the front and rear arm line segments of the tower crane A according to the current moment t 1 Calculating current time t by using plane coordinates of front end of lifting arm and plane coordinates of rear end of counterweight arm of tower crane B 1 Front and rear arm line segments of a tower crane B;
separately calculate t 1 The plane coordinates of the front ends of the lifting arms and the back ends of the counterweight arms of the tower cranes A and B at the moment of +/-deltat, passing through t 1 Calculating t by using plane coordinates of front end of lifting arm and plane coordinates of rear end of counterweight arm of tower crane A at moment of +/-delta t 1 The front and rear arm line segments of the tower crane A at the moment of +/-delta t pass through t 1 Calculating t by using plane coordinates of front end of lifting arm and plane coordinates of rear end of counterweight arm of tower crane B at moment of +/-delta t 1 And c, front and rear arm line segments of the tower crane B at the moment of +/-delta t.
6. The tower crane group tower anti-collision method based on motion trend as claimed in claim 5, wherein the current time t is 1 Crane arm front end plane coordinate P of tower crane A qa1 (X qa1 ，Y qa1 ) And the plane coordinate P of the rear end of the counterweight arm pa1 (X pa1 ，Y pa1 ) The specific calculation formula is as follows:
X qa1 ＝X a +R qa sinθ a1
Y qa1 ＝Y a +R qa cosθ a1
X pa1 ＝X a +R pa sin(θ a1 +180°)
Y pa1 ＝Y a +R pa cos(θ a1 +180°)
wherein, X a ，Y a Respectively represent the horizontal and vertical coordinates, R, of the plane A of the tower crane qa Representing radius of boom A, R of tower crane pa Representing the length, theta, of the balance arm A of the tower crane a1 Indicates the current time t 1 A boom of the tower crane A rotates by an angle;
t 1 planar coordinate P of front end of lifting arm of tower crane A at moment of +/-delta t qat (X qat ，Y qat ) And the plane coordinate P of the rear end of the counterweight arm pat (X pat ，Y pat ) The specific calculation formula is as follows:
X qat ＝X a +R qa sinθ at
Y qat ＝Y a +R qa cosθ at
X pat ＝X a +R pa sin(θ at +180°)
Y pat ＝Y a +R pa cos(θ at +180°)
wherein, theta at Represents t 1 The rotating angle of the crane arm A of the tower crane at the moment of +/-delta t is calculated by the following formula:
Figure FDA0003751062570000041
Figure FDA0003751062570000042
Figure FDA0003751062570000043
wherein, theta a0 Represents t 0 Moment tower crane A boom rotation angle, omega qa1 ，ω qa0 Respectively representing the current time t 1 And t 0 Angular velocity of tower crane A boom at time, a qa1 Indicates the current time t 1 Angular acceleration of the jib of tower crane a.
7. The tower crane group tower anti-collision method based on motion trend as claimed in claim 6, wherein the current time t is 1 Coordinate P of central point of lifting rope of tower crane A da1 (X da1 ，Y da1 ) The specific calculation formula is as follows:
X da1 ＝X a +R fa1 sinθ a1
Y da1 ＝Y a +R fa1 cosθ a1
wherein, X a ，Y a Respectively representing the horizontal and vertical coordinates theta of the plane A of the tower crane a1 Indicates the current time t 1 Slewing angle of tower crane A boom, R fa1 Indicates the current time t 1 A trolley amplitude value of the tower crane A;
t 1 coordinate P of center point of lifting rope A of tower crane at moment of +/-delta t dat (X dat ，Y dat ) The specific calculation formula is as follows:
X dat ＝X a +R fat sinθ at
Y dat ＝Y a +R fat cosθ at
wherein, theta at Represents t 1 B, rotating angle of A boom of tower crane at moment of +/-delta t, R fat Represents t 1 The amplitude value of the trolley A of the tower crane at the moment of +/-deltat is calculated by the following specific formula:
Figure FDA0003751062570000051
Figure FDA0003751062570000052
Figure FDA0003751062570000053
wherein R is fa0 、R fa1 Represents t 0 Time and current time t 1 Amplitude value of tower crane A car, v fa0 And v fa1 Respectively represent t 0 Time and current time t 1 Speed of movement of tower crane A car, a fa1 Respectively representing the current time t 1 And (5) accelerating the movement of the trolley of the tower crane A.
8. The tower crane group tower anti-collision method based on motion trend as claimed in claim 5, wherein the current time t is 1 Crane arm front end plane coordinate P of tower crane B qb1 (X qb1 ，y qb1 ) And the plane coordinate P of the rear end of the counterweight arm pb1 (X pb1 ，Y pb1 ) The specific calculation formula is as follows:
X qb1 ＝X b +R qb sinθ b1
Y qb1 ＝Y b +R qb sinθ b1
X pb1 ＝X b +R pb sin(θ b1 +180°)
Y pb1 ＝Y b +R pb sin(θ b1 +180°)
wherein, X b ，Y b Respectively represent the horizontal and vertical coordinates, R, of the plane B of the tower crane qb Representing radius of boom of tower crane B, R pb Representing the length, theta, of the balance arm of the tower crane B b1 Indicates the current time t 1 A boom rotation angle of a tower crane B;
t 1 planar coordinate P of front end of lifting arm of tower crane B at moment of +/-delta t qbt (X qbt ，Y qbt ) And the plane coordinate P of the rear end of the counterweight arm pbt (X pbt ，Y pbt ) The specific calculation formula is as follows:
X qbt ＝X b +R qb sinθ bt
Y qbt ＝Y b +R qb sinθ bt
X pbt ＝X b +R pb sin(θ bt +180°)
Y pbt ＝Y b +R pb sin(θ bt +180°)
wherein, theta bt Represents t 1 The rotating angle of the cargo boom of the tower crane B at the moment of +/-deltat is calculated by the following formula:
Figure FDA0003751062570000061
Figure FDA0003751062570000062
Figure FDA0003751062570000063
wherein, theta b0 Represents t 0 Moment tower crane B boom rotation angle, omega qb1 ，ω qb0 Indicates the current time t 1 And t 0 Angular velocity of the jib of the tower crane B at that moment, a qb1 Indicates the current time t 1 Angular acceleration of the jib of tower crane B.
9. The tower crane group tower anti-collision method based on motion trend as claimed in claim 8, wherein the current time t is 1 Coordinate P of central point of lifting rope of tower crane B db1 (X db1 ，Y db1 ) The specific calculation formula is as follows:
X db1 ＝X b +R fb1 sinθ b1
Y db1 ＝Y b +R fb1 sinθ b1
wherein, X b ，Y b Respectively representing the horizontal and vertical coordinates theta of the plane B of the tower crane b1 Indicates the current time t 1 Slewing angle of jib of tower crane B, R fb1 Indicates the current time t 1 The trolley amplitude value of the tower crane B;
t 1 coordinate P of center point of lifting rope B of tower crane at moment of +/-delta t dbt (X dbt ，Y dbt ) The specific calculation formula is as follows:
X dbt ＝X b +R fbt sinθ bt
Y dbt ＝Y b +R fbt cosθ bt
wherein, theta bt Represents t 1 Time of +. DELTA.tSlewing angle of jib of tower crane B, R fbt Represents t 1 The tower crane B trolley amplitude value at the moment of +/-deltat has the specific calculation formula as follows:
Figure FDA0003751062570000071
Figure FDA0003751062570000072
Figure FDA0003751062570000073
wherein R is fb0 ，R fb1 Represents t 0 Time and current time t 1 Amplitude value of tower crane B fb0 And v fb1 Respectively represent t 0 Time and current time t 1 Speed of movement of tower crane B carriage, a fb1 Respectively representing the current time t 1 And (5) accelerating the movement of the trolley of the tower crane B.
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