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Modeling of a conveyor belt

In this example, we will look at the calculation and modeling of a conveyor belt using physical modeling blocks.

Introduction

In general, the conveyor belt device can be represented as shown in the diagram.:

image.png

As an assumption for the final model, we will not take into account the dynamics of tension and sagging of the conveyor belt, therefore, the model can be simplified to several elements.:

  • electric drive,

  • gearbox,

  • drive drum with bearings,

  • end drum with bearings,

  • Conveyor belt.

  • cargo of variable mass.

Calculation of pipeline parameters

For an example of calculation and modeling, let's take the conveyor 5025-40, the equipment parameters of which will be selected according to [1].

Setting the length L of the pipeline:

In [ ]: 
L = 30; # Расстояние между барабанами [м]

Electric drive

The motor used in this example is asynchronous with a closed-loop rotor (AD KZR) AIR 132 S4. Power - 7.5 kW, rotation speed - 1455 rpm. It was calculated and modeled earlier, in the example of blood pressure parameterization.

Drums

The drums for the specified type of conveyor - drive and end have a standard size of 5025G-40. It defines the following characteristics necessary for physical modeling:

In [ ]: 
Dб = 250e-3; # Диаметр барабана [м]
Lб = 500e-3; # Длина барабана [м]
Mб = 58; # Масса барабана [кг]
Jб = 0.5*Mб*(Dб/2)^2; # Момент инерции барабана [кг·м²]

In the model, the reels are represented by blocks:

  • inertia - to generate the torque of the drum,

  • wheel and axle - to convert rotational motion into translational motion (drive drum) and vice versa (end drum).

Reducer

One of the typical gearboxes for the 1TS2U-160 rear:

In [ ]: 
I = 31.5; # Передаточное число редуктора
J = 0.0227+0.01; # Момент инерции редуктора и ротора АД, приведённый к валу двигателя [кг·м²]
ηр = 0.97; # КПД редуктора

In the model, it is described in two blocks:

  • gear transmission - it should be noted that this gearbox is two-stage, therefore, the direction of rotation of the input and output shafts coincide,

  • inertia - to generate the total torque of the motor rotor and gearbox shafts driven to the motor shaft.

Drum bearings

The type of bearings corresponding to a given drum is 3608. The following variables can be defined for them:

In [ ]: 
Tb = 12e-3; # Момент трения подшипника - покоя [Н·м] 
Tc = 6e-3; # Момент трения подшипника - скольжения [Н·м]
Vc = Tc*0.05; # Коэффициент вязкого трения [Н·м/(рад/с)]

In the model, they are represented by blocks of rotational терния - with double coefficients and moments of friction (two bearings per drum axis).yu

Conveyor belt

Conveyor belt - general purpose, type 2L. Its parameters:

In [ ]: 
Bл = Lб; # Ширина ленты [м]
Lл = round((L*2+pi*Dб)*1.05); # Длина ленты [м]
mл = 3.75; # Удельная масса ленты [кг/п.м.]
Mл = mл*Lл; # Масса ленты [кг]

In the model, it is represented by the [mechanical mass] block (https://engee.com/helpcenter/stable/ru/fmod-mechanical-translational-elements/mass.html ). The elasticity, tensile strength and damping effects of the tape are not taken into account.

Cargo

The load in the model is formed using the [force source] block (https://engee.com/helpcenter/stable/ru/fmod-mechanical-translational-sources/force-source.html ) - with periodic delivery of random-value cargo.

In [ ]: 
Fгруза_max = 5e3; # Максимальное натяжение ленты от груза [Н]
Fгруза_min = 1e3; # Минимальное натяжение ленты от груза [Н]

The model takes into account the accumulation of cargo on the belt and the removal of cargo at the end of the conveyor after 51 seconds. The non-linearity of the characteristic of the movement of each load on the belt requires further more correct accounting.

The example model

The general view of the conveyor model is shown in the figure below.:

image.png

Let's run the model using software modeling control and pre-prepared functions for ease of working with the model and simulation results:

In [ ]: 
example_path = @__DIR__; # Получаем абсолютный путь к директории, содержащей текущий скрипт
cd(example_path); # Переходим в директорию примера
include("useful_functions.jl"); # Подключаем скрипт Julia со вспомогательными функциями
In [ ]: 
simout = get_sim_results("conveyor.engee", example_path) #запускаем моделирование
Out[0]:
SimulationResult(
    "Перемещение ленты" => WorkspaceArray{Float64}("conveyor/Перемещение ленты")
,
    "Сила натяжения грузов" => WorkspaceArray{Float64}("conveyor/Груз случайной массы/Сила натяжения грузов")
,
    "Ток статора" => WorkspaceArray{Float64}("conveyor/Ток статора")
,
    "Сила натяжения от груза" => WorkspaceArray{Float64}("conveyor/Груз случайной массы/Сила натяжения от груза")
,
    "Снятые грузы.1" => WorkspaceArray{Float64}("conveyor/Груз случайной массы/Снятые грузы.1")
,
    "Добавленные грузы.main_out" => WorkspaceArray{Float64}("conveyor/Груз случайной массы/Добавленные грузы.main_out")
,
    "Обороты (у.е)" => WorkspaceArray{Float64}("conveyor/Обороты (у.е)")
,
    "Скорость ленты" => WorkspaceArray{Float64}("conveyor/Скорость ленты")

)

Simulation results

Engine

We obtain the variables of the signals recorded in the model, measured on the engine:

In [ ]: 
t = thin(get_sim_data(simout, "Ток статора", 1, "time"), 50);
Is = thin(get_sim_data(simout, "Ток статора", 1, "value"), 50);
n = thin(get_sim_data(simout, "Обороты (у.е)", 1, "value"), 50);

Let's plot these variables:

In [ ]: 
gr(fmt=:png, aspectratio=:auto, xlims=:auto, ylims=:auto, size = (900,400))
I_graph = plot(t, Is; label = "I(t)", title = "Ток статора", ylabel = "I [A]", xlabel = "t [с]")
n_graph = plot(t, n; label = "n(t)", title = "Частота вращения ротора", ylabel = "n [у.е.]", xlabel = "t [с]")
plot(I_graph, n_graph)
Out[0]:
No description has been provided for this image

The graphs show how the stator current periodically increases by a variable amount, while the rotor frequency decreases - this indicates an increase in the load on the motor shaft. After 51 seconds, you can see that the load stops increasing - loads continue to arrive on the belt, but those who hit it first are already being removed from the conveyor.

Conveyor belt

We will get variables from the signals recorded in the model on the conveyor belt:

In [ ]: 
Vл = thin(get_sim_data(simout, "Скорость ленты", 1, "value"), 50);
Sл = thin(get_sim_data(simout, "Перемещение ленты", 1, "value"), 50);

Let's plot these variables:

In [ ]: 
gr(fmt=:png, aspectratio=:auto, xlims=:auto, ylims=:auto, size = (900,400))
V_graph = plot(t, Vл; label = "V(t)", title = "Скорость ленты", ylabel = "V [м/с]", xlabel = "t [с]")
S_graph = plot(t, Sл; label = "S(t)", title = "Перемещение ленты", ylabel = "S [м]", xlabel = "t [с]")
plot(V_graph, S_graph)
Out[0]:
No description has been provided for this image

The speed of the belt is directly proportional to the rotational speed of the motor shaft, the average value corresponds to the speed determined by the reference book for this type of conveyor:

In [ ]: 
import Pkg; Pkg.add("Statistics")

   Resolving package versions...
  No Changes to `~/.project/Project.toml`
  No Changes to `~/.project/Manifest.toml`
In [ ]: 
using Statistics
Vл_ср = round(mean(Vл)*100, digits=2)
println("Средняя скорость ленты конвейера - $Vл_ср см/с")

Средняя скорость ленты конвейера - 61.27 см/с

Loads on the conveyor

At the end of the analysis of the simulation results, we will analyze the tension forces of the belt from the loads on the belt.:

In [ ]: 
Tmain = thin(get_sim_data(simout, "Сила натяжения грузов", 1, "value"), 50);
Tsub = thin(get_sim_data(simout, "Снятые грузы.1", 1, "value"), 50);
Tadd = thin(get_sim_data(simout, "Добавленные грузы.main_out", 1, "value"), 50);

Let's plot the recorded signals:

In [ ]: 
gr(aspectratio=:auto, xlims=:auto, ylims=:auto, size = (900,500))
plot(t, Tmain; label = "Результирующее", title = "Натяжение ленты от грузов", ylabel = "T [Н]", xlabel = "t [с]")
plot!(t, Tadd; label = "От добавленных", ls=:dot)
plot!(t, -Tsub; label = "От снятых", ls=:dot)
Out[0]:
No description has been provided for this image

Conclusion

As a result of the calculation and modeling, a physical model of a conveyor belt with cargo delivery was developed that takes into account the dynamics of belt tension from cargo. In further work on the project, you can proceed to the development of a conveyor management system.

Literature

  1. Stationary general-purpose conveyor belts with a rubber-cloth belt. Catalog. Part I. Equipment // JSC "Belokholunitskiy zavod" - 2002