CN106021672B - It is electrolysed the method for building up of the kinetic model of dedicated OTC's trolley - Google Patents

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

Establishment method of dynamic model of bridge crane trolley for electrolysis

technical field

The invention relates to the field of special-purpose bridge cranes for electrolysis, in particular to a method for establishing a dynamics model of a special-purpose bridge crane trolley for electrolysis.

Background technique

Overhead cranes, also known as cranes and cranes, are an indispensable lifting and handling tool in modern industrial production. They are mainly used for lifting, handling, loading and unloading of various materials. It has been widely used in various production departments such as factories, mines, ports, bridges, hydropower stations, construction sites, warehouses, etc.

The bridge crane for electrolysis is mainly composed of a cart, a trolley and a hoisting device. The cart runs horizontally in the horizontal direction, the trolley moves longitudinally, and the lifting spreader moves in the vertical direction. For example, in the copper electrolysis workshop, the electrolysis cycle of the cathode and anode plates is fixed. When the electrolysis cycle ends, the bridge crane must be able to quickly complete the plate renewal work. Productivity. In addition, due to the small distance between the electrolytic cell and the electrolytic cell, the distance between the cathode and anode plates, in order to avoid the occurrence of serious accidents such as short circuit of electrolytic current of tens of thousands of amperes in the electrolytic cell, it is required that the spreader can accurately stop at the target when it is in the lifting tank. Right above the electrolytic cell, the positioning accuracy is generally millimeters. Due to factors such as acceleration and deceleration during the transportation of the trolley, the electrolytic electrode plate oscillates during the hoisting and transportation process. The sway is approximately an undamped vibration. Naturally eliminating the sway by air damping takes up a lot of auxiliary work time, and also causes positioning. Not allowed, resulting in repeated positioning of the operator. Therefore, it is very important to study the control problem of the bridge crane in the copper electrolysis process, and its foundation is to establish a dynamic model that is close to the actual situation.

At present, there have been many studies on general overhead cranes, and a variety of modeling methods and models have been proposed. However, due to its special spreader structure and specific application occasions, the modeling method of this kind of special crane is currently blank.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a method for establishing a dynamic model of a special-purpose bridge crane trolley for electrolysis, so as to solve the technical problem that the model cannot be modeled for a special-purpose bridge crane for electrolysis.

In order to achieve the above object, the present invention provides a method for establishing a dynamic model of a special-purpose bridge crane trolley for electrolysis, comprising the following steps:

S1: According to the density of the air, the acceleration of gravity, the swing angle of the pole plate, and the length and width of the pole plate, use Bernoulli's equation to establish the relationship between the wind resistance of the pole plate during the swing process and the swing angle of the pole plate;

S2: Taking the trolley, spreader and pole plate as a vibration system, according to the relationship between the wind resistance of the pole plate during the swinging process and the swing angle of the pole plate, the dynamic equation of the system is derived from the Lagrangian equation;

S3: Select generalized coordinates, analyze the degrees of freedom of the system, and obtain the dynamics model of the car.

As a further improvement of the method of the present invention:

The relationship between the wind resistance of the pole plate during the swinging process and the swing angle of the pole plate is:

Among them, f _m is the wind resistance on the pole plate; ρ and g are the density of air and the acceleration of gravity respectively; 2l ₃ and 2l ₄ are the length and width of the pole plate respectively; ds is an area element on the pole plate; θ ₂ is the swing angle of the polar plate; Σ is the polar plate area; x and y are the abscissa and ordinate of the area element of the established coordinate system, respectively, is the plate swing angular velocity.

The dynamic equation of the system is:

Where: L=TV, T is the kinetic energy of the system, V is the potential energy of the system, Q' _j is the generalized force corresponding to the generalized coordinate, q _j is the generalized coordinate, and k is the degree of freedom of the system.

Kinetic energy of the system:

in, are the kinetic energy of the trolley, the inner frame of the spreader and the pole plate respectively, M is the mass of the trolley, m ₁ is the mass of the inner frame, and m ₂ is the mass of the pole plate.

In step S3, three generalized coordinates are selected, namely x, θ ₁ , θ ₂ , and θ ₁ is the swing angle of the inner frame hanging rope, then:

Kinetic energy of the system:

Among them, a is the length of the sling, It is the swing angular velocity of the inner frame suspending rope.

In formula (10):

The kinetic energy of the car is:

The kinetic energy of the inner frame of the spreader is:

The kinetic energy of the plate is:

in, is the translational kinetic energy of the plate, and:

is the rotational kinetic energy of the plate, and:

in, is the moment of inertia of the plate, and:

in, is the speed of the car.

The calculation formula (5) of the kinetic energy of the inner frame of the spreader is derived through the following steps:

Kinetic energy of the inner frame of the spreader:

are the abscissa and ordinate of the center of mass of the inner frame of the spreader, respectively, and are calculated as:

Thus, the calculation formula (5) is obtained.

After selecting three generalized coordinates, we get:

Potential energy of the system:

in, is the potential energy of the inner frame of the spreader, is the potential energy of the plate, and 2l ₂ is the height of the inner frame of the spreader.

Lagrange operator:

Then the dynamic equation of the system can be obtained from the Lagrange equation as:

where F is the driving force, is the swing angular acceleration of the inner frame of the spreader, is the pendulum angular acceleration of the pole plate, for the car acceleration.

The degrees of freedom of the system include the state variables: Let the state space equation of the system be:

Side by side:

Since the inner frame of the spreader and the swing angle of the pole plate are small, the original equation can be linearized by the Taylor series

in

Then the state equation of the system is:

The present invention has the following beneficial effects:

The method for establishing the dynamic model of the bridge crane trolley for electrolysis of the present invention, by analyzing the mechanical mechanism characteristics of the bridge crane special for electrolysis, establishes a dynamic model that is very close to the actual situation on the basis of reasonable equivalent simplification, which is Subsequent research on the precise positioning and anti-swing control of bridge cranes for electrolysis provides a basis, which has wide application significance in the field of non-ferrous metallurgy.

In addition to the objects, features and advantages described above, the present invention has other objects, features and advantages. The present invention will be described in further detail below with reference to the accompanying drawings.

Description of drawings

The accompanying drawings constituting a part of the present application are used to provide further understanding of the present invention, and the exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the attached image:

Fig. 1 is the structural representation of the bridge crane specially used for electrolysis;

2 is a schematic flowchart of a method for establishing a dynamic model of a special-purpose bridge crane trolley for electrolysis according to a preferred embodiment of the present invention;

Fig. 3 is the force analysis diagram of the special-purpose bridge crane for electrolysis of the preferred embodiment of the present invention;

Fig. 4 is the wind resistance of the pole plate in the swing process of the preferred embodiment of the present invention Schematic diagram of calculation coordinates;

Fig. 5 is the schematic diagram of the polar plate of the preferred embodiment of the present invention;

FIG. 6 is a simulation result diagram of a dynamic model of a bridge crane dedicated to electrolysis according to a preferred embodiment of the present invention.

Detailed ways

The embodiments of the present invention are described in detail below with reference to the accompanying drawings, but the present invention can be implemented in many different ways as defined and covered by the claims.

FIG. 1 is a schematic structural diagram of a bridge crane dedicated to electrolysis in this embodiment, and a bridge crane dedicated to electrolysis referred to in this embodiment. It is mainly composed of bridge frame, cart running mechanism, trolley, driver's cab device, complete set of spreader equipment, mobile electric hoist and electrical equipment. The cart moves laterally in the horizontal direction, the trolley moves longitudinally, and the lifting sling moves in the vertical direction. The cart is a double-girder and double-track structure running on the track of hundreds of meters in the workshop, and the trolley runs on the track laid on the bridge frame of the cart. The hoisting mechanism is mainly composed of a motor, a reducer, a brake, a reel group, a wire rope fixing device, a guide rope device, a wire rope, etc. There are 4 wire ropes installed, which are divided into left and right rotations to prevent the spreader from twisting during the lifting process.

The complete set of spreader equipment is composed of outer frame, inner frame, hanger assembly, left and right anode hook assembly, left and right cathode hook assembly plus hydraulic system and electrical system. The hydraulic and electrical systems are not shown in the figure. The special sling and the crane can lift the cathode plate, anode plate, electrolytic cathode and residual electrode of the whole tank respectively. The hooks at both ends of the sling have independent actuators to facilitate the replacement of the anode plate at the end of the tank. The main body of the inner frame is a welded structure, which is installed on the inner side of the outer frame and the main function of the inner frame is to provide guidance and positioning for the hanger to rise and fall smoothly. The hanger is installed at the four corners inside the inner frame with sliding rails. The inner frame can move up and down along the track installed on the inner side of the outer frame through the guide wheels on the upper four sides. However, in order to prevent the inner and outer frames from being stuck during the lifting or lowering process, a certain gap is reserved between the inner and outer frames. The cathode and anode plates are placed on the cathode and anode hooks.

Different from ordinary cranes, during the operation of the special crane for electrolysis, due to factors such as acceleration and deceleration, the inner frame of the spreader and the cathode and anode plates will oscillate, forming a special secondary pendulum system with complex nonlinear and strong coupling. underactuated system.

Referring to Fig. 2, the method for establishing the dynamics model of the special-purpose bridge crane trolley for electrolysis of the present invention comprises the following steps:

S1: According to the density of the air, the acceleration of gravity, the swing angle of the pole plate, and the length and width of the pole plate, use Bernoulli's equation to establish the relationship between the wind resistance of the pole plate during the swing process and the swing angle of the pole plate;

S2: Taking the trolley, spreader and pole plate as a vibration system, according to the relationship between the wind resistance of the pole plate during the swinging process and the swing angle of the pole plate, the dynamic equation of the system is derived from the Lagrangian equation;

S3: Select generalized coordinates, analyze the degrees of freedom of the system, and obtain the dynamics model of the car.

By analyzing the characteristics of the mechanical mechanism of the bridge crane for electrolysis, a dynamic model that is very close to reality is established on the basis of reasonable equivalent simplification, which provides a basis for the subsequent research on the precise positioning and anti-swing control of the bridge crane for electrolysis. It has a wide range of application significance in the field of non-ferrous metallurgy.

In practical application, on the basis of the above steps, the method for establishing the dynamic model of the special-purpose bridge crane trolley for electrolysis of the present invention can also be optimized, and the following examples are used to illustrate:

In this embodiment, the mechanical structure characteristics of the special-purpose bridge crane for electrolysis are analyzed in depth, and it is abstracted and simplified into an equivalent simplified model diagram as shown in FIG. 3, which is convenient for force analysis.

First define the following parameters of the system: M is the mass of the trolley, m ₁ is the mass of the inner frame of the spreader, m ₂ is the mass of the pole plate, the friction force on the trolley is f _M , the driving force is F, is the wind resistance of the pole plate, θ ₁ is the swing angle of the inner frame suspending rope, θ ₂ is the pole plate swing angle, a and b are the length of the suspending rope and the distance between the suspending ropes respectively, 2l ₁ and 2l ₂ are the hanging ropes respectively With the length and height of the inner frame, 2l ₃ and 2l ₄ are the length and width of the plate respectively (see Figure 5).

Referring to Figure 4, take an area element ds on the pole plate, where ρ and g are the density of the air and the acceleration of gravity, respectively, and Σ is the plate area, then the wind resistance of the pole plate during the swing process can be obtained from the relevant aerodynamic theory. The relationship between the swing angles of the plates is:

Among them, x and y are the abscissa and ordinate of the area element of the established coordinate system, respectively, is the plate swing angular velocity.

The dynamic model is derived by using the Lagrangian equation of analytical mechanics. For a particle system with complete ideal constraints, if the degree of freedom of the system is k, the dynamic equation of the system is:

Where: L=TV, T is the kinetic energy of the system, V is the potential energy of the system, Q' _j is the generalized force corresponding to the generalized coordinate, and q _j is the generalized coordinate. The analysis system has three generalized coordinates, namely x, θ ₁ , θ ₂ .

Then the kinetic energy of the system is:

in, are the kinetic energy of the trolley, the inner frame of the spreader and the pole plate respectively, M is the mass of the trolley, m ₁ is the mass of the inner frame, and m ₂ is the mass of the pole plate.

The kinetic energy of the car is:

The kinetic energy of the inner frame of the spreader: are the horizontal and vertical coordinates of the center of mass of the inner frame of the spreader, which can be easily calculated from Figure 3:

Then the kinetic energy of the inner frame of the spreader is calculated as:

kinetic energy of the plate is the translational kinetic energy of the plate, is the rotational kinetic energy of the plate. are the horizontal and vertical coordinates of the centroid of the polar plate, which can be easily calculated from Figure 3:

Then the translational kinetic energy of the plate is calculated

in, is the speed of the car.

is the moment of inertia of the plate:

The rotational kinetic energy of the plate

Therefore, the total kinetic energy of the plate is:

The total kinetic energy of the system:

The total potential energy of the system:

Then the Lagrange operator:

Then the dynamic equation of the system can be obtained from the Lagrange equation as:

where F is the driving force, is the swing angular acceleration of the inner frame of the spreader, is the pendulum angular acceleration of the pole plate, for the car acceleration.

For this system, the state variables of the system are:

Let the state space equation of the system be:

Side by side:

Since the inner frame of the spreader and the swing angle of the pole plate are small, the original equation can be linearized by the Taylor series:

in

Then the state equation of the system is:

Take m ₁ =5kg, m ₂ =20kg, l ₄ =0.6m, a = 6m, g = 9.8m/s ² , carry out model simulation verification, and the simulation results are shown in Figure 6 . It can be seen from Figure 6 that the swing angles of the inner frame and the pole plate of the spreader both show a decaying trend in the step response, and decay to zero within a certain period of time, and the oscillation period of the swing angle of the inner frame lags behind the swing angle of the pole plate, and the swing angle The amplitude is smaller than the swing angle of the pole plate, which is very close to the actual situation.

To sum up, it can be seen that the present invention establishes a dynamic model that is very close to the actual situation on the basis of reasonable equivalent simplification by analyzing the characteristics of the mechanical mechanism of the special bridge crane for electrolysis, and realizes the modeling of the special bridge crane for electrolysis. The analysis of the mechanical structure of the actual crane is carried out on the basis of reasonable abstract simplification and necessary force analysis. The crane system is modeled using the Lagrangian equations of theoretical mechanics and fluid mechanics. Through simulation verification, this has important guiding significance for the follow-up study of the control problem of the special bridge crane for electrolysis.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and changes. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims (10)

1. the establishment method of the dynamics model of a special-purpose bridge crane trolley for electrolysis, is characterized in that, comprises the following steps: S1: According to the density of the air, the acceleration of gravity, the swing angle of the pole plate, and the length and width of the pole plate, use Bernoulli's equation to establish the relationship between the wind resistance of the pole plate during the swing process and the swing angle of the pole plate; S2: Taking the trolley, spreader and pole plate as a vibration system, according to the relationship between the wind resistance of the pole plate during the swinging process and the swing angle of the pole plate, the dynamics of the system is derived from the Lagrange equation equation; S3: Select generalized coordinates, analyze the degrees of freedom of the system, and obtain the dynamics model of the car. 2. the establishment method of the dynamic model of the special-purpose bridge crane trolley for electrolysis according to claim 1, is characterized in that, the relation between the wind resistance of described pole plate in swing process and the swing angle of pole plate is: Among them, f _m is the wind resistance on the pole plate; ρ and g are the density of air and the acceleration of gravity respectively; 2l ₃ and 2l ₄ are the length and width of the pole plate respectively; ds is an area element on the pole plate; θ ₂ is the swing angle of the polar plate; Σ is the polar plate area; x and y are the abscissa and ordinate of the area element of the established coordinate system, respectively, is the plate swing angular velocity. 3. the establishment method of the dynamic model of the special-purpose bridge crane trolley for electrolysis according to claim 2, is characterized in that, the dynamic equation of described system is: Where: L=TV, T is the kinetic energy of the system, V is the potential energy of the system, Q' _j is the generalized force corresponding to the generalized coordinate, q _j is the generalized coordinate, is the first derivative of q _j , and k is the degree of freedom of the system. 4. the establishment method of the dynamic model of the special-purpose bridge crane trolley for electrolysis according to claim 3, is characterized in that, the kinetic energy of described system: Among them, T _M , are the kinetic energy of the trolley, the inner frame of the spreader and the pole plate respectively, M is the mass of the trolley, m ₁ is the mass of the inner frame, and m ₂ is the mass of the pole plate. 5. The method for establishing the dynamic model of the special-purpose bridge crane trolley for electrolysis according to claim 4, wherein in the step S3, three generalized coordinates are selected, which are respectively x, θ ₁ , θ ₂ , θ ₁ is the swing angle of the inner frame sling, then: Kinetic energy of the system: Among them, a is the length of the sling, is the swing angular velocity of the inner frame sling, is the speed of the car. 6. the establishment method of the dynamic model of the special-purpose bridge crane trolley for electrolysis according to claim 5, is characterized in that, in described formula (10): The kinetic energy of the trolley is: The kinetic energy of the inner frame of the spreader is: The kinetic energy of the plate is: in, is the translational kinetic energy of the plate, and: is the rotational kinetic energy of the plate, and: in, is the moment of inertia of the plate, and: 7. the establishment method of the dynamic model of the special-purpose bridge crane trolley for electrolysis according to claim 6, is characterized in that, the calculation formula (5) of the kinetic energy of described spreader inner frame is derived by following steps: Kinetic energy of the inner frame of the spreader: are the horizontal and vertical coordinates of the center of mass of the inner frame of the spreader, respectively, is the first derivative of x _m1 , is the first derivative of y _m1 , calculated as: Thus, the calculation formula (5) is obtained. 8. the establishment method of the dynamic model of the special-purpose bridge crane trolley for electrolysis according to claim 7, is characterized in that, after choosing three generalized coordinates, obtains: Potential energy of the system: in, is the potential energy of the inner frame of the spreader, is the potential energy of the plate, and 2l ₂ is the height of the inner frame of the spreader. 9. the establishment method of the dynamic model of the special-purpose bridge crane trolley for electrolysis according to claim 8, is characterized in that, Lagrangian operator: Then the dynamic equation of the system obtained from the Lagrange equation is: where F is the driving force, is the swing angular acceleration of the inner frame of the spreader, is the pendulum angular acceleration of the pole plate, is the acceleration of the car, and f _M is the friction force on the car. 10. the establishment method of the dynamic model of the special-purpose bridge crane trolley for electrolysis according to claim 9, is characterized in that, the degree of freedom of the system comprises state variable: Let the state space equation of the system be: in, is the first derivative of X, and A, B, C and D are different coefficient matrices; Side by side: Since the inner frame of the spreader and the swing angle of the pole plate are small, the original equation is linearized by the Taylor series in where k ₁₁ , k ₁₂ ...... k ₂₇ are constants, equation (14) is a typical space state equation form, X is the state vector, Y is the output vector, and u is the input vector; Then the state equation of the system is: