CN106021672B - It is electrolysed the method for building up of the kinetic model of dedicated OTC's trolley - Google Patents
It is electrolysed the method for building up of the kinetic model of dedicated OTC's trolley Download PDFInfo
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- CN106021672B CN106021672B CN201610316506.2A CN201610316506A CN106021672B CN 106021672 B CN106021672 B CN 106021672B CN 201610316506 A CN201610316506 A CN 201610316506A CN 106021672 B CN106021672 B CN 106021672B
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/30—Circuit design
- G06F30/36—Circuit design at the analogue level
- G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
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- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
Abstract
The invention discloses a kind of method for building up of kinetic model for being electrolysed dedicated OTC's trolley, comprising steps of according to the density of air, acceleration of gravity, the pivot angle of pole plate, the length of pole plate and width, the relationship between pole plate windage during the swing and the pivot angle of pole plate is established using aerodynamics；Using trolley, suspender and pole plate as a vibrational system, according to the relationship between pole plate windage during the swing and the pivot angle of pole plate, the kinetics equation of system is derived from by Lagrange's equation；Generalized coordinates is chosen, the freedom degree of analysis system obtains the kinetic model of trolley.The present invention is electrolysed the mechanical mechanism feature of dedicated bridge crane by analysis, it is established on the basis of reasonable equivalent-simplification and practical very close kinetic model, the precise positioning of dedicated bridge crane is electrolysed for follow-up study and anti-swing control provides basis, has a wide range of applications meaning in nonferrous metallurgy field.
Description
Technical field
The present invention relates to be electrolysed dedicated bridge-type crane field, more particularly to the power of the dedicated OTC's trolley of electrolysis
Learn the method for building up of model.
Background technique
Bridge crane also known as driving, overhead traveling crane, are a kind of lifting handbarrows indispensable in modern industrial production, main
It is used for the lifting, carrying, handling etc. of various materials.In factory, mine, harbour, bridge, power station, construction site, warehouse etc.
In each production division, all it is widely applied.
It is electrolysed dedicated bridge crane to be mainly made of cart, trolley and lifting means, wherein cart is in the horizontal direction
Do it is lateral operation, trolley does longitudinal movement, hoisting hanger moves in the vertical direction.Such as in cupric electrolysis workshop, cathode-anode plate electricity
The solution period is certain, and when electrolysing period terminates, the confidential pole plate that can quickly complete of overhead traveling crane updates work, this requires trolley reciprocal
When handling pole plate, the speed of travel is fast, to guarantee the production efficiency of potroom.And due between electrolytic cell and electrolytic cell, yin,
Distance is smaller between anode plate, for the generation of the major accidents such as the Faradaic current short circuit that avoids tens of thousands of amperes of electrolytic cell, it is desirable that hang
Tool can be rested in precisely right above target electrolytic cell when playing low water, and positioning accuracy is generally grade.Since trolley transported
The factors such as acceleration, retarded motion in journey make electrolytic pole board generate swing during hoisting transportation, and it is approximately without hindrance that this, which is waved,
Buddhist nun's vibration, the pendulum that disappears naturally by air damping will occupy a large amount of service working time, can also cause positioning inaccurate, cause operative employee
People positions repeatedly.Therefore research copper electrolytic process bridge crane control problem it is particularly important, and its basis then be establish with
Actually close kinetic model.
It is existing to the research of general bridge crane at present very much, and propose multi-modeling method and model.But
For dedicated bridge crane is electrolysed, due to its special hanger structure and specific application, current such dedicated lifting
The modeling method of machine is in blank.
Summary of the invention
It is an object of that present invention to provide a kind of method for building up of kinetic model for being electrolysed dedicated OTC's trolley, with
It solves to be electrolysed the technical issues of can not modeling of dedicated bridge crane.
To achieve the above object, building the present invention provides a kind of kinetic model for being electrolysed dedicated OTC's trolley
Cube method, comprising the following steps:
S1: it according to the density of air, acceleration of gravity, the pivot angle of pole plate, the length of pole plate and width, is built using Bernoulli equation
Relationship between vertical pole plate windage during the swing and the pivot angle of pole plate；
S2: using trolley, suspender and pole plate as a vibrational system, according to pole plate windage during the swing and pole plate
Pivot angle between relationship, the kinetics equation of system is derived from by Lagrange's equation；
S3: choosing generalized coordinates, and the freedom degree of analysis system obtains the kinetic model of trolley.
As further improvements in methods of the invention:
Relationship between pole plate windage during the swing and the pivot angle of pole plate are as follows:
Wherein, fmFor windage suffered by pole plate；ρ, g are respectively the density and acceleration of gravity of air；2l3、2l4Respectively
The length and width of pole plate；Ds is the cell area on pole plate；θ2For the pivot angle of pole plate；Σ is plate regions；X and y is respectively to establish
Coordinate system cell area abscissa and ordinate,For pole plate pivot angle speed.
The kinetics equation of system are as follows:
Wherein: L=T-V, T are the kinetic energy of system, and V is the potential energy of system, Q'jFor the corresponding generalized force of generalized coordinates, qjFor
Generalized coordinates, k are the freedom degree of system.
The kinetic energy of system:
Wherein,The respectively kinetic energy of trolley, suspender inner frame and pole plate, M are the quality of trolley, m1For inside casing
The quality of frame, m2For the quality of pole plate.
In step S3, three generalized coordinates, respectively x, θ are chosen1,θ2, θ1For the pivot angle of inner frame lifting rope, then can obtain:
The kinetic energy of system:
Wherein, a is lifting rope length,For the pivot angle speed of inner frame lifting rope.
In formula (10):
The kinetic energy of trolley are as follows:
The kinetic energy of suspender inner frame are as follows:
The kinetic energy of pole plate are as follows:
Wherein,For the translational kinetic energy of pole plate, and:
For the rotational kinetic energy of pole plate, and:
Wherein,For the rotary inertia of pole plate, and:
Wherein,For moving of car speed.
The calculation formula (5) of the kinetic energy of suspender inner frame is derived from by following steps:
The kinetic energy of suspender inner frame:
The respectively transverse and longitudinal coordinate of the mass center of suspender inner frame, calculates:
To obtain calculation formula (5).
After choosing three generalized coordinates, it can obtain:
The potential energy of system:
Wherein,For suspender inner frame potential energy,For pole plate potential energy, 2l2For suspender inner frame height.
Lagrangian:
The kinetics equation of system can be then obtained by Lagrange's equation are as follows:
Wherein, F is driving force,For suspender inner frame pivot angle acceleration,For pole plate pivot angle acceleration,For trolley plus
Speed.
The freedom degree of system includes state variable:If the state space equation of system are as follows:
And it sets:
Since suspender inner frame and pole plate pivot angle are smaller, then original equation can be linearized by Taylor series
Wherein
The then state equation of system are as follows:
The invention has the following advantages:
The method for building up of the kinetic model of the dedicated OTC's trolley of electrolysis of the invention, it is dedicated by analysis electrolysis
The mechanical mechanism feature of bridge crane establishes and practical very close dynamics on the basis of reasonable equivalent-simplification
Model is electrolysed the precise positioning of dedicated bridge crane for follow-up study and anti-swing control provides basis, in nonferrous metallurgy field
Have a wide range of applications meaning.
Other than objects, features and advantages described above, there are also other objects, features and advantages by the present invention.
Below with reference to accompanying drawings, the present invention is described in further detail.
Detailed description of the invention
The attached drawing constituted part of this application is used to provide further understanding of the present invention, schematic reality of the invention
It applies example and its explanation is used to explain the present invention, do not constitute improper limitations of the present invention.In the accompanying drawings:
Fig. 1 is the structural schematic diagram for being electrolysed dedicated bridge crane；
Fig. 2 is the method for building up of the kinetic model of the dedicated OTC's trolley of electrolysis of the preferred embodiment of the present invention
Flow diagram；
Fig. 3 is the force analysis figure of the dedicated bridge crane of electrolysis of the preferred embodiment of the present invention；
Fig. 4 is the windage of the pole plate of the preferred embodiment of the present invention during the swingCoordinates computed schematic diagram；
Fig. 5 is the schematic diagram of the pole plate of the preferred embodiment of the present invention；
Fig. 6 is the kinetic model simulation result diagram of the dedicated bridge crane of electrolysis of the preferred embodiment of the present invention.
Specific embodiment
The embodiment of the present invention is described in detail below in conjunction with attached drawing, but the present invention can be defined by the claims
Implement with the multitude of different ways of covering.
Fig. 1 is the structural schematic diagram of the so-called dedicated bridge crane of electrolysis in the present embodiment, and alleged in the present embodiment
The dedicated bridge crane of electrolysis.It is mainly by gantry, traveling mechanism of the larger traveller, trolley, operator cabin device, suspender complete set of equipments,
Mobile electric cucurbit and electrical equipment several major composition.Wherein cart does transverse movement in the horizontal direction, trolley does longitudinal direction
Movement, hoisting hanger move in the vertical direction.Cart is that twin beams double track structure is run on the track in hundreds of meters of workshop, trolley
It runs on the track for the cart bridge-frame that is laid in.Lifting mechanism is mainly by motor, speed reducer, brake, reel group, wirerope
The compositions such as fixed device, guide rope device, wirerope, guide rope device is for limiting winding of the wirerope on reel, it is ensured that not disorderly
Slot；4 wirerope are installed, point left and right rotation prevents suspender from reversing during raising on reel.
Suspender complete set of equipments is by outer framework, inner frame, hanger assembly, the assembly of left and right anode suspension hook, left and right cathode suspension hook
Assembly plus hydraulic system and electrical system composition.Hydraulic, electrical system is not shown in the figure.Special hanger cooperation crane can be distinguished
It lifts by crane whole slot cathode plate, anode plate, carry electrolysis cathode, anode scrap, suspender both ends suspension hook, which has, independently executes mechanism in order to replace
The anode plate at slot end.Inside casing frame body is a welding structural element, and it is flat for hanger to be mounted on inner frame major function on the inside of outer framework
Steady up and down provide guidance positioning.Hanger is mounted on the position at four angles on the inside of inner frame with dragging track.Inner frame passes through
Directive wheel on the four sides of top can move above and below along the track being mounted on the inside of outer framework.But in order to prevent in raising or decline
Internal and external frame is stuck in the process, therefore certain gap has been reserved between internal and external frame.Cathode-anode plate is then placed on anode and cathode suspension hook.
It is different from general crane, in the operational process of electrolysis special purpose crane, due to factors such as acceleration and deceleration, make to hang
Tool inner frame and cathode-anode plate can all generate swing, form special second level oscillator system, and there is non-linear, close coupling complexity to owe
Drive system.
Referring to fig. 2, the method for building up of the kinetic model of the dedicated OTC's trolley of electrolysis of the invention, including it is following
Step:
S1: it according to the density of air, acceleration of gravity, the pivot angle of pole plate, the length of pole plate and width, is built using Bernoulli equation
Relationship between vertical pole plate windage during the swing and the pivot angle of pole plate；
S2: using trolley, suspender and pole plate as a vibrational system, according to pole plate windage during the swing and pole plate
Pivot angle between relationship, the kinetics equation of system is derived from by Lagrange's equation；
S3: choosing generalized coordinates, and the freedom degree of analysis system obtains the kinetic model of trolley.
It is electrolysed the mechanical mechanism feature of dedicated bridge crane by analysis, is established on the basis of reasonable equivalent-simplification
With practical very close kinetic model, the precise positioning and anti-swing control of dedicated bridge crane are electrolysed for follow-up study
Basis is provided, has a wide range of applications meaning in nonferrous metallurgy field.
In practical applications, on the basis of above-mentioned steps, the power of the dedicated OTC's trolley of electrolysis of the invention
The method for building up for learning model can also optimize, and be illustrated below using embodiment:
The present embodiment analyses in depth the mechanical structure feature for being electrolysed dedicated bridge crane, is abstracted and is simplified to such as Fig. 3
Shown in equivalent simplified model figure, be convenient for force analysis.
Define the following parameter of system first: M is the quality of trolley, m1For the quality of suspender inner frame, m2For the matter of pole plate
Amount, trolley friction are fM, driving force F,For windage suffered by pole plate, θ1For the pivot angle of inner frame lifting rope, θ2For pole
Plate pivot angle, a, b are respectively the spacing between lifting rope length and lifting rope, 2l1、2l2The respectively length and height of suspender inner frame, 2l3、
2l4The respectively length of pole plate and width (referring to Fig. 5).
Referring to fig. 4, it is respectively the density and acceleration of gravity of air that cell area a ds, ρ, g is taken on pole plate, and Σ is pole plate
Region can then be obtained the relationship between pole plate windage during the swing and the pivot angle of pole plate by aerodynamics correlation theory
Are as follows:
Wherein, x and y is respectively the abscissa and ordinate of the cell area for the coordinate system established,For pole plate pivot angle speed.
Kinetic model is derived using the Lagrange's equation of Analytical Mechanics, for the particle with complete ideal constraint
System, if the freedom degree of system is k, the kinetics equation of system are as follows:
Wherein: L=T-V, T are the kinetic energy of system, and V is the potential energy of system, Q'jFor the corresponding generalized force of generalized coordinates, qjFor
Generalized coordinates.Analyzing this system, there are three generalized coordinates, respectively x, θ1,θ2。
The then kinetic energy of system:
Wherein,The respectively kinetic energy of trolley, suspender inner frame and pole plate, M are the quality of trolley, m1For inside casing
The quality of frame, m2For the quality of pole plate.
The kinetic energy of trolley are as follows:
Suspender inner frame kinetic energy: The respectively mass center of suspender inner frame
Transverse and longitudinal coordinate is easily calculated by Fig. 3:
Then calculate suspender inner frame kinetic energy are as follows:
The kinetic energy of pole plate For the translational kinetic energy of pole plate,For the rotational kinetic energy of pole plate. The respectively transverse and longitudinal coordinate of pole plate mass center is easily calculated by Fig. 3:
Then calculate pole plate translational kinetic energy
Wherein,For moving of car speed.
For the rotary inertia of pole plate:
The then rotational kinetic energy of pole plate
Therefore the total kinetic energy of pole plate:
The total kinetic energy of system:
Total potential energy of system:
Then Lagrangian:
The kinetics equation of system can be then obtained by Lagrange's equation are as follows:
Wherein, F is driving force,For suspender inner frame pivot angle acceleration,For pole plate pivot angle acceleration,For trolley plus
Speed.
For this system, the state variable of system are as follows:
If the state space equation of system are as follows:
And it sets:
Since suspender inner frame and pole plate pivot angle are smaller, then original equation can be linearized by Taylor series:
Wherein
The then state equation of system are as follows:
Take m1=5kg, m2=20kg, l4=0.6m, a=6m, g=9.8m/s2, carry out model emulation verifying, simulation result
As shown in Figure 6.As seen from Figure 6 the pivot angle of suspender inner frame and pole plate step response be in attenuation trend, certain
Zero is decayed in time, and inner frame pivot angle cycle of oscillation lags behind pole plate pivot angle, pivot angle amplitude is less than pole plate pivot angle, with reality
Situation very close to.
In summary, the present invention is electrolysed the mechanical mechanism feature of dedicated bridge crane by analysis, reasonable equivalent
Established on the basis of simplification with practical very close kinetic model, realize the modeling for being electrolysed dedicated bridge crane be
To the analysis of the mechanical structure of practical crane carry out it is reasonable it is abstract simplify and carry out on the basis of necessary force analysis into
Capable.Crane system is modeled with the Lagrange's equation and hydrodynamics of rational mechanics.By simulating, verifying, this
The control problem for being electrolysed dedicated bridge crane for follow-up study has important directive significance.
The foregoing is only a preferred embodiment of the present invention, is not intended to restrict the invention, for the skill of this field
For art personnel, the invention may be variously modified and varied.All within the spirits and principles of the present invention, made any to repair
Change, equivalent replacement, improvement etc., should all be included in the protection scope of the present invention.
Claims (10)
1. a kind of method for building up for the kinetic model for being electrolysed dedicated OTC's trolley, which is characterized in that including following step
It is rapid:
S1: according to the density of air, acceleration of gravity, the pivot angle of pole plate, the length of pole plate and width, pole is established using Bernoulli equation
Relationship between plate windage during the swing and the pivot angle of pole plate；
S2: using trolley, suspender and pole plate as a vibrational system, according to pole plate windage during the swing and pole plate
Pivot angle between relationship, the kinetics equation of system is derived from by Lagrange's equation；
S3: choosing generalized coordinates, and the freedom degree of analysis system obtains the kinetic model of trolley.
2. the method for building up of the kinetic model of the dedicated OTC's trolley of electrolysis according to claim 1, feature
It is, the relationship between pole plate windage during the swing and the pivot angle of pole plate are as follows:
Wherein, fmFor windage suffered by pole plate；ρ, g are respectively the density and acceleration of gravity of air；2l3、2l4Respectively pole plate
Length and width；Ds is the cell area on pole plate；θ2For the pivot angle of pole plate；Σ is plate regions；X and y is respectively the seat established
The abscissa and ordinate of the cell area of system are marked,For pole plate pivot angle speed.
3. the method for building up of the kinetic model of the dedicated OTC's trolley of electrolysis according to claim 2, feature
It is, the kinetics equation of the system are as follows:
Wherein: L=T-V, T are the kinetic energy of system, and V is the potential energy of system, Q'jFor the corresponding generalized force of generalized coordinates, qjFor broad sense
Coordinate,For qjFirst derivative, k be system freedom degree.
4. the method for building up of the kinetic model of the dedicated OTC's trolley of electrolysis according to claim 3, feature
It is, the kinetic energy of the system:
Wherein, TM,The respectively kinetic energy of trolley, suspender inner frame and pole plate, M are the quality of trolley, m1For inner frame
Quality, m2For the quality of pole plate.
5. the method for building up of the kinetic model of the dedicated OTC's trolley of electrolysis according to claim 4, feature
It is, in the step S3, chooses three generalized coordinates, respectively x, θ1,θ2, θ1For the pivot angle of inner frame lifting rope, then obtain:
The kinetic energy of the system:
Wherein, a is lifting rope length,For the pivot angle speed of inner frame lifting rope,For moving of car speed.
6. the method for building up of the kinetic model of the dedicated OTC's trolley of electrolysis according to claim 5, feature
It is, in the formula (10):
The kinetic energy of the trolley are as follows:
The kinetic energy of suspender inner frame are as follows:
The kinetic energy of pole plate are as follows:
Wherein,For the translational kinetic energy of pole plate, and:
For the rotational kinetic energy of pole plate, and:
Wherein,For the rotary inertia of pole plate, and:
7. the method for building up of the kinetic model of the dedicated OTC's trolley of electrolysis according to claim 6, feature
It is, the calculation formula (5) of the kinetic energy of the suspender inner frame is derived from by following steps:
The kinetic energy of suspender inner frame:
The respectively transverse and longitudinal coordinate of the mass center of suspender inner frame,It is xm1First derivative,It is ym1Single order
Derivative calculates:
To obtain the calculation formula (5).
8. the method for building up of the kinetic model of the dedicated OTC's trolley of electrolysis according to claim 7, feature
It is, after choosing three generalized coordinates, obtains:
The potential energy of system:
Wherein,For suspender inner frame potential energy,For pole plate potential energy, 2l2For suspender inner frame height.
9. the method for building up of the kinetic model of the dedicated OTC's trolley of electrolysis according to claim 8, feature
It is, Lagrangian:
The kinetics equation of system is then obtained by Lagrange's equation are as follows:
Wherein, F is driving force,For suspender inner frame pivot angle acceleration,For pole plate pivot angle acceleration,For trolley acceleration,
fMFor trolley friction.
10. the method for building up of the kinetic model of the dedicated OTC's trolley of electrolysis according to claim 9, feature
It is, the freedom degree of system includes state variable:If the state space equation of system are as follows:
Wherein,It is the first derivative of X, A, B, C and D are respectively different coefficient matrixes；
And it sets:
Since suspender inner frame and pole plate pivot angle are smaller, then original equation is linearized by Taylor series
Wherein
Wherein k11、k12......k27For constant, equation (14) is typical state-space equation form, and X is state vector, and Y is
Output vector, u are input vector；
The then state equation of system are as follows:
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| CN106865416A (en) * | 2017-04-20 | 2017-06-20 | 中南大学 | A kind of automatic anti-swinging control method in bridge crane walking process |
| CN108828959A (en) * | 2018-08-30 | 2018-11-16 | 太原科技大学 | A kind of novel bridge crane is anti-sway with position control method and device |
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| CN201359784Y (en) * | 2009-02-27 | 2009-12-09 | 武汉市特种设备监督检验所 | Signal acquisition system of operating mechanism used for bridge crane virtual training system |
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